Efficient low-scaling computation of NMR shieldings at the second-order Møller–Plesset perturbation theory level with Cholesky-decomposed densities and an attenuated Coulomb metric

Abstract

A method for the computation of nuclear magnetic resonance (NMR) shieldings with second-order Møller–Plesset perturbation theory (MP2) is presented which allows to efficiently compute the entire set of shieldings for a given molecular structure. The equations are derived using Laplace-transformed atomic orbital second-order Møller–Plesset perturbation theory as a starting point. The Z-vector approach is employed for minimizing the number of coupled-perturbed self-consistent-field equations that need to be solved. In addition, the method uses the resolution-of-the-identity approximation with an attenuated Coulomb metric and Cholesky decomposition of pseudo-density matrices. The sparsity in the three-center integrals is exploited with sparse linear algebra approaches, leading to reduced computational cost and memory demands. Test calculations show that the deviations from NMR shifts obtained with canonical MP2 are small if appropriate thresholds are used. The performance of the method is illustrated in calculations on DNA strands and on glycine chains with up to 283 atoms and 2864 basis functions.

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

“…In order to avoid the evaluation of the derivatives of the perturbed occupied and virtual pseudodensities, these intermediates are expanded in terms of the regular occupied and virtual densities P occ and P virt as Thus, the derivatives of eq 8 are given by By further making use of the identity the perturbed virtual density can be related to the perturbed occupied density as Note again that eq 11 does not contain the derivative of the overlap matrix S , due to S being independent of ξ′. By making use of the above relations for the densities, eq 6 becomes Cyclic permutation under the trace was applied above to obtain terms of the general form with which can be solved for Y by recursion, as detailed in refs ( 25 ) and ( 12 ). Let Y̅ η be the solution of eq 13 with A ≡ τ κ P occ η F η and B ≡ P occ η R̅ η , and let Y̲ η be the solution with A ≡ – τ κ P virt η F η and B ≡ P virt η R̲ η .…”

“…To reduce the memory footprint of the ERIs, tensor decomposition methods, particularly the resolution-of-the-identity (RI) ansatz, 26 − 29 have been broadly applied in the context of MP2 derivatives. 5 , 6 , 12 , 30 However, with increasing molecule size, even the third-order RI tensors eventually exceed the available disk space of conventional high performance computing nodes. To overcome this storage limitation, further reduction of the dimensionality of the ERIs is desirable.…”

“…As opposed to coupled cluster theory (CC), MP n lacks infinite-order corrections present in the cluster operator expansion of the CC models, which generally makes MP n less accurate . However, when going from energies to gradients and molecular properties, MP n , especially second-order MP n (MP2), was shown to yield accurate hyperfine coupling constants (HFCCs) − and relative nuclear magnetic resonance (NMR) shifts. − However, MP2 is sensitive to spin-contamination in the Hartree–Fock wave function, which can be improved upon when used in its orbital-optimized variant or as part of double-hybrid density functionals …”

“…Since canonical ERIs are fourth-order tensors, their memory requirements prohibitively scale with the forth power of the number of basis functions and saving multiple such tensors quickly becomes unfeasible. To reduce the memory footprint of the ERIs, tensor decomposition methods, particularly the resolution-of-the-identity (RI) ansatz, − have been broadly applied in the context of MP2 derivatives. ,,, However, with increasing molecule size, even the third-order RI tensors eventually exceed the available disk space of conventional high performance computing nodes. To overcome this storage limitation, further reduction of the dimensionality of the ERIs is desirable.…”

Accurate Prediction of Nuclear Magnetic Resonance Parameters via the XYG3 Type of Doubly Hybrid Density Functionals

“…The formal scaling of MP2 can be reduced through the scaled-opposite-spin (SOS) MP2 approach by neglecting the SS contribution and by adopting the Laplace transformation technique . Other techniques, such as resolution of identity (RI), the atomic orbital (AO)-based Laplace transformation, the domain-based local pair natural orbital (DLPNO), the Cholesky decomposition (CD), have pushed the applicability of MP2-based NMR calculations up to ∼100 atoms and more than 1000 basis functions recently.…”