Generalization of Brillouin theorem for the non-relativistic electronic Schrödinger equation in relation to coupling strength parameter, and its consequences in single determinant basis sets for configuration interactions

2017-09-07T20:39:50Z (GMT) by Sandor Kristyan
<p> The Brillouin theorem has been generalized for the extended non-relativistic electronic Hamiltonian (H<sub>Ñ</sub>+ H<sub>ne</sub>+ aH<sub>ee</sub>) in relation to coupling strength parameter (a), as well as for the configuration interactions (CI) formalism in this respect. For a computation support, we have made a particular modification of the SCF part in the Gaussian package: essentially a single line was changed in an SCF algorithm, wherein the operator r<sub>ij</sub><sup>-1</sup> was overwritten as r<sub>ij</sub><sup>-1</sup> ® ar<sub>ij</sub><sup>-1</sup>, and “a” was used as input. The case a=0 generates an orto-normalized set of Slater determinants which can be used as a basis set for CI calculations for the interesting physical case a=1, removing the known restriction by Brillouin theorem with this trick. The latter opens a door from the theoretically interesting subject of this work toward practice. </p>