Hua-Gen Yu

Quantum theory of bimolecular chemical reactions

In this review we discuss quantum dynamically based theoretical methods for studying bimolecular gas phase chemical reactions. The scope is largely limited to reactions occurring on a single Born-Oppenheimer potential energy surface and mainly to time-independent Hamiltonians. An introductory overview is given, which includes a general discussion on approaches aiming to solve the time-independent and the time-dependent Schrodinger equation respectively, and how the resulting scattering matrix can be related to observables. The main topics of the review are the time-dependent wavepacket and the time-independent hyperspherical coordinate approaches to quantum dynamics. To perform such calculations it is necessary to first specify the relevant Hamiltonian operator, which has a kinetic and a potential part. The kinetic energy operator is easy to obtain in Cartesian coordinates, but more cumbersome in curvilinear coordinates. Two procedures are described. We also describe how to obtain the potential energy surfaces. The required input data are often obtained using ab initio methods, which themselves are not discussed. A very brief section on Green function methods for quantum scattering is also included. Rigorous quantum dynamic calculations quickly become expensive as the size of the problem grows. Therefore, reduced dimensionality calculations are often performed. However, only the most important degrees of freedom are treated explicitly. We discuss how the other degrees of freedom can be handled. An alternative way to reduce computational cost is to use semiclassical approaches, which have recently received renewed interest and we briefly review the main approaches. A few examples of reactions that have been studied with quantum dynamic theories are also included.

Four-dimensional quantum scattering calculations on the H+CH4→H2+CH3 reaction

Time-independent quantum scattering calculations have been performed to study the H+CH4→H2+CH3 reaction, using the analytic potential-energy surface developed by Jordan and Gilbert. A rotating bond umbrella (RBU) approximation with the implementation of a guided spectral transform subspace iteration technique has been applied together with a log-derivative method in hyperspherical coordinates. A single sector hyperspherical projection method was used to apply the boundary conditions to extract the S matrix at a large hyperradius. The results show that the H+CH4→H2+CH3 reaction occurs via a direct mechanism. The tunneling effect is pronounced, while there is little recrossing. Vibrational excitation of the C–H stretch and/or the H–CH3 bending modes of CH4 significantly enhance the reactivity. Exciting the umbrella mode of CH4 also enhance the reactivity, although less efficiently. The calculated thermal rate constants are larger than the experimental ones. However, good agreement has been obtained by inclu...

A four dimensional quantum scattering study of the Cl+CH4⇌HCl+CH3 reaction via spectral transform iteration

We present a quantum dynamics study of the Cl+CH4⇌HCl+CH3 reaction using a four-dimensional rotating bond umbrella (RBU) model. A semiempirical potential energy surface is employed, where the zero point energy of the modes not explicitly treated in the RBU calculations is approximately included. The potential gives a vibrationally adiabatic ground state barrier height of 3.48 kcal/mol. The calculations have been performed in hypercylindrical coordinates using a log-derivative method. A single sector hyperspherical projection method has been developed for applying boundary conditions. A guided spectral transform (GST) Krylov subspace method has been constructed to find the eigenstates of the coupling matrix appearing in the coupled channel equations. The results show that the product methyl is rotationally cold for the forward reaction. A pronounced tunneling effect on the rate constants was obtained. The calculated thermal rate constants are 12%–45% smaller than the experimental results over the temperatu...

Quantum dynamics of the O(3P)+CH4→OH+CH3 reaction: An application of the rotating bond umbrella model and spectral transform subspace iteration

We have applied the rotating bond umbrella (RBU) model to perform time-independent quantum scattering calculations of the O(3P)+CH4→OH+CH3 reaction based on a realistic analytic potential energy surface. The calculations are carried out in hypercylindrical coordinates with a log-derivative method incorporating a guided spectral transform (GST) subspace iteration technique. A single sector hyperspherical projection method is used for applying the boundary conditions. The results show that ground-state CH4 gives CH3 that is rotationally cold. For CH4 initially vibrationally excited in the C–H stretch or the H–CH3 bending mode, a bimodal CH3 rotational distribution has been observed. The product OH is a little vibrationally excited, while the umbrella mode of CH3 is moderately excited. Vibrational excitation enhances the reactivity substantially. The calculated rate constants are in good agreement with experimental measurements.

REACTION DYNAMICS OF CHLORINE ATOM WITH METHANE : DUAL-LEVEL AB INITIO ANALYTIC POTENTIAL ENERGY SURFACE AND ISOTOPE EFFECTS

An analytic potential energy surface for the Cl+CH4⇌HCl+CH3 reaction in C3V symmetry has been obtained by fitting to 1136 energy points from a dual-level MP2/SAC (Mo/ller–Plesset second order perturbation/scaling all correlation) calculation using the 6-311G(2d,d,p) basis set. A zero-point energy correction is made to account for all modes not explicitly treated with the time-independent quantum scattering rotating line umbrella (RLU) model, which is used for the dynamics calculations. The effective potential gives a vibrationally adiabatic ground-state barrier height of 3.36 kcal/mol and an endothermicity (0 K) of 1.19 kcal/mol for the Cl+CH4 reaction, and 4.43 kcal/mol and 2.29 kcal/mol, respectively, for Cl+CD4. Thermal rate constants, tunneling and kinetic isotope effects have been investigated in detail. Calculated differential cross sections for Cl+CD4→DCl+CD3, with reactants and products in their vibrational ground states, show that the DCl product is strongly backward scattered. Further, ground st...

Reduced dimensionality quantum scattering calculations on the Cl+CH4→HCl+CH3 reaction

Reduced dimensionality quantum scattering calculations using the Rotating Line Approximation, RLA, are performed on the Cl+CH4→HCl+CH3 reaction, treating CH4 as a pseudo-diatom QH. A LEPS potential energy surface is used, where the zero-point energy of the modes not explicitly treated in the RLA calculations are included. The calculations are performed using hyperspherical coordinates and the improved log-derivative method of Manolopoulos. Boundary conditions have been applied using a hyperspherical projection method and an approximate method where the boundary conditions are applied directly in the hyperspherical coordinates. It is explicitly shown that the agreement between the methods is good. Scattering resonances are observed and related to the shape of the hyperspherical adiabats. Cumulative and state-to-state reaction probabilities are also presented. Vibrational adiabaticity is found to dominate without being exclusive. For Cl+CH4(v=1)→HCl(n=1)+CH3 and a translational energy of 0.159 eV, measured ...

Quantum approaches to polyatomic reaction dynamics

In this review we discuss some quantum dynamical approaches to studying chemical reactions. We begin with a brief introductory section on how thermal rate constants can be calculated. This is followed by a section on time-dependent wave-packet calculations, where a brief description of the Multi-Configurational Time-Dependent Hartree (MCTDH) approach is included with emphasis on aspects relevant to thermal rate constant calculations. The next section is the main focus and treats time-independent quantum scattering theory biased to areas of our own interest. This includes a description of the guided spectral transform method to obtain eigenstates and the two-layer Lanczos method to treat presently up to twelve degrees of freedom. We end with concluding remarks and summary.

A SPECTRAL TRANSFORM KRYLOV SUBSPACE ITERATION APPROACH TO QUANTUM SCATTERING

Abstract A spectral transform Lanczos iteration method is suggested to find the eigenvalues and eigenvectors of the coupling matrix appearing in quantum scattering calculations. Three main attributes which improve previous implementations are (a) partial reorthogonalization, (b) exponential filter, and (c) discrete variable representation basis. The method is applied to the 3D rotating line umbrella calculations of the reaction Cl+CH 4 ⇌ HCl+CH 3 which shows that it is substantially faster than the direct diagonalization method. Calculated state-to-state reaction probabilities as well as adiabats are in good agreement with previous results.

Interpolated ab initio quantum scattering for the reaction of OH with HCl

We present an interpolated ab initio quantum scattering (AIQS) approach to studying chemical reactions. The dynamics calculations were performed by solving the time-independent Schrodinger equation. The potential energy surface used was interpolated from a set of grid energy points by a generalized discrete variable representation method. The guided spectral transform technique developed by the authors and the single-sector hyperspherical projection method for boundary conditions were extended to the rotating bond approximation model. The AIQS approach has been applied to the OH+HCl→Cl+H2O reaction, where the grid energy points were calculated by a dual level ab initio theory. The results obtained show that there exist a van der Waals complex in the entrance channel and an early saddle point with nonplanar geometry. Calculated thermal rate constants are in good agreement with the experimental results. They are nearly temperature-independent at low temperatures (T<300 K) while a sharp increase with tempera...

Quantum dynamics of the reaction of hydrogen atom with methane

Abstract Time-independent quantum scattering calculations on the H + CH 4 → H 2 + CH 3 reaction have been performed by using a four-dimensional rotating bond umbrella (RBU) model, based on a modified potential energy surface of Espinosa-Garcia and Corchado. The new surface gives a vibrationally adiabatic ground state barrier height of 14.1 kcal/mol. Calculated thermal rate constants are in good agreement with the experimental results. At room temperature the rate constant obtained is 8.16×10 −19 cm 3 molec −1 s −1 . It is found that the simple energy minimization approximation gives significantly small thermal rate constants for this reaction.