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

International audienceWe propose a new strategy to solve 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 (DFT). First, in order 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 DIIS 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

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

We propose a new strategy to solve 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 (DFT). First, in order 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 DIIS 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

Molecular Dynamics Using Non-Variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. By making use of a Lagrange formalism, however, this computational demanding task can be re- placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </div

Molecular Dynamics using Non-variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

International audienceWe extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all electrostatic parameters for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. By making use of a Lagrange formalism, however, this computational demanding task can be replaced by solving a single equation similar to that for determining the polarization energy itself. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic parameters from the energy expression depending on these parameters without a large computational penalty provides flexibility in the design of new force fields

Accurate Deep Learning-aided Density-free Strategy for Many-Body Dispersion-corrected Density Functional Theory

Using a Deep Neuronal Network model (DNN) trained on the large ANI-1 data set of small organic molecules, we propose a transferable density-free many-body dispersion model (DNN-MBD). The DNN strategy bypasses the explicit Hirshfeld partitioning of the Kohn-Sham electron density required by MBD models to obtain the atom-in-molecules volumes used by the Tkatchenko-Scheffler polarizability rescaling. The resulting DNN-MBD model is trained with minimal basis iterative Stockholder atomic volumes and, coupled to Density Functional Theory (DFT), exhibits comparable (if not greater) accuracy to other approaches based on different partitioning schemes. Implemented in the Tinker-HP package, the DNN-MBD model decreases the overall computational cost compared to MBD models where the explicit density partitioning is performed. Its coupling with the recently introduced Stochastic formulation of the MBD equations (J. Chem. Theory. Comput., 2022, 18, 3, 1633-1645) enables large routine dispersion-corrected DFT calculations at preserved accuracy. Furthermore, the DNN electron density-free features extend MBD's applicability beyond electronic structure theory within methodologies such as force fields and neural networks