Ivan S. Ufimtsev

Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics.

We demonstrate that a video gaming machine containing two consumer graphical cards can outpace a state-of-the-art quad-core processor workstation by a factor of more than 180× in Hartree-Fock energy + gradient calculations. Such performance makes it possible to run large scale Hartree-Fock and Density Functional Theory calculations, which typically require hundreds of traditional processor cores, on a single workstation. Benchmark Born-Oppenheimer molecular dynamics simulations are performed on two molecular systems using the 3-21G basis set - a hydronium ion solvated by 30 waters (94 atoms, 405 basis functions) and an aspartic acid molecule solvated by 147 waters (457 atoms, 2014 basis functions). Our GPU implementation can perform 27 ps/day and 0.7 ps/day of ab initio molecular dynamics simulation on a single desktop computer for these systems.

GPU-accelerated molecular modeling coming of age

Graphics processing units (GPUs) have traditionally been used in molecular modeling solely for visualization of molecular structures and animation of trajectories resulting from molecular dynamics simulations. Modern GPUs have evolved into fully programmable, massively parallel co-processors that can now be exploited to accelerate many scientific computations, typically providing about one order of magnitude speedup over CPU code and in special cases providing speedups of two orders of magnitude. This paper surveys the development of molecular modeling algorithms that leverage GPU computing, the advances already made and remaining issues to be resolved, and the continuing evolution of GPU technology that promises to become even more useful to molecular modeling. Hardware acceleration with commodity GPUs is expected to benefit the overall computational biology community by bringing teraflops performance to desktop workstations and in some cases potentially changing what were formerly batch-mode computational jobs into interactive tasks.

Quantum Chemistry on Graphical Processing Units. 2. Direct Self-Consistent-Field Implementation

We demonstrate the use of graphical processing units (GPUs) to carry out complete self-consistent-field calculations for molecules with as many as 453 atoms (2131 basis functions). Speedups ranging from 28× to 650× are achieved as compared to a mature third-party quantum chemistry program (GAMESS) running on a traditional CPU. The computational organization used to construct the Coulomb and exchange operators is discussed. We also present results using three GPUs in parallel, combining coarse and fine-grained parallelism.

Graphical Processing Units for Quantum Chemistry

The paper provide a brief overview of electronic structure theory and details the implementation of quantum chemistry methods on a graphical processing unit. The paper also analyze algorithm performance in terms of floating-point operations and memory bandwidth, and assess the adequacy of single-precision accuracy for quantum chemistry applications.

Excited-State Electronic Structure with Configuration Interaction Singles and Tamm–Dancoff Time-Dependent Density Functional Theory on Graphical Processing Units

Excited-state calculations are implemented in a development version of the GPU-based TeraChem software package using the configuration interaction singles (CIS) and adiabatic linear response Tamm–Dancoff time-dependent density functional theory (TDA-TDDFT) methods. The speedup of the CIS and TDDFT methods using GPU-based electron repulsion integrals and density functional quadrature integration allows full ab initio excited-state calculations on molecules of unprecedented size. CIS/6-31G and TD-BLYP/6-31G benchmark timings are presented for a range of systems, including four generations of oligothiophene dendrimers, photoactive yellow protein (PYP), and the PYP chromophore solvated with 900 quantum mechanical water molecules. The effects of double and single precision integration are discussed, and mixed precision GPU integration is shown to give extremely good numerical accuracy for both CIS and TDDFT excitation energies (excitation energies within 0.0005 eV of extended double precision CPU results).

Dynamic Precision for Electron Repulsion Integral Evaluation on Graphical Processing Units (GPUs)

It has recently been demonstrated that novel streaming architectures found in consumer video gaming hardware such as graphical processing units (GPUs) are well-suited to a broad range of computations including electronic structure theory (quantum chemistry). Although recent GPUs have developed robust support for double precision arithmetic, they continue to provide 2-8× more hardware units for single precision. In order to maximize performance on GPU architectures, we present a technique of dynamically selecting double or single precision evaluation for electron repulsion integrals (ERIs) in Hartree-Fock and density functional self-consistent field (SCF) calculations. We show that precision error can be effectively controlled by evaluating only the largest integrals in double precision. By dynamically scaling the precision cutoff over the course of the SCF procedure, we arrive at a scheme that minimizes the number of double precision integral evaluations for any desired accuracy. This dynamic precision scheme is shown to be effective for an array of molecules ranging in size from 20 to nearly 2000 atoms.

Observation of a Zundel-like transition state during proton transfer in aqueous hydroxide solutions

It is generally accepted that the anomalous diffusion of the aqueous hydroxide ion results from its ability to accept a proton from a neighboring water molecule; yet, many questions exist concerning the mechanism for this process. What is the solvation structure of the hydroxide ion? In what way do water hydrogen bond dynamics influence the transfer of a proton to the ion? We present the results of femtosecond pump-probe and 2D infrared experiments that probe the O-H stretching vibration of a solution of dilute HOD dissolved in NaOD/D2O. Upon the addition of NaOD, measured pump-probe transients and 2D IR spectra show a new feature that decays with a 110-fs time scale. The calculation of 2D IR spectra from an empirical valence bond molecular dynamics simulation of a single NaOH molecule in a bath of H2O indicates that this fast feature is due to an overtone transition of Zundel-like H3O2− states, wherein a proton is significantly shared between a water molecule and the hydroxide ion. Given the frequency of vibration of shared protons, the observations indicate the shared proton state persists for 2–3 vibrational periods before the proton localizes on a hydroxide. Calculations based on the EVB-MD model argue that the collective electric field in the proton transfer direction is the appropriate coordinate to describe the creation and relaxation of these Zundel-like transition states.

An atomic orbital-based formulation of the complete active space self-consistent field method on graphical processing units

Despite its importance, state-of-the-art algorithms for performing complete active space self-consistent field (CASSCF) computations have lagged far behind those for single reference methods. We develop an algorithm for the CASSCF orbital optimization that uses sparsity in the atomic orbital (AO) basis set to increase the applicability of CASSCF. Our implementation of this algorithm uses graphical processing units (GPUs) and has allowed us to perform CASSCF computations on molecular systems containing more than one thousand atoms. Additionally, we have implemented analytic gradients of the CASSCF energy; the gradients also benefit from GPU acceleration as well as sparsity in the AO basis.

Analytic first derivatives of floating occupation molecular orbital-complete active space configuration interaction on graphical processing units

The floating occupation molecular orbital-complete active space configuration interaction (FOMO-CASCI) method is a promising alternative to the state-averaged complete active space self-consistent field (SA-CASSCF) method. We have formulated the analytic first derivative of FOMO-CASCI in a manner that is well-suited for a highly efficient implementation using graphical processing units (GPUs). Using this implementation, we demonstrate that FOMO-CASCI gradients are of similar computational expense to configuration interaction singles (CIS) or time-dependent density functional theory (TDDFT). In contrast to CIS and TDDFT, FOMO-CASCI can describe multireference character of the electronic wavefunction. We show that FOMO-CASCI compares very favorably to SA-CASSCF in its ability to describe molecular geometries and potential energy surfaces around minimum energy conical intersections. Finally, we apply FOMO-CASCI to the excited state hydrogen transfer reaction in methyl salicylate.

Implementation of scientific computing applications on the Cell Broadband Engine

The Cell Broadband Engine architecture is a revolutionary processor architecture well suited for many scientific codes. This paper reports on an effort to implement several traditional high-performance scientific computing applications on the Cell Broadband Engine processor, including molecular dynamics, quantum chromodynamics and quantum chemistry codes. The paper discusses data and code restructuring strategies necessary to adapt the applications to the intrinsic properties of the Cell processor and demonstrates performance improvements achieved on the Cell architecture. It concludes with the lessons learned and provides practical recommendations on optimization techniques that are believed to be most appropriate.