Method of configuration interaction

Lowdin, P.-O., Phys. Rev. 97, 1474, 1490, 1509, Quantum theory of many-particle systems. I. Physical interpretations by means of density matrices, natural spin-orbitals and convergence problems in the method of configuration interaction. II. Study of the ordinary Hartree-Fock approximation. III. Extension of the Har-tree-Fock scheme to include degenerate systems and correlation effects. ... 

Shavitt I (1977) The method of configuration interaction. In Schaefer III HF (ed) Methods of Electronic Structure Theory, vol. 4 of Modern Theoretical Chemistry Plenum Press, New York pp 189-275... 

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) . 

An approach such as this belongs to the method of configuration interaction (Cl) mentioned in Chap. 1. It is sufficient to cite a simple example to illustrate the usefulness of such Cl treatments. It is well known that the Weinbaum wave function 53> for the hydrogen molecule... 

Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction. 

I. Shavitt The Method of Configuration Interaction., in H. F. S. Ill (ed.) Methods of Electronic Stmcture Theory., Plenum Press, New York, pp 189(1977). 

I. Shavitt, The Method of Configuration Interaction. In H. F. Schaefer III (Ed.) Methods of Electronic Structure Theory Modem Theoretical Chemistry, Vol. 3. (Plenum, New York, 1977), pp. 189-275 The Treatment of Electron Correlation Where Do We Go from Here In C. E. Dykstra (Ed.) Advanced Theories and Computational Approaches to the Electronic Structure of Molecules (Reidel, Dordrecht, 1984), pp. 185-196. 

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. 

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. 

There are many ways to improve this independent-particle model by incorporating electron correlation in the spatial part Hylleraas function [Hyl29] and the method of configuration interaction (Cl) will be used as illustrations. 

I. Shavitt, The Method of Configuration Interaction, in Modem Theoretical Chemistry, vol. 3, H. F. Schaeffer III Ed., Plenum, New York, 1977... 

The parentheses have been included to facilitate comparison with the method of configuration interaction. Defining C, consecutively with the terms in parentheses, the exact wave function can be written as... 

P.-O. Lowdin, Phys. Rev., 97, 1474 (1955). Quantum Theory of Many-Particle Systems. I. Physical Interpretation by Means of Density Matrices, Natural Spin Orbitals, and Convergence Problems in the Method of Configuration Interaction. 

I. Shavitt, The method of configuration interaction, in H.F. Schaefer, III (Ed.), Methods of electronic stmcture theory. Plenum Press, New York, 1977, pp. 189-275. 

Boys S F 1950 Electronic wave functions II. A calculation for the ground state of the beryllium atom Proc. R. Soc. A 201 125-37 Shavitt I 1977 The method of configuration interaction Modern Theoretical Chemistry vo 3, ed H F III Schaefer (New York Plenum) pp 189-275... 

The method of configuration interaction can be made to give the most accurate wavefunctions ever calculated for many-electron systems. The results arc strictly variationaJ and therefore provide true upper bounds to exact energies. ... 

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