Improving Predicted Nuclear Magnetic Resonance Chemical Shifts Using the Quasi-Harmonic Approximation

Abstract

Ab initio nuclear magnetic resonance chemical shift prediction plays an important role in the determination or validation of crystal structures. The ability to predict chemical shifts more accurately can translate to increased confidence in the resulting chemical shift or structural assignments. Standard electronic structure predictions for molecular crystal structures neglect thermal expansion, which can lead to an appreciable underestimation of the molar volumes. This study examines this volume error and its impact on 68 13C- and 28 15N-predicted chemical shifts taken from 20 molecular crystals. It assesses the ability to recover more realistic room-temperature crystal structures using the quasi-harmonic approximation and how refining the structures impacts the chemical shifts. Several pharmaceutical molecular crystals are also examined in more detail. On the whole, accounting for quasi-harmonic expansion changes the 13C and 15N chemical shifts by 0.5 and 1.0 ppm on average. This, in turn, reduces the root-mean-square errors relative to experiment by 0.3 ppm for 13C and 0.7 ppm for 15N. Although the statistical impacts are modest, changes in individual chemical shifts can reach multiple ppm. Accounting for thermal expansion in molecular crystal chemical shift prediction may not be needed routinely, but the systematic trend toward improved accuracy with the experiment could be useful in cases where discrimination between structural candidates is challenging, as in the pharmaceutical theophylline.

Overcoming the difficulties of predicting conformational polymorph energetics in molecular crystals via correlated wavefunction methods

“…The molar volume of typical organic crystals expands several percent upon heating from 0 K to room temperature. 91 This expansion alters the lattice energy and introduces anharmonicity into the phonons. Accounting for it is important for quantitatively comparing thermochemistry, 82,92-94 mechanical properties, 93 and spectroscopic observables 91,95 between theory and experiment.…”

“…96 The quasi-harmonic approximation is oen successfully used to approximate the volumedependent contributions to the phonons and lattice energies. 13,23,28,82,[91][92][93][94][97][98][99][100] Nevertheless, quasi-harmonic calculations remain considerably more expensive than purely harmonic calculations that neglect thermal expansion.…”

Accurate and Efficient Prediction of NMR Parameters of Condensed-Phase Systems with the Generalized Energy-Based Fragmentation Method

“…Recently, the fragment-based many-body expansion method (truncated at the two-body level) with embedding has been applied to compute the chemical shifts ( 1 H, 13 C, 15 N, and 17 O) of molecular crystals containing small molecules. − Good results have been obtained with various density functionals and Gaussian basis sets. Nevertheless, it is unclear whether the same protocol without higher order (3- or 4-body) terms is accurate enough for solution systems, since energy calculations of large water clusters showed that 3- or 4-body interactions are still nontrivial …”

Polarizable continuum models provide an effective electrostatic embedding model for fragment‐based chemical shift prediction in challenging systems

“…36,37 Fragment methods have also proved highly effective in molecular crystals. [38][39][40][41][42][43][44][45] Many of the fragment approaches can be unified under a common framework of a generalized many-body expansion, 46,47 with key distinctions between methods involving whether the fragments overlap or not, the level of interactions between fragments considered explicitly (e.g. are properties computed only on individual fragments or also with pairwise or higher-order interactions?…”