Hartree-Fock Scheme Research Articles

Symmetry of the superconducting order parameter in the Anderson lattice modelwith nearest-neighbor attractive interaction

We study an extended version of the Anderson lattice model including a density-density attractive interaction between correlated electrons on nearest-neighbor sites. Using a perturbative expansion around the atomic limit for the normal phase and the broken-symmetry Hartree-Fock scheme for the attractive potential, we examine which of the possible symmetries of the superconducting order parameter leads to the highest transition temperatures, in the case of nearest-neighbor hopping on a square lattice. We find that in a wide range of electron densities around the half filling, the increase of the on-site Coulomb f-repulsion U changes the pairing symmetry from d-wave into p- or into anisotropic s-wave, depending on the parameter regime. For large values of U compared to the bandwidth, the superconducting phase is suppressed, regardless of the symmetry of the order parameter. The effects introduced by variations in the hybridization coupling are also analyzed.

Static electronic and vibrational polarizabilities of poly(dimethylsilane) chains

The static electronic and vibrational contributions to the polarizability of poly(dimethylsilane) chains have been computed ab initio within the coupled Hartree-Fock and double harmonic schemes, respectively. Both vibrational and electronic components present a supralinear increase with chain length that can be attributed to σ-conjugation. With respect to the polysilane chains which adopt, in their equilibrium structure, an all-trans backbone conformation, the poly(dimethylsilane) chains present a helical conformation characterized by a 165 ° torsion angle. On one hand, the electronic component is larger than in polysilane chains due to the intrinsic contribution of the methyl groups and their inductive effects which decrease the band gap, while, on the other hand, its vibrational counterpart, which is mainly due to wagging motions, remains nearly unchanged by the methyl substitution.

Superconductivity in Anderson Lattice Model

We study the superconducting instabilities generated by the inclusion in the Anderson lattice model of a density—density attractive potential between correlated electrons on nearest-neighbouring sites. Using a description of the normal phase based on a perturbative expansion around the atomic limit, we treat the attractive potential in the broken-symmetry Hartree—Fock scheme and analyze which of the possible symmetries of the superconducting order parameter leads to the highest possible transition temperature in the case of a two-dimensional square lattice. For values of the on-site f-repulsion large compared to the hopping amplitude, a suppression of any possible superconducting phase occurs, regardless of the symmetry of the order parameter. PACS numbers: 74.72.—h, 74.70.Tx, 74.25.—q

Transition structures for hydride transfer reactions in vacuo and their role in enzyme catalysis

A general discussion as to the role of in vacuo transition structure in enzyme catalysis is presented. Quantum mechanical aspects are emphasized. The transition structures defined as saddle points of index one (SPi-1) for the hydride transfer step on different model enzyme systems from flavoproteins to dehydrogenases have been characterized with analytical gradients at different levels of theory: semi-empirical; ab initio with different basis sets within the Hartree-Fock scheme; density functional theory using different approaches. Quantum chemical characteristics of the SPi-1 are used to discuss hydride transfer step in enzyme catalyzed reactions and mechanistic implications. With the exception of dihydrofolate reductase, the results for all other systems studied suggest that the endo relative orientation imposed by the active site on the reactants is essential for polarizing the C dH t bond and situating the system in the quadratic region of the endo SPi-1. The geometry and transition vector components are both model independent and weakly dependent on the level of theory used in their determination. Comparisons of the SPi-1 geometries with available X-ray coordinates show that the SPi-1 can be fitted without any stress at the active site. The geometrical arrangement of the SPi-1 results in optimal frontier LUMO orbital interactions, and the transition vector amplitudes show primary and secondary isotope effects to be strongly coupled. A comparison between simple and sophisticated molecular models shows that there is a minimal molecular model associated with geometrical parameters describing the essentials of the chemical interconversion step. For hydride transfer, the corresponding transition vector is an invariant feature.

Ab initio calculation of excited state energies using basis set optimization and open-shell Møller-Plesset perturbation theory

For high-spin open-shell systems a consistent approach for determining the correlation energy of ground and excited states (ES) is proposed. An effective method of taking the orthogonality constraints into account is used to construct an optimal single reference wave function (WF) for the ES. On the one hand, it is an eigenfunction of Ŝ 2 and, on the other hand, the WF is determined by means of an unrestricted Hartree-Fock scheme. This allows one to develop an open-shell perturbation theory based on the well-defined zeroth-approximation for the ES and to keep the advantages of the genuine Møller-Plesset PT. A comparison with other methods is made. The potential curves of low-lying ES for HeH are presented to test the performance of the proposed method. Basis set optimization was found to be essential to achieve correct results for the ES.

Ab initio studies on the structure and stability of P 3H 5

Ab initio studies applying the 3-21G, 6-31G, 6-31G ∗ and 6-31G ∗∗ basis sets and also including MP2 corrections were carried out on four conformations of triphosphine. First, the geometry of the four molecules was optimized using the theoretical methods mentioned in the Hartree-Fock (HF) scheme. The energies of the molecules at stationary points corresponding to HF/ 6-31G ∗∗ geometries were subsequently calculated including electron correlation effects on the level of the second-order Moller-Plesset (MP2) perturbation theory. Other physicochemical characteristics of the hydrides, such as vibrational frequencies, dipole moments, net charges, and energies of the lowest unoccupied and highest occupied molecular orbitals were obtained from theoretical calculations. The results of our ab initio calculations indicate that the gauche conformer between adjacent lone electron pairs and between P bonds with adjacent P bonds is the most stable conformer.

Study of the equation of state for asymmetric nuclear matter and interaction potential between neutron-rich nuclei using the density-dependent M3Y interaction

Abstract Realistic versions of the M3Y effective nucleon-nucleon interaction have been used to calculate the basic properties of asymmetric nuclear matter within a non-relativistic Hartree-Fock scheme. Special attention was devoted to the dependence of the binding energy, pressure and incompressibility upon the neutron-proton asymmtry. Our results reproduce reasonably well the empirical value of the symmetry energy and the softening of the equation of state for neutron-rich nuclear matter, as suggested in several supernova studies. The same effective interaction has been further used to calculate the interaction potential between neutron-rich nuclei within an extended version of the double-folding model, where the knock-on exchange and the isospin dependence of the nucleon-nucleon interaction are treated explicitly. The symmetry (isospin-dependent) term of the central nucleus-nucleus potential was found to be negligible compared to the isoscalar term. An exploratory study of the elastic 8He, 11Li+14C scattering was performed using the new folded potentials, and possible signatures of the 8He,11Li neutron halos in these processes have been discussed.

Exact treatment of exchange in Kohn-Sham band-structure schemes.

A Kohn-Sham (KS) scheme for solids treating exchange exactly is introduced. The scheme emerges from a recently introduced exact formal KS procedure [A. G\"orling and M. Levy, Phys. Rev. A 50, 196 (1994)]. The exact density-functional exchange potential is obtained in terms of its Fourier components. The method can easily be implemented on the basis of existing Hartree-Fock schemes for solids employing plane waves as basis sets. \textcopyright{} 1996 The American Physical Society.

Revisiting the potential energy surface for [H3N ··· HCl]: An ab initio and density functional theory investigation

Theoretical calculations of the potential energy surface (PES) for the [NH3 + HCl] system are presented using several standard ab initio methods such as Hartree-Fock (HF), second-order Møller-Plesset perturbation theory (MP2), coupled cluster (CC), complete active space self-consistent-field (CASSCF), density functional theory (DFT), and less traditional ab initio approaches such as Dirac-Fock four-components and the use of effective Hamiltonian techniques, such as the recently proposed K functional. All calculations predict a single minimum for the complex, corresponding to a hydrogen-bonded structure, confirming early studies. The dynamical and nondynamical contributions to the correlation energy are discussed for different cuts of the PES, involving different N(SINGLE BOND)Cl distances. The complex has also been characterized by performing a full geometry optimization within the HF and DFT schemes; with the latter we have performed also the vibrational analysis. The predicted binding energies and infrared (IR) spectrum are compared with other theoretical and experimental results. For the gas phase, we propose a binding energy of −5.3 ± 0.5 kcal/mol, thus revising the experimental value of −8.0 ± 2.8 kcal/mol; for the minimum, the predicted N(SINGLE BOND)H and H(SINGLE BOND)Cl distances are 5.91 ± 0.05 and 2.46 ± 0.05 a.u., respectively. When the computation is done with approximate inclusion of solvent effects (Onsager reaction field), the minimum is shifted and it corresponds to the ion pair NH+4·Cl− structure, similar to Mulliken's outer complex. Since the first ab initio computation for the NH4Cl complex is the pioneer work in 1967 by E. Clementi, the present work provides us with an opportunity to comment on some aspects of the evolution in computational chemistry, particularly for energy determinations. We have concluded our comments with the invitation to use four-components Fock-Dirac for molecules both with high and low Z atoms, rather than the traditional Hartree-Fock and related methods. In other words, we are of the opinion that the time is ready in quantum chemistry to switch from the Schrödinger to the Dirac representation, due to new developments in computer hardware and software. In addition, the use of effective Hamiltonians, like the recently proposed “K functional,” seems to deserve attention, because of their computational simplicity and physical reliability in predicting correlation corrections. © 1996 John Wiley & Sons, Inc.

Revisiting the potential energy surface for [H3N ��� HCl]: An ab initio and density functional theory investigation

Theoretical calculations of the potential energy surface (PES) for the [NH3 + HCl] system are presented using several standard ab initio methods such as Hartree-Fock (HF), second-order Møller-Plesset perturbation theory (MP2), coupled cluster (CC), complete active space self-consistent-field (CASSCF), density functional theory (DFT), and less traditional ab initio approaches such as Dirac-Fock four-components and the use of effective Hamiltonian techniques, such as the recently proposed K functional. All calculations predict a single minimum for the complex, corresponding to a hydrogen-bonded structure, confirming early studies. The dynamical and nondynamical contributions to the correlation energy are discussed for different cuts of the PES, involving different N(SINGLE BOND)Cl distances. The complex has also been characterized by performing a full geometry optimization within the HF and DFT schemes; with the latter we have performed also the vibrational analysis. The predicted binding energies and infrared (IR) spectrum are compared with other theoretical and experimental results. For the gas phase, we propose a binding energy of −5.3 ± 0.5 kcal/mol, thus revising the experimental value of −8.0 ± 2.8 kcal/mol; for the minimum, the predicted N(SINGLE BOND)H and H(SINGLE BOND)Cl distances are 5.91 ± 0.05 and 2.46 ± 0.05 a.u., respectively. When the computation is done with approximate inclusion of solvent effects (Onsager reaction field), the minimum is shifted and it corresponds to the ion pair NH+4·Cl− structure, similar to Mulliken's outer complex. Since the first ab initio computation for the NH4Cl complex is the pioneer work in 1967 by E. Clementi, the present work provides us with an opportunity to comment on some aspects of the evolution in computational chemistry, particularly for energy determinations. We have concluded our comments with the invitation to use four-components Fock-Dirac for molecules both with high and low Z atoms, rather than the traditional Hartree-Fock and related methods. In other words, we are of the opinion that the time is ready in quantum chemistry to switch from the Schrödinger to the Dirac representation, due to new developments in computer hardware and software. In addition, the use of effective Hamiltonians, like the recently proposed “K functional,” seems to deserve attention, because of their computational simplicity and physical reliability in predicting correlation corrections. © 1996 John Wiley & Sons, Inc.

Nuclear ground-state properties and ion-ion potentials in semiclassical calculations with the Gogny force

The ground-state properties of magic nuclei have been studied by means of the Gogny force within the Hartree-Fock Scheme using the Slater approximation for the exchange part. A similar analysis has been carried out within the semiclassical framework by considering the extended Thomas-Fermi approach for the kinetic energy density. Comparisons with the complete Hartree-Fock results are made. The ion-ion potential for two colliding nuclei has been obtained in the energy density functional and the double-folded model approaches by using self-consistent semiclassical densities calculated with the Gogny force. These potentials have been applied in the study of 40Ca-40Ca elastic scattering.

THE GENERALIZED HARTREE-FOCK METHOD IN THE GROSS-NEVEU MODEL

In the generalized Hartree-Fock scheme one can incorporate nonperturbative effects from the beginning of a diagrammatic expansion. In order to make a detailed analysis of the method, we apply it to the Gross-Neveu model as an example and calculate the chiral condensate at large N by using a direct diagrammatic expansion. The unperturbed Gaussian kernel is adjusted to be massive by adding fermion mass terms and the mass terms are subtracted from the interaction part, thus not changing the full Lagrangian. The chiral condensate <gσ> is expanded in powers of the renormalized coupling constant and then improved by the method of effective charges. We find that our diagrammatic expansion is compatible with renormalization. By using the principle of minimal sensitivity, we evaluate <gσ> and show that the exact broken and unbroken solutions for the discrete γ5 symmetry are obtained at each order of the expansion.

Unrestricted Hartree-Fock upper bounds for the total energy of the Hubbard model on a Bethe lattice of infinite connectivity.

An unrestricted Hartree-Fock (UHF) scheme is used to obtain approximate solutions of the Hubbard model on a Bethe lattice of infinite connectivity. The UHF energy yields a correct upper bound of the total energy over the whole phase diagram. In addition to the disappearance of antiferromagnetic long-range order away from half-filling, our results give a line separating the magnetic region of the phase diagram from the nonmagnetic one.

A CDW Model for MX Complexes: Hartree–Fock Scheme of Ground State11The project supported by National Natural Science Foundation of China and Advanced Material Committee of China.

We study the effects of screened Coulomb electron-electron interactions in halogen-bridged. mixed-valence transition metal linear chain complexes (MX chains) applying lattice model with a double-well potential to simulate CDW ground state. With the periodicity of MX chain, we construct a complete set of orthogonal and normalized wave functions in view of the second-neighbor approximation. Starting from the restricted Hartree–Fock scheme, we diagnolize the Fock matrix analytically and calculate the LCAO-MO-SCF solutions. Our theory shows the dependence of charge transfer on the strength and screened coefficient of electron-electron interaction.

Model potential method in molecular calculation: application to SrX 2 and BaX 2 (X = F, Cl, Br, and I)

Electronic structures of SrX 2 and BaX 2 (X = F, Cl, Br, and I) were calculated in the Hartree—Fock scheme using newly determined model potentials and valence basis sets. Calculated bond lengths agree well with the experimental data. BaF 2, BaCl 2, BaBr 2, and SrF 2 were calculated to be bent. Total energy minimums for the other molecules were found at the apex angle of 180°. However, the potential energy surfaces for bending motions were extremely flat for these molecules. The linear or bent nature of these molecules is discussed in detail with reference to the results of population analysis, Walsh diagram, and contour maps of MOs and of the electron density change upon molecular formation

Model potential method in molecular calculation: application to SrX 2 and BaX 2 (X = F, Cl, Br, and I)

Electronic structures of SrX 2 and BaX 2 (X = F, Cl, Br, and I) were calculated in the Hartree-Fock scheme using newly determined model potentials and valence basis sets. Calculated bond lengths agree well with the experimental data. BaF 2, BaCl 2, BaBr 2, and SrF 2 were calculated to be bent. Total energy minimums for the other molecules were found at the apex angle of 180°. However, the potential energy surfaces for bending motions were extremely flat for these molecules. The linear or bent nature of these molecules is discussed in detail with reference to the results of population analysis, Walsh diagram, and contour maps of MOs and of the electron density change upon molecular formation.

Possibility of vibrational excitation by a uniform electric field

The vibrational state transition of a polyatomic molecule due to a uniform electric field (EF) has been studied. Depending on the changing rate of the applied EF, either sudden or adiabatic approximation can be applied for the state transition; the former leads to a vibrational excitation and the latter to a distortion of molecular geometry without excitation. The case of the H 2O molecule in a uniform EF is demonstrated by the second-order Møller-Plesset method based on the unrestricted Hartree-Fock scheme with 6-3 1G ∗∗ basis sets. A new concept, “equi-quantum number map”, has been presented to analyze the transition of the vibrational state due to the EF.

Localized π electron states in polydiacetylene oligomers

It is shown that the particular bond alternation pattern of short chain polydiacetylene intermediates gives rise to the occurrence of two nonbonding and nearly degenerate π molecular orbitals (MOs) which are localized at the chain ends of the longer oligomers. These orbitals evolve with increasing chain length from the highest bonding and the lowest antibonding π MOs leading to a loss of the closed shell structure of the π system, which is characterized by an increasing admixture of a doubly excited configuration to the ground configuration. We present a Hartree-Fock scheme which optimizes the coefficients of this configurational mixing and the MO coefficients simultaneously. The configuration interaction (CI) calculation is reformulated in terms of a simple two-site Hubbard model in a localized basis.

DIAGRAMMATIC APPROACH TO THE VACUUM ENERGY DENSITY: THE GROSS-NEVEU MODEL AT LARGE-N

An approach to the vacuum energy density based on a direct diagrammatic expansion in the generalized Hartree-Fock scheme is studied in the Gross-Neveu model as an example. To keep the coherence with the calculation of the chiral condensate, the vacuum energy density, ε, is expanded in terms of the effective charge associated with the condensate. Then ε is calculated by substituting the optimal value of the effective charge which specifies the solution for the condensate. The result agrees well with the exact energy density to several higher orders of the expansion, showing that our procedure works well.

Elastic electron scattering from rare gases with exact exchange: a new correlation-polarisation potential

The many-body correlation forces which act between the impinging electron and the bound electrons of the target atoms are treated here using a newly developed correlation-polarisation potential that originates from the calculation of correlation energies in electronic bound states of atoms and molecules. The new formulation of such forces is shown to be particularly effective for the present systems once all the other forces at play are treated exactly within the Hartree-Fock scheme. The calculations of this paper compare our new density functional theory (DFT) approach (Gianturco and Rodriguez-Ruiz, 1993) with an earlier homogeneous electron gas (FEG) model for correlation forces (O'Connell and Lane, 1983) and clearly indicate the superior quality of a more realistic Hartree-Fock description of the density functional for the bound electrons. Excellent accord is obtained between experimental cross-sections and theoretical results, both for differential and integral elastic electron scattering cross-sections, over a very broad range of collision energies.