Daniel Opalka

High-order expansion of T2×t2 Jahn–Teller potential-energy surfaces in tetrahedral molecules

Methods from Jahn-Teller theory and invariant theory have been combined for the construction of analytic diabatic potential-energy surfaces of triply degenerate states in tetrahedral molecules. The potentials of a threefold degenerate electronic state of T(2) symmetry, subject to the T(2)xt(2) or T(2)x(t(2)+t(2)) Jahn-Teller effect in a three-dimensional or six-dimensional space of nuclear coordinates, respectively, are considered. The permutation symmetry of four identical nuclei is taken into account in the polynomial expansion of the diabatic surfaces. Symmetry adapted polynomials up to high orders are explicitly given and a simple combinatorial scheme was developed to express terms of arbitrary order as products of a small number of polynomials which are invariant under the permutation of identical nuclei. The method is applied to the methane cation in its triply degenerate ground state. The parameters of the analytic surfaces have been fitted to accurate ab initio data calculated at the full-valence CASSCF/MRCI/cc-pVTZ level. A three-sheeted six-dimensional analytic potential-energy surface of the (2)T(2) ground state of CH(4) (+) is reported, which involves terms up to eighth order in the degenerate stretching coordinate, up to 12th order in the degenerate bending coordinate, and up to fourth order in the stretch-bend coupling.

Ab initio study of dynamical E × e Jahn-Teller and spin-orbit coupling effects in the transition-metal trifluorides TiF3, CrF3, and NiF3.

Multiconfiguration ab initio methods have been employed to study the effects of Jahn-Teller (JT) and spin-orbit (SO) coupling in the transition-metal trifluorides TiF(3), CrF(3), and NiF(3), which possess spatially doubly degenerate excited states ((M)E) of even spin multiplicities (M = 2 or 4). The ground states of TiF(3), CrF(3), and NiF(3) are nondegenerate and exhibit minima of D(3h) symmetry. Potential-energy surfaces of spatially degenerate excited states have been calculated using the state-averaged complete-active-space self-consistent-field method. SO coupling is described by the matrix elements of the Breit-Pauli operator. Linear and higher order JT coupling constants for the JT-active bending and stretching modes as well as SO-coupling constants have been determined. Vibronic spectra of JT-active excited electronic states have been calculated, using JT Hamiltonians for trigonal systems with inclusion of SO coupling. The effect of higher order (up to sixth order) JT couplings on the vibronic spectra has been investigated for selected electronic states and vibrational modes with particularly strong JT couplings. While the weak SO couplings in TiF(3) and CrF(3) are almost completely quenched by the strong JT couplings, the stronger SO coupling in NiF(3) is only partially quenched by JT coupling.

Interpolation of multi-sheeted multi-dimensional potential-energy surfaces via a linear optimization procedure

Significant progress has been achieved in recent years with the development of high-dimensional permutationally invariant analytic Born-Oppenheimer potential-energy surfaces, making use of polynomial invariant theory. In this work, we have developed a generalization of this approach which is suitable for the construction of multi-sheeted multi-dimensional potential-energy surfaces exhibiting seams of conical intersections. The method avoids the nonlinear optimization problem which is encountered in the construction of multi-sheeted diabatic potential-energy surfaces from ab initio electronic-structure data. The key of the method is the expansion of the coefficients of the characteristic polynomial in polynomials which are invariant with respect to the point group of the molecule or the permutation group of like atoms. The multi-sheeted adiabatic potential-energy surface is obtained from the Frobenius companion matrix which contains the fitted coefficients. A three-sheeted nine-dimensional adiabatic potential-energy surface of the (2)T2 electronic ground state of the methane cation has been constructed as an example of the application of this method.

Relativistic Jahn-Teller effects in the photoelectron spectra of tetrahedral P4, As4, Sb4, and Bi4.

The group-V tetrahedral cluster cations P(4)(+), As(4)(+), Sb(4)(+), and Bi(4)(+) are known to exhibit exceptionally strong Jahn-Teller (JT) effects of electrostatic origin in their (2)E ground states and (2)T(2) excited states. It has been predicted that there exist, in addition, JT couplings of relativistic origin (arising from the spin-orbit (SO) operator) in (2)E and (2)T(2) states of tetrahedral systems, which should become relevant for the heavier elements. In the present work, the JT and SO couplings in the group-V tetramer cations have been analyzed with ab initio relativistic electronic structure calculations. The vibronic line spectra and the band shapes of the photoelectron spectra were simulated with time-dependent quantum wave-packet methods. The results provide insight into the interplay of electrostatic and relativistic JT couplings and SO splittings in the complex photoelectron spectra of these systems.

The (E + A) × (e + a) Jahn–Teller and Pseudo-Jahn–Teller Hamiltonian Including Spin–Orbit Coupling for Trigonal Systems

The Hamiltonian describing E × e Jahn-Teller (JT) coupling and (E + A) × (e + a) pseudo-JT (PJT) coupling is developed beyond the standard JT theory for the example of XY3 systems, taking the bending modes of a and e symmetry into account. For the electrostatic (spin-free) Hamiltonian, the conventional Taylor expansion up to second order in symmetry-adapted displacements is replaced by an expansion in invariant polynomials up to arbitrarily high orders. The relevance of a systematic high-order expansion in the three large-amplitude bending modes is illustrated by the construction of an eighth-order three-sheeted three-dimensional ab initio potential-energy surface for PH3+. The theory of spin-orbit coupling in trigonal JT/PJT systems is extended beyond the standard model of JT theory by an expansion of the microscopic Breit-Pauli operator up to second order in symmetry-adapted vibrational coordinates. It is shown that a linear E × e JT effect of relativistic origin exists in C(3v) systems which vanishes at the planar (D(3h)) geometry. The linear relativistic 2E – 2A PJT coupling, on the other hand, persists at the planar geometry

Relativistic theory of the Jahn-Teller effect: p-orbitals in tetrahedral and trigonal systems.

A relativistic generalization of Jahn-Teller theory is presented which includes spin-orbit coupling effects beyond low-order Taylor expansions in vibrational coordinates. For the example of a p-electron in tetrahedral and trigonal environments, the matrix elements of the Breit-Pauli spin-orbit-coupling operator are expressed in terms of the matrix elements of the electrostatic electronic potential. Employing expansions of the latter in invariant polynomials in symmetry-adapted nuclear coordinates, the spin-orbit induced Jahn-Teller coupling terms are derived for the T2 × (t2 + e) and (E + A) × (e + a) Jahn-Teller problems up to arbitrarily high orders. The linear G3/2 × (t2 + e) Jahn-Teller Hamiltonian of Moffitt and Thorson [Phys. Rev. 108, 1251 (1957)] for tetrahedral systems is generalized to higher orders in vibrational displacements. The Jahn-Teller Hamiltonians derived in the present work are useful for the interpolation and extrapolation of Jahn-Teller distorted potential-energy surfaces of molecules and complexes with heavy elements as well as for the calculation of vibronic spectra of such systems.

Mechanism of Photocatalytic Water Oxidation by Graphitic Carbon Nitride

Carbon nitride materials are of great interest for photocatalytic water splitting. Herein, we report results from first-principles simulations of the specific electron- and proton-transfer processes that are involved in the photochemical oxidation of liquid water with heptazine-based molecular photocatalysts. The heptazine chromophore and the solvent molecules have been described strictly at the same level of electronic structure theory. We demonstrate the critical role of solvent molecules for the absorption properties of the chromophore and the overall photocatalytic cycle. A simple model is developed to describe the photochemical water oxidation mechanism. Our results reveal that heptazine possesses energy levels that are suitable for the water oxidation reaction. We suggest design principles for molecular photocatalysts which can be used as descriptors in future experimental and computational screening studies.

Photodetachment–photoelectron spectroscopy of HS−·H2S and DS−·D2S: the transition states of the SH + H2S and SD + D2S reactions

The transition state region for neutral hydrogen transfer reactions can be accessed by photodetachment of a stable negative ion with a geometry similar to that of the neutral transition state. In this work the SH + H(2)S and SD + D(2)S reactions are investigated by photodetachment-photoelectron spectroscopy of HS(-) x H(2)S and DS(-) x D(2)S. The spectra exhibit vibrational structure which is attributed to the antisymmetric stretching mode (H-atom motion) of the neutral transitions state for H-atom transfer. The spectra are compared to one-dimensional simulations performed using a wave packet propagation scheme. Electronic structure calculations of the anionic, neutral and transition-state geometries and calculations of the vertical detachment energy at different levels of theory are used to support the analysis of the spectra. A vertical detachment energy VDE of 3.06 eV has been determined.