Andreas W. Götz

Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 2. Explicit Solvent Particle Mesh Ewald

We present an implementation of explicit solvent all atom classical molecular dynamics (MD) within the AMBER program package that runs entirely on CUDA-enabled GPUs. First released publicly in April 2010 as part of version 11 of the AMBER MD package and further improved and optimized over the last two years, this implementation supports the three most widely used statistical mechanical ensembles (NVE, NVT, and NPT), uses particle mesh Ewald (PME) for the long-range electrostatics, and runs entirely on CUDA-enabled NVIDIA graphics processing units (GPUs), providing results that are statistically indistinguishable from the traditional CPU version of the software and with performance that exceeds that achievable by the CPU version of AMBER software running on all conventional CPU-based clusters and supercomputers. We briefly discuss three different precision models developed specifically for this work (SPDP, SPFP, and DPDP) and highlight the technical details of the approach as it extends beyond previously reported work [Götz et al., J. Chem. Theory Comput. 2012, DOI: 10.1021/ct200909j; Le Grand et al., Comp. Phys. Comm. 2013, DOI: 10.1016/j.cpc.2012.09.022].We highlight the substantial improvements in performance that are seen over traditional CPU-only machines and provide validation of our implementation and precision models. We also provide evidence supporting our decision to deprecate the previously described fully single precision (SPSP) model from the latest release of the AMBER software package.

Routine Microsecond Molecular Dynamics Simulations with AMBER on GPUs. 1. Generalized Born

We present an implementation of generalized Born implicit solvent all-atom classical molecular dynamics (MD) within the AMBER program package that runs entirely on CUDA enabled NVIDIA graphics processing units (GPUs). We discuss the algorithms that are used to exploit the processing power of the GPUs and show the performance that can be achieved in comparison to simulations on conventional CPU clusters. The implementation supports three different precision models in which the contributions to the forces are calculated in single precision floating point arithmetic but accumulated in double precision (SPDP), or everything is computed in single precision (SPSP) or double precision (DPDP). In addition to performance, we have focused on understanding the implications of the different precision models on the outcome of implicit solvent MD simulations. We show results for a range of tests including the accuracy of single point force evaluations and energy conservation as well as structural properties pertainining to protein dynamics. The numerical noise due to rounding errors within the SPSP precision model is sufficiently large to lead to an accumulation of errors which can result in unphysical trajectories for long time scale simulations. We recommend the use of the mixed-precision SPDP model since the numerical results obtained are comparable with those of the full double precision DPDP model and the reference double precision CPU implementation but at significantly reduced computational cost. Our implementation provides performance for GB simulations on a single desktop that is on par with, and in some cases exceeds, that of traditional supercomputers.

SPFP: Speed without compromise—A mixed precision model for GPU accelerated molecular dynamics simulations

Abstract A new precision model is proposed for the acceleration of all-atom classical molecular dynamics (MD) simulations on graphics processing units (GPUs). This precision model replaces double precision arithmetic with fixed point integer arithmetic for the accumulation of force components as compared to a previously introduced model that uses mixed single/double precision arithmetic. This significantly boosts performance on modern GPU hardware without sacrificing numerical accuracy. We present an implementation for NVIDIA GPUs of both generalized Born implicit solvent simulations as well as explicit solvent simulations using the particle mesh Ewald (PME) algorithm for long-range electrostatics using this precision model. Tests demonstrate both the performance of this implementation as well as its numerical stability for constant energy and constant temperature biomolecular MD as compared to a double precision CPU implementation and double and mixed single/double precision GPU implementations.

Numerically stable optimized effective potential method with balanced Gaussian basis sets

A solution to the long-standing problem of developing numerically stable optimized effective potential (OEP) methods based on Gaussian basis sets is presented by introducing an approach consisting of an exact exchange OEP method with an accompanying construction and balancing scheme for the involved auxiliary and orbital Gaussian basis sets that is numerically stable and that properly represents an exact exchange Kohn-Sham method. The method is a purely analytical method that does not require any numerical grid, scales like Hartree-Fock or B3LYP procedures, is straightforward to implement, and is easily generalized to take into account orbital-dependent density functionals other than the exact exchange considered in this work. Thus, the presented OEP approach opens the way to the development and application of novel orbital-dependent exchange-correlation functionals. It is shown that adequately taking into account the continuum part of the Kohn-Sham orbital spectrum is crucial for numerically stable Gaussian basis set OEP methods. Moreover, it is mandatory to employ orbital basis sets that are converged with respect to the used auxiliary basis representing the exchange potential. OEP calculations in the past often did not meet the latter requirement and therefore may have led to erroneously low total energies.

Application of adaptive QM/MM methods to molecular dynamics simulations of aqueous systems

The difference-based adaptive solvation quantum mechanics/molecular mechanics (adQM/MM) method (J. Chem. Theory Comput.2009, 5, 2212) as implemented in the Amber software was applied to the study of several chemical processes in solution. The adQM/MM method is based on an efficient selection scheme that enables quantum-mechanical treatment of the active region of a molecular system in solution taking explicitly into account diffusion of solvent molecules between the QM and the MM regions. Specifically, adQM/MM molecular dynamics simulations are carried out to characterize (1) the free energy profiles of halide exchange SN2 reactions in water, (2) the hydration structure of the Cl(-) ion, and (3) the solvation structure of the zwitterionic form of glycine in water. A comparison is made with the results obtained using standard MM and QM/MM methods as well as with the available fully QM and experimental data. In all cases, it is shown that the adaptive QM/MM simulations provide a physically realistic description of the system of interest.

On the representation of many-body interactions in water

Recent work has shown that the many-body expansion of the interaction energy can be used to develop analytical representations of global potential energy surfaces (PESs) for water. In this study, the role of short- and long-range interactions at different orders is investigated by analyzing water potentials that treat the leading terms of the many-body expansion through implicit (i.e., TTM3-F and TTM4-F PESs) and explicit (i.e., WHBB and MB-pol PESs) representations. It is found that explicit short-range representations of 2-body and 3-body interactions along with a physically correct incorporation of short- and long-range contributions are necessary for an accurate representation of the water interactions from the gas to the condensed phase. Similarly, a complete many-body representation of the dipole moment surface is found to be crucial to reproducing the correct intensities of the infrared spectrum of liquid water.

An extensible interface for QM/MM molecular dynamics simulations with AMBER.

We present an extensible interface between the AMBER molecular dynamics (MD) software package and electronic structure software packages for quantum mechanical (QM) and mixed QM and classical molecular mechanical (MM) MD simulations within both mechanical and electronic embedding schemes. With this interface, ab initio wave function theory and density functional theory methods, as available in the supported electronic structure software packages, become available for QM/MM MD simulations with AMBER. The interface has been written in a modular fashion that allows straight forward extensions to support additional QM software packages and can easily be ported to other MD software. Data exchange between the MD and QM software is implemented by means of files and system calls or the message passing interface standard. Based on extensive tests, default settings for the supported QM packages are provided such that energy is conserved for typical QM/MM MD simulations in the microcanonical ensemble. Results for the free energy of binding of calcium ions to aspartate in aqueous solution comparing semiempirical and density functional Hamiltonians are shown to demonstrate features of this interface.

PyADF — A scripting framework for multiscale quantum chemistry

Applications of quantum chemistry have evolved from single or a few calculations to more complicated workflows, in which a series of interrelated computational tasks is performed. In particular multiscale simulations, which combine different levels of accuracy, typically require a large number of individual calculations that depend on each other. Consequently, there is a need to automate such workflows. For this purpose we have developed PYADF, a scripting framework for quantum chemistry. PYADF handles all steps necessary in a typical workflow in quantum chemistry and is easily extensible due to its object‐oriented implementation in the Python programming language. We give an overview of the capabilities of PYADF and illustrate its usefulness in quantum‐chemical multiscale simulations with a number of examples taken from recent applications.

On the accuracy of the MB-pol many-body potential for water: Interaction energies, vibrational frequencies, and classical thermodynamic and dynamical properties from clusters to liquid water and ice

The MB-pol many-body potential has recently emerged as an accurate molecular model for water simulations from the gas to the condensed phase. In this study, the accuracy of MB-pol is systematically assessed across the three phases of water through extensive comparisons with experimental data and high-level ab initio calculations. Individual many-body contributions to the interaction energies as well as vibrational spectra of water clusters calculated with MB-pol are in excellent agreement with reference data obtained at the coupled cluster level. Several structural, thermodynamic, and dynamical properties of the liquid phase at atmospheric pressure are investigated through classical molecular dynamics simulations as a function of temperature. The structural properties of the liquid phase are in nearly quantitative agreement with X-ray diffraction data available over the temperature range from 268 to 368 K. The analysis of other thermodynamic and dynamical quantities emphasizes the importance of explicitly including nuclear quantum effects in the simulations, especially at low temperature, for a physically correct description of the properties of liquid water. Furthermore, both densities and lattice energies of several ice phases are also correctly reproduced by MB-pol. Following a recent study of DFT models for water, a score is assigned to each computed property, which demonstrates the high and, in many respects, unprecedented accuracy of MB-pol in representing all three phases of water.

Virial theorem in the Kohn-Sham density-functional theory formalism: accurate calculation of the atomic quantum theory of atoms in molecules energies.

A new approach for computing the atom-in-molecule [quantum theory of atoms in molecule (QTAIM)] energies in Kohn-Sham density-functional theory is presented and tested by computing QTAIM energies for a set of representative molecules. In the new approach, the contribution for the correlation-kinetic energy (T(c)) is computed using the density-functional theory virial relation. Based on our calculations, it is shown that the conventional approach where atomic energies are computed using only the noninteracting part of the kinetic energy might be in error by hundreds of kJ/mol.