Introducing Time-dependent Molecular Fields: Derivation of the Wave Equations

TL;DR

This paper derives wave equations for molecular systems interacting with high-intensity, short-duration external fields, revealing the coexistence of a novel vectorial field and an ordinary electric field within molecules, with implications for understanding molecular singularities.

Contribution

It introduces a new theoretical framework deriving wave equations for molecular interactions with intense, short fields, highlighting the emergence of a novel vectorial field linked to non-adiabatic couplings.

Findings

Derivation of coupled wave equations for molecular fields.

Identification of a new vectorial field from external interactions.

Visualization of NACTs at conical intersections as cosmic black-holes.

Abstract

This article is part of a series of articles trying to establish the concept Molecular Field. The theory that induced us to introduce this novel concept is based on the Born-Huang expansion as applied to the Schroedinger equation that describes the interaction of a molecular system with an external electric field. Assuming the molecular system is made up of two coupled adiabatic states the theory leads from a single spatial Curl Equation, two space-time Curl equations and one single space-time Divergent equation to a pair of decoupled Wave Equations usually encountered within the theory of fields. In the present study the Wave Equations are derived for an external field having two features: (a) its intensity is high enough; (b) its duration is short enough. For this situation the study reveals that the just described interaction creates two fields that coexist within a molecule: one is a novel vectorial field formed via the interaction of the external field with the Born-Huang non-adiabatic coupling terms (NACT) and the other is an ordinary, scalar, electric field essentially identical to the original external field. Part of the present study is devoted to the visualization of the outcomes via two intersecting Jahn-Teller cones which contain NACTs that become singular at their intersection point, also known as the point of Conical Intersection. This description is reminiscent of a metaphoric cosmic Black-Hole which swallows one type of an electric field and creates a new type. Finally, the fact that eventually we are facing a kind of a cosmic situation may bring us to speculate that singular NACTs are a result of cosmic phenomena. Thus, if indeed this singularity is somehow connected to reality then, like other singularities in physics, it is formed at (or immediately after) the Big Bang (and because of that, eventually the ability to form molecules).