Correlation by Multiconfigurational SCF Methods

If it is necessary to drastically reduce the number of terms to be handled in a Cl process, it seems to be profitable to optimize the orbitals pi (v) from which the (Pk s are constructed, in such a way that the leading terms in the expansion produce the maximum efficiency as concerns correlation. This optimization is the aim of the multi-configuration (MC)—SCF (in which a limited set of functions k is constructed and the expansion coefficients of the determinants and those of orbitals are optimized) and of alternative methods based on the use of natural orbitals. 

To solve MC—SCF equations, several methods have been suggested, but few of them have been applied numerically to molecular calculations involving more than two configurations one uses the Brillouin theorem as an optimization criterion (88), the other tries to reach the minimum point on the energy surface directly (89). 

In the first method, variation of the orbitals q u from which the Pk s are constructed, is made through the transformation 

The XifS are the matrix dements of X with respect to the f s i, j being creation and annihilation operators for spinorbitals (pi and (pj. The condition for optimum orbitals is then the generalized Brillouin theorem  

If this condition is not fulfilled, the expression for the derivatives is used to progress towards the solution. The relationship of this treatment to other methods, involving pseudo-eigenvalue problems, can also be established but the present method showed a better convergency in the case of simple polyatomic molecules as formaldehyde 88), ethylene and ethane 90). 

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