Polymorph Identification for Flexible Molecules: Linear Regression Analysis of Experimental and Calculated Solution- and Solid-State NMR Data

Abstract

The Δδ regression approach of Blade et al. [ J. Phys. Chem. A 2020, 124(43), 8959-8977] for accurately discriminating between solid forms using a combination of experimental solution- and solid-state NMR data with density functional theory (DFT) calculation is here extended to molecules with multiple conformational degrees of freedom, using furosemide polymorphs as an exemplar. As before, the differences in measured ¹H and ¹³C chemical shifts between solution-state NMR and solid-state magic-angle spinning (MAS) NMR (Δδ_experimental) are compared to those determined by gauge-including projector augmented wave (GIPAW) calculations (Δδ_calculated) by regression analysis and a t-test, allowing the correct furosemide polymorph to be precisely identified. Monte Carlo random sampling is used to calculate solution-state NMR chemical shifts, reducing computation times by avoiding the need to systematically sample the multidimensional conformational landscape that furosemide occupies in solution. The solvent conditions should be chosen to match the molecule's charge state between the solution and solid states. The Δδ regression approach indicates whether or not correlations between Δδ_experimental and Δδ_calculated are statistically significant; the approach is differently sensitive to the popular root mean squared error (RMSE) method, being shown to exhibit a much greater dynamic range. An alternative method for estimating solution-state NMR chemical shifts by approximating the measured solution-state dynamic 3D behavior with an ensemble of 54 furosemide crystal structures (polymorphs and cocrystals) from the Cambridge Structural Database (CSD) was also successful in this case, suggesting new avenues for this method that may overcome its current dependency on the prior determination of solution dynamic 3D structures.

Figure 1

(Top) Two-dimensional (2D) structure of furosemide. (Middle) A conformation of furosemide showing atom nomenclature and torsional degrees of freedom. (Bottom) Torsion definitions are (1) O1–C4–C5–N1, (2) C4–C5–N1–C6, (3) C5–N1–C6–C11, (4) C8–C9–S1–N2, (5) C6–C11–C12–O3, and (6) C9–S1–N2–H9. Atoms are colored by element (carbon gray), and nonpolar hydrogens have been omitted for clarity.

Figure 2

Solution dynamic 3D structure of furosemide in a conformational ensemble representation. (Top) All of the conformers (i.e., the mean positions of all of the modes permuted together; bright conformations) are overlaid together on the central aromatic ring as an ensemble of conformations representing the Gaussian libration about those mean positions (faded conformations). The Gaussian probability distributions determined for each torsion that underlie this representation are shown in Figure 3. (Middle, Bottom) Two different single conformation conformers from the dynamic solution 3D structure; the values for their individual torsions are shown in Figure 3 by dotted (middle) and dashed lines (bottom). Atoms are colored by element (carbon gray), and nonpolar hydrogens have been omitted for clarity.

Figure 3

Solution dynamic 3D structure of furosemide in a torsion-population representation. For each torsion, the changing population with torsion angle (x-axis) is given relative to its maximum occupancy (y-axis). Each torsion has a dynamic behavior that is described as one or more modes that each have a Gaussian libration about their central (mean) values. The torsion values of the conformers shown in Figure 2 are indicated with dotted and dashed lines (middle and bottom, respectively). All conformational parameter values of the solution dynamic 3D structure are given in Table S3.

Figure 4

Graph of Δδ_calculated¹³C data at 100 K for Forms I, II, and III against Δδ_experimental for Form I Molecules A and B of furosemide (plotted separately), showing that the approach clearly discriminates Form I molecules from all other forms and each other (Molecule A Δδ_calculated against Δδ_experimentalr² = 0.44, p = 0.0131; Molecule B r² = 0.45, p = 0.0115). See Tables 3 and 4 for data.

Figure 5

Graph of Δδ_calculated¹H data at 100 K for Forms I, II, and III against Δδ_experimental for Form I Molecules A and B of furosemide (plotted separately), showing that the approach clearly discriminates Form I molecules from all other forms and each other (Molecule A Δδ_calculated against Δδ_experimentalr² = 0.82, p = 0.0066; Molecule B r² = 0.57, p = 0.0406). See Tables 3 and 4 for data.

Figure 6

Histograms of torsion values from all crystal structures in the CSD containing neutral furosemide (also comprising neutral solvates and cocrystals, bars) compared to the solution dynamic 3D structure (lines). The histograms comprise data from 45 single-crystal diffraction structures, constituting 108 conformations (see the text and Table S30). For each torsion (see Figure 1 for definitions), the changing population with torsion angle (x-axis) is given relative to its maximum occupancy (y-axis).