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Pes F, Polack É, Mazzeo P, Dusson G, Stamm B, Lipparini F. A Quasi Time-Reversible Scheme Based on Density Matrix Extrapolation on the Grassmann Manifold for Born-Oppenheimer Molecular Dynamics. J Phys Chem Lett 2023; 14:9720-9726. [PMID: 37879072 PMCID: PMC10626629 DOI: 10.1021/acs.jpclett.3c02098] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 10/11/2023] [Indexed: 10/27/2023]
Abstract
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.
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Affiliation(s)
- Federica Pes
- Dipartimento
di Chimica e Chimica Industriale, Università
di Pisa, Via G. Moruzzi 13, 56124 Pisa, Italy
| | - Étienne Polack
- CERMICS, École des Ponts and Inria Paris, 6 & 8 avenue Blaise Pascal, 77455 Marne-la-Valée, France
| | - Patrizia Mazzeo
- Dipartimento
di Chimica e Chimica Industriale, Università
di Pisa, Via G. Moruzzi 13, 56124 Pisa, Italy
| | - Geneviève Dusson
- Laboratoire
de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besançon, France
| | - Benjamin Stamm
- Institute
of Applied Analysis and Numerical Simulation, University of Stuttgart, 70569 Stuttgart, Germany
| | - Filippo Lipparini
- Dipartimento
di Chimica e Chimica Industriale, Università
di Pisa, Via G. Moruzzi 13, 56124 Pisa, Italy
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Kulichenko M, Barros K, Lubbers N, Fedik N, Zhou G, Tretiak S, Nebgen B, Niklasson AMN. Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation. J Chem Theory Comput 2023. [PMID: 37163680 DOI: 10.1021/acs.jctc.3c00234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.
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Affiliation(s)
- Maksim Kulichenko
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Kipton Barros
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Nicholas Lubbers
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Nikita Fedik
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Guoqing Zhou
- NVIDIA Corporation, 2788 San Tomas Expy, Santa Clara, California 95051, United States
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Benjamin Nebgen
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Anders M N Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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Niklasson AMN, Negre CFA. Shadow energy functionals and potentials in Born-Oppenheimer molecular dynamics. J Chem Phys 2023; 158:2882249. [PMID: 37093997 DOI: 10.1063/5.0146431] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2023] [Accepted: 04/03/2023] [Indexed: 04/26/2023] Open
Abstract
In Born-Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born-Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born-Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born-Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born-Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original "zeroth-level" shadow energy functionals and potentials used in extended Lagrangian BOMD [Niklasson, Eur. Phys. J. B 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree-Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.
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Affiliation(s)
- Anders M N Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Christian F A Negre
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Negre CFA, Wall ME, Niklasson AMN. Graph-based quantum response theory and shadow Born-Oppenheimer molecular dynamics. J Chem Phys 2023; 158:074108. [PMID: 36813723 DOI: 10.1063/5.0137119] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Abstract
Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.
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Affiliation(s)
- Christian F A Negre
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Michael E Wall
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Anders M N Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Finkelstein J, Smith JS, Mniszewski SM, Barros K, Negre CFA, Rubensson EH, Niklasson AMN. Quantum-Based Molecular Dynamics Simulations Using Tensor Cores. J Chem Theory Comput 2021; 17:6180-6192. [PMID: 34595916 DOI: 10.1021/acs.jctc.1c00726] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency but with the caveat that they were designed for tensor contractions (matrix-matrix multiplications) using only low-precision floating-point operations. Despite this perceived limitation, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born-Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born-Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low-precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.
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Affiliation(s)
- Joshua Finkelstein
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545 New Mexico, United States
| | - Justin S Smith
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545 New Mexico, United States
| | - Susan M Mniszewski
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, 87545 New Mexico, United States
| | - Kipton Barros
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545 New Mexico, United States
| | - Christian F A Negre
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545 New Mexico, United States
| | - Emanuel H Rubensson
- Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden
| | - Anders M N Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, 87545 New Mexico, United States
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Cruzeiro VWD, Manathunga M, Merz KM, Götz AW. Open-Source Multi-GPU-Accelerated QM/MM Simulations with AMBER and QUICK. J Chem Inf Model 2021; 61:2109-2115. [PMID: 33913331 DOI: 10.1021/acs.jcim.1c00169] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
The quantum mechanics/molecular mechanics (QM/MM) approach is an essential and well-established tool in computational chemistry that has been widely applied in a myriad of biomolecular problems in the literature. In this publication, we report the integration of the QUantum Interaction Computational Kernel (QUICK) program as an engine to perform electronic structure calculations in QM/MM simulations with AMBER. This integration is available through either a file-based interface (FBI) or an application programming interface (API). Since QUICK is an open-source GPU-accelerated code with multi-GPU parallelization, users can take advantage of "free of charge" GPU-acceleration in their QM/MM simulations. In this work, we discuss implementation details and give usage examples. We also investigate energy conservation in typical QM/MM simulations performed at the microcanonical ensemble. Finally, benchmark results for two representative systems in bulk water, the N-methylacetamide (NMA) molecule and the photoactive yellow protein (PYP), show the performance of QM/MM simulations with QUICK and AMBER using a varying number of CPU cores and GPUs. Our results highlight the acceleration obtained from a single or multiple GPUs; we observed speedups of up to 53× between a single GPU vs a single CPU core and of up to 2.6× when comparing four GPUs to a single GPU. Results also reveal speedups of up to 3.5× when the API is used instead of FBI.
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Affiliation(s)
- Vinícius Wilian D Cruzeiro
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States.,Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Madushanka Manathunga
- Department of Chemistry, Department of Biochemistry and Molecular Biology, Institute of Cyber-Enabled Research, Michigan State University, East Lansing, Michigan 48824, United States
| | - Kenneth M Merz
- Department of Chemistry, Department of Biochemistry and Molecular Biology, Institute of Cyber-Enabled Research, Michigan State University, East Lansing, Michigan 48824, United States
| | - Andreas W Götz
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States
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Niklasson AMN. Extended Lagrangian Born-Oppenheimer molecular dynamics for orbital-free density-functional theory and polarizable charge equilibration models. J Chem Phys 2021; 154:054101. [PMID: 33557538 DOI: 10.1063/5.0038190] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] is formulated for orbital-free Hohenberg-Kohn density-functional theory and for charge equilibration and polarizable force-field models that can be derived from the same orbital-free framework. The purpose is to introduce the most recent features of orbital-based XL-BOMD to molecular dynamics simulations based on charge equilibration and polarizable force-field models. These features include a metric tensor generalization of the extended harmonic potential, preconditioners, and the ability to use only a single Coulomb summation to determine the fully equilibrated charges and the interatomic forces in each time step for the shadow Born-Oppenheimer potential energy surface. The orbital-free formulation has a charge-dependent, short-range energy term that is separate from long-range Coulomb interactions. This enables local parameterizations of the short-range energy term, while the long-range electrostatic interactions can be treated separately. The theory is illustrated for molecular dynamics simulations of an atomistic system described by a charge equilibration model with periodic boundary conditions. The system of linear equations that determines the equilibrated charges and the forces is diagonal, and only a single Ewald summation is needed in each time step. The simulations exhibit the same features in accuracy, convergence, and stability as are expected from orbital-based XL-BOMD.
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Affiliation(s)
- Anders M N Niklasson
- Theoretical Division T-1, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Niklasson AMN. Density-Matrix Based Extended Lagrangian Born–Oppenheimer Molecular Dynamics. J Chem Theory Comput 2020; 16:3628-3640. [DOI: 10.1021/acs.jctc.0c00264] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Anders M. N. Niklasson
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
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