GEN1INT: A unified procedure for the evaluation of one‐electron integrals over Gaussian basis functions and their geometric derivatives

Abstract

AbstractWe propose a unified procedure for evaluating a variety of one‐electron integrals and their (arbitrary‐order) geometric derivatives by using a generalized one‐electron operator, which is formed as the product of four operators: (1) a scalar depending on the displacement of the two basis function centers A and B: (Ax − Bx)(Ay − By)(Az − Bz), (2) a multipole moment operator (x − Mx)(y − My)(z − Mz) around origin M, (3) an arbitrary central potential operator f(|r − C|) around center C, and (4) an electronic differential operator (∂/∂x)(∂/∂y)(∂/∂z). The use of Hermite Gaussian functions enables us to evaluate both the integrals and their geometric derivatives on a common footing. This unified computational scheme has been implemented in an open‐ended integral package GEN1INT, and interfaced to the DALTON program, using the Q5Cost library to ensure the portability of the code. Operators of the form f(|r − C|) = |r − C|−1, |r − C|−2, and Dirac delta function δ(r − C) have been implemented, and improvements in the evaluation of integrals involving the operator |r − C|−2 are proposed. The integral package GEN1INT can compute complicated one‐electron property integrals and their arbitrary‐order geometric derivatives, and is therefore expected to be a valuable tool when calculating higher order molecular properties, in particular, in combination with a recently proposed open‐ended quasi‐energy derivative approach (Thorvaldsen et al., J Chem Phys 2008, 129, 214108). © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011