Electronic structure wave function description

In practice, each CSF is a Slater determinant of molecular orbitals, which are divided into three types inactive (doubly occupied), virtual (unoccupied), and active (variable occupancy). The active orbitals are used to build up the various CSFs, and so introduce flexibility into the wave function by including configurations that can describe different situations. Approximate electronic-state wave functions are then provided by the eigenfunctions of the electronic Flamiltonian in the CSF basis. This contrasts to standard FIF theory in which only a single determinant is used, without active orbitals. The use of CSFs, gives the MCSCF wave function a structure that can be interpreted using chemical pictures of electronic configurations [229]. An interpretation in terms of valence bond sti uctures has also been developed, which is very useful for description of a chemical process (see the appendix in [230] and references cited therein). 

Dirac s relativistic theory for the motion of electrons in molecules was introduced in the preceding chapters. The appearance of positron solutions and the four-component form of the wave function looks problematic at first sight but in practice it turns out that the real challenge is, like in non-relativistic electronic structure theory, the description of the correlation between the motion of electrons. The mean-field approximation that is made in the Dirac-Hartree-Fock (DHF) approach provides a good first step, but gives bond energies and structures that are often too inaccurate for chemical purposes. 

Let us now return to the wave function description of electronic structure. The separation of the wave function into two parts is convenient since these two parts relate to different properties. The radial part determines the energy of the... 

Accounting for electron correlation in a second step, via the mixing of a limited number of Slater determinants in the total wave function. Electron correlation is very important for correct treatment of interelectronic interactions and for a quantitative description of covalence effects and of the structure of multielec-tronic states. Accounting completely for the total electronic correlation is computationally extremely difficult, and is only possible for very small molecules, within a limited basis set. Formally, electron correlation can be divided into static, when all Slater determinants corresponding to all possible electron populations of frontier orbitals are considered, and dynamic correlation, which takes into account the effects of dynamical screening of interelectron interaction. 

As was mentioned in Section 6.2.3, phenomenological CF models have been extensively used in the past to rationalize the electronic structure of lanthanide complexes [4, 40-50], and they are still in use nowadays [38, 39, 78, 79]. The ab initio approach described above is, in principle, able to provide accurate energies and wave functions of multiplets in lanthanide complexes. Nevertheless, even if ab initio calculations appear to be successful, CF description is still of great... 

The dispersive force arises due to the intermolecular electron correlation between the solute and the solvent. Further, it is also important to include the changes in intramolecular and intermolecular solvent electron correlation upon insertion of the solute in the solvent continuum. Further, electron correlation affects the structure of the solute and its charge distribution. Hence, the wave function obtained from the calculation with electron correlation provides a more accurate description of reaction field. 

Establishing a hierarchy of rapidly converging, generally applicable, systematic approximations of exact electronic wave functions is the holy grail of electronic structure theory [1]. The basis of these approximations is the Hartree-Fock (HF) method, which defines a simple noncorrelated reference wave function consisting of a single Slater determinant (an antisymmetrized product of orbitals). To introduce electron correlation into the description, the wave function is expanded as a combination of the reference and excited Slater determinants obtained by promotion of one, two, or more electrons into vacant virtual orbitals. The approximate wave functions thus defined are characterized by the manner of the expansion (linear, nonlinear), the maximum excitation rank, and by the size of one-electron basis used to represent the orbitals. 

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