Self-consistent field methods, effective

In the bibliography, we have tried to concentrate the interest on contributions going beyond the Hartree-Fock approximation, and papers on the self-consistent field method itself have therefore not been included, unless they have also been of value from a more general point of view. However, in our treatment of the correlation effects, the Hartree-Fock scheme represents the natural basic level for study of the further improvements, and it is therefore valuable to make references to this approximation easily available. For atoms, there has been an excellent survey given by Hartree, and, for solid-state, we would like to refer to some recent reviews. For molecules, there does not seem to exist something similar so, in a special list, we have tried to report at least the most important papers on molecular applications of the Hartree-Fock scheme, t... 

Recently, the effects of static and dynamic structural fluctuations on the electron hole mobility in DNA were studied using a time-dependent self-consistent field method [33]. The motion of holes was coupled to fluctuations of two step parameters of a duplex, rise and twist (Fig. 1), namely the distances and the dihedral angles between base pairs, respectively. The hole mobility in an ideally ordered poly(G)-poly(C) duplex was found to be decreased by two orders of magnitude due to twisting of base pairs and static energy disorder. A hole mobility of 0.1 cm V s was predicted for a homogeneous system the mobility of natural duplexes is expected to be much lower [33]. In this context, one can mention several theoretical studies, based on band structure approaches, to estimate the electrical conductivity of DNA [85-87]. 

This expression excludes self-interaction. There have been a number of attempts to include into the Hartree-Fock equations the main terms of relativistic and correlation effects, however without great success, because the appropriate equations become much more complex. For a large variety of atoms and ions both these effects are fairly small. Therefore, they can be easily accounted for as corrections in the framework of first-order perturbation theory. Having in mind the constantly growing possibilities of computers, the Hartree-Fock self-consistent field method in various... 

Chaban, I. A., "Calculation of the Effective Parameters of Micro-Inhomogeneous media by the Self-Consistent Field Method," Sov. Phvs. -Acoust.. 1965, PP. 81-86. 

The third entry refers to the self-consistent field method, developed by Hartree. Even for the best possible choice of one-electron functions V (r), there remains a considerable error. This is due to failure to include the variable rn in the wave-function. The effect is known as electron correlation. The fourth entry, containing a simple correction for correlation, gives a considerable improvement. Hylleraas in 1929 extended this approach with a variational function of the form... 

Looking at the history of correlation from the fifties to the seventies, one may be led to ask whether correlation has been a scientific fashion or a real problem. Twenty years ago, almost everybody seemed to accept the idea that the simple molecular orbital method (MO) must be completed by configuration interaction (Cl), in order to obtain reliable prediction for the physical properties of atoms and molecules. Ten years ago, electron correlation was considered as the central problem of Quantum Chemistry (7). Nowadays, about 90% of the quantum-mechanical calculations on molecules are performed by the self-consistent-field method (SCF) using more or less extended sets of basis functions, without any consideration of the possible effects of correlation. 

Aspects of the relativistic theory of quantum electrodynamics are first reviewed in the context of the electronic structure theory of atoms and molecules. The finite basis set parametrization of this theory is then discussed, and the formulation of the Dirac-Hartree-Fock-Breit procedure presented with additional detail provided which is specific to the treatment of atoms or molecules. Issues concerned with the implementation of relativistic mean-field methods are outlined, including the computational strategies adopted in the BERTHA code. Extensions of the formalism are presented to include open-shell cases, and the accommodation of some electron correlation effects within the multi-configurational Dirac-Hartree-Fock approximation. We conclude with a survey of representative applications of the relativistic self-consistent field method to be found in the literature. 

The anomalous dispersion effect is associated with the ejection of photoelectrons from inner shell electrons in an atom. The normal scattering describes the interaction of all the electrons in the atom with the X-ray beam. The radial distribution of the electrons in an atom can be calculated using quantum mechanics, originally by Hartree s self-consistent field method (Hartree 1933). In figure 9.12 this distribution is given for rubidium, which has a K edge at 0.8155 A the mean radius for... 

Maroulis117 has applied the finite field method to a study of HC1. In a systematic analysis with large basis sets, MBPT and CC techniques, the dipole, quadrupole, octupole and hexadecapole moments have been calculated at the experimental internuclear distance. The polarizability and several orders of hyperpolarizability have been calculated and the mean a and -values for the 18-electron systems HC1, HOOH, HOF, A, F2, H2S are compared. Fernandez et a/.118 have calculated the frequency dependent a, / and tensors for HC1 and HBr using the Multiple Configuration Self Consistent Field method (MCSCF), including the effect of molecular vibration. The results show good agreement with available experimental and theoretical data. 

Y. S. Kim, Y. S. Lee. The Kramers restricted complete active space self-consistent-field method for two-component molecular spinors and relativistic effective core potentials including spin-orbit interactions. /. Chem. Phys., 119 (2003) 12169. 

The group used experimental values to decide for or against alternative quantitative methods, and in other cases experimental difficulties in the preparation of certain compounds were circumvented by recourse to theoretical studies of their properties. In one instance, Alberte Pullman turned to butadiene, a relatively simple molecule studied previously by Mulliken s and Coulson s groups, to test the effects of introducing configuration interaction in the results of the self-consistent field method (A. Pullman 1954 Pullman and Baudet 1954). 

Conjugated polymers have been studied theoretically since 1937. Quantum chemical calculations applied to conjugated chains include (i) Hiickel methods, for the rapid assessment of band structures " (ii) the Paiser-Parr-Pople configuration interaction method " (iii) complete neglect of differential overlap (CNDO) self-consistent field methods " (iv) ab initio Hartree-Fock calculations, which have given very close agreement with experimental results " " and (v) the valence effective Hamiltonian (VEH) method, which offers a considerable reduction in computational effort. ... 

If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

The frequency dependence is taken into accoimt through a mixed time-dependent method which introduces a dipole-moment factor (i.e. a polynomial of first degree in the electronic coordinates ) in a SCF-CI (Self Consistent Field with Configuration Interaction) method (3). The dipolar factor, ensuring the gauge invariance, partly simulates the molecular basis set effects and the influence of the continuum states. A part of these effects is explicitly taken into account in an extrapolation procedure which permits to circumvent the sequels of the truncation of the infinite sum-over- states. 

A completely different route to the A-electron problem is provided by DPT. On an operational level it can be thought of as an attempt to improve on the HE method by including correlation effects into the self-consistent field procedure. 

---