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

Abstract

We employ our recently introduced tensor-hypercontracted (THC) second-order Møller–Plesset perturbation theory (MP2) method [Bangerter, F. H., Glasbrenner, M., Ochsenfeld, C. J. Chem. Theory Comput. 2021 , 17 , 211–221] for the computation of hyperfine coupling constants (HFCCs). The implementation leverages the tensor structure of the THC factorized electron repulsion integrals for an efficient formation of the integral-based intermediates. The computational complexity of the most expensive and formally quintic scaling exchange-like contribution is reduced to effectively subquadratic, by making use of the intrinsic, exponentially decaying coupling between tensor indices through screening based on natural blocking. Overall, this yields an effective subquadratic scaling with a low prefactor for the presented THC-based AO-MP2 method for the computation of isotropic HFCCs on DNA fragments with up to 500 atoms and 5000 basis functions. Furthermore, the implementation achieves considerable speedups with up to a factor of roughly 600–1000 compared to previous implementations [Vogler, S., Ludwig, M., Maurer, M., Ochsenfeld, C. J. Chem. Phys. 2017 , 147 , 024101] for medium-sized organic radicals, while also significantly reducing storage requirements.

Analytic Gradients for Density Fitting MP2 Using Natural Auxiliary Functions

“…The theory and implementation of MP2 analytic gradients and second derivatives are also well established. Analytic derivatives for conventional MP2 have been available for a long time. − Of the above reduced-cost approaches, analytic gradients have been implemented for DF-MP2, − CD-MP2, THC-MP2, , the dual-basis MP2, AO-MP2, divide and conquer MP2, and for various local MP2 methods. − Analytic gradients are also available for spin-scaled and explicitly correlated MP2 even in conjunction with the considered cost-reduction techniques. − …”

Dissecting the Molecular Origin of g-Tensor Heterogeneity and Strain in Nitroxide Radicals in Water: Electron Paramagnetic Resonance Experiment versus Theory

“…The field of theoretical spectroscopy has been very active in recent years (for reviews, see refs –) The challenges under investigation are manifold and include the explicit treatment of solvent effects for systems of nontrivial size, ,− the development and validation of improved density functionals − and correlated ab initio methods, ,,− the treatment of relativistic- , and vibronic- ,, effects as well as conceptual and algorithmic advances ,,− ,,,− to name only a few. The characterizing parameters of a nitroxide’s EPR spectrum, namely, the g - and A -tensors, are accessible at different levels of theory .…”