Relation between ab initio molecular dynamics and electron-phonon interaction formalisms

TL;DR

This paper establishes the exact equivalence between ab initio molecular dynamics and electron-phonon interaction formalisms, enabling their combined use for more accurate ab initio modeling of thermal vibrations and electronic structures.

Contribution

It demonstrates the formal equivalence of AIMD and ES-DWF formalisms, enabling their integration for enhanced ab initio analysis of thermal effects and electronic properties.

Findings

The two formalisms are exactly equivalent.

Combining formalisms extends ab initio modeling capabilities.

Self-consistent band structures can be obtained from AIMD.

Abstract

The relation between ab initio molecular dynamics formalism and the electron-phonon interaction formalism [P.B. Allen and V. Heine, J. Phys. C 9, 2305 (1976)] is explored. The fundamental quantity obtained in the AIMD formalism - total energy for any configuration - is also obtained from the formalism (ES-DWF) that incorporates the role of Debye-Waller Factor in electronic structure calculations. The two formalisms are exactly equivalent and represent the direct and perturbation theory approaches to determine total energy. This equivalence allows either formalism to be used depending on the requirement - ES-DWF for a priori theoretical analysis and AIMD for ab initio modeling of the effect of thermal vibrations. Combining the two formalisms makes the ES-DWF formalism into an ab initio method and increases the range of problems that can be modeled ab initio. It is also theoretically possible to obtain self-consistent band structures from AIMD calculations. This study clarifies the incorrect assumptions regarding the two formalisms that exist in published literature. By combining the two formalisms and including self-energy effects, more accurate results can be obtained, ab initio, within the adiabatic approximation, than by using AIMD alone.