Density-Matrix Based Extended Lagrangian Born-Oppenheimer Molecular Dynamics.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Molecular Dynamics

Background:

• Standard Born-Oppenheimer molecular dynamics (BO-MD) requires computationally expensive self-consistent field (SCF) optimizations before each force evaluation.
• SCF convergence issues arise in BO-MD when simulating systems with small or vanishing electronic band gaps, limiting its applicability.
• Extended Lagrangian Born-Oppenheimer molecular dynamics (X-LG-BO-MD) offers an alternative by treating electronic degrees of freedom dynamically.

Purpose of the Study:

• To present an Extended Lagrangian Born-Oppenheimer molecular dynamics method applicable to Hartree-Fock theory.
• To introduce an adaptive integration scheme for extended electronic degrees of freedom to improve sampling.
• To provide a general framework for implementing X-LG-BO-MD in various quantum chemistry methods.

Main Methods:

• Formulation of X-LG-BO-MD using a density matrix representation for extended electronic degrees of freedom, including fractional occupations.
• Development of an adaptive integration scheme based on a tunable, low-rank approximation of a fourth-order kernel.
• The scheme determines the metric tensor for the extended harmonic oscillator in the Lagrangian governing electronic dynamics.

Main Results:

• Elimination of the need for iterative SCF optimization prior to force calculations, significantly accelerating simulations.
• Successful sampling of potential energy landscape regions with small or vanishing electronic gaps, overcoming convergence problems of standard BO-MD.
• Demonstration of a generalizable approach for implementing X-LG-BO-MD across different quantum chemistry methodologies.

Conclusions:

• The presented X-LG-BO-MD formulation provides a computationally efficient alternative to traditional BO-MD for Hartree-Fock calculations.
• The adaptive integration scheme effectively addresses convergence challenges in simulations of systems with small electronic gaps.
• The developed algorithms serve as a foundation for applying X-LG-BO-MD to density functional theory and semiempirical methods.