Improvements on the Hartree-Fock wave function

If a wave function of higher accuracy than the single-determinant HF wave function is desired, a number of techniques are available. The most frequently used method is that of configuration interaction, in which the wave function has the form  

From Brillouin s Theorem (Levine, 1983), we know that Hu vanishes if i and j differ by a single one-electron excitation. A consequence is that the HF wave function gives one-electron properties (expectation values of an operator that is a sum of n terms, each depending on the coordinates of a single electron) that are correct to first order. A well-known one-electron property of a molecule is the dipole moment. The operator for the x component of the dipole moment is  

In principle, a Cl approach provides an exact solution of the many-electron problem. In practice, however, only a finite set of Slater determinants can be handled in the linear expansion. A common procedure is to retain all Slater determinants that differ from the HF determinant by one or two excitations (although one-electron excitations do not couple directly to the ground state they couple with two-electron excitations, which in turn affect the ground state indirectly). Unfortunately, such a procedure is not size consistent. For example, the energy of two highly separated monomers will not be twice that of a single monomer in such a truncated Cl calculation. Fortunately, a slightly modified approach called quadratic Cl has recently been developed (Pople et al., 1987) that is size consistent. 

An alternative method treats the effect of electron correlation according to perturbation theory. The perturbation is the difference between the 

The effects of including correlation on the calculated bond distance in HjO is shown in Table 3.3, using data taken from Szabo and Ostlund (1989). Introduction of correlation effects generally results in increases in bond distance, and for HjO the best correlated calculations give almost exact agreement with experiment. 

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In the section that follows this introduction, the fundamentals of the quantum mechanics of molecules are presented first that is, the localized side of Fig. 1.1 is examined, basing the discussion on that of Levine (1983), a standard quantum-chemistry text. Details of the calculation of molecular wave functions using the standard Hartree-Fock methods are then discussed, drawing upon Schaefer (1972), Szabo and Ostlund (1989), and Hehre et al. (1986), particularly in the discussion of the agreement between calculated versus experimental properties as a function of the size of the expansion basis set. Improvements on the Hartree-Fock wave function using configuration-interaction (Cl) or many-body perturbation theory (MBPT), evaluation of properties from Hartree-Fock wave functions, and approximate Hartree-Fock methods are then discussed. 

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