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

摘要

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: (A_x - B_x)~K_x(A _y - B_y)~K_y(A_z - B _z)~K_z, (2) a multipole moment operator (x - M_x)~K_x(y - M_y)~K_y(z - M~z)~K_z around origin M, (3) an arbitrary central potential operator f(|r - C|) around center C, and (4) an electronic differential operator (?/?_x)~n_x(?/?_y)~n_y(?/?_z) ~n_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).