Hartree-Fock Ground State Research Articles

Atomic correlation energies. III. Second-order corrections to the Hartree-Fock ground state of B, C, N, O and F

For pt.II see ibid., vol.11, no.12, p.2069 (1978). The authors have calculated the second-order perturbative corrections to the Hartree-Fock ground state energies of B, C, N, O and F. The basis used was sufficiently large to assure truncation errors less than 10-3 au in all cases. They found EB(2)=-0.1113 au, EC(2)=-0.1476 au, EN(2)=-0.1840 au, EO(2)=-0.2540 au and EF(2)=-0.3206 au which represent 89.2%, 94.3%, 97.6%, 98.5% and 99.6% respectively of the empirical correlation energies.

Description of intraatomic correlations by the Local Approach

The Local Approach for calculating correlation energies of molecules is formulated for intraatomic correlations. This is an extension of earlier work in which it was successfully applied to interatomic correlations. In order to treat intraatomic correlations the atomic volume is divided into subspaces. The Hartree-Fock ground state is modified by decreasing electronic double occupancies of those subspaces. This leads to a generation of a correlation hole. A detailed description is given for the construction of the required subspaces. The theory is applied for the purpose of demonstration to the He and Be atoms, to the H2-molecule and to a system of two He atoms. A comparison with CI-calculations shows that only few percents of the correlation energy are missing when similar basis sets are used. The advantage of the Local Approach is its intrinsic simplicity and that it operates in a much smaller configuration space than the CI-method. This makes it an appropriate method for the treatment of larger systems.

Universal atomic basis sets

A single Slater-orbital basis set, consisting of nine 1s and six 2p functions, is used to calculate matrix Hartree—Fock ground state energies for several light atoms. The resulting energies are compared with the most accurate calculations of these energies obtained using different basis sets individually optimized for each atom.

Atomic correlation energies. II. Converged E(2)values for Ne and Ne+

For pt.I see ibid., vol.11, p.1157 (1978). The second-order perturbative corrections to the Hartree-Fock ground-state energies of Ne and Ne+ are calculated using a Hartree-Fock-Roothaan approach with practically complete basis sets. The results are ENe(2)=-0.3855 au and ENe+(2)=-0.3214 au. It was found necessary to include virtual orbitals with relatively high angular momenta in the basis sets in order to saturate the E(2) values. The Ne result represents 98.8% of the empirical correlation energy. From ENe(2), ENe+(2) and the Hartree-Fock ground-state energies the authors find an ionisation potential, IPNe,calc=0.7934 au or 21.59 eV, in excellent agreement with the measured value, IPNe=21.56 eV.

The Approximate Self-Consistent Renormalized RPA: The Electronic Excited States of DNA Bases in the CNDO/S Method

Abstract Comments are given upon the approximate self-consistent renormalized RPA(SCrRPA) presented in our previous papar which assumes the correlated ground state wavefunction to be the linear combination of the Hartree-Fock ground state and doubly excited states, in the CI language. The rationalization of the approximate SCrRPA is made from the results computed by the complete SCrRPA, whose recipe is simply made. Finally, a numerical comparison of the several RPA methods is made as to the electronic spectra of four DNA bases by using the CNDO/S method.

Giant multipole resonances

The positions and the transition strengths of the giant multipole resonances of the spherical nuclei ( 16O, 40Ca, 90Zr and 208Pb) are calculated with large configuration spaces in the random phase approximation based on the Hartree-Fock ground states of a newly developed Skyrme interaction. Positions of many giant resonances are reproduced within 5 % of the experimental values. Most of the energy-weighted sum rules calculated from the double commutators are exhausted to within 13 % by the contribution from the RPA response function.

Antisymmetry in the three-nucleon-interaction matrix elements

The inclusion of three-body forces to the effective nucleon-nucleon interaction has been frequently applied in nuclear self-consistent Hartree-Fock calculations. Thus, a dependence of the effective force on the nucleon density is exhibited, stimulating great interest in this manner. Antisymmetrized three- body matrix elements are evaluated, and applied with a zero-range three-body force within a finite basis of spherical single-particle states. The imposed antisymmetry ignores the existence of matrix elements of three identical nucleons. It provides for a better understanding of the structure of the three-body contribution to the Hartree-Fock ground state energy and for the exact relation between the three-body force and a density dependent two-body force. The discussion is given as well for spherical as for deformed nuclei. Problems concerning possible overbinding and violation of the spin stability by the zero- range three-body interaction are examined and represented in the angular momentum picture.

Determination of the state of hybridization of unsaturated hydrocarbons chemisorbed on nickel

The uv photoemission valence orbital spectra of adsorbed acetylene, ethylene, propylene, and benzene on Ni(lll) are compared with gas-phase spectra as well as Hartree-Fock ground-state orbital energies calculated using a self-consistent-field linear-combination-of-atomic-orbitals method for a range of possible hybridizations of the carbon atoms. We conclude that the chemisorption bonding of these unsturated hydrocarbons involves predominantly $\ensuremath{\pi}\ensuremath{-}d$ bonding without any significant rehybridization relative to their gas-phase counterparts.

Spin saturation and the Skyrme interaction

Of existing variants of the Skyrme interaction, those with strong three-body terms - in particular the variant SIII that is in best accord with experiment - overbind odd-mass and odd-odd nuclei and produce unstable spin-saturated Hartree-Fock ground states in nuclear matter and in even-even light nuclei. This difficulty can be removed either by imposition of an additional stability condition or by abandoning the three-body term in favor of the two-body density-dependent interaction equivalent to it in spin-saturated HF states.

Variational wavefunctions for low-lying excited states

The multiconfiguration method based on the generalized Brillouin theorem is well suited to optimize orbitals in variational wavefunctions for low-lying excited states of a given symmetry. Such wavefunctions are constrained to be orthogonal to and noninteracting with the wavefunctions for all lower states of the same symmetry. Test calculations were performed on the lowest excited 1S state of Be. For a Hartree-Fock ground state wavefunction, singly excited configurations were insufficient to describe the lowest excited state, and triply excited configurations had to be added. For multiconfiguration ground state wavefunctions, however, singly excited configurations gave good results.

Projection of the uhf ground state wave function of the high-conductivity 1 ∶ 1 TCNQ salts

The unrestricted Hartree-Fock ground state wave function of a TCNQ salt with one electron per molecule and with the regular one-dimensional lattice of the TCNQ molecules is decomposed into states with sharp values of the total momentum of the electronic system. The properties of the components are discussed and the relation of the results to the double periodicity of the well known spin wave spectrum is emphasized.

Study of the photodetachment ofC−andF−by many-body perturbation theory

Photodetachment cross sections of ${\mathrm{C}}^{\ensuremath{-}}$ and ${\mathrm{F}}^{\ensuremath{-}}$ are calculated by means of the many-body perturbation theory with multiple basis sets. The ${V}^{N\ensuremath{-}1}$ basis set is defined to include the intrachannel interaction. The ${V}^{N\ensuremath{-}2}$ basis set is introduced to describe the correlation in the Hartree-Fock ground states of negative ions. The lowest-order cross sections agree very well with experiment. The first-order corrections are calculated in the case of ${\mathrm{F}}^{\ensuremath{-}}$, and a large cancellation is found between the initial-state correlation and the final-state interchannel interactions. The importance of the use of the energy relations in the lower-order calculations is pointed out.

Calculations of the giant dipole resonance for sd-shell nuclei in the open-shell random phase approximation

The systematics of the giant dipole resonance have been calculated in the open-shell RPA for all the self-conjugate sd-shell nuclei, using (i) a phenomenological Rosenfeld interaction, (ii) Barret, Hewitt and McCarthy G-matrix elements and (iii) Kuo G-matrix elements. The excitations are based on shell model ground states for all nuclei except 28Si for which a projected Hartree-Fock ground state was used.

Green's function approach to the direct perturbation calculation of the excitation energies of closed shell fermion systems

General expressions to the third order of perturbation theory for a direct calculation of the excitation energies of closed shell atomic and molecular systems are presented. The Hartree-Fock ground state orbitals are used as single particle states, but the method may be easily generalized for an arbitrary one-electron basis. The derivation is based on the Green function and diagrammatic approaches. A ``double projection'' scheme is developed which enables not only a very effective reduction of the number of Feynman diagrams which must be explicitly considered but also yields very compact formulas for the excitation energies, which may be easily implemented on a computer. The method is illustrated and checked on a simple six-electronic model system for which the exact solutions are available.

Observation of the Compton modified band for the scattering of keV electrons by H2, He, Ne, and Ar

Measurements of the energy loss spectrum using keV electrons scattered from H2, He, Ne, and Ar at large scattering angles which define a portion of the Bethe surface are reported. The results are in good agreement with the theory of the Compton effect where the incident x-ray is replaced by a high-energy electron. The angular dependence of the inelastic scattering from H2, He, and Ne with 45 keV incident electrons is found to be in agreement with the first Born approximation including interference and exchange effects assuming weakly bound target electrons. The ratio of the inelastic peak height to the elastic peak height is compared with the results of the binary encounter theory using Hartree-Fock ground state wavefunctions and the results of experiment and theory are found to be in agreement within experimental uncertainties.

Collective vibrations of intrinsic excited states

We propose a method for studying the collective vibrations of an excited intrinsic state, which is based on the generator-coordinate theory. The new aspect introduced is the description of the intrinsic excited state as a Tamm-Dancoff solution, whereas previously the intrinsic state associated with the generator-coordinate method has always been the Hartree-Fock ground state. The method has been applied with very good results to the solvable model of Lipkin et al.

Theory of Spin Waves in Nonferromagnetic Metals

A simple quantum-mechanical theory of spin waves in nonferromagnetic metals has been developed. This theory consists of a description of the spin-wave excitations superimposed on the paramagnetic Hartree-Fock ground state of an interacting electron gas subjected to a constant uniform magnetic field. Use has been made of a gauge-independent density-matrix formalism. It is shown that to first order in the magnetic field the transport equation for the transverse spin magnetization has the same form as the corresponding phenomenological Fermi-liquid equation proposed by Silin and by Platzman and Wolff. It is also shown that for large fields, such that the cyclotron radius is smaller than the interelectronic distance, the term in the transport equation related to the cyclotron motion of the electrons is not affected by the exchange interactions. The theory presented here lends additional credence to the validity of Platzman and Wolff's phenomenological analysis of the experimental spin-wave spectra in the alkali metals.

Higher Random-Phase Approximation as an Approximation to the Equations of Motion

Starting from the equations of motion expressed as ground-state expectation values, we have derived a higher-order random-phase approximation (RPA) for excitation frequencies of low-lying states. The matrix elements in the expectation value are obtained up to terms linear in the ground-state correlation coefficients. We represent the ground state as eU|HF〉, where U is a linear combination of two particle-hole operators, and |HF〉 is the Hartree-Fock ground state. We then retain terms only up to those linear in the correlation coefficients in the equation determining the ground state. This equation and that for the excitation energy are then solved self-consistently. We do not make the quasiboson approximation in this procedure, and explicitly discuss the overcounting characteristics of this approximation. The resulting equations have the same form as those of the RPA, but this higher RPA removes many deficiencies of the RPA.

Stability Conditions for the Solutions of the Hartree-Fock Equations for Atomic and Molecular Systems. VI. Singlet-Type Instabilities and Charge-Density-Wave Hartree-Fock Solutions for Cyclic Polyenes

The singlet-stability conditions of the symmetry-adapted Hartree-Fock (HF) ground state of cyclic polyenes (linear metal with Born-K\'arm\'an cyclic boundary conditions) are studied, using the Pariser-Parr-Pople Hamiltonian and three different parametrization schemes. It is shown that the HF ground states are singlet-unstable for large enough cycles, so that the diamagnetic (pure singlet) symmetry-nonadapted HF solutions (broken-symmetry HF solutions), having lower energy than the symmetry-adapted HF solutions, must exist. In fact a number of broken-symmetry diamagnetic HF solutions, displaying the charge density waves (CDW's), exist for large enough cyclic polyenes. The most important ones, corresponding to the maximum quasi-momentum transfer and having lowest energy, are studied. The HF equations for these symmetry-nonadapted solutions are given in the BCS-Bogoliubov form, and their solutions are found numerically for cycles containing up to 170 atomic sites. It is shown that these new HF solutions display different types of CDW's, which may be conveniently classified as diagonal and off-diagonal CDW's. Finally, it is shown that the diagonal CDW HF solutions not only have generally higher energy than the off-diagonal HF solutions, but are, moreover, singlet-unstable, while the off-diagonal CDW solutions are singlet-stable. The implications of the existence of singlet instabilities for the occurrence of the energy-gap and bond-length alternation (sublattice formation), as well as for the applicability of some many-body techniques to these systems, are briefly discussed.

An effective exchange potential for the Hartree-fock ground state energy in a solid

A new approximation of the effective exchange potential is derived by a simple method. Its Fourier coefficient V X ( q) is exact when q ⪢ k F (Fermi momentum) (the Kohn and Sham approximation is exact when q ⪢ k F. The discrepancy with a recent result of Kleinman and Langreth is briefly discussed.