Analytic first derivatives for explicitly correlated, multicenter, Gaussian geminals

Variational calculations utilizing the analytic gradient of explicitly correlated Gaussian molecular integrals are presented for the ground state of the hydrogen molecule. Preliminary results serve to motivate the need for general formulas for analytic first derivatives of molecular integrals involving multicenter, explicitly correlated Gaussian geminals with respect to Gaussian exponents and coordinates of the orbital centers. Explicit formulas for analytic first derivatives of Gaussian functions containing correlation factors of the form exp(-βr_ii²) are derived and discussed.