The Special Theory of Relativity as Applied to the Born-Oppenheimer-Huang Approach

TL;DR

This paper explores how the special theory of relativity influences the Born-Oppenheimer-Huang approach, revealing the existence of molecular fields and their effects near conical intersections, with implications for quantum chemistry and electromagnetic analogies.

Contribution

It introduces a relativistic extension of the Born-Oppenheimer-Huang approach, deriving relativistically affected non-adiabatic coupling terms and equations.

Findings

Relativistic effects modify non-adiabatic coupling terms.

Existence of molecular fields analogous to electromagnetic fields.

Implications for behavior near conical intersections.

Abstract

In two recent publications ( Int. J. Quant. Chem. 114, 1645 (2014) and Molec. Phys. 114, 227 (2016)) it was shown that the Born -Hwang (BH) treatment of a molecular system perturbed by an external field yields a set of decoupled vectorial Wave Equations, just like in Electromagnetism. This finding led us to declare on the existence of a new type of Fields, which were termed Molecular Fields. The fact that such fields exist implies that at the vicinity of conical intersections exist a mechanism that transforms a passing-by electric beam into a field which differs from the original electric field. This situation is reminiscent of what is encountered in astronomy where Black Holes formed by massive stars may affect the nature of a near-by beam of light. Thus if the NonAdiabatic-Coupling-Terms (NACT) with their singular points may affect the nature of such a beam (see the above two publications) then it would be interesting to know to what extend NACTs (and consequently also the BH equation) will be affected by the special theory of relativity as introduced by Dirac. Indeed while applying the Dirac approach we derived the relativistic affected NACTs as well as the corresponding BH equation.