Analytical energy gradient for multiconfigurational self-consistent field wave-functions with frozen core orbitals

A method to calculate analytical energy gradients for multiconfiguration self-consistent field (MCSCF) wave functions with frozen core orbitals is presented. Since the core orbitals, which are taken from a closed shell SCF calculation, are not variationally optimized in the MCSCF procedure, it is necessary to determine their derivatives by solving a set of coupled perturbed Hartree-Fock (CPHF) equations. The technique is similar to the calculation of energy gradients for CI wave functions, but is complicated by the fact that the SCF and MCSCF orbitals are different. This makes it necessary to perform a transformation between the two orbital basis sets at an intermediate stage. The CPHF equations are solved by an iterative method, in which optionally part of the Hessian matrix can be constructed and inverted explicitly. Some applications of the method are presented. For the molecule P2S, optimized geometries for two isomers and a saddle point are compared for MCSCF wave functions with frozen and fully optimized core orbitals. It is demonstrated that in both cases virtually identical results are obtained and that the frozen-core approximation leads to significant saving in computer time. Some preliminary results are also reported for tetrasilabicyclo[1.1.0]butane, Si4H6.