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

We 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

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