NMR chemical shift computations at second-order Møller–Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals

Abstract

We report on a formulation and implementation of a scheme to compute nuclear magnetic resonance (NMR) shieldings at second-order Møller–Plesset (MP2) perturbation theory using gauge-including atomic orbitals (GIAOs) to ensure gauge-origin independence and Cholesky decomposition (CD) to handle unperturbed and perturbed two-electron integrals. We investigate the accuracy of the CD for the derivatives of the two-electron integrals with respect to an external magnetic field and for the computed NMR shieldings, before we illustrate the applicability of our CD-based GIAO-MP2 scheme in calculations involving up to about 100 atoms and more than 1000 basis functions.

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

“…composed of a standard Gaussian χ µ centered at K µ and a complex phase factor (in which k = 1 2 B × (K µ − G), B is the magnetic field and G is the gauge origin) can be approximated by the CD 12,[21][22][23][27][28][29][30][31][32][33][34][35][36] as…”

“…31 Besides developments that enable the efficient calculation of single-point energies, developments also include the calculation of properties via the implementation of CD for nuclear gradients [32][33][34][35] at various levels of theory as well as CD for MP2 nuclear magnetic resonance shieldings. 36 Thus, using CD, studies for systems with more than thousand basis functions are these days readily available. The situation is still somewhat different when turning to quantum-chemical predictions for molecules in finite magnetic fields.…”

Cholesky decomposition of two-electron integrals in quantum-chemical calculations with perturbative or finite magnetic fields using gauge-including atomic orbitals

“…Since then many quantum-chemical schemes have been combined with CD; to be mentioned are implementations using CD for Hartree-Fock (HF) calculations, 3,4 second-order Møller-Plesset (MP2) perturbation theory, 3,5 complete-active space self-consistent-field (CASSCF) treatments, 6,7 multiconfigurational second-order perturbation theory (CASPT2), 8 and coupled-cluster (CC) and equation-of-motion coupled-cluster (EOM-CC) approaches. 9 CD has not only been used in energy calculations and corresponding implementations for geometrical gradients [10][11][12] but also for the computation of NMR shieldings 13,14 together with the use of gauge-including atomic orbitals (GIAOs). [15][16][17][18][19] Furthermore, the efficiency of CD for finite magnetic-field quantum-chemical calculations has been demonstrated.…”

“…In the initial CD implementation for finite magnetic fields, 20 symmetries of the Cholesky vectors were not exploited. For the treatment of derivative integrals in case of perturbative magnetic fields, 13 antisymmetry of the perturbed Cholesky vectors was deduced and exploited in the actual implementation. However, a more rigorous discussion seems to be warranted together with an exploration of further possible savings in the corresponding CD procedure for the magnetic derivative two-electron integrals.…”

A black-box, general purpose quadratic self-consistent field code with and without Cholesky Decomposition of the two-electron integrals

“…To achieve some computational efficiency, we offer instead an implementation that can either proceed in a traditional fashion, reading pre-computed two-electron integrals from disk, or use their Cholesky decomposition [31][32][33][34][35][36][37] (CD). The latter possibility comes as a part of a long-term goal to deploy the CD machinery for subsequent post-HF calculations [30] that has been actively pursued by several developers of the CFOUR suite of programs and that has recently been proposed for complete active space-SCF calculations [38] and for the calculation of NMR chemical shielding tensors at second-order Møller-Plesset perturbation theory (MP2) using gauge-including atomic orbitals [39]. On the other hand, having a robust, almost black box SCF implementation is particularly attractive for the users of CFOUR that deal with open-shell systems, where the unrestricted (UHF) and high-spin restricted-open-shell HF (ROHF) [5] SCF equations can be particularly hard to converge.…”