On the ground and some low-lying excited states of ScB: a multiconfigurational study.

The electronic structure of a series of low-lying excited triplet and quintet states of scandium boride (ScB) was examined using multireference configuration interaction (including Davidson's correction for quadruple excitations) and single-reference coupled cluster (CC) methods with averaged natural orbital (ANO) basis sets. The CC approach was used only for the lowest quintet state. The authors have analyzed eight low-lying triplets 3Sigma-(2), 3Sigma+, 3Pi(3), and 3Delta(2) dissociating to Sc(2D)/B(2P) atoms and eight low-lying quintet states 5Sigma-, 5Sigma+, 5Pi(2), 5Phi, and 5Delta(3) dissociating to Sc(4F)/B(2P) atoms. They report the potential energy curves and spectroscopic parameters of ScB obtained with the multireference configuration interaction (MRCI) technique including all singly and doubly excited configurations obtained with the ANO-S basis set. For the two lowest states they obtained also improved ANO-L spectroscopic constants, dipole and quadrupole moments as well as scalar relativistic effects based on the Douglas-Kroll-Hess Hamiltonian. They provide the analysis of the bonding based on Mulliken populations and occupation numbers. Since the two lowest states, 3Sigma- and 5Sigma-, lie energetically very close, their principal goal was to resolve the nature of the ground state of ScB. Their nonrelativistic MRCI(Q) (including Davidson correction) results indicate that the quintet is more stable than the triplet by about 800 cm(-1). Inclusion of scalar relativistic effects reduces this difference to about 240 cm(-1). The dissociation energies for 5Sigma- ScB range from 3.20 to 3.30 eV while those for the 3Sigma- range from 1.70 to 1.80 eV.

The Diels-Alder reaction of ethene and 1,3-butadiene: an extended multireference ab initio investigation.

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.

Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. I. Formalism.

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.

Analytic evaluation of nonadiabatic coupling terms at the MR-CI level. II. Minima on the crossing seam: formaldehyde and the photodimerization of ethylene.

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.

Determination of energy minima and saddle points using multireference configuration interaction methods in combination with reduced gradient following: the S(0) surface of H(2)CO and the T(1) and T(2) surfaces of acetylene.

The implementation of the reduced gradient following (RGF) method into the COLUMBUS quantum-chemical program system is reported using the newly developed analytic MR-CISD/AQCC gradient feature. By this combination a very useful tool has been developed for general searches of stationary points on ground- and excited-state energy surfaces. This procedure is applied to the S(0) surface of H(2)CO and the T(1) and T(2) surfaces of acetylene. For H(2)CO we investigated three minima (formaldehyde, s-trans, and s-cis hydroxycarbene) and five saddle points. For the T(1) and T(2) states of acetylene the cis- and trans-minima and the planar and nonplanar saddle points were computed.