Accurate Hydrogen Positions in Organic Crystals: Assessing a Quantum-Chemical Aide

Abstract

Organic molecules crystallize in manifold structures. The last few decades have seen the rise of high-resolution X-ray diffraction techniques that make the structures of even the most complex crystals easily accessible. Still, an intrinsic challenge lies in assigning hydrogen atoms’ positions from X-ray experiments alone. Quantum chemistry plays a fruitful, complementary role here, and so ab initio optimization techniques for organic crystals are on the rise as well. In this context, we review and evaluate a popular ab initio strategy based on plane-wave density-functional computations, namely, selectively relaxing H positions in an otherwise fixed cell. Our data show that such-optimized C–H, N–H, O–H, and B–H bond lengths coincide well with results from neutron diffractionthe experimental technique that sets the “gold standard” for H positions in molecular crystals but which is far less easily available. We have thus justified the use of a quantum-chemical aide with a broad variety of possible applications.

Single‐Crystal X‐Ray Diffraction, Isolated‐Molecule and Cluster Electronic Structure Calculations, and Scanning Electron Microscopy in an Organic solid: Models for Intramolecular Motion in 4,4′‐Dimethoxybiphenyl

“…[47,48] For example, the X-ray positioning of the H atoms in 4,4'-dimethoxybiphenyl gives the methyl C-H bonds as 98.1 pm whereas the calculations give these bond lengths as 107.6, 108.0, and 108.1 pm, a difference of approximately 10 pm, consistent with previous studies. [47,48] The X-ray positions the ring H atoms such that all the ring C-H bonds are 94.9 pm. The calculated distances vary between 106.7 and 107.0 pm so here the difference is approximately 12 pm.…”

Synthesis, Crystal Structure, Polymorphism, and Magnetism of Eu(CN3H4)2 and First Evidence of EuC(NH)3

“…Then, we selectively optimized the hydrogen positions, leaving lattice vectors and all other positions fixed. The resulting hydrogen positions are expected to be qualitatively comparable to those from neutron-diffraction experiments [46].…”

“…This compound is isostructural to SrC(NH)3 [30] and YbC(NH)3 [31] and crystallizes in the hexagonal space group P63/m with a = 5.1634(7) Å, c = 7.1993(9) Å, V = 166.23(4) Å 3 , and Z = 2 ( Figure 8; Table 2). As for YbC(NH)3, DFT calculations were used to locate the hydrogen atoms, a method validated in reference [46] (Table 4). So far, EuC(NH)3 was only obtained together with an unidentified side phase.…”

Monitoring a simple hydrolysis process in an organic solid by observing methyl group rotation

“…Various sizes of the clusters allow us to see the convergent behavior of the methyl group rotational barrier as the cluster size increases. Since the positions of the H atoms are not accurately determined by the Xray diffraction experiments [17,18], their positions were optimized at the B3LYP/6-31G(d) level while fixing all the other atoms (C and O) in the clusters at their X-ray determined positions. The rotational barrier of the methyl group on the central molecule of the cluster was calculated.…”

“…The H-H distances between the three H atoms in a CH 3 group is taken to be r intraCH3 = 0.170 nm. This is determined by the electronic structure calculations in the clusters presented here since X-ray diffraction experiments give C-H bond lengths that are approximately 0.01 nm too short [17,18], resulting in H-H distances in a methyl group that are also too short (typically 0.16 nm). Since A intraCH3 ∝ r -6 , a 1/16 = 6.3% error in r results in a 38% error in A intraCH3 .…”