An intrinsic reaction coordinate (IRC) driven VQE algorithm (IRC-VQE) to trace chemical reaction pathways accurately*

The intrinsic reaction coordinate (IRC) of a molecule is defined as the minimum energy reaction pathway (MERP) on the BOPES in mass-weighted cartesian coordinates between the transition state of a reaction and its reactants and products. We report here an IRC-driven variational quantum eigensolver (IRC-VQE) algorithm to trace accurately chemical reaction pathways as a function of molecular bond stretching, bending or torsional degrees of freedom, where we estimate the ground state energy using VQE and trace the pathway in two different modes, viz., a perturbative-distortion based approach for traversing points along the IRC path, or a finite-difference based geometry optimization in eigenmode basis. We have applied IRC-VQE to simulate the umbrella inversion phenomenon of ammonia (NH₃) as a function of N-H bond stretching, which could resolve the tiny 8 mH barrier height between the planar (D_3h) and pyramidal (C_3v) configurations of NH₃. In another example, the experimentally observed tiny rotational energy barrier of 12 kJ/mol between staggered and eclipsed conformers of ethane (C₂H₆) has been traced accurately as a function of H-C-C-H torsional angle chosen as IRC. In future, we plan to improve the scalability of this framework to handle molecules of larger size and higher degrees of freedom. The incorporation of finite-difference based energy gradient could help the classical nonlinear optimizers to trace the reaction paths more accurately than force-field based methods which are approximate.