Orbital-orthogonality constraints and basis-set optimization

A new procedure is presented for introducing arbitrary orbital-orthogonality constraints in the variational optimization of otherwise nonorthogonal multiconfiguration electronic wave functions. It is based on suitable analytical changes to the expressions for the first and second derivatives of the electronic energy with respect to the independent variational parameters, and can be applied in the presence of symmetry constraints. It is tested using a second-derivative optimization procedure, the Optimized Basis Set -- Generalized Multiconfiguration Spin-Coupled (OBS-GMCSC) approach, that can treat basis-function exponential parameters as variational parameters, to be optimized simultaneously with configuration, spin-coupling, and orbital coefficients. This enables rigorous optimization of basis-set exponential parameters even for fully orthogonal multiconfiguration wave functions. Test calculations are carried out, with optimized even-tempered basis sets, on Li(2) and on the CH radical. For the latter, special attention is paid to the electronic spin density at the nuclei.