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

Area of Science:

• Quantum Computing
• Computational Chemistry
• Quantum Mechanics

Background:

• Atomic forces are crucial for quantum chemistry simulations, typically computed via energy derivatives.
• Quantum computing presents a novel approach for complex quantum chemistry problems.
• Existing methods for calculating atomic forces can be computationally intensive or less accurate for certain systems.

Purpose of the Study:

• To develop and validate an analytical method for calculating atomic forces using the Hellmann-Feynman theorem within a quantum computing framework.
• To demonstrate the accuracy and efficiency of this quantum-based approach compared to classical methods.
• To showcase the practical applicability of the method in molecular geometry optimization and ab initio molecular dynamics.

Main Methods:

• Employed the Hellmann-Feynman theorem for analytical force calculations.
• Utilized the variational quantum eigensolver (VQE) algorithm on a quantum computing platform.
• Validated results against high-level classical methods like full configuration interaction (FCI).

Main Results:

• Achieved accurate analytical calculations of atomic forces for H2, LiH, H2O, and NH3 molecules.
• Demonstrated superior accuracy of the analytical quantum approach over finite-difference methods, especially for systems with degenerate molecular orbitals.
• Successfully applied the calculated forces to optimize molecular geometries and perform ab initio molecular dynamics simulations.

Conclusions:

• The developed analytical force calculation method is accurate and feasible for practical quantum chemistry simulations.
• This quantum computing approach offers significant advantages, particularly for systems with degenerate orbitals, without increased computational cost.
• The method paves the way for more efficient and accurate simulations in computational chemistry using quantum computers.