Restricted configuration interaction

The HE, GVB, local MP2, and DFT methods are available, as well as local, gradient-corrected, and hybrid density functionals. The GVB-RCI (restricted configuration interaction) method is available to give correlation and correct bond dissociation with a minimum amount of CPU time. There is also a GVB-DFT calculation available, which is a GVB-SCF calculation with a post-SCF DFT calculation. In addition, GVB-MP2 calculations are possible. Geometry optimizations can be performed with constraints. Both quasi-Newton and QST transition structure finding algorithms are available, as well as the SCRF solvation method. 

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. 

In principle, one can extract from G(ti)) the complete series of the primary (one-hole, Ih) and excited (shake-up) states of the cation. In practice, one usually restricts the portion of shake-up space to be spanned to the 2h-lp (two-hole, one-particle) states defined by a single-electron transition, neglecting therefore excitations of higher rank (3h-2p, 4h-3p. ..) in the ionized system. In the so-called ADC[3] scheme (22), elertronic correlation effects in the reference ground state are included through third-order. In this scheme, multistate 2h-lp/2h-lp configuration interactions are also accounted for to first-order, whereas the couplings of the Ih and 2h-lp excitation manifolds are of second-order in electronic correlation. 

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 this section, we describe calculations of the P,T-odd interaction constant Wd for the ground (X2E, 2) states of YbF and BaF molecules using all-electron DF orbitals and a restricted active space (RAS) configuration interaction (Cl) treatment. 

Historically, Hartree-Fock methods were the first to attack many-particle problems, with considerable success for atoms and molecules. Cluster calculations can be employed to study impurities in this scheme. Ab initio Hartree-Fock methods are very computationally intensive, however, and thus restricted to small clusters. Correlation effects are neglected. The use of expanded basis sets (only a first step towards configuration-interaction analysis) rapidly increases computation time. 

The most popular technique to include correlation effects is known as configuration interaction (Cl). Instead of restricting the wave function to be a single determinant, a linear combination of determinants is used. In the case of two determinants, where... 

Determinant Based Configuration Interaction Algorithms for Complete and Restricted Configuration Interaction Spaces. 

I. Selection of parameters and the basis of configuration interaction in closed shell and restricted open shell semiempirical methods. J. Phys. Chem. 77, 107 (1973). 

In this section we explicitly demonstrate how the antiresonant line shapes characteristic of configuration interaction between a discrete BO state and BO continuum can be obtained from the Green s function formalism. We restrict attention to the case of one discrete BO state interacting with one BO continuum. We shall assume that the ground state is connected to both the discrete BO state and the BO continuum by nonvanishing dipole matrix elements. 

There have also been many more calculations in which geometry optimizations are carried out, and in which the basis sets in SCF calculations have been extended to DZ or DZ+P quality, and more recently one sees an increasing use of methods which include at least some electron correlation, especially via configuration interaction (Cl). Examples of the latter calculation were until recently restricted to molecules containing up to three atoms, but the recent development of efficient Cl programmes had enabled these calculations to be carried out without too great expense on a variety of larger molecules, and this work is referred to later on in this Report. 

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