Newton–Raphson optimization of the explicitly correlated Gaussian functions for the ground state of the beryllium atom

Explicitly correlated Gaussian functions have been used in variational calculations on the ground state of the beryllium atom. In such calculations on systems with more electrons, it becomes imminent and essential to develop effective strategies for optimizing the parameters involved in the basis functions. The theory of analytical first and second derivatives of the variational functional with respect to the Gaussian exponents and its computational implementation in conjunction with the Newton–Raphson optimization technique is described. Some numerical results are presented to illustrate the performance of the method. © 1995 John Wiley & Sons, Inc.