Electron correlation configuration interaction approach

The Configuration Interaction Approach to Electron Correlation - The Coupled Cluster Method... 

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. 

J. Karwowski, The configuration interaction approach to electron correlation, in Methods in Computational Molecular Physics, edited by S. Wilson and G. H. F. Diercksen, pages 65-98. Plenum Press, New York, 1992. 

Finally we note that In the case of a Feshbach resonance a single configuration Is Insufficient to account for both the resonance and decay channels, as shown by McCurdy, Resclgno, Davidson and Lauderdale (22), so that multiconfiguration complex SCF (or some other configuration Interaction approach) Is required. This point brings us to variational methods for electronic resonances which do Incorporate the effects of electronic correlation. 

Thus, the method described above allows us to obtain a number of new physical results partially presented in this communication. These calculations are carried out in the Hartree-Fock approximation for multi-electron systems and are exact solutions of the Schrodinger equation for the single-electron case. As the following development of the method we plan to implement the configuration interaction approach in order to study correlation effects in multi-electron systems both in electric and magnetic fields. 

In addition to MP2, MP3, and MP4 calculations, CCSD(T), CASSCF, FOCI (First-Order Configuration Interaction), and sometimes SOCI (Second-Order Configuration Interaction) approaches have been used to ensure the convergence of the results. The complete definitions of the variational spaces used are given in [61,62,63]. Electronically-excited states have been obtained by means of the MC/P method, recently developed in our group [64,65] it couples a variational treatment to deal with the nondynamic correlation effects and a perturbation treatment to account for the dynamic correlation effects as well as the non-dynamic effects not treated at the variational level becanse of their limited contributions to the phenomena investigated. All electronic transitions reported here are vertical transition energies. 

In Tables 2 and 3, triplet doubly excited energies of 2s ns (n = 3,4,. .10) states and 3s ns (n = 4, 5,11) states of He, computed at the CSCF level, are presented. Calculations of Ref. [46] were restricted to only singly excited states. Therefore, we compare our CSCF calculations with accurate theoretical calculations based on a configuration interaction approach with the explicitly correlated HyUeraas basis set functions [48]. One can see that the accuracy of the CSCF calculations is improved when n increases. This observation is in agreement with Ref. [46]. whose authors pointed out that In those states where n 1, the electrons are spatially well separated and one might anticipate intuitively that they will be weakly correlated and that the Hartree-Fock method, which neglects such effects, may be an excellent approximation. ... 

Siegbahn, P. E. M. The Configuration Interaction Method. In Lecture Notes in Quantum Chemistry European Summer School in Quantum Chemistry, Roos, B. O., Ed. Springer-Verlag New York, 1992 Vol. 58, pp 255-293. Karwowski, J. The Configuration Interaction Approach to Electron Correlation. In Methods in Computational Molecular Physics, Wilson, S., Diercksen, G. H. F., Eds. Plenum Press New York, 1992 pp 65-98. 

The most commonly employed tool for introducing such spatial correlations into electronic wavefunctions is called configuration interaction (Cl) this approach is described briefly later in this Section and in considerable detail in Section 6. 

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. 

Such a wave function is represented by a linear combination of wave functions for more than one electron configuration, and is called a "multi-configurational" wave function. The consideration of more than one configuration can reduce the correlation error. Such an approach is referred to as the method of configuration interaction (Cl) . 

The difference between the Hartree-Fock energy and the exact solution of the Schrodinger equation (Figure 60), the so-called correlation energy, can be calculated approximately within the Hartree-Fock theory by the configuration interaction method (Cl) or by a perturbation theoretical approach (Mpller-Plesset perturbation calculation wth order, MPn). Within a Cl calculation the wave function is composed of a linear combination of different Slater determinants. Excited-state Slater determinants are then generated by exciting electrons from the filled SCF orbitals to the virtual ones ... 

---