Analytical gradients for Singer's multicenter n-electron explicitly correlated Gaussians

Analytical gradients for Singer's basis of n-electron multicenter explicitly correlated Gaussian functions are derived and implemented to variationally optimize the energy and wave function of molecular systems within the Born-Oppenheimer approximation. Wave functions are optimized with respect to (1/2n(n + 1) + 3n) nonlinear variational parameters and one linear coefficient per term in the basis set. Preliminary results for the ground states of H₃⁺ and H₃ suggest that the method can be more flexible and can achieve lower energies than previously reported calculations.