^{1,a)}, Michael J. Frisch

^{1}and H. Bernhard Schlegel

^{2}

### Abstract

The theoretical treatment of chemical reactions inevitably includes the integration of reaction pathways. After reactant, transition structure, and product stationary points on the potential energy surface are located, steepest descent reaction path following provides a means for verifying reaction mechanisms. Accurately integrated paths are also needed when evaluating reaction rates using variational transition state theory or reaction path Hamiltonian models. In this work an Euler-based predictor–corrector integrator is presented and tested using one analytic model surface and five chemical reactions. The use of Hessian updating, as a means for reducing the overall computational cost of the reaction path calculation, is also discussed.

I. INTRODUCTION

II. METHODS

III. NUMERICAL TESTS

A. Müller–Brown surface

B. Chemical reaction tests using analytic Hessians

C. Chemical reaction tests using Hessian updating

IV. CONCLUSIONS

### Key Topics

- Chemical reactions
- 17.0
- High performance computing
- 13.0
- Hydrogen reactions
- 10.0
- Chemical reaction theory
- 7.0
- Reaction mechanisms
- 7.0

## Figures

Reaction path following on the Müller–Brown surface using a step size of 0.10 with (a) Euler (×) and LQA (○) integrators, and (b) EulerPC (×) and HPC (○) integrators. Stationary points are indicated by solid circles and the reference reaction path is given by the solid curve connecting the stationary points. See the text for details.

Reaction path following on the Müller–Brown surface using a step size of 0.10 with (a) Euler (×) and LQA (○) integrators, and (b) EulerPC (×) and HPC (○) integrators. Stationary points are indicated by solid circles and the reference reaction path is given by the solid curve connecting the stationary points. See the text for details.

Reaction path following on the Müller–Brown surface using a step size of 0.20 with (a) Euler (×) and LQA (○) integrators, and (b) EulerPC (×) and HPC (○) integrators. Stationary points are indicated by solid circles and the reference reaction path is given by the solid curve connecting the stationary points. See the text for details.

Reaction path following on the Müller–Brown surface using a step size of 0.20 with (a) Euler (×) and LQA (○) integrators, and (b) EulerPC (×) and HPC (○) integrators. Stationary points are indicated by solid circles and the reference reaction path is given by the solid curve connecting the stationary points. See the text for details.

HCN angle vs C–H bond distance along the HCN → HNC reaction pathway using the EulerPC integration and step sizes of 0.10 (×) and 0.40 (○) amu bohr. Results of Euler integration using a step size of 0.40 amu bohr are also shown (△). The reference reaction path results are given by the solid curve.

HCN angle vs C–H bond distance along the HCN → HNC reaction pathway using the EulerPC integration and step sizes of 0.10 (×) and 0.40 (○) amu bohr. Results of Euler integration using a step size of 0.40 amu bohr are also shown (△). The reference reaction path results are given by the solid curve.

Four center elimination reaction pathway using the EulerPC integration and step sizes of 0.10 (×) and 0.40 (○) amu bohr. Results of Euler integration using a step size of 0.40 amu bohr are also shown (△). The reference reaction path results are given by the solid curve.

Four center elimination reaction pathway using the EulerPC integration and step sizes of 0.10 (×) and 0.40 (○) amu bohr. Results of Euler integration using a step size of 0.40 amu bohr are also shown (△). The reference reaction path results are given by the solid curve.

Reaction path for Cl + HCCl → ClCH + Cl, using the EulerPC integration and step sizes of 0.10 (×) and 0.40 (○) amu bohr. Results of Euler integration using a step size of 0.40 amu bohr are also shown (△). The reference reaction path results are given by the solid curve.

Reaction path for Cl + HCCl → ClCH + Cl, using the EulerPC integration and step sizes of 0.10 (×) and 0.40 (○) amu bohr. Results of Euler integration using a step size of 0.40 amu bohr are also shown (△). The reference reaction path results are given by the solid curve.

HCOH → HCO reaction path using the EulerPC integration and step sizes of 0.10 (×) and 0.40 (○) amu bohr. Results of Euler integration using a step size of 0.40 amu bohr are also shown (△). The reference reaction path results are given by the solid curve.

HCOH → HCO reaction path using the EulerPC integration and step sizes of 0.10 (×) and 0.40 (○) amu bohr. Results of Euler integration using a step size of 0.40 amu bohr are also shown (△). The reference reaction path results are given by the solid curve.

SiH + H → SiH reaction path using the EulerPC integration and step sizes of 0.10 (×) and 0.40 (○) amu bohr. Results of Euler integration using a step size of 0.40 amu bohr are also shown (△). The reference reaction path results are given by the solid curve.

SiH + H → SiH reaction path using the EulerPC integration and step sizes of 0.10 (×) and 0.40 (○) amu bohr. Results of Euler integration using a step size of 0.40 amu bohr are also shown (△). The reference reaction path results are given by the solid curve.

## Tables

RMS and maximum integration errors for reaction paths solved using EulerPC with analytic Hessians at all predictor integration steps.^{a}

RMS and maximum integration errors for reaction paths solved using EulerPC with analytic Hessians at all predictor integration steps.^{a}

RMS and maximum integration errors for reaction paths solved using EulerPC with a step size of 0.10 amu bohr incorporating Hessian updating for some or all predictor integration steps.^{a}

RMS and maximum integration errors for reaction paths solved using EulerPC with a step size of 0.10 amu bohr incorporating Hessian updating for some or all predictor integration steps.^{a}

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