Molecular integrals over the gauge-including atomic orbitals

Abstract

Each general formula can be derived by the use of the solid harmonic gradient operator [K. Ishida, Recent Res. Dev. Quantum Chem. 2, 147 (2001)] for each of the ten kinds of molecular integral over the gauge-including atomic orbitals (GIAOs). Each is obtained with the accompanying coordinate expansion (ACE) formula. These ten kinds are the overlap, the kinetic energy, the nuclear attraction, the electron repulsion, the angular momentum, the quadrupole moment, the field, the first kind field gradient, the second kind field gradient, and the “dipole-field” integrals. Except for the overlap and angular momentum integrals, we derive the general formula of these eight molecular integrals at the first level. These ACE formulas will be useful, for example, for a calculation of a molecule in a uniform magnetic field, for a relativistic calculation, and so on, using GIAO as a basis function.