Extended Lagrangian Born-Oppenheimer molecular dynamics using a Krylov subspace approximation.

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Extended Lagrangian Born-Oppenheimer molecular dynamics (M.D.) is crucial for simulating molecular systems.
• Accurate integration of electronic equations of motion is computationally intensive.
• Existing methods often require full inverse Jacobian kernel calculations or iterative optimizations.

Purpose of the Study:

• To develop a computationally efficient method for integrating electronic equations of motion in extended Lagrangian Born-Oppenheimer M.D. simulations.
• To enable the application of these simulations to a broader range of challenging chemical systems.
• To reduce the computational cost associated with inverse Jacobian kernel calculations.

Main Methods:

• Utilizing low-rank approximations of the inverse Jacobian kernel.
• Deriving kernel approximation from a pseudoinverse of a low-rank Jacobian estimate.
• Employing Krylov subspace approximations for directional derivatives.

Main Results:

• A tunable and adaptive kernel approximation is proposed.
• The method allows for efficient preconditioning techniques.
• Enables extended Lagrangian first-principles M.D. for reactive systems with sensitive charge solutions.

Conclusions:

• The proposed low-rank approximation offers a viable alternative to exact Jacobian calculations in M.D. simulations.
• This approach extends the applicability of first-principles molecular dynamics to complex chemical problems.
• It provides a formulation related to quasi-Newton and Newton-Krylov methods for nonlinear systems.