*ab initio*calculations

^{1,a)}, Jose L. Bravo

^{2}and Joaquin Espinosa-Garcia

^{1}

### Abstract

A new analytical potential energy surface is presented for the reaction of hydrogen abstraction from methane by a hydrogen atom. It is based on an analytical expression proposed by Jordan and Gilbert [J. Chem. Phys.102, 5669 (1995)], and its fittable parameters were obtained by a multibeginning optimization procedure to reproduce high-level *ab initio* electronic structure calculations obtained at the CCSD(T)/cc-pVTZ level. The *ab initio*information employed in the fit includes properties (equilibrium geometries, relative energies, and vibrational frequencies) of the reactants, products, saddle point, points on the reaction path, and points on the reaction swath. No experimental information is used. By comparison with the reference results we show that the resulting surface reproduces well not only the *ab initio* data used in the fitting but also other thermochemical and kinetic results computed at the same *ab initio* level, such as equilibrium constants, rate constants, and kinetic isotope effects, which were not used in the fit. In this way we show that the new potential energy surface is correctly fitted and almost as accurate as the CCSD(T)/cc-pVTZ method in describing the kinetics of the reaction. We analyze the limitations of the functional form and the fitting method employed, and suggest some solutions to their drawbacks. In a forthcoming communication, we test the quality of the new surface by comparing its results with experimental values.

This work was partially supported by the Junta de Extremadura, Spain (Project No. PRI07A009).

I. INTRODUCTION

II. ELECTRONIC STRUCTURE CALCULATIONS

III. THE ANALYTICAL PES FUNCTION AND ITS FITTING PROCEDURE

A. The analytical PES

B. Mathematical details of the fitting procedure

C. Practical details of the fitting procedure: Fitting strategies

IV. QUALITY OF THE FIT

V. ACCURACY OF THE PES: KINETICS CALCULATIONS

VI. CONCLUSIONS

### Key Topics

- Ab initio calculations
- 32.0
- Tunneling
- 22.0
- Hydrogen reactions
- 18.0
- Optimization
- 10.0
- Surface dynamics
- 9.0

## Figures

Classical potential energy as a function of the reaction coordinate, . Solid line: CCSD(t)/cc-pVTZ reaction path; dotted line: analytical PES reaction path.

Classical potential energy as a function of the reaction coordinate, . Solid line: CCSD(t)/cc-pVTZ reaction path; dotted line: analytical PES reaction path.

Vibrational frequencies as functions of the reaction coordinate. Solid line: CCSD(t)/cc-pVTZ values; dashed line: analytical PES frequencies.

Vibrational frequencies as functions of the reaction coordinate. Solid line: CCSD(t)/cc-pVTZ values; dashed line: analytical PES frequencies.

Changes in the energy of the saddle point [optimized at the CCSD(t)/cc-pVTZ level] as the angle is bent from linear to 90°. The zero of energy is set at the energy of the saddle point geometry optimized at the CCSD(t)/cc-pVTZ level. Solid line: CCSD(t)/cc-pVTZ energies; dashed line: analytical PES energies.

Changes in the energy of the saddle point [optimized at the CCSD(t)/cc-pVTZ level] as the angle is bent from linear to 90°. The zero of energy is set at the energy of the saddle point geometry optimized at the CCSD(t)/cc-pVTZ level. Solid line: CCSD(t)/cc-pVTZ energies; dashed line: analytical PES energies.

Contour plots of the analytical PES and CCSD(t)/cc-pVTZ surface in the proximity of the saddle point. The symbol × indicates the location of the CCSD(t)/cc-pVTZ saddle point, while the symbol ○ is the saddle point in the analytical PES.

Contour plots of the analytical PES and CCSD(t)/cc-pVTZ surface in the proximity of the saddle point. The symbol × indicates the location of the CCSD(t)/cc-pVTZ saddle point, while the symbol ○ is the saddle point in the analytical PES.

Classical potential energy along the reaction path as a function of the (left panel) and (right panel) bond distances. Solid line: CCSD(t)/cc-pVTZ values; dotted line: analytical PES values.

Classical potential energy along the reaction path as a function of the (left panel) and (right panel) bond distances. Solid line: CCSD(t)/cc-pVTZ values; dotted line: analytical PES values.

Vibrationally adiabatic ground-state energy as a function of the reaction coordinate. The zero of energy is located at the reactants classical potential energy. Solid line: CCSD(t)/cc-pVTZ energies; dotted line: analytical PES energies.

Vibrationally adiabatic ground-state energy as a function of the reaction coordinate. The zero of energy is located at the reactants classical potential energy. Solid line: CCSD(t)/cc-pVTZ energies; dotted line: analytical PES energies.

Transmission probabilities and Boltzmann-averaged transmission probabilities computed using the small-curvature tunneling method as a function of the total energy at 250, 350, and 500 K. The zero of energy is located at the reactants potential energy. Solid line: CCSD(t)/cc-pVTZ probabilities; dashed line: analytical PES probabilities.

Transmission probabilities and Boltzmann-averaged transmission probabilities computed using the small-curvature tunneling method as a function of the total energy at 250, 350, and 500 K. The zero of energy is located at the reactants potential energy. Solid line: CCSD(t)/cc-pVTZ probabilities; dashed line: analytical PES probabilities.

## Tables

Saddle point geometry and energy parameters for the abstraction reaction. (Distances in Å; is the imaginary frequency, in , , is the classical energy of reaction, is the reaction enthalpy at 0 K, is the classical barrier height, is the activation enthalpy at 0 K. All energy values in .)

Saddle point geometry and energy parameters for the abstraction reaction. (Distances in Å; is the imaginary frequency, in , , is the classical energy of reaction, is the reaction enthalpy at 0 K, is the classical barrier height, is the activation enthalpy at 0 K. All energy values in .)

Parameters of the new PES.

Parameters of the new PES.

Properties of the stationary points. (Geometries in Å and degrees, frequencies in , energies in and measured with respect to reactants, is the hydrogen being transferred, and the attacking hydrogen. The *ab initio* level used is CCSD(T)/cc-pVTZ.)

Properties of the stationary points. (Geometries in Å and degrees, frequencies in , energies in and measured with respect to reactants, is the hydrogen being transferred, and the attacking hydrogen. The *ab initio* level used is CCSD(T)/cc-pVTZ.)

Rate and equilibrium constants. (Rate constants in , equilibrium constants are dimensionless. In parentheses, percentage of reaction that occurs by tunneling.)

Rate and equilibrium constants. (Rate constants in , equilibrium constants are dimensionless. In parentheses, percentage of reaction that occurs by tunneling.)

Selected KIEs computed using the PES and *ab initio* rate constants. (KIEs are defined as the rate for the perprotio reaction over the overall rate for the reaction given in parentheses.)

Selected KIEs computed using the PES and *ab initio* rate constants. (KIEs are defined as the rate for the perprotio reaction over the overall rate for the reaction given in parentheses.)

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