Coupled-cluster theory, electron correlation configuration interaction calculations

There are three main methods for calculating electron correlation Configuration Interaction (Cl), Many Body Perturbation Theory (MBPT) and Coupled Cluster (CC). A word of caution before we describe these methods in more details. The Slater determinants are composed of spin-MOs, but since the Hamilton operator is independent of spin, the spin dependence can be factored out. Furthermore, to facilitate notation, it is often assumed that the HF determinant is of the RHF type. Finally, many of the expressions below involve double summations over identical sets of functions. To ensure only the unique terms are included, one of the summation indices must be restricted. Alternatively, both indices can be allowed to run over all values, and the overcounting corrected by a factor of 1/2. Various combinations of these assumptions result in final expressions which differ by factors of 1 /2, 1/4 etc. from those given here. In the present book the MOs are always spin-MOs, and conversion of a restricted summation to an unrestricted is always noted explicitly. 

There is also a hierarchy of electron correlation procedures. The Hartree-Fock (HF) approximation neglects correlation of electrons with antiparallel spins. Increasing levels of accuracy of electron correlation treatment are achieved by Mpller-Plesset perturbation theory truncated at the second (MP2), third (MP3), or fourth (MP4) order. Further inclusion of electron correlation is achieved by methods such as quadratic configuration interaction with single, double, and (perturbatively calculated) triple excitations [QCISD(T)], and by the analogous coupled cluster theory [CCSD(T)] [8],... 

In this paper, the main features of the two-step method are presented and PNC calculations are discussed, both those without accounting for correlation effects (PbF and HgF) and those in which electron correlations are taken into account by a combined method of the second-order perturbation theory (PT2) and configuration interaction (Cl), or PT2/CI [100] (for BaF and YbF), by the relativistic coupled cluster (RCC) method [101, 102] (for TIF, PbO, and HI+), and by the spin-orbit direct-CI method [103, 104, 105] (for PbO). In the ab initio calculations discussed here, the best accuracy of any current method has been attained for the hyperfine constants and P,T-odd parameters regarding the molecules containing heavy atoms. 

The set of atomic orbitals Xk is called a basis set, and the quality of the basis set will usually dictate the accuracy of the calculations. For example, the interaction energy between an active site and an adsorbate molecule might be seriously overestimated because of excessive basis set superposition error (BSSE) if the number of atomic orbitals taken in Eq. [4] is too small. Note that Hartree-Fock theory does not describe correlated electron motion. Models that go beyond the FiF approximation and take electron correlation into account are termed post-Flartree-Fock models. Extensive reviews of post-HF models based on configurational interaction (Cl) theory, Moller-Plesset (MP) perturbation theory, and coupled-cluster theory can be found in other chapters of this series. ... 

Basis Sets Correlation Consistent Sets Configuration Interaction Coupled-cluster Theory Density Functional Applications Density Functional Theory Applications to Transition Metal Problems G2 Theory Integrals of Electron Repulsion Integrals Overlap Linear Scaling Methods for Electronic Structure Calculations Localized MO SCF Methods Mpller-Plesset Perturbation Theory Monte Carlo Quantum Methods for Electronic Structure Numerical Hartree-Fock Methods for Molecules Pseudospectral Methods in Ab Initio Quantum Chemistry Self-consistent Reaction Field Methods Symmetry in Hartree-Fock Theory. 

Consideration of the effect of electron correlation is needed to arrive at predicted intensities comparable in quantitative terms with experimental values. Since the number of molecules treated in calculations accounting for large proportion of correlation energy is limited, definite conclusions as to what approach is best for quantitative IR intensity predictions are still to come. Analytical derivative methods for higher order perturbation frieory proaches, configuration interaction treatment and, especially, coupled cluster theory, tq>pear to be the best hopes. Whether such calculations would become a routine exercise is yet to be seen. Fortunately, the studies carried out show that die double harmonic approximation works quite well as far as ab initio intensity predictimis are concerned. 

Various ab initio methods in GAUSSIAN can generate. wfx files for DDEC analysis. These ab initio calculations can be performed in a vacuum or in an implicit solvent. DDEC analysis should work with any of these ab initio methods. We strongly recommend using methods such as DFT, coupled-cluster theory, configuration interaction, etc. that accurately account for electron electron correlations. Low-level theories that do not accurately account for... 

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. 

In ab initio methods the HER approximation is used for build-up of initial estimate for and which have to be further improved by methods of configurational interaction in the complete active space (CAS) [39], or by Mpller-Plesset perturbation theory (MPn) of order n, or by the coupled clusters [40,41] methods. In fact, any reasonable result within the ab initio QC requires at least minimal involvement of electron correlation. All the technical tricks invented to go beyond the HFR calculation scheme in terms of different forms of the trial wave function or various perturbative procedures represent in fact attempts to estimate somehow the second term of Eq. (5) - the cumulant % of the two-particle density matrix. 

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