Critical test of equation‐of‐motion–Green’s function methods. I. Theory of higher order terms

The equation‐of‐motion–Green’s function method for calculating ionization potentials is analyzed within the framework of a linear matrix eigenvalue representation, and an extended form of the theory is developed. The utility of the modifications presented in this paper is strongly suggested by recent numerical studies which successfully employ a generalized definition of the primary operator space in analogy with configuration selection procedures that have proven useful in configuration interaction calculations. The basic theoretical questions are associated with the choice of the basis operators for the primary space and the approximations to be employed in the evaluation of the individual matrix elements. This extended form of the theory incorporates the lowest order effects of ground state correlation on matrix elements between the shakeup basis operators in the primary operator space. A first approximation to the contributions of basis operators involving ionization and double excitation or ionization and double de‐excitation is incorporated. These terms can contribute in second order to the generalized EOM primary matrix. The possible importance of yet higher order contributions are analyzed in light of the modified primary space. The effect of these generalizations of the theory are studied numerically in the following paper and comparison is made with accurate configuration interaction results on the same systems using identical basis sets.