A new discretization for the polarizable continuum model within the domain decomposition paradigm

Assessing Implicit and Explicit Polarizable Solvation Models for Nuclear-Electronic Orbital Systems: Quantum Proton Polarization and Solvation Energetics

Accurate simulations of many chemical processes require the inclusion of both nuclear quantum effects and a solvent environment. The nuclear-electronic orbital (NEO) approach, which treats electrons and select nuclei quantum mechanically on the same level, combined with a polarizable continuum model (PCM) for the solvent environment, addresses this challenge in a computationally practical manner. In this work, the NEO-PCM approach is extended beyond the IEF-PCM (integral equation formalism PCM) and C-PCM (conductor PCM) approaches to the SS(V)PE (surface and simulation of volume polarization for electrostatics) and ddCOSMO (domain decomposed conductor-like screening model) approaches. IEF-PCM, SS(V)PE, C-PCM, and ddCOSMO all exhibit similar solvation energies as well as comparable nuclear polarization within the NEO framework. The calculations show that the nuclear density does not leak out of the molecular cavity because it is much more localized than the electronic density. Finally, the polarization of quantized protons is analyzed in both continuum solvent and explicit solvent environments described by the polarizable MB-pol model, illustrating the impact of specific hydrogen-bonding interactions captured only by explicit solvation. These calculations highlight the relationship among solvation formalism, nuclear polarization, and energetics.

Cavity-Free Continuum Solvation: Implementation and Parametrization in a Multiwavelet Framework

We present a multiwavelet-based implementation of a quantum/classical polarizable continuum model. The solvent model uses a diffuse solute-solvent boundary and a position-dependent permittivity, lifting the sharp-boundary assumption underlying many existing continuum solvation models. We are able to include both surface and volume polarization effects in the quantum/classical coupling, with guaranteed precision, due to the adaptive refinement strategies of our multiwavelet implementation. The model can account for complex solvent environments and does not need a posteriori corrections for volume polarization effects. We validate our results against a sharp-boundary continuum model and find a very good correlation of the polarization energies computed for the Minnesota solvation database.

Linear scaling computation of forces for the domain-decomposition linear Poisson-Boltzmann method

The Linearized Poisson-Boltzmann (LPB) equation is a popular and widely accepted model for accounting solvent effects in computational (bio-) chemistry. In the present article, we derive the analytical forces using the domain-decomposition-based LPB-method with a van-der Waals or solvent-accessible surface. We present an efficient strategy to compute the forces and its implementation, allowing linear scaling of the method with respect to the number of atoms using the fast multipole method. Numerical tests illustrate the accuracy of the computation of the analytical forces and compare the efficiency with other available methods.

Coarse-Graining ddCOSMO through an Interface between Tinker and the ddX Library

The domain decomposition conductor-like screening model is an efficient way to compute the solvation energy of solutes within a polarizable continuum medium in a linear scaling computational time. Despite its efficiency, the application to very large systems is still challenging. A possibility to further accelerate the algorithm is resorting to coarse-graining strategies. In this paper we present a preliminary interface between the molecular dynamics package Tinker and the ddX library. The interface was used to test a united atom coarse-graining strategy that allowed us to push ddCOSMO to its limits by computing solvation energies on systems with up to 7 million atoms. We first present benchmarks to find an optimal discretization, and then, we discuss the performance and results obtained with fine- and coarse-grained solvation energy calculations.

Linearly scaling computation of ddPCM solvation energy and forces using the fast multipole method

This paper proposes the first linear scaling implementation for the domain decomposition approach of the polarizable continuum model (ddPCM) for the computation of the solvation energy and forces. The ddPCM-equation consists of a (non-local) integral equation on the van der Waals or solvent accessible surface of the solute's cavity resulting in a dense solution matrix, and, in turn, one matrix-vector multiplication has a quadratic arithmetic complexity with respect to the number of atoms of the solute molecule. The use of spherical harmonics as basis functions makes it natural to employ the fast multipole method (FMM) in order to provide an asymptotically linear scaling method. In this paper, we employ the FMM in a non-uniform manner with a clusterization based on a recursive inertial bisection. We present some numerical tests illustrating the accuracy and scaling of our implementation.

Quantum chemistry for molecules at extreme pressure on graphical processing units: Implementation of extreme-pressure polarizable continuum model

Pressure plays essential roles in chemistry by altering structures and controlling chemical reactions. The extreme-pressure polarizable continuum model (XP-PCM) is an emerging method with an efficient quantum mechanical description of small- and medium-sized molecules at high pressure (on the order of GPa). However, its application to large molecular systems was previously hampered by a CPU computation bottleneck: the Pauli repulsion potential unique to XP-PCM requires the evaluation of a large number of electric field integrals, resulting in significant computational overhead compared to the gas-phase or standard-pressure polarizable continuum model calculations. Here, we exploit advances in graphical processing units (GPUs) to accelerate the XP-PCM-integral evaluations. This enables high-pressure quantum chemistry simulation of proteins that used to be computationally intractable. We benchmarked the performance using 18 small proteins in aqueous solutions. Using a single GPU, our method evaluates the XP-PCM free energy of a protein with over 500 atoms and 4000 basis functions within half an hour. The time taken by the XP-PCM-integral evaluation is typically 1% of the time taken for a gas-phase density functional theory (DFT) on the same system. The overall XP-PCM calculations require less computational effort than that for their gas-phase counterpart due to the improved convergence of self-consistent field iterations. Therefore, the description of the high-pressure effects with our GPU-accelerated XP-PCM is feasible for any molecule tractable for gas-phase DFT calculation. We have also validated the accuracy of our method on small molecules whose properties under high pressure are known from experiments or previous theoretical studies.