Vibrational averaging of the chemical shift in crystalline α‐glycine

Abstract

Averaging of the chemical shift over the molecular motion improves the simulated data and provides additional information about the temperature dependence and system dynamics. However, crystal modeling is difficult due to the limited precision of the plane-wave density functional theory (DFT) methods and approximate vibrational schemes. On the glycine example, we investigate how the averaging can be achieved within the periodic boundary conditions at the DFT level. The nuclear motion is modeled with the vibrational configuration interaction, with other simplified quantum anharmonic schemes, and the classical Born-Oppenheimer molecular dynamics (BOMD). The results confirm a large vibrational contribution to the isotropic shielding values. Both the first and second derivatives of the shielding were found important for the quantum averaging. The first derivatives influence the shielding mostly due to the anharmonic character of the CH and NH stretching modes, whereas second derivatives produce most vibrational corrections associated with the lower-frequency vibrational modes. Temperature excitations of the lowest-frequency vibrational states and the expansion of the crystal cell both determine the temperature dependence of nuclear magnetic resonance parameters. The vibrational quantum approach as well as classical BOMD schemes provided temperature dependencies of the chemical shifts that are consistent with the previous experimental data.

A molecular dynamics study of the effects of fast molecular motions on solid-state NMR parameters

“…It has been shown that dispersion correction did not significantly affect the calculated shieldings of solid glycine when the lattice parameters were fixed during geometry optimization in ref. 19 , in which the temperature dependence of the chemical shifts was studied. The center of mass was fixed to ensure that the random initial velocities did not result in translational motion.…”

“…[18][19] This method is computationally demanding and many approximations have to be adopted in practical computations, in particular for the treatment of the variation of the shielding with vibrational coordinates. However, the results confirmed an important vibrational contribution (up to almost 10 ppm for nitrogen atom) to isotropic chemical shifts, which was in qualitative agreement with the results of DFT-MD.…”

Exploring Systematic Discrepancies in DFT Calculations of Chlorine Nuclear Quadrupole Couplings

“…It was shown previously that a dispersion correction did not affect the calculated magnetic shielding values of solid glycine significantly when the lattice parameters were fixed during geometry optimization. 63 The centre of mass in the simulation cell was fixed to ensure into 16 beads (which was found to be satisfactory in previous studies of molecular solids at 300 K [64][65] ) and total simulation time of 10 ps were used.…”

Crystallographic and Dynamic Aspects of Solid‐State NMR Calibration Compounds: Towards ab Initio NMR Crystallography

“…The accuracy of the force field used for the MD simulations was shown to be crucial for the results. By publishing more and more fitted reference shieldings, research groups in the field of NMR crystallography can collectively build up increasingly more accurate and independent estimates of a universal reference shielding, σ ref . This ab initio NMR crystallography approach, together with state‐of‐the‐art experimental NMR spectroscopy, will be valuable for the elucidation of the structural and dynamic properties of challenging solid‐state phases, even if no single crystals are available.…”

“…In reality, all molecular crystals undergo motion and lattice expansion due to the effect of temperature, and averaging over thermally occupied states is of significance to reduce the discrepancy between ss‐NMR theoretical calculations and experiments, even for non‐plastic phases. These phenomena have been studied in combination with, for example, vibrational averaging on a series of generated configurations at zero and finite temperatures, classical molecular dynamics (MD) simulations and ab initio MD simulations (including Born–Oppenheimer MD and path integral MD) …”