The [3+1] Formulation of Chemical Dynamics in Curved Spacetime under an Eulerian Observer

Abstract

Traditionally, gravity is generally considered to exert an extremely weak effect in chemistry because Newtonian gravitation is typically negligible compared to the dominant Coulomb potentials in a molecular system. In this work, we propose a primitive framework of chemical dynamics in curved spacetime through a [3 + 1] formulation. To implement this framework, the nuclear Hamiltonian operator is revised by the metric tensor of the space rather than by simply adding Newtonian gravitation in the potential energy term. For the primitive framework, the reference frames fixed on the Eulerian observers are chosen, where the absolute space and universal time viewpoint of Galileo can be adopted. This choice can be directly interfaced with the existing flat-spacetime framework, enabling us to explore the present framework for a curved spacetime. Taking spherically symmetric curved spacetime (i.e., Schwarzschild spacetime) as a numerical demonstration, we explore (1) the H + H₂ reaction dynamics, (2) the H₂ + H₂ scattering dynamics, (3) the dynamics of dissociative chemisorption of H₂O on Cu(111), (4) the spectrum band of the anthracene cation, and (5) the Berry phase in the nuclear wave function of a 98D surface scattering model. These calculations predict that (i) the reaction or scattering probability and (ii) the spectrum band decrease abruptly to zero as the spacetime curvature increases; meanwhile, the geometric phase is unaffected by the spacetime curvature. Finally, discussions on these numerical results, together with perspectives on the applications of quantum field theory to chemical dynamics in curved spacetime, are given.