Application of the fully correlated basis of exponential functions for molecular hydrogen

Abstract

Precision tests with the hydrogen molecule are presently limited by unknown higher-order quantum electrodynamical effects. These corrections are represented by matrix elements of some effective operators, most of which are singular. The evaluation of matrix elements of singular operators puts high demands on the quality of the representation of the nonrelativistic wave functions. The basis of fully correlated exponential functions is well suited for representing the H${}_{2}$ wave function, as it has the correct properties both at coalescent points and at asymptotic distances. Moreover, the matrix elements of all operators can be conveniently obtained in this basis via integration or differentiation with respect to nonlinear parameters. In this work we develop an approach that paves the way to practical calculations with this basis.