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A scheme to interpolate potential energy surfaces and derivative coupling vectors without performing a global diabatization

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10.1063/1.3660686

### Abstract

Simulation of non-adiabatic molecular dynamics requires the description of multiple electronic state potential energy surfaces and their couplings. *Ab initio*molecular dynamics approaches provide an attractive avenue to accomplish this, but at great computational expense. Interpolation approaches provide a possible route to achieve flexible descriptions of the potential energy surfaces and their couplings at reduced expense. A previously developed approach based on modified Shepard interpolation required global diabatization, which can be problematic. Here, we extensively revise this previous approach, avoiding the need for global diabatization. The resulting interpolated potentials provide only adiabatic energies, gradients, and derivative couplings. This new interpolation approach has been integrated with the *ab initio* multiple spawning method and it has been rigorously validated against direct dynamics. It is shown that, at least for small molecules, constructing an interpolated PES can be more efficient than performing direct dynamics as measured by the total number of *ab initio* calculations that are required for a given accuracy.

© 2011 American Institute of Physics

Received 18 April 2011
Accepted 21 October 2011
Published online 13 December 2011

Acknowledgments: This work was performed under DOE Contract No. DE-AC02-7600515.

Article outline:

I. INTRODUCTION

II. THEORY

A. Global diabatic interpolation

B. Local diabatic interpolation

III. TREATING DEGENERACIES

A. Original assignment algorithm

B. Revised assignment algorithm

1. The optimization step

2. The total algorithm

IV. MULTIPLE SOLUTIONS IN *AB INITIO* METHODS

V. TRUNCATION OF THE DIABATIC STATES

VI. COMPUTATIONAL DETAILS

VII. RESULTS AND DISCUSSION

VIII. CONCLUSIONS

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2011-12-13

2014-04-25

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