Configuration Interaction method approximation

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 ... 

Szalay, P. G. Bartlett, R. J. Approximately extensive modifications of the multireference configuration interaction method a theoretical and practical analysis, J. Chem. Phys. 1995,103, 3600-3612. 

P. G. Szalay and R. J. Bartlett, /. Chem. Phys., 103, 3600 (1995). Approximately Extensive Modifications of the Multireference Configuration Interaction Method A Theoretical and Practical Analysis. 

The generalized Sturmian method for solving the iV-electron Schrodinger equation [11 -20] is a direct configuration interaction method, using basis functions which are antisymmetrized isoenergetic solutions of the approximate iV-electron equation... 

The generalized Sturmian method [1-22] for solving the Schrodinger equation of an /V-particle system is a direct configuration interaction method, in which the configurations are chosen to be isoenergetic solutions to the approximate many-particle Schrodinger equation... 

Relativistic and electron correlation effects play an important role in the electronic structure of molecules containing heavy elements (main group elements, transition metals, lanthanide and actinide complexes). It is therefore mandatory to account for them in quantum mechanical methods used in theoretical chemistry, when investigating for instance the properties of heavy atoms and molecules in their excited electronic states. In this chapter we introduce the present state-of-the-art ab initio spin-orbit configuration interaction methods for relativistic electronic structure calculations. These include the various types of relativistic effective core potentials in the scalar relativistic approximation, and several methods to treat electron correlation effects and spin-orbit coupling. We discuss a selection of recent applications on the spectroscopy of gas-phase molecules and on embedded molecules in a crystal enviromnent to outline the degree of maturity of quantum chemistry methods. This also illustrates the necessity for a strong interplay between theory and experiment. 

The usual methods of theoretical atomic physics, such as the Hartree-Fock approximation or configuration interaction methods, are not capable of yielding results of spectroscopic accuracy. For this reason, specialized methods have been developed. As long ago as 1929, Hylleraas suggested expanding the wave function in an explicitly correlated variational basis set of the form... 

X and x were also calculated for different origins by a variational method yielding the susceptibilities of localized P-H bonds [16] and for the origin at the center of mass by an ab initio sum-over-states (SOS) configuration interaction method [17]. x =-40.93 was obtained from a united-atom approximation, and x was estimated to be 16.35 (or 7.70) [18]. 

It is well known that Hartree-Fock (HF) theory not only has been proven to be quite suitable for calculations of ground state (GS) properties of electronic systems, but has also served as a starting point to develop many-parti-cle approaches which deal with electronic correlation, like perturbation theory, configuration interaction methods and so on (see e.g., [1]). Therefore, a large number of sophisticated computational approaches have been developed for the description of the ground states based on the HF approximation. One of the most popular computational tools in quantum chemistry for GS calculations is based on the effectiveness of the HF approximation and the computational advantages of the widely used many-body Mpller-Plesset perturbation theory (MPPT) for correlation effects. We designate this scheme as HF + MPPT, here after denoted HF -f- MP2. ... 

In spite of its computational intractability the full configuration interaction method forms the basis of a many-body theory. As stated above, the implementation of the algebraic approximation restricts the domain of the Hamiltonian operator, Jf, to a finite dimensional subspace 8 of the Hilbert space 1). If tP denotes the projector onto the subspace 8, then the Hamiltonian operator, Jf, is replaced by... 

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