Analytic nuclear gradients including oriented external electric fields in a molecule-fixed frame

TL;DR

This paper develops a formalism for calculating analytic nuclear gradients in molecules under oriented external electric fields, improving control and understanding of electric field effects on molecular structure and reactivity.

Contribution

It introduces two molecular reference frames to define oriented electric fields and derives analytic nuclear gradients for accurate geometry optimization under these fields.

Findings

Validated the formalism with geometry optimizations of formamides.

Revealed distinct structural responses to electric fields.

Demonstrated robustness of the gradient calculations.

Abstract

Electric field-assisted chemistry has attracted much attention in recent years, particularly in the context of oriented external electric fields for controlling molecular structure and reactivity. Such fields have been explored in a wide range of applications, including switching materials, nanoparticles, controllable catalysts, medicines, and clinical therapies. However, the determination of fixed fields in the laboratory frame becomes ineffective for flexible molecules, as conformational changes can significantly alter the relative orientation between the applied field and molecular structure. In this work, we propose two molecular reference frames -- the principal axis frame and the local reference frame -- to define oriented electric fields within the molecular framework. These coordinate systems powerfully eliminate ambiguities in the relative orientation between the applied field and the molecule. Analytic nuclear gradients in the presence of external electric fields are derived and implemented, with an initial application to field-dependent geometry optimizations of cis- and trans-formanilide. Analysis of the resulting field-induced equilibrium structures reveals distinct structural responses, validating the accuracy and robustness of the proposed formalism. The analytic gradient framework enables systematic investigations of molecular properties and reactivity under arbitrarily oriented electric fields, opening new opportunities for computational modeling and rational design in electric field-controlled chemistry.