Reactive Transition Probabilities Research Articles

The geometric phase effect in chemical reactions

We investigate the influence of a vector potential arising due to the presence of a conical intersection in the adiabatic potential energy surface of a quasi-Jahn–Teller (JT) model and in the adiabatic hypersurface of an A+B 2 type reactive system. Reactive and non-reactive transition probabilities, calculated by time-dependent wave packet approach for a quasi-JT model, demonstrate the effect of a topological phase. The geometric phase (GP) effect has been introduced either by including a vector potential in the system Hamiltonian or by incorporating a phase factor in the adiabatic nuclear wave function. Even when we replace the operators in the Hamiltonian (with or without introducing a vector potential) with their classical variables and calculate integral and differential cross sections, we clearly observe the signature of the GP effect. Results obtained by semi-classical calculation on the same system also confirm this effect. In this context, we present also recent results obtained by quasi-classical trajectory calculations for the H+D 2 reaction.

Extended approximated Born-Oppenheimer equation. II. Application

In this work is applied the extended-approximated Born-Oppenheimer (BO) equation, as derived in the preceding article [Phys. Rev. A 62, 032506, (2000)], to a tristate system. For this sake an appropriate scattering two-arrangement\char21{}two-coordinate model was devised. The calculations for each energy were done three times: once without doing any approximation, and two times by approximating the three coupled Schr\odinger equations by two different, but gauge-related, single (extended) BO equation. State-to-state (reactive and nonreactive) transition probabilities were obtained, indicating that the new extended approximate BO equations yield relevant results for a tristate system.

Identifying collective dynamical observables bearing on local features of potential surfaces

A singular value decomposition of dynamical sensitivities provides insight into the relationship between a data set and the potential which is often not evident from the sensitivities of individual observables. An illustration is treated consisting of data sets drawn from reactive transition probabilities as a function of energy for the collinear H+H2 system. While the sensitivities of individual reactive transition probabilities to the two-dimensional potential are highly structured functions of the potential coordinates, a set of reactive transition probabilities is identified which collectively has localized sensitivity primarily to the saddle point region and secondarily to the slope along the H3 symmetric stretch line in the outer corner tunneling region and to the width of the barrier. Information of this type garnered from a principal component sensitivity analysis can be especially valuable when attempting to use dynamics data to refine potential surfaces.

Adiabaticity of the nonreactive bond in atom-triatom reactions: a quantum mechanical study of the hydrogen atom + water .fwdarw. hydroxyl + hydrogen system

This work is a quantum mechanical study of the four-atom process H + HzO - H2 + OH and its isotopic analogs. State-to-state reactive probabilities were calculated for the collinear configuration. The adiabaticity behavior with regard to the nhreactive bond, as established by Sinha et al. (J. Chem. Phys. 1991,94,4298), was confirmed for the H + HOD system but not for the H + H2O one. Enhancement of the reaction process due to vibrational excitation as was established by Sinha et al. and Bronikowski et al. (J. Chem. Phys. 1991, 95, 8645) was fully confirmed for the H + HOD system and for the H + HzO system. The calculations were carried out employing negative imaginary potentials to form absorbing boundary conditions. I. Iatroduction Confidence in the reliability of applying negative imaginary potentials (NIPS) to study time-independent scattering processes in general and exchange processes in particular has been steadily growing.l-l0 These potentials were applied not only t0collinear~9~9~ and other frozen configurations3 but to three-dimensional systems as ell.^.^ In case of the process D + Hz(uj) - HD (~7’) + H, state-testate reactive probabilities were calculated6 and the results compared with the results from more established approaches;’ very encouraging fits were obtained. Other groups have studied NIPS.~-~O In a detailed study, Seideman and Miller,lo confirmed that accurate reactive transition probabilities are well reproduced employing these potentials. These authors reported, moreover, that different types of potentials, e.g., the WoodsSaxon potential and/or power-law potentials, also yield accurate results, for a wide range of parameters. The present work extends these treatments to four-atom systems. We report on state-to-state reactive transition probabilities for the three isotopic reactions:

Exact quantum mechanical three-dimensional reactive probabilities for the D + H 2 system: variational calculations based on negative imaginary absorbing potentials

We report on the first exact three-dimensional state-to-state reactive transition probabilities as obtained employing a variation (time independent) treatment based on negative imaginary absorbing potentials. The calculations were carried out for the D + H 2( vj| J=0)→HD( v′ j′| J=0) + H process. The results were found to fit reasonably well with those obtained by other methods.

Quantum functional sensitivity analysis for the collinear H+H2 reaction rate coefficient

The effects of features in the potential energy surface on the collinear H+H2 reaction rate coefficient are investigated by the method of quantum functional sensitivity analysis (QFSA). The calculations use QFSA to connect features in the microscopic realm, with their response upon macroscopic quantities of chemical interest, via the intermediary sensitivities of the reactive transition probabilities. While the sensitivities of the individual transition probabilities show considerable structure, there is an attendant loss of structure in the rate coefficient sensitivities because of the thermal averaging. For the range of temperatures used in our study (200–2400 K), the most important region of the potential energy surface is found to be not at the top of the barrier, but rather at the lower energy shoulders of the barrier. There are also regions near the barrier where an increase in the potential surface actually increases the reaction rate! The effects of using different underlying potentials [the Porter–Karplus (PK2), Liu–Siegbahn–Truhlar–Horowitz (LSTH), and double many-body expansion (DMBE) surfaces] on the nature of the results were also compared. The absolute sensitivity magnitudes on the PK2 surface vary considerably from the other two, but the relative change in the rate coefficient is about the same on all three surfaces. Furthermore, the identified regions of importance on the potential surfaces remain essentially the same. The reactive scattering calculations were performed with the log-derivative version of the Kohn variational principle.

Perturbative reactive scattering within a quasiadiabatic representation: Multichannel application

Low energy reactive transition probabilities for a model multichannel collision problem, are determined within a so-called quasiadiabatic (QA) representation of the system electronic energy. The procedure involves setting up a set of coupled nonreactive surfaces (the QA representation) and then perturbatively mixing coupled-channel wave functions on the QA surfaces. It is applied to a hard-sphere-type model of the collinear A+BC reaction and for a relatively high system mass (5.0×104 a.u.). Optimization of the representation (which we have previously argued should temper maximization of the QA reactivity with a drive for balance between its diabatic and nonadiabatic components) yields results which are in very good agreement with exact ones (errors <10%) over a wide range of collision energies. At the same time, as the collision energy approaches the classical reactive threshold, we see evidence of QA failure; we trace this to difficulties with our particular optimization procedure when the diabatic contribution becomes dominant. ‘‘Conventional’’ perturbative results are generated for the same model problem and found to be poor in general (errors ≂40%–50%). It is demonstrated that the ineffectiveness of the conventional approach may be ascribed to the system’s high mass.

The Newton variational functional for the log-derivative matrix: Use of the reference energy Green’s function in an exchange problem

The Newton Variational Principle for the log-derivative matrix (the Y-NVP) is studied in the context of a collinear exchange problem. In contrast to the integral equation methods that calculate the K or the T matrices directly, the matrix elements of the log-derivative Newton functional can be made independent of the scattering energy. This promises considerable savings in computational effort when state to state transition probabilities are calculated at several energies, since the matrix elements of the functional need be calculated only once. Green’s functions defined with respect to a reference energy, called the reference energy Green’s functions (or the REGFs), play a central role in the Y-NVP functional. The REGFs may be defined with or without reference to asymptotic channel energies. If channel dependent REGFs are used, the Y-NVP converges at the same rate as the GNVP for the K or T matrices, when the scattering energy is the same as the reference energy. On the other hand, channel independent REGFs permit even further reductions in computational effort. We use both types of REGFs in the present paper, and compare the rates of convergence. These comparisons show that the convergence rate of the method is not significantly altered by the type of REGF used. Further, we show that the Y-NVP is able to achieve rapid convergence of reactive transition probabilities over a large range of scattering energies, even when scattering resonances are present. An analysis of the computational effort required for each part of the calculation leads to the conclusion that a Y-NVP calculation using a channel independent REGF requires essentially only the same amount of computer time as a log-derivative Kohn (Y-KVP) calculation, while, presumably, offering faster convergence.

Contracted basis functions for variational solutions of quantum mechanical reactive scattering problems

A new method for constructing efficient basis functions for f variational calculations of quantum mechanical rearrangements is presented and tested. With this method, using the same contracted basis functions for all channels in a given vibrational manifold, we can obtain reactive transition probabilities for F + H, H + HF(u’), where v’is the final vibrational state, that are accurate to 0.01 absolute accuracy or 5% relative accuracy with 40% less basis functions than are required for the same accuracy using primitive basis sets and with 60% less basis functions than were used for our previous calculations that uere converged to 1%

A time-dependent wave packet approach to atom–diatom reactive collision probabilities: Theory and application to the H+H2 (J=0) system

This paper describes a new approach to the study of atom–diatom reactive collisions in three dimensions employing wave packets and the time-dependent Schrödinger equation. The method uses a projection operator approach to couple the inelastic and reactive portions of the total wave function and optical potentials to circumvent the necessity of using product arrangement coordinates. Reactive transition probabilities are calculated from the state resolved flux of the wave packet as it leaves the interaction region in the direction of the reactive arrangement channel. The wave packet does not need to be propagated into the asymptotic reactive region in order to determine accurate vibrationally resolved, but rotationally summed reaction probabilities. The present approach is used to obtain such vibrationally resolved reaction probabilities for the three-dimensional H+H2 (J=0) hydrogen exchange reaction, using a body-fixed system of coordinates.

A new accurate (time-independent) method for treating three-dimensional reactive collisions: The application of optical potentials and projection operators

This work describes a new (time-independent) approach to the study of atom–diatom reactive collisions in three dimensions. The method is based on the idea of converting a reactive multiarrangement problem into an inelastic single-arrangement problem. This conversion is done by applying optical potentials which are located at all exits of the reagents arrangement. The reactive transition probabilities are calculated applying flux formulas. The method is reminiscent of a previous time-dependent method successfully applied for both collinear and three-dimensional reactive collisions.

A new accurate (time-independent) method for treating reactive collisions: conversion of a scattering problem into a bound problem

This work describes a new (time-independent) approach to the study of atom–diatom reactive collisions in the collinear case and in three dimensions. The method is based on the idea of converting a reactive multi-arrangement problem into an inelastic single-arrangement problem. This conversion is done by applying optical potentials which are located at all exits of the reagents arrangement. The reactive transition probabilities are calculated applying flux formulae. The method is reminiscent of a previous time-dependent method that was successfully applied for both collinear and three-dimensional reactive collisions.

Resonances in collinear He + H 2+ collisions

Reactive and non-reactive transition probabilities are reported for the collinear He + H 2 + collisions in the energy range 0.955–1.5 eV. An interesting mirror-image relation between states of the same symmetry is pointed out. The scattering resonances are interpreted qualitatively in terms of the bound states supported by the vibrational adiabatic potential in hyperspherical coordinates.

On the construction of perturbation integrals for the description of reactive molecular collisions

We continue our investigation of the relative effectiveness of conventional and quasiadiabatic (QA) perturbation schemes in the determination of reactive transition probabilities. The simple problem of particle reflection and transmission at a one-dimensional potential barrier (loosely based on the minimum energy path interaction of the H+H2 system) is again adopted for our calculations. By examining the accumulation with reaction coordinate of exact and conventional perturbative probability integrals over a wide range of energies and for both low and high system masses (on a molecular scale), we have been able to account for our recent observations with regard to the high mass ineffectiveness of the conventional scheme. The effectiveness of a QA based scheme at high mass, also observed in our earlier work, is here give more substance by the development of a procedure for optimizing parameters of the (QA) representation. The procedure tempers maximization of the QA transmission (with respect to parameter variation) by also driving for a balance between its diabatic and nonadiabatic component contributions. Comparing for the optimized QA parameters and at a high system mass, exact and QA accumulating probability integrals, we find very good agreement.

A test of two approximate two-state treatments for the dynamics of H-atom transfers between two heavy particles

Reactive transition probabilities and Boltzmann-averaged reactive transition probabilities for a slightly off-resonant model H-atom transfer system with an appreciable energy barrier are calculated using the approximate methods of Babamov et al. and of Crothers–Stückelberg. Both are compared with the corresponding quantities obtained from a numerical two-state treatment of the same model system. The method of Babamov et al. is seen to give more accurate results for the transition probabilities at energies below and around the reaction threshold, and much more accurate results for the Boltzmann-averaged probabilities in a wide range of temperatures than the second method. The relative merits of the two formulas are discussed.

On the perturbative analysis of the dynamics of reactive collisions

This paper explores the application of quantum mechanical perturbation theory to the determination of reactive transition probabilities. The very simple problem of particle reflection and transmission at a one-dimensional potential barrier is examined over a wide range of energies and for alternate perturbative schemes. The first scheme is conventional; the second is based on a quasi-adiabatic (QA) description of the dynamics. We find that for a choice of model parameter values, loosely based on the H+H2 system, the first (conventional) scheme provides quantitatively accurate results. However, at higher system masses, the first scheme results are in only moderate agreement with exact results and are highly sensitive to the variation of distortion potential parameters. For the high system mass case, the QA results are in much better agreement with the exact results. However, the QA results are also highly sensitive to the variation of QA potential parameters. We discuss finally a number of avenues for further investigation.

Quantal and semiclassical studies of reactions in strong laser fields: F(2P3/2, 2P1/2)+H2+ℏω (0.117, 0.469, 1.17 eV)

The effects of three photons, namely the CO2 photon (hν=0.117 eV), the HF photon (hν=0.469 eV), and the Nd:glass photon (hν=1.17 eV), on the reactive [F(2P3/2), F(2P1/2)]+H2 systems were studied. Results due to exact quantal, approximate quantal (curve crossing model), and semiclassical (trajectory surface hopping model) treatments are presented for the collinear arrangement. It was found that the existence of field intensities of 0.1–2.5 TW/cm2 hardly affect the reactive process for the system F(2P3/2)+H2. In the interaction of F(2P1/2) and H2 which is, for all practical purposes, elastic in the field-free case, the field-induced electronic inelastic (the spin conversion process) and electronic reactive transition probabilities are not large. For an intensity of 0.1 TW the largest probability encountered is 20%. In comparing the quantal and the semiclassical treatments, it was found that except for one case where a quantitative fit was obtained in all (five) other cases the agreement is at most qualitative. In general, the semiclassical results are lower than the quantal ones.

Quantum mechanical study of the D+H2→HD+H reaction

A quantum mechanical study is made of the D+H2(vi=0,1)→ HD(vf=0,1,2)+H reactions within the infinite order sudden approximation (IOSA) for the total energy interval 0.28≤Et≤1.28 eV. Results at various stages of the calculation are given ranging from most detailed reactive transition probabilities through opacity functions and γ-dependent cross sections to total and state-to-state integral and differential cross sections, as well as rate constants. The cross sections and rate constants are compared with other available theoretical results and experiments. It is found that the IOSA total cross sections for vi=0,1 overlap very nicely with the corresponding quasiclassical trajectory cross sections, except for the tunneling region. A less satisfactory fit is obtained with the distorted wave born approximation results. The calculated rate constants are compared with experiment and a rather good fit is obtained, in particular for rate constants from the ground state.

Quantum-mechanical reactive transition probability. Application of the arrangement channel approach

The first reactive transition probabilities obtained by solving coupled arrangement channel integral equations are presented. The uniqueness of this approach is that no matching is employed in transforming from one arrangement channel to the other. The results when compared with those obtained by other (propagative) methods are satisfactory.

Vibrational deactivation on chemically reactive potential surfaces: An exact quantum study of a low barrier collinear model of H + FH, D + FD, H + FD and D + FH

We study vibrational deactivation processes on chemically reactive potential energy surfaces by examining accurate quantum mechanical transition probabilities and rate constants for the collinear H + FH(v), D + FD(v), H + FD(v), and D + FH(v) reactions. A low barrier (1.7 kcal/mole) potential surface is used in these calculations, and we find that for all four reactions, the reactive inelastic rate constants are larger than the nonreactive ones for the same initial and final vibrational states. However, the ratios of these reactive and nonreactive rate constants depend strongly on the vibrational quantum number v and the isotopic composition of the reagents. Nonreactive and reactive transition probabilities for multiquantum jump transitions are generally comparable to those for single quantum transitions. This vibrationally nonadiabatic behavior is a direct consequence of the severe distortion of the diatomic that occurs in a collision on a low barrier reactive surface, and can make chemically reactive atoms like H or D more efficient deactivators of HF or DF than nonreactive collision partners. Many conclusions are in at least qualitative agreement with those of Wilkin’s three dimensional quasiclassical trajectory study on the same systems using a similar surface. We also present results for H + HF(v) collisions which show that for a higher barrier potential surface (33 rather than 1.7 kcal/mole), the deactivation process becomes similar in character to that for nonreactive partners, with v→v−1 processes dominating.