Analytical energy gradient in variational calculations of the two lowest 3P states of the carbon atom with explicitly correlated Gaussian basis functions

Abstract

Variational calculations of ground and excited bound states on atomic and molecular systems performed with basis functions that explicitly depend on the interparticle distances can generate very accurate results provided that the basis function parameters are thoroughly optimized by the minimization of the energy. In this work we have derived the algorithm for the gradient of the energy determined with respect to the nonlinear exponential parameters of explicitly correlated Gaussian functions used in calculating n-electron atomic systems with two p-electrons and n−2 s-electrons. The atomic Hamiltonian we used was obtained by rigorously separating out the kinetic energy of the center of mass motion from the laboratory-frame Hamiltonian and explicitly depends on the finite mass of the nucleus. The advantage of having the gradient available in the variational minimization of the energy is demonstrated in the calculations of the ground and the first excited 3P state of the carbon atom. For the former the lowest energy upper bound ever obtained is reported