Victor Ryaboy

Three‐dimensional study of predissociation resonances by the complex scaled discrete variable representation method: HCO/DCO

Predissociation resonances of the radicals HCO and DCO were calculated using a three‐dimensional (J=0) complex scaled discrete variable representation (DVR) method that was applied previously to a study of the weakly bound van der Waals complex NeICl [Lipkin, Moiseyev, and Leforestier, J. Chem. Phys. 98, 1888 (1993)]. This study represents a first application of the complex scaling method to a full dimensional chemical reactive system described by a fitted ab initio potential energy surface [Bowman, Bittman, and Harding, J. Chem. Phys. 85, 911 (1986)]. It is shown that the calculation method, being applied to a strongly coupled three‐dimensional system, provides a unique criteria that makes it possible to identify all resonances in a given energy range as stationary solutions with respect to a complex variational parameter, independently of the resonance widths and their mutual overlapping. About 50 resonances were found for the radical HCO in the energy range between the ground and the second vibrational...

Resonance positions and widths by complex scaling and modified stabilization methods: van der Waals complex NeICl

The discrete variable representation (DVR) formulation of the complex coordinate method as has been used for calculating several resonances of NeICl [J. Chem. Phys. 98, 1888 (1993)], and a modified version of the recent developed stabilization method [Phys. Rev. Lett. 70, 1932 (1993)] are used for calculating all 30 isolated narrow resonances of NeICl (B, ν=2). The two L2 methods require a similar computational effort. The modified stabilization method requires the calculations of eigenvalues of real and symmetric Hamiltonian matrices in a sequence of ever larger enclosing boxes. The complex DVR method requires the use of complex arithmetic and calculations of eigenvalues of complex symmetrical matrices.

Cumulative reaction probability from Siegert eigenvalues: Model studies

A simple approach to cumulative reaction probability, N(E), calculation is described and tested using one‐dimensional symmetric and nonsymmetric Eckart potential barriers. This approach combines semiclassical transition state theory formulated by Miller [Faraday Discuss. Chem. Soc. 62, 40 (1977)] and reviewed recently by Seideman and Miller [J. Chem. Phys. 95, 1768 (1991)] and the complex coordinate method for calculations of Siegert eigenvalues. Siegert eigenvalues calculated numerically and analytically are found in excellent agreement with each other. It is demonstrated that corresponding eigenfunctions are localized in the potential barrier region and can be counted by their nodes. Perfect agreement between semiclassical N(E) dependence and exact quantum mechanical results was found in a broad energy range.

Flux–flux correlation function study of resonance effects in reactive collision

Thermal rate constants for a one‐dimensional model of a reactive collision involving a transient resonance are calculated by using autocorrelation functions of the flux operator in a finite basis set representation [Miller, Schwartz, and Tromp (MST), J. Chem. Phys. 79, 4889 (1983)] and performing either integration over time (MST) or Pade extrapolation to zero of an energy parameter [Lefebvre, Ryaboy, and Moiseyev, J. Chem. Phys. 98, 8601 (1993)]. The two procedures prove to be equally successful. We observe that in the time dependent approach, the correlation function of the reactive flux operator shows, as expected, damped oscillations with a period which slightly depends on the temperature. However, these oscillations are decaying on a time scale that is significantly shorter than the resonance lifetime. This finding shows that the flux–flux correlation function approach is applicable to calculations of thermal rate constants for reactions which proceed via formation of intermediate complexes as well a...

Quantum mechanical thermal rate constants using flux–flux correlation functions and Padé analytical continuation procedures

A new expression for a thermal reaction rate is derived. It is based on the flux–flux correlation function approach and a finite basis set representation but differs from the Miller–Schwartz–Tromp (MST) formulation [J. Chem. Phys. 79, 4889 (1983)] by substitution of time dependent sine functions by parameter dependent Lorentzians. Then we apply Pade extrapolation procedure to eliminate the parameter. This operation replaces the search for stability of the time dependent rate in the MST approach. The convergence of the method is checked on the one dimensional Eckart barrier as an illustrative example.

Cumulative reaction probabilities using Padé analytical continuation procedures

New computational techniques for calculation of cumulative reaction probabilities, N(E), are suggested. They are based on the expression of N(E) through the imaginary part of the Green function G [Seideman and Miller, J. Chem. Phys. 96, 4412 (1992)]. We use three methods to overcome numerical problems arising from branch cuts of G located along the real positive energy axes, addition of constant imaginary part ie to the Hamiltonian, addition of unoptimized optical potentials of the form iλ‖s‖ or iλ‖s‖2, and complex rotation of the reaction coordinate s→s⋅exp(iϑ). When N(E,u) is calculated on a grid of values of the numerical parameter u (u being e, λ, or ϑ), Pade analytical continuation to their zero values gives correct energy dependence of N(E). The method makes it possible to save computer time by using unoptimized parameters of the optical potential or of the complex scaling when calculating N(E,u). Test calculations on a one dimensional Eckart barrier and a model H+H2(ν=1) potential which supports a ...

Scattering matrix determination by asymptotic analysis of complex scaled resonance wave functions: Model Cl+H2 nonadiabatic dynamics

It has previously been shown that partial widths of resonance states can be calculated by the asymptotic analysis of the complex scaled resonance wave function [U. Peskin, N. Moiseyev, and R. Lefebvre, J. Chem. Phys. 92, 2902 (1990)] and by the complex coordinate scattering theory [N. Moiseyev and U. Peskin, Phys. Rev. A 42, 255 (1990)]. Here we use these methods for the first time to calculate complex partial width amplitudes. The complex amplitudes are independent of the complex scaling parameters and are used for calculating the resonance contribution to the scattering matrix (the S matrix) in the case of Cl+H2 scattering described by two coupled one-dimensional potential energy curves. The background contribution to the S matrix was calculated by the use of one ClH2 potential energy curve only. The sum of the resonance and the background contributions provides accurate complex S matrix elements and transition probabilities, even at the resonance energy for which total reflection is obtained due to the...

Cumulative reaction probability by the complex coordinate scattering theory

A new computational approach for the calculation of the cumulative reaction probability N(E) is introduced. As distinct from the optical potential method, recently applied by Seideman and Miller [J. Chem. Phys. 96, 4412 (1992)], we use the complex coordinate scattering theory to overcome the numerical difficulties in calculating the Green’s operator. Illustrative numerical examples for the 1D H+H2 collinear collision (Eckhart barrier) using complex scaling, in which both the physical potential and the flux matrix elements are perturbed, and smooth exterior complex scaling, in which both are left unchanged as in the Seideman–Miller procedure, are presented.

Thermal rate constants of multi-mode systems for the price of one: aziridine

Abstract An accurate and highly efficient method for calculating thermal rate constants in the automerization reaction of aziridine is presented. Theoretical results are in good agreement with available experimental data obtained by Borchardt and Bauer. The kinetics of aziridine inversion involve strong coupling of the reaction coordinate with other internal modes. Therefore, it is expected that in order to account for the energy redistribution processes in aziridine, the multi-mode Schrodinger equation should be solved. We show, however, that accurate rate constants for this system can be obtained by performing only one- (or two-) dimensional calculations. The key point in our approach is the insertion of absorbing boundary conditions in the products region of the potential surface, which prevent reflections from the products well to the reactants well, and thereby replace the role of the “neglected” internal modes in the dynamics.

Resonance and reaction

Abstract We examine two thermal reaction rates which can be defined for a one-dimensional model of a reaction dominated by a transient resonance. One of the rates corresponds to thermally equilibrated reactants in the region preceding the symmetrical double barrier potential supporting the intermediate complex. The other rate corresponds to pre-reaction thermal equilibration extending over the intermediate species. One rate is found to be twice the other. Numerical and analytical arguments are given to reach this conclusion. This discussion leads to a restrictive condition in the application of a formula given previously (R. Lefebvre and N. Moiseyev, J. Chem. Phys., 93 (1990) 7173) to relate the rate in the tunnelling regime to the set of artificial resonances produced by box quantization.