By I. PRIGOGINE, STUART A. RICE
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Additional info for Advances in Chemical Physics, Vol. 48
A comparison of G , ( E ) and the EOM method with its expanded P-space can be accomplished by folding the partitioned EOM equation, which has the dimensionality of the P-space, into the 1-1 subblock. The P-space repartitioned EOM pseudoeigenvalue equation (38) is written in block matrix form with an orthogonal operator basis assumed in (43). Equation 43 explictly displays the o dependence of the L ( w ) matrix that arises from the -AfQ(AqQ - W I ~ ~ ) - ~ A term ~ , ,in (37), and (AQQ-wIQP)-I is approximated by its diagonal elements (through first order) in the present formulation of the theory.
On the other hand, when unshifted w-dependent denominators are employed, M I includes the first-order diagonal elements as well. In any event, the evaluation of this term involves a double summation 38 M . F. HERMAN, K . F . FREED, AND D . L . , the 3-block here). There is a contribution of this type to each element of the partitioned EOM matrix (which has the dimensionality of the P-space). Thus inclusion of these terms constitutes a substantial increase in the labor involved in solving the EOM equation, and this is, prehaps, the motivation for its neglect in the 2;-order theories.
This high degree of accuracy certainly would not be expected of CI calculations with such primitive sets of orbitals. Griffing and Simonsm vary the exponents of those basis functions with large expansion coefficients in the highest occupied orbital in the SCF determinant, to maximize the ionization potential in C N - and BO-, claiming that this simple variation procedure leads to orbital basis sets that yield accurate IPS and EAs. Liu9*has criticized this method of basis set “optimization,” presenting results for CN showing that the major effect of this variation is an increase (worsening) of the SCF energy of CN, while the SCF energy of CN - remains relatively unchanged.
Advances in Chemical Physics, Vol. 48 by I. PRIGOGINE, STUART A. RICE