Étienne Polack — Hollved

About

I am a postdoctoral researcher at Cermics (École Nationale des Ponts et Chaussées) and Matherials (Inria), where I work with Éric Cancès and Antoine Levitt.

My research interests consist in different issues arising when modeling chemical systems and materials:

Multiphysics models (quantum-mechanics, molecular mechanics & implicit solvation);
Efficient use of clusters of computers (high-performance computing);
Extrapolation methods to provide more accurate and faster results.

In January 2022, I defended my doctoral research project, Development of efficient multiscale methods and extrapolation techniques for multiphysics molecular chemistry, under the supervision of Yvon Maday at the Jacques-Louis Lions lab (Sorbonne Université).

Publications

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Pes, F., Polack, É., et al. (2023). A Quasi Time-Reversible Scheme Based on Density Matrix Extrapolation on the Grassmann Manifold for Born–Oppenheimer Molecular Dynamics. The Journal of Physical Chemistry Letters. DOI arXiv HAL🔗
This Letter introduces the so-called Quasi Time-Reversible scheme based on Grassmann extrapolation (QTR G-Ext) of density matrices for an accurate calculation of initial guesses in Born–Oppenheimer Molecular Dynamics (BOMD) simulations. The method shows excellent results on four large molecular systems that are representative of real-life production applications, ranging from 21 to 94 atoms simulated with Kohn–Sham (KS) density functional theory surrounded with a classical environment with 6k to 16k atoms. Namely, it clearly reduces the number of self-consistent field iterations while at the same time achieving energy-conserving simulations, resulting in a considerable speed-up of BOMD simulations even when tight convergence of the KS equations is required.
Polack, É., Maday, Y. & Savin, A. (2022). FLEIM: A Stable, Accurate and Robust Extrapolation Method at Infinity for Computing the Ground State of Electronic Hamiltonians. Book Chapter. DOI arXiv HAL🔗
The Kohn-Sham method uses a single model system, and corrects it by a density functional the exact user friendly expression of which is not known and is replaced by an approximated, usable, model. We propose to use instead more than one model system, and use a greedy extrapolation method to correct the results of the model systems. Evidently, there is a higher price to pay for it. However, there are also gains: within the same paradigm, e.g., excited states and physical properties can be obtained.
Polack, É., Dusson, G., et al. (2021). Grassmann Extrapolation of Density Matrices for Born–Oppenheimer Molecular Dynamics. Journal of Chemical Theory and Computation. DOI arXiv HAL🔗
Born–Oppenheimer molecular dynamics (BOMD) is a powerful but expensive technique. The main bottleneck in a density functional theory BOMD calculation is the solution to the Kohn–Sham (KS) equations that requires an iterative procedure that starts from a guess for the density matrix. Converged densities from previous points in the trajectory can be used to extrapolate a new guess; however, the nonlinear constraint that an idempotent density needs to satisfy makes the direct use of standard linear extrapolation techniques not possible. In this contribution, we introduce a locally bijective map between the manifold where the density is defined and its tangent space so that linear extrapolation can be performed in a vector space while, at the same time, retaining the correct physical properties of the extrapolated density using molecular descriptors. We apply the method to real-life, multiscale, polarizable QM/MM BOMD simulations, showing that sizeable performance gains can be achieved, especially when a tighter convergence to the KS equations is required.
Polack, É., Mikhalev, A., et al. (2020). An Approximation Strategy to Compute Accurate Initial Density Matrices for Repeated Self-Consistent Field Calculations at Different Geometries. Molecular Physics. DOI arXiv HAL🔗
Repeated computations on the same molecular system, but with different geometries, are often performed in quantum chemistry, for instance, in ab-initio molecular dynamics simulations or geometry optimisations. While many efficient strategies exist to provide a good guess for the self-consistent field procedure, little is known on how to efficiently exploit the abundance of information generated during the many computations. In this article, we present a strategy to provide an accurate initial guess for the density matrix, expanded in a set of localised basis functions, within the self-consistent field iterations for parametrised Hartree–Fock problems where the nuclear coordinates are changed along with a few user-specified collective variables, such as the molecule's normal modes. Our approach is based on an offline-stage where the Hartree–Fock eigenvalue problem is solved for some particular parameter values and an online-stage where the initial guess is computed very efficiently for any new parameter value. The method allows nonlinear approximations of density matrices, which belong to a non-linear manifold that is isomorphic to the Grassmann manifold, by mapping such a manifold onto the tangent space. Numerical tests on different amino acids show promising initial results.
Lindgren, E. B., Stace, A. J., et al. (2018). An Integral Equation Approach to Calculate Electrostatic Interactions in Many-Body Dielectric Systems. Journal of Computational Physics. DOI🔗
In this article, a numerical method to compute the electrostatic interaction energy and forces between many dielectric particles is presented. The computational method is based on a Galerkin approximation of an integral equation formulation, which is sufficiently general, as it is able to treat systems embedded in a homogeneous dielectric medium containing an arbitrary number of spherical particles of arbitrary size, charge, dielectric constant and position in the three-dimensional space. The algorithmic complexity is linear scaling with respect to the number of particles for the computation of the energy which has been achieved through the use of a modified fast multipole method. The method scales with the third power of the degree of spherical harmonics used in the underlying expansions, for general three-dimensional particle configurations. Several simple numerical examples illustrate the capabilities of the model, and the influence of mutual polarization between particles in an electrostatic interaction is discussed.
Stamm, B., Lagardère, L., et al. (2018). A Coherent Derivation of the Ewald Summation for Arbitrary Orders of Multipoles: The Self-Terms. The Journal of Chemical Physics. DOI arXiv HAL🔗
In this work, we provide the mathematical elements we think essential for a proper understanding of the calculus of the electrostatic energy of point-multipoles of arbitrary order under periodic boundary conditions. The emphasis is put on the expressions of the so-called self-parts of the Ewald summation where different expressions can be found in the literature. Indeed, such expressions are of prime importance in the context of new generation polarizable force field where the self-field appears in the polarization equations. We provide a general framework, where the idea of the Ewald splitting is applied to the electric potential and, subsequently, all other quantities such as the electric field, the energy, and the forces are derived consistently thereof. Mathematical well-posedness is shown for all these contributions for any order of multipolar distribution.
Narth, C., Lagardère, L., et al. (2016). Scalable Improvement of SPME Multipolar Electrostatics in Anisotropic Polarizable Molecular Mechanics Using a General Short-Range Penetration Correction up to Quadrupoles. Journal of Computational Chemistry. DOI HAL🔗
We propose a general coupling of the Smooth Particle Mesh Ewald SPME approach for distributed multipoles to a short-range charge penetration correction modifying the charge-charge, charge-dipole and charge-quadrupole energies. Such an approach significantly improves electrostatics when compared to ab initio values and has been calibrated on Symmetry-Adapted Perturbation Theory reference data. Various neutral molecular dimers have been tested and results on the complexes of mono- and divalent cations with a water ligand are also provided. Transferability of the correction is adressed in the context of the implementation of the AMOEBA and SIBFA polarizable force fields in the TINKER-HP software. As the choices of the multipolar distribution are discussed, conclusions are drawn for the future penetration-corrected polarizable force fields highlighting the mandatory need of non-spurious procedures for the obtention of well balanced and physically meaningful distributed moments. Finally, scalability and parallelism of the short-range corrected SPME approach are addressed, demonstrating that the damping function is computationally affordable and accurate for molecular dynamics simulations of complex bio- or bioinorganic systems in periodic boundary conditions.
Loco, D., Polack, É., et al. (2016). A QM/MM Approach Using the AMOEBA Polarizable Embedding: From Ground State Energies to Electronic Excitations. Journal of Chemical Theory and Computation. DOI HAL🔗
A fully polarizable implementation of the hybrid quantum mechanics/molecular mechanics approach is presented, where the classical environment is described through the AMOEBA polarizable force field. A variational formalism, offering a self-consistent relaxation of both the MM induced dipoles and the QM electronic density, is used for ground state energies and extended to electronic excitations in the framework of time-dependent density functional theory combined with a state specific response of the classical part. An application to the calculation of the solvatochromism of the pyridinium N-phenolate betaine dye used to define the solvent ET(30) scale is presented. The results show that the QM/AMOEBA model not only properly describes specific and bulk effects in the ground state but it also correctly responds to the large change in the solute electronic charge distribution upon excitation.
Lagardère, L., Lipparini, F., et al. (2015). Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics: II. Toward Massively Parallel Computations Using Smooth Particle Mesh Ewald. Journal of Chemical Theory and Computation. DOI HAL🔗
In this article, we present a parallel implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The smooth particle mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the direct inversion in the iterative subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy and force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package, which is the first implementation of a polarizable model that makes large-scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of SPME and a noticeable improvement of the memory management, giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to nonoptimized, sequential implementations, giving new directions for polarizable molecular dynamics with periodic boundary conditions using massively parallel implementations.

Étienne Polack
Postdoctoral researcher in applied mathematics

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