Symbolic Algebra Development for Higher-Order Electron Propagator Formulation and Implementation.

Through the use of symbolic algebra, implemented in a program, the algebraic expression of the elements of the self-energy matrix for the electron propagator to different orders were obtained. In addition, a module for the software package Lowdin was automatically generated. Second- and third-order electron propagator results have been calculated to test the correct operation of the program. It was found that the Fortran 90 modules obtained automatically with our algorithm succeeded in calculating ionization energies with the second- and third-order electron propagator in the diagonal approximation. The strategy for the development of this symbolic algebra program is described in detail. This represents a solid starting point for the automatic derivation and implementation of higher-order electron propagator methods.