Quantum Chemistry in Dataflow: Density-Fitting MP2

Cooper, Bridgette; Girdlestone, Stephen; Burovskiy, Pavel; Gaydadjiev, Georgi; Averbukh, Vitali; Knowles, Peter J.; Luk, Wayne

doi:10.1021/acs.jctc.7b00649

Cited by 9 publications

(11 citation statements)

References 68 publications

(95 reference statements)

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“…We have implemented RPA and RPA+SOSSX correlation energies using (21). In analogy to (18) and in the same way as in typical MP2 implementations in quantum chemistry codes, 116,118 the last term on the r.h.s of ( 21) is evaluated directly in the MO basis. The second term on the r.h.s of ( 21) is evaluated in the space of auxiliary basis functions.…”

Section: Technical and Comptational Detailsmentioning

confidence: 99%

Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems

Förster,

Visscher

2021

Preprint

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Electron correlation in finite and extended systems is often described in an effective single-particle framework within the GW approximation. Here, we use the statically screened second-order exchange contribution to the self-energy (G3W 2) to calculate a perturbative correction to the GW self-energy. We use this correction to calculate total correlation energies of atoms, relative energies, as well as charged excitations of a wide range of molecular systems. We show that the second-order correction improves correlation energies with respect to the RPA and also improves relative energies for many, but not all considered systems. While the full G3W 2 contribution does not give consistent improvements over GW , taking the average of GW and GW + G3W 2 generally gives excellent results. Improvements over quasiparticle self-consistent GW , which we show to give very accurate charged excitations in small and medium molecules by itself, are only minor. G0W0 quasiparticle energies evaluated with eigenvalue and orbitals from range-separated hybrids, however, are tremendously improved upon: The second-order corrected G0W0 outperforms all existing GW methods for the systems considered herein and also does not come with substantially increased computational cost compared to G0W0 for systems with up to 100 atoms.

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Section: Technical and Comptational Detailsmentioning

confidence: 99%

Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems

Förster,

Visscher

2021

Preprint

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“…Using reconfigurable hardware accelerators rather than CPUs helps to deal iteratively with large volumes of data. DFEs have recently been successfully applied to a wide range of scientific problems, including geoscience (Gan et al, 2017), fluid-dynamics (Düben et al, 2015), artificial neural networks (Liang et al, 2018), quantum chemistry (Cooper et al, 2017), and genomics (Arram et al, 2015).…”

Section: Data Modelmentioning

confidence: 99%

Fast sampling from Wiener posteriors for image data with dataflow engines

Jeffrey

Heavens

Fortio

2018

Astronomy and Computing

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We use Dataflow Engines (DFE) to construct an efficient Wiener filter of noisy and incomplete image data, and to quickly draw probabilistic samples of the compatible true underlying images from the Wiener posterior. Dataflow computing is a powerful approach using reconfigurable hardware, which can be deeply pipelined and is intrinsically parallel. The unique Wiener-filtered image is the minimumvariance linear estimate of the true image (if the signal and noise covariances are known) and the most probable true image (if the signal and noise are Gaussian distributed). However, many images are compatible with the data with different probabilities, given by the analytic posterior probability distribution referred to as the Wiener posterior. The DFE code also draws large numbers of samples of true images from this posterior, which allows for further statistical analysis. Naive computation of the Wiener-filtered image is impractical for large datasets, as it scales as n 3 , where n is the number of pixels. We use a messenger field algorithm, which is well suited to a DFE implementation, to draw samples from the Wiener posterior, that is, with the correct probability we draw samples of noiseless images that are compatible with the observed noisy image. The Wiener-filtered image can be obtained by a trivial modification of the algorithm. We demonstrate a lower bound on the speed-up, from drawing 10 5 samples of a 128 2 image, of 11.3 ± 0.8 with 8 DFEs in a 1U MPC-X box when compared with a 1U server presenting 32 CPU threads. We also discuss a potential application in astronomy, to provide better dark matter maps and improved determination of the parameters of the Universe.

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“…To accelerate the evaluation of MP2 energies, DF is the only approach which has found widespread use. [ 104–115 ] Reducing the prefactor of canonical implementations by at least one order of magnitude, it retains their N 5 scaling. However, relying on the short‐rangedness of dynamical electron correlation, [ 116–119 ] many reduced‐scaling MP2 algorithms, employing localized molecular orbitals (MO), [ 120–122 ] relying on fragmentation approaches, [ 113,114,123,124 ] or evaluating the MP2 energy in the AO basis and exploiting sparsity in the ERI tensor [ 125–143 ] have been developed.…”

Section: Introductionmentioning

confidence: 99%

Double hybrid DFT calculations with Slater type orbitals

Förster

Visscher

2020

J Comput Chem

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On a comprehensive database with 1,644 datapoints, covering several aspects of main-group as well as of transition metal chemistry, we assess the performance of 60 density functional approximations (DFA), among them 36 double hybrids (DH). All calculations are performed using a Slater type orbital (STO) basis set of triple-ζ (TZ) quality and the highly efficient pair atomic resolution of the identity approach for the exchange-and Coulomb-term of the KS matrix (PARI-K and PARI-J, respectively) and for the evaluation of the MP2 energy correction (PARI-MP2). Employing the quadratic scaling SOS-AO-PARI-MP2 algorithm, DHs based on the spin-opposite-scaled (SOS) MP2 approximation are benchmarked against a database of large molecules. We evaluate the accuracy of STO/PARI calculations for B3LYP as well as for the DH B2GP-PLYP and show that the combined basis set and PARI-error is comparable to the one obtained using the well-known def2-TZVPP Gaussian-type basis set in conjunction with global density fitting. While quadruple-ζ (QZ) calculations are currently not feasible for PARI-MP2 due to numerical issues, we show that, on the TZ level, Jacob's ladder for classifying DFAs is reproduced. However, while the best DHs are more accurate than the best hybrids, the improvements are less pronounced than the ones commonly found on the QZ level. For conformers of organic molecules and noncovalent interactions where very high accuracy is required for qualitatively correct results, DHs provide only small improvements over hybrids, while they still excel in thermochemistry, kinetics, transition metal chemistry and the description of strained organic systems. K E Y W O R D S ADF, benchmark, double-hybrid, KS-DFT, STO

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Quantum Chemistry in Dataflow: Density-Fitting MP2

Cited by 9 publications

References 68 publications

Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems

Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems

Fast sampling from Wiener posteriors for image data with dataflow engines

Double hybrid DFT calculations with Slater type orbitals

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