Aktuelle Artikel (Abstracts) zur Forschung auf dem Gebiet der Theoretischen Chemie - veroeffentlicht in wissenschaftlichen Fachzeitschriften.
Die Urheberrechte und
Veroeffentlichungsrechte der in der nachfolgenden Liste aufgefuehrten
Fachartikel liegen bei den jeweiligen Verlagen, die am Ende des
jeweiligen Artikels
als Quelle genannt werden. Diese sind auch fuer die Inhalte
verantwortlich.
Hinweise zur Veroeffentlichung Ihrer
Pressmitteilung unter Internetchemie.Info entnehmen Sie bitte der
entsprechenden Info-Seite.
Diese Seite koennen Sie mit folgender Tastenkombination nach Stichwoertern
durchsuchen: <STRG> und <F>.
Auf dieser Seite
beruecksichtige naturwissenschaftliche Journale:
Journal of Mathematical Chemistry - published by
Springer -
JOMC publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals.
Theoretical Chemistry Accounts - published by
Springer -
TCA publishes papers in all fields of theoretical chemistry, computational chemistry, and modeling. Fundamental studies as well as applications are included in the scope.
Aktuelle wissenschaftliche Fachartikel der
genannten Journale:
A quantum mechanics (QM)/molecular mechanics (MM)-based free energy perturbation (FEP) method, developed recently, provides
most accurate estimation of binding affinities. The validity of the method was evaluated for a large set of diverse inhibitors
for fructose 1,6-bisphosphatase (FBPase), a target enzyme for type-II diabetes mellitus. The validation set comprises of 22 important structurally different mutations. The calculated relative binding free energies
using the QM/MM-based FEP method reproduce the experimental values with exceptional precision of less than ±0.5 kcal/mol.
The CPU requirements for QM/MM-based FEP are about fivefold greater than conventional FEP methods, but it is superior in accuracy
of predictions. In addition, the QM/MM-based FEP method eliminates the need for time-consuming development of MM force field
parameters, which are frequently required for novel inhibitors described by MM. Future automation of the method and parallelization
of the code for 128/256/512 cluster computers is expected to enhance the speed and increase its use for drug design and lead
optimization. The present application of QM/MM-based FEP method for structurally diverse set of analogs serves to enhance
the scope of FEP method and demonstrate the utility of QM/MM-based FEP method for its potential in drug discovery.
Content Type Journal Article
Category Regular Article
Pages 1-10
DOI 10.1007/s00214-012-1096-z
Authors
R. S. Rathore, Bioinformatics Infrastructure Facility, School of Life Sciences, University of Hyderabad, Hyderabad, 500046 India
R. Nageswara Reddy, Rational Labs Pvt Ltd, Plot # 177, IDA Mallapur, Hyderabad, 500076 India
A. K. Kondapi, Bioinformatics Infrastructure Facility, School of Life Sciences, University of Hyderabad, Hyderabad, 500046 India
P. Reddanna, Department of Animal Sciences, School of Life Sciences, University of Hyderabad, Hyderabad, 500046 India
M. Rami Reddy, RR Labs, Inc., 8013 Los Sabalos Street, San Diego, CA 92126, USA
It was recently shown that complexes of the type F–Cl···CN–R, ostensibly halogen bonded, sometimes have properties (relatively
high binding energies, short Cl–C separations and considerably lengthened F–Cl distances) that are inconsistent with typical
halogen bonds (Del Bene et al. in J Phys Chem A 114:12958–12962, 2010). We attribute these anomalous features, as well as analogous observations for F–Cl···SiN–R systems, to the strong polarization
of the CN–R carbons and SiN–R silicons by the electric field of the positive σ-hole of the F–Cl chlorine. This polarization
may evolve into some degree of dative sharing of electrons by the carbons and silicons. This interpretation is supported by
the fact that complexes of CN–R and SiN–R with Cl–Cl, which has a much weaker positive σ-hole than F–Cl, are considerably
less likely to show the unusual features. It is demonstrated that the full ranges of binding energies of the CN–R and SiN–R
complexes with either F–Cl or Cl–Cl can be represented well (R2 > 0.96) in terms of the most negative electrostatic potentials and the lowest local ionization energies on the carbon and
silicon surfaces. These properties reflect the electrostatic components of the interactions and the polarizabilities/dative
reactivities of the carbons and silicons.
Content Type Journal Article
Category Regular Article
Pages 1-10
DOI 10.1007/s00214-012-1114-1
Authors
Peter Politzer, CleveTheoComp, 1951 W. 26th Street, Suite 409, Cleveland, OH 44113, USA
Jane S. Murray, CleveTheoComp, 1951 W. 26th Street, Suite 409, Cleveland, OH 44113, USA
Conformational analysis of tyrosine (YN) and its ionized counter parts cations (YC), anions (YA) and biologically relevant zwitterionic form (YZ) has been carried out. An exhaustive and systematic exploration of l-tyrosine dimer (YD) conformations resulted in about 59 distinct minima on the potential energy surface. The hydrogen bonds and a variety of
non-covalent interactions such as OH–π, NH–π, CH–π, CH–O and π–π interactions stabilized the different forms of tyrosine and
its dimers. Atoms in molecules analysis was performed to evaluate the nature and strength of the non-covalent interactions.
Over all the NH–O, hydrogen bonds have showed higher stability than other non-covalent interactions in this study. The most
stable dimers predominantly possess hydrogen bonding interactions, while the ones with aromatic side chain interactions are
less stable. A delicate balance of non-covalent interactions governed the stability of different forms of tyrosine and its
dimers.
Content Type Journal Article
Category Regular Article
Pages 1-14
DOI 10.1007/s00214-012-1093-2
Authors
Uppula Purushotham, Molecular Modeling Group, Indian Institute of Chemical Technology, Tarnaka, Hyderabad, 500 007 India
G. Narahari Sastry, Molecular Modeling Group, Indian Institute of Chemical Technology, Tarnaka, Hyderabad, 500 007 India
The reaction of CH3OCF2CF2OCHO with Cl atom has been investigated theoretically by direct dynamics method. The BB1K hybrid functional in conjunction
with the 6-31 + G(d,p) basis set has been used to optimize the geometries for the stationary points and explore the potential
energy surface of the reaction. Four rotation conformers (RC1-4) of CH3OCF2CF2OCHO are identified, and they are all considered in the kinetic calculation. For each conformer, there are two kinds of H-abstraction
channels and one displacement channel, and the latter one should be negligible due to involving much higher energy barrier
than the former two. The individual rate constants for each H-abstraction channel are evaluated by the improved canonical
variational transition-state theory with a small-curvature tunneling correction. The overall rate constant is evaluated by
the Boltzmann distribution function, and a fitted four-parameter rate constant expression is obtained over a wide temperature
range of 200–2,000 K. The agreement between the calculated and available experimental value at 296 K is good. The contribution
of each conformer to the title reaction is discussed with respect to the temperature. In addition, because of the lack of
available experimental data for the species involved in the reactions, the enthalpies of the formation (ΔHf,298°) for the reactant and its product radicals are predicted via isodesmic reaction at the BB1K/6-31 + G(d,p) level.
Content Type Journal Article
Category Regular Article
Pages 1-10
DOI 10.1007/s00214-012-1119-9
Authors
Tong-yin Jin, State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, 130023 People’s Republic of China
Hong-bo Yu, State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, 130023 People’s Republic of China
Cheng-gang Ci, State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, 130023 People’s Republic of China
Jing-yao Liu, State Key Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, 130023 People’s Republic of China
The autocatalytic Soai reaction gives abundant evidence of the enantioselective adsorption of organic compounds on a variety
of crystals. Computational modelling can provide insight into mechanisms of enantioselectivity. Here, we use a combination
of simulated annealing, forcefield, and quantum mechanical methods to examine interactions of pyrimidyl-5-carbaldehyde and
2-methylpyrimidyl-5-carbaldehyde with surfaces of γ-glycine. Using binding energy results, we predict the exposure of the pro-stereogenic S face of pyrimidyl-5-carbaldehyde (~65%) and 2-methylpyrimidyl-5-carbaldehyde (>90%) on the (1
-
1
0) and (
-
1
1 0) surfaces. The aim is to develop a robust computational methodology that can be applied to understanding crystal-biased
asymmetric synthesis.
Content Type Journal Article
Category Regular Article
Pages 1-7
DOI 10.1007/s00214-012-1125-y
Authors
Damien J. Carter, Department of Chemistry, Nanochemistry Research Institute, Curtin University, Perth, WA, Australia
Bart Kahr, Department of Chemistry, New York University, New York, NY, USA
Andrew L. Rohl, Department of Chemistry, Nanochemistry Research Institute, Curtin University, Perth, WA, Australia
The electron localizability indicator (ELI-D) is suitable to describe certain aspects of the bonding situation of molecules
and solids. ELI-D is based on integrals of electron pair density over very small regions. Recently proposed functional Cp, derived from the electron population in regions of fixed amount of electron density inhomogeneity, is based on the same
approach as ELI-D, that is, ω-restricted space partitioning. The electron density inhomogeneity is given by the distance of
electron density values to the averaged density within chosen region. Thus, in contrast to ELI-D, Cp is a single-electron property. The distance measure depends on a parameter that can be optimized in such way that Cp mimics the topology of the ELI-D distribution for atoms. Such an optimization was performed for the atoms Li to Xe. The optimal
parameter p = 0.6 yields the functional C0.6 that was exemplary applied to a few chosen molecules. In case of molecules the topology of the inner shell and lone-pair
regions as given by C0.6 is comparable with that of the ELI-D representation. However, in the bonding region between the atoms the topology of C0.6 is dominated by the low density gradient close to the bond critical point. This may result in rather different topologies
when comparing C0.6 and ELI-D.
Content Type Journal Article
Category Regular Article
Pages 1-8
DOI 10.1007/s00214-012-1106-1
Authors
K. Finzel, Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany
Yu. Grin, Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany
M. Kohout, Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187 Dresden, Germany
To identify the transition state accurately and efficiently on a high-dimensional potential energy surface is one of the most
important topics in kinetic studies on chemical reactions. We present here an algorithm to search the transition state by
so-called force reversed method, which only requires a rough reaction direction instead of knowing the initial state and final
state. Compared to the nudged elastic band method and the dimer method that require multiple images, the present algorithm
with only single image required saves significantly the computational cost. The algorithm was implemented in the first-principle
periodic total energy calculation package and applied successfully to several prototype surface processes such as the adsorbate
diffusion and dissociation on metal surfaces. The results indicate that the force reversed method is efficient, robust to
identify the transition state of various surface processes.
Content Type Journal Article
Category Regular Article
Pages 1-10
DOI 10.1007/s00214-012-1118-x
Authors
Keju Sun, State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023 China
Yonghui Zhao, State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023 China
Hai-Yan Su, State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023 China
Wei-Xue Li, State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023 China
The recently discovered ditantalaboranes Cp2Ta2BnHn+6 (n = 4, 5) are isoelectronic with the previously discovered dimetallaboranes Cp2M2BnHn+4 of the group 6 metals Cr, Mo, and W where Cp = η5-cyclopentadienyl or substituted cyclopentadienyl. Their oblatonido polyhedral structures can be derived from the oblate (flattened) deltahedra of the oblatocloso dirhenaboranes Cp2Re2Bn+1Hn+1 by removal of an equatorial BH vertex with adjustment of the skeletal electron count by changing the metal atoms and adding
hydrogen atoms. In these oblatocloso dirhenaborane deltahedra, the approximately antipodal rhenium atoms are close enough together to form a formal Re=Re double
bond with lengths in the range 2.69–2.82 Å. Similarly, short M=M distances are maintained in the related oblatonido derivatives Cp2Ta2BnHn+6 (n = 4, 5) and Cp2M2BnHn+4 (M=Cr, Mo, W). However, the synthesis of Cp2Ta2BnHn+6 (n = 4, 5) from CpTaCl4 + LiBH4/BH3 also gives a less-reduced product Cp2Ta2Cl2B5H11 with a longer Ta–Ta distance of ~3.2 Å. This may be regarded as a formal single bond bridged by one of the hydrogen atoms.
Vertices of degree 5 (excluding terminal atoms/groups but not edge-bridging hydrogens) are sites of highest stability/lowest
chemical reactivity not only in metal-free boranes but also in the dimetallaboranes discussed in this paper. For example,
all four boron vertices in Cp2Ta2B4H10 have the favorable degree or 5.
Graphical Abstract
The recently discovered ditantalaboranes Cp2Ta2BnHn+6 (n = 4, 5) are isoelectronic with the previously discovered dimetallaboranes Cp2M2BnHn+4 (M=Cr, Mo, W). They have oblatonido structures derived by removal of one BH vertex from the flattened oblatocloso polyhedra of the dirhenaboranes Cp2Re2BnHn. All of these structures have internal M=M formal double bonds inside the deltahedron.
Content Type Journal Article
Category Regular Article
Pages 1-8
DOI 10.1007/s00214-012-1087-0
Authors
R. Bruce King, Department of Chemistry, University of Georgia, Athens, GA 30602, USA
Sundargopal Ghosh, Department of Chemistry, Indian Institute of Technology Madras, Chennai, 600036 India
Acetylene clusters are prototypical of simple non-aromatic systems bonded through C–H…π interactions. The present work explores
structures and properties of acetylene clusters (C2H2)n, n = 8 and 10, employing cluster-building algorithm and molecular tailoring approach (MTA). The former uses electrostatics guidelines
for building (C2H2)8 and (C2H2)10 structures. These clusters are treated at MP2 level of theory with correlation-consistent basis sets using MTA. The Hessian
matrix and vibrational spectra for the best five structures of (C2H2)8 and (C2H2)10 are computed employing MTA. Actual calculations on these clusters using conventional methods employing large basis sets are
prohibitively difficult to perform. All the frequencies for these structures extracted using MTA-based Hessian matrix are
found to be real, confirming their local minimum nature. This study points to the possibility of using the present approach
for exploring structures, energetics and vibrational spectra of even larger clusters at higher levels of theory.
Content Type Journal Article
Category Regular Article
Pages 1-7
DOI 10.1007/s00214-012-1095-0
Authors
Anuja P. Rahalkar, Department of Chemistry, Indian Institute of Technology, Kanpur, 208016 India
Sachin D. Yeole, Department of Chemistry, Indian Institute of Technology, Kanpur, 208016 India
Shridhar R. Gadre, Department of Chemistry, Indian Institute of Technology, Kanpur, 208016 India
A method introduced by Mayer (Theor Chem Acc 104:163, 2000) for generating an orthogonal set of basis vectors, perpendicular to an arbitrary start vector, is examined. The procedure
provides the complementary vectors in closed form, expressed with the components of the start vector. Mayer’s method belongs
to the family of orthogonalization schemes, which keep an arbitrary vector intact without introducing any non-physical sequence-dependence.
It is shown that Mayer’s orthogonalization is recovered by performing a two-step combination of the Gram-Schmidt and Löwdin’s
symmetrical orthogonalization. Processor time requirement of constructing Mayer’s orthonormal set is proportional to ∼N2, in contrast to the rough ∼N3 CPU requirement of performing either a full Gram-Schmidt or Löwdin’s symmetrical orthogonalization. Utility of Mayer’s orthogonalization
is demonstrated on an electronic structure application using perturbation theory to improve multiconfigurational wavefunctions.
Content Type Journal Article
Category Regular Article
Pages 1-6
DOI 10.1007/s00214-012-1109-y
Authors
Péter R. Nagy, Laboratory of Theoretical Chemistry, Eötvös University, POB 32, Budapest, 1518 Hungary
Péter R. Surján, Laboratory of Theoretical Chemistry, Eötvös University, POB 32, Budapest, 1518 Hungary
Ágnes Szabados, Laboratory of Theoretical Chemistry, Eötvös University, POB 32, Budapest, 1518 Hungary
With the aim of designing new inorganic photosensitizers for photovoltaic applications, the structural and electronic properties
of two Ru(II) complexes containing terpyridine-based ligands derived from expanded pyridiniums both branched—polyphenyl—and
fused—polycyclic—were investigated by the means of density functional theory (DFT) and time-dependent DFT (TD-DFT). In particular,
the structure and electronic absorption of the fused architectures—including the isolated ligand and its complex—were compared
with those of their respective branched precursors with the aim to account for the their enhanced electronic features in the
visible spectral region. The theoretical insights gained into the “large-surface” ligand and its associated complex open the
route for a joint experimental and theoretical design of new inorganic photosensitizers based on fused expanded pyridiniums.
Content Type Journal Article
Category Regular Article
Pages 1-10
DOI 10.1007/s00214-012-1107-0
Authors
Samira Zeroual, LECIME, Laboratoire d’Électrochimie, Chimie des Interfaces et Modélisation pour l’Énergie, UMR 7575 CNRS, École Nationale Supérieure de Chimie de Paris – Chimie ParisTech, 11 rue P. et M. Curie, 75231 Paris Cedex 05, France
Nathalie Bouet, LECIME, Laboratoire d’Électrochimie, Chimie des Interfaces et Modélisation pour l’Énergie, UMR 7575 CNRS, École Nationale Supérieure de Chimie de Paris – Chimie ParisTech, 11 rue P. et M. Curie, 75231 Paris Cedex 05, France
Fabien Tuyèras, Laboratoire ITODYS, UMR 7086 CNRS, Université Paris Diderot, Sorbonne Paris Cité, Bâtiment Lavoisier, 15, rue Jean-Antoine de Baïf, 75205 Paris Cedex 13, France
Cyril Peltier, LECIME, Laboratoire d’Électrochimie, Chimie des Interfaces et Modélisation pour l’Énergie, UMR 7575 CNRS, École Nationale Supérieure de Chimie de Paris – Chimie ParisTech, 11 rue P. et M. Curie, 75231 Paris Cedex 05, France
Nadia Ouddai, Laboratoire de chimie de materiaux et des vivants: Activité, Réactivité, Université de Batna, 05000 Batna, Algeria
Philippe Ochsenbein, Laboratoire de Cristallographie et Modélisation Moléculaire du Solide, Sanofi-Aventis LGCR, 371 rue du Professeur Blayac, 34184 Montpellier Cedex 04, France
Carlo Adamo, LECIME, Laboratoire d’Électrochimie, Chimie des Interfaces et Modélisation pour l’Énergie, UMR 7575 CNRS, École Nationale Supérieure de Chimie de Paris – Chimie ParisTech, 11 rue P. et M. Curie, 75231 Paris Cedex 05, France
Philippe P. Lainé, Laboratoire ITODYS, UMR 7086 CNRS, Université Paris Diderot, Sorbonne Paris Cité, Bâtiment Lavoisier, 15, rue Jean-Antoine de Baïf, 75205 Paris Cedex 13, France
Ilaria Ciofini, LECIME, Laboratoire d’Électrochimie, Chimie des Interfaces et Modélisation pour l’Énergie, UMR 7575 CNRS, École Nationale Supérieure de Chimie de Paris – Chimie ParisTech, 11 rue P. et M. Curie, 75231 Paris Cedex 05, France
A theoretical investigation at the density functional theory level (B3LYP) has been conducted to elucidate the impact of ligand
basicity on the binding interactions between ethylene and copper(I) ions in [Cu(η2-C2H4)]+ and a series of [Cu(L)(η2-C2H4)]+ complexes, where L = substituted 1,10-phenanthroline ligands. Molecular orbital analysis shows that binding in [Cu(η2-C2H4)]+ primarily involves interaction between the filled ethylene π-bonding orbital and the empty Cu(4s) and Cu(4p) orbitals, with less interaction observed between the low energy Cu(3d) orbitals and the empty ethylene π*-orbital. The presence of electron-donating ligands in the [Cu(L)(η2-C2H4)]+ complexes destabilizes the predominantly Cu(3d)-character filled frontier orbital of the [Cu(L)]+ fragment, promoting better overlap with the vacant ethylene π*-orbital and increasing Cu → ethylene π-backbonding. Moreover, the energy of the filled [Cu(L)]+ frontier orbital and mixing with the ethylene π*-orbital increase with increasing pKa of the 1,10-phenanthroline ligand. Natural bond orbital analysis reveals an increase in Cu → ethylene electron donation with
addition of ligands to [Cu(η2-C2H4)]+ and an increase in backbonding with increasing ligand pKa in the [Cu(L)(η2-C2H4)]+ complexes. Energy decomposition analysis (ALMO-EDA) calculations show that, while Cu → ethylene charge transfer (CT) increases
with more basic ligands, ethylene → Cu CT and non-CT frozen density and polarization effects become less favorable, yielding
little change in copper(I)–ethylene binding energy with ligand pKa. ALMO-EDA calculations on related [Cu(L)(NCCH3)]+ complexes and calculated free energy changes for the displacement of acetonitrile by ethylene reveal a direct correlation
between increasing ligand pKa and the favorability of ethylene binding, consistent with experimental observations.
Content Type Journal Article
Category Regular Article
Pages 1-12
DOI 10.1007/s00214-012-1105-2
Authors
Naomi C. Pernicone, Department of Chemistry, Stetson University, DeLand, FL 32723, USA
Jacob B. Geri, Department of Chemistry, Stetson University, DeLand, FL 32723, USA
John T. York, Department of Chemistry, Stetson University, DeLand, FL 32723, USA
The reactivity of H2O and the Si-terminated silicon carbide surface (001) was investigated on the triplet potential energy surface with the combined
first principle and molecular mechanics ONIOM(CASSCF:AM1:UFF) method for the (SiC)192·H2O model. It was found that the H2O molecule and the surface can form three physisorption complexes and follow five reaction paths to produce eight products,
in which there are five main products having necessary energy barriers less than 300 kJ mol−1. Compared with that on the C-terminated surface, the interaction with the Si-terminated surface has stronger physisorption
energy, smaller lowest necessary energy barrier, more main and more stable products.
Content Type Journal Article
Category Regular Article
Pages 1-7
DOI 10.1007/s00214-012-1101-6
Authors
Yan Liu, Key Laboratory of Space Applied Physics and Chemistry of the Ministry of Education, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an, 710072 Shaanxi, People’s Republic of China
Ke-He Su, Key Laboratory of Space Applied Physics and Chemistry of the Ministry of Education, School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an, 710072 Shaanxi, People’s Republic of China
Qing-Feng Zeng, National Key Laboratory of Thermostructure Composite Materials, Northwestern Polytechnical University, Xi’an, 710072 Shaanxi, People’s Republic of China
Lai-Fei Cheng, National Key Laboratory of Thermostructure Composite Materials, Northwestern Polytechnical University, Xi’an, 710072 Shaanxi, People’s Republic of China
Li-Tong Zhang, National Key Laboratory of Thermostructure Composite Materials, Northwestern Polytechnical University, Xi’an, 710072 Shaanxi, People’s Republic of China
Sadlej’s electric polarization method of Gaussian basis functions was applied to the double-zeta effective core potential
basis sets of Stevens, Basch, Krauss, Jasien and Cundari to generate a new augmented polarized valence double-zeta set, named
as pSBKJC, which is appropriate for the calculation of dynamic polarizabilities and Raman intensities. The pSBKJC basis set
was developed for the atoms of families 14–17 (from C to F, Si to Cl, Ge to Br and Sn to I). In order to assess the performance
of this new basis set, these properties were compared to those evaluated using Sadlej’s set, available in the EMSL online library under the name of Sadlej-pVTZ. In these tests, Hartree-Fock/pSBKJC calculations have proved to be less demanding
of the computer than the Hartree-Fock/Sadlej-pVTZ ones but give results in excellent agreement with those from the Sadlej-pVTZ
basis set. Since the Stevens et al. pseudopotential can represent the scalar relativistic effects, the results obtained at
the Hartree-Fock/pSBKJC level show a better agreement with the results of Dirac-Hartree-Fock/Sadlej-pVTZ relativistic calculations
using Dyall’s spin-free Hamiltonian. When comparing Hartree-Fock/pSBKJC data of Raman scattering activities, at the excitation
wavelength of 488 nm, with those of spin-free Dirac-Hartree-Fock/Sadlej-pVTZ calculations, a very good agreement is observed,
where the RMS error is 8.5 Å4a.m.u.−1 and the averaged percentage error is 3.4%. In terms of computer savings in calculations of dynamic Raman intensities, a 20%
reduction in the CPU time in the coupled cluster singles and doubles intensities of C6H6 and about 40% reduction in the time-dependent Hartree-Fock intensities for C6F6 molecules were attained.
Content Type Journal Article
Category Regular Article
Pages 1-8
DOI 10.1007/s00214-012-1111-4
Authors
Luciano N. Vidal, Chemistry and Biology Department, Federal Technological University of Paraná, Curitiba, PR, Brazil
Pedro A. M. Vazquez, Physical-Chemistry Department, Chemistry Institute, State University of Campinas, Campinas, SP, Brazil
In order to understand the mechanism of nucleation of (NH4)2SO4 aerosol, the reaction between sulfuric acid and ammonia in the absence of water molecule is performed at M06/6-311++G(d,p)
level. The results show that the (NH4)2SO4 and NH4HSO4 units may exist instantaneously in gas phase without water molecule, which is a theoretical prediction that needs detection
by further experiment. To further study the growth of the primary nuclei, the geometries, energies, and harmonic frequencies
of (NH4)2SO4 · (H2O)n (n = 0–9) are calculated both at M06/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels. The tendency of the theoretical vibration
frequencies is in accordance with the experimental results. The influence of the water molecule on the properties of (NH4)2SO4 is also analyzed. Our results indicate that M06 is more accurate than B3LYP for this kind of system. Moreover, the first
principle molecular dynamics method is used to simulate the structural transformation for two representative isomers whose
energies are close, to understand the relationship between solvent-shared ion pairs and contact ion pairs.
Content Type Journal Article
Category Regular Article
Pages 1-10
DOI 10.1007/s00214-012-1103-4
Authors
Wei-Wei Liu, Key Laboratory of Cluster Science of Ministry of Education, School of Chemistry, The Institute for Chemical Physics, Beijing Institute of Technology, Beijing, 100081 People’s Republic of China
Xiao-Lin Wang, Key Laboratory of Cluster Science of Ministry of Education, School of Chemistry, The Institute for Chemical Physics, Beijing Institute of Technology, Beijing, 100081 People’s Republic of China
Shi-Lu Chen, Key Laboratory of Cluster Science of Ministry of Education, School of Chemistry, The Institute for Chemical Physics, Beijing Institute of Technology, Beijing, 100081 People’s Republic of China
Yun-Hong Zhang, Key Laboratory of Cluster Science of Ministry of Education, School of Chemistry, The Institute for Chemical Physics, Beijing Institute of Technology, Beijing, 100081 People’s Republic of China
Ze-Sheng Li, Key Laboratory of Cluster Science of Ministry of Education, School of Chemistry, The Institute for Chemical Physics, Beijing Institute of Technology, Beijing, 100081 People’s Republic of China
We report on a quantum-chemical study of the electronic and optical properties of a series of β, β′-edge-fused zinc porphyrin
with different aromatic rings, in order to design efficient sensitizers for dye-sensitized solar cells (DSSCs). Our calculations
found that the replacement of quinoxaline moiety in ZnQMA (having high power conversion efficiency η of 6.3%) with other aromatic rings decreases the HOMO–LUMO energy gap mainly due to destabilization of the HOMO level. For
all of the investigated compounds, the reorganization energies of electron and hole are in the same order of magnitude as
and similar to those of ZnQMA. The absorption spectra in both Soret and Q bands for most of the considered molecules exhibit red shifts to some extent
with respect to that of ZnQMA. In the simulated dye-sensitized TiO2 systems, the bidentate adsorption mode of porphyrin derivatives is computed to be energetically favored compared to the monodentate
one, which well confirms the experimental results observed by X-ray photoelectron spectroscopy. The slightly shorter Ti–O
bond lengths calculated for D–TiO2 systems point toward a stronger interaction of the dye with the titania surface compared to ZnQMA–TiO2 systems. Our calculation indicates that the designed molecule D is promising to challenge the current photoelectric conversion efficiency record 6.3% of ZnQMA.
Content Type Journal Article
Category Regular Article
Pages 1-11
DOI 10.1007/s00214-012-1102-5
Authors
Hao Dong, Institute of Chemistry for Functionalized Material, College of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, 116029 China
Xin Zhou, State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023 China
Chunjie Jiang, Institute of Chemistry for Functionalized Material, College of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, 116029 China
For the 54 atoms from H to Xe, compact yet accurate segmented Gaussian-type basis sets have been constructed for all electron
calculations. Non-relativistic nZP (Sapporo-nZP) sets for Li–Xe and relativistic nZP (Sapporo-DK-nZP) sets for K–Xe are developed (n = D, T, Q), which efficiently incorporate valence and core electron correlations. Test calculations at the coupled-cluster
level of theory are performed for spectroscopic constants of 12 hydrides of s- and d-block atoms and 12 diatomics of p-block atoms in their ground states. For all molecules, the calculated spectroscopic constants approach to the experimental
values smoothly as the basis set quality increases.
Content Type Journal Article
Category Regular Article
Pages 1-8
DOI 10.1007/s00214-012-1124-z
Authors
Takeshi Noro, Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Hokkaido 060-0810, Japan
Masahiro Sekiya, Department of Intercultural Studies, Tomakomai Komazawa University, Tomakomai, Hokkaido 059-1292, Japan
Toshikatsu Koga, Applied Chemistry Research Unit, Graduate School of Engineering, Muroran Institute of Technology, Muroran, Hokkaido 050-8585, Japan
π–π and CH···N interactions are vital in biological systems. In this study, stacking and hydrogen-bonded interactions in pyrazine
and triazine dimers were investigated by density functional theory combined with symmetry-adapted perturbation theory (DFT-SAPT)
and counterpoise (CP)-corrected supermolecular MP2, SCS-MP2, B3LYP-D and CCSD(T) calculations. All interaction energies were
computed using the optimized structures at the CP-corrected SCS/aug-cc-pVDZ level, which gave 1–2 kJ/mol lower interaction
energies than the ones computed at the MP2 level. For both dimers, doubly hydrogen-bonded and cross-(displaced) stacked orientations
were found to be the lowest energy ones. The reference CCSD(T) calculations favored the former structure in both dimer systems,
whereas MP2 and SCS-MP2 located the latter as the lowest energy isomer. In particular, the former was found to be lower in
energy than the latter by 2.28 and 1.01 kJ/mol at the CCSD(T)/aug-cc-pVDZ level for pyrazine and triazine, respectively. B3LYP-D
produced interaction energies in agreement with the CCSD(T) at the equilibrium geometries, but it overestimates them at the
short range and underestimates at the long intermonomer separations. Furthermore, it tends to give smaller equilibrium distances
compared to the CCSD(T). DFT-SAPT method was in a good agreement with the reference CCSD(T) calculations. This suggests that
DFT-SAPT can be employed to compute the full potential energy surface of these dimers. Moreover, DFT-SAPT calculations showed
that the electrostatic and dispersion contributions are the most important energy components stabilizing these dimers. The
present study aims to show which theoretical method is the most promising one for the investigation of intermolecular interactions
dominated by π–π and CH···N. Therefore, the findings obtained in this study can be used to unravel the structures of nucleic
acid bases and other systems stabilized by π–π and CH···N interactions.
We report on ab-initio calculations of the electronic structure and optical absorption response of the black dye sensitizer
in gas phase. We show that, despite the large size of this molecule, the second-order multiconfiguration quasi-degenerate
perturbation theory (MC-QDPT) can be used to calculate vertical excitation energies, oscillator strengths and optical absorption
spectra. The zeroth-order reference states entering perturbation calculations are complete active space (CAS) configuration
interaction (CI) wave functions computed for 12 active electrons distributed in 12 active orbitals. We found that the CI approach
is not enough for taking into account the strong dynamical correlation effects in this system. In fact, the excitation energies
of the CAS-CI target states are strongly renormalized by the MC-QDPT calculations. In the calculated absorption spectra, the
analysis of the perturbed wavefunctions revealed that the stronger absorption bands correspond to metal-to-ligand and ligand-to-ligand
charge transfer processes. Comparison with independent time-dependent extension (TDDFT) calculations performed with different
functionals shows that corrections to the long-range behavior of the functional is pivotal to achieve agreement with the MC-QDPT
results.
Content Type Journal Article
Category Regular Article
Pages 1-14
DOI 10.1007/s00214-012-1115-0
Authors
Alain Delgado, CNR-NANO S3, Institute for Nanoscience, Via Campi 213/A, 41125 Modena, Italy
Stefano Corni, CNR-NANO S3, Institute for Nanoscience, Via Campi 213/A, 41125 Modena, Italy
Guido Goldoni, CNR-NANO S3, Institute for Nanoscience and Physics Department, University of Modena and Reggio Emilia, Via Campi 213/A, 41125 Modena, Italy
The role of exchange–correlation is well known for accurate calculations of electric response properties. The exchange–correlation
functional in density functional theory (DFT) has been well studied for ground state equilibrium geometry. However, the behaviour
of these functional in stretched geometries, where static correlation play an important role, has not been studied systematically,
particularly for response electric properties. Thus, we present here the rigorous calculation of electric response properties
at distorted geometries of the molecules. We have considered dipole polarizability and dipole–quadrupole polarizability for
description of role of static and dynamic correlation for electric response properties. The calculations are performed with
our new approach, non-iterative approximation to coupled-perturbed Kohn–Sham method. These DFT results are compared with higher
level ab initio such as coupled perturbed singles and doubles and fully correlated full CI. We have studied single, double
and triple-bonded systems at different inter-nuclear separation. We report here the dipole polarizability and dipole–quadrupole
polarizability of HF, BH, H2CO, CO and NO+. We also present the effect of basis and functional on polarizability and dipole–quadrupole polarizability.
Content Type Journal Article
Category Regular Article
Pages 1-10
DOI 10.1007/s00214-012-1094-1
Authors
Sapana V. Shedge, Physical Chemistry Division, National Chemical Laboratory, Pune, 411008 India
Sayali P. Joshi, Physical Chemistry Division, National Chemical Laboratory, Pune, 411008 India
Sourav Pal, Physical Chemistry Division, National Chemical Laboratory, Pune, 411008 India
The Al–Al multiple bond in Na2[Arx′AlAlArx′] (Arx′ = C6H3-2,6-(C6H5)2) was investigated and compared with H2[Arx′AlAlArx′] by electron localization function (ELF) method. The roles of sodium, hydrogen atoms, and bulky ligands in these
two complexes were also discussed. The calculated results show that Na2[Arx′AlAlArx′] and H2[Arx′AlAlArx′] have different structural and electronic features. In Na2[Arx′AlAlArx′], the Al–Al bond includes a σ bond, a normal π bond and a slipped π bond. In H2[Arx′AlAlArx′], the direct Al–Al bond was substituted by two 3-center, 2-electron (3c–2e) bridged bonding, which formed by
the hydrogen and two aluminum atoms. The bulky ligands play important stabilizing roles in both Na2[Arx′AlAlArx′] and H2[Arx′AlAlArx′].
Content Type Journal Article
Category Regular Article
Pages 1-7
DOI 10.1007/s00214-012-1116-z
Authors
Xiaoyan Li, College of Chemistry, Institute of Computational Quantum Chemistry, Hebei Normal University, Yuhua Road, Shijiazhuang, 050016 China
Jie Sun, College of Chemistry, Institute of Computational Quantum Chemistry, Hebei Normal University, Yuhua Road, Shijiazhuang, 050016 China
Lingpeng Meng, College of Chemistry, Institute of Computational Quantum Chemistry, Hebei Normal University, Yuhua Road, Shijiazhuang, 050016 China
Yanli Zeng, College of Chemistry, Institute of Computational Quantum Chemistry, Hebei Normal University, Yuhua Road, Shijiazhuang, 050016 China
Shijun Zheng, College of Chemistry, Institute of Computational Quantum Chemistry, Hebei Normal University, Yuhua Road, Shijiazhuang, 050016 China
Electrophilicity and hardness have been shown to be adequate in constructing structure-stability diagrams. Maximum hardness
principle and minimum electrophilicity principle provide a rough guide toward locating the domains of stability and reactivity
in a fitness landscape. Bonding in solids, aromaticity, magic alkali clusters, bond—stretch isomers, multivalent superatoms,
etc. have been analyzed within this purview.
Content Type Journal Article
Category Regular Article
Pages 1-8
DOI 10.1007/s00214-012-1089-y
Authors
Pratim Kumar Chattaraj, Department of Chemistry and Center for Theoretical Studies, Indian Institute of Technology Kharagpur, Kharagpur, 721302 India
Ranjita Das, Department of Chemistry and Center for Theoretical Studies, Indian Institute of Technology Kharagpur, Kharagpur, 721302 India
Soma Duley, Department of Chemistry and Center for Theoretical Studies, Indian Institute of Technology Kharagpur, Kharagpur, 721302 India
Jean-Louis Vigneresse, Nancy-Université, UMR 7566 G2R, BP 23, 54501 Vandoeuvre cédex, France
We determine the limit sets of a system modelling suicide substrate kinetics, and show that a result by Tatsunami et al. (Biochim
Biophys Acta 662:226–235, 1981), derived under additional quasi-steady state assumptions, holds generally.
Content Type Journal Article
Category Brief Communication
Pages 1-5
DOI 10.1007/s10910-012-9979-8
Authors
Alexandra Goeke, Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany
Christian Schilli, Lehrstuhl D für Mathematik, RWTH Aachen, 52056 Aachen, Germany
Sebastian Walcher, Lehrstuhl A für Mathematik, RWTH Aachen, 52056 Aachen, Germany
Eva Zerz, Lehrstuhl D für Mathematik, RWTH Aachen, 52056 Aachen, Germany
The Lindstedt–Poincare technique has traditionally been used to deal with oscillators with power-law potentials. We show how
this method can be extended to deal with molecular potentials for which the frequency goes to zero as the energy approaches
zero. The extension requires the use of an asymptotic analysis which is combined with perturbation theory. For the Morse potential,
we get an exact answer while for the Lennard Jones class of potentials
V=V0 [ ( \fracax)2n-(\fracax)n]
, the answer is generally approximate with some values of n giving exact results. For the widely studied case, n=6, our approximation
gives better than 1% accuracy at the lowest order of calculation. We show that as
n ® ¥
, the result tends to that for the Morse potential. We also point out that the time period obtained by us can be used to
obtain the quantum mechanical energy levels of these potentials within the Bohr-Sommerfeld scheme.
Content Type Journal Article
Category Original Paper
Pages 1-13
DOI 10.1007/s10910-012-9978-9
Authors
Shayak Bhattacharjee, Department of Physics, Indian Institute of Technology Kanpur, Kanpur, 208016 India
J. K. Bhattacharjee, S. N. Bose National Centre for Basic Sciences, Salt Lake, Kolkata, 700098 India
A reaction-pathway identification procedure has two distinct phases. The first phase enumerates exhaustively the feasible
candidate pathways, and the second phase identifies the ultimate feasible pathway or pathways among them. Probably the most
efficient way to execute the first phase is to algorithmically generate the networks of feasible candidate pathways from a
predefined set of plausible elementary reactions. The available algorithmic methods for this purpose can be roughly grouped
into two major classes, one based on graph theory and the other on linear algebra. Both classes of methods consider any chemical
reaction system as a network of elementary reactions, thereby implying that the two classes are interrelated. This paper studies
the linear algebraic concept termed direct mechanism introduced in the mid-eighties and the graph-theoretical concept termed
structurally minimal pathway introduced two decades later. Herein, it has been formally proven that the two concepts are equivalent.
Content Type Journal Article
Category Original Paper
Pages 1-15
DOI 10.1007/s10910-012-9974-0
Authors
Mate Barany, Department of Computer Science and Systems Technology, University of Pannonia, Egyetem u. 10, 8200 Veszprém, Hungary
Botond Bertok, Department of Computer Science and Systems Technology, University of Pannonia, Egyetem u. 10, 8200 Veszprém, Hungary
Csanad Imreh, Department of Computer Algorithms and Artifical Intelligence, University of Szeged, Árpád tér 2, 6720 Szeged, Hungary
L. T. Fan, Department of Chemical Engineering, Kansas State University, Manhattan, KS 66506, USA
Ferenc Friedler, Department of Computer Science and Systems Technology, University of Pannonia, Egyetem u. 10, 8200 Veszprém, Hungary
Polyhedral links have been used to model DNA polyhedra and protein catenanes. Some topological characteristics of a type of
polyhedral links fabricated from a polyheron by the method of ‘n-branched curve and X-tangled covering’ have been elucidated. In this paper, we pay close attention to their braid index considered significant
in view of DNA nanotechnology, and proved that the MFW inequality is sharp for the polyhedral links. Our results demonstrate
that the braid index of the links is directed by their crossing numbers. In addition, the studies of the polyhedral links
can facilitate the research of the properties of DNA molecules, and can characterize their structural complexity.
Content Type Journal Article
Category Original Paper
Pages 1-12
DOI 10.1007/s10910-012-9976-y
Authors
Xiao-Sheng Cheng, Department of Mathematics, Huizhou University, Huizhou, 516007 Guangdong, People’s Republic of China
Xiaoyan Jiang, Department of Mathematics, Huizhou University, Huizhou, 516007 Guangdong, People’s Republic of China
Huawei Dai, Department of Mathematics, Huizhou University, Huizhou, 516007 Guangdong, People’s Republic of China
For arbitrary values n and ℓ quantum numbers, we present the solutions of the 3-dimensional Schrödinger wave equation with the pseudoharmonic potential
via the SU(1, 1) Spectrum Generating Algebra (SGA) approach. The explicit bound state energies and eigenfunctions are obtained. The
matrix elements r2 and
r\fracddr
are obtained (in a closed form) directly from the creation and annihilation operators. In addition, by applying the Hellmann–Feynman
theorem, the expectation values of r2 and p2 are obtained. The energy states, the expectation values of r2 and p2 and the Heisenberg uncertainty products (HUP) for set of diatomic molecules (CO, NO, O2, N2, CH, H2, ScH) for arbitrary values of n and ℓ quantum numbers are obtained. The results obtained are in excellent agreement with the available results in the literature.
It is also shown that the HUP is obeyed for all diatomic molecules considered.
Content Type Journal Article
Category Review
Pages 1-21
DOI 10.1007/s10910-011-9967-4
Authors
K. J. Oyewumi, Theoretical Physics Section, Department of Physics, University of Ilorin, P. M. B. 1515, Ilorin, Kwara state, Nigeria
K. D. Sen, School of Chemistry, University of Hyderabad, Hyderabad, 50046 India
The Asymptotic Linearity Theorem (ALT), which proves the Fukui conjecture in a broader context, plays a significant role in
the repeat space theory (RST), which is the central unifying theory in the First and the Second Generation Fukui Project.
Proving the Asymptotic Linearity Theorem Extension Conjecture (ALTEC) is a fundamental problem in the repeat space theory.
The present paper constructs a class of functions MagicMtθ, which serves as a powerful tool for proving the Asymptotic Linearity Theorem Extension Conjecture and related propositions.
The d-dimensional generalization μd,n,θ of MagicMtθ, which is given in the present paper and is called a ‘d-dimensional Magic Mountain’, provides inwardly repeating fractals in multidimensional spaces useful for interdisciplinary
research that uses the generalized repeat space theory.
Content Type Journal Article
Category Original Paper
Pages 1-14
DOI 10.1007/s10910-011-9963-8
Authors
Shigeru Arimoto, Division of General Education and Research, Tsuyama National College of Technology, 624-1 Numa, Tsuyama, Okayama 708-8509, Japan
of an N-gonal charge distribution, i.e., a set of unit charges occupying vertices of a regular N-gon with a unit circumradius,
is derived. Application of Padé approximants to truncations of this expansion produces compact approximate formulae capable
of estimating
E1(N)
with great accuracy. A closed-form expression for the energy of electrostatic interaction of two polygonal charge distributions
is obtained from the respective Fourier series. The availability of this expression allows for a rapid calculation of the
relevant energy with computational effort independent of the numbers of particles involved.
Content Type Journal Article
Category Original Paper
Pages 1-8
DOI 10.1007/s10910-012-9975-z
Authors
Jerzy Cioslowski, Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
Joanna Albin, Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
In this paper, we will investigate the fuzzy layer group symmetries of two-dimensional (2D) periodic molecules. Here, we select
several graphene molecules as typical examples to discuss. For these two-dimensional graphene molecules, their MO energies,
symmetries and fuzzy symmetries are preliminarily studied. In addition, we especially make a detailed comparison between the
zigzag and armchair graphene molecules. These studies will develop a theoretical framework that will help us to investigate
the fuzzy symmetries of various layer group molecules as well as molecules with 3D periodic structure.
Content Type Journal Article
Category Original Paper
Pages 1-24
DOI 10.1007/s10910-011-9972-7
Authors
Shengkai Xing, College of Chemistry, Nankai University, Tianjin, 300071 People’s Republic of China
Yun Li, College of Chemistry, Nankai University, Tianjin, 300071 People’s Republic of China
Xuezhuang Zhao, College of Chemistry, Nankai University, Tianjin, 300071 People’s Republic of China
Zunsheng Cai, College of Chemistry, Nankai University, Tianjin, 300071 People’s Republic of China
Zhenfeng Shang, College of Chemistry, Nankai University, Tianjin, 300071 People’s Republic of China
Xiufang Xu, College of Chemistry, Nankai University, Tianjin, 300071 People’s Republic of China
Ruifang Li, College of Chemistry, Nankai University, Tianjin, 300071 People’s Republic of China
Guichang Wang, College of Chemistry, Nankai University, Tianjin, 300071 People’s Republic of China
In the past decade, the random phase approximation (RPA) has emerged as a promising post-Kohn–Sham method to treat electron
correlation in molecules, surfaces, and solids. In this review, we explain how RPA arises naturally as a zero-order approximation
from the adiabatic connection and the fluctuation-dissipation theorem in a density functional context. This is contrasted
to RPA with exchange (RPAX) in a post-Hartree–Fock context. In both methods, RPA and RPAX, the correlation energy may be expressed
as a sum over zero-point energies of harmonic oscillators representing collective electronic excitations, consistent with
the physical picture originally proposed by Bohm and Pines. The extra factor 1/2 in the RPAX case is rigorously derived. Approaches
beyond RPA are briefly summarized. We also review computational strategies implementing RPA. The combination of auxiliary
expansions and imaginary frequency integration methods has lead to recent progress in this field, making RPA calculations
affordable for systems with over 100 atoms. Finally, we summarize benchmark applications of RPA to various molecular and solid-state
properties, including relative energies of conformers, reaction energies involving weak and covalent interactions, diatomic
potential energy curves, ionization potentials and electron affinities, surface adsorption energies, bulk cohesive energies
and lattice constants. RPA barrier heights for an extended benchmark set are presented. RPA is an order of magnitude more
accurate than semi-local functionals such as B3LYP for non-covalent interactions rivaling the best empirically parametrized
methods. Larger but systematic errors are observed for processes that do not conserve the number of electron pairs, such as
atomization and ionization.
Content Type Journal Article
Category Regular Article
Pages 1-18
DOI 10.1007/s00214-011-1084-8
Authors
Henk Eshuis, Department of Chemistry, University of California, 1102 Natural Sciences II, Irvine, CA 92697-2025, USA
Jefferson E. Bates, Department of Chemistry, University of California, 1102 Natural Sciences II, Irvine, CA 92697-2025, USA
Filipp Furche, Department of Chemistry, University of California, 1102 Natural Sciences II, Irvine, CA 92697-2025, USA
Explicit formulas for computing the Zhang–Zhang polynomial of cyclo-polyphenacenes, presented by Guo et al. (J. Math. Chem.
46:347, 2009) are found to be erroneous. In the present comment, a corrected version of Theorem 4.2 is given. The new formulation has
been extensively tested by comparison with the Zhang–Zhang polynomials computed by brute force using a new, completely automatized
computer code.
Content Type Journal Article
Category Letter to the Editor
Pages 1-3
DOI 10.1007/s10910-011-9969-2
Authors
Chien-Pin Chou, Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu City, 30010 Taiwan
Henryk A. Witek, Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu City, 30010 Taiwan
The theoretical model of the steady-state immobilized enzyme electrodes is discussed. This model is based on diffusion equation
containing a non-linear term related to Michaelis–Menten kinetics of the enzymatic reaction. Homotopy perturbation method
(HPM) is employed to solve the non-linear diffusion equation for the steady-state condition. Simple and approximate polynomial
expression of concentration and flux are derived for all small values of parameters
fp
(Theiele modulus) and β (kinetic parameter). Furthermore, in this work the numerical solution of the problem is also reported using SCILAB/MATLAB
program. The analytical results are compared with the numerical results and found to be in good agreement.
Content Type Journal Article
Category Original Paper
Pages 1-14
DOI 10.1007/s10910-011-9973-6
Authors
V. Margret PonRani, Department of Mathematics, The Madura College, Madurai, 625011 Tamilnadu, India
L. Rajendran, Department of Mathematics, The Madura College, Madurai, 625011 Tamilnadu, India
Garca Guirao and Lampart (J Math Chem 48:66–71, 2010; J Math Chem 48:159–164, 2010) said that for non-zero couplings constant, the lattice dynamical system is more complicated. Motivated by this, in this
paper, we prove that this coupled map lattice system is Li–Yorke chaotic for coupling constant
0 < e < 1
.
Content Type Journal Article
Category Original Paper
Pages 1-5
DOI 10.1007/s10910-011-9971-8
Authors
Xinxing Wu, School of Mathematics, University of Electronic Science and Technology of China, Chengdu, 611731 Sichuan, People’s Republic of China
Peiyong Zhu, School of Mathematics, University of Electronic Science and Technology of China, Chengdu, 611731 Sichuan, People’s Republic of China
Advancements in computing architecture and in theoretical techniques allow for the modeling of complex, extended systems.
This section of the 50th anniversary issue of Theoretical Chemistry Accounts highlights modeling work performed on nanostructured systems and underscores the enormous potential for synergy between theory
and experiment in modern nanoscience.
Content Type Journal Article
Category Regular Article
Pages 1-2
DOI 10.1007/s00214-011-1067-9
Authors
Gino A. DiLabio, National Institute for Nanotechnology, 11421 Saskatchewan Drive, Edmonton, AB T6G 2M9, Canada
We summarize explicitly correlated electronic structure theory in perspective of future work in the field. Earlier stages
of approaches with different Ansätze in physics and chemistry are described. We then discuss recent advances focusing on explicitly correlated wave functions
using cusp conditions. Removal of Coulomb singularities in terms of the rational generator is brought out from the viewpoint
of many-body perturbation theory. On the basis of decomposition schemes for many-electron integrals in R12 and F12 methods,
we further discuss the possibility of increasing the accuracy of molecular numerical integration and massively parallel calculations
of explicitly correlated methods.
Content Type Journal Article
Category Regular Article
Pages 1-11
DOI 10.1007/s00214-011-1070-1
Authors
Seiichiro Ten-no, Graduate School of System Informatics, Kobe University, Nada-ku, Kobe 657-8501, Japan
The refinement of protein crystal structures currently involves the use of empirical restraints and force fields that are
known to work well in many situations but nevertheless yield structural models with some features that are inconsistent with
detailed chemical analysis and therefore warrant further improvement. Ab initio electronic structure computational methods
have now advanced to the point at which they can deliver reliable results for macromolecules in realistic times using linear-scaling
algorithms. The replacement of empirical force fields with ab initio methods in a final refinement stage could allow new structural
features to be identified in complex structures, reduce errors and remove computational bias from structural models. In contrast
to empirical approaches, ab initio refinements can only be performed on models that obey basic qualitative chemical rules,
imposing constraints on the parameter space of existing refinements, and this in turn inhibits the inclusion of unlikely structural
features. Here, we focus on methods for determining an appropriate ensemble of initial structural models for an ab initio
X-ray refinement, modeling as an example the high-resolution single-crystal X-ray diffraction data reported for the structure
of lysozyme (PDB entry “2VB1”). The AMBER force field is used in a Monte Carlo calculation to determine an ensemble of 8 structures
that together embody all of the partial atomic occupancies noted in the original refinement, correlating these variations
into a set of feasible chemical structures while simultaneously retaining consistency with the X-ray diffraction data. Subsequent
analysis of these results strongly suggests that the occupancies in the empirically refined model are inconsistent with protein
energetic considerations, thus depicting the 2VB1 structure as a deep-lying minimum in its optimized parameter space that
actually embodies chemically unreasonable features. Indeed, density-functional theory calculations for one specific nitrate
ion with an occupancy of 62% indicate that water replaces this ion 38% of the time, a result confirmed by subsequent crystallographic
analysis. It is foreseeable that any subsequent ab initio refinement of the whole structure would need to locate a globally improved structure involving significant changes to 2VB1 which correct these identified local structural inconsistencies.
Content Type Journal Article
Category Regular Article
Pages 1-16
DOI 10.1007/s00214-011-1076-8
Authors
Olle Falklöf, School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia
Charles A. Collyer, School of Molecular Bioscience, The University of Sydney, Sydney, NSW 2006, Australia
Jeffrey R. Reimers, School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia
The purpose of this contribution is the description of the progress in theoretical investigations on electronically excited
states in connection with photodynamical simulations made within the last years and to provide an outlook on the scope of
future applications and challenges. An overview over excited-state phenomenology is given and the applicability of different
computational methods is discussed. Both electronic structure- and dynamics methods are considered. The examples presented
comprise the explanation of the photostability of individual DNA nucleobases, the photodynamics of DNA including excitonic
and charge-transfer processes, the primary processes of vision and the broad field of photovoltaics, photodevices, and molecular
machines.
Content Type Journal Article
Category Regular Article
Pages 1-14
DOI 10.1007/s00214-011-1073-y
Authors
Felix Plasser, Institute for Theoretical Chemistry, University of Vienna, Waehringerstrasse 17, 1090 Vienna, Austria
Mario Barbatti, Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
Adélia J. A. Aquino, Institute for Theoretical Chemistry, University of Vienna, Waehringerstrasse 17, 1090 Vienna, Austria
Hans Lischka, Institute for Theoretical Chemistry, University of Vienna, Waehringerstrasse 17, 1090 Vienna, Austria
The current state of the art in wavefunction-based electronic structure methods is illustrated via discussions of the most
important effects incorporated into a selection of high-accuracy methods chosen from the chemical literature. If one starts
with a high-quality correlation treatment, such as provided by the CCSD(T) coupled cluster method, the leading effects include
convergence of the results with respect to the 1-particle basis set, (outer)core/valence correlation, scalar relativistic
effects and a number of smaller effects. For thermochemical properties such as the heat of formation, the zero-point vibrational
energy also becomes important, introducing its own set of difficulties to the computational approach. Changes in the various
components as the chemical systems incorporate heavier elements and as the size of the systems grows are also considered.
Finally, challenges arising from the desire to extend existing methods to transition metal and heavier elements are considered.
Content Type Journal Article
Category Regular Article
Pages 1-20
DOI 10.1007/s00214-011-1079-5
Authors
Kirk A. Peterson, Department of Chemistry, Washington State University, Pullman, WA 99164-4630, USA
David Feller, Department of Chemistry, Washington State University, Pullman, WA 99164-4630, USA
David A. Dixon, Department of Chemistry, The University of Alabama, Shelby Hall, Box 870336, Tuscaloosa, AL 35487-0336, USA
We present a classical trajectory study of the dynamics of collisions between OH radicals and fluorinated self-assembled monolayers
(F-SAMs). The gas/surface interaction potential required in the simulations has been derived from high-level ab initio calculations
(focal-point-CCSD(T)/aug-cc-pVQZ) of various approaches of OH to a model fluorinated alkane. The two lowest-energy doublet
potential energy surfaces considered in the electronic structure calculations have been averaged to produce a pairwise analytic
potential. This analytic potential has been subsequently employed to propagate classical trajectories of collisions between
OH and F-SAMs at initial conditions relevant to recent experiments on related systems. The calculated rotational distributions
of the inelastically scattered OH agree well with the experiment, which serves to validate the accuracy of the simulations.
Investigation of the dynamics of energy transfer for different initial rotational states of OH indicates that an increase
in the initial rotation of OH results in increases in both the final average OH rotational and translational energy and in
a slight decrease in the amount of energy transferred to the surface. Analysis of the dynamics as a function of the desorption
angle of OH from the surface shows that while there is a correlation between the final scattering angle and OH’s amount of
final translational energy, the amount of rotational energy in OH is largely independent of the desorption angle. The mechanism
of the collisions is found to be mostly direct; in about 90% of most trajectories, OH only collides with the surface once
before desorbing, which exemplifies the rigidity of fluorinated monolayer surfaces and their inability to efficiently accommodate
gas species.
Content Type Journal Article
Category Regular Article
Pages 1-12
DOI 10.1007/s00214-011-1072-z
Authors
Diego Troya, Department of Chemistry, Virginia Tech, 107 Davidson Hall, Blacksburg, VA 24061-0212, USA
Full-dimensional time-dependent wave packet calculations were made to study the
OH+CO ® H+CO2
reaction on the Lakin–Troya–Schatz–Harding potential energy surface. Because of the presence of deep wells supporting long-lived
collision complex, one needs to propagate the wave packet up to 450,000 a.u. of time to fully converge the total reaction
probabilities. Our calculation revealed that the CO bond was substantially excited vibrationally in the complex wells, making
it necessary to include sufficient CO vibration basis functions to yield quantitatively accurate results for the reaction.
We calculated the total reaction probabilities from the ground initial state and two vibrationally excited states for the
total angular momentum J = 0. The total reaction probability for the ground initial state is quite small in magnitude with many narrow and overlapping
resonances due to the small complex-formation reaction probability and small probability for complex decaying into product
channel. Initial OH vibrational excitation considerably enhances the reactivity because it enhances the probability for complex
decaying into product channel, while initial CO excitation has little effects on the reactivity. We also calculated the reaction
probabilities for a number of J > 0 states by using the centrifugal sudden approximation. By doing some calculations with multiple K-blocks included, we found that the centrifugal sudden approximation can be employed to calculate the rate constant for the
reaction rather accurately. The calculated rate constants only agree with experimental measurements qualitatively, suggesting
more theoretical studies be carried out for this prototypical complex-formation four-atom reaction.
Content Type Journal Article
Category Regular Article
Pages 1-7
DOI 10.1007/s00214-011-1068-8
Authors
Shu Liu, State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023 People’s Republic of China
Xin Xu, State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023 People’s Republic of China
Dong H. Zhang, State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computational Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, 116023 People’s Republic of China
The aim of electronic structure theory is to solve the electronic Schrödinger equation, which is a coupled high-dimensional
partial differential equation with numerous singularities in the operator and complex boundary conditions arising from the
fermion symmetry. This article briefly summarizes how electronic structure theorists have overcome the immense difficulties
of solving this with quantitative accuracy. This has been achieved by elucidating the structure of wave functions and exploiting
this knowledge to drastically expedite the numerical solutions, enabling predictive simulations for a broad range of chemical
properties and transformations. It also lists some of the outstanding challenges that are to be or being addressed.
Content Type Journal Article
Category Regular Article
Pages 1-4
DOI 10.1007/s00214-011-1071-0
Authors
So Hirata, Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, IL 61801, USA
The role of the negative energy states in relativistic quantum chemistry is shortly discussed. They must be included in a
sum over states formula that arises for second-order properties. Relativistic calculations for the electric dipole polarizability
and the diamagnetic susceptibility (with on-center and displaced gauge origins) for hydrogen-like ions are presented to illustrate
the problem. Relativistic electron correlation calculations mostly use a configuration space Dirac-Coulomb operator together
with the no-pair approximation, which excludes the negative energy states from the correlation treatment. Despite all efforts,
no consistent theoretical description between this and a full QED treatment seems to exist.
Content Type Journal Article
Category Regular Article
Pages 1-6
DOI 10.1007/s00214-011-1082-x
Authors
Christoph van Wüllen, Fachbereich Chemie and Forschungszentrum OPTIMAS, Technische Universität Kaiserslautern, Erwin-Schrödinger-Straße, 67663 Kaiserslautern, Germany
Reaction dynamics is a central topic in physical chemistry, and tremendous progress has been made in theoretical characterization
of gas phase and surface scattering processes. Here, an overview is given on several important frontiers represented by the
following articles.
Content Type Journal Article
Category Regular Article
Pages 1-3
DOI 10.1007/s00214-011-1077-7
Authors
Hua Guo, Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, NM 87131, USA
A new approach for propagating time-dependent quantum wave packets is presented based on the direct numerical solution of
the quantum hydrodynamic equations of motion associated with the de Broglie–Bohm formulation of quantum mechanics. A generalized
iterative finite difference method (IFDM) is used to solve the resulting set of non-linear coupled equations. The IFDM is
2nd-order accurate in both space and time and exhibits exponential convergence with respect to the iteration count. The stability
and computational efficiency of the IFDM is significantly improved by using a “smart” Eulerian grid which has the same computational
advantages as a Lagrangian or Arbitrary Lagrangian Eulerian (ALE) grid. The IFDM is generalized to treat higher-dimensional
problems and anharmonic potentials. The method is applied to a one-dimensional Gaussian wave packet scattering from an Eckart
barrier, a one-dimensional Morse oscillator, and a two-dimensional (2D) model collinear reaction using an anharmonic potential
energy surface. The 2D scattering results represent the first successful application of an accurate direct numerical solution
of the quantum hydrodynamic equations to an anharmonic potential energy surface.
Content Type Journal Article
Category Regular Article
Pages 1-19
DOI 10.1007/s00214-011-1075-9
Authors
Brian K. Kendrick, Theoretical Division (T-1, MS-B268), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
Optical response in silver/polyvinylidene fluoride nanocomposite materials with nonspherical inclusions was examined using
direct dipolar interband transitions, from density functional theory. We discuss here the dependence of the optical response
of the material on the geometry, crystallographic makeup and end-cap morphology of the metallic inclusions, as well as on
their orientation relative to the polarization direction of the applied electromagnetic field. Each periodic unit cell contained
a single inclusion and a polymer matrix; thus, the composite behaved as a monodisperse, perfectly oriented material. Overall,
the spectral location of the composite excitation spectrum was tied to that of the metallic inclusions and correlated well
to quantum confinement models for the direction of polarization: As linear size of the inclusion increased in a given direction,
the excitation spectrum of light polarized in that direction was red-shifted. The effect of the polymer matrix was also examined.
Coulomb repulsion from matrix energy states led to splitting of nanoparticle-based energy levels, and the matrix conduction
band became involved in high-energy transitions. These effects led to extensions of the spectra of nanocomposites with less
stable {100}–basal plane inclusions to very low excitation energies. Attenuation or redshifting of nanoparticle peaks with
high photon energies was also observed for materials with small linear sizes along the excitation direction. Comparisons with
experimental and time-dependent density functional theory results suggest that estimating the complex dielectric constant
from interband transition dipole moments, in a time-independent fashion, provides reliable qualitative spectra for these systems.
Content Type Journal Article
Category Regular Article
Pages 1-11
DOI 10.1007/s00214-011-1078-6
Authors
Christopher K. Rowan, Department of Chemistry, University of Victoria, PO Box 3065, Victoria, BC V8W 3V6, Canada
Irina Paci, Department of Chemistry, University of Victoria, PO Box 3065, Victoria, BC V8W 3V6, Canada
A historical perspective is given contrasting challenges and advances in theoretical chemistry at the time the first issue
of Theoretical Chemistry Accounts appeared in 1962 and the progress achieved since then as expressed in current state-of-the-art
applications in photochemistry and thermochemistry.
Content Type Journal Article
Category Regular Article
Pages 1-3
DOI 10.1007/s00214-011-1086-6
Authors
Fernando R. Ornellas, Departamento de Química Fundamental, Instituto de Química, Universidade de São Paulo, Av. Lineu Prestes, 748, São Paulo, São Paulo 05508-000, Brazil
The imaginary-time quantum dynamics is implemented in Cartesian coordinates using the momentum-dependent quantum potential
approach. A nodeless wavefunction, represented in terms of quantum trajectories, is evolved in imaginary time according to
the quantum-mechanical Boltzmann operator in the Eulerian frame-of-reference. The quantum potential and its gradient are determined
approximately, from the global low-order (quadratic) polynomial fit to the trajectory momenta, which makes the approach practical
in high dimensions. Implementation in the Cartesian coordinates allows one to work with the Hamiltonian of the simplest form,
to setup calculations in the molecular dynamics-compatible framework and to naturally mix quantum and classical description
of particles. Localization of wavefunctions in the center-of-mass degrees of freedom and in the overall rotation, which makes
the quadratic polynomial fitting in Cartesian coordinates accurate, is accomplished by the addition of a quadratic constraining
potential, and its contribution to the zero-point energy is analytically subtracted. For illustration, the zero-point energies
are computed for model clusters consisting of up to 11 atoms (33 dimensions).
Content Type Journal Article
Category Regular Article
Pages 1-10
DOI 10.1007/s00214-011-1083-9
Authors
Sophya Garashchuk, Department of Chemistry and Biochemistry, University of South Carolina, Columbia, SC 29208, USA
Nuclear magnetic shielding and spin–spin coupling constants are intrinsically all-electron relativistic properties and demand
in principle fully relativistic treatments. Here, the magnetic balance (MB) condition plays an essential role, both conceptually
and computationally. The various formulations can be unified in terms of the idea of "orbital decomposition." Further combined
with the ansatz of "gauge-including atomic orbitals" (GIAO) for distributed gauge origins leads to very efficient four-component
relativistic methods at both the mean-field and correlated levels. To illustrate the latter, the no-pair MB-GIAO-MP2 expressions
for nuclear shieldings are derived in two different ways, one with the derivative technique and the other through the induced
current. Due to the non-variational nature of MP2, the two expressions are not identical. The current-dependent expression
is much simpler and appears more natural in view of the experimental measurement.
Content Type Journal Article
Category Regular Article
Pages 1-17
DOI 10.1007/s00214-011-1080-z
Authors
Yunlong Xiao, Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing, 100871 People’s Republic of China
Qiming Sun, Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing, 100871 People’s Republic of China
Wenjian Liu, Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing, 100871 People’s Republic of China
Mass action type deterministic kinetic models of ion channels are usually constructed in such a way as to obey the principle
of detailed balance (or, microscopic reversibility) for two reasons: first, the authors aspire to have models harmonizing
with thermodynamics, second, the conditions to ensure detailed balance reduce the number of reaction rate coefficients to
be measured. We investigate a series of ion channel models which are asserted to obey detailed balance, however, these models
violate mass conservation and in their case only the necessary conditions (the so-called circuit conditions) are taken into
account. We show that ion channel models have a very specific structure which makes the consequences true in spite of the
imprecise arguments. First, we transform the models into mass conserving ones, second, we show that the full set of conditions
ensuring detailed balance (formulated by Feinberg) leads to the same relations for the reaction rate constants in these special
cases, both for the original models and the transformed ones.
Content Type Journal Article
Category Original Paper
Pages 1-21
DOI 10.1007/s10910-011-9961-x
Authors
Ilona Nagy, Department of Mathematical Analysis, Budapest University of Technology and Economics, Egry J. u. 1, Budapest, 1111 Hungary
János Tóth, Department of Mathematical Analysis, Budapest University of Technology and Economics, Egry J. u. 1, Budapest, 1111 Hungary
For the realization of molecular electronics, one essential goal is the ability to systematically fabricate molecular functional
components in a well-controlled manner. Experimental techniques have been developed such that π-stacked ethylbenzene molecules
can now be routinely induced to self-assemble on an H-terminated Si(100) surface at precise locations and along precise directions.
Electron transport calculations predict that such molecular wires could indeed carry an electrical current, but the Si substrate
may play a considerable role as a competing pathway for conducting electrons. In this work, we investigate the effect of placing
substituent groups of varying electron donating or withdrawing strengths on the ethylbenzene molecules to determine how they
would affect the transport properties of such molecular wires. The systems consist of a line of π-stacked ethylbenzene molecules
covalently bonded to a Si substrate. The ethylbenzene line is bridging two Al electrodes to model current through the molecular
stack. For our transport calculations, we employ a first-principles technique where density functional theory (DFT) is used
within the non-equilibrium Green’s function formalism (NEGF). The calculated density of states suggest that substituent groups
are an effective way to shift molecular states relative to the electronic states associated with the Si substrate. The electron
transmission spectra obtained from the NEGF–DFT calculations reveal that the transport properties could also be extensively
modulated by changing substituent groups. For certain molecules, it is possible to have a transmission peak at the Fermi level
of the electrodes, corresponding to high conduction through the molecular wire with essentially no leakage into the Si substrate.
Content Type Journal Article
Category Regular Article
Pages 1-8
DOI 10.1007/s00214-011-1085-7
Authors
Manuel Smeu, Department of Physics, Center for the Physics of Materials, McGill University, Montreal, QC, Canada
Robert A. Wolkow, National Institute for Nanotechnology, National Research Council of Canada, Edmonton, AB, Canada
Hong Guo, Department of Physics, Center for the Physics of Materials, McGill University, Montreal, QC, Canada
It is generally acknowledged that the inclusion of relativistic effects is crucial for the theoretical description of heavy-element-containing
molecules. Four-component Dirac-operator-based methods serve as the relativistic reference for molecules and highly accurate
results can be obtained—provided that a suitable approximation for the electronic wave function is employed. However, four-component
methods applied in a straightforward manner suffer from high computational cost and the presence of pathologic negative-energy
solutions. To remove these drawbacks, a relativistic electron-only theory is desirable for which the relativistic Fock operator
needs to be exactly decoupled. Recent developments in the field of relativistic two-component methods demonstrated that exact
decoupling can be achieved following different strategies. The theoretical formalism of these exact-decoupling approaches
is reviewed in this paper followed by a comparison of efficiency and results.
Content Type Journal Article
Category Regular Article
Pages 1-20
DOI 10.1007/s00214-011-1081-y
Authors
Daoling Peng, Laboratorium für Physikalische Chemie, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland
Markus Reiher, Laboratorium für Physikalische Chemie, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zurich, Switzerland
Most nanodevices under investigation adopt a computational approach such as molecular dynamics simulations, which gives a
numerical value for the potential energy as calculated from the interaction of every atom on one molecule with every atom
on a second molecule. Although the simulation only involves short range atom–atom interactions and ignores those interactions
at longer distances, the simulation still involves significant computational time. In this paper, we determine analytical
formulae for four types of Lennard–Jones interactions: (i) a solid spherical nanoparticle with an atom, (ii) two distinct
radii hollow spherical fullerenes, (iii) a solid spherical nanoparticle with a hollow spherical fullerene and (iv) two distinct
radii solid spherical nanoparticles. The interaction energy using the 6–12 Lennard–Jones potential for these four situations
are determined using the continuum approximation, which assumes that a discrete atomic structure can be replaced by either
an average atomic surface density or an average atomic volume density. Using these formulae the computational time for a simulation
might be dramatically reduced for those molecular interactions involving spherical nanoparticles or fullerenes. Such formulae
might be exploited in hybrid analytical-computational numerical schemes, as well as in metallofullerenes and certain assumed
spherical models of molecules such as methane and ammonia. As an illustration of the formulae presented here we determine
both the most stable and the maximum radii of a solid spherical nanoparticle inside a fullerene, modelling the centre of a
carbon onion or metallofullerenes. We also determine new cut-off formulae for interacting spherical nanoparticles and fullerenes
which might be useful in computational schemes.
Content Type Journal Article
Category Original Paper
Pages 1-15
DOI 10.1007/s10910-011-9970-9
Authors
Richard K. F. Lee, Nanomechanics Group, School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
James M. Hill, Nanomechanics Group, School of Mathematical Sciences, The University of Adelaide, Adelaide, SA 5005, Australia
The analytical solutions of the non-steady-state concentrations of species at a planar microelectrode are discussed. The analytical
expression of the kinetics of CE mechanism under first or pseudo-first order conditions with equal diffusion coefficients
at planar electrode under non-steady-state conditions are obtained by using Homotopy perturbation method. These simple new
approximate expressions are valid for all values of time and possible values of rate constants. Analytical equations are given
to describe the current when the homogeneous equilibrium position lies heavily in favour of the electroinactive species. Working
surfaces are presented for the variation of limiting current with a homogeneous kinetic parameter and equilibrium constant.
In this work we employ the Homotopy perturbation method to solve the boundary value problem. Furthermore, in this work the
numerical simulation of the problem is also reported using Scilab program. The analytical results are found to be in excellent
agreement with the numerical results.
Content Type Journal Article
Category Original Paper
Pages 1-12
DOI 10.1007/s10910-011-9968-3
Authors
K. Indira, Department of Mathematics, The Madura College, Madurai, 625011 India
L. Rajendran, Department of Mathematics, The Madura College, Madurai, 625011 India
In this project we evaluate second virial coefficient of some inert gases via classical cluster expansion, assuming each atomic
pair interaction is of Lennard-Jones type. We also try to numerically evaluate the third virial coefficient of Argon gas based
on bipolar-coordinate integration (Mas et al. in J Chem Phys 10:6694, 1999), assuming the same Lennard-Jones potential as before. The second virial coefficient (Vega et al. in Phys Chem Chem Phys
4:3000–3007, 2002) calculated from our model are compatible to the experimental data [19] The temperature at which B2(T) → 0 is called the Boyle’s temperature TB (Vega et al. in Phys Chem Chem Phys 4:3000–3007, 2002) for the Lennard-Jines (12-6) potential. For the second virial coefficient of He, we obtain the Boyle’s temperature as follow:
TB = 34.9312438964844 (K) B2(T) = 9.82958 × 10−6 (cm3/mol).
Content Type Journal Article
Category Original Paper
Pages 1-15
DOI 10.1007/s10910-011-9966-5
Authors
Artit Hutem, Forum for Theoretical and Computational Physics, Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900 Thailand
Sutee Boonchui, Forum for Theoretical and Computational Physics, Department of Physics, Faculty of Science, Kasetsart University, Bangkok, 10900 Thailand
In this paper we study the connection between: (i) closed Newton-Cotes formulae of high order, (ii) trigonometrically-fitted
and exponentially-fitted differential methods, (iii) symplectic integrators. Several one step symplectic integrators have
been produced based on symplectic geometry during the last decades (see the relevant literature and the references here).
However, the study of multistep symplectic integrators is very poor. In this paper we investigate the High Order Closed Newton-Cotes
Formulae and we write them as symplectic multilayer structures. We develop trigonometrically-fitted and exponentially-fitted
symplectic methods which are based on the closed Newton-Cotes formulae. We apply the symplectic schemes in order to solve
the resonance problem of the radial Schrödinger equation. Based on the theoretical and numerical results, conclusions on the
efficiency of the new obtained methods are given.
Content Type Journal Article
Category Original Paper
Pages 1-38
DOI 10.1007/s10910-011-9965-6
Authors
T. E. Simos, Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451 Saudi Arabia
Molecules arranging themselves into predictable patterns on silicon chips could lead to microprocessors with much smaller
circuit elements. Mathematically, assembling in predictable patterns is equivalent to packing in graphs. An H-packing of a graph G is a set of vertex disjoint subgraphs of G, each of which is isomorphic to a fixed graph H. If H is the complete graph K2, the maximum H-packing problem becomes the familiar maximum matching problem. In this paper we give algorithms to find a perfect packing
of HC(n) with P6 and K1,3 when n is even and thus determines their packing numbers. Further we also study the packing of HC(n) with 1, 3-dimethyl cyclohexane.
Content Type Journal Article
Category Original Paper
Pages 1-10
DOI 10.1007/s10910-011-9962-9
Authors
Indra Rajasingh, Department of Mathematics, Loyola College, Chennai, 600 034 India
Albert Muthumalai, Department of Mathematics, Loyola College, Chennai, 600 034 India
R. Bharati, Department of Mathematics, Loyola College, Chennai, 600 034 India
A. S. Shanthi, Department of Mathematics, Loyola College, Chennai, 600 034 India
Shifting the origin of a known quantum object set (QOS) or of some discrete molecular point cloud (MPC) by choosing the centroid
of such sets, leads to the way to produce quantum similarity matrices (SM) and tensors, which can be systematically referred to a canonical origin, whatever their nature, dimension or cardinality. In this paper the source, significance and properties of such centroid
origin shift and the characteristics of the resultant shifted SM are discussed in deep. From such an analysis some interesting
applications emerge; as, for instance, a new collection of MPC ordering possibilities. In addition, although all the procedures
in this work are described by means of a quantum similarity theoretical background, based on QOS structure within the space
of molecules, everything can be also easily implemented in a classical QSPR framework made of molecular numerical images attached
to discrete molecular vectors, constructed with well-defined descriptor parameters.
Content Type Journal Article
Category Original Paper
Pages 1-18
DOI 10.1007/s10910-011-9960-y
Authors
Ramon Carbó-Dorca, Institute of Computational Chemistry, University of Girona, Girona, 17071 Catalonia, Spain
Emili Besalú, Institute of Computational Chemistry, University of Girona, Girona, 17071 Catalonia, Spain
It is well known that oscillations in models of biochemical reaction networks can arise as a result of a single negative cycle.
On the other hand, methods for finding general network conditions for potential oscillations in large biochemical reaction
networks containing many cycles are not well developed. A biochemical reaction network with any number of species is represented
by a simple digraph and is modeled by an ordinary differential equation (ODE) system with non-mass action kinetics. The obtained
graph-theoretic condition generalizes the negative cycle condition for oscillations in ODE models to the existence of a pair
of subnetworks, where each subnetwork contains an even number of positive cycles. The technique is illustrated with a model
of genetic regulation.
Content Type Journal Article
Category Original Paper
Pages 1-15
DOI 10.1007/s10910-011-9955-8
Authors
Maya Mincheva, Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA
A power-series potential energy function that is analogous to that of the Molski potential is proposed herein such that reductions
to the Dunham and Simons-Parr-Finlan (SPF) potential functions are obtained by prescribing numerical values of 0 and 1 respectively
to a type parameter. The type parameter takes the form of an index instead of a multiplier in the case of the Molski potential.
Verification of the proposed potential function was performed by comparing it alongside the Dunham, SPF and Ogilvie potentials
in being fitted to the RKR results of CO diatomic molecule. The proposed potential with the selection of central value to
its type parameter is a geometric mean analogy to the Ogilvie potential’s arithmetic mean of the Dunham and SPF potential
functions. Although prescription of any numerical value to the type parameter allows good curve fit within the range of RKR
data, the extent of convergence is influenced by the choice of type parameter. Having shown the validity of the proposed potential,
further studies is proposed in order to establish the comparative advantages of this potential with other power-series potential
energy function.
Content Type Journal Article
Category Original Paper
Pages 1-9
DOI 10.1007/s10910-011-9952-y
Authors
Teik-Cheng Lim, School of Science and Technology, SIM University, 461 Clementi Road, Singapore, 599491 Singapore
Spherical harmonics in an arbitrary dimension are employed widely in quantum theory. Spherical harmonics are also called hyperspherical
harmonics when the dimension is larger than 3. In this paper, we derive some integral identities involving spherical harmonics
in an arbitrary dimension.
Content Type Journal Article
Category Original Paper
Pages 1-10
DOI 10.1007/s10910-011-9956-7
Authors
Weimin Han, Department of Mathematics and Program in Applied Mathematical and Computational Sciences, University of Iowa, Iowa City, IA 52242, USA
Kendall Atkinson, Department of Computer Science and Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA
Hao Zheng, Department of Chemistry, Zhejiang University, Hangzhou, 310027 China
In this paper we expand the equations governing Michaelis–Menten kinetics in a total quasi-steady state setting, finding the
first order uniform expansions. Our results improve previous approximations and work well especially in presence of an enzyme
excess.
Content Type Journal Article
Category Original Paper
Pages 1-13
DOI 10.1007/s10910-011-9957-6
Authors
Guido Dell’Acqua, Dipartimento di Scienze di Base e Applicate per l’Ingegneria (S.B.A.I.), “Sapienza” University, Via A. Scarpa 16, 00161 Rome, Italy
Alberto Maria Bersani, Dipartimento di Scienze di Base e Applicate per l’Ingegneria (S.B.A.I.), “Sapienza” University, Via A. Scarpa 16, 00161 Rome, Italy
Factorization formulas are used to derive a uniform semiclassical approximation of transition probabilities. The latter are
determined in the analytical form where the basis transition probabilities are set by the analytical formula. As an example,
we consider the rigid rotor, harmonic oscillator, and Morse oscillator in collisions with structureless particles.
Content Type Journal Article
Category Original Paper
Pages 1-12
DOI 10.1007/s10910-011-9958-5
Authors
M. L. Strekalov, Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, Theoretical Chemistry Laboratory, 3 Institutskaya Street, 630090 Novosibirsk, Russia
We report on a comparison of the diffraction pattern observed for nanocrystalline n-diamond and i-carbon forms by other investigative
teams, with the calculated diffraction pattern of glitter based upon lattice parameters optimized using the DFT-CASTEP method.
The close fit of the latter dataset to that observed for n-diamond and i-carbon, as reported herein, suggests that indeed
i-carbon may be of the same structure as n-diamond, and that they both may have the tetragonal glitter structure.
Content Type Journal Article
Category Brief Communication
Pages 1-5
DOI 10.1007/s10910-011-9954-9
Authors
Michael J. Bucknum, Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Buenos Aires, Republic of Argentina
Eduardo A. Castro, Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Buenos Aires, Republic of Argentina
In this work, firstly in the Hilbert space of vector-functions all selfadjoint extensions of the minimal operator generated
by linear singular symmetric differential expression with a selfadjoint operator coefficient A in any Hilbert space H, are described in terms of boundary values. Later structure of the spectrum of these extensions is investigated.
Content Type Journal Article
Category Original Paper
Pages 1-11
DOI 10.1007/s10910-011-9953-x
Authors
Elgiz Bairamov, Department of Mathematics, Faculty of Sciences, Ankara University, 06100 Ankara, Turkey
Rukiye Özturk Mert, Department of Mathematics, Faculty of Sciences, Karadeniz Technical University, 61080 Trabzon, Turkey
Zameddin Ismailov, Department of Mathematics, Faculty of Sciences, Karadeniz Technical University, 61080 Trabzon, Turkey
Collisional energy transfer between highly vibrationally excited molecules and a bath gas is considered as a stochastic process
occurring in energy space. An exact solution to master equation for the conditional probability is given in terms of simple
analytical formulas for weak and strong collisions. The strong collisions are shown to manifest themselves in the distribution
pattern composed of maxima and minima in the energy dependence of conditional probability. This effect is explained in detail
on physical grounds.
Content Type Journal Article
Category Letter to the Editor
Pages 1-10
DOI 10.1007/s10910-011-9951-z
Authors
M. L. Strekalov, Theoretical Chemistry Laboratory, Institute of Chemical Kinetics and Combustion, Siberian Branch of the Russian Academy of Sciences, 3 Institutskaya Street, 630090 Novosibirsk, Russia
We show that the traditional concept of the uniform electron gas (UEG)—a homogeneous system of finite density, consisting
of an infinite number of electrons in an infinite volume—is inadequate to model the UEGs that arise in finite systems. We
argue that, in general, a UEG is characterized by at least two parameters, viz. the usual one-electron density parameter ρ
and a new two-electron parameter η. We outline a systematic strategy to determine a new density functional E (ρ, η) across the spectrum of possible ρ and η values.
Content Type Journal Article
Category Regular Article
Pages 1-9
DOI 10.1007/s00214-011-1069-7
Authors
Peter M. W. Gill, Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia
Pierre-François Loos, Research School of Chemistry, Australian National University, Canberra, ACT 0200, Australia
The momentum entropic moments and Rényi entropies of a one-dimensional particle in an infinite well potential are found by
means of explicit calculations of some Dirichlet-like trigonometric integrals. The associated spreading lengths and quantum
uncertainty-like sums are also provided.
Content Type Journal Article
Category Original Paper
Pages 1-12
DOI 10.1007/s10910-011-9950-0
Authors
A. I. Aptekarev, Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow State University, Moscow, Russia
J. S. Dehesa, Institute “Carlos I” for Computational and Theoretical Physics, University of Granada, Granada, Spain
P. Sánchez-Moreno, Institute “Carlos I” for Computational and Theoretical Physics, University of Granada, Granada, Spain
D. N. Tulyakov, Keldysh Institute for Applied Mathematics, Russian Academy of Sciences, Moscow State University, Moscow, Russia
Complete analytical resolution of the network of chemical reactions involving the flavylium compounds was achieved by means
of the Laplace transform, general partial fraction theorem and Vieta’s formulae. The kinetic model includes basic and acid
catalysis of the hydration and tautomerization reactions. The formation of phenyl-2H-chromen-4-ol (B4) and the role it plays in the kinetics in the case of compounds lacking of the hydroxyl substituents was also accounted for.
In all cases four kinetic steps could be individualized and the pH dependent mole fraction distribution of the several species
monitored as a function of time, the last one leading to the equilibrium. It is worth of note the role of B4 in the network, which like the quinoidal base is a kinetic product that retards the formation of Ct. The evolution of B4 is also dependent on the existence or not of the cis-trans isomerisation barrier. Application of the model to the data of flavylium networks previously reported in literature, predicts
with great accuracy the respective behavior.
Content Type Journal Article
Category Original Paper
Pages 1-17
DOI 10.1007/s10910-011-9948-7
Authors
Vesselin Petrov, Departamento de Química, REQUIMTE, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Lisbon, Portugal
Fernando Pina, Departamento de Química, REQUIMTE, Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Lisbon, Portugal
A comprehensive mathematical model for styrene stereoregular polymerization was carried out. This model was generated by coupling
the single particle growth model (SPGM) with kinetics model, to predict the effect of intraparticle mass transfer resistance
and initial catalyst size on the polymerization kinetics. SPGM was derived based on a modified multigrain model (MMGM) to
calculate the spatial-time evolution of styrene concentration under intraparticle mass transfer limitations. Then, the SPGM
was solved simultaneously with kinetics model to estimate the polymerization rate and molecular weight distribution (MWD)
under the above mentioned limitations. The results show that a significant radial distribution of styrene concentration across
polymer growing. Moreover, the diffusion resistance was most intense at the early step of the polymerization and the effects
of the polymerization rate are more strongly. Additionally, it is appear that increasing the initial catalyst size leads to
a decrease in the rate of polymerization. For MWD, the model simulation show that the diffusion resistance led to have an
increase in the molecular weight within a period of time similar to the one needed in the catalyst decay. The validation of
the model with experimental data given a agreement results and shows that the model is able to predict monomer profile, polymerization
rate, and MWD of syndiotactic polystyrene.
Content Type Journal Article
Category Original Paper
Pages 1-19
DOI 10.1007/s10910-011-9949-6
Authors
S. R. Sultan, School of Chemical Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia
W. J. N. Fernando, School of Chemical Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia
Suhairi A. Sata, School of Chemical Engineering, Universiti Sains Malaysia, 14300 Nibong Tebal, Penang, Malaysia
A simple model for describing the non-quasi-equivalent icosahedral virus capsid composed of 72 pentameric capsomeres is developed.
By means of six-step operations, a new 4-gons polyhedron P is obtained which contains 72 pentagons, 80 trigons and 210 quadrilaterals. More importantly, it bears icosahedral symmetry.
The rationality of the existence of the 4-gons polyhedron P is further discussed. The results show that this model can be used to represent the capsids of papovaviruses.
Content Type Journal Article
Category Original Paper
Pages 1-7
DOI 10.1007/s10910-011-9947-8
Authors
Dan Lu, Department of Chemistry, State Key Laboratory of Applied Organic Chemistry, Lanzhou University, Lanzhou, 730000 People’s Republic of China
Pan-Pan Zhou, Department of Chemistry, State Key Laboratory of Applied Organic Chemistry, Lanzhou University, Lanzhou, 730000 People’s Republic of China
Wen-Yuan Qiu, Department of Chemistry, State Key Laboratory of Applied Organic Chemistry, Lanzhou University, Lanzhou, 730000 People’s Republic of China
The global behavior of solutions is described for the smallest chemical reaction system that exhibits a Hopf bifurcation,
discovered in [12]. This three-dimensional system is a competitive system and a monotone cyclic feedback system. The Poincaré–Bendixson theory
extends to such systems [2,3,6,8] and a Bendixson criterion exists to rule out periodic orbits [4].
Content Type Journal Article
Category Original Paper
Pages 1-7
DOI 10.1007/s10910-011-9946-9
Authors
Hal L. Smith, School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA
General properties of the electrostatic molecular potential (EMP) when obtained by means of the atomic shell approximation
(ASA) density function (DF) are discussed. In the present study it is proved that in general and without exceptions promolecular
ASA DF provide EMP which are everywhere repulsive. The polarized ASA DF version, providing an alternative enhanced kind of
EMP, behaves in such a way that in the neighborhood of negative charged atoms, attractive regions appear resembling the ab
initio results.
Content Type Journal Article
Category Original Paper
Pages 1-8
DOI 10.1007/s10910-011-9945-x
Authors
Ramon Carbó-Dorca, Institut de Química Computacional, Universitat de Girona, 17071 Catalonia, Girona, Spain
Emili Besalú, Institut de Química Computacional, Universitat de Girona, 17071 Catalonia, Girona, Spain
Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schrödinger equation are studied for
the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are obtained and
seen that they are the same with the ones obtained before. The energy eigenvalues of the inverse square plus square potential
and three-dimensional harmonic oscillator are given as special cases. It is shown the variation of the first six normalized
wavefunctions of the above potentials. It is also given numerical results for the bound states of two diatomic molecular potentials,
and compared the results with the ones obtained in literature.
Content Type Journal Article
Category Original Paper
Pages 1-10
DOI 10.1007/s10910-011-9944-y
Authors
Altuğ Arda, Department of Physics Education, Hacettepe University, 06800 Ankara, Turkey
Ramazan Sever, Department of Physics, Middle East Technical University, 06531 Ankara, Turkey
The fragment shape variation index approach is applied to intramolecular interactions involving C6 aromatic molecular fragments
in the special case where the shape-modifying interactions are also caused primarily by other C6 aromatic fragments of the
same molecule. This report is a part of a series of studies aimed at the detailed modeling of various components of intramolecular
interactions among molecular fragments, including aromatic ring interactions, aromatic ring and non-aromatic conjugated and
non-conjugated system interactions, and more general through-space and through-bond interactions. The ultimate purpose of
these studies is a better understanding of the electron density shape modifying effects of intramolecular interactions.
Content Type Journal Article
Category Original Paper
Pages 1-7
DOI 10.1007/s10910-011-9940-2
Authors
Zoltan Antal, Scientific Modeling and Simulation Laboratory (SMSL), Department of Chemistry, Memorial University of Newfoundland, 283 Prince Philip Drive, St. John’s, NL A1B 3X7, Canada
Paul G. Mezey, Scientific Modeling and Simulation Laboratory (SMSL), Department of Chemistry and Department of Physics and Physical Oceanography, Memorial University of Newfoundland, 283 Prince Philip Drive, St. John’s, NL A1B 3X7, Canada
A quantum description adapted to scrutinize chemical reaction mechanisms obtains by implementing an electronuclear separation
via quantum numbers method; truly diabatic base states obtain that sustain quantum states expressed as linear superpositions.
A proto-type bond breaking/formation case:
H2+Û H(1s)+H+
test possibilities via mathematical modeling. Asymptotic states
(|HñÄ|H+ñ
and
(|H+ñÄ|Hñ)
and basis states for quantized electromagnetic radiation complete the model; Feshbach-resonance-like quantum states obtain
that play pivotal roles gating association/dissociation processes. A fixed grid of floating Gaussian orbitals permits actual
computations compatible with this method. The information therefrom gleaned is used to construct model Hamiltonians easily
adaptable to second quantization formalisms. Theoretical developments and non-routine computations results can directly be
related to experiment.
Content Type Journal Article
Category Original Paper
Pages 1-22
DOI 10.1007/s10910-011-9942-0
Authors
Gustavo A. Arteca, Département de Chimie et Biochimie & Biomolecular Sciences Programme, Laurentian University, Ramsey Lake Road, Sudbury, ON P3E 2C6, Canada
Josep M. Aulló, Departament de Química Física, Universitat de València, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain
O. Tapia, Department of Physical and Analytical Chemistry, Uppsala University, Box 259, 751 05 Uppsala, Sweden
The ground-state wave function Ψ for a given force constant k = 1/4 a.u. of the two-electron Hookean atom is known in exact analytical form. Here the corresponding first-order density
matrix γ(r, r′) is studied, particular attention being focussed on its equation of motion. The exact form which results from the known
Ψ is displayed, and given a physical interpretation. Harmonic confined model two-electron atoms with arbitrary interaction
u(r12) are also briefly referred to in the present context.
Content Type Journal Article
Category Original Paper
Pages 1-6
DOI 10.1007/s10910-011-9934-0
Authors
N. H. March, Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
G. G. N. Angilella, Dipartimento di Fisica e Astronomia, Università di Catania, Via S. Sofia, 64, 95123 Catania, Italy
R. Pucci, Dipartimento di Fisica e Astronomia, Università di Catania, Via S. Sofia, 64, 95123 Catania, Italy
In our recent paper, the electron spin torque is found to be counter-balanced by the chiral electron density. In this paper,
we shall show that the origin of the chiral nature is manifest in the principle of equivalence in general relativity.
Content Type Journal Article
Category Brief Communication
Pages 1-20
DOI 10.1007/s10910-011-9943-z
Authors
Akitomo Tachibana, Department of Micro Engineering, Kyoto University, Kyoto, 606-8501 Japan
A special adaptation of the fragment shape variation index approach is applied to a series of rod-like structures obtained
by replacing all C–C atom pairs by B–N atom pairs in linear polymers constructed by stacking adamantane units on top of each
other. A special feature of these structures is a systematic, monotonic increase of the length of B–N bonds roughly parallel
with the axis of the rods when moving from the B-terminus towards the N-terminus of the rods. All other changes in the unit
cells of these short polymers are less important and less systematic, consequently, focusing on these B–N bonds of the given
structures is especially suitable for the application of the fragment shape variation index approach used for a single type
of internal coordinate shape descriptor. The results reveal additional trends which are easy to miss if one is restricted
to a simple inspection of the data. The study also confirms that in special cases one may replace the detailed electron density
shape descriptors with the far simpler bond length data as formal, but limited shape descriptors, whenever the overall structures
and shapes show only minor changes, affecting primarily only one type of the internal coordinates.
Content Type Journal Article
Category Original Paper
Pages 1-8
DOI 10.1007/s10910-011-9939-8
Authors
Eva Simon, Department of Chemistry, Scientific Modeling and Simulation Laboratory (SMSL), Memorial University of Newfoundland, 283 Prince Philip Drive, St. John’s, NL A1B 3X7, Canada
Paul G. Mezey, Department of Chemistry, Scientific Modeling and Simulation Laboratory (SMSL), Memorial University of Newfoundland, 283 Prince Philip Drive, St. John’s, NL A1B 3X7, Canada
For a specific functional group, considered as a molecular fragment, the rest of the molecule produces a range of interactions
which influence various properties of the functional group. Considering a family of molecules with the “same” functional group,
the range of variations in properties determines the range of chemical reactivity of the functional group, and a similar conclusion
is valid for more general molecular fragments. By the application of conventional as well as more advanced indices of fragment
properties, including local electron density shape characterization, various shape variation indices can be introduced for
fragments, and their relations to the holographic properties of electron densities can be examined.
Content Type Journal Article
Category Original Paper
Pages 1-8
DOI 10.1007/s10910-011-9938-9
Authors
Paul G. Mezey, Department of Chemistry, Scientific Modeling and Simulation Laboratory (SMSL), Memorial University of Newfoundland, 283 Prince Philip Drive, St. John’s, NL A1B 3X7, Canada
Scaling properties near the critical point indicates the existence of self-similarity behavior for the critical phenomena.
Although the system considered here is not a truly dynamic one, we propose a specific set of relations between fractal dimensions
and critical exponents in the Ising model of statistical mechanics. In particular, we put forward, corresponding to six critical
exponents for the Ising model, six fractal dimensions. Assuming the latter proposals, we can then derive relationships between
such fractal dimensions.
Content Type Journal Article
Category Original Paper
Pages 1-6
DOI 10.1007/s10910-011-9935-z
Authors
Z. D. Zhang, Shenyang National Laboratory for Materials Science, Institute of Metal Research and International Centre for Materials Physics, Chinese Academy of Sciences, 72 Wenhua Road, Shenyang, 110016 People’s Republic of China
N. H. March, Department of Physics, University of Antwerp, Antwerp, Belgium
Erratum to: Proposed model for growth preference of plate-like nanohydroxyapatite crystals on superhydrophilic vertically aligned carbon nanotubes by electrodeposition
Content Type Journal Article
Category Erratum
Pages 1083-1083
DOI 10.1007/s00214-011-1065-y
Authors
A. O. Lobo, Laboratorio de Nanotecnologia Biomedica (NanoBio), Universidade do Vale do Paraíba (UniVaP), Avenida Shishima Hifumi 2911, Urbanova, São José dos Campos, SP 12244-000, Brazil
F. R. Marciano, Laboratorio de Nanotecnologia Biomedica (NanoBio), Universidade do Vale do Paraíba (UniVaP), Avenida Shishima Hifumi 2911, Urbanova, São José dos Campos, SP 12244-000, Brazil
I. Regiani, Instituto Tecnológico de Aeronáutica (ITA), Praça Marechal Eduardo Gomes 50, Vila das Acácias, São José dos Campos, SP 12228-900, Brazil
S. C. Ramos, Laboratorio Associado de Sensores e Materiais (LAS), Instituto Nacional de Pesquisas Espaciais (INPE), Avenida dos Astronautas 1758, Jardin da Granja, São José dos Campos, SP 12227-010, Brazil
J. T. Matsushima, Laboratorio Associado de Sensores e Materiais (LAS), Instituto Nacional de Pesquisas Espaciais (INPE), Avenida dos Astronautas 1758, Jardin da Granja, São José dos Campos, SP 12227-010, Brazil
E. J. Corat, Laboratorio Associado de Sensores e Materiais (LAS), Instituto Nacional de Pesquisas Espaciais (INPE), Avenida dos Astronautas 1758, Jardin da Granja, São José dos Campos, SP 12227-010, Brazil
Density functional and MP2 calculations with extended basis sets were performed on the species participating in both the previously
suggested and a newly proposed mechanisms of partial dechlorination of chloropicrin by simple sulfur species, both in gas
phase and in a simulated water environment. Thermochemistry of both mechanisms in the gas phase was also studied using the
chemical models G3 and G4. It is shown that the previously proposed reductive dehalogenation is not thermodynamically feasible
at room temperature, as it should be according to the experimental evidence. Although inclusion of the solvent improves the
results with respect to gas phase, the thermodynamics of the proposed mechanism by Zheng et al. is still unfavorable for obtaining
the experimental products. An alternative mechanism is then proposed, involving the formation of HSCl, which is the intermediate
that then undergoes redox reactions. Such a mechanism is exothermic and spontaneous, according to the computational results,
and produces elementary sulfur in agreement with the experimental facts.
Content Type Journal Article
Category Regular Article
Pages 955-963
DOI 10.1007/s00214-011-1057-y
Authors
Oscar N. Ventura, Computational Chemistry and Biology Group, DETEMA, Facultad de Química, UdelaR, CC1157, 11800 Montevideo, Uruguay
Patricia Saenz-Méndez, Computational Chemistry and Biology Group, DETEMA, Facultad de Química, UdelaR, CC1157, 11800 Montevideo, Uruguay
Fiorentina Bottinelli, Computational Chemistry and Biology Group, DETEMA, Facultad de Química, UdelaR, CC1157, 11800 Montevideo, Uruguay
Peter Pulay, Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, AR 72701, USA
Shigeyoshi Sakaki, Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto-Daigaku-Katsura, Nishikyo-ku, Kyoto, 615-8510 Japan
Erratum to: (Hyper)polarizability density analysis for open-shell molecular systems based on natural orbitals and occupation numbers
Content Type Journal Article
Category Erratum
Pages 725-726
DOI 10.1007/s00214-011-1064-z
Authors
Masayoshi Nakano, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
Hitoshi Fukui, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
Takuya Minami, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
Kyohei Yoneda, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
Yasuteru Shigeta, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
Ryohei Kishi, Department of Materials Engineering Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
Benoît Champagne, Laboratoire de Chimie Théorique, Facultés Universitaires Notre-Dame de la Paix (FUNDP), rue de Bruxelles, 61, 5000 Namur, Belgium
Edith Botek, Laboratoire de Chimie Théorique, Facultés Universitaires Notre-Dame de la Paix (FUNDP), rue de Bruxelles, 61, 5000 Namur, Belgium
Takashi Kubo, Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
Koji Ohta, Research Institute for Ubiquitous Energy Devices, National Institute of Advanced Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, Japan
Kenji Kamada, Research Institute for Ubiquitous Energy Devices, National Institute of Advanced Industrial Science and Technology (AIST), Ikeda, Osaka 563-8577, Japan
In this work, we present the state of the art in the use of theory (first principles, molecular dynamics, and statistical
methods) for interpreting and understanding the infrared (vibrational) absorption and Raman scattering spectra. It is discussed
how they can be used in combination with purely experimental studies to generate infrared and Raman images of biomolecules
in biologically relevant solutions, including fluids, cells, and both healthy and diseased tissue. The species and conformers
of the individual biomolecules are in many cases not stable structures, species, or conformers in the isolated state or in
non-polar non-strongly interacting solvents. Hence, it is better to think of the collective behavior of the system. The collective
interaction is not the simple sum of the individual parts. Here, we will show that this is also not true for the infrared
and Raman spectra and images and that the models used must take this into account. Hence, the use of statistical methods to
interpret and understand the infrared and Raman spectra and images from biological tissues, cells, parts of cells, fluids,
and even whole organism should change accordingly. As the species, conformers and structures of biomolecules are very sensitive
to their environment and aggregation state, the combined use of infrared and Raman spectroscopy and imaging and theoretical
simulations are clearly fields, which can benefit from their joint and mutual development.
Content Type Journal Article
Category Regular Article
Pages 1261-1273
DOI 10.1007/s00214-011-1063-0
Authors
J. A. A. C. Piva, Laboratory of Biomedical Vibrational Spectroscopy, Institute of Research and Development, Universidade do Vale do Paraíba, UniVaP, Avenida Shishima Hifumi, 2911, Urbanova, São José dos Campos, São Paulo, 1244-000 Brazil
J. L. R. Silva, Laboratory of Biomedical Vibrational Spectroscopy, Institute of Research and Development, Universidade do Vale do Paraíba, UniVaP, Avenida Shishima Hifumi, 2911, Urbanova, São José dos Campos, São Paulo, 1244-000 Brazil
L. Raniero, Laboratory of Biomedical Vibrational Spectroscopy, Institute of Research and Development, Universidade do Vale do Paraíba, UniVaP, Avenida Shishima Hifumi, 2911, Urbanova, São José dos Campos, São Paulo, 1244-000 Brazil
A. A. Martin, Laboratory of Biomedical Vibrational Spectroscopy, Institute of Research and Development, Universidade do Vale do Paraíba, UniVaP, Avenida Shishima Hifumi, 2911, Urbanova, São José dos Campos, São Paulo, 1244-000 Brazil
H. G. Bohr, Department of Physics, Quantum Protein Center, QuP, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark
K. J. Jalkanen, Laboratory of Biomedical Vibrational Spectroscopy, Institute of Research and Development, Universidade do Vale do Paraíba, UniVaP, Avenida Shishima Hifumi, 2911, Urbanova, São José dos Campos, São Paulo, 1244-000 Brazil
Cytochrome c peroxidase (CCP) contains a five-coordinate heme active site. The reduction potential for the ferric to ferrous couple in
CCP is anomalously low and pH dependent (Eo = ~−180 mV vs. S.H.E. at pH 7). The contribution of the protein environment to
the tuning of the redox potential of this couple is evaluated using site-directed mutants of several amino acid residues in
the environment of the heme. These include proximal pocket mutation of residues Asp-235, Trp-191, Phe-202, and His-175, distal
pocket mutation of residues Trp-51, His-52, and Arg-48; and a heme edge mutation of Ala-147. Where unknown, the structural
changes resulting from the amino acid substitution have been studied by X-ray crystallography. In most cases, ostensibly polar
or charged residues are replaced by large hydrophobic groups or alternatively by Ala or Gly. These latter have been shown
to generate large, solvent-filled cavities. Reduction potentials are measured as a function of pH by spectroelectrochemistry.
Starting with the X-ray-derived structures of CCP and the mutants, or with predicted structures generated by molecular dynamics
(MD), predictions of redox potential changes are modeled using the protein dipoles Langevin dipoles (PDLD) method. These calculations
serve to model an electrostatic assessment of the redox potential change with simplified assumptions about heme iron chemistry,
with the balance of the experimentally observed shifts in redox potential being thence attributed to changes in the ligand
set and heme coordination chemistry, and/or other changes in the structure not directly evident in the X-ray structures (e.g.,
ionization states, specific roles played by solvent species, or conformationally flexible portions of the protein). Agreement
between theory and experiment is good for all mutant proteins with the exception of the mutation Arg 48 to Ala, and His 52
to Ala. In the former case, the influence of phosphate buffer is adduced to account for the discrepancy, with evidence for
phosphate binding in the distal pocket, and measurements made in a bis–tris propane/2-(N-morpholino)ethanesulfonic acid buffer
system agree well with theory. For the latter case, an unknown structural element relevant to His-52 and/or solvent influence
in the mutant akin to anion binding in the distal pocket (though lacking proof that it is, and in this case lacking a phosphate
effect) manifests in this mutant. The use of exogenous (sixth) ligands in dissecting the contributions to control of redox
potential is also explored as a pathway for model building.
Content Type Journal Article
Category Regular Article
Pages 1185-1196
DOI 10.1007/s00214-011-1062-1
Authors
G. M. Jensen, Department of Molecular Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, MB8, La Jolla, CA 92037, USA
D. B. Goodin, Department of Molecular Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, MB8, La Jolla, CA 92037, USA
We present theoretical methods and computational strategies of the effects of nanoparticles on linear optical properties of
molecules. We present quantum mechanical-molecular mechanics response methods for calculating electromagnetic properties of
molecules interacting with nanoparticles and we report strategies for calculating electronic and redox states of molecules
sandwiched between gold nanoparticles.
Content Type Journal Article
Category Regular Article
Pages 839-850
DOI 10.1007/s00214-011-1060-3
Authors
Stine T. Olsen, Department of Chemistry, H. C. Ørsted Institute, University of Copenhagen, 2100 Copenhagen, Denmark
Thorsten Hansen, Department of Chemical Physics, Lund University, 22100 Lund, Sweden
Kurt V. Mikkelsen, Department of Chemistry, H. C. Ørsted Institute, University of Copenhagen, 2100 Copenhagen, Denmark
Retinal proteins are excellent systems for understanding essential physiological processes such as signal transduction and
ion pumping. Although the conjugated polyene system of the retinal chromophore is best described with quantum mechanics, simulations
of the long-timescale dynamics of a retinal protein in its physiological, flexible, lipid-membrane environment can only be
performed at the classical mechanical level. Torsional energy barriers are a critical ingredient of the classical force-field
parameters. Here we review briefly current retinal force fields and discuss new quantum mechanical computations to assess
how the retinal Schiff base model and the approach used to derive the force-field parameters may influence the torsional potentials.
Content Type Journal Article
Category Regular Article
Pages 1169-1183
DOI 10.1007/s00214-011-1054-1
Authors
Ana-Nicoleta Bondar, Theoretical Molecular Biophysics, Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
Michaela Knapp-Mohammady, Molecular Biophysics Department and Division of Functional Genome Analysis, German Cancer Research Center, Im Neuenheimer Feld 580, 69120 Heidelberg, Germany
Sándor Suhai, Molecular Biophysics Department, German Cancer Research Center, Im Neuenheimer Feld 580, 69120 Heidelberg, Germany
Stefan Fischer, Computational Biochemistry, IWR, University of Heidelberg, Speyerstrasse 6, room H304, 69115 Heidelberg, Germany
Jeremy C. Smith, Oak Ridge National Laboratory, PO Box 2008 MS6164, Oak Ridge, TN 37831-6164, USA
We recently reported an algorithm to count Kekulé (resonance) structures for convex cyclofusenes using a combinatorial/geometric
approach. Previously, we presented an algorithm for counting resonance structures for parallelogram-like benzenoids with holes
by counting descending paths using rectangular meshes with holes. In this article, we employ a similar combinatorial/geometric
approach to determine algorithms that will facilitate counting of the resonance structures in parallelogram-like benzenoids
with no holes.
Content Type Journal Article
Category Original Paper
Pages 1-10
DOI 10.1007/s10910-011-9933-1
Authors
Sasan Karimi, Chemistry Department, Queensborough Community College, Bayside, NY 11364, USA
Anthony Delgado, New York University, New York, NY, USA
Marty Lewinter, Math Department, Purchase College, Purchase, NY 10577, USA
We apply our recently proposed proper quantization rule,
ó õ
xB
xA
k(x) dx -
ó õ
x0B
x0A
k0(x) dx=np
, where
k(x)=
Ö
2 M [E-V(x) ]
/(h/2p)
to obtain the energy spectrum of the modified Rosen-Morse potential. The beauty and symmetry of this proper rule come from
its meaning—whenever the number of the nodes of
f(x)
or the number of the nodes of the wave function ψ(x) increases by one, the momentum integral
ó õ
xB
xA
k(x)dx
will increase by π. Based on this new approach, we present a vibrational high temperature partition function in order to study thermodynamic
functions such as the vibrational mean energy U, specific heat C, free energy F and entropy S. It is surprising to note that the specific heat C (k = 1) first increases with β and arrives to the maximum value and then decreases with it. However, it is shown that the entropy S (k = 1) first increases with the deepness of potential well λ and then decreases with it.
Content Type Journal Article
Category Original Paper
Pages 1-12
DOI 10.1007/s10910-011-9931-3
Authors
Shi-Hai Dong, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico, DF 07738, Mexico
M. Cruz-Irisson, ESIME-Culhuacan, Instituto Politécnico Nacional, Av. Santa Ana 1000, Mexico, DF 04430, Mexico
Flag graphs have been used in the past for describing maps on closed surfaces. In this paper we use them for the first time
in mathematical chemistry for describing benzenoids and some other similar structures. Examples include catacondensed and
pericondensed benzenoids. Several theorems are included. Symmetries of benzenoid systems, flag graphs, and symmetry type graphs
are briefly discussed.
Content Type Journal Article
Category Original Paper
Pages 1-11
DOI 10.1007/s10910-011-9932-2
Authors
Tomaž Pisanski, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia
Alexandru T. Balaban, Department of Marine Sciences, Texas A&M University at Galveston, Galveston, TX 77553-1675, USA
This paper is the second in a series of two. The first paper has been devoted to the detailed explanation of the mathematical
formulation of the underlying theoretical framework. Specifically, the first paper shows that it is possible to construct
an infinite linear ODE set, which describes a probabilistic evolution. The evolution is probabilistic because the unknowns
are expectations, with appropriate initial conditions. These equations, which we name, Probabilistic Evolution Equations (PEE)
are linear at the level of ODEs and initial conditions. In this paper, we first focus on the phenomenological reasoning that
lead us to the derivation of PEE. Second, the aspects of the PEE construction is revisited with a focus on the spectral nature
of the probabilistic evolution. Finally, we postulate fruitful avenues of research in the fields of dynamical causal modeling
in human neuroimaging and effective connectivity analysis. We believe that this final section is a prime example of how the
rigorous methods developed in the context of mathematical chemistry can be influential in other fields and disciplines.
Content Type Journal Article
Category Original Paper
Pages 1-11
DOI 10.1007/s10910-011-9930-4
Authors
Emre Demiralp, Department of Psychology, University of Michigan, 1012 East Hall, 530 Church Street, Ann Arbor, MI 41809-1043, USA
Metin Demiralp, İstanbul Teknik Üniversitesi Bilişim Enstitüsü, Maslak, Istanbul, 34469 Turkey
Luis Hernandez-Garcia, University of Michigan, 1096 BIRB, 2360 Bonisteel St., Ann Arbor, MI 48105-2108, USA
In this paper we describe a probabilistic framework for describing dynamical systems. The approach is inspired by quantum
dynamical expectation dynamics. Specifically, an abstract evolution operator corresponding to the Hamiltonian in quantum dynamics
is constructed. The evolution of this operator defining PDE’s solution is isomorphic to the functional structure of the wave
function as long as its initial form permits. This operator enables us to use one of the most important probabilistic concepts,
namely expectations. The expectation dynamics are governed by equations which are constructed via commutator algebra. Based
on inspiration from quantum dynamics, we have used both the independent variables and the symmetric forms of their derivatives.
For construction of the expectation dynamics, the algebraic independent variable operators which multiply their operands by
the corresponding independent variable suffice. In our descriptions, we remain at the conceptual level in a self-consistent
manner. The phenomenological implications and the tremendous potential of this approach for scientific discovery and advancement
is described in the companion to this paper.
Content Type Journal Article
Category Original Paper
Pages 1-20
DOI 10.1007/s10910-011-9929-x
Authors
Metin Demiralp, İstanbul Teknik Üniversitesi Bilişim Enstitüsü, Maslak, 34469 Istanbul, Turkey
Emre Demiralp, Department of Psychology, University of Michigan, 1012 East Hall, 530 Church Street, Ann Arbor, MI 41809-1043, USA
Luis Hernandez-Garcia, 1096 BIRB, 2360 Bonisteel St., Ann Arbor, MI 48105-2108, USA
Since Adrian Brown and Victor Henri’s work, the simplest enzyme kinetics model, which contains only three rate constants k1, k2 and k−1 in 1902, has been thoroughly explored in many directions. By using the Michaelis–Menten equation, KM and k2 can be measured quickly. All the three rate constants can be derived by temperature jump method or transient state kinetics,
but both methods need more complicated techniques and equipments. In our previous paper (Li et al. in J Math Chem 46:290–301,
2009), we gave a method to measure all the rate constants which does not require any additional equipment other than those needed
for measuring KM and k2. Here, we propose a new one which needs no additional equipment either. This method is based on a study of inflection points
of integral curves. Numerical results show that the new one is much better than the previous one in two aspects: near the
end of the reaction, the new one gives more accurate estimation; during the quasi-steady state of the reaction, it also gives
good estimations while the previous one can not. Hence, this method not only advances the estimation accuracy, but also has
more choices for measuring.
Content Type Journal Article
Category Original Paper
Pages 1-13
DOI 10.1007/s10910-011-9922-4
Authors
Banghe Li, Center of Bioinformatics and Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 China
Bo Li, Center of Bioinformatics and Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 China
Yuefeng Shen, Center of Bioinformatics and Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190 China
Latent molecular properties are not exhibited by the given molecular structure but are reproducibly exhibited by the same
molecule in a different electronic state or if some molecular interactions have taken place. A consequence of the Holographic
Electron Density Theorem, as applied to latent properties, provides a framework that allows an extension of the expectation
value formalism, leading to “unexpected” expectation value expressions for latent properties. Connections of special cases
of this approach to earlier density matrix extrapolation methods are pointed out.
Content Type Journal Article
Category Original Paper
Pages 1-7
DOI 10.1007/s10910-011-9928-y
Authors
Paul G. Mezey, Scientific Modeling and Simulation Laboratory (SMSL), Departments of Chemistry, Physics and Physical Oceanography, Memorial University of Newfoundland, 283 Prince Philip Drive, St. John’s, NL A1B 3X7, Canada
We combine, within the Bohr Sommerfeld quantization rule, a systematic perturbation with asymptotic analysis of the action
integral for potentials which support a finite number of bound states with E < 0 to obtain an interpolation formula for the energy eigenvalues. We find interpolation formulae for the Morse potential
as well as potentials of the form
V=V0 [ ( \fracax )2k-( \fracax)k ]
. For k = 6 i.e. the well known Lennard Jones potential this yields results within 1 per cent of the highly accurate numerical values.
For the Morse potential this procedure yields the exact answer. We find that the result for the Morse potential which approaches
zero exponentially is the
k®¥
limit of the Lennard Jones class of potentials.
Content Type Journal Article
Category Original Paper
Pages 1-14
DOI 10.1007/s10910-011-9926-0
Authors
Shayak Bhattacharjee, Department of Physics, Indian Institute of Technology Kanpur, Kanpur, 208016 India
D. S. Ray, Department of Physical Chemistry, Indian Association for the Cultivation of Science, Jadavpur, Kolkata, 700032 India
J. K. Bhattacharjee, S. N. Bose National Centre for Basic Sciences, Salt Lake, Kolkata, 700098 India
We study the dependence of chronoamperometric data on the kinetic parameters for a bimolecular reaction, characterizing the
behavior of an electrochemical mechanism that pertains to lithium/sulfur dioxide batteries. The reaction entails first the
reduction of a reactant O to a product R by an instantaneous charge transfer, followed by a homogeneous chemical reaction
between O and R to produce an electrochemically inert product P. We model this by a semilinear reaction-diffusion system with
discontinuous initial conditions and mixed Dirichlet and Neumann boundary conditions, and develop a procedure to extract from
a single potential step experiment the forward and reverse rate constants for the reaction. To do so we define a function
J(t):=j(t)Öt
, where j(t) is the current density from the chronoamperometric output, and use maximum principle and scaling arguments to exploit the
location of the minimum of
J(t)
versus t.
Content Type Journal Article
Category Original Paper
Pages 1-14
DOI 10.1007/s10910-011-9925-1
Authors
K. T. Gimre, Department of Mathematics, Columbia University, New York City, NY, USA
R. V. Whiteley, Department of Chemistry, Pacific University, Forest Grove, OR, USA
C. M. Guenther, Department of Mathematics and Computer Science, Pacific University, Forest Grove, OR, USA
In this paper we present new modified open Newton Cotes integrators and we develop a new modified trigonometrically-fitted
open Newton-Cotes method. We study the connection between the new proposed schemes, the differential methods and the symplectic
integrators. although The research on multistep symplectic integrators is very poor, although, much research has been done
on one step symplectic integrators and several of then have obtained based on symplectic geometry. In this paper a new open
modified numerical algorithm of Newton-Cotes type is produced. We present the new obtained method as symplectic multilayer
integrator. The new obtained symplectic schemes are applied for the solution of the resonance problem of the radial Schrödinger
Equation. The results show the efficiency of the new proposed algorithm.
Content Type Journal Article
Category Original Paper
Pages 1-23
DOI 10.1007/s10910-011-9924-2
Authors
Ibraheem Alolyan, Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451 Saudi Arabia
T. E. Simos, Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451 Saudi Arabia
