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., that assume off-diagonal contributions are zero. The current methods and underpinnings for calculating both of these quantities, gradients and DCTs, for the State-Averaged MultiReference Configuration Interaction with Singles and Doubles (MRCI-SD) wavefunctions in COLUMBUS are reviewed. Before this work, these methods were not available for wavefunctions of a relativistic MRCI-SD Hamiltonian. Calculation of these terms is critical in successfully modeling the dynamics of systems that depend on transitions between potential energy surfaces split by the spin-orbit operator, such as diode-pumped alkali lasers. A formalism for calculating the transition density matrices and analytic derivative coupling terms for such systems is presented.

Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. II. Derivative coupling terms and coupling angle for KHeA2Π1/2⇔KHeB2Σ1/2.

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. The nonadiabatic coupling angle calculated by integrating the radial analytic DCTs using these different techniques matches extremely well. The resultant nonadiabatic energy surfaces for KHe are presented.

Excited interatomic potential energy surfaces of Rb + He that correlate with Rb terms 52S through 72S.

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. The spin-orbit energies in the limit of complete basis set are obtained by replacing the energy eigenvalues in the spin-orbit matrix by the relativistic-corrected MRCI+Q energies extrapolated to the complete basis set limit. MRCI diabatic potential energy surfaces for a few selected 2Σ states are calculated to study the general topology and avoided crossings and repulsive form of the 6s 2Σ+ state. Important features of the potential energy surfaces are discussed with implications for alkali laser spectroscopy.

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]3s 23p 6,1S), Ar([Ne]3s 23p 54s 1, 3P, 1P), and Ar([Ne]3s 23p 54p 1, 3D, 3P, 3S, 1D, 1P, 1S) 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. Spin-orbit eigenstates are computed by diagonalizing the Breit-Pauli matrix between internal configurations with no electrons in external orbitals and added to the scalar relativistic results. A total of 32 molecular PECs are computed with spin-orbit contributions, which correlate with 1s1, 1s5-2, and 2p10-1 atomic Ar energies in Paschen notation. Important features of the PECs and system crossings are discussed.

Theoretical Cross Sections of the Inelastic Fine Structure Transition M(2P1/2) + Ng ↔ M(2P3/2) + Ng for M = K, Rb, and Cs and Ng = He, Ne, and Ar.

Scattering matrix elements of the inelastic fine structure transition M(2P1/2) + Ng ↔ M(2P3/2) + 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 VA2Π1/2(R), VA2Π3/2(R), and VB2Σ1/2(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. This matrix is diagonal in the asymptotic limit of large internuclear separation with eigenvalues that correlate to the 2Pj alkali atomic energy levels. Scattering matrix elements are computed using the CPM by preparing reactant and product wave packets on the effective potential energy surfaces that correspond to the excited 2Pj alkali states of interest. The reactant wave packet is then propagated forward in time using the split operator method together with a unitary transformation between the adiabatic and diabatic representations. The Fourier transformation of the correlation function between the evolving reactant wave packet and stationary product wave packet yields state-to-state scattering matrix elements as a function of energy for a particular choice of total angular momentum J. Calculations are performed for energies that range from 0.0 to 0.01 hartree and values of J that start with a minimum of J = 0.5 for all M + Ng pairs up to a maximum that ranges from J = 450.5 for KAr to J = 100.5 for CsAr. A sum over J together with an average over energy is used to compute thermally averaged cross sections for a temperature range of T = 0-400 K.

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. The comparison of potential energy curves for different alkali atom and noble gas atom combinations is facilitated by using the same level of theory for all nine M + Ng pairs.

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. Alexander, J. Chem. Phys. 99, 6041 (1993)]. The 1 2A' and 2 2A', adiabatic electronic potential energy surfaces are transformed to yield diabatic electronic potential energy surfaces that, when combined with the total B+H2 rotational kinetic energy, yield a set of effective potential energy surfaces [M. H. Alexander et al., J. Chem. Phys. 103, 7956 (1995)]. Within the framework of the CPM, the number of effective potential energy surfaces used for the scattering matrix calculation is then determined by the size of the angular momentum basis used as a representation. Twenty basis vectors are employed for these calculations, and the corresponding effective potential energy surfaces are identified in the asymptotic limit by the H2 rotor quantum numbers j=0, 2, 4, 6 and B electronic states 2Pja, ja=1/2, 3/2. Scattering matrix elements are obtained from the Fourier transform of the correlation function between channel packets evolving in time on these effective potential energy surfaces. For these calculations the H2 bond length is constrained to a constant value of req=1.402 a.u. and state to state scattering matrix elements corresponding to a total angular momentum of J=1/2 are discussed for j=0<-->j'=0,2,4 and 2P1/2<-->2P1/2, 2P3/2 over a range of total energy between 0.0 and 0.01 a.u.