Low-Scaling Tensor Hypercontraction in the Cholesky Molecular Orbital Basis Applied to Second-Order Møller–Plesset Perturbation Theory

Abstract

We employ various reduced scaling techniques to accelerate the recently developed least-squares tensor hypercontraction (LS-THC) approximation [ParrishR. M.HohensteinE. G.MartínezT. J.SherrillC. D. Parrish, R. M. Hohenstein, E. G. Martínez, T. J. Sherrill, C. D. J. Chem. Phys.2012137224106] for electron repulsion integrals (ERIs) and apply it to second-order Møller–Plesset perturbation theory (MP2). The grid-projected ERI tensors are efficiently constructed using a localized Cholesky molecular orbital basis from density-fitted integrals with an attenuated Coulomb metric. Additionally, rigorous integral screening and the natural blocking matrix format are applied to reduce the complexity of this step. By recasting the equations to form the quantized representation of the 1/r operator Z into the form of a system of linear equations, the bottleneck of inverting the grid metric via pseudoinversion is removed. This leads to a reduced scaling THC algorithm and application to MP2 yields the (sub-)­quadratically scaling THC-ω-RI-CDD-SOS-MP2 method. The efficiency of this method is assessed for various systems including DNA fragments with over 8000 basis functions and the subquadratic scaling is illustrated.

Linear-Scaling Open-Shell MP2 Approach: Algorithm, Benchmarks, and Large-Scale Applications

“…The Laplace transform (LT) technique 29 , 30 proposed by Almlöf to eliminate the energy denominator of MP2 has also become fundamental to reduce the fifth-power-scaling computational complexity of MP2. 31 − 39 Aiming toward the same goal, the particularly simple form of MP2 was also utilized in a number of creative developments on the basis of, for instance, Cholesky-decomposed pseudo-density matrices; 40 − 43 stochastic, 44 , 45 quadrature-based, 46 and pseudospectral 47 , 48 approaches; nonorthogonal 49 , 50 or Slater-type orbitals; 51 , 52 tensor hypercontraction; 53 , 54 as well as large-scale parallelization. 35 , 55 , 56 …”

“…Especially when combined with the resolution-of-identity or density-fitting (DF) technique, MP2-based methods can target systems of more than 100 atoms, thereby extending the about 30-atom applicability limit of CCSD­(T) considerably. The Laplace transform (LT) technique , proposed by Almlöf to eliminate the energy denominator of MP2 has also become fundamental to reduce the fifth-power-scaling computational complexity of MP2. − Aiming toward the same goal, the particularly simple form of MP2 was also utilized in a number of creative developments on the basis of, for instance, Cholesky-decomposed pseudo-density matrices; − stochastic, , quadrature-based, and pseudospectral , approaches; nonorthogonal , or Slater-type orbitals; , tensor hypercontraction; , as well as large-scale parallelization. ,, …”

Tensor-Hypercontracted MP2 First Derivatives: Runtime and Memory Efficient Computation of Hyperfine Coupling Constants

“…In this work, we make use of our recently reported low-scaling THC method 41 based on the ω-RI approximation for the ERIs contained in Z and natural blocking (NB). 57 , 58 However, in contrast to our work on THC-MP2 energies, 41 in the present work the AO ERIs are fitted, since the gradient for calculating the MP2 HFCCs is based on our RI-CDD approach to the computation of AO-MP2 energy gradients. 6 It is important to note here, that while the equations for the THC-based gradient method are derived by inserting the THC factorization into the equations of the RI-CDD-MP2 gradient with respect to ξ′, there is no difference to directly differentiating the THC-AO-MP2 energy equations.…”

“…As will be discussed in section 2.4 , the resulting equations are identical to the ones obtained by differentiating the THC-AO-MP2 energy equation. As a representative case of these kinds of perturbations, we apply our recently developed low-scaling LS-THC algorithm 41 to the AO-MP2 energy derivative with respect to the nuclear magnetic moment, for the computation of HFCCs on the MP2 level of theory.…”

Cholesky decomposition of complex two-electron integrals over GIAOs: Efficient MP2 computations for large molecules in strong magnetic fields

“…[9][10][11][12][13][14][15] Additionally, any tensor such as the full ERI or likewise the associated RI representation can be further factorised a) Electronic mail: siblasch@uni-mainz.de b) Electronic mail: sstopkow@uni-mainz.de through the use of tensor hypercontractions. [16][17][18][19][20] The performance of the RI approach is tied to the quality of an externally optimized auxiliary basis set. A more general approach which does not require an auxiliary basis, is the Cholesky decomposition (CD).…”