bluuebunny/crossref_metadata_2025_split huggingface dataset:
Free‐electron model for hyperpolarizability of the π‐electron system in benzene
Authors: Sen Purnendranath , Basu Sadhan 
Published: December 2004

AbstractThe hyperpolarizabilities of benzene have been calculated using a free‐electron model for the π‐electron system. The first hyperpolarizability is identically zero. For the second hyperpolarizability only the components γzzzz; γxxxx; γyyyy; γzzxx; γzzyy; γxxyy are non‐zero. Some of these γ quantities show dispersion near the characteristic absorption band of the benzene molecule. The polarizability α of the π‐electron system also shows similer dispersion.
Derivation of the Clebsch–Gordan coefficients by means of projection operators
Authors: Calais Jean‐Louis 
Published: December 2004

AbstractThe Clebsch–Gordan coefficients for the coupling of two angular momenta are derived by using the projection operator technique, developed by Löwdin. The derivation is done in two steps; first for the so‐called principal case, i.e. k = m, then for the general case with an arbitrary m. Two different derivations are given for the principal case, a direct one and one based on a recursion procedure. The general case is obtained from the principal case with a step‐down operator.
A variation principle for energy differences between states of two different Hamiltonians
Authors: Marron Michael T. , Weare Johan H. 
Published: December 2004

AbstractA modification of a variation principle due to Delves, is derived which permits the direct calculation of energy differences between states of two different Hamiltonians: [Δ ℋ︁] = 〈X0| ℋ︁x – Wx|X1〉 – 〈Y0|ℋ︁y – Wy|y1〉 + 〈X0| Δ ℋ︁|Y0〉 · 〈X0| Y0〉−1. Δ ℋ︁ = ℋ︁y – ℋ︁x, |X0〉 and |Y0〉 are the wave functions for the X and Y states and |X1〉 and |Y1〉 are functions defined in the text. The principle is applied to a few simple examples.
Comment on a perturbation treatment of the ground state of two‐electron atoms using the coordinates r< and r>
Authors: White Ronald J. , Ramaker D. E. , Schrader David M. 
Published: December 2004

AbstractA perturbation variation treatment of two‐electron atoms using exp (–αr< – βr>) as the zeroth order wave function is presented. The parameters α and β are variationally determined and the results are compared with the “physical” choice α = Z, β = Z – 1, and with Z−1 theory. The energy is given through fifth order in the perturbation.
A minimum principle for molecular systems allowing the use of discontinuous wave functions
Authors: Hall G. G. , Hyslop J. , Rees D. 
Published: December 2004

AbstractIn this paper the minimum principle proposed for atomic systems by Hall, Hyslop and Rees [1] is generalized to molecules. It is shown that this generalization retains the advantage of admitting the use of a larger class of trial wave functions, for example those with discontinuities, than is possible in the usual minimum energy principle. The further advantage that the upper bounds obtained by this treatment are always at least as good as those of the Rayleigh‐Ritz method is also preserved.The theory is applied to the H ion, potential energy curves are obtained for various “cut‐off” wave functions, and the equilibrium internuclear distance is calculated. The optimization of the “cut‐off” region so that the upper bound is minimized is also discussed.
A multi‐configuration LCAO–MO study for complex unsaturated molecules. I. General theory and its application to the benzene anion
Authors: Nakayama M. , I'Haya Y. J. 
Published: December 2004

AbstractA multi‐configuration LCAO–MO approach using a π‐bond order–bond length linear relation is introduced to predict the geometrical structures for the electronic ground and excited states of unsaturated hydrocarbons. The procedure is designed to include configuration interaction in each iterative computation where the π‐electron approximation is employed under the Pariser–Parr type semi‐empirical treatment.The π‐bond order–bond length relation is determined as rpq = 1.523 – 0.193Ppq, when the bond lengths of ethylene, benzene and naphthalene are used and the groundstate functions including the singly and doubly excited configurations are taken into account to obtain the bond orders Ppq.The iterative calculation is applied to the ground state and the two lowest excited states of the benzene anion in both D6h and D2h molecular geometries. The geometrical structures and the π‐electron energies are computed for the ground and excited states of the anion; for the latter, two types of configuration species are used. It is found that the first lowest excited state is not subjected to the Jahn–Teller effect and the calculated excited state energies do not agree with the observed values (c. 1.0 ∼ 2.5 eV higher than the observed values). The latter point is discussed in detail. It is also found that the resultant ground state energy depression due to configuration mixing is not very large and the two types of configuration species used give different CI effects on the energy levels of the two lowest excited states of the anion.Finally, the stabilization energy due to the Jahn–Teller distortion is estimated for the ground state of the anion.
Hartree–Fock MO–LCAO equations with charge‐dependent atomic integrals
Authors: Karlsson Göran 
Published: December 2004

AbstractThe Hartree–Fock equations are derived in the MO‐LCAO approximation for the case when the integrals (except overlap integrals) over the atomic orbitals are charge‐dependent. It is shown that inclusion of the overlap matrix in the iterative procedure gives equations which are too complicated for the simple model under consideration. The approach is applied to the VESCF method in the PPP scheme.
Inter‐level differences in iron group atomic systems in the extended method of calculation
Authors: Jucys A. P. , Stasiukaitis V. J. 
Published: December 2004

AbstractThe extended method of calculation has been applied to calculate the inter‐level differences of the shell of 3d‐electrons in the iron group atomic system. The hydrogen‐like radial orbitals have been used. The results are compared with those obtained by ordinary methods of calculation as well as with experimental data.
Theoretical calculations on σ‐systems, part 1: Ethers and chloro‐substituted ethers
Authors: Ghosh Kunal , Bhattacharyya Subirnath , Sen Purnendranath 
Published: December 2004

AbstractThe charge on each atom of some ethers and chloro‐substituted ethers, their dipole moments and the quadrupole coupling constants of the chloroethers have been calculated with the method suggested by Del Re. There appears to be an intimate connection between the charge density on the oxygen atoms and the capacity of forming hydrogen bond.
Molecular formation and electron correlation in HeH+
Authors: Banyard K. E. , Baker C. C. 
Published: December 2004

AbstractA one‐centre CI wave function for HeH+ reported by Stuart and Matsen for 0.1 ⩽ R ⩽ 5.0 has been analysed in detail from the viewpoint of molecular formation. Further, by means of a natural orbital analysis, it was possible to obtain some measure of the electron correlation contained within such wave functions for various R values. These effects were illustrated by means of a series of difference maps for the electron density. One‐ and two‐particle expectation values were obtained as a function of R. Thus, it was possible to study several aspects of the influence of the proton on the electron charge cloud as we pass from He through to the united atom Li+. The occupation numbers within the natural expansions were compared with those which arise from a similar analysis of a two‐centre wave function for HeH+. The “character” of such wave functions for HeH+, and also for He and Li+, were analysed and compared.
A new SCF procedure and its applications to ab initio calculations of the states of the fluorosulphate radical
Authors: Hillier I. H. , Saunders V. R. 
Published: December 2004

AbstractAb initio calculations using a small Gaussian basis set, including 3d orbitals on the sulphur atom, have been performed on the fluorosulphate radical and the related ions SO3F+ and SO3F−. A new SCF procedure is described and applied to the open shell cases discussed here. The results are compared with recent CNDO calculations and with the experimental transition energies of the radical.
Wellenmechanische Behandlung der Protonisierung von F‐ und CH3‐monosubstituierten Äthylenen
Authors: Fratev F. , Janoschek R. , Preuss H. 
Published: December 2004

AbstractThe systems C2H4F+ and C2H4CH have been investigated by the SCF–MO‐P (LCGO) method. It will be shown that the results agree with the empirical rule of Markownikoff. An explanation of the rule of Markownikoff is given by means of the computed results.
Molecular modelling with spherical Gaussians
Authors: Ford B. , Hall G. G. , Packer J. C. 
Published: December 2004

AbstractA mathematical model of a molecule is proposed. The electronic structure is described using a molecular orbital wave function constructed from a small number of spherical Gaussians with optimized parameters. The models exhibit the desirable properties of numerical stability, objectivity and transferability. Results are given for CH4, C2H6, cyclo‐propane, H2O, CH2O and C2H4. They can be given a chemical interpretation in terms of chemical bonds, lone pairs and atomic cusps.
Note on the space part of anti‐symmetric wave functions in the many‐electron problem
Authors: Slater John C. 
Published: December 2004

AbstractIt is pointed out that if a many‐electron antisymmetric wave function is expanded as a sum of spin‐product functions, each multiplied by a function of coordinates, the resulting functions of coordinates have many of the same useful features found with the symmetric and antisymmetric functions representing singlet and triplet states in a two‐electron system. For finding the energy, or any function of coordinates only, in the approximation in which spin‐orbit interaction is neglected, one such function of coordinates can be used, the spins being disregarded. Simple procedures allow one to find matrix components of such operators as S2 and L . S from the functions of coordinates. These procedures are much easier to visualize than the use of projection operators, the permutation group, or other methods in current use. The general procedures are illustrated by application to the three‐electron problem of the lithium atom, as treated by Lunell, Kaldor, and Harris, and their application to the contact hyperfine structure is pointed out.
Time‐dependent Hartree–Fock calculations in the Pariser–Parr–Pople model. Applications to aniline, azulene and pyridine
Authors: Jørgensen Poul , Linderberg Jan 
Published: December 2004

AbstractPropagator or Green's function methods are used to analyze the time‐dependent Hartree–Fock model. The non‐hermitian matrix problem for the time‐dependent Hartree–Fock solution is reduced to a problem related only to hermitian matrices. Particular attention is given to the calculation of oscillator strength in different approximations. The connection between the stability of the Hartree–Fock solution and the solution of the time‐dependent Hartree–Fock problem is demonstrated. The results of numerical calculations are given for aniline, azulene and pyridine.
Time–dependent quantum theory I. An absorber in an intense radiation field
Authors: Schurr J. M. 
Published: December 2004

AbstractA function analogue of the formal operator theory of Goldberger and Watson for the decay of prepared states is developed with a modification that permits treatment of degenerate, interacting intermediate states. The theory is applied to the problem of absorption of radiation by an absorber in a very intense monochromatic beam. In particular, a simple two‐level absorber in a resonant monochromatic beam of sufficient intensity to induce transitions from the ground state at a rate exceeding the spontaneous emission rate from the excited state, but still lying well below the optical frequency characterizing the transition, is investigated with the conclusion that the absorption cross‐section falls off with the one‐half power of the incident intensity. Conditions for the possible experimental verification of this result are presented.
Computation of LCAO wave functions for ground states of polymers and solids
Authors: Andre J. M. , Delhalle J. , Fripiat J. G. , Leroy G. 
Published: December 2004

AbstractThe LCAO form of the Hartree–Fock method is discussed in its application to crystals. General formulae are given for obtaining Fourier coefficient of electronic density (in direct space) as well as of the band structure (in momentum space). Finally, it is shown that in its LCAO form, Slater–Hartree–Fock equations are very simple and that this method is of interest for numerical applications. Special integrals occurring in this formalism are evaluated for a Gaussian basis in the last part of this paper.
Perturbational calculation of the exchange forces in the two lowest states of the hydrogen molecule
Authors: Piela Lucjan 
Published: December 2004

AbstractThe interaction energies in the ground (X1Σ) and the first excited (b3Σ)states of the hydrogen molecule were calculated using the modified Jansen and Byers Brown perturbation method. Calculations were performed for nine values of the internuclear distance R in the range 5 a.u. ≦ R ≦ 9 a.u. The present results were compared with the interaction energies calculated by four other perturbation methods as the expectation values of the H – E0 operator with the function accurate up to the first order. The results show that the method can give satisfactory values of the interaction energies.
On the theory of electron correlation in atoms and molecules: Relation between cluster expansion theory and the correlated wave functions method
Authors: Roby Keith R. 
Published: December 2004

AbstractA relation between the cluster expansion theory of many electron wave functions and the correlated wave functions method is established. In this way, the theoretical basis of the method is elucidated and the approximations involved in its application become apparent. General forms of the correlated wave function, differing in certain important respects from that form usually assumed, are derived.
Time‐Dependent quantum theory. IV. Effect of lattice relaxation on the optical spectra
Authors: Schurr J. Michael 
Published: December 2004

AbstractThe absorption and emission spectra of a diatomic “molecule” connected to an unstrained linear crystal are calculated for the circumstance where the diatomic undergoes a change of equilibrium internuclear separation in the electronic transition. The expansion (or contraction) of the diatomic results in a frequency dependent line‐width in the customary Lorentzian expression, and is manifested in the absorption spectrum as an asymmetric tailing to the blue, and in the emission spectrum as an asymmetric tailing to the red. The interaction of the diatomic with the lattice also produces a blue‐shift of the absorption spectrum and a red‐shift of the emission spectrum. An important consequence of the asymmetry is the apparent loss of integrated intensity of the line. The striking similarity, both in the width and the over‐all shape, of the emission line calculated here with those observed in the Vegard–Kaplan band of N2 dissolved in rare gas crystals is discussed.
Laplace transform method in two‐photon spectroscopy theory
Authors: Makhanek A. G. , Korolkov V. S. , Fedorov A. F. 
Published: December 2004

AbstractThis paper formulates a number of problems of the two‐photon spectral theory and characterizes the analytical methods of solving them as worked out by the authors. The efficiency and wide application of the Laplace transform method is demonstrated by the most typical examples of the cross section analytical calculations of two‐photon processes, dynamical polarizability, and bremsstrahlung at the scattering.
Spin‐Free quantum chemistry. XX. The alternancy quantum number
Authors: Matsen F. A. , Welsher T. L. 
Published: December 2004

AbstractThe assignment of the alternancy quantum number to the N‐electron states of neutral alternant hydrocarbons is discussed within the spin‐free unitary group formulation. Alternancy is defined with respect to both molecular graphs and molecular orbital eigenvalues. The properties of the molecular orbitals of alternant hydrocarbons result from requiring the assignments in terms of atomic orbital and molecular orbital Gel'fand states to be consistent. State correlation arguments are used to remove the arbitrary phase factor present in previous treatments.
A variational treatment of the potential of impurity ions in semiconductors with spatially variable dielectric constants
Authors: Csavinszky P. 
Published: December 2004

AbstractThe primary purpose of the present paper consists in obtaining a correction to Dingle's potential for a (point) impurity ion (embedded) in Si or Ge. This goal is accomplished by making use of a variational principle in taking into account the effect of the spatial variation of the dielectric constant in the respective medium. It is found that the resulting impurity‐ion potential can be represented as the product of Dingle's potential and a factor which, with increasing distance from the charged impurity, approaches unity. The secondary purpose of the present paper consists in suggesting a way for the modification of an impurity‐ion potential that has been obtained previously with a boundary condition, that, in retrospect, is open to criticism. It is shown that the modified impurity‐ion potential can be represented as the product of the author's previous potential and a factor which, with increasing distance from the charged impurity, approaches unity.
Evaluation of some trigonometric series occurring in infinite chain polymer calculations
Authors: Delhalle J. , Delhalle S. , Harris F. E. 
Published: December 2004

AbstractClosed formulas are presented for a number of trigonometric series whose summands contain inverse powers of one or two quadratic forms. It is shown how to arrange the formulas to remove apparent numerical instabilities, and useful numerical approximations are identified together with the range of their validity.
Density matrix methods in orbital optimization for MCSCF calculations
Authors: Garrod Claude 
Published: December 2004

AbstractThe problem considered is that of selecting the finite orbital basis which will minimize the energy in a given size CI calculation. (1) A one‐body operator is defined which has as eigenfunctions the desired optimal basis. The operator is defined in terms of the basis which leads to a self‐consistency problem of Hartree‐Fock type. (2) A method of successive orbital rotations is defined which is shown to have desirable convergence properties.
Incompletely symmetric non‐bloch electron states in perfect cubic crystals. I. Eigenproblem and its solution
Authors: Kunert A. 
Published: December 2004

AbstractIn the studies on impure metals where the perturbation potential due to the impurity has symmetry of the point group of the crystal, subdivision of the electron density of the pure metal into irreducible representations of the point group is of significance. A method is presented for the calculation of wave functions of the perfect cubic crystal which transform according to the incompletely symmetric irreducible representations of the point group. The functions were evaluated in the LCAO approximation using s‐type AOS for the face centered cubic lattice. These are in the form of standing waves, and their coefficient functions are linear combinations of the products of the cubic harmonics of a suitable type and the spherical Bessel functions. Properties of the solutions obtained were examined. Numerical calculations were made for four irreducible representations of the point group.
Incompletely symmetric non‐bloch electron states in perfect cubic crystals. II. Density of states in the FCC lattice
Authors: Kunert A. , Olszewski S. , Wierzbicki A. 
Published: December 2004

AbstractThe electron density of both the perturbed and unperturbed crystal can be made up of individual terms described by the basis functions of irreducible representations of the crystal point group. For the perfect FCC lattice, a detailed comparison was made between the density of states, calculated in terms of the LCAO wave functions classified according to representations of the crystal point group, and the density of states, provided by the Bloch theory.
Determination of the charge distribution in nonmetallic crystals. I. Theory and application to tetrahedrally coordinated solids
Authors: Julg André , Marinelli Francis , Pellégatti Alain 
Published: December 2004

AbstractA SCF method using localized molecular orbitals which are built up on hybrid atomic orbitals is proposed to obtain the charges in infinite crystals. Hybrid orbitals are built up on a minimal STO basis set. The formalism has been adapted in order to take into account the periodicity of the system and its infinite size by introducing the Madelung constant. The total energy is given by an infinite sum of terms each corresponding to the energy of a bond in the crystal field. Minimizing this bond energy with respect to eigenvectors it is straightforward to obtain the electronic charges, whence the polarity, i.e., the ionicity, of bonds. In this first paper, we study and discuss the polarity of bonds in zincblende and wurtzite‐type compounds built up on first and second row elements. Our values are coherent between themselves and in agreement with other authors' results. The connection with electronegativity and polarizability is discussed.
Regularity and asymptotic properties of the discrete spectrum of electronic hamiltonians
Authors: Combes J. M. , Seiler R. 
Published: December 2004

AbstractWe analyze the electronic part of diatomic molecular Hamiltonians as a function of the internuclear distance, x. We prove analyticity outside x ≠ 0 of eigenvalues in the discrete spectrum and differentiability up to second order for the associated projection operators. Furthermore, it is shown that for large internuclear distances they converge to eigenvalues and eignprojectors of the separated atoms.
Accurate and stable numerical Hartree–Fock calculations for atoms. I. The 1s2 ground state of H−, He, Li+, and Be++
Authors: Roothaan C. J. Clemens , Soukup George A. 
Published: December 2004

AbstractNew techniques have been developed for atomic self‐consistent‐field calculations by numerical integration. For the origin and tail regions we present analytical expansions which can represent the solutions to high accuracy. For the numerical integration in the central region a five‐point generalization of the Numerov formula is used; the error term is of the order h10. While this formula is unstable if used in the customary way, stability is achieved by using a Gaussian elimination technique. The new procedures are tested on the ground state of the helium isoelectronic series; with 251 integration points all quantities are calculated with an inherent accuracy of better than 10–11.
Isoscalar factors for tetragonal, orthorhombic, monoclinic and triclinic shubnikov point groups
Authors: Kotzev J. N. , Aroyo M. I. , Angelova M. N. 
Published: December 2004

AbstractThe relations between isoscalar factors for corepresentations of antiunitary magnetic point groups are discussed in the case of associated corepresentations. The tables of the isoscalar factors for the single‐ and double‐valued corepresentations of all tetragonal, orthorhombic, monoclinic, and triclinic Shubnikov point groups are given. Some peculiarities of the calculation method of the isoscalar factors for corepresentations are considered.