Gaussian orbitals optimized for lower bounds of hydrogenic atoms

Various optimization criteria are compared for the hydrogen atom to find orbitals which improve lower bounds computed from the Weinstein, Temple, and Stevenson‐Crawford formulas. Minimization of squared energy deviation, “variance,” is recommended because the resulting lower bound orbitals give excellent lower bounds, converge to the exact wave function, are relatively easy to optimize, and are insensitive to the estimated energy eigenvalue. New linear combinations of Gaussian orbitals which minimize the variance are presented for the 1 s , 2 s , 2 p , 3 s , 3 p , and 3 d orbitals. These orbitals are compared with previous linear combinations with regard to their expectation values and local properties.