Density functional theory electron correlation procedures

There are several problems in the physics of quantum systems whose importance is attested to by the time and effort that have been expended in search of their solutions. A class of such problems involves the treatment of interparticle correlations with the electron gas in an atom, a molecule (cluster) or a solid having attracted significant attention by quantum chemists and solid-state physicists. This has led to the development of a large number of theoretical frameworks with associated computational procedures for the study of this problem. Among others, one can mention the local-density approximation (LDA) to density functional theory (DFT) [1, 2, 3, 4, 5], the various forms of the Hartree-Fock (HF) approximation, 2, 6, 7], the so-called GW approximation, 9, 10], and methods based on the direct study of two-particle quantities[ll, 12, 13], such as two-particle reduced density matrices[14, 15, 16, 17, 18], and the closely related theory of geminals[17, 18, 19, 20], and configuration interactions (Cl s)[21]. These methods, and many of their generalizations and improvements[22, 23, 24] have been discussed in a number of review articles and textbooks[2, 3, 25, 26]. 

An important issue with regard to any perturbation treatment is the convergence behavior of the perturbation series. This is considered in Section 4 where problematic cases are identified. Then a potentially viable treatment of such cases, based on vibrational SCF and post-SCF procedures, is elaborated in Section 5. In Section 6 we turn to tire practical Issues of basis set requirements and treatment of electron correlation. Here tire emphasis is on quasilinear pi-conjugated molecules and, for that case, we examine the difficulties encountered with tire use of density functional theory. 

Density functional theory The DF approach is a calculational procedure according to which all of the electronic properties of a chemical system, including the energy, can be derived from the electronic density. Local DF theory which is steadily gaining popularity in the chemical computational community takes into account electron correlation. It requires considerably less computer time and disk space than ab initio calculations making it feasible to deal with much larger atoms and molecular systems. 

We shall see that the method of Kohn and Sham in density functional theory actually provides a sound theoretical base for this method which has been used Over the years simply as a numerical convenience. The density functional method uses a set of fictional molecular orbitals which do not themselves have any physical interpretation and whose only property is to generate an electron density which is exact. The whole of the experimental calibration procedure is thrown into the generation of a potential (the exchange/correlation potential) which can, in principle, be universal that is, not dependent on the particular molecule under study. The huge number of parameters required in earlier semi-empirical methods (some for every atom) is replaced by choice of a form for this potential and a few universal parameters (up to a dozen). 

Today we know that the HF method gives a very precise description of the electronic structure for most closed-shell molecules in their ground electronic state. The molecular structure and physical properties can be computed with only small errors. The electron density is well described. The HF wave function is also used as a reference in treatments of electron correlation, such as perturbation theory (MP2), configuration interaction (Cl), coupled-cluster (CC) theory, etc. Many semi-empirical procedures, such as CNDO, INDO, the Pariser-Parr-Pople method for rr-eleetron systems, ete. are based on the HF method. Density functional theory (DFT) can be considered as HF theory that includes a semiempirical estimate of the correlation error. The HF theory is the basie building block in modern quantum chemistry, and the basic entity in HF theory is the moleeular orbital. 

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