Conformations in Solution and in Solid-State Polymorphs: Correlating Experimental and Calculated Nuclear Magnetic Resonance Chemical Shifts for Tolfenamic Acid

Abstract

A new approach for quantitively assessing putative crystal structures with applications in crystal structure prediction (CSP) is introduced that is based upon experimental solution- and magic-angle spinning (MAS) solid-state NMR data and density functional theory (DFT) calculation. For the specific case of tolfenamic acid (TFA), we consider experimental solution-state NMR for a range of solvents, experimental MAS NMR of polymorphs I and II, and DFT calculations for four polymorphs. The change in NMR chemical shift observed in passing from the solution state to the solid state (Δδ_Experimental) is calculated as the difference between ¹H and ¹³C experimental solid-state chemical shifts for each polymorphic form (δ_{Solid expt}) and the corresponding solution-state NMR chemical shifts (δ_{Solution expt}). Separately, we use the gauge-included projector augmented wave (GIPAW) method to calculate the NMR chemical shifts for each form (δ_{Solid calc}) and for TFA in solution (δ_{Solution calc}) using the dynamic 3D solution conformational ensemble determined from NMR spectroscopy. The calculated change in passing from the solution state to the solid state (Δδ_Calculated) is then calculated as the difference of δ_{Solid calc} and δ_{Solution calc}. Regression analysis for Δδ_Calculated against Δδ_Experimental followed by a <i>t</i>-test for statistical significance provides a robust quantitative assessment. We show that this assessment clearly identifies the correct polymorph, <i>i.e.,</i> when comparing Δδ_Experimental based on the experimental MAS NMR chemical shifts of form I or II with Δδ_Calculated based on calculated chemical shifts for polymorphs I, II, III, and IV. Complementarity to the established approach of comparing δ_{Solid expt} to δ_{Solid calc} is explored. We further show that our approach is applicable if there are no solid-state crystal structure data. Specifically, δ_{Solid calc} in Δδ_Calculated is replaced by the chemical shift for an isolated molecule with a specific conformation. Sampling conformations at specific 15° angle values and comparing them against experimental ¹³C chemical shift data for forms I and II identifies matching narrow ranges of conformations, successfully predicting the conformation of tolfenamic acid in each form. This methodology can therefore be used in crystal structure prediction to both reduce the initial conformational search space and also quantitatively assess subsequent putative structures to reliably and unambiguously identify the correct structure.