Correlation problem self-consistent field

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. 

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. 

The problem of the sign of AR/R for the divalent tin compounds was investigated by Lees and Flinn (16). In the relationship between the quadrupole splitting and chemical shift for the stannous compounds, two distinct correlations became apparent—compounds with a linear covalent bond, and compounds with a predominantly planar bond. Furthermore, there exists a linear relationship between the number of 5 p electrons and the chemical shift and hence the total 5 electron density. Using free tin ion wave functions in a self-consistent field calculation, they showed that the direct eflEect of adding 5 electrons is considerably... 

Methods are introduced for generating many-electron Sturmian basis sets using the actual external potential experienced by an N-electron system, i.e. the attractive potential of the nuclei. When such basis sets are employed, very few basis functions are needed for an accurate representation of the system the kinetic energy term disappears from the secular equation solution of the secular equation provides automatically an optimal basis set and a solution to the many-electron problem is found directly, including electron correlation, and without the self-consistent field approximation. In the case of molecules, the momentum-space hyperspherical harmonic methods of Fock, Shibuya and Wulfman are shown to be very well suited to the construction of many-electron Sturmian basis functions. 

Density-Functional Theory. Transition metals pose a problem for classical quantum chemical methods like self-consistent field (SCF), perturbation theory, configuration interaction (Cl), and variations on these methods, because of the very large electron correlation. SCF underestimates binding substantially, and post-SCF methods are so expensive for transition metals that one can do a calculation only on models with few atoms. DFT on the other hand is relatively cheap it is about as expensive as SCF. Moreover, with the development of the generalized-gradient approximations it is also reasonably accurate. A large majority of quantum chemical... 

With the success of these calculations for isolated molecules, we began a systematic series of supermolecule calculations. As discussed previously, these are ab initio molecular orbital calculations over a cluster of nuclear centers representing two or more molecules. Self-consistent field calculations include all the electrostatic, penetration, exchange, and induction portions of the intermolecular interaction energy, but do not treat the dispersion effects which can be treated by the post Hartree-Fock techniques for electron correlation [91]. The major problems of basis set superposition errors (BSSE) [82] are primarily associated with the calculation of the energy. 

This review is necessarily selective, and is divided into several sections. Initially we give an overview of the availability of supercomputers in the U.K., and summarise the experience gained in the implementation of various quantum chemistry packages. Optimization of Quantum Chemistry codes on the CRAY-1 is considered, with integral evaluation, self-consistent-field and integral transformation phases of quantum chemical studies being considered together with some aspects of the correlation problem. 

A number of important trends can be drawn from Table 4.1, which are trends that have influenced how computational chemists approach related (and sometimes even largely unrelated) problems. Hartree-Fock (HF) self-consistent field (SCF) computations vastly overestimate the barrier, predicting a barrier twice as large as experiment. The omission of any electron correlation more seriously affects the transition state, where partial bonds require correlation for proper description, than the ground-state reactants. Inclusion of nondynamical correlation is also insufficient to describe this reaction complete active space self-consistent field (CASSCF) computations also overestimate the barrier by some 20 kcal... 

The CURES-EC method was named because it CURES the ELECTRON CORRELATION problem in semi-empirical calculations. This is accomplished by adding multiconfiguration configuration interaction (MCCI) to the wave functions. The acronym CURES-EC stands for configuration interaction or unrestricted orbitals to relate experimental electron affinities to self-consistent field values by estimating electron correlation. Electron affinities of radicals can be obtained from experimental gas phase acidities by calculating C—H bond dissociation... 

Shadwick, 1976) and thus by extrapolation to the fully correlated problem via application to the multiconfiguration self-consistent field (MCSCF) problem. In spite of the fact that the mathematics of simultaneously averaging a nonlocal potential and proceeding to self-consistency is cumbersome at present, this approach seems a most promising avenue toward Slater s goal of using a local potential for orbital generation in Cl calculations. 

The quantitative evaluation of the corresponding interaction energies had to await the development of computers and ab initio systems in the 1960s. By the early 1970s it was apparent that self-consistent field (SCF) theory provides a reasonably accurate description of hydrogen-bonded complexes like (H O) while theories that explicitly account for electron correlation " must be used for systems which are predominantly bound by dispersion forces, such as He-H2 and Hcj. Rapid developments in both hardware and software have since taken place and ab initio calculations on weakly bound systems are now routinely being carried out. Useful information is gathered in this way and the potential surfaces obtained find application in simulation studies of liquids, solids and various solvation problems. ... 

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