Efficient and portable acceleration of quantum chemical many-body methods in mixed floating point precision using OpenACC compiler directives

Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: Theory, implementation, and role of the Green's function second-order exchange for intermolecular interactions

We present an efficient MPI-parallel algorithm and its implementation for evaluating the self-consistent correlated second-order exchange term (SOX), which is employed as a correction to the fully self-consistent GW scheme called scGWSOX (GW plus the SOX term iterated to achieve full Green's function self-consistency). Due to the application of the tensor hypercontraction (THC) in our computational procedure, the scaling of the evaluation of scGWSOX is reduced from O(nτnAO5) to O(nτN2nAO2). This fully MPI-parallel and THC-adapted approach enabled us to conduct the largest fully self-consistent scGWSOX calculations with over 1100 atomic orbitals with only negligible errors attributed to THC fitting. Utilizing our THC implementation for scGW, scGF2, and scGWSOX, we evaluated energies of intermolecular interactions. This approach allowed us to circumvent issues related to reference dependence and ambiguity in energy evaluation, which are common challenges in non-self-consistent calculations. We demonstrate that scGW exhibits a slight overbinding tendency for large systems, contrary to the underbinding observed with non-self-consistent RPA. Conversely, scGWSOX exhibits a slight underbinding tendency for such systems. This behavior is both physical and systematic and is caused by exclusion-principle violating diagrams or corresponding corrections. Our analysis elucidates the role played by these different diagrams, which is crucial for the construction of rigorous, accurate, and systematic methods. Finally, we explicitly show that all perturbative fully self-consistent Green's function methods are size-extensive and size-consistent.

State-of-the-art local correlation methods enable affordable gold standard quantum chemistry for up to hundreds of atoms

In this feature, we review the current capabilities of local electron correlation methods up to the coupled cluster model with single, double, and perturbative triple excitations [CCSD(T)], which is a gold standard in quantum chemistry. The main computational aspects of the local method types are assessed from the perspective of applications, but the focus is kept on how to achieve chemical accuracy (i.e., <1 kcal mol-1 uncertainty), as well as on the broad scope of chemical problems made accessible. The performance of state-of-the-art methods is also compared, including the most employed DLPNO and, in particular, our local natural orbital (LNO) CCSD(T) approach. The high accuracy and efficiency of the LNO method makes chemically accurate CCSD(T) computations accessible for molecules of hundreds of atoms with resources affordable to a broad computational community (days on a single CPU and 10-100 GB of memory). Recent developments in LNO-CCSD(T) enable systematic convergence and robust error estimates even for systems of complicated electronic structure or larger size (up to 1000 atoms). The predictive power of current local CCSD(T) methods, usually at about 1-2 order of magnitude higher cost than hybrid density functional theory (DFT), has become outstanding on the palette of computational chemistry applicable for molecules of practical interest. We also review more than 50 LNO-based and other advanced local-CCSD(T) applications for realistic, large systems across molecular interactions as well as main group, transition metal, bio-, and surface chemistry. The examples show that properly executed local-CCSD(T) can contribute to binding, reaction equilibrium, rate constants, etc. which are able to match measurements within the error estimates. These applications demonstrate that modern, open-access, and broadly affordable local methods, such as LNO-CCSD(T), already enable predictive computations and atomistic insight for complicated, real-life molecular processes in realistic environments.

CuGBasis: High-performance CUDA/Python library for efficient computation of quantum chemistry density-based descriptors for larger systems

CuGBasis is a free and open-source CUDA®/Python library for efficient computation of scalar, vector, and matrix quantities crucial for the post-processing of electronic structure calculations. CuGBasis integrates high-performance Graphical Processing Unit (GPU) computing with the ease and flexibility of Python programming, making it compatible with a vast ecosystem of libraries. We showcase its utility as a Python library and demonstrate its seamless interoperability with existing Python software to gain chemical insight from quantum chemistry calculations. Leveraging GPU-accelerated code, cuGBasis exhibits remarkable performance, making it highly applicable to larger systems or large databases. Our benchmarks reveal a 100-fold performance gain compared to alternative software packages, including serial/multi-threaded Central Processing Unit and GPU implementations. This paper outlines various features and computational strategies that lead to cuGBasis's enhanced performance, guiding developers of GPU-accelerated code.

A Perspective on Sustainable Computational Chemistry Software Development and Integration

The power of quantum chemistry to predict the ground and excited state properties of complex chemical systems has driven the development of computational quantum chemistry software, integrating advances in theory, applied mathematics, and computer science. The emergence of new computational paradigms associated with exascale technologies also poses significant challenges that require a flexible forward strategy to take full advantage of existing and forthcoming computational resources. In this context, the sustainability and interoperability of computational chemistry software development are among the most pressing issues. In this perspective, we discuss software infrastructure needs and investments with an eye to fully utilize exascale resources and provide unique computational tools for next-generation science problems and scientific discoveries.

Quantum Mechanics/Molecular Mechanics Simulations on NVIDIA and AMD Graphics Processing Units

We have ported and optimized the graphics processing unit (GPU)-accelerated QUICK and AMBER-based ab initio quantum mechanics/molecular mechanics (QM/MM) implementation on AMD GPUs. This encompasses the entire Fock matrix build and force calculation in QUICK including one-electron integrals, two-electron repulsion integrals, exchange-correlation quadrature, and linear algebra operations. General performance improvements to the QUICK GPU code are also presented. Benchmarks carried out on NVIDIA V100 and AMD MI100 cards display similar performance on both hardware for standalone HF/DFT calculations with QUICK and QM/MM molecular dynamics simulations with QUICK/AMBER. Furthermore, with respect to the QUICK/AMBER release version 21, significant speedups are observed for QM/MM molecular dynamics simulations. This significantly increases the range of scientific problems that can be addressed with open-source QM/MM software on state-of-the-art computer hardware.

GPU acceleration of rank-reduced coupled-cluster singles and doubles

We have developed a graphical processing unit (GPU) accelerated implementation of our recently introduced rank-reduced coupled-cluster singles and doubles (RR-CCSD) method. RR-CCSD introduces a low-rank approximation of the doubles amplitudes. This is combined with a low-rank approximation of the electron repulsion integrals via Cholesky decomposition. The result of these two low-rank approximations is the replacement of the usual fourth-order CCSD tensors with products of second- and third-order tensors. In our implementation, only a single fourth-order tensor must be constructed as an intermediate during the solution of the amplitude equations. Owing in large part to the compression of the doubles amplitudes, the GPU-accelerated implementation shows excellent parallel efficiency (95% on eight GPUs). Our implementation can solve the RR-CCSD equations for up to 400 electrons and 1550 basis functions-roughly 50% larger than the largest canonical CCSD computations that have been performed on any hardware. In addition to increased scalability, the RR-CCSD computations are faster than the corresponding CCSD computations for all but the smallest molecules. We test the accuracy of RR-CCSD for a variety of chemical systems including up to 1000 basis functions and determine that accuracy to better than 0.1% error in the correlation energy can be achieved with roughly 95% compression of the ov space for the largest systems considered. We also demonstrate that conformational energies can be predicted to be within 0.1 kcal mol^-1 with efficient compression applied to the wavefunction. Finally, we find that low-rank approximations of the CCSD doubles amplitudes used in the similarity transformation of the Hamiltonian prior to a conventional equation-of-motion CCSD computation will not introduce significant errors (on the order of a few hundredths of an electronvolt) into the resulting excitation energies.

Harnessing the Power of Multi-GPU Acceleration into the Quantum Interaction Computational Kernel Program

We report a new multi-GPU capable ab initio Hartree-Fock/density functional theory implementation integrated into the open source QUantum Interaction Computational Kernel (QUICK) program. Details on the load balancing algorithms for electron repulsion integrals and exchange correlation quadrature across multiple GPUs are described. Benchmarking studies carried out on up to four GPU nodes, each containing four NVIDIA V100-SXM2 type GPUs demonstrate that our implementation is capable of achieving excellent load balancing and high parallel efficiency. For representative medium to large size protein/organic molecular systems, the observed parallel efficiencies remained above 82% for the Kohn-Sham matrix formation and above 90% for nuclear gradient calculations. The accelerations on NVIDIA A100, P100, and K80 platforms also have realized parallel efficiencies higher than 68% in all tested cases, paving the way for large-scale ab initio electronic structure calculations with QUICK.

Accelerating seminumerical Fock-exchange calculations using mixed single- and double-precision arithmethic

We investigate the applicability of single-precision (fp32) floating point operations within our linear-scaling, seminumerical exchange method sn-LinK [Laqua et al., J. Chem. Theory Comput. 16, 1456 (2020)] and find that the vast majority of the three-center-one-electron (3c1e) integrals can be computed with reduced numerical precision with virtually no loss in overall accuracy. This leads to a near doubling in performance on central processing units (CPUs) compared to pure fp64 evaluation. Since the cost of evaluating the 3c1e integrals is less significant on graphic processing units (GPUs) compared to CPU, the performance gains from accelerating 3c1e integrals alone is less impressive on GPUs. Therefore, we also investigate the possibility of employing only fp32 operations to evaluate the exchange matrix within the self-consistent-field (SCF) followed by an accurate one-shot evaluation of the exchange energy using mixed fp32/fp64 precision. This still provides very accurate (1.8 µEh maximal error) results while providing a sevenfold speedup on a typical "gaming" GPU (GTX 1080Ti). We also propose the use of incremental exchange-builds to further reduce these errors. The proposed SCF scheme (i-sn-LinK) requires only one mixed-precision exchange matrix calculation, while all other exchange-matrix builds are performed with only fp32 operations. Compared to pure fp64 evaluation, this leads to 4-7× speedups for the whole SCF procedure without any significant deterioration of the results or the convergence behavior.

Accurate Reduced-Cost CCSD(T) Energies: Parallel Implementation, Benchmarks, and Large-Scale Applications

The accurate and systematically improvable frozen natural orbital (FNO) and natural auxiliary function (NAF) cost-reducing approaches are combined with our recent coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] implementations. Both of the closed- and open-shell FNO-CCSD(T) codes benefit from OpenMP parallelism, completely or partially integral-direct density-fitting algorithms, checkpointing, and hand-optimized, memory- and operation count effective implementations exploiting all permutational symmetries. The closed-shell CCSD(T) code requires negligible disk I/O and network bandwidth, is MPI/OpenMP parallel, and exhibits outstanding peak performance utilization of 50-70% up to hundreds of cores. Conservative FNO and NAF truncation thresholds benchmarked for challenging reaction, atomization, and ionization energies of both closed- and open-shell species are shown to maintain 1 kJ/mol accuracy against canonical CCSD(T) for systems of 31-43 atoms even with large basis sets. The cost reduction of up to an order of magnitude achieved extends the reach of FNO-CCSD(T) to systems of 50-75 atoms (up to 2124 atomic orbitals) with triple- and quadruple-ζ basis sets, which is unprecedented without local approximations. Consequently, a considerably larger portion of the chemical compound space can now be covered by the practically "gold standard" quality FNO-CCSD(T) method using affordable resources and about a week of wall time. Large-scale applications are presented for organocatalytic and transition-metal reactions as well as noncovalent interactions. Possible applications for benchmarking local CCSD(T) methods, as well as for the accuracy assessment or parametrization of less complete models, for example, density functional approximations or machine learning potentials, are also outlined.

Performance of Coupled-Cluster Singles and Doubles on Modern Stream Processing Architectures

We develop a new implementation of coupled-cluster singles and doubles (CCSD) optimized for the most recent graphical processing unit (GPU) hardware. We find that a single node with 8 NVIDIA V100 GPUs is capable of performing CCSD computations on roughly 100 atoms and 1300 basis functions in less than 1 day. Comparisons against massively parallel implementations of CCSD suggest that more than 64 CPU-based nodes (each with 16 cores) are required to match this performance.

Single-precision open-shell CCSD and CCSD(T) calculations on graphics processing units

It has been shown that coupled-cluster calculations with single-precision data are able to provide correlation energy with insignificant loss of accuracy.

GPU-Accelerated Large-Scale Excited-State Simulation Based on Divide-and-Conquer Time-Dependent Density-Functional Tight-Binding

The present study implemented the divide-and-conquer time-dependent density-functional tight-binding (DC-TDDFTB) code on a graphical processing unit (GPU). The DC method, which is a linear-scaling scheme, divides a total system into several fragments. By separately solving local equations in individual fragments, the DC method could reduce slow central processing unit (CPU)-GPU memory access, as well as computational cost, and avoid shortfalls of GPU memory. Numerical applications confirmed that the present code on GPU significantly accelerated the TDDFTB calculations, while maintaining accuracy. Furthermore, the DC-TDDFTB simulation of 2-acetylindan-1,3-dione displays excited-state intramolecular proton transfer and provides reasonable absorption and fluorescence energies with the corresponding experimental values. © 2019 Wiley Periodicals, Inc.

Optimization of the linear-scaling local natural orbital CCSD(T) method: Redundancy-free triples correction using Laplace transform

An improved algorithm is presented for the evaluation of the (T) correction as a part of our local natural orbital (LNO) coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme [Z. Rolik et al., J. Chem. Phys. 139, 094105 (2013)]. The new algorithm is an order of magnitude faster than our previous one and removes the bottleneck related to the calculation of the (T) contribution. First, a numerical Laplace transformed expression for the (T) fragment energy is introduced, which requires on average 3 to 4 times fewer floating point operations with negligible compromise in accuracy eliminating the redundancy among the evaluated triples amplitudes. Second, an additional speedup factor of 3 is achieved by the optimization of our canonical (T) algorithm, which is also executed in the local case. These developments can also be integrated into canonical as well as alternative fragmentation-based local CCSD(T) approaches with minor modifications. As it is demonstrated by our benchmark calculations, the evaluation of the new Laplace transformed (T) correction can always be performed if the preceding CCSD iterations are feasible, and the new scheme enables the computation of LNO-CCSD(T) correlation energies with at least triple-zeta quality basis sets for realistic three-dimensional molecules with more than 600 atoms and 12 000 basis functions in a matter of days on a single processor.