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

We propose a new strategy to solve the key equations of the many-body dispersion (MBD) model by Tkatchenko, DiStasio Jr., and Ambrosetti. Our approach overcomes the original O ( N 3 ) computational complexity that limits its applicability to large molecular systems within the context of O ( N ) density functional theory. First, to generate the required frequency-dependent screened polarizabilities, we introduce an efficient solution to the Dyson-like self-consistent screening equations. The scheme reduces the number of variables and, coupled to a direct inversion of the iterative subspace extrapolation, exhibits linear-scaling performances. Second, we apply a stochastic Lanczos trace estimator resolution to the equations evaluating the many-body interaction energy of coupled quantum harmonic 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.