We present theory and implementation for a new approach for studying solvent effects: the multiconfigurational self-consistent reaction-field (MCSCRF) method. The atom, molecule, or supermolecule is assumed to be surrounded by a linear, homogeneous, continuous medium described by its macroscopic dielectric constant. The electronic structure of the compound is described by a multiconfigurational self-consistent field (MCSCF) wave function. The wave function is fully optimized with respect to all variational parameters in the presence of the surrounding polarizable dielectric medium. We develop a second-order convergent optimization procedure for the solvent states. The solvent integrals are evaluated by an efficient and general algorithm. The flexible description of the electronic structure allows us to accurately describe ground, excited, or ionized states of the solute. Deficiencies in the calculation can therefore be assigned to the cavity model rather than the description of the solute.
We have used multiconfiguration self-consistent-field theory to determine indirect nuclear spin–spin coupling constants. The Fermi contact, spin dipole, and paramagnetic spin–orbit contributions are evaluated as multiconfiguration linear response functions at zero frequency and the diamagnetic spin–orbit contribution as an average value of the multiconfiguration wave function. Sample calculations on HD and CH4 demonstrate that most of the correlation contributions can be recovered in relatively small complete active space (CAS) reference state calculations.
Multiconfigurational self-consistent-field (MCSCF) theory is presented for the gauge-origin independent calculation of vibrational circular dichroism. Origin independence is attained by the use of London atomic orbitals (LAO). MCSCF calculations on ammonia and its isotopomer NHDT demonstrate that atomic axial tensors and vibrational rotational strengths converge fast with the size of the basis set when LAOs are used. The correlation effects are significant both for the atomic tensors and the vibrational rotational strengths even for the single configuration dominated NHDT molecule.
Spin-orbit coupling constants between singlet and triplet states are evaluated as residues of multiconfiguration linear response functions. In this approach, the spin-orbit coupling constants are automatically determined between orthogonal and noninteracting states. Sample calculations are presented for the X 31'.g--b Il'.g+ transition in O 2 and the IAI_3BI transition in CH 2 • The convergence of the coupling constants is examined as a function of basis set and level of correlation. An exotic behavior is observed in the correlation of the IA I state for CH 2 when increasing the active space, demonstrating an intricate coupling between the dynamic and static correlation. In general, the results indicate that reliable spin--orbit coupling constants between valence states may be obtained with a 4s3p2d 1fbasis set for first row atoms and a modest active orbital space.
The restricted step optimization algorithm is applied to potential energy surfaces calculated from multiconfiguration self-consistent-field wave functions. Equilibrium and transition-state geometries are determined by iteratively solving a set of level-shifted Newton–Raphson equations. At each geometry the molecular gradient and Hessian are calculated analytically, and a first-order prediction of the wave function at the next geometry is obtained by combining the geometrical derivatives of the wave function with the geometrical step vector. The usefulness of this prediction is discussed and illustrated by test calculations. The numerical accuracy which is required in the wave function and its geometrical derivatives in order to maintain quadratic convergence in the optimization of the molecular geometry is analyzed. It is demonstrated that the Newton–Raphson step vector and the wave function prediction may be determined without calculating the molecular Hessian explicitly. Sample calculations are carried out for the potential energy surfaces of diazene (N2H2) and the diazenyl radical (N2H). Equilibrium geometries are determined in less than five iterations and the optimization of transition states requires typically ten iterations.
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