Shadow energy functionals and potentials in Born-Oppenheimer molecular dynamics.

Area of Science:

• Computational Chemistry
• Molecular Dynamics Simulations
• Quantum Chemistry

Background:

• Born-Oppenheimer molecular dynamics (BOMD) simulations, commonly used with density functional theory (DFT), rely on iterative self-consistent field (SCF) procedures.
• Incomplete convergence of SCF in BOMD leads to approximate energies and forces, potentially causing unphysical energy drift and simulation instabilities.

Purpose of the Study:

• To present an alternative shadow BOMD approach based on backward error analysis to overcome the limitations of traditional BOMD.
• To develop a method that ensures conservative forces and long-term energy stability in molecular dynamics simulations.

Main Methods:

• The shadow BOMD approach calculates exact electron densities, energies, and forces for an approximate shadow Born-Oppenheimer potential energy surface.
• Shadow potentials are constructed at varying accuracy levels based on the integration time step, using constrained minimization of approximate shadow energy density functionals.
• This method is integrated into an extended Lagrangian framework where electronic degrees of freedom are propagated dynamically.

Main Results:

• The shadow BOMD method generates accurate molecular trajectories with improved long-term energy conservation.
• Demonstrated construction of shadow potentials and energy functionals as generalizations of previous work.
• The approach ensures force conservatism with respect to the approximate shadow potential.

Conclusions:

• The shadow BOMD method offers a robust alternative for achieving stable and accurate molecular dynamics simulations.
• The developed shadow potentials and energy functionals are applicable within an extended dynamical framework for electronic degrees of freedom.
• The methodology is versatile, applicable to various electronic structure methods including approximate DFT, Hartree-Fock, and semi-empirical models.