Electron repulsion integrals for self-energy calculations

A fast algorithm for the calculation of the electron repulsion integrals in an atomic basis is a prerequisite of any ab initio   quantum chemistry method. Unlike the case of a self-consistent field (SCF) approach, correlated methods often require a full or partial integral transformation to the molecular basis. The run-time of such an algorithm scales unfavorably as O(Nχ5), where NχNχ is the number of the basis function, and additionally poses high requirements on the computer memory. The problem is aggravated in the case of large highly symmetric molecules which can only be modeled by fully taking the symmetry into account (as was recently demonstrated by us in J. Chem. Phys. 135 (2011) 201103). We describe here the algorithm for the calculation of the electron repulsion integrals, the transformation and their use in the correlated Green’s function approach for systems with icosahedral symmetry.