The Configuration Interaction Approach

Where IT o) = ) is a singly excited determinant formed by deoccupying orbital 

The Cl coefficients, along with the total Cl energy, are obtained by constructing and diagonalising the Cl Hamiltonian matrix, 

As an example of the application of the Cl approach, we consider the dissociation of molecular hydrogen. Near the H2 equilibrium geometry, the exact two electron wavefunction is well approximated by that obtained via application of the Hartree-Fock approach. Assuming 

Whilst the first two terms on the right-hand side correspond to correct dissociation, i.e., H2 — H+H, the latter two correspond to incorrect ionic dissociation, i.e., H2 — H+ -h H . These spurious ionic terms correspond to both electrons being found on the same nucleus and therefore lead to a significant overestimation of the dissociation energy at the HF level. 

The minimal basis description of H2 allows for the construction of three excited configurations two singly excited determinants logOul and r cr, along with one doubly excited determinant of the form 4 d) = r a . From Brillouin s theorem, only the doubly excited configuration interacts directly with the reference and, in the limit Tab — 00, 

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In addition, if one goes beyond the Hartree-Fock approximation to something like the configuration interaction approach there is an important sense in which one has gone beyond the picture of a certain number of electrons into a set of orbitals.10 If one insists on picturing this, then rather than just every electron being in eveiy possible orbital... 

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

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. 

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. 

Some of the more abstract ab initio approaches have already been described above. They are the Hartree-Fock method and the configuration interaction approach. 

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. 

Wlien first proposed, density llinctional theory was not widely accepted in the chemistry conununity. The theory is not rigorous in the sense that it is not clear how to improve the estimates for the ground-state energies. For wavefiinction-based methods, one can include more Slater detenuinants as in a configuration interaction approach. As the wavellmctions improve via the variational theorem, the energy is lowered. In density fiinctional theory, there is no... 

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. 

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 ... 

Overall, we seem to find reasons to be hopeful about the possibilities of the RQDO formalism for predicting spectral properties of complex atoms. Very recently, some lifetime calculations in Yb 11 have also been successfully performed [30]. These reasons rest on the correctness of the results so far obtained, as well as the low computational expense and avoidance of the frequent convergence problems that are common in configuration interaction approaches. 

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