O(N)Stochastic Evaluation of Many-Body van der Waals Energies in Large Complex Systems

23 December 2021, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


We propose a new strategy to solve the Tkatchenko-Scheffler Many-Body Dispersion (MBD) model’s equations. Our approach overcomes the original O(N**3) computational complexity that limits its applicability to large molecular systems within thecontext of O(N) Density Functional Theory (DFT). First, in order to generate the required frequency-dependent screenedpolarizabilities, we introduce an efficient solution to the Dyson-like self-consistent screening equations. The scheme reducesthe number of variables and, coupled to a DIIS extrapolation, exhibits linear-scaling performances. Second, we apply astochastic Lanczos trace estimator resolution to the equations evaluating the many-body interaction energy of coupled quantumharmonic oscillators. While scaling linearly, it also enables communication-free pleasingly-parallel implementations. As the resulting O(N) stochastic massively parallel MBD approach is found to exhibit minimal memory requirements, it opens up the possibility of computing accurate many-body van der Waals interactions of millions-atoms’ complex materials and solvated biosystems with computational times in the range of minutes.


quantum chemistry
many-body dispersion
van der Waals
Tkatchenko-Scheffler Many-Body Dispersion
Density Functional Theory

Supplementary materials

Supplementary Informations
Additionnal details.


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