Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Reduced Order Model approach for First-Principles Molecular Dynamics Computations

Siu Wun Cheung, Youngsoo Choi, Jean-Luc Fattebert, Jonas Kaufman, Daniel Osei-Kuffuor

Abstract

To leverage the redundancy between the electronic structure computed at each step of first-principles molecular dynamics, we present a data-driven modeling framework for Kohn-Sham Density Functional Theory that bypasses the explicit optimization of electronic wavefunctions. We sample a priori representative atomic configurations and construct a low-dimensional basis that efficiently approximates the electronic structure subspace. Subsequently, we employ this reduced basis in a direct solver for the electronic single particle density matrix, thereby enabling the efficient determination of ground state without iterative wavefunction optimization. We demonstrate the efficacy of our approach in a Born-Oppenheimer molecular dynamics of a water molecule, showing that the resulting simulations accurately reproduce key structural properties, such as bond lengths and bond angle, obtained from full first-principles molecular dynamics. This work highlights the potential of data-driven approaches to develop efficient electronic structure solvers for first-principles simulations.

A Reduced Order Model approach for First-Principles Molecular Dynamics Computations

Abstract

To leverage the redundancy between the electronic structure computed at each step of first-principles molecular dynamics, we present a data-driven modeling framework for Kohn-Sham Density Functional Theory that bypasses the explicit optimization of electronic wavefunctions. We sample a priori representative atomic configurations and construct a low-dimensional basis that efficiently approximates the electronic structure subspace. Subsequently, we employ this reduced basis in a direct solver for the electronic single particle density matrix, thereby enabling the efficient determination of ground state without iterative wavefunction optimization. We demonstrate the efficacy of our approach in a Born-Oppenheimer molecular dynamics of a water molecule, showing that the resulting simulations accurately reproduce key structural properties, such as bond lengths and bond angle, obtained from full first-principles molecular dynamics. This work highlights the potential of data-driven approaches to develop efficient electronic structure solvers for first-principles simulations.
Paper Structure (15 sections, 26 equations, 7 figures, 7 tables, 4 algorithms)

This paper contains 15 sections, 26 equations, 7 figures, 7 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. First-Principles Molecular Dynamics
  3. Electronic structure calculation
  4. Electronic structure solver
  5. Ionic Forces and Dynamics
  6. Reduced Order Model Molecular Dynamics
  7. Sampling and subspace construction
  8. Electronic structure calculation
  9. Ionic Forces and Dynamics
  10. Empirical example: pinned water molecule
  11. Sampling and subspace construction
  12. Accuracy in forces
  13. Accuracy in atomic trajectories
  14. Conclusion
  15. Nonlinear compression

Figures (7)

  • Figure 1: Configurations of the water molecule parametrized by two bond lengths $(L_1, L_2)$ and one bond angle $\theta$.
  • Figure 2: Histogram of the magnitude of the difference in force (in Hartree/Bohr) between FPMD and ROM-MD for hydrogen atoms H1 (top row) and H2 (bottom row). The left column shows results for the 18 reproductive cases, and the right column shows results for the 708 predictive unseen configurations. The mean force difference is reported in each panel.
  • Figure 3: Schematic diagram for the procedure of reduced Born-Oppenheimer molecular dynamics in Algorithm \ref{['alg:rom-born-oppenheimer']} in the example of water molecule.
  • Figure 4: Evolution of bond lengths $L_1$ and $L_2$ and bond angle $\theta$ during the 500 time steps of molecular dynamics. Left column: Comparison between FPMD (blue) and ROM-MD (red). Right column: Difference between FPMD and ROM-MD results.
  • Figure 5: Evolution of total energy during the 500 time steps of molecular dynamics. Left column: Comparison between FPMD (blue) and ROM-MD (red). Right column: Difference between FPMD and ROM-MD results.
  • ...and 2 more figures