Implementation of gradient formulas for correlated gaussians: He,?He, Ps2,9Be, and?Be test results

New formulas in the basis of explicitly correlated Gaussian basis functions, derived in a previous article using powerful matrix calculus, are implemented and applied to find variational upper bounds for nonrelativistic ground states of 4He, ∞He, Ps2, 9Be, and ∞Be. Analytic gradients of the energy are included to speed optimization of the exponential variational parameters. Five different nonlinear optimization subroutines (algorithms) are compared: TN, truncated Newton; DUMING, quasi-Newton; DUMIDH, modified Newton; DUMCGG, conjugate gradient; and POWELL, direction set (nongradient). The new analytic gradient formulas are found to significantly accelerate optimizations that require gradients. We found that the truncated Newton algorithm out-performs the other optimizers for the selected test cases. Computer timings and energy bounds are reported.