Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. II. Derivative coupling terms and coupling angle for KHeAΠ⇔KHeBΣ.

A method for calculating the analytic nonadiabatic derivative coupling terms (DCTs) for spin-orbit multi-reference configuration interaction wavefunctions is reviewed. The results of a sample calculation using a Stuttgart basis for KHe are presented. Additionally, the DCTs are compared with a simple calculation based on the Nikitin's 3 × 3 description of the coupling between the Σ and Π surfaces, as well as a method based on Werner's analysis of configuration interaction coefficients.

Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. I. Formalism.

Analytic gradients of electronic eigenvalues require one calculation per nuclear geometry, compared to at least 3n + 1 calculations for finite difference methods, where n is the number of nuclei. Analytic nonadiabatic derivative coupling terms (DCTs), which are calculated in a similar fashion, are used to remove nondiagonal contributions to the kinetic energy operator, leading to more accurate nuclear dynamics calculations than those that employ the Born-Oppenheimer approximation, i.e.

Interatomic potentials for ground and excited states of Ar+He.

The potential energy curves (PECs) of the ground and excited states that correlate in the atomic limit with Ar([Ne]3 3 ,S), Ar([Ne]3 3 4 , P, P), and Ar([Ne]3 3 4 , D, P, S, D, P, S) are calculated at the multireference configuration interaction (MRCI+Q) theoretical level with extrapolations to the complete basis set limit using all-electron correlation consistent triple-, quadruple-, and quintuple-zeta basis sets. Scalar relativistic corrections are calculated using second-order Douglas-Kroll-Hess Hamiltonian with the corresponding basis sets contracted for scalar relativistic Hamiltonians. For these calculations, the 3s orbitals of the Ar atom are not included in the active space but are correlated through single and double excitations.

Excited interatomic potential energy surfaces of Rb + He that correlate with Rb terms 5S through 7S.

The excited state interatomic potential energy surfaces for Rb + He are computed at the spin-orbit multi-reference configuration interaction level of theory using all-electron basis sets of triple and quadruple-zeta quality that have been contracted for Douglas-Kroll-Hess (DKH) Hamiltonian and includes core-valence correlation. Davidson-Silver corrections (MRCI+Q) are employed to ameliorate size consistency error. An extrapolation of CASSCF energies is performed using the procedure of Karton and Martin whereas extrapolation of correlation energy is performed using an expression involving the inverse powers of (lmax + 1/2), the highest angular momentum value present in the basis set.

Theoretical Cross Sections of the Inelastic Fine Structure Transition M(P) + Ng ↔ M(P) + Ng for M = K, Rb, and Cs and Ng = He, Ne, and Ar.

Scattering matrix elements of the inelastic fine structure transition M(P) + Ng ↔ M(P) + Ng are computed using the channel packet method (CPM) for alkali-metal atoms M = K, Rb, and Cs, as they collide with noble-gas atoms Ng = He, Ne, and Ar. The calculations are performed within the block Born-Oppenheimer approximation where excited state V(R), V(R), and V(R) adiabatic potential energy surfaces are used together with a Hund's case (c) basis to construct a 6 × 6 diabatic representation of the electronic Hamiltonian. Matrix elements of the angular kinetic energy of the nuclei incorporate Coriolis coupling and, together with the diabatic representation of the electronic Hamiltonian, yield a 6 × 6 effective potential energy matrix.

M + Ng potential energy curves including spin-orbit coupling for M = K, Rb, Cs and Ng = He, Ne, Ar.

The X(2)Σ(1/2)(+), A(2)Π(1∕2), A(2)Π(3∕2), and B(2)Σ(1/2)(+) potential energy curves and associated dipole matrix elements are computed for M + Ng at the spin-orbit multi-reference configuration interaction level, where M = K, Rb, Cs and Ng = He, Ne, Ar. Dissociation energies and equilibrium positions for all minima are identified and corresponding vibrational energy levels are computed. Difference potentials are used together with the quasistatic approximation to estimate the position of satellite peaks of collisionally broadened D2 lines.

Inelastic scattering matrix elements for the nonadiabatic collision B(2P1/2)+H2(1Sigmag+,j)<-->B(2P3/2)+H2(1Sigmag+,j').

Inelastic scattering matrix elements for the nonadiabatic collision B(2P1/2)+H2(1Sigmag+,j)<-->B(2P3/2)+H2(1Sigmag+,j') are calculated using the time dependent channel packet method (CPM). The calculation employs 1 2A', 2 2A', and 1 2A" adiabatic electronic potential energy surfaces determined by numerical computation at the multireference configuration-interaction level [M. H.