Jahn−Teller Effect versus Spin−Orbit Coupling in X2E CH3S: An ab Initio Study by the Equation-of-Motion Coupled Cluster Method and Multiconfiguration Quasi-Degenerate Second-Order Perturbation Theory

The Unified Hamiltonian Formalism of Spin-Orbit Jahn-Teller and Pseudo-Jahn-Teller Problems in All Axial Symmetries

Spatial degeneracy of electronic states closely connects spin-orbit coupling and vibronic coupling, which together determine properties of materials, especially heavy element compounds. Accurate description of those materials entails accurate mathematical formulas for spin-orbit vibronic Hamiltonians. For the first time ever, we in this work derive the Hamiltonian formalism to describe all spin-orbit Jahn-Teller and pseudo-Jahn-Teller vibronic problems in all axial symmetries. The conventional one-electron approximation of spin-orbit coupling, which was the foundation of all previous studies in this field, is not involved in the present work. Actually, the present formalism is applicable to all time-reversal symmetric hermitian Hamiltonian that has a Rank-1 dependence on the spin operator, without any restriction on the type and the number of term symbols and vibrational modes.

Unified one-electron Hamiltonian formalism of spin-orbit Jahn-Teller and pseudo-Jahn-Teller problems in axial symmetries

Spin-orbit coupling and vibronic coupling are both closely related to orbital degeneracy of electronic states. Both types of coupling play significant roles in determining properties of heavy element compounds and shall be treated on the same footing. In this work, we derive a unified one-electron Hamiltonian formalism for spin-orbit and vibronic interactions for systems in all axial symmetries. The one-electron formalism is usually adequate as the spin-orbit interaction can often be approximated as a one-electron interaction. For the first time, the formalism covers spin-orbit and vibronic couplings in all axial symmetries from C₁ to D_∞h, arbitrary types of vibrational modes in those symmetries, and an arbitrary number of those modes and gives Hamiltonian expansions up to an arbitrary order.

Hamiltonian formalism of spin–orbit Jahn–Teller and pseudo-Jahn–Teller problems in trigonal and tetragonal symmetries

A formalism for expansions of all bimodal spin–orbit Jahn–Teller and pseudo-Jahn–Teller Hamiltonian operators in trigonal and tetragonal symmetries is presented.

Photodissociation of the CH3O and CH3S radical molecules: an ab initio electronic structure study

The electronic states and the spin-orbit couplings between them involved in the photodissociation process of the radical molecules CH₃X, CH₃X → CH₃ + X (X = O, S), taking place after the Ã(²A₁) ← X[combining tilde](²E) transition, have been investigated using highly correlated ab initio techniques. A two-dimensional representation of both the potential-energy surfaces (PESs) and the couplings is generated. This description includes the C-X dissociative mode and the CH₃ umbrella mode. Spin-orbit effects are found to play a relevant role in the shape of the excited state potential-energy surfaces, particularly in the CH₃S case where the spin-orbit couplings are more than twice more intense than in CH₃O. The potential surfaces and couplings reported here for the present set of electronic states allow for the first complete description of the above photodissociation process. The different photodissociation mechanisms are analyzed and discussed in light of the results obtained.

K selection in one-photon mass-analyzed threshold ionization of CH3I and CD3I to the X2E3/2 state cations

One-photon mass-analyzed threshold ionization (MATI) spectra for the X (2)E(3/2) states of CH(3)I(+) and CD(3)I(+) were measured using vacuum ultraviolet radiation generated by four-wave mixing in Kr. Spin-orbit density functional theory calculations at the B3LYP/aug-cc-pVTZ level and spin-orbit/Jahn-Teller calculations were made to aid vibrational assignment. Each vibrational band consisted of several peaks due to different DeltaK transitions, which could be assigned by using molecular parameters determined in the previous high resolution photodissociation spectroscopic study. Possibility of generating mass-selected, vibronically selected and K-selected ion beam with decent intensity by one-photon MATI was demonstrated. The ionization energies to the X (2)E(3/2) states of CH(3)I(+) and CD(3)I(+) corrected for the rotational contribution were 9.5386+/-0.0006 and 9.5415+/-0.0006 eV, respectively.

On the simulation of photoelectron spectra in molecules with conical intersections and spin-orbit coupling: The vibronic spectrum of CH3S

A method to simulate photoelectron spectra for states coupled by conical intersections and the spin-orbit interaction is reported. The algorithm is based on the multimode vibronic coupling model and treats the spin-orbit interaction in a nonperturbative manner. Since the algorithm is not dependent on molecular symmetry, the approach is generally applicable to accidental conical intersections as well as the symmetry required intersections found in Jahn-Teller molecules. The method is also computationally efficient using energy gradient and derivative coupling information to limit the number of nuclear configurations at which ab initio data are required. This approach is applied to simulate the negative ion photoelectron spectrum of the methylthio radical. The two-state Hamiltonian employed to describe this system was determined employing ab initio gradients and derivative couplings at only 17 nuclear configurations.

Towards a highly efficient theoretical treatment of Jahn-Teller effects in molecular spectra: The 1A2 and 2A2 electronic states of the ethoxy radical

Nonadiabatic effects in the two lowest electronic states of the ethoxy radical, the 1 (2)A and 2 (2)A states, are considered, using multireference configuration interaction (MRCI) wave functions comprised of over 15x10(6) configuration state functions. The lowest point on the seam of conical intersection is located. Using this point as the origin, a quasidiabatic Hamiltonian suitable for use in a multimode vibronic coupling treatment of the coupled 1 (2)A and 2 (2)A electronic states is determined. The Hamiltonian includes all contributions from all internal coordinates through second order in displacements from the origin and is comprised of over 500 parameters. By using the average energy gradient, the energy difference gradients, and the derivative couplings, all of which are obtained at little additional cost once the requisite eigenstates are known, the second order Hamiltonian is determined from MRCI calculations at only 35 nuclear configurations. This is essentially the same number of points required to obtain the frequencies for the ground state equilibrium structure using centered differences of gradients. The diabatic Hamiltonian provides a good description of the seam space, the (N(int)-2)-dimensional space of conical intersection points, continuously connected to the minimum energy crossing point, enabling, for the first time, an analysis of the changes in the branching plane induced by seam curvature in the full seam space. Comparing the diabatic representation and MRCI results we find a good agreement for the ground state equilibrium structure, R(eq)(1 (2)A), as well as the ground state energy and vertical excitation energy. In good agreement with the available experimental data are the ground state equilibrium structure and the excitation energy to the A (2)A state, predicted here to involve a cone state level. Agreement between the harmonic frequencies at R(eq)(1 (2)A) computed from the MRCI wave function and from the diabatic Hamiltonian is excellent for all but the three lowest energy normal modes where significant deviations are observed indicating the need for selected cubic and/or quartic terms. For the low-lying vibrational levels, the diabatic representation can be used to partition the normal modes into two groups, those that involve inter(diabatic) state coupling and those that are spectators as far as nonadiabatic effects are concerned. The spin-orbit coupling interaction is determined using the Breit-Pauli approximation and its incorporation into the diabatic Hamiltonian is discussed.

Dissociation Potential Curves of Low-Lying States in Transition Metal Hydrides. 3. Hydrides of Groups 6 and 7

The dissociation curves of low-lying spin-mixed states in monohydrides of groups 6 and 7 were calculated by using an effective core potential (ECP) approach. This approach is based on the multiconfiguration self-consistent field (MCSCF) method, followed by first-order configuration interaction (FOCI) calculations, in which the method employs an ECP basis set proposed by Stevens and co-workers (SBKJC) augmented by a set of polarization functions. Spin-orbit coupling (SOC) effects are estimated within the one-electron approximation by using effective nuclear charges, since SOC splittings obtained with the full Breit-Pauli Hamitonian are underestimated when ECP basis sets are used. The ground states of group 6 hydrides have Omega = (1)/(2)(X(6)Sigma(+)(1/2)), where Omega is the z component of the total angular momentum quantum number. Although the ground states of group 7 hydrides have Omega = 0(+), their main adiabatic components are different; the ground state in MnH originates from the lowest (7)Sigma(+), while in TcH and ReH the main component of the ground state is the lowest (5)Sigma(+). The present paper reports a comprehensive set of theoretical results including the dissociation energies, equilibrium distances, electronic transition energies, harmonic frequencies, anharmonicities, and rotational constants for several low-lying spin-mixed states in these hydrides. Transition dipole moments were also computed among the spin-mixed states and large peak positions of electronic transitions are suggested theoretically for these hydrides. The periodic trends of physical properties of metal hydrides are discussed, based on the results reported in this and other recent studies.