bluuebunny/crossref_metadata_2025 huggingface dataset:
SC‐MEH‐MO calculations on high Tc superconductors. 1: The YBa2Cu8O cluster in YBa2Cu3O7
Authors: Boudreaux Edward A. , Baxter Eric
Published: January 2005

SC‐MEH‐MO calculations have been carried out on select clusters of the YBa2Cu3O7 lattice structure. The results of an earlier computation on small CuO clusters are presented for comparison with the finding obtained on a YBa2Cu8O26+ extended cluster. In the latter, the antiferromagnetic coupling of singularly occupied Cu and O levels is analyzed.
Hydrogenlike atoms in uniformly charged sphere model of atomic nucleus. I. Reference calculations of energy levels
Authors: Hasegawa T. , Fujimura N. , Matsuoka O.
Published: January 2005

We have adopted the uniformly charged sphere model of atomic nucleus for one‐electron atoms H, Ar17+, Xe53+, Hg79+, and U91+ and calculated several energy levels by solving the matching equations of the inward and the outward radial wave functions for the Schrödinger as well as for the Dirac equations. The finite‐size effect (FSE) of the atomic nucleus on the energy levels of nonrelativistic atoms has been found one order of magnitude smaller than the effect on the relativistic atoms. The FSE works mainly on s states for nonrelativistic atoms, whereas for relativistic atoms, it works on s and p1/2 states. The energy levels of p states have been calculated lower than the energies of the corresponding s states when we have included the FSE.
On the connection between certain properties of the second‐order reduced density matrix and the occurrence of coherent‐dissipative structures in disordered condensed matter
Authors: Brändas E. J. , Chatzidimitriou‐Dreismann C. A.
Published: January 2005

It is demonstrated, from general physical principles, that a new kind of quantum correlations, associated with the appropriate reduced density matrix, Γ, exist in amorphous condensed matter. The treatment starts from general representation properties of the second‐order reduced density matrix. The derivations, using general statistical notions in a quantum mechanical framework, lead to a decomposition of the two‐matrix into the large‐, the small‐, and the unpaired components. Since this result can be identified with the extreme case of Coleman, the formulation is automatically ensemble‐representable. Introducing the complex scaling method (CSM) into the Bloch–Liouville equation for Γ it is shown how the temperature T in the aforementioned ensemble can be specified. This defines, in the present development, thermalization in a system far from equilibrium. It is further shown that this thermalization leads to the formation of certain irreducible (Jordan) blocks containing some (incomplete) phase information. The connection between these irreducible blocks and the concept of a coherent‐dissipative structure is made. The treatment reveals general features of the coherent‐dissipative structure and a certain universality of the coherence‐breaking mechanism. The main equations relate the relaxation time Trcl and the temperature T with the minimum degrees of freedom Smin and the associated spatial domain dmin of the structure. Relevant examples are, e.g., proton transfer and H+ conductivity in water, conductivity of molten alkali chlorides, quantum correlation effects in high‐Tc superconductors, and spin dynamics of Gd far above the Curie point.
On the prüfer transformation in the H2+ problem
Authors: Úlehla Ivan
Published: January 2005

The application of the Prüfer transformation to the Schrödinger equation leads to a nonlinear first‐order differential equation. The advantage of this transformation is demonstrated in the calculation of the energy spectrum of the H2+ ion. In the second section, the classical problem is recalled and the transition to Prüfer transformation prepared. The definition of this transformations is contained in the third section. In the final paragraphs, the numerical results concerning the eigenvalues of H2+ energy are presented.
A pair‐excitation MCSCF calculation based on CNDO/INDO approximation I
Authors: Kumakura Shigekazu , Shiraishi Satoshi , Izawa Masaru , Hanamura Mitsuyasu
Published: January 2005

Second‐order multiconfigurational self‐consistent field (MCSCF) calculation has been programmed on the basis of CNDO/INDO molecular orbital bases, in which the configuration space employed is restricted within pair‐excitations. Test calculations have been carried out for 17 small molecules. All the MCSCF ground states of these molecules have been successfully converged to their respective optimal states by employing a simple weighting scheme. This procedure provides a great savings in computer time. The MCSCF calculation on azetidine required only 27 min on a HITAC M‐680H. The MCSCF energies of HF, F2, and BH show improved behaviors up to large atomic distances (∼7au).
Ab initio calculations on 5α‐androstane
Authors: Paša‐Tolić Lj. , Klasinc L. , Spiegl H. , Knop J. V. , McGlynn S. P.
Published: January 2005

The electronic structure of 5α‐androstane, the parent hydrocarbon of the hormonal steroids, has been computed by ab initio SCF methods in an STO‐3G basis. The results are compared with existing MNDO computations and are used to discuss long‐range electronic interactions between distant substituents that might be appended to rings A and D of 5α‐androstane. It is thought that these interactions are mediated by the ribbonlike MO'S of the parent molecule.
On geometric concepts in sensitivity analysis of molecular charge distribution
Authors: Nalewajski Roman F.
Published: January 2005

A geometric interpretation of molecular charge redistributions [polarization (P) and/or charge transfer (CT)] is proposed. It regards the atoms‐in‐a‐molecule (AIM) electron populations, N = (N1,…, Nm), as components of the global electron population vector, \documentclass{article}\pagestyle{empty}\begin{document}$\overrightarrow N \equiv N$\end{document}, in a system of orthogonal AIM electron population axes, \documentclass{article}\pagestyle{empty}\begin{document}$(\overrightarrow N _1 ,...,\overrightarrow N _m )$\end{document}. The normal (decoupled) representation corresponds to the rotated, principal axes coordinate system, \documentclass{article}\pagestyle{empty}\begin{document}$(\overrightarrow Q _1 ,...,\overrightarrow Q _m )$\end{document}, in which the canonical AIM hardness tensor becomes diagonal. Such transformation preserves 𝒩 while not preserving the global electron population, N = ∑miNi, the usual parameter of the sensitivity analysis. The chemical potential, hardness, softness, and related concepts associated with 𝒩 are defined and their properties examined. A simple geometric model of a chemical reaction is proposed within the \documentclass{article}\pagestyle{empty}\begin{document}$ \{ \overrightarrow Q _\alpha \}$\end{document} space. It consists of two intersecting effective states representing the charge activation of reactants and the charge relaxation of products, respectively. Only the normal modes of reactants, which include the CT component, can participate in the CT reaction coordinate, whereas the pure P modes contribute only to the entropy factor of the reaction rate constant. The implications of the model for the chemical reactivity are briefly explored. Finally, the linear vector space interpretation of charge sensitivities is given and applied to define the optimum hybrid charge displacement modes of reactants.
Calculations on model systems using quasi‐degenerate variational perturbation theory with an average pair correction
Authors: Murray Christopher , Racine Stephen C. , Davidson Ernest R.
Published: January 2005

A correction to quasi‐degenerate variational perturbation theory is proposed that is similar to the average coupled pair functional method. The correction is shown to lack solid theoretical justification when applied to importance‐selected multireference calculations and to systems with irreducible interpair contributions to the correlation energy. The method is shown to give improved results when applied to small model systems.
The properties of n‐electron wave functions built up with two kinds of geminals
Authors: Liu Chengbu , Deng Conghao , Hu Haiquan , Jin Beiyan
Published: January 2005

The properties of the n‐electron wave functions
equation image
with symplectic symmetries have been discussed. These functions are built up with two kinds of geminals. The well‐known antisymmetrized geminal power (AGP) function is only a special case of them. The first‐ and second‐order reduced density matrices and the natural expansions of these functions have been given, and the uniform expressions for system energies in the states corresponding to these functions have been deduced. It has been shown that the special case
equation image
is probably another consistent ground state for the particle‐hole propegator or random‐phase approximation (RPA) besides the AGP function.
Vibrational self‐consistent‐field approximation for triatomic molecules using hyperspherical modes with application to H2O
Authors: Bastida Adolfo , Zúlñiga José , Molina Antonio M. , Requena Alberto
Published: January 2005

The vibrational self‐consistent‐field approximation is used to calculate excited vibrational energy levels of the water molecule in hyperspherical coordinates. The calculations are made for a global realistic Sorbie–Murrell‐type potential surface for which exactum quantum variational results are known for comparison. The coupled SCF equations are solved using the discrete variable representation (DVR) method, which allows computation of the coupled multidimensional integrals in a very simple and efficient way. The results are in good agreement with exactum quantum calculations and are more accurate than SCF energy eigenvalues obtained using normal mode coordinates.
Extended Gaussian‐type valence basis sets for calculations involving nonempirical core pseudopotentials. II. PS‐21 G Basis for Li to Ca and Ga to Kr atoms
Authors: Hannachi Y. , Barthelat J. C. , Jolly L.‐H. , Silvi B. , Bouteiller Y.
Published: January 2005

Split valence basis sets adapted to Durand and Barthelat core pseudopotentials have been optimized for the three first rows of the main group elements. The reliability of these PS‐21G basis functions has been checked by performing test calculations on about 30 small molecule and crystalline systems. These studies indicate a satisfactory overall agreement between the PS‐21G results and those of all‐electron calculations carried out with basis sets having similar valence‐shell contractions.
Semianalytical method for four‐center molecular integrals over Slater‐type orbitals
Authors: Jones Herbert W.
Published: January 2005

A strategy for the evaluation of four‐center molecular integrals over Slater‐type orbitals is developed using the Löwdin α‐function approach in which displaced orbitals are expanded in spherical harmonics. The harmonic potentials are produced analytically and evaluated along a grid. The harmonic charge distributions are given an analytical formulation and are evaluated over the common grid, and numerical integrations are performed for each harmonic. Using an example with 1s orbitals, only nine harmonics are needed for good results. Computer algebra and integer arithmetic are used to generate C, E, and F matrices that are stored as part of the data base. One‐dimensional T and X matrices are introduced as an aid in computation. The employment of look‐up tables and vector and parallel processing promises to make this method, which can be generalized, practical.
A method of calculating eigenvectors of real symmetric tridiagonal matrices in a hyperspherical space
Authors: Novosadov Boris K. , Zhogina Vera V.
Published: January 2005

A novel direct method of calculating eigenvectors for real symmetric tridiagonal matrices has been proposed. An eigenvector is represented as a unit vector in a hyperspherical space set by hyperpolar angle coordinates. An algorithm has been examined for a series of tridiagonal matrices. Numerical calculations as compared with a conventional Householder algorithm have shown a good agreement within 8‐byte double precision for most eigenvectors computed.
Mills–Nixon effect in heteroanalogs of cyclopropabenzene
Authors: Eckert‐Maksić M. , Maksić Z. B. , Hodošček M. , Poljanec K.
Published: January 2005

Structural properties of cyclopropabenzene and its heteroanalogs are studied at the SCF 6‐31G level of theory. It is found that the Mills–Nixon (MN) type of localization within the benzene ring is present in these systems. The origin of the bond fixation lies in rehybridization at the carbon junction atoms. π‐electron bond orders usually follow changes within the sigma framework but can be misleading sometimes. It is shown that a judicious choice of heteroatoms can considerably enhance the MN effect. A refined and better definition of the MN effect is offered. Finally, present calculations and analysis of the results in terms of hybridization model and π‐bond orders strongly indicate that experimental 4J(HCCMe) proton–proton spin–spin couplings over four bonds can be used in identification of the MN effect only with extreme caution.
Nonadiabatic theory of triatomics: Formalism for 1Πu/1Φg interaction, for electronic spin, and for 2Λ Renner–Teller effect
Authors: Petrongolo Carlo
Published: January 2005

A recent theory of nonadiabatic effects in triatomic molecules is specialized to the four‐state Renner–Teller and Jahn–Teller 1Πu/1Φg interactions and is then generalized by including the electronic spin and by considering the 2Λ Renner–Teller effect.
Dicretization to avoid singularities in vibration–rotation Hamiltonians: A bisector embedding for AB2 triatomics
Authors: Tennyson Jonathan , Sutcliffe Brian T.
Published: January 2005

A previously proposed [Sutcliffe and Tennyson, Int. J. Quantum Chem. 29, 183 (1991)] body‐fixed Hamiltonian is applied to AB2 systems in Radau coordinates with the x‐axis embedded along the bisector of the angle. It is shown that by using a discrete variable representation for the angular coordinate it is possible to avoid singular regions of the Hamiltonian. A two‐step variational procedure is used to obtain rotationally excited states of the system. The results of test calculations H2S and D2S with J = 0, 1, 5, and 10 are discussed along with computer‐usage characteristics.
The structure of the bitetrahedryl molecule—A major shift due to electron correlation: Effects of carbonyl substituents, implications for the structure of coupled tricyclo[3.1.0.02,6]hexyl, and extension to cubylcubane
Authors: Xie Yaoming , Schaefer Henry F. , Aped Pinchas , Chen Kuohsiang , Allinger Norman L.
Published: January 2005

Ab initio molecular quantum mechanics has been applied to a number of coupled ring systems including biterahedryl and cubylcubane. Basis sets at least as large as double zeta augmented by carbon d functions (DZ+d) were used throughout. For biterahedryl, electron correlation effects qualitatively alter the molecular structure, decreasing the central CC bond distance while increasing the adjacent CC distance. Carbonyl substituents, contrary to some previous thinking, do not qualitatively alter the bitetrahedryl structure. This finding points to a structural problem with the monomer bicyclo[3.1.0.02,6]hexane that carries over to the coupled bicyclo[3.1.0.02,6]hexyl molecule. Finally, for the cubylcubane molecule synthesized in 1988, the only significant difference between Hartree–Fock theory and experiment occurs for the central CC distance, which, as in the other coupled molecules, is too long. These results significantly lengthen the (still very short) list of closed‐shell hydrocarbon molecules for which Hartree–Fock theory encounters structural difficulties.
Development of the quadratic Korringa–Kohn–Rostoker band theory method
Authors: Faulkner J. S.
Published: January 2005

A great deal of effort in recent years has been put into the development of a new band theory technique based on multiple‐scattering theory. Some of the highlights of this development are described.
Near‐equilibrium ordering of the crystalline phases of atomic hydrogen
Authors: Nobel J. A. , Wilson G. A. , Trickey S. B.
Published: January 2005

Some time ago Min et al. [Phys. Rev. B 30, 5076 (1984)] found the near‐equilibrium sequence of phases of paramagnetic crystalline H to be (in order of increasing energy) simple cubic (SC), hexagonal close packed (HCP), body‐centered cubic (BCC), and face‐centered cubic (FCC), with FCC and HCP substantially separated (about 60 mRy/atom). This result is counterintuitive on three counts when compared with crystalline Li. That comparison suggests that HCP should lie only slightly below FCC and both should be substantially below BCC. (Simple cubic should lie lowest in H but not in Li because of the difference in orbital occupancy.) We have redone the calculations with our published full‐potential linearized augmented plane wave code WIEN. We find the sequence of phases with increasing energy to be SC, HCP, FCC, and BCC, the ordering expected from solid Li. By direct exploration of dense k‐space meshes, we show that the difference in predictions results from a k‐space mesh extrapolation technique used by Min et al.
Ab initio studies on the Ziegler–Natta catalytic process
Authors: Novaro O.
Published: January 2005

A survey of the development of the application of quantum chemical techniques to Ziegler–Natta polymerization starting from the pioneering work of Clementi and co‐workers is presented. In the latter, the role of the catalyst was elucidated, a feasible reaction pathway was proposed, and several properties of the catalyzed reaction (heats of formation, activation barriers, physisorption and chemisorption energies, etc.) were obtained without semiempirical approximations. Furthermore, a few proposals for enhancing catalytic activity for the oligomerization process proved to be of great practical value and led to several patents. This turns out to be a good example of the usefulness of the computational techniques to provide intense interactions between theoretical and applied chemistry.
Effects of exchange on equilibrium bond lengths of heavy, almost spherical, tetrahedral molecules XH4
Authors: Egorov S. A. , March N. H. , Santamaria R.
Published: January 2005

The simplest nonrelativistic density functional theory, namely, that of Thomas, Fermi, and Dirac, is used to study the effect of exchange on the equilibrium bond lengths of heavy tetrahedral molecules XH4. In particular, the limiting bond length as the central atom X becomes infinitely heavy is shown to be reduced by exchange by some 0.34 Å. Comparison with experiment shows that the main features of the bond‐length variation through the series CH4PbH4 are reflected by the Thomas–Fermi–Dirac predictions, though the bond lengths remain too large for finite atomic number Z of the central atom. Therefore, a semiempirical correction is proposed, which, however, tends to zero as Z tends to infinity.
The calculation of frequency‐dependent hyperpolarizabilities including electron correlation effects
Authors: Rice Julia E. , Handy Nicholas C.
Published: January 2005

The theory for the calculation of the frequency‐dependent hyperpolarizabilities β(−2ω; 0, ω), β(−ω; 0, ω), and β(0; ω, −ω) is discussed. New relations between these tensors are derived for those wave functions that obey the time‐dependent Hellmann–Feynman theorem (e.g., the self‐consistent field [SCF] or the exact wave function). Using second‐order Møller–Plesset perturbation theory (MP2), expressions are obtained for the hyperpolarizabilities in terms of derivatives of appropriately defined linear polarizability tensors with respect to a static electric field. Results are presented for ammonia and formaldehyde for the optical Kerr effect and for secondharmonic generation. These results indicate that it is desirable to determine the frequency‐dependent contribution to the hyperopolarizability at the MP2 rather than the SCF level of theory, in cases where the static hyperpolarizability has a large contribution from electron correlation and/or where the frequency‐dependent contribution may be more significant, such as for secondharmonic generation.
Theory of molecular optoelectronics. IX. Calculation of χ(2) from theoretical hyperpolarizabilities for DAN
Authors: Munn R. W.
Published: January 2005

Components of the crystal quadratic susceptibility tensor χ(2) for second‐harmonic generation are calculated for the title compound, 4‐(N, N‐dimethylamino)‐2‐acetamido‐nitrobenzene. Input data are the crystal structure and refractive indices and CNDO hyperpolarizabilities; two different sets of refractive indices give similar results. The calculations yield effective polarizabilities as well as both rigorous and anisotropic Lorentz local electric fields. Susceptibility components are close to 10 pm V−1, rather smaller than those deduced experimentally and showing a weaker dependence on direction; Kleinman symmetry is mostly observed within 10%. Screened dipoledipole interactions using CNDO dipole moments amount to −80 kJ mol−1, implying permanent fields of 2 GV m−1.
Calculation of the probabilities for transitions into the continuous spectrum by using the L2 basis: A new method of solving the wave‐function renormalization problem
Authors: Smelov G. V.
Published: January 2005

A new method is presented for calculating the normalization factor for continuous spectrum functions in the L2 basis. One variant of this method is applicable to operators given in the form of a tridiagonal matrix and does not require explicit calculation of the roots of the characteristic equation. The other variant of the method can be used in the general case, where after the basis is introduced, its length is gradually increased.
Superconductivity and the effective electron–electron interaction mechanism in the light of the configuration interaction study
Authors: Svrček Michal , Baňacký Pavol , Zajac Anton
Published: January 2005

The effect of electron–phonon interactions, described by the effective electron–electron interaction mechanism, on the electronic structure of molecular systems has been investigated by the configuration interaction method. For systems with strongly quasi‐degenerate electronic states near to the Fermi surface, this interaction mechanism, according to the BCS theory, results in the electronic ground‐state energy lowering and in the gap formation. A more rigorous treatment of the configuration interaction method as applied in this paper confirms the electronic ground‐state energy lowering, but the obtained results indicate that the effective electron–electron interaction term does not yield the experimentally detected temperature dependence of the gap. Accordingly, the two‐particle mechanism seems not to be the key factor for the gap formation and for the microscopic mechanism of superconductivity, which agrees with the results of the molecular nonadiabatic theory of electron–vibrational interactions.
Classical trajectories for two ring‐shaped potentials
Authors: Kibler Maurice , Lamot Georges‐Henri , Winternitz Pavel
Published: January 2005

The present paper deals with the classical trajectories for two superintegrable systems: a system known in quantum chemistry as the Hartmann system and a system of potential use in quantum chemistry and nuclear physics. Both systems correspond to ring‐shaped potentials. They admit two maximally superintegrable systems as limiting cases, viz., the isotropic harmonic oscillator system and the Coulomb–Kepler system in three dimensions. The planarity of the trajectories is studied in a systematic way. In general, the trajectories are quasi‐periodic rather than periodic. A constraint condition allows to pass from quasi‐periodic motions to periodic ones. When written in a quantum mechanical context, this constraint condition leads to new accidental degeneracies for the two systems studied. © 1992 John Wiley & Sons, Inc.
On the calculation of first‐order properties: Expectation value versus energy derivative approach
Authors: Ernzerhof M. , Marian C. M. , Peyerimhoff S. D.
Published: January 2005

The definition of so‐called first‐order properties is, in general, not unique for approximate solutions of the Schrödinger equation. In the present work, the determination of molecular properties as the expectation value or energy derivative are compared for a wide class of electron correlation treatments that are based on the stationarity of certain modified energy functionals. The case in which all perturbation‐dependent parameters in the energy expression are optimized is taken as a reference point, to which the derivative and the expectation value approaches are related by a sequence of approximations. By analyzing the validity of these approximations, we are in a position to give general criteria for the choice of the method to be employed. The derivative approach is shown to be a special case of a general method to improve the calculation of molecular properties. Furthermore, this method is extended to give a correction to the energy itself. © 1992 John Wiley & Sons, Inc.
The dynamic and the stochastic reaction rate approaches to nonradiative processes in condensed media
Authors: Christov S. G.
Published: January 2005

A comparison is made between the exact classical dynamic theory and the stochastic theory of reaction rates in dense media. The conditions of their equivalence are derived on the basis of a harmonic oscillator model. It is shown in a direct way that in the general case of a multidimensional system the approximate activated complex (transition‐state) theory is not identical to the stochastic theory at any value of the viscosity coefficient. © 1992 John Wiley & Sons, Inc.
Empirical methods for computing molecular partition coefficients: II. Inclusion of conformational flexibility within fragment–based approaches
Authors: Richards Nigel G. J. , Williams Philip B. , Tute Michael S.
Published: January 2005

A novel algorithm for computing the water/1‐octanol partition coefficient, logP, of conformationally flexible molecules, has been investigated using calculations upon a number of uncharged, linear dipeptides. In this method (which appears to be the first to consider explicitly the effects of the population of accessible conformational minima inbothphases), the partition coefficient for each dipeptide was calculated from the overall energy change associated with moving the relevant gas‐phase conformational distribution into waterandinto 1‐octanol. These energies were computed using solvation contributions based upon the solvent accessible molecular surface area and two sets of empirical parameters. In these initial studies, gas‐phase conformational minima were generated using systematic search methods. While the standard error in the computed logPvalues was disappointing, reasonable agreement was observed between calculated and experimental logPvalues for the set of model dipeptides, especially when specific hydration interactions involving polar fragments were correctly included in the empirical solvation term. These results indicate that the physical basis of many correction factors employed in the ClogP algorithm for computing logPprobably arise from neglect of the redistribution of conformer populations as flexible molecules partition between water and 1‐octanol.
An Ab initio study of tautomerism between formhydroxamic acid and formhydroximic acid
Authors: Yuanqi Tao , Wengui Duan
Published: January 2005

Ab initio MO calculations including electron correlation with the 4‐31G and 4‐31G** basis sets were performed in order to study the formhydroxamic acid‐formhydroximic acid tautomerism. The geometries, relative energies, and activation energy of the tautomer and transition state were determined. Based on total‐energy calculations at the MP4/4‐31G**//RHF/4‐31G** plus the scaled zero‐point vibration energy level, the energy of formhydroxamic acid is determined to be lower than that of formhydroximic acid by 40.7 kJ/mol. The activation energy of the formhydroxamic acid‐formhydroximic acid tautomerism via a 1,3‐intramolecular hydrogen shift is 151.4 kJ/mol. © 1992 John Wiley & Sons, Inc.
Substituents effects in phospha alkynes: A computational investigation
Authors: Jayasuriya Keerthi
Published: January 2005

Ab initio self‐consistent field (SCF) molecular orbital calculations were carried out at the MP2/431G* level to determine the effect of substituent groups, F, NH2, OH, CH3, CH2CH, and HCC—on the CP triple bond. Although there are considerable differences between the electronegativities of these substituent groups, a characteristic feature found in phospha alkyne derivatives is the weak sensitivity of the CP bond length to the substituent at the carbon atom. The molecular electrostatic potential analysis clearly reflects the strength of the electronegativity of these substituent groups and their ability to attract the polarizable charge from the CP triple bond. MEP analyzes further indicates that these derivatives of phospha alkynes are most likely to attract incoming electrophiles to the π‐electron region of the Ctriple bond. Transition metals are coordinated “sideways” with phospha alkynes, and in this configuration, the lone‐pair electrons of the phosphorus atom are unlikely to interact with the metal. © 1992 John Wiley & Sons, Inc.
Transition‐state structures for the reaction between styrene and tbutyl cyanoketene: Theoretical evidence for antarafacial characteristics in a π2 + π2 thermal cycloaddition
Authors: Rzepa Henry S. , Wylie William A.
Published: January 2005

Semiempirical AM1 SCFMO models for the cycloaddition between monosubstituted alkenes (RCH = CH2, R = Me, Ph, CF3) and tbutyl cyanoketene predict the lowest‐energy transition state to be relatively polar and asynchronous in character and to have a cis relationship between the R and the tbutyl groups, in agreement with the experimentally determined product for R = Ph. We interpret this stereochemistry as resulting from the presence of a significant antarafacial component in the transition state, which enables these two bulky groups to adopt pseudoequatorial positions in which steric interactions are minimized. The alternative higher energy trans geometry forces the R and the cyano groups to adopt more sterically hindered pseudoaxial positions. Alternative biradical‐like transition states inferred by others from ab initio MCSCF calculations on the reaction between ketene and ethene do not retain any significant antarafacial component on the ketene and, therefore, form less satisfactory models for this specific reaction. © 1992 John Wiley & Sons, Inc.
Consistent parametrization of semiempirical MO methods
Authors: Jug Karl , Krack Matthias
Published: January 2005

The parametrization of semiempirical molecular orbital methods is reviewed. The parametrization procedures are classified in three categories. The newly proposed category of consistency of parameters in a row of elements is applied in SINDO1 to the Si atom. The calculations on test molecules and silicon clusters demonstrate that significant improvements in accuracy can be obtained in this way. © 1992 John Wiley & Sons, Inc.
A semiempirical SCF MO study of the interaction of odorant molecules with a biological substrate
Authors: Wu C. S. , Myers L. J. , Worley S. D.
Published: January 2005

The AM1 semiempirical SCF MOmethod developed by Dewar and co‐workers has been employed to compute possible interaction processes of the odorant molecules cocaine, methyl benzoate, and benzaldehyde with the biological substrate lysine. The only process predicted as possible in each case was nucleophilic attack on the carbonyl carbons of each odorant by the nitrogen lone pairs on lysine. The remote amino group of lysine in each case was predicted to react with lower activation enthalpy than did the α‐amino group, a prediction consistent with preliminary experimental data from these laboratories. Although the computed activation enthalpies were high (ca. 40 kcal mol−1) for the gas‐phase processes, it is conceivable that such processes could occur by alternate pathways with considerably lower ctivation energies in solvated media such as exists in the presence of mucus‐containing olfactory binding protein in vertebrate olfactory reception. © 1992 John Wiley & Sons, Inc.
Prototropic changes in cationic base‐pair adducts. II. Guanine methylation
Authors: Ford George P. , Wang Bingze
Published: January 2005

AM1 calculations have been used to study the effects of CH attachment on the structures, energies, and, in some cases, proton transfer reactions of guanine cytosine base pairs. Methylation of both the guanine 3‐ and O6‐positions is predicted to lead to chemically significant concentrations of intermediate base pairs arising from proton transfer from the guanine 1‐ to the cytosine 3‐position. The possible biological implications of such intermediates in nucleic acids is discussed in relation to the formation of either doubly abasic sites or abasic sites opposite potentially miscoding DNA lesions. © 1992 John Wiley & Sons, Inc.
Spin‐independent three‐body effective valence‐shell operators: Application to molecular oxygen
Authors: Kanzler Alfred W. , Freed Karl F. , Sheppard Maurice G.
Published: January 2005

A mathematical construction is presented that uniquely defines a set of spin‐independent effective valence‐shell Hamiltonian (Hv) three‐body matrix elements. These spin‐independent Hv matrix elements separate direct and exchange portions of the three‐body Hv matrix elements and therefore provide the most natural form for comparisons with parameterization schemes of semiempirical electronic structure methods in which the three‐body matrix elements are incorporated into semiempirical one‐ and two‐body Hamiltonian matrix elements in an averaged manner. Ab initio Hv three‐body matrix elements of O2 are computed through third order of quasidegenerate perturbation theory and are analyzed as a function of internuclear distance and atomic orbital overlap to aid in understanding how these three‐body matrix elements may be averaged into semiempirical one‐ and two‐body matrix elements. © 1992 John Wiley & Sons, Inc.
Magnetic susceptibility of some derivatives of cellulose and their mixtures: Theory and experiment
Authors: Sadykova A. Yu. , Saykaeva A. S. , Kostochko A. V. , Glebov A. N. , Moozyukov V. G.
Published: January 2005

The calculations of the magnetic susceptibility (χ) of the selected derivatives of cellulose have been performed using the localized molecular orbitals with the basis set of Gaussian functions. The advantages of the variational procedure in the framework of the approximation of the additivity of the localized molecular fragments for the evaluation of the magnetic susceptibility and nuclear magnetic shielding (σ) and the comparison with the NMR of high‐resolution data have been discussed. Theoretical values for χ of the 50 sizable organic molecules have been presented. © 1992 John Wiley & Sons, Inc.
Broken symmetry solutions of the two‐dimensional extended hubbard model and their instability conditions
Authors: Yamamoto Shoji , Ozaki Masa‐Aki
Published: January 2005

Instabilities of the restricted Hartree–Fock (HF) state of the two‐dimensional extended Hubbard model under doping are studied with the linear response theory employing the linearized Bethe–Salpeter equation. Boundaries of the instabilities for the ordering vectors q = Q ≡ (π, π) and q = Q0 ≡ (0, 0) are given in terms of the interaction strength parameters at various doping levels. With doping, dominant instabilities generally change from ones for q = Q to ones for q = Q0. Broken symmetry phases obtained from the instabilities are also studied and classified using the group‐theoretical technique. For q = Q, two more new phases are obtained in addition to the four nonmagnetic and five magnetic phases that have been already derived by one of the authors. For q = Q0, three nonmagnetic and five magnetic phases are obtained. Deriving the explicit forms of the charge current and spin current operators in the HF approximation, charge current and spin current densities in the broken symmetry states are discussed in detail. © 1992 John Wiley & Sons, Inc.
A regional embedding method
Authors: Zou P. F.
Published: January 2005

A new variational embedding method is derived. This method couples Nesbet's use of theR‐matrix in the determination of the electronic structure of a crystal with the energy variational technique. The procedure is based on the observation that in many cases the properties for a spatial region of a system change by relatively small amounts when the region is transferred to another system. The transfer of the region from one system to another is accomplished by the embedding potential that is obtained by the inversion of theR‐matrix and its energy derivative. It is shown that the interaction between two connected regions can be written as a surface term that is obtained by the continuity conditions on the wave function and its derivative on the surface. The existence of an identity resolution on the surface is demonstrated and this result is used to derive theR‐matrix and its inverse. An application of this method to His given, which shows that the method is accurate and reliable if one chooses the appropriate basis set to construct theR‐matrix and to perform the variation. © 1992 John Wiley & Sons, Inc.
Some solutions in the graph theory of alternant benzenoids
Authors: Hall George G.
Published: January 2005

A new formulation of the eigenvector equations for certain polymeric molecules is given. The electronic bands for the infinite molecules are deduced. For the finite molecules, the use of ghost molecules allows an exact specialization of the infinite to the finite eigenvector equations. The complete solution of the equations depends on the solution of a simple transcendental equation. Approximate solutions of this equation are given that bracket the accurate solutions so that, for molecules with many repeated moieties, the approximations become good. The general theory is illustrated by applications to the chrysene series and to the polyphenyls. © 1993 John Wiley & Sons, Inc.
The fundamental syntopy of quasi‐symmetric systems: Geometric criteria and the underlying syntopy of a nuclear configuration space
Authors: Mezey Paul G. , Maruani Jean
Published: January 2005

Point symmetry is a discrete concept; A nuclear configuration for a given stoichiometry either has or has not a particular point symmetry. By contrast, both static and dynamic properties of actual molecules exhibit continuous features. Using the formalism of fuzzy‐set theory, we had previously proposed the concept of syntopy as a continuous extension of the symmetry concept for quasi‐symmetric systems: This was based on an energetic criterion taking into account the energy costs of nuclear rearrangements. This extension of symmetry was necessarily dependent on the considered electronic state: For a given geometric arrangement of the nuclei, the energy cost of some rearrangement is dependent on the actual potential surface, that is, on the electronic state, in the Born–Oppenheimer approximation. In the extension of the syntopy model reported in the present work, we consider a syntopy criterion that is common to all electronic states. The syntopy thus defined—called the fundamental syntopy of the reduced nuclear configuration space—is independent of the potential surface and of the electronic state: It is defined only in terms of a geometric condition, which makes it more appropriate to rationalize mesoscopic structures. This new syntopy model provides a connection between all possible syntopies generated by the various potential‐energy surfaces supported by the considered family of atomic nuclei. © 1993 John Wiley & Sons, Inc.
On the applicability of a nonlinear Schrödinger equation to the determination of rate constants in Kramers' theory of chemical reactions
Authors: Schuch Dieter
Published: January 2005

In 1940, Kramers derived an expression for the rate constant of chemical reactions in viscous media. In this theory, chemical reactions are modeled as Brownian processes in the presence of potential barriers. The derivation of the rate constant is based on the solution of the Smoluchowski equation, a Fokker–Planck‐type equation in position space. Kramers' theory has been confirmed for reactions in systems ranging from nuclear processes to biochemical problems. The reaction rate can be obtained from the diffusion currents appearing in the Smoluchowski equation. A Smoluchowski‐type equation in position space, similar to the one applied by Kramers, has been used to find a nonlinear Schrödinger equation (NLSE) for dissipative, frictionally damped systems, taking into account wave‐particle duality. For several potentials, the NLSE can be solved exactly, and analytic expressions for the currents, appearing in the Smoluchowski equation and necessary to determine the rate constants, can be obtained. These currents are not only stationary, but can also be time‐dependent. It will be shown that, essentially, the determination of the time‐dependence of the currents can be reduced to the solution of Newton‐type equations of motion. © 1993 John Wiley & Sons, Inc.
Perturbation expansions, symanzik scaling, and padé‐type approximants: The anharmonic oscillator problem
Authors: Chandra A. K. , Bhattacharyya K.
Published: January 2005

The problem of representing an observable F(z) in the Padé scheme from its formal perturbative (Taylor) expansion in z is considered. It is demonstrated how the representation could be improved by incorporating in a simple manner, in the course of constructing such approximants, the knowledge of asymptotic (z → ∞) power‐law behavior of F(z). Comparison with the usual approximants is made with a thorough numerical survey on error estimates and variations of error with z, input information, and quantum number. Spectacular performance of the new strategy is exemplified. Test calculations chiefly involve various properties of the first five eigenenergy states of the quartic anharmonic oscillator system. A few consistency requirements, including the virial theorem, are also studied. © 1993 John Wiley & Sons, Inc.
Husimi representation for stationary states
Authors: Harriman John E. , Casida Mark E.
Published: January 2005

This paper considers a Husimi representation of quantum mechanics in which the (stationary) state of a system or ensemble is described by a Husimi function and an observable is described by a phase space function or distribution such that the expectation value of the observable is given by an integral over phase space of the product of that function or distribution and the Husimi function. The density matrix, Wigner function, and Husimi function are considered to be alternative ways of describing the state of a system or ensemble, and methods of recovering the Wigner function or density matrix from the Husimi function are discussed. The classical limits of the Wigner and Husimi functions and of the relationship between them are considered. © 1993 John Wiley & Sons, Inc.
Coupling coefficients for systems with two open electronic shells: Transition metal ions with pM dN configuration
Authors: Plakhutin B. N. , Arbuznikov A. V. , Trofimov A. B.
Published: January 2005

We derived the necessary conditions to which the vector coupling coefficients (VCC) amn and bmn, describing atomic L, S‐multiplets of pMdN and dNs1 configurations (1 ⩽ N ⩽ 9, 1 ⩽ M ⩽ 5), should satisfy. It is shown that for two‐open‐shell systems under consideration the unknown VCC should satisfy not only usual restrictions resulting from the spheric symmetry, but also some additional equation introduced in the present paper in the form of a postulate. VCC obtained were used for the ab initio calculations (by the general SCF coupling operator method) of several transitionmetal atoms and ions with electronic configurations 3d14p1, 3p43d3, and 3p53d3. To check the presented theory, we carried out a detailed comparison between these results and analogous data, obtained by the atomic Roothaan‐Hartree‐Fock method [2]. © 1993 John Wiley & Sons, Inc.
Unrestricted Hartree–Fock method for infinite systems with antiferromagnetic array: Analysis of antiferromagnetic state of trans‐polyacetylene
Authors: Yoshizawa Kazunari , Ito Akihiro , Tanaka Kazuyoshi , Yamabe Tokio
Published: January 2005

An improved unrestricted Hartree–Fock (UHF) crystal orbital method for infinite one‐dimensional systems having antiferromagnetic spin array is presented. This variational version of the UHF method is composed of two steps of self‐consistent‐field (SCF) calculations. The second SCF equation is to be solved using the canonical transformation between specific crystal orbitals around the Fermi level of the first conventional SCF solution. The energy gain and the forbidden band gap (correlation gap) associated with the hypothetical antiferromagnetic state of trans‐polyacetylene are examined as an example. © 1993 John Wiley & Sons, Inc.
Time scales and other problems in linking simulations of simple chemical systems to more complex ones
Authors: Clementi Enrico , Corongiu Giorgina , Estrin Dario , Hollauer Eduardo , Stradella Omar G.
Published: January 2005

We shall start with very small systems like H2 and H3, computed with very accurate methods (Hylleraas–CI) or atomic systems up to Zn with accurate methods (CI), then move to more complex ones, like C60, but now with somewhat less accurate methods, specifically Hartree–Fock with density functionals, the latter for the correlation energy but not for the exchange energy. For even more complex tasks like geometry optimization of C60, we have resorted to even simpler and parametrized methods, like local density functionals. Then, we could use quantum mechanics either to provide interaction potentials for classical molecular dynamics or to directly solve dynamical systems, in a quantum molecular dynamics approximation. Having demonstrated that we can use the computational output from small systems as input to larger ones, we discuss in detail a new model for liquid water, which is borne out entirely from ab initio methods and nicely links spectroscopic, thermodynamics, and other physicochemical data. Concerning time scales, we use classical molecular dynamics to determine friction coefficients, and with these we perform stochastic dynamic simulations. The use of simulation results from smaller systems to provide inputs for larger system simulations is the “global simulation” approach, which, today, with the easily available computers, is becoming more and more feasible. Projections on simulations in the 1996–1998 period are discussed, new computational areas are outlined, and a N4 complexity algorithm is compared to density functional approaches. © 1993 John Wiley & Sons, Inc.
4‐Currents in relativistic quantum chemistry
Authors: Avery John , Antonsen Frank , Shim Irene
Published: January 2005

Some topics in relativistic quantum chemistry are reviewed with special emphasis on 4‐currents and 4‐potentials. It is shown that, both in molecular quantum theory and in solid‐state physics, calculations can include relativistic and magnetic effects by means of 4‐currents without an excessive increase in complication, provided that 4‐component Dirac spinors are used rather than the Pauli approximation. © 1993 John Wiley & Sons, Inc.
Looking at atomic orbitals through fourier and wavelet transforms
Authors: Fischer Patrick , Defranceschi Mireille
Published: January 2005

Solutions of Hartree–Fock equations expressed as Gaussian functions are studied in various spaces: position, momentum, and position–momentum spaces. The use of the wavelet transform allows one to visualize position and momentum characteristics of atomic orbitals on the same drawing. A complementary viewpoint is then obtained on top of usual position and momentum representations. Applications to Gaussian “atomic” orbitals modeled as one‐dimensional functions are performed. © 1993 John Wiley & Sons, Inc.