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

Duc Anh Lai, Devin A. Matthews

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 use of fixed fields in the laboratory frame becomes ineffective for flexible molecules, as conformational changes can significantly alter their orientations. 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.

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

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 use of fixed fields in the laboratory frame becomes ineffective for flexible molecules, as conformational changes can significantly alter their orientations. 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.

Paper Structure

This paper contains 10 sections, 23 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theory
  3. Analytic nuclear gradients
  4. Principal Axis Frame
  5. Local Reference Frame
  6. Implementation
  7. Results
  8. Geometry optimization of cis-formanilide in the PAF
  9. Geometry optimization of trans-formanilide in the LRF
  10. Conclusions

Figures (4)

  • Figure 1: A) cis-formanilide in the PAF. B) trans-formanilide in the LRF.
  • Figure 2: Potential energy surface along the C_1-C_2-N-C_3 dihedral angle of cis-formanilide under $\mathbf c$-aligned fields in the PAF.
  • Figure 3: Total energies of trans-formanilide under OEEFs in the LRF.
  • Figure 4: Out-of-plane twisting of trans-formanilide phenyl ring due applied $\mathbf b$-aligned field of 0.04 a.u.