Smooth Particle Mesh Ewald-integrated stochastic Lanczos Many-body Dispersion algorithm

We derive and implement an alternative formulation of the Stochastic Lanczos algorithm to be employed in connection with the Many-Body Dispersion model (MBD). Indeed, this formulation, which is only possible due to the Stochastic Lanczos' reliance on matrix-vector products, introduces generalized dipoles and fields. These key quantities allow for a state-of-the-art treatment of periodic boundary conditions via the O(Nlog(N)) Smooth Particle Mesh Ewald (SPME) approach which uses efficient fast Fourier transforms. This SPME-Lanczos algorithm drastically outperforms the standard replica method which is affected by a slow and conditionally convergence rate that limits an efficient and reliable inclusion of long-range periodic boundary conditions interactions in many-body dispersion modelling. The proposed algorithm inherits the embarrassingly parallelism of the original Stochastic Lanczos scheme, thus opening up for a fully converged and efficient periodic boundary condition treatment of MBD approaches

Achieving Linear Scaling in Computational Cost for a Fully Polarizable MM/Continuum Embedding

In this paper, we present a new, efficient implementation of a fully polarizable QM/MM/continuum model based on an induced-dipoles polarizable force field and on the Conductor-like Screening Model as a polarizable continuum in combination with a self-consistent field QM method. The paper focuses on the implementation of the MM/continuum embedding, where the two polarizable methods are fully coupled to take into account their mutual polarization. With respect to previous implementations, we achieve for the first time a linear scaling with respect to both the computational cost and the memory requirements without limitations on the molecular cavity shape. This is achieved thanks to the use of the recently developed ddCOSMO model for the continuum and the Fast Multipole Method for the force field, together with an efficient iterative procedure. Therefore, it becomes possible to include in the classical layer as much as several tens of thousands of atoms with a limited computational effort

Targeting the Major Groove of the Palindromic d(GGCGCC)2 Sequence by Oligopeptide Derivatives of Anthraquinone Intercalators

GC-rich sequences are recurring motifs in oncogenes and retroviruses, and could be targeted by non-covalent major-groove therapeutic ligands. We considered the palindromic sequence d(G1G2C3G4C5C6)2, and designed several oligopeptide derivatives of the anti-cancer intercalator mitoxantrone. The stability of their complexes with a 18-mer oligonucleotide encompassing this sequence in its center was validated using polarizable molecular dynamics. We report the most salient structural features of two novel compounds, having a dialkylammonium group as a side-chain on both arms. The anthraquinone ring is intercalated in the central d(CpG)2 sequence with its long axis perpendicular to that of the two base-pairs. On each strand, this enables each ammonium group to bind in-register to O6/N7 of the two facing G bases upstream. We subsequently designed tris-intercalating derivatives, each dialkylammonium substituted with a connector to an N9-aminoacridine intercalator extending our target range from six- to a ten-base pair palindromic sequence, d(C1G2G3G4C5G6C7C8C9G10)2. The structural features of the complex of the most promising derivative are reported. The present design strategy paves the way for designing intercalator-oligopeptide derivatives with an even higher selectivity, targeting an increased number of DNA bases, going beyond ten

ANKH: A Generalized O(N) Interpolated Ewald Strategy for Molecular Dynamics Simulations

To evaluate electrostatics interactions, Molecular dynamics (MD) simulations rely on Particle Mesh Ewald (PME), an O(Nlog(N)) algorithm that uses Fast Fourier Transforms (FFTs) or, alternatively, on O(N) Fast Multipole Methods (FMM) approaches. However, the FFTs low scalability remains a strong bottleneck for large-scale PME simulations on supercomputers. On the opposite, - FFT-free - FMM techniques are able to deal efficiently with such systems but they fail to reach PME performances for small- to medium-size systems, limiting their real-life applicability. We propose ANKH, a strategy grounded on interpolated Ewald summations and designed to remain efficient/scalable for any size of systems. The method is generalized for distributed point multipoles and so for induced dipoles which makes it suitable for high performance simulations using new generation polarizable force fields towards exascale computing

Pushing the limits of Multiple-Timestep Strategies for Polarizable Point Dipole Molecular Dynamics

International audienceWe propose an incremental construction of multi-timestep integrators to accelerate polarizable point dipole molecular dynamics while preserving sampling efficiency. We start by building various integrators using frequency-driven splittings of energy terms and a Velocity-Verlet evaluation of the most rapidly varying forces, and compare a standard dual bonded/non-bonded split to a 3-groups split dividing non-bonded forces (including polarization) into short- and long-range levels. We then introduce new approaches by coupling these splittings to Langevin Dynamics and to Leimkuhler's BAOAB integrator to reach larger timesteps of 6~fs for long-range forces maintaining accuracy. We further increase sampling efficiency by: i) accelerating the polarization evaluation using a fast/non-iterative Truncated Conjugate Gradient (TCG-1) as short-range solver; ii) pushing the outer timestep to 10~fs using hydrogen mass repartitioning. Finally, our Tinker-HP implementation of BAOAB-RESPA1-Langevin integrators demonstrates a 4 to 7-fold acceleration over standard 1~fs integration while preserving the evaluation of static and dynamical properties

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