Analytic energy second derivatives for general MCSCF wave functions

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Abstract
Expressions for the determination of analytic energy second derivatives for general MCSCF wave functions are presented. Equations for two distinct approaches: (1) direct differentiation of the energy expression and associated Lagrangian condition; and (2) power series expansion of the Hamiltonian and exponential-i-lambda transformation of the wave function, are developed. The problem of the nonzero nullity of the Hessian, and the resultant existence of redundant variables in the coupled perturbed multiconfiguration Hartree Fock (CPMCHF) equations, is discussed and a straightforward solution proposed. The viability of the methods presented in this paper are illustrated by a sample calculation on formaldehyde, using a double zeta (DZ) basis set and including 325 MCSCF configurations in the state space.