A method for the efficient evaluation of nonadiabatic coupling matrix elements of the form 〈ΨI‖∂/∂RαΨJ〉 is presented. The wave functions ΨI and ΨJ are assumed to be multiconfiguration self-consistent field (MCSCF) wave functions optimized within the state averaged approximation. The method, which can treat several states simultaneously, derives its efficiency from the direct solution of the coupled perturbed state averaged MCSCF equations and the availability of other appropriate derivative integrals. An extension of this approach to SA-MCSCF/CI wave functions is described. Here it is shown that computational efficiencies can be achieved by exploiting analogies with analytic CI gradient methods. Numerical examples for C2v approach of Mg to H2 are presented.

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A systematic approach to symmetry breaking in molecular calculations, based on MCSCF and multireference CI (MRCI) wave functions, is presented. A series of MCSCF expansions is generated by successively incorporating resonance effects and size effects into the wave functions. The character of the potential surface obtained at each level is analyzed. As an example, the potential energy curves of the ground state (σ) and the first excited state (π) of the formyloxyl radical (HCO2) are characterized. The σ and π equilibrium structures are shown to be symmetric, with an adiabatic σ−π excitation energy of 9.2 kcal/mol. Unlike earlier theoretical studies, our MCSCF model produces a qualitatively correct potential surface. Therefore, we are able to extract reliable vibrational frequencies from the MRCI potential surface.

A quadratically convergent general MCSCF algorithm is presented which is suitable for both ground state and excited state calculations. This method converges more rapidly than annihilation of singles techniques and is computationally very attractive as it does not involve the contraction of a potentially large Hamiltonian matrix on each interation. Sample calculations are performed on the two lowest states of the same symmetry for Li2, Li4, and BeO. For BeO, a symmetry restricted full valence MCSCF (81 configuration state functions) and a first order CI calculation using the MCSCF orbitals yielded good agreement with the experimental splitting of the two lowest 1Σ+ states. The results demonstrate that the algorithm described is capable of providing an efficient solution of large, general, MCSCF problems.

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