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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.

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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.

A quantitative survey on the performance of multireference (MR), con®guration interaction with all singles and doubles (CISD), MRCISD with the Davidson correction and MR-average quadratic coupled cluster (AQCC) methods for a wide range of excited states of the diatomic molecules B 2 , C 2 , N 2 and O 2 is presented. The spectroscopic constants r e , x e , T e and D e for a total of 60 states have been evaluated and critically compared with available experimental data. Basis set extrapolations and size-extensivity corrections are essential for highly accurate results: MR-AQCC mean-errors of 0.001 A Ê , 10 cm À1 , 300 cm À1 and 300 cm À1 have been obtained for r e , x e , T e and D e , respectively. Owing to the very systematic behavior of the results depending on the basis set and the choice of method, shortcomings of the calculations, such as Rydberg state coupling or insucient con®guration spaces, can be identi®ed independently of experimental data. On the other hand, signi®cant discrepancies with experiment for states which indicate no shortcomings whatsoever in the theoretical treatment suggest the re-evaluation of experimental results. The broad variety of states included in our survey and the uniform quality of the results indicate that the observed systematics is a general feature of the methods and, hence, is molecule-independent.

The concerted and stepwise mechanisms of the Diels-Alder reaction between 1,3-butadiene and ethene have been investigated using highly correlated multireference methods (MRAQCC) and extended basis sets. Full MRAQCC geometry optimizations have been performed in all cases. The best estimate for the energy barrier of the Diels-Alder reaction is 22 kcalmol(-1). Anti- and gauche-out minima for the biradical structures and corresponding fragmentation saddle points have been determined. The biradical anti fragmentation saddle point is located 6.5 kcalmol(-1) above the concerted saddle point. The gauche-in structure does not correspond to a local minimum, but leads on geometry optimization directly to cyclohexene.

Valence-excited singlet (S1,S2) and triplet (T1–T4) states of acetylene have been studied by means of extended multireference electron correlation techniques (MR-CISD, MR-CISD+Q, and MR-AQCC). Extrapolations to the basis set limit have been performed. Minima and saddle points have been calculated using a recently developed analytic gradient method for excited states. Planar as well as nonplanar structures have been considered. In particular, the existence of an asymmetric, planar cis-type minimum on the S2 surface has been confirmed conclusively. Moreover, an intersection S1/S2 has been located close to this minimum. This situation will most probably affect the interpretation of the absorption bands attributed to the trans 1 1Bu state. In-plane and out-of-plane saddle points for cis–trans isomerization have been determined and characterized by harmonic vibrational analysis. Several interesting surface crossings for different electronic states (S1/S2, T2/T3, and S1/T3) have been characterized. Implications of the flatness of the T3 surface around linear structures and the location of the S1/T3 crossing seam on the anomalities observed in the ZAC spectrum of the Ã 1Au state are discussed.