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

Anders M N Niklasson¹

¹Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA and Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden.

The Journal of Chemical Physics

|March 16, 2020

Summary

This summary is machine-generated.

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This study introduces a low-rank approximation for integrating electronic equations of motion in extended Lagrangian Born-Oppenheimer molecular dynamics. This method enhances simulations for complex chemical systems without full inverse Jacobian calculations.

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.

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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.