bluuebunny/crossref_metadata_2025 huggingface dataset:
Fourth‐order diagrammatic MB–RSPT calculations of the correlation energy: N2, CO, F2 and the reaction energy of the process ½F2 + ½H2 = HF
Authors: Kellö Vladimir , Urban Miroslav
Published: December 2004

The correlation energies obtained by the fourth‐order diagrammatic perturbation theory were analyzed for three diatomic molecules: N2, CO, and F2. The results were compared with correlation energies obtained previously for the ten‐electron hydrides HF, H2O, and NH3. The relative importance of contributions which arise from the double excitations, from the quadruple excitations, as well as from the renormalization term was investigated. It is shown that for the diatomic molecules under study these contributions are considerably larger than for the ten‐electron hydrides not only in absolute value but also in percentage: they represent about 3, 3, and 5%, respectively, of the valence shell correlation energy obtained by the perturbation theory up to the fourth order. A careful analysis of the fourth‐order correlation effects is also presented for the reaction energy of the process ½H2 + ½F2 = HF.
Algebraic reductions of the real symmetric 4 × 4 secular problem
Authors: Linderberg Jan
Published: December 2004

Procedures for the construction of the eigenvector matrix and the spectrum of 4 × 4 real and symmetric matrices are given. The Lie algebra of the group O(4)† is used as well as the relation to O(3)†. Perturbations are analyzed in terms of the group parameters.
Theoretical study of excitation energies of some CoF6n− complexes
Authors: Miyoshi Eisaku , Takada Toshikazu , Obara Shigeru , Kashiwagi Hiroshi , Ohno Kimio
Published: December 2004

Ab initio LCAO SCF MO calculations are carried out on the ground state and d–d transition states of CoF64−, CoF63−, and CoF62− complexes with a basis set of more than double‐zeta quality. To obtain a better description for the excitation energy of d–d transition states, a ligand field configuration interaction calculation is performed. The calculation is improved further by taking into account the correlation energy in the central metal atom and it gives good results for the observed excitation energies. Especially, the excitation energies for the states which have the same configuration as the ground state agree with observed ones within about 1 kK. The excitation energies of several charge transfer states in the CoF62− complex are also computed at the level of SCF MO calculation and the assignments are made for the four strong bands observed in the energy region higher than the weak d–d bands.
Additivity of resonance energy in benzenoid hydrocarbons
Authors: El‐Basil Sherif
Published: December 2004

A simple method is described for the calculation of resonance energies (RE) of linear acenes based on their number of Kekulé structures. The values obtained for the first five linear acenes are used to graph–theoretically calculate RES of a wide variety of benzenoid hydrocarbons. Excellent linear relationships are found between RES and each of A‐II, graph‐theoretical (GT), Hess–Schaad (HS), and Dewar resonance energies (SCF). These relations apply to 42 hydrocarbons and lead to the following equations: A‐II = 0.084RE + 0.080 (0.9999); GT = 0.072RE + 0. 135 (0.9832); HS = 0. 106RE + 0. 169 (0.9889); and SCF = 0.316RE + 0. 166 (0.9899). Correlation coefficients are shown in parentheses. A linear relation also exists between RES and the square roots of the wavelengths of the UV spectra of hydrocarbons of the linear acenes and phene series. Least‐squares analysis of the data leads to the following equation: RE= 0.412(λ)½ −15.479, with a correlation coefficient equal to 0.9903, in which λ is the wavelength of the β band of the UV spectra of these hydrocarbons. The method predicts no resonance energies for both open chain polyenes and the radialenes.
Direct calculation of resonant states in reactive scattering. Application to linear triatomic systems
Authors: Basilevsky M. V. , Ryaboy V. M.
Published: December 2004

A direct method for calculating resonant states in reactive scattering is suggested, permitting us to obtain the characteristics of multichannel resonances (partial width amplitudes). The method is based on the construction of a Laurent expansion of the scattering matrix S(ϵ −iΓ/2) in the complex plane. The position of the poles of the S matrix are derived by solving the dynamical problem with complex energy values. The residue at the pole gives all the information concerning the partial widths. The method is applied to a linear triatomic reactive scattering problem. The properties of the resonant states in the H + H2 system are calculated as an example. Two broad resonances are found which have not been reported in previous calculations. The interference of overlapping resonances is shown to have a profound effect on the energy dependence of the transition probabilities.
Some aspects of bonding and binding in polymeric chains
Authors: André J. M. , Brédas J. L. , Delhalle J.
Published: December 2004

The status of theoretical calculations on polymers is illustrated by two specific problems. The first one is the interpretation of ESCA results on polymers by suitable ab initio calculations. The second problem is the very timely one of bond alternation in polymers. The reliability of theoretical calculations at various levels and the possible central role of electron correlation are discussed.
Hydrogen bonding in clusters and molecular crystals
Authors: Karpfen A. , Beyer A. , Schuster P.
Published: December 2004

Ab initio calculations on the Hartree–Fock level are used to study the effects of cooperativity in ternary complexes and in infinite chains on the example of hydrogen fluoride. SCF energy partitioning demonstrates that polarization forces dominate three‐body energies in these aggregates. The crystal orbital method is applied to investigate the structural differences between dimers and molecular crystals.
Mechanism of chromosome banding: A phenomenological approach
Authors: Talekar Manjubala S. , Talekar Subhash V.
Published: December 2004

A quantitative expression is derived, using Fick's diffusion law, for varieties of experimentally observed band patterns in metaphase chromosomes.
Tautomerism of pyrimidines and purines in the gas phase and in low‐temperature matrices, and some biological implications
Authors: Shugar David , Szczepaniak Krystyna
Published: December 2004

Infrared spectra in the NH, OH, and CO stretching regions are reviewed for various methylated and halogenated 2(4)‐oxopyrimidines and uracils, as well as other nucleic acid derivatives, in the vapor phase and in low‐temperature matrices. The 2‐oxopyrimidines are predominantly in the enol form both in the vapor phase and in low‐temperature matrices. By contrast, the 4‐oxopyrimidines exhibit comparable populations of the keto and enol forms, with KT ≈ 1–2, and a difference in chemical binding energy between the two forms in the gaseous phase of the order of 1–2 kcal/mol. The observed tautomeric equilibria in the gas phase point to the need for a drastic revision of interpretations of theoretical methods, and simultaneously provide the appropriate quantitative data necessary for testing the results of quantum mechanical calculations. In sharp contrast to other heterocyclic systems, several of the bases found in natural nucleic acids were found to exist predominantly in the keto or amino forms, as in the solution phase. In particular, uracils exist predominantly in the keto form. This has made possible, for this class of compounds, to evaluate the heats of sublimation and vaporization, and to relate these data to hydrogen bonding and stacking interactions in the condensed phases. Examples are presented of base analogs which do exhibit appreciable tautomerism in solution. Some biological implications of the foregoing are presented in relation to the types of heterocyclic bases found in natural nucleic acids, and to concepts of spontaneous and induced mutagenesis.
Estimation of dissociation energy of alkali diatomics using an extended Linderberg relation
Authors: Raina V. , Sane K. V. , Saxena R. P. , Srivastava P. K.
Published: December 2004

The ground state wave function of a model potential consisting of a zero‐range square well joined to a Coulomb tail is used in a two equivalent centre problem to evaluate the overlap integral (S) and the resonance integral (β). It is shown that an extended Linderberg relation of the form β = K/R (dS/dR) is generally well obeyed. The extended relation has been used within a LCAO framework to obtain dissociation energies of the homonuclear diatomic molecules of the alkali atoms.
Electron correlation described by an extended geminal model
Authors: Røeggen I.
Published: December 2004

A scheme for obtaining approximate solutions of the electronic Schrödinger equation is proposed in terms of an extended geminal model. The model is formulated within the context of the method of moments. The advocated approach is nonvariational, but size‐consistent as long as breaking and/or formation of new bonds can be grouped into at most four‐particle systems. The correlation energy, with respect to a separated pair approximation, is obtained as a sum of intrapair corrections and a sum of interpair corrections. An approximate model for calculating interpair correlation energies is introduced. In a test calculation on LiH, it is demonstrated that this approximate model recovers 98.0% of the correlation energy obtainable by a complete configuration interaction calculation.
Improved Hylleraas calculations for ground state energies of lithium ISO–electronic sequence
Authors: Ho Y. K.
Published: December 2004

The 2S ground state of lithium iso–electronic sequence is calculated by the use of Hylleraas‐type wave functions. A 92 term one‐spin wave function was used for lithium atom calculations. The energy obtained was −7.478031 a.u. as compared with the previous best value of −7.478025 a.u. calculated by Larsson. In addition, improved energies for Z = 4 to 8 were calculated by the use of 60 term wave functions. This work thus provides the lowest ab initio ground state energies for lithium sequence to date.
Compton profiles for ejected electrons: Determination of momentum densities
Authors: Dal Cappello C. , Tavard C.
Published: December 2004

Electron Compton scattering effects usually lead to the determination of momentum densities in atoms and molecules by cross‐section measurements on scattered electrons. Similar information is also shown to be directly available from the study of ejected electrons. The proposed treatment results from a simple alteration of the impulse assumptions and appears to give a satisfactory representation of ejected profiles for medium and high energy electron scattering. Preliminary investigations are discussed here for hydrogen and helium atoms.
Simple derivation of conditions for instability in the Hartree–Fock and projected Hartree–Fock schemes
Authors: Löwdin Per–olov , Calais Jean–Louis , Calazans Jacques M.
Published: December 2004

The conditions for instability of solutions of Hartree–Fock and projected Hartree–Fock equations are derived in a form involving finite real symmetric matrices. These conditions are also expressed in terms of the Fock–Dirac density matrix, both at the spin–orbital and at the orbital level. The particular variations which give rise to the so‐called singlet and triplet instabilities are described.
Catecholamine interaction with anionic sites—A model study
Authors: ŠOlmajer T. , Kocjan D. , Hadži D.
Published: December 2004

Interactions of catecholamines with acidic sites in the biophase are likely to be involved in the control of the receptors activity as well as in storage and transport mechanisms. In view of the importance of the phenomena a model study of ethanolamine–phosphate complexes was made. The electrostatic interaction energy surface was calculated in the charge density multipole expansion approximation with terms up to quadrupole. The consecutive minimal energy conformation shows the importance for the interaction with the biophase of the catechol ring steric and electronic relation to the side chain.
Exponential transformation of molecular orbitals. II. General formulation for UHF calculations and application to diatomics and molecular fragments
Authors: Bruceñta A. , Vermeulin P. , Archirel P. , Berthier G.
Published: December 2004

The exponential transformation of the molecular orbitals, that has been previously used to achieve a process with a convergence of quadratic quality in SCF closed‐shell calculations [J. Chem. Phys. 72, 1452 (1980)] has been extended to UHF determinantal wave functions built from different orbitals for different spins. Explicit formulas are given for the first and second derivatives of the energy to be varied. The method is illustrated by UHF calculations for systems described as standard singlets (Li2 and F2) or triplets (NH) at the RHF approximation level, as well as for CH, CH2, CH3 molecular fragments in their valence states.
Large orders and summability of eigenvalue perturbation theory: A mathematical overview
Authors: Simon Barry
Published: December 2004

The study of large orders of perturbation theory in various problems is reviewed: the anharmonic oscillator, the Zeeman and Stark problems, double wells, and the like. Padé and Borel summability and path integral ideas are discussed. The rigorous results on the subject are summarized.
Padé summations for the real and imaginary parts of atomic stark eigenvalues
Authors: Reinhardt William P.
Published: December 2004

The problem of direct Padé summation of Rayleigh–Schrödinger perturbation coefficients for the H atom Stark effect is discussed in light of the location of the Padé representation of the expected Bender‐Wu branch cuts in the complex F (field) plane. The resulting conclusion that such direct summation of the divergent perturbation expansion [for the real part of E(F)] might give suggestive, but certainly not convergent, results is documented. The relationship between the Padé problem of representation of cuts and corresponding problems in L2‐discretized scattering theory is pointed out. An alternative Padé expansion with newly placed cuts is proposed which is expected to, and indeed does, have excellent convergence properties for real F. The real and imaginary parts of the Stark broadened and shifted hydrogenic ground state are thus obtained directly from the (real) Rayleigh–Schrödinger perturbation coefficients for a large range of fields indicating the power and simplicity of the method.
Perturbation theory via the Ricatti equation
Authors: Au C. K.
Published: December 2004

We present summary results of a bound‐state perturbation theory for a one‐space and one‐time dimension nonrelativistic spinless (Schrödinger) particle, a relativistic spinless (Klein‐Gordon) particle, and a relativistic spin‐half (Dirac) particle in central fields due to scalar or fourth‐component vector‐type interactions for an arbitrary bound state. This is accomplished by the reduction of the wave equations to Ricatti form. This enables a decoupling between the pair of coupled first order differential equations on the large and small component Dirac wave functions or a decoupling of the second order differential equation in the Schrödinger or Klein‐Gordon equations. All corrections to the energies and wave functions, including corrections to the positions of the nodes in excited states, are expressed in quadratures in a hierarchial scheme, without the use of either the Green's function or the sum over intermediate states. For the ground states of a Schrödinger particle, it is possible to extend this technique to multidimension in the case where the perturbation is due to noncentral fields, for example, in the problem of a nonrelativistic hydrogen atom in a linear combination of multiple fields.
Some properties of reduced density matrices, correlated and uncorrelated, for pure and mixed states
Authors: Goscinski Osvaldo
Published: December 2004

Some results pertaining to the form of Γ(1) usually assumed in density functional theory, the properties of natural states of mixed states, their variational characterization, and a representation of pure states through reproducing kernels are given.
Momentum space properties of various orbital basis sets used in quantum chemical calculations
Authors: Simas Alfredo M. , Thakkar Art J. , Smith Vedene H.
Published: December 2004

Momentum expectation values (pk), values of the momentum density P(p) at selected points, and coefficients in the MacLaurin and asymptotic expansions of P(p) are used to test the quality of various orbital basis sets previously used for the atomic helium Hartree‐Fock problem. The wellknown position‐space defects of Gaussian‐type orbital expansions are shown to have their momentum‐space counterparts. Expansions of even‐tempered Slater‐type orbitals are found to be rather accurate. The exponentially damped rational function is found to be the outstanding two‐parameter unconventional orbital.
Note on calculations by hypervirial relations and sufficient conditions for these relations: Box potential and harmonic oscillator models
Authors: Terasaka Toshitaka , Sakamoto Kazuyoshi
Published: December 2004

The calculations by the diagonal and the off‐diagonal hypervirial relations and by the sufficient conditions for these relations have been performed for the one‐dimensional box potential and the harmonic oscillator models. In the case of the box potential model, the variation method gave the unsymmetrical wave functions for trial functions though it gave the best energies, but some of these hypervirial calculations gave the symmetrical functions and therefore they showed the exact expectation values of x, though they did not give the best energies. On the contrary, in the case of the harmonic oscillator model such a discrepancy for wave function and excitation energy did not happen. For the box potential model the expectation values of some operators were evaluated and compared with the results by the exact solution and the variation method. A weakness of the off‐diagonal hypervirial calculation was pointed out and the removal of this weakness was tried. The effectiveness of these calculations were investigated.
Hypervirial analysis of enclosed quantum mechanical systems. IV. Further comments
Authors: Ferńndez Francisco M. , Castro Eduardo A.
Published: December 2004

New formal results regarding the hypervirial analysis of enclosed systems are given. Novel applications are presented and several previous equations are reformulated in a more appropriate form.
Molecular tight‐binding method. II. One‐ and many‐electron method for excess electron bands of molecular crystals
Authors: Stolarczyk Leszek Z.
Published: December 2004

An ab initio method for calculating the energies of excess‐electron bands in a molecular crystal is developed. These energies represent the electron affinities of a crystal. The present method employs a tight‐binding approximation to describe the molecules in a crystal and a set of local functions to describe the excess electron. One‐ and many‐electron formulations of the method are given, the latter takes into account the effect of polarization of all the molecules in the crystal by the excess electron. A scheme for approximate determination of the electronic‐correlation corrections to the one‐electron bands is developed and applied to calculation of the excess‐electron bands in the HCP helium crystal.
Particlelike excitations in the polypeptide chain model
Authors: Fedyanin V. K. , Yakushevich L. V.
Published: December 2004

The α‐helical protein molecule is modeled by a one‐dimensional crystal chain with three peptide groups in the lattice cell and with the nearest and third neighbor interactions. Three types of solitonlike solutions describing excitation motion along the model have been obtained. The first one is three modulated waves which are in phase. The other two are modulated waves with phase shifts equal to ⅔π and \documentclass{article}\pagestyle{empty}\begin{document}$ {\textstyle{4 \over 3}} $\end{document}π, respectively.
Some comments about tensor virial theorem and linear transformations
Authors: Fernandez Francisco M. , Castro Eduardo A.
Published: December 2004

The tensor virial theorem is discussed in relation to different transformation matrices which are compatible with it.
Derivation of theoretical formulas for resonance integrals from Heisenberg equation of motion
Authors: Lipiński Józef , Leszczyński Jerzy
Published: December 2004

On the basis of the Heisenberg equation of motion and the Linderberg–Seamans approximations, useful formulas for, β‐resonance integrals in the all‐valence NDO‐like semiempirical methods have been derived. The case of s, p, d basis sets of atomic orbitals has been considered.
Instabilities of the symmetry‐adapted restricted‐Hartree–Fock ground state in infinite polyenes. II. Nonsinglet instabilities
Authors: Castan̄o O. , Karadakov P.
Published: December 2004

The stability of the possible ground states of an infinite linear equidistant polyene model has been discussed in the PPP approximation of the unrestricted‐Hartree–Fock (UHF) method. The emphasis has been placed upon the investigation of nonsinglet (triplet) instabilities: the spin‐density waves (SDW's) and the spin‐bond‐order alternation waves (SBAW's). For physically realistic parameter sets the SDW ground state of the infinite linear equidistant polyene has been shown to be lowest in energy. Whereas the symmetry‐adapted restricted HF (RHF) solution (SAS) has been shown to be unstable to the formation of SDW's and SBAW's for all investigated parametrizations, the bond‐order alternation wave (BAW) solution has been found to be unstable to the formation of SDW's, but stable to the formation of SBAW's; in fact, the BAW's and the SBAW's have been shown to yield identical gap widths and ground‐state energies (at least in the PPP method). It has been shown that there exist such sets of semiempirical parameters for which the charge‐density wave (CDW) ground state is nonsinglet stable irrespective of the existence of an energetically advantageous SDW solution for the same parameter set.
Orbital symmetry, orbital stability, and orbital pairing rules for organic reactions in the ground state
Authors: Yamaguchi Kizashi
Published: December 2004

A generalization of the Hartree–Fock molecular orbital (MO) theory for treating diradical intermediates was explained pictorially by drawing molecular orbitals of diradical species such as ring‐opened trimethylene. The generalized MO theory applied to elucidate electronic mechanisms of concerted, ionic, radical, and ion‐radical reactions of organic reactants in the ground state. Generalized MO computations revealed the most essential characteristics of these reactions and mutal relationships between the worlds of Woodward–Hoffmann and Hughes–Ingold. Generalized MO studies supported our orbital symmetry, stability and pairing rules for concerted, ionic and radical reactions in the ground state, respectively. An extension of MO treatments to excited states reactions was briefly pointed out in relation to the density and spin correlation functions by the multireference CI wave functions.
Method of recurrent construction of Löwdin spin‐adapted wave functions. I. Addition and subtraction operators
Authors: Panin A. I.
Published: December 2004

Addition and subtraction operators defined on some subspaces of the full CI space are introduced. It is shown that the effect of these operators on Löwdin many‐electron wave functions consists in adding or removing an electron without destroying spin symmetry. Upward and downward recurrence relations for the Sanibel‐type coefficients are presented. A strategy for employing the Löwdin functions for the matrix element evaluation and some special decomposition of the fermion creation–annihilation operators are discussed.
B‐DNA structural determination of Na+ counterions at different humidities, ionic concentrations, and temperatures
Authors: Clementi E. , Corongiu G.
Published: December 2004

Seventeen different computer experiments are presented and analyzed. In each experiment a three‐turn B‐DNA double helix fragment interacts with a variable number of water molecules (from 60 to 1200), with a variable number of sodium ions (from 30 to 63), at one or more temperatures (280, 300, 320 K). The experiments are performed with the Monte Carlo method using quantum‐mechanically derived potentials. In the analysis of the experiments we partition the water molecules (and the corresponding interactions) as being either bound or in the first solvation shell or in the groove regions relative to DNA; for the former two cases, the number of water molecules and the water interaction energy are reported for selected atoms or groups of atoms. The entire study is condensed into eight tables. The use of these tables is exemplified by considering, in detail, some of the trends emerging from these experiments. The analyses are complemented by graphical representations presented either to elucidate the very complex pattern of hydrogen bonded water molecules, or to show the statistical distributions of the oxygen and hydrogen atoms of the water molecules.
Symmetry analysis of cycloadditions and electrocyclic reactions
Authors: Sun Chia‐Chung , Zhang Jing‐Chang , Jin Guang‐Zhu , Sun Wei‐Guo
Published: December 2004

The groups with local symmetries are employed to explore the intrinsic symmetries of various kinds of cycloadditions to become apparent ones. For the electrocyclic reactions, the concept of local symmetry can still be applied equivalently, but no new result can be achieved. Furthermore, the local symmetries are generalized to the systems as a many body treatment performed by Matsen.
Theoretical study of the adsorption of silver atoms on the (111) face of silicon
Authors: Julg André , Allouche Alain
Published: December 2004

The adsorption of one or many silver atoms on a (111) silicon face (reduced to 61 dangling atomic orbitals) is investigated by means of a self‐consistent Hartree–Fock method parametrized from atomic and thermodynamical data. The valley sites (above three Si atoms) are favored over the top sites (above one Si atom). The extrapolation of the results obtained for several structures corresponding to the adsorption of n = 1, 2, 3, 4, 6, and 7 Ag atoms allows us to conclude that the most stable structures correspond: for \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = \frac{1}{3} $\end{document} to linear Ag chains (3 × 1 phase), for \documentclass{article}\pagestyle{empty}\begin{document}$ \theta = \frac{2}{3} $\end{document} to an honeycomb lattice (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 3 \times \sqrt 3 $\end{document} phase), and for θ = 1 to a centred hexagonal lattice (\documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt 3 \times \sqrt 3 $\end{document} phase), the Ag atoms located at the centers of the hexagons being beneath the plan of the hexagons. The adsorption energies corresponding to the various θ are practically equal (ca. 3 eV/Ag). The net charges of Ag atoms are equal to 0.35.
Peierls instability and vibrational spectra of polyacetylene
Authors: Ovchinnikov A. A. , Belinskii A. E. , Misurkin I. A. , Ukrainskii I. I.
Published: December 2004

It is shown that the Peierls instability in conjugated polymers is modified by the interaction of π electrons. This modification gives rise to the absence of a soft mode of stretching CC vibrations. Taking into account electron correlations we obtain reasonable agreement between the calculated and measured frequencies of the carbon skeleton of polyacetylene with all the CC bonds being equal in length. It is shown that the conclusion for the bond length alternation in polyacetylene does not follow from the experimental data on the vibrations of polyacetylene.
Symmetric group graphical approach to the direct configuration interaction method
Authors: Duch Wlodzislaw , Karwowski Jacek
Published: December 2004

An approach to the configuration interaction method based on symmetric groups (SGA) is developed. The formalism is an alternative of the unitary group approach (UGA). In many aspects the present formulation seems to be superior to UGA. In particular, in SGA the orbital and the spin parts of the configuration state functions may be processed separately. In consequence its graphical formulation is much simpler and the coupling constant expressions are more compact than the UGA analogs. A special emphasis is put on direct CI implementations. In addition to formulas for coupling constants, explicit expressions allowing for separation of external and internal space contributions are also presented.
Peierls‐ and Mott‐type instabilities in one‐dimensional chains—coexistence or contradiction
Authors: Kventsel G. F.
Published: December 2004

Two possible effects—Peierls instability (bond alternation) and Mott‐type correlation spin ordering—leading to metal–insulator transition (energy gap formation) in one–dimensional chains, have been considered using UHF treatment of the Hubbard‐type Hamiltonian. It has been found that in the framework of approximations applied these two instabilities are mutually exclusive.
Calculation of the 4S4P0 spectrum of lithiumlike ions by the Hylleraas method
Authors: Larsson Sven , Crossley Richard
Published: December 2004

The energies of the five lowest 4S and 4P0 states for three‐electron ions for 3⩽Z⩽10 have been calculated by the Hylleraas method. The largest basis set used contained 97 terms with odd as well as even powers of rij. The change of scale r′ = Zr was applied to the Hamiltonian so that the same basis sets could be used for all the three‐electron ions leading to great savings in computing time.
Integrals Irs and Jrs used in the computation of magnetic quantities by means of the McWeeny coupled perturbation method
Authors: Baba‐Ahmed A. , Gayoso J.
Published: December 2004

We have shown that integrals Irs and Jrs which occur in coupled Hartree–Fock perturbation, on a basis of gauge invariant atomic orbitals with the London approximation and neglect differential overlap, can be reduced, by appropriate transformations, to the overlap integral type. The computational program of Srs, Irs, and Jrs integrals is elaborated for Slater‐type atomic orbitals. The process proposed presents a double advantage: it is extended over the entire Periodical Table and does not use the analytical formulas of Mulliken.
Some analytical properties of the dilated SCF Equations
Authors: Froelich Piotr , Brändas Erkki
Published: December 2004

The self‐consistent field (SCF) equations for many‐electron systems, suitable within the complex‐coordinate method, are derived. The formulation is based on a general bivariational theorem for non‐Hermitian operators, with an emphasis on the analytic structure invoked by the complex dilation of the total Hamiltonian. The dilation structure of the resulting SCF equations is stressed and the concomitant analytical properties are discussed. The solutions are classified with respect to these properties, and interpreted in terms of a general form of the symmetry dilemma. The role of the dilated SCF equations for resonance calculations is discussed.
Clebsch–Gordan coefficients for chains of groups of interest in quantum chemistry. III. The point symmetry groups
Authors: Kibler M. R.
Published: December 2004

This work amalgamates some basic elements defined in the first paper of this series and in related papers with the theory of coupling coefficients for an arbitrary group with the view of generating the Clebsch–Gordan coefficients and V symbols for point symmetry groups. The connection between Clebsch–Gordan coefficients and V symbols is established for an arbitrary group in a form that reduces to the one known for the chain SU(2) ⊃ U(1). The Clebsch–Gordan coefficients and V symbols of any point symmetry group G are shown to be obtainable from Clebsch–Gordan coefficients and \documentclass{article}\pagestyle{empty}\begin{document}$ {\bar f} $\end{document} symbols of the chain SU(2) ⊃ G through the resolving of a system of nonlinear equations.
Correlation effects in externally perturbed many‐electron systems
Authors: Sadlej Andrzej J.
Published: December 2004

Different methods for the calculation of the electron correlation contribution to atomic and molecular properties are analyzed and evaluated. The methods based on the self‐consistent solution of the external perturbation problem are shown to offer several formal and computational advantages. The analysis of the correlation perturbation series for properties of many‐electron systems indicates the importance of the appropriate treatment of unlinked diagrammatic contributions. In particular, the standard limited configuration interaction scheme based on single and double substitutions in the reference function may significantly suffer from the erratic treatment of unlinked clusters and needs to be corrected appropriately. The basis set choice for the calculation of highly accurate values of properties is also discussed. In order to circumvent the dimensionality problem the use of basis sets with explicit dependence on the external perturbation strength is recommended and methods for their choice and optimization are presented. A particular attention is paid to the many‐body perturbation theory involving singly and doubly substituted intermediate states and based on the coupled Hartree–Fock solution for the one‐electron perturbation problem. Different computational aspects of this method are discussed and compared with other techniques currently in use.
Characteristic operators and unitarily invariant decomposition of hermitian operators
Authors: Au‐Chin Tang , Hong Guo
Published: December 2004

A set of characteristic operators {F} is proposed for performing the decomposition of p‐particle Hermitian operators {Dp} to constitute irreducible components {D} of the unitary group D = FDp, q = 0,1,2,…,p. For a deeper expolration of the properties of the characteristic operators, a few theorems are presented. As an illustration, the expected values for symmetric p‐particle Hermitian operators are obtained as a number of terms having invariant group‐theoretical meaning.
Momentum space properties of atoms
Authors: Harmalkar Anjali , Simas Alfredo M. , Smith Vedene H. , Westgate William M.
Published: December 2004

A systematic investigation of momentum densities Π(p), Compton profiles J(q), and internally folded densities B(r) has been made for the ground states of the atoms from H to Kr. The data are presented in reduced form by means of the characteristic momentum p* = q* and length r* = 1/p*, where p* = [J(0)/2πΠ(0)]½. The results indicate that p* and J(0) contain the gross qualitative behavior of the atomic properties in momentum space. They also show that subtle effects over and above the gross scale and size are mostly periodic.
A simple treatment of intermolecular interactions: Synthesis of ab initio calculations and combination rules
Authors: Hoinkis J. , Ahlrichs R. , Böhm H.‐J.
Published: December 2004

A new technique for a simple and efficient treatment of intermolecular interactions is proposed and tested. The method is based on an approximation of the first order SCF term ESCF(1) which is the most structured contribution to the total interaction. ESCF(1) is represented by a site–site potential V of (exp, 1/R)‐type, which accounts for the exchange plus penetration and the long range Coulomb forces (by means of a point charge model). The individual contributions to V are obtained by means of combination rules from corresponding site parameters of interacting molecules. The site parameters are consequently molecular and not intermolecular properties and can conveniently be determined by probing a molecule with appropriate test particles. Site parameters are reported for He, Ne, Ar, N2, CO, CO2, CS2, and HCl. Comprisons show close agreement of V with E which in turn is close to ΔESCF if polarization and charge transfer effects are small.
C2V Insertion pathway for BeH2: A test problem for the coupled‐cluster single and double excitation model
Authors: Purvis George D. , Shepard Ron , Brown Franklin B. , Bartlett Rodney J.
Published: December 2004

The coupled‐cluster single and double excitation model (CCSD) is applied to an energy path for the insertion of Be into H2 and compared to the full configuration interaction (FCI) and full valence–multiconfiguration self‐consistent field (FV–MCSCF) results. This model problem is a severe test of a single‐reference‐function correlated method since two configurations are heavily weighted in the FCI description. CCSD is demonstrated to describe the FCI results using a single reference function which, however, changes orbital characteristics along the sampling path. In this case CCSD gives excellent agreement with the FCI results.
Use of effective core potentials in perturbation corrections to the Koopmans theorem: Vertical ionization potentials of Cl2, ClN3, and ClNCO
Authors: Langhoff Stephen R. , Jaffe Richard L. , Chong Delano P.
Published: December 2004

The valence‐shell vertical ionization potentials of Cl2 were calculated by perturbation corrections to the Koopmans theorem using a traditional effective core potential based on a Phillips–Kleinman derivation and an improved effective core potential obtained by Christiansen, Lee, and Pitzer. Comparison of the results with an all‐electron calculation demonstrated the reliability of the Christiansen–Lee–Pitzer effective core potential, which was then used to compute the vertical ionization potentials of ClN3 and ClNCO. The results shed new light in the interpretation of the photoelectron spectra of these molecules.
Quantum study of the ground state of a series of unsaturated boron–nitrogen compounds by the MNDO method. I. Geometries and stabilities
Authors: Maouche Boubekeur , Gayoso José
Published: December 2004

A MNDO study of molecular geometries, enthalpies, formation, atomization, bond separation, and hydrogenation of a series of unsaturated boron–nitrogen compounds, linear with two and three members and cyclic with three, four, five, and six members are presented. For all these molecules, MNDO calculations are in excellent agreement with available ab initio calculations or experimental data. The high rotational barrier in aminoborane H2BNH2, 30.6 kcal/mol, and the length of bond in iminoborane HBNH, 1.183 Å, imply strong double and triple BN bond character in these two molecules. In the odd membered heterocycles, examination of the molecular geometries and energies of equilibrium states shows that in all cases, the stability of the compounds grows with the number of boron atoms and decreases with that of the nitrogen atoms. Moreover, compared study of the two BN‐fulvenes with their homologous hydrocarbon shows that only BN (BB)‐fulvene has a polyenic structure similar to that of fulvene.
Hypervirial theorems for some simple quantum chemistry systems
Authors: Fernández Francisco M. , Castro Eduardo A.
Published: December 2004

A very general form of the hypervirial theorems, which can be applied to several quantum systems of great interest for the theoretical quantum chemists is presented.
Multiconfigurational Hartree–Fock response functions
Authors: Jørgensen Poul , Swanstrøm Peter , Yeager Danny L. , Olsen Jeppe
Published: December 2004

The linear, quadratic, and cubic response of a multiconfigurational Hartree–Fock state to a time independent one‐electron perturbation has been derived. A comparison between the exact response functions as obtained from Rayleigh–Schrödinger perturbation theory and the multiconfigurational Hartree–Fock response functions allows a identification of matrix elements of the perturbation operator between the ground and excited states and between excited states. We discuss some ambiguities which result from such an identification.
Excited states of linear polyenes in the SCF–RPA method
Authors: Baldo Marcello , Pucci Renato , Tomasello Pasquale
Published: December 2004

In the framework of the PPP Hamiltonian, we have studied the low‐lying spectra of all trans linear polyenes with the dielectirc function method. It is shown that higher order processes, not included in the RPA scheme as local field correction (LFC) and self‐energy (SE) effects can be introduced in a effective way by a suitable parametrization of the residual coulomb interaction. This parametrization is fixed along the polyene series both for singlet and triplet states, at variance with previous RPA calculations. Comparison with the most refined CI calculations, as well as with the experimental findings shows very good agreement. Furthermore, chain length and geometry dependence of the electron–electron correlation is briefly discussed.
Calculation of excited‐state properties of some small molecules: Comparative study of the CNDO/S and CNDO/2‐vn−1 potential methods
Authors: Sannigrahi A. B. , Mukherjee D. C. , De B. R.
Published: December 2004

The transition energy and geometry of the lowest excited (nπ*) singlet and triplet states of CO, CS, HNO, H2CO, HFCO, and F2CO molecules are calculated by CNDO/S and CNDO/2‐VN−1 potential methods, and the results are compared with those of experimental and ab initio theoretical studies, wherever available. In the calculation of the vertical transition energy, the performance of the CNDO/S method is seen to be generally more satisfactory than that of the CNDO/2‐VN−1 potential method, while the reverse is true for the excited‐state geometry. The CNDO/S method as such fails to describe the geometry of the excited state, but a combined version (CNDO/S‐2) of CNDO/S and CNDO/2, as well as the CNDO/2‐VN−1 potential method is fairly successful in this regard.
Ab initio MO Calculations of benzene + TCNE and naphthalene + TCNE complexes with STO‐3G π‐split basis set
Authors: Watanabe Yoshitaka , Kashiwagi Hiroshi
Published: December 2004

Ab initio SCF MO calculations have been carried out on benzene + TCNE (tetracyanoethylene) and naphthalene + TCNE complexes with the STO‐3G, STO‐3G π‐split (STO‐3G for π orbitals and a split basis for π orbitals), and 4–31G basis sets. The interaction energy, gross charges, dipole moment, and the electron density in the middle plane of the complexes have also been evaluated. The STO‐3G π‐split basis set is appropriate for the calculation of large π–π stacking complexes from two points of view, production of reliable results and ease of computations. The approximation scheme based on the semiorthogonalized orgitals is revealed to be very efficient to save CPU time and storage in such calculations. The stable conformation and the charge‐transfer interaction of the two complexes are discussed on the basis of the calculated quantities.
Reduction of the excited state into the ground state of a super‐Hamiltonian
Authors: Katriel Jacob
Published: December 2004

A reformulation of the Hylleraas–Undheim–MacDonald variational procedure for excited states, involving the application of Löwdin's supersecular equation to a variational problem concerning the ground state of an appropriate super‐Hamiltonian, is proposed. Some formal applications are presented.
Electronic correlation contribution to the three‐body potentials for water trimers
Authors: Habitz P. , Bagus P. , Siegbahn P. , Clementi E.
Published: December 2004

A number of trimers of water molecules have been computed with an extended basis set in the Hartree–Fock and in the direct CI approximations. It has been verified that the three‐body interaction energy can be calculated within the Hartree–Fock method. Therefore, the correlation corrections to the Hartree–Fock level are essentially additive and do not contribute significantly to three‐body effects.
Calculations of core‐electron binding energies by transition operator method followed by Rayleigh–Schröudinger perturbation theory
Authors: Chong Delano P. , Minato Tsutomu , Mukherjee Prasanta K.
Published: December 2004

Vertical ionization potentials for core orbitals of HF, H2O, and CO are calculated with the ab initio transition operator method. The results are improved by third‐order Rayleigh–Schrödinger perturbation theory. The effect of basis sets is also investigated. The computed core‐electron binding energies are compared with the experimental values and with those obtained by other theoretical methods. The comparison shows that the present approach leads to reliable core ionization energies, the average absolute deviation from experiment being only 0.4 eV for the cases studied.
Molecular basis set generation: Accurate slater basis sets for LiH− ground and excited state and Li2− ground state
Authors: Adamowicz Ludwik , McCullough E. A.
Published: December 2004

A procedure for generating basis sets for diatomic molecule electronic structure calculations is described. In essence, this procedure maps the results of nearly exact numerical Hartree–Fock calculations into basis set form. Two applications of the procedure are proposed: (a) generation of very high accuracy basis sets, and (b) investigation of basis sets for unusual systems. The latter application is illustrated by some results for diatomic anions.
Expectation values and density matrices in the Coupled‐Cluster theory
Authors: Kümmel H. G.
Published: December 2004

A scheme for calculating expectation values in coupled‐cluster wave functions is given. The unlinked terms originating from the norm of the wave function are eliminated. Hermiticity and trace conditions for the density matrices are exhibited in such a way as to guarantee their conservation in any reasonable truncation scheme.
Theoretical study of equilibrium CoF bond distance of CoF6n− complexes (n = 4, 3, and 2) in crystals
Authors: Miyoshi Eisaku , Kashiwagi Hiroshi
Published: December 2004

The equilibrium CoF bond distance and the a1g vibrational frequency of CoF6n− complexes (n = 4, 3, and 2) in crystals were investigated from a theoretical point of view. Ab initio SCF MO calculations were performed for the isolated CoF6n− complexes in order to obtain the potential energy curves against the CoF distance. These potential energy curves were improved by considering the effect of the surrounding ions. It is shown that the effects of the next‐nearest neighbors (eight K+ ions) and the next‐next‐nearest neighbors (six Co2+ ions) are very important in determining these properties for “ionic” KCoF3 crystal. On the other hand, for Cs2CoF6 crystal, in which the CoF bond has considerable degree of covalency, the shape of the potential energy curve is almost completely determined by the nonelectrostatic component of the intramolecular interaction of the isolated CoF62− unit.
Parametrization and comparative analysis of the BFGS optimization algorithm for the determination of optimum linear coefficients
Authors: Kari Roy
Published: December 2004

This paper examines the numerical performance of the BFGS variable‐metric algorithm and compares this performance with that of the DFP, SR1, and OC algorithms. Numerical results indicate that the BFGS algorithm is far superior to the DFP and SR1 algorithms and comparable to the OC algorithm. Although the BFGS algorithm offers a viable method for the direct determination of localized molecular orbital coefficients, the method is not yet competitive with the more traditional methods.
Calculation of localized molecular orbitals
Authors: Leonard Joseph M. , Luken William L.
Published: December 2004

Two techniques are presented for reducing the effort required to determine localized orbitals based on the energy or density criteria. The first, population weighted editing of the electronic repulsion integrals, reduces the effort required for each iteration of the localization procedure. The second, damping/extrapolation of the transformation matrix, reduces the number of iterations required to reach convergence. Numerical results are provided for methane and formaldehyde (for the editing method) and for carbon monoxide and boron fluoride (for the damping/extrapolation technique).