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Register a new userEnabling Large-Scale Condensed-Phase Hybrid Density Functional Theory Based $Ab$ $Initio$ Molecular Dynamics II: Extensions to the Isobaric-Isoenthalpic and Isobaric-Isothermal Ensembles
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In the previous paper of this series [JCTC 2020, 16, 3757], we presented a theoretical and algorithmic framework based on a localized representation of the occupied space that exploits the inherent sparsity in the real-space evaluation of the EXX interaction in finite-gap systems. This was accompanied by a detailed description of exx, a massively parallel hybrid MPI/OpenMP implementation of this approach in Quantum ESPRESSO that enables linear-scaling hybrid DFT based AIMD in the NVE/NVT ensembles of condensed-phase systems containing 500--1000 atoms (in fixed orthorhombic cells) with a wall time cost comparable to semi-local DFT. In this work, we extend exx to enable hybrid DFT based AIMD of large-scale condensed-phase systems with general and fluctuating cells in the NpH/NpT ensembles. Our theoretical extension includes an analytical derivation of the EXX contribution to the stress tensor for systems in general cells with a computational complexity that scales linearly with system size. The corresponding algorithmic extensions to exx include optimized routines that: (i) handle static/fluctuating cells with non-orthogonal lattice symmetries, (ii) solve Poissons equation in general cells via an automated selection of the auxiliary grid directions in the Natan-Kronik representation of the discrete Laplacian operator, and (iii) evaluate the EXX contribution to the stress tensor. We also critically assess the computational performance of the extended exx module across several different HPC architectures via case studies on ice Ih, II, and III as well as ambient liquid water. We find that the extended exx can evaluate the EXX contribution to the stress tensor with negligible cost (< 1%) and remains highly scalable, thereby bringing us another step closer to routinely performing hybrid DFT based AIMD for large-scale condensed-phase systems across a wide range of thermodynamic conditions.
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By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semi-local density functional theory (DFT), and thereby furnish a more accurate and reliable description of the electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we have devised a linear-scaling yet formally exact approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions, MLWFs) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems at the hybrid DFT level. We provide a comprehensive description of the exx algorithm, which is currently implemented in the Quantum ESPRESSO program and employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize high-performance computing (HPC) resources. This is followed by a critical assessment of the accuracy and parallel performance of this approach when performing AIMD simulations of liquid water in the canonical ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT based AIMD simulations of condensed-phase systems containing 500-1000 atoms with a walltime cost that is comparable to semi-local DFT. In doing so, exx takes us closer to routinely performing AIMD simulations of large-scale condensed-phase systems for sufficiently long timescales at the hybrid DFT level of theory.
We propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isothermal-isobaric ensembles. We also present a symplectic algorithm in the constant normal pressure and lateral surface area ensemble and that combined with the Parrinello-Rahman algorithm. Employing the symplectic integrators for MD algorithms, there is a conserved quantity which is close to Hamiltonian. Therefore, we can perform a MD simulation more stably than by conventional nonsymplectic algorithms. We applied this algorithm to a TIP3P pure water system at 300 K and compared the time evolution of the Hamiltonian with those by the nonsymplectic algorithms. We found that the Hamiltonian was conserved well by the symplectic algorithm even for a time step of 4 fs. This time step is longer than typical values of 0.5-2 fs which are used by the conventional nonsymplectic algorithms.
Isothermal-isobaric molecular dynamics simulations have been performed to examine a broad set of properties of the model water-1,2-dimethoxyethane (DME) mixture as a function of composition. The SPC-E and TIP4P-Ew water models and the modified TraPPE model for DME were applied. Our principal focus was to explore the trends of behaviour of the structural properties in terms of the radial distribution functions, coordination numbers and number of hydrogen bonds between molecules of different species, and of conformations of DME molecules. Thermodynamic properties, such as density, molar volume, enthalpy of mixing and heat capacity at constant pressure have been examined. Finally, the self-diffusion coefficients of species and the dielectric constant of the system were calculated and analyzed.
We propose a method to extend the fast on-the-fly weight determination scheme for simulated tempering to two-dimensional space including not only temperature but also pressure. During the simulated tempering simulation, weight parameters for temperature-update and pressure-update are self-updated independently according to the trapezoidal rule. In order to test the effectiveness of the algorithm, we applied our proposed method to a peptide, chignolin, in explicit water. After setting all weight parameters to zero, the weight parameters were quickly determined during the simulation. The simulation realised a uniform random walk in the entire temperature-pressure space.
We present generalized-ensemble algorithms for isobaric-isothermal molecular simulations. In addition to the multibaric-multithermal algorithm and replica-exchange method for the isobaric-isothermal ensemble, which have already been proposed, we propose a simulated tempering method for this ensemble. We performed molecular dynamics simulations with these algorithms for an alanine dipeptide system in explicit water molecules to test the effectiveness of the algorithms. We found that these generalized-ensemble algorithms are all useful for conformational sampling of biomolecular systems in the isobaric-isothermal ensemble.
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