Enabling large-scale correlated electronic structure calculations

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The primary focus of GAMESS over the last 5 years has been the development of new high-performance codes that are able to take effective and efficient advantage of the most advanced computer architectures, both CPU and accelerators. These efforts include employing density fitting and fragmentation methods to reduce the high scaling of well-correlated (e.g., coupled-cluster) methods as well as developing novel codes that can take optimal advantage of graphical processing units and other modern accelerators. Because accurate wave functions can be very complex, an important new functionality in GAMESS is the quasi-atomic orbital analysis, an unbiased approach to the understanding of covalent bonds embedded in the wave function. Best practices for the maintenance and distribution of GAMESS are also discussed.

Section: Graphical Processing Unitsmentioning

confidence: 99%

The General Atomic and Molecular Electronic Structure System (GAMESS): Novel Methods on Novel Architectures

Zahariev,

Xu,

Westheimer

et al. 2023

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“…For this reason, more efficient algorithms and approximate implementations have been developed to improve the scaling of both RPA and MP2. Common strategies are the usage of localized orbitals, − cluster-in-molecule (CIM) approaches, , or implementations which rely on sparsity in the atomic orbital basis. − In the latter class of methods, implementations using local DF approximations have gained increasing popularity. ,, While they do not achieve linear scaling with systems sizes, they typically come with a very small prefactor and are believed to only introduce minor errors compared to canonical, molecular orbital based implementations. , …”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Toward Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy

Edoardo

Philipsen

Förster

et al. 2023

Pair atomic density fitting (PADF) has been identified as a promising strategy to reduce the scaling with system size of quantum chemical methods for the calculation of the correlation energy like the direct random-phase approximation (RPA) or second-order Møller–Plesset perturbation theory (MP2). PADF can however introduce large errors in correlation energies as the two-electron interaction energy is not guaranteed to be bounded from below. This issue can be partially alleviated by using very large fit sets, but this comes at the price of reduced efficiency and having to deal with near-linear dependencies in the fit set. One posibility is to use global density fitting (DF), but in this work, we introduce an alternative methodology to overcome this problem that preserves the intrinsically favorable scaling of PADF. We first regularize the Fock matrix by projecting out parts of the basis set which gives rise to orbital products that are hard to describe by PADF. After having thus obtained a reliable self-consistent field solution, we then also apply this projector to the orbital coefficient matrix to improve the precision of PADF-MP2 and PADF-RPA. We systematically assess the accuracy of this new approach in a numerical atomic orbital framework using Slater type orbitals (STO) and correlation consistent Gaussian type basis sets up to quintuple-ζ quality for systems with more than 200 atoms. For the small and medium systems in the S66 database we show the maximum deviation of PADF-MP2 and PADF-RPA relative correlation energies to DF-MP2 and DF-RPA reference results to be 0.07 and 0.14 kcal/mol, respectively. When the new projector method is used, the errors only slightly increase for large molecules and also when moderately sized fit sets are used the resulting errors are well under control. Finally, we demonstrate the computational efficiency of our algorithm by calculating the interaction energies of large, non-covalently bound complexes with more than 1000 atoms and 20000 atomic orbitals at the RPA@PBE/CC-pVTZ level of theory.

“…All of these factors make it especially challenging to port Gaussian integral kernels onto accelerated coprocessors, such as general-purpose graphical processing units (GPGPUs, or, simply, GPUs), that have become the norm both on the commodity and high-end platforms. Hence there has been an intense effort to address these challenges, both on the modern central processing units (CPUs) with wide single-instruction-multiple-data (SIMD) instructions and on GPUs. ,,,,− …”

Section: Introductionmentioning

confidence: 99%

Memory-Efficient Recursive Evaluation of 3-Center Gaussian Integrals

Asadchev

Valeev

2023

To improve the efficiency of Gaussian integral evaluation on modern accelerated architectures, FLOP-efficient Obara-Saika-based recursive evaluation schemes are optimized for the memory footprint. For the 3-center 2-particle integrals that are key for the evaluation of Coulomb and other 2-particle interactions in the density-fitting approximation, the use of multiquantal recurrences (in which multiple quanta are created or transferred at once) is shown to produce significant memory savings. Other innovations include leveraging register memory for reduced memory footprint and direct compile-time generation of optimized kernels (instead of custom code generation) with compile-time features of modern C++/CUDA. Performance of conventional and CUDA-based implementations of the proposed schemes is illustrated for both the individual batches of integrals involving up to Gaussians with low and high angular momenta (up to L = 6) and contraction degrees, as well as for the density-fitting-based evaluation of the Coulomb potential. The computer implementation is available in the open-source library.