Perturbative Configuration Interaction description

Kaufman, Joyce J., "A Suggested Procedure to Improve the Description of Lone Pairs in the PCIL0 or More General Ab-Initio Perturbative Configuration Interaction Schemes Based... 

Cl methods [21] add a certain number of excited Slater determinants, usually selected by the excitation type (e.g. single, double, triple excitations), which were initially not present in the CASSCF wave function, and treat them in a non-perturbative way. Inclusion of additional configurations allows for more degrees of freedom in the total wave function, thus improving its overall description. These methods are extremely costly and therefore, are only applicable to small systems. Among this class of methods, DDCI (difference-dedicated configuration interaction) [22] and CISD (single- and double excitations) [21] are the most popular. 

In electronic structure theory, the single-configuration picture (e.g., the ls22s22p4 description of the Oxygen atom) forms the mean-field starting point the configuration interaction (Cl) or perturbation theory techniques are then used to systematically improve this level of description. 

A more accurate description is obtained by including other additional terms in the Hamiltonian. The first group of these additional terms represents the mutual magnetic interactions which are provided by the Breit equation. The second group of additional terms are known as effective interactions and represent, to second order perturbation treatment, interaction with distant configurations . These weak interactions will not be considered here. 

Although HF theory is useful in its own right for many kinds of investigations, there are some applications for which the neglect of electron correlation or the assumption that the error is constant (and so will cancel) is not warranted. Post-Hartree-Fock methods seek to improve the description of the electron-electron interactions using HF theory as a reference point. Improvements to HF theory can be made in a variety of ways, including the method of configuration interaction (Cl) and by use of many-body perturbation theory (MBPT). It is beyond the scope of this text to treat Cl and MBPT methods in any but the most cursory manner. However, both methods can be introduced from aspects of the theory already discussed. 

The complete description of hydrogen bond and van der Waals interactions requires of course the inclusion of electron correlation effects however, almost always, a very useful starting point for subsequent refinements is represented by a Hartree-Fock description, which serves as the basis for both perturbation theory and variational configuration interaction approaches to the treatment of electron correlation. 

Using a single determinant to derive the Hartree-Fock wavefunction does not take into account the correlation between electrons of different spins. If the wavefunction is described by a linear combination of determinants, then configuration interaction is incorporated. Another method to model correlation energy involves Moller-Plesset perturbation theory. A more detailed description of this may be found in Ref. 41. 

The computationally viable description of electron correlation for stationary state molecular systems has been the subject of considerable research in the past two decades. A recent review1 gives a historical perspective on the developments in the field of quantum chemistry. The predominant methods for the description of electron correlation have been configuration interactions (Cl) and perturbation theory (PT) more recently, the variant of Cl involving reoptimization of the molecular orbitals [i.e., multiconfiguration self-consistent field (MCSCF)] has received much attention.1 As is reasonable to expect, neither Cl nor PT is wholly satisfactory a possible alternative is the use of cluster operators, in the electron excitations, to describe the correlation.2-3... 

SM calculations are broadly based on either the (i) Hartree-Fock method (ii) Post-Hartree-Fock methods like the Mpller-Plesset level of theory (MP), configuration interaction (Cl), complete active space self-consistent field (CASSCF), coupled cluster singles and doubles (CCSD) or (iii) methods based on DFT [24-27]. Since the inclusion of electron correlation is vital to obtain an accurate description of nearly all the calculated properties, it is desirable that SM calculations are carried out at either the second-order Mpller-Plesset (MP2) or the coupled cluster with single, double, and perturbative triple substitutions (CCSD(T)) levels using basis sets composed of both diffuse and polarization functions. 

As indicated above, neither the SCF nor the DFT method is able to treat the Van der Waals interaction. This is well established for the SCF approximation [14, 15]. The Van der Waals interaction is a typical correlation effect therefore, its description requires the use of a correlated method . In wave function based ab initio methods correlation effects are described by adding singly, doubly and higher excited configurations to the SCF or to a multi-configuration SCF (MC-SCF or complete active space SCF, CASSCF) wave function. This can be done by means of perturbation theory (PT),by configuration interaction (Cl)... 

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