No abstract

An efficient and general method for the analytic computation of the nonandiabatic coupling vector at the multireference configuration interaction (MR-CI) level is presented. This method is based on a previously developed formalism for analytic MR-CI gradients adapted to the use for the computation of nonadiabatic coupling terms. As was the case for the analytic energy gradients, very general, separate choices of invariant orbital subspaces at the multiconfiguration self-consistent field and MR-CI levels are possible, allowing flexible selections of MR-CI wave functions. The computational cost for the calculation of the nonadiabatic coupling vector at the MR-CI level is far below the cost for the energy calculation. In this paper the formalism of the method is presented and in the following paper [Dallos et al., J. Chem. Phys. 120, 7330 (2004)] applications concerning the optimization of minima on the crossing seam are described.

The method for the analytic calculation of the nonadiabatic coupling vector at the multireference configuration-interaction (MR-CI) level and its program implementation into the COLUMBUS program system described in the preceding paper [Lischka et al., J. Chem. Phys. 120, 7322 (2004)] has been combined with automatic searches for minima on the crossing seam (MXS). Based on a perturbative description of the vicinity of a conical intersection, a Lagrange formalism for the determination of MXS has been derived. Geometry optimization by direct inversion in the iterative subspace extrapolation is used to improve the convergence properties of the corresponding Newton-Raphson procedure. Three examples have been investigated: the crossing between the 1(1)B1/2(1)A1 valence states in formaldehyde, the crossing between the 2(1)A1/3(1)A1 pi-pi* valence and ny-3py Rydberg states in formaldehyde, and three crossings in the case of the photodimerization of ethylene. The methods developed allow MXS searches of significantly larger systems at the MR-CI level than have been possible before and significantly more accurate calculations as compared to previous complete-active space self-consistent field approaches.

No abstract

We describe a general procedure to resolve the problem of artifical valence/Rydberg mixing encountered in ab initio CI calculations on the V (1 1B1u) state of ethylene. Davidson and McMurchie realized that the key to this problem are orbitals which adequately represent the V state. A two-step procedure is proposed, in which the first step focuses on generating appropriate molecular orbitals and the second step aims to describe the electron correlation quantitatively. A series of the currently most extensive MCSCF, MR-CISD, and MR-AQCC calculations for basis sets up to quadruple zeta quality and up to 80 million configurations are presented. Size extensivity corrections turn out to be crucial for highly accurate excitation energies. Our best estimate for the N–V state excitation energy of 7.7 eV lies between the experimental absorption maximum of 7.66 eV and a vibrationally corrected value of 7.8 eV. Hence, we do not find it necessary to refer to nonadiabatic effects in order to achieve agreement with the experimental data. The V state is characterized by its spatial extent, measured through the expectation value 〈x2〉, where x is the out-of-plane direction. With 16.5–17.0a02 it has a strong valence character, as compared to ≈90a02 for the 2 1B1u Rydberg state and 11.7a02 for the ground state.