Stochastic Evaluation of Many-Body van der Waals Energies in Large Complex Systems

Area of Science:

• Computational chemistry
• Materials science
• Quantum mechanics

Background:

• The many-body dispersion (MBD) model is crucial for accurately describing van der Waals interactions.
• Its computational complexity, particularly within density functional theory (DFT), limits its application to large molecular systems.
• Efficient calculation of frequency-dependent screened polarizabilities is essential for MBD.

Purpose of the Study:

• To develop a computationally efficient strategy for solving the MBD model equations.
• To overcome the limitations of existing methods for large-scale molecular systems.
• To enable accurate van der Waals interaction calculations for complex materials and biological systems.

Main Methods:

• Introduced an efficient solution for Dyson-like self-consistent screening equations to obtain screened polarizabilities.
• Implemented a direct inversion of the iterative subspace (DIIS) extrapolation for linear-scaling performance.
• Applied a stochastic Lanczos trace estimator (SLTE) for evaluating many-body interaction energy, enabling parallel implementation.

Main Results:

• The proposed method achieves linear-scaling performance in calculating screened polarizabilities.
• The stochastic approach for MBD energy evaluation is communication-free and highly parallelizable.
• The stochastic massively parallel MBD approach demonstrates minimal memory requirements.

Conclusions:

• The new strategy significantly reduces the computational complexity of the MBD model.
• This approach allows for accurate computation of many-body van der Waals interactions in systems with millions of atoms.
• The method paves the way for rapid analysis of complex materials and solvated biosystems.