Abstract
Accurate calculation of electric field gradients (EFGs) in molecular crystals, despite big advances in ab initio techniques, is still a challenge. Here, we present a new approach to calculate the EFGs in molecular crystals by employing the many-body expansion (MBE) technique with electrostatic embedding. This allows for (i) a reduction in the computational cost or an alternative increase in the level of theory (we use the MP2/6-311++G) and (ii) the ability to monitor EFG convergence by progressively adding more surrounding molecules and/or adding higher many-body interactions. We focus on the 14N EFG and study four (model) compounds in more detail: solid nitrogen, ethylamine, methylamine, and ammonia. Solid nitrogen is rather insensitive to neighbors; for ethylamine and methylamine, the 3-body interactions are found sufficient for a converged EFG, whereas for ammonia, even the inclusion of 5-body interactions is insufficient although convergence is anticipated. We then validate our technique by comparing the experimental and ab initio14N EFGs for 116 organic compounds utilizing their known crystal structures and published EFG. Overall, we find a very good agreement, with a small EFG rms error, which is probably due to other sources, rather than the MBE approximation.
Highlights
An Electric Field Gradient (EFG) in molecules is of significant interest in physical chemistry since an EFG at the position of nuclei is very sensitive to the local charge density and can be used to study molecular structures and monitor structural changes
Experimental 14N EFG values are accessible for free molecules using microwave spectroscopy and for solids, using nuclear quadrupole resonance (NQR), nuclear quadrupole double resonance (NQDR), and solid-state NMR
Common to all four samples is the presence of a single crystallographically distinct nitrogen site so that we can monitor a single EFG tensor per crystal structure. We limit this analysis to the Vzz component which is calculated in all cases in a fixed frame coinciding with the EFG principal axis system (PAS) of the converged Vμν for a particular substance
Summary
An Electric Field Gradient (EFG) in molecules is of significant interest in physical chemistry since an EFG at the position of nuclei is very sensitive to the local charge density and can be used to study molecular structures and monitor structural changes. The EFGs are in many cases straightforward to determine from experimental data; interpretation of these values requires more effort and is seldom possible without the aid of some theoretical calculations. In the past, this was mainly achieved with the semi-empirical Townes–Dailey theory, while nowadays, the highly successful density functional theory (DFT) is mostly used. This was mainly achieved with the semi-empirical Townes–Dailey theory, while nowadays, the highly successful density functional theory (DFT) is mostly used This is true for free molecules as has been demonstrated by many DFT studies showing excellent agreements between calculated and experimental EFGs.. For EFGs at the nitrogen site, he found an impressively small root-mean-square (rms) error of 30 kHz, representing an overall error of just 1.3%
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