bluuebunny/crossref_metadata_2025_split huggingface dataset:
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

AbstractThe 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.
Padé summations for the real and imaginary parts of atomic stark eigenvalues
Authors: Reinhardt William P. 
Published: December 2004

AbstractThe 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

AbstractWe 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.
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

AbstractMomentum 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

AbstractThe 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.
Molecular tight‐binding method. II. One‐ and many‐electron method for excess electron bands of molecular crystals
Authors: Stolarczyk Leszek Z. 
Published: December 2004

AbstractAn 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

AbstractThe 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.
Derivation of theoretical formulas for resonance integrals from Heisenberg equation of motion
Authors: Lipiński Józef , Leszczyński Jerzy 
Published: December 2004

AbstractOn 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

AbstractThe 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

AbstractA 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

AbstractAddition 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

AbstractSeventeen 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

AbstractThe 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

AbstractThe 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

AbstractIt 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

AbstractAn 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

AbstractTwo 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

AbstractThe 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

AbstractWe 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

AbstractThe 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

AbstractThis 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

AbstractDifferent 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

AbstractA 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

AbstractA 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

AbstractA 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

AbstractThe 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.