Accurate and efficient calculations of Hellmann-Feynman forces for quantum computation

Juntao Lai; Yi Fan; Qiang Fu; Zhenyu Li; Jinlong Yang

doi:10.1063/5.0167444

Accurate and efficient calculations of Hellmann-Feynman forces for quantum computation

J Chem Phys. 2023 Sep 21;159(11):114113. doi: 10.1063/5.0167444.

Authors

Juntao Lai¹, Yi Fan², Qiang Fu^{1

2

3}, Zhenyu Li^{3

4}, Jinlong Yang^{3

4}

Affiliations

¹ School of Future Technology, University of Science and Technology of China, Hefei 230026, China.
² Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei 230026, China.
³ Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China.
⁴ Key Laboratory of Precision and Intelligent Chemistry, University of Science and Technology of China, Hefei, Anhui 230026, China.

PMID: 37724727
DOI: 10.1063/5.0167444

Abstract

First-order derivatives of energies with respect to atomic coordinates are widely computed and used in quantum chemistry simulations. The rapidly emerging technology of quantum computing offers a new paradigm for solving relevant quantum chemistry equations. In this work, we have achieved analytical calculations of atomic forces based on the Hellmann-Feynman theorem within the framework of the variational quantum eigensolver. The accuracy of the approach is demonstrated by calculating the atomic forces of H2, LiH, H2O, and NH3 molecules, which are in excellent agreement with values obtained from full configuration interaction calculations. In particular, for systems with degenerate molecular orbitals, the analytical approach has a significant accuracy advantage over finite-difference-based methods and will not involve additional computational effort on a quantum computer. The calculated forces are further used to optimize the geometries of NH3 and CH4 molecules and to perform ab initio molecular dynamics simulations for the umbrella inversion of NH3, demonstrating the feasibility of the approach in practical quantum chemistry simulations.