Michal Dallos

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.

The ethylene 1 1B1u V state revisited

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 ...

The valence-excited states T1–T4 and S1–S2 of acetylene: A high-level MR-CISD and MR-AQCC investigation of stationary points, potential energy surfaces, and surface crossings

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...

Determination of energy minima and saddle points using multireference configuration interaction methods in combination with reduced gradient following: The S0 surface of H2CO and the T1 and T2 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 S0 surface of H2CO and the T1 and T2 surfaces of acetylene. For H2CO we investigated three minima (formaldehyde, s‐trans, and s‐cis hydroxycarbene) and five saddle points. For the T1 and T2 states of acetylene the cis‐ and trans‐minima and the planar and nonplanar saddle points were computed.

Revisiting the stationary points on the potential energy surface of tetramethylene at the MR-AQCC level using analytic gradients

The stationary points on the potential energy surface (PES) of tetramethylene have been investigated using highly correlated multireference methods and extended basis sets. Full geometry optimization using analytic gradients as well as systematic scans of the PES employing different basis sets show that all minima and most of the saddle points found at the lower computational level (mostly CASSCF) cease to exist. Finally, only the G2 (gauche cyclization with conrotatory double CH2 twist) and the CT (cis–trans isomerization) saddle points have been confirmed. Activation and reaction enthalpies have been computed and are within 1–2 kcal/mol in agreement with experimental results.

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 Davidsons 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.