Efficient Evaluation of the Matrix Elements of the Coulomb Potential between Plane Waves and Gaussians

We present an efficient method for the calculation of matrix elements between two plane waves interacting with a molecular Coulombic field. The molecular charge density is considered a sum of the nuclear point charges and the electronic part developed in products of Gaussian-type functions. The Gaussians may have arbitrary powers of x, y, z before the exponential term. The same method is also applied to the calculation of derivatives of the Coulomb matrix elements with respect to the positions of atomic nuclei. These elements are useful in multichannel treatment of electron–molecule collisions with vibrational excitation of the molecule. Sample calculations of Coulombic matrix elements for the H2 molecule with Cartesian Gaussian basis set are reported.