Do Models beyond Hybrid Density Functionals Increase the Agreement with Experiment for Predicted NMR Chemical Shifts or Electric Field Gradient Tensors in Organic Solids?

Abstract

Ab initio predictions of chemical shifts and electric field gradient (EFG) tensor components are frequently used to help interpret solid-state nuclear magnetic resonance (NMR) experiments. Typically, these predictions employ density functional theory (DFT) with generalized gradient approximation (GGA) functionals, though hybrid functionals have been shown to improve accuracy relative to experiment. Here, the performance of a dozen models beyond the GGA approximation are examined for the prediction of solid-state NMR observables, including meta-GGA, hybrid, and double-hybrid density functionals and second-order Møller–Plesset perturbation theory (MP2). These models are tested on organic molecular crystal data sets containing 169 experimental 13C and 15N chemical shifts and 114 17O and 14N EFG tensor components. To make these calculations affordable, gauge-including projector augmented wave (GIPAW) Perdew–Burke–Ernzerhof (PBE) calculations with periodic boundary conditions are combined with a local intramolecular correction computed at the higher level of theory. Within the context of typical NMR property calculations performed on a static, DFT-optimized crystal structure, the benchmarking finds that the double-hybrid DFT functionals produce errors versus experiment that are no smaller than those of hybrid functionals in the best cases, and they can be larger. MP2 errors versus experiment are even bigger. Overall, no practical advantages are found for using any of the tested double-hybrid functionals or MP2 to predict experimental solid-state NMR chemical shifts and EFG tensor components for routine organic crystals, especially given the higher computational cost of those methods. This finding likely reflects error cancellation benefiting the hybrid functionals. Improving the accuracy of the predicted chemical shifts and EFG tensors relative to experiment would probably require more robust treatments of the crystal structures, their dynamics, and other factors.

Computation of CCSD(T)-Quality NMR Chemical Shifts via Δ-Machine Learning from DFT

“…The last major error source is conformational flexibility, which is considered, e.g., by the CREST (conformer–rotamer ensemble sampling tool) approach in combination with CENSO (command-line energetic sorting of conformer–rotamer ensembles) that can be used to calculate ensemble-based NMR spectra . In addition, it has been suggested that other dynamic effects are of great importance especially for solid state NMR shift predictions, where their contribution to the final value can be larger than the contribution of the electron correlation . In these cases, (path integral) molecular dynamics simulations can be used to treat the dynamic effects.…”

Assessment of Approximations to the Embedding Potential in Frozen-Density Embedding Theory for the Calculation of Electric Field Gradients

“…The three components on the diagonal, by convention, are referred to as | V x x | ≤ | V y y | ≤ | V z z | A number of metrics can be used to evaluate the quality of an EFG calculation, including consideration of all three independent components of the EFG tensor. Experiments related to the EFG are only sensitive to V zz and, as has been done in other recent reports, , we will only consider V zz in our analyses and not the other, smaller elements.…”

“…The Sternheimer approximation is computationally advantageous and has been used effectively in simulations of EFG dynamics, − but its usefulness is limited due to the dependence of the empirical coefficients used in relation on the specific system and its geometry. − Additionally, its validity in the condensed phase has been questioned, and the addition of higher-order terms in the electronic response has been proposed. , The need for explicit quantum mechanical treatment of the electrons in the molecule is thus commonly recognized in the community; therefore, several non-embedding quantum mechanical approaches have been used by various researchers. One method models only the nearest atoms in the system and neglects the environment completely, another targets only the shift in the largest diagonal component of the EFG relative to a reference calculation, and other approaches are based on the error compensation ansatz. , In this work, we turn to the explicit quantum-mechanical treatment of the embedded species and embedding methods based on frozen-density embedding theory (FDET), in which the embedding potential (multiplicative embedding operator) is given as a sum of the classical electrostatic component and the nonclassical part representing the quantum confinement by means of a universal bifunctional. − …”

Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials

“…NMR crystallography can frequently solve the experimental crystal structure even when that structure is not the most stable one predicted by the CSP. Unsurprisingly, models which predict chemical shis more accurately [263][264][265][266] enhance the discrimination between correct and incorrect structural assignments in NMR crystallography. 267 Further synergies between experiment and computation are also possible in NMR crystallography.…”