Vladimir I. Osherov

Ab initio analysis of the transition states on the lowest triplet H2O2 potential surface

The lowest triplet H2O2 potential surface was analyzed for the transition and minimum-energy structures in the range from −0.2 to +5.4 eV with respect to the H2+O2 energy. All the transition structures, the reaction pathways, and the local minima were found to have planar configurations for the atoms. We focus on the transition structures responsible for the main bimolecular chemical reactions formally possible on this surface: H2+O2↔2HO, H+HO2, and H2O+O; H+HO2↔2HO and H2O+O; and 2HO↔H2O+O. For these reactions, activation energies and rate constants in the transition state approximation were evaluated. Our computed rate constants confirm the recommended values for the H+HO2→H2+O2 and HO+HO→H2O+O reactions. The results obtained refute the elementary character of the H+HO2→H2O+O process and call into question the possibility of chain initiation in the H2/O2 system by means of a bimolecular reaction. Most likely, the chain initiation in the gas phase is owing to trimolecular reactions H2+2O2→2HO2, 2HO+O2. S...

Quantum mechanically exact analytical solutions of a two‐state exponential model

A certain two‐state exponential potential model is solved quantum mechanically exactly. Compact expressions for nonadibatic transition matrices are obtained. Interesting quantum mechanical threshold effects are found. Simple very accurate expressions are found from a semiclassical viewpoint for the nonadiabatic transition probabilities, indicating that the exponential model may present a third important basic model in addition to the Landau–Zener–Stueckelberg and the Rosen–Zener–Demkov models. Extension to general cases is also briefly discussed.

On the dynamics of a triatomic system in the vicinity of a conical intersection between electronic potential-energy surfaces

Abstract The dynamics of a triatomic system in the vicinity of a conical intersection for the Π and Δ states of linear complex is investigated. The dynamics of the nuclear motion is analysed for a highly symmetrical hamiltonian, which is linear in the nuclear displacements. Full separation of the variables is acheived and for a particular case an exact solution is found. From the positions and widths of the resonances in the upper conical term, the lifetimes of triatomic collision complexes are estimated.

Quantum and semiclassical dynamics of quasilinear triatomic system near the adiabatic term intersection point of Σ=Π=Σ− type

Under consideration are the configuration dynamics of a quasilinear triatomic system near the adiabatic term intersection point of Σ+ = Π = Σ--type. The dynamics are described by a two-dimensional four-channel hamiltonian, which is formulated in the paper. The two-dimensional angular momentum conservation law allows us to perform the separation of variables in the corresponding Schrodinger equation. The quantum and semiclassical configuration dynamics of a triatomic system are studied under some limiting relations between the energy and angular momentum. The 2 × 2 S-matrix for the two open channels, the position and widths of resonances, and the nonadiabatic transition probabilities are also determined.

Non-adiabatic transitions in a two-state exponential potential model

A general two-state exponential potential model is investigated and the corresponding two-channel scattering problem is solved by means of semiclassical theory. The analytical expression for the non-adiabatic transition matrix yields a unified expression in the repulsive and previously studied attractive case. The final formulae are expressed in terms of model-independent quantities, i.e. the contour integrals of adiabatic local momenta. Oscillations of the overall transition probability below the crossing of diabatic potentials are observed in the case of strong coupling. The theory is demonstrated to work very well even at energies lower than the diabatic crossing region. Based on our results the unified theory of non-adiabatic transitions, covering the Landau-Zener-Stueckelberg and Rozen-Zener-Demkov models in such an energy range, is possible.

The Stokes multipliers and quantization of the quartic oscillator

The asymptotic representation of the general solution of the triconfluent Heun equation is obtained with some restrictions on the parameters. The connection between the Stokes multipliers in various domains of the complex plane is established. The basic Stokes multipliers are obtained by matching the solutions of Thome recurrences with the Birkhoff asymptotic set. The quantization condition for the quartic oscillator is derived and analyzed.

The intersection of vibronic levels

The basic one-dimensional vibronic problem has been solved exactly in an analytical form for degenerate configurations. The solution using the intermediate p-representation and the Heun functions expansion on the Gauss basis set has indicated the existence of dynamic symmetry. The direct solution in x-representation has specified an effective method for the calculation of vibronic problems. Conical intersection parameters have been obtained and analyzed for a few lower levels.

Semiclassical treatment of resonances in the collinear O + HO exchange reaction

Abstract Feshbach type sharp resonances appearing in the O+HO collinear reaction are analyzed by the newly completed semiclassical theory for the Landau-Zener-Stueckelberg type curve crossings. Not only the resonance positions but also the widths are nicely reproduced in comparison with the exact numerical calculations, even when the widths are as small as 10 −8 ∼10 −11 au. The semiclassical theory is extended so as to be applicable to the case that the bottom of the upper adiabatic potential is higher than the crossing point.

Relativistic pseudo-Jahn-Teller effect in the square-planar molecules with a central atom

ABSTRACT We consider the relativistic multi-mode pseudo-Jahn-Teller effect (2Eu + 2A2u) × (big + b2g + eu) for square-planar molecular complexes with a heavy central atom and the odd number of electrons. All 32 elements of the double spin group D4h are determined in the form of space-matrix operators. The 6 × 6 vibronic matrix is derived in the quadratic (with respect to the normal coordinates) approximation for the contributions of electrostatic (non-relativistic) Hamiltonian and in linear approximation for contribution of spin-orbital coupling. Vibronic matrix is represented on the basis of double-value irreducible representations of the symmetry group D4h

Dynamic phase for the vibronic problem

The quantization condition for the basic vibronic problem is formulated in frames of the advanced semiclassical (WKB) approximation. The analytical representation of the dynamic phase is found in the asymptotic limit ℏ → 0. The numerical tests confirm that the accuracy of the approach proposed supersedes the accuracy of the matching method.