Self-consistent field theory Slater determinants

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

Another class of methods uses more than one Slater determinant as the reference wave function. The methods used to describe electron correlation within these calculations are similar in some ways to the methods listed above. These methods include multiconfigurational self-consistent field (MCSCF), multireference single and double configuration interaction (MRDCI), and /V-clcctron valence state perturbation theory (NEVPT) methods.5... 

The most uniformly successful family of methods begins with the simplest possible n-electron wavefunction satisfying the Pauli antisymmetry principle - a Slater determinant [2] of one-electron functions % r.to) called spinorbitals. Each spinorbital is a product of a molecular orbital xpt(r) and a spinfunction a(to) or P(co). The V /.(r) are found by the self-consistent-field (SCF) procedure introduced [3] into quantum chemistry by Hartree. The Hartree-Fock (HF) [4] and Kohn-Sham density functional (KS) [5,6] theories are both of this type, as are their many simplified variants [7-16],... 

PHF methods can, in turn, be classified as the variational and nonvariational ones. In the former gronp of methods the coefficients in linear combination of Slater determinants and in some cases LCAO coefficients in HF MOs are optimized in the PHF calculations, in the latter such an optimization is absent. To the former group of PHF methods one refers different versions of the configuration interaction (Cl) method, the multi-configuration self-consistent field (MCSCF) method, the variational coupled cluster (CC) approach and the rarely used valence bond (VB) and generaUzed VB methods. The nonvariational PHF methods inclnde the majority of CC reaUza-tions and many-body perturbation theory (MBPT), called in its molecular realization the MoUer-Plessett (MP) method. In MP calculations not only RHF but UHF MOs are also used [107]. 

The technique was applied to the atoms of He, Rb, Na, Cl . And it was the justification of Hartree s method that got Slater (1929) to think more about the theory of complex spectra, introducing determinants and the variational method for deriving analytically the self-consistent field equations with the right symmetry properties, as we have already discussed in chapter 2. Furthermore, Vladimir Fock (1930) also... 

All the ab initio methods discussed here are based on the Hartree-Fock (HF) or self-consistent field method. In closed-shell HF theory the unperturbed many-electron wavefunction is approximated by a single Slater determinant... 

In 1926, he began studying radiative transitions in Hj, and in so doing, he examined Heisenberg s ideas of symmetric and antisymmetric two-electron states in helium. When Douglas Hartree introduced the self-consistent field method for the electronic structure of atoms in 1928, Slater saw the connection with Heisenberg s two-electron states. Slater published a major paper the next year. It described a theory of complex spectra, and in it he showed that with a determinantal many-electron wavefunction (the Slater determinant) one could achieve a self-consistent field wavefunction and also have the proper symmetry for electron systems (antisymmetric with respect to particle exchange). 

---