The basic principles of SCF SE methods

The SE methods we saw in chapter 4 simply eonstruct a Fock matrix and diagonalize it to get molecular orbital (MO) energy levels and MOs (i.e. the coefficients of the basis 

As stated above, the following discussion applies to SE methods that use the SCF procedure and so pay some service to Eq. (6.1). As with an ab initio calculation, to initiate the process we need an initial guess of the coefficients, to calculate the density matrix values Ptui the guess can come from a simple Hiickel calculation (for a n electron theory like the PPP method) or from an extended Hiickel calculation (for an all-valence-electron theory, like CNDO and its descendants). The Fock matrix of Frs elements is diagonalized repeatedly to refine energy levels and coefficients. 

The divergence from the ab initio method lies in (1) treating only valence or n electrons, i.e. in the meaning of the core, (2) the mathematical functions used to expand the MOs (the basis set functions), (3) how the core and two-electron repulsion integrals are evaluated, and (4) the treatment of the overlap matrix. These approximations are discussed in detail by Dewar [7]. An excellent yet compact survey of the principles behind all the major SE methods is given by Levine [8], and SE methods have also been reviewed by Thiel [9] a detailed exposition of the basic (pre-1970) theory behind these methods can be fonnd in the book by Pople and Beveridge [10]. Expanding on points (l)-(4)  

SE methods differ amongst themselves in (amongst other ways) the criteria for setting dS = 0, i.e. for applying zero differential overlap (ZDO). 

The two-electron integrals are evaluated by applying the ZDO approximation (above) to all different orbitals r and. y  

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