On the “level-shifting” method for converging hartree-fock wave functions

A new formulation of level-shifting method is presented, which provides a more economical procedure for computations.     

Huckel-hubbard相关图

Huckel模型和Heisnberg-Dirac模型考虑了两种不同的相互作用,前者为单电子作用,而后者仅考虑了电子相关作用,它们是 Hubbard 模型的两种极限情形.本文以四轨道四电子体系为例讨论了三种模型,所得到的Huckel-Hubbard相关图展示了它们的适用范围及其相互关系,这样处理具有代表性,可以推广到较大的共轭体系.     

State correlation diagrams for the photochemical reactions of organometallics

State correlation diagrams are proposed for a number of photochemical reactions of organometallics. Spin-orbit coupling is found important to understand the reactivity of these organometallics.     

Hydrodynamic correlation functions for molten salts

Abstract

The linearized hydrodynamic equations for a binary ionic fluid, with specific reference to a dissociated molten salt, are used to evaluate correlation functions of local fluctuation variables and the corresponding response functions. Previous results for the instantaneous correlation functions are extended and connected with thermodynamic fluctuation theory. Different dynamical behaviours, depending on the relative magnitude of the relaxation frequency for charge fluctuations and the sound wave frequency, are demonstrated. When 4πσ/? > ck, charge fluctuations are uncoupled from mass fluctuations, the latter being isomorphous to those of a one-component neutral fluid. Kubo relations for the transport coefficients are derived in this regime. When 4πσ/? < ck, the behaviour of the ionic fluid becomes isomorphous to that of a neutral mixture, with electrical conduction playing a role analogous to interdiffusion and contributing, in particular, to the damping of sound waves. An interpolation formula between these two limiting behaviours of the relaxation frequencies is also derived. The consequences of these results for the light scattering spectrum of an ionic fluid are briefly discussed     

Extended universal correlation diagrams for the quantum mechanical one-electron two-centre problem

We have recomputed exact correlation diagrams for the energy of excited states; the system consists of an electron (or a different negatively charged particle) moving in the field of two fixed point chargesZ _a ,Z _b . The ratiosq=Z _a/Z_b taken into consideration here were 1, 2, and 3. In the caseq=3, three avoided crossings of energy curves belonging to states of equal symmetry type are contained in the diagram.     

Second-order perturbation theory for the angular pair correlation function in molecular fluids

Second-order perturbation theory is used to calculate spherical harmonic coefficients of the angular pair correlation function g(rω₁ω₂) for a liquid in which the molecules interact with a pair potential that is the sum of Lennard-Jones and quadrupole-quadrupole parts. The theory is compared with both molecular dynamics results and with the predictions of the GMF ≡ LHNC, QHNC and first-order perturbation theories. Second-order perturbation theory gives excellent results for the harmonic coefficient g(224,r), but is poorer for g(222,r) and g(202,r).     

Second-order Kohn-Sham perturbation theory: correlation potential for atoms in a cavity

Second-order perturbation theory based on the Kohn-Sham Hamiltonian leads to an implicit density functional for the correlation energy E(c) (MP2), which is explicitly dependent on both occupied and unoccupied Kohn-Sham single-particle orbitals and energies. The corresponding correlation potential v(c) (MP2), which has to be evaluated by the optimized potential method, was found to be divergent in the asymptotic region of atoms, if positive-energy continuum states are included in the calculation [Facco Bonetti et al., Phys. Rev. Lett. 86, 2241 (2001)]. On the other hand, Niquet et al., [J. Chem. Phys. 118, 9504 (2003)] showed that v(c) (MP2) has the same asymptotic -alpha(2r(4)) behavior as the exact correlation potential, if the system under study has a discrete spectrum only. In this work we study v(c) (MP2) for atoms in a spherical cavity within a basis-set-free finite differences approach, ensuring a completely discrete spectrum by requiring hard-wall boundary conditions at the cavity radius. Choosing this radius sufficiently large, one can devise a numerical continuation procedure which allows to normalize v(c) (MP2) consistent with the standard choice v(c)(r-->infinity)=0 for free atoms, without modifying the potential in the chemically relevant region. An important prerequisite for the success of this scheme is the inclusion of very high-energy virtual states. Using this technique, we have calculated v(c) (MP2) for all closed-shell and spherical open-shell atoms up to argon. One finds that v(c) (MP2) reproduces the shell structure of the exact correlation potential very well but consistently overestimates the corresponding shell oscillations. In the case of spin-polarized atoms one observes a strong interrelation between the correlation potentials of the two spin channels, which is completely absent for standard density functionals. However, our results also demonstrate that E(c) (MP2) can only serve as a first step towards the construction of a suitable implicit correlation functional: The fundamental variational instability of this functional is recovered for beryllium, for which a breakdown of the self-consistent Kohn-Sham iteration is observed. Moreover, even for those atoms for which the self-consistent iteration is stable, the results indicate that the inclusion of v(c) (MP2) in the total Kohn-Sham potential does not lead to an improvement compared to the complete neglect of the correlation potential.     

Second-order correlation potential in the Kohn–Sham approximation for atoms

A new type of correlation functional derived from the second-order expression for the correlation energy of an atom is proposed. The derived correlation potential contains one free parameter, which is determined by fitting the known pair correlation energy. The calculations with this potential in the Kohn–Sham approximation give rather accurate values for the matrix elements of different operators.     

Grid points of Gauss-Legendre quadrature as exponent parameters of basis functions of atomic hartree-fock wavefunctions

Use of the grid points of the Gauss-Legendre numerical quadrature is examined as the exponent parameters of the basis functions of atomic Hartree-Fock wavefunctions. Calculations on He, Be, and Ne have been performed and reasonably accurate wavefunctions are obtained using 20 grid points or basis functions per symmetry species without any optimization of non-linear parameters.     

Simulated transition state for the hartree-fock and hartree-fock-slater methods

A simple model based on screening effects is used to calculate ionization and excitation energies of atoms using only ground-state information. The results obtained show better agreement with the experimental values than those obtained through the use of Koopmans' approximation, specially for the inner shells.     

Nonorthogonal ultralocalized functions and fitted Wannier functions for local electron correlation methods for solids

Despite the formal exponential decay behavior of Wannier functions (WFs), their spatial extent, which is a key parameter determining the computational cost of local correlation calculations for solids, is still rather large. The problems with the localization of the WFs can partly be attributed to their mutual orthogonality. Possibilities of reduction of the spatial extent of the WFs without losing the accuracy of the calculations are investigated. A method for generation of nonorthogonal ultralocalized functions based on maximization of their Löwdin populations is developed. A scheme for fitting of the WFs and nonorthogonal localized functions with a limited support is proposed. The calculations show that by combining both techniques one can obtain quite compact linearly independent localized functions, which may significantly decrease the computational cost in post-HF calculations.     

The modified hartree-fock self-consistent field equation

The electron density at the pyridine nitrogen atom and the π-electron density of the pyridine ring were calculated by the CNDO /2-MO method assuming standard bond lengths and angles. The indices were found to correlate with the pK_a values of pyridine derivatives and with the electronic substituent constants of the Hammett type. The correlations were best for four-substituted pyridines, making the routine CNDO /2-MO calculations useful for studies of quantitative relations between structure and biological activity of the compounds.     

The continuity dilemma and hartree-fock instabilities

The stability criteria of the Hartree-Fock wavefunctions are implemented in the context of the Roothaan-Hartree-Fock procedure. Use is made of modified SCF equations, in which the total energy, rather than orbital energies, appears. The procedure is applied to the 2³S state of helium.     

Modeling thymine photodimerizations in DNA: mechanism and correlation diagrams

The basic mechanistic traits of the main photochemical reactions in DNA, the formation of the cyclobutane and oxetane thymine dimerization adducts, are established with the help of CASSCF and CASPT2 calculations for a gas-phase model of two stacked thymines. Both reactions go through conical intersections between the ground and the excited state that are connected through minimum energy paths to the corresponding products. This explains the ultrafast formation of the cyclobutane adduct detected experimentally, and it suggests that the oxetane formation also occurs on that time scale. Moreover, the states responsible for the photoproduct formation correlate with two high-lying states of the pair in its ideal B-DNA conformation. These states are different from the delocalized states resulting from coupling of the localized ones, which suggests that the origin of the reactive electronic states lies in the pi stacking. Formation of the photoproducts requires population of these states, by direct excitation of favorable conformations, or preceded by a localized excitation.     

Landscapes and their correlation functions

Fitness landscapes are an important concept in molecular evolution. Many important examples of landscapes in physics and combinatorial optimization, which are widely used as model landscapes in simulations of molecular evolution and adaptation, are elementary, i.e., they are (up to an additive constant) eigenfunctions of a graph Laplacian. It is shown that elementary landscapes are characterized by their correlation functions. The correlation functions are in turn uniquely determined by the geometry of the underlying configuration space and the nearest neighbor correlation of the elementary landscape. Two types of correlation functions are investigated here: the correlation of a time series sampled along a random walk on the landscape and the correlation function with respect to a partition of the set of all vertex pairs.     

New correlation factors for explicitly correlated electronic wave functions

We have investigated the correlation factors exp(-zetar12), r12 exp(-zetar12), erfc(zetar12), and r12 erfc(zetar12) in place of the linear-r12 term for use in explicitly correlated electronic-structure methods. The accuracy obtained with all of these correlation factors is significantly greater than that obtained with the plain correlation factor r12. Polarization functions that are more diffuse than those of standard basis sets give even better results. The correlation factor exp(-zetar12) is very close to the optimum correlation factor for helium and outperforms the others.     

Current and spin density correlation functions for computer nitrogen

Current and spin density correlation functions are simulated for computer nitrogen using the algorithm of Tidesley and Streett. The functions are oscillatory and non-exponential even for the lowest values of momentum transfer κ. A semi-empirical interpretation on the basis of a three-variable Mori approximant is attempted.