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Refining Crystal Structures with Quadrupolar NMR and Dispersion-Corrected Density Functional Theory Sean T. Holmes, and Robert W. Schurko J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b12314 • Publication Date (Web): 20 Dec 2017 Downloaded from http://pubs.acs.org on January 3, 2018

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The Journal of Physical Chemistry

Refining Crystal Structures with Quadrupolar NMR and Dispersion-Corrected Density Functional Theory

Sean T. Holmes and Robert W. Schurko* Department of Chemistry and Biochemistry, University of Windsor, Windsor, ON, Canada N9B 3P4 *Author to whom correspondence should be addressed. E-mail: [email protected] Tel: (519) 253-3000 x3548 - Fax: (519) 973-7098

1 ACS Paragon Plus Environment

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ABSTRACT Nuclear electric field gradient (EFG) tensors obtained from solid-state NMR spectroscopy are highly responsive to variations in structural features. The orientations and principal components of EFG tensors show great variation between different molecular structures; hence, extraction of EFG tensor parameters, either experimentally or computationally, provides a powerful means for structure determination and refinement. Here, dispersioncorrected plane-wave density functional theory (DFT) is used to refine atomic coordinates in organic crystals determined initially through single-crystal X-ray diffraction (XRD) or neutron diffraction methods. To accomplish this, an empirical parameterization of a two-body dispersion force field is illustrated, in which comparisons of experimental and calculated 14N, 17O, and 35Cl EFG tensor parameters are used to assess the quality of energy-minimized structures. The parameterization is based on a training set of 17 organic solids. The analysis is applied subsequently to the structural refinements of structural models from over 60 different materials. For the prediction of 35Cl EFG tensor parameters in particular, the optimization protocols described herein lead to a substantial improvement in agreement with experiment relative to structures obtained by XRD methods or by refinement with plane-wave DFT without the inclusion of the force field. The results further demonstrate that crystal structures with atomic coordinates refined with the present methods are able to pinpoint the positions of hydrogen atoms participating in H···Cl- hydrogen bonding with a higher degree of precision than is possible through neutron diffraction. This methodology, which is facile to implement within most DFT software packages, should prove to be very useful for future structural refinements using NMR crystallographic methods.


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INTRODUCTION Solid-state nuclear magnetic resonance (SSNMR) spectroscopy is an extremely powerful technique for studying molecular-level structure and dynamics.1-3 The determination of threedimensional molecular structure is a central concern for crystallographers, solid-state chemists, and crystal engineers due to connections between molecular-level properties and bulk physicochemical properties.4 Relationships between molecular structures and NMR observables can be elucidated through first-principles calculations, typically performed in the framework of density functional theory (DFT).5-10 The interdisciplinary field of NMR crystallography combines SSNMR spectroscopy, X-ray diffraction (XRD) methods, and computational approaches, to provide unrivaled insight into molecular-level structures; these insights extend to the enhancement of structures solved by refinement of XRD powder patterns, or even to the solution of crystal structures independent of XRD data. Successes in this field include the ability to measure distances between spins,11-13 characterize disorder in solids,14-18 detect weak intermolecular interactions,19 study biologically-relevant materials that are often unsuited for other types of analyses,20-24 and reveal distortions in molecular symmetry that are not observed by diffraction methods alone.25 Several reports have illustrated that the precision of atomic positions obtained through SSNMR can rival that obtained through neutron diffraction.26-28 The majority of NMR crystallographic refinements have utilized measurements of isotropic chemical shifts or chemical shift tensors of spin-½ nuclides.29-34 There are numerous impediments associated with refining crystal structures using chemical shifts, including difficulties in measuring 1H chemical shifts (due to strong homonuclear dipolar coupling), complications in 13C or 15N SSNMR spectra due to overlapping peaks (especially in larger molecules), and the fact that much of the three-dimensional structural information revealed by



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the chemical shift anisotropy is only obtainable from measurements of the principal elements of the chemical shift tensors (often, this requires lengthy two-dimensional NMR experiments). SSNMR of quadrupolar nuclides (I > ½) is particularly useful for probing molecular-level structure, since nuclear electric field gradient (EFG) tensors are responsive to even the smallest variation in structural features.35-40 For the study of organic solids, two of the most ubiquitous quadrupolar NMR nuclides are 14N41-50 and 17O,47, 51-60 which both have been used to study molecular-level structure and dynamics in solids.

14

N (I = 1) is a quadrupolar nucleus with a

high natural abundance (99.63%) and a low magnetogyric ratio [γ(14N) = 1.934 × 107 rad T-1 s-1]. Ultra-wideline 14N SSNMR patterns are inhomogeneously broadened by the first-order quadrupolar interaction, and can be up to several MHz in breadth, making their acquisition challenging; however, signal enhancing pulse sequences and the increasing availability of highfield NMR spectrometers have made such measurements tenable.61, 62 5

17

O SSNMR spectra (I =

/2) are also very challenging to obtain due to the low natural abundance (0.037%) and the low

magnetogyric ratio [γ(17O) = -3.628 × 107 rad T-1 s-1] of 17O the nucleus, and the possibility of substantial inhomogeneous line broadening that is complicated by the presence of both the second-order quadrupolar and chemical shift anisotropy interactions.63 Analysis of 17O sites in organic solids through SSNMR spectroscopy is becoming more tenable because of advances in sensitivity enhancing techniques (including dynamic nuclear polarization)13 and new synthetic pathways for isotopic labeling.64 There also exists a substantial body of literature dealing with nuclear quadrupole resonance (NQR) spectroscopy studies of 17O sites in organic solids.65-67 When solids contain cations or anions, which are frequently quadrupolar nuclides, analysis of the NMR quadrupolar powder patterns can reveal significant structural information because of the key role that these sites play in crystal packing.36, 37 Chloride anions in


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hydrochloride (HCl) and metal chloride salts act as hydrogen bond acceptors, forming both charge-assisted hydrogen bonds and weaker hydrogen bonds with neutral hydrogen-bond donating moieties.68 The variability in local chloride anion environments makes 35Cl (I = 3/2) SSNMR spectroscopy a powerful fingerprinting tool that is highly sensitive to solvation and polymorphism, as has been illustrated in 35Cl SSNMR analyses of chloride-anion-containing materials.69-81 These observations are particularly relevant for the characterization of active pharmaceutical ingredients (APIs), of which, greater than 50% of solid-state formulations are prepared as HCl salts.82 Prior work has demonstrated difficulties associated with first-principles predictions of 35

Cl EFG tensors of chloride anions,69-71, 77-80, 83 limiting the utility of this sensitive NMR probe

for resolving structural features of solids. It is not uncommon for calculated values of the individual principal elements of 35Cl EFG tensors to overestimate experimental values by several MHz when calculations are performed on structures obtained from diffraction methods, or DFT refinements of XRD-derived structures. Ab initio molecular dynamics study has illustrated that fast molecular dynamics (fs – ps time scales) do not have a large enough impact on calculated 35

Cl EFG tensor parameters to be the leading cause of this error.83, 84 Calculated 35Cl EFG

tensors differ substantially between structures refined with different model chemistries,85 suggesting that the source of the discrepancy between experiment and theory results from inadequate structures in the computational models. The positions of hydrogen atoms, which are essential components of the structures of HCl salts due to H···Cl- hydrogen bonding, are poorly resolved by single-crystal (sc)XRD analyses. It is therefore likely that the proper positioning of hydrogen atoms is the most significant factor for calculating 35Cl EFG tensors.



In ab initio calculations on models representing solids, dispersion, electrostatic, and exchange-correlation (xc) interactions control crystal packing.86 Calculations of physical quantities that are highly dependent upon structural parameters are affected strongly by the manner in which these interactions are treated.87-89 The dispersion interaction is often introduced into calculations as a parameterized force field that depends explicitly upon the set of atomic coordinates defining the positions of the atoms in the solid. Various quantities, including cohesive energies, lattice constants, bulk moduli, lattice vibrations, etc., have been employed to parameterize, or to benchmark, the performance of dispersion force fields to aid in their prediction in organic crystals.87-89 Calculations of nuclear EFG tensors are also suitable for parameterizing the dispersion force field, because these quantities are strongly responsive to structural variation, including both nuclear positions and electronic structure.85 One advantage to this approach is that anisotropic NMR interactions, such as nuclear EFG tensors, require proper modeling of three-dimensional structure to obtain agreement between experiment and theory. An empirically parameterized force field model based on quadrupolar NMR parameters could correct errors in both the treatments of dispersion and xc interactions, with wide-ranging applicability to the field of NMR crystallography. This study assesses the quality of crystal structure refinements through calculations of 14

N, 17O, and 35Cl EFG tensor parameters in neutral organic molecules and salts in the solid state.

Calculations are performed within the framework of plane-wave DFT, which inherently accounts for the long-range periodic order of crystal structures. Consistent with previous work on calculations of 35Cl EFG tensors in organic solids,69 we illustrate that conventional plane-wave DFT approaches alone are insufficient to refine atomic coordinates in crystals such that the resulting structures are able to accurately predict nuclear EFG tensor parameters.85 We


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demonstrate that much of the discrepancy between experimental and calculated values arises from uncertainties or errors in the positions of atoms (especially hydrogen atoms) in crystal structures obtained by diffraction methods. Crystal structures are refined by combing DFT with a force field that is parameterized such that the refined structures yield accurate and reliable predictions of EFG tensors in organic solids. This analysis is applied subsequently to a test set consisting of 69 organic solids and 160 NMR-active nuclear sites. The resulting NMR-driven structures are able to model experimental nuclear EFG tensor parameters with a higher degree of accuracy than is obtained by previous calculations on XRD-based structures or structures refined by conventional plane-wave DFT. Finally, calculated 35Cl EFG tensor parameters obtained from calculation on the NMR-driven structures are demonstrated to be superior to those structures obtained by neutron diffraction methods.

COMPUTATIONAL DETAILS Overview of Computational Protocols. All calculations were performed on models of structures determined from previous scXRD or neutron diffraction studies, as indicated. Crystal structures were obtained from the Cambridge Structural Database (CSD) using CCDC ConQuest (version 1.19). For the XRD-derived structures of L-phenylalanine HCl, dibucaine HCl, and alprenolol HCl, several hydrogen atoms were absent from the experimentally-derived crystal structures, and were placed manually to satisfy the valences of the directly bonded atoms. In addition, a disordered oxygen atom in the crystal structure of 4-nitrobenzene was removed. All final sets of xyz atomic coordinates are provided in the Supporting Information (SI). Several strategies for refining the atomic coordinates in the crystal structures were explored, based on plane-wave DFT calculations,5 as implemented in the CASTEP module of



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BIOVIA Materials Studio 2017 R2.90-92 All CASTEP calculations employed the generalized gradient approximation (GGA) revised Perdew-Burke-Ernzerhof (rPBE) xc functional,93 which performs well for the calculation of NMR parameters for 3rd- and 4th-period nuclides in solids.94, 95

Core-valence interactions were modeled with ultrasoft pseudopotentials generated on the

fly.96 Integrals over the Brillouin zone were evaluated using a Monkhorst-Pack grid with a kpoint spacing of 0.07 Å-1, and a plane-wave cutoff energy of 700 eV was used in all calculations. These parameters were chosen on the basis of a series of benchmark calculations on HCl salts (see Additional Methodological Information in the SI). Structural refinements employed the Broyden-Fletcher-Goldfarb-Shanno energy-minimizing scheme.97 Lattice constants remained fixed during the geometry optimizations; however, the computational methodologies outlined in this work could be applied to future analyses in which unit cell volumes vary during geometry optimizations. The thresholds for structural convergence include a maximum change in energy of 5 × 10-6 eV atom-1, a maximum displacement of 5 × 10-4 Å atom-1, and a maximum Cartesian force of 0.01 eV Å-1. Where indicated, dispersion was included in the calculations through the semi-empirical two-body force field model of Grimme,86, 98 or a modification thereof (vide infra). Practical implementation of the force field model in CASTEP is discussed in the SI. Statistical Analysis. The nuclear EFG is characterized by a symmetric, traceless, second-rank tensor with principal elements defined such that |V33| ≥ |V22| ≥ |V11|. The interaction between a nuclear electric quadrupole moment and the EFG with its origin at the nucleus is typically characterized by the quadrupolar coupling constant (CQ) and the asymmetry parameter (ηQ):

= /ℎ ,

η = ( − )/ . 8 ACS Paragon Plus Environment

(1) (2)

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In the above expressions, e is the elementary charge, h is Planck’s constant, and Q is the nuclear quadrupole moment [Q(14N) = 2.044 fm2, Q(17O) = -2.558 fm2, Q(35Cl) = -8.165 fm2].99 Because the sign of CQ cannot be determined from the NMR experiments in most cases, our analysis only compares the absolute values of the experimentally and theoretically derived values. We utilize several metrics to evaluate the agreement between calculated and experimental principal elements of EFG tensors. The first of these metrics is the root mean square relative error (rmsre), which is given by the following expression: , − , 1 = $ . !"# 3 , %

!"#

(3)

Here, , and , are the calculated and experimental principal elements, respectively, of the !"#

EFG tensor of nuclear site m. The summations are over the M nuclear sites (m = 1, 2, . . . M) and the k principal elements of each EFG tensor (k = 1, 2, 3). Errors are reported relative to V33 (rather than Vkk) to avoid overweighting values of V11 near zero. The root mean square error (rmse) is given by the following expression:

1 !"# = &, − , ' . ℎ 3 %

(4)

In addition, we use as a figure of merit the maximum positive deviation [max(+)] and maximum negative deviation [max(-)] between calculation and experiment in the magnitude of the principal elements, multiplied by eQ/h. Because the EFG tensor is traceless ( + + = 0), the

mean error for each dataset is essentially zero.



RESULTS AND DISCUSSION Overview. Herein, we present a DFT-based computational protocol for refining the coordinates of atoms in crystal structures derived from diffraction methods, such that calculations on the resulting structures reproduce experimental nuclear EFG tensor parameters derived from NMR or NQR spectroscopy. Calculations employ a force field that is parameterized empirically to aid in the refinement of atomic coordinates in organic solids: specifically, the parameterization utilizes DFT calculations of 14N, 17O, and 35Cl EFG tensor parameters. The parameterization of the force field employs a training set of organic solids, including urea, formic acid, acetic acid, oxalic acid (two polymorphs), glycine (three polymorphs), glycine HCl, L-alanine HCl, L-valine HCl, L-cysteine HCl·H2O, L-threonine HCl, L-aspartic acid HCl, Lhistidine HCl·H2O, aminoguanidine HCl, and dopamine HCl. The training set contains 34 unique nuclear sites, with 8, 17, and 9 sites for 14N, 17O, and 35Cl nuclides, respectively. The crystal structures and quadrupolar NMR parameters of these solids are summarized in Table S5. Results are presented for structures in which the atomic coordinates determined from XRD are not refined, and for structures refined (i) with the reparameterized version of the force field, (ii) with a previous parameterization of the dispersion force field,86 and (iii) without any force field (i.e., structures are refined using DFT alone). Differences in structural parameters among the energy-minimized structures and XRD-derived structures are discussed. Calculations using the parameterized dispersion-corrected DFT structural refinement protocol are applied to the prediction of 14N, 17O, and 35Cl EFG tensors in a large test set of organic solids (Tables S7 – S10). Together with the materials included in the training set, the complete analysis consists of 86 solid materials and 160 nuclear sites, including, 58, 56, and 46


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sites for 14N, 17O, and 35Cl nuclides, respectively. Finally, calculations of 35Cl EFG tensor parameters in a subset of materials that have also been characterized through neutron diffraction are examined. Parameterization of the Dispersion Force Field using the Training Set. In Grimme’s two-body semi-empirical dispersion model (DFT-D2),86 the isotropic two-body dispersion energy (*+,-# ) is treated as an atomic-pairwise correction to the Kohn-Sham energy (*./ ). The total energy in the DFT-D2 scheme is given by:

*01230 = *./ + *+,-# .

(5)

The dispersion energy is defined by the following unscaled expression: ;

*+,-# = −

6,7 4.0. Figure 1 illustrates the rmsre between experimental and calculated principal elements of EFG tensors, obtained from calculations on structures with atomic coordinates refined for values of d between 2.5 and 10.0. The rmsre for the three sets of nuclides vary significantly over the range of values of 2.5 ≤ d ≤ 10, but vary little for values of d greater than 10. rmsre minima are observed at d = 4.00, 3.50, and 3.25 for 14N, 17O, and 35Cl sites, respectively. Considering all 34 sites together, regardless of the type of nucleus, a global minimum is observed at d = 3.25. Structures resulting from refinements employing the rPBE-D2 model chemistry, with the damping parameter set to a value of 3.25, are denoted rPBE-D2* structures. Structures obtained from refinements using the more common form of the dispersion function, where the damping parameter is set to a value of 20.0, are denoted rPBE-D2 structures. Table 1 summarizes statistical data associated with the prediction of EFG tensor parameters on training set using model structures obtained by XRD, and on structures with atomic coordinates refined at the rPBE, rPBE-D2, and rPBE-D2* levels. Calculations on structures refined at the rPBE-D2* level result in lower rmsre and rmse values than those obtained from the XRD structures and structures refined at the rPBE and rPBE-D2 levels. Calculations on rPBE and rPBE-D2 refined structures result in EFG tensor principal elements


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that are similar in a statistical sense and frequently on a case-by-case basis: calculated values of the principal elements of 35Cl EFG tensors in the training set differ by only 160 kHz between the two classes of structures. In comparison, differences in the same values between rPBE-D2 and rPBE-D2* structures are an order of magnitude larger (1.25 MHz). Because nuclear EFG tensor parameters obtained for structures optimized at the rPBE and rPBE-D2 levels are similar, calculations at the rPBE-D2 level are not reported subsequently. The empirical structural corrections are based on experimental NMR parameters collected typically at room temperature, whereas the single crystal XRD structures were obtained between 77 K and room temperature. The effect of small lattice expansions/contractions associated with changes in temperature appear to have only small effects on calculated EFG tensor parameters. For instance, the calculated values of CQ(35Cl) for the chloride anion in Lhistidine HCl·H2O differ by only 120 kHz for structures obtained at room temperature and 100 K, following optimizations. The effects of fast molecular dynamics on calculated EFG tensor parameters are beyond the scope of the present study. As implemented in this study, the dispersion correction plays only an indirect role in calculations of EFG tensors: specifically, inclusion of dispersion does not affect the algorithm that provides the EFG tensor; rather, it affects the structural refinements, which in turn yield atomic coordinates and ground state electron densities that determine the nature of the EFG tensor. Calculations of the principal elements of the 35Cl EFG tensor on a single structural model of L-histidine HCl·H2O differ by only a few hundred hertz, whether or not the dispersion force field is included during the calculation of the EFG tensors (Table S4). This difference reflects the numerical convergence of the calculations.



Analysis of Training Set Structures. Geometry optimization of the training set organic solids at any level leads to a reduction of the mean forces on the atoms by three to four orders of magnitude (Table S5). Mean atomic forces for the training set solids never differ by more than 0.006 eV Å-1 between structures obtained using different structural refinement protocols. However, variation in calculated EFG tensor parameters between structures refined at the rPBE and rPBE-D2* levels suggests that the energy-minimized structures differ substantially. Limiting the discussion of structural parameters to the nine hydrochloride salts in the training set, refinement of atomic coordinates at the rPBE-D2* level results in shorter covalent bond lengths than predicted at the rPBE level (Figure S1). Relative to bond lengths observed by XRD, covalent bonds between non-hydrogen atoms are predicted to be longer, following refinement at the rPBE level (by an average of 0.014 Å), and shorter, following refinement at the rPBE-D2* level (by an average of 0.012 Å). Covalent bonds involving hydrogen atoms are lengthened relative to XRD-derived structures by both structural refinement protocols (by 0.117 Å and 0.048 Å for rPBE and rPBE-D2* refinements, respectively). Root-mean-square deviations (RMSDs) in atomic positions highlight differences in structures prior to and following geometry optimization (Figure S2).26-28 Considering the positions of non-hydrogen atoms, the RMSD between XRD and rPBE structures is 0.057 Å on average, with a maximum deviation of 0.16 Å for any material. The equivalent deviations between XRD and rPBE-D2* structures are 0.044 Å and 0.11 Å. These data indicate that refinements at the rPBE-D2* level result in smaller deviations from the XRD structures than refinements at the rPBE level, on average. For hydrogen atoms, the RMSDs between XRDderived structures and refined structures are much larger (0.178 Å and 0.126 Å for the rPBE and rPBE-D2* refinements, respectively) than observed for the heavier atoms (Figure S3). The


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hydrogen atom RMSDs are generally smaller between the two types of optimized structures (0.099 Å) than between the refined structures and the XRD-derived structures. RMSDs between scXRD-derived structures and dispersion-corrected DFT structures reported herein are well within the expected range reported by van de Streek.103 The large variation in calculated 35Cl EFG tensor parameters between the XRD, rPBE, and rPBE-D2* structures suggests that the chloride anion environments in the vicinity of these sites differs significantly between the various types of structures. Table 2 lists the H···Cl- contact types and contact distances for a subset of the training set organic solids, as obtained by XRD and refinement by the two model chemistries. Included are all H···Cl- contacts under 2.64 Å, as this is the sum of the van der Waals’ radii of the hydrogen and chlorine atoms used in the dispersion force field (Eq. 7).86 In nearly every case, rPBE-D2* H···Cl- contacts are longer than those obtained at the rPBE level. Differences in H···Cl- contacts are typically largest for the shortest contact, with variations over 0.1 Å, in some cases. This observation does not hold for Lhistidine HCl·H2O, where the first two contacts are of comparable length. Compared to H···Clcontacts determined by XRD, rPBE-D2* contacts differ by as much as 0.2 Å. Calculations of EFG tensor parameters for the test set. The performance of rPBED2* for materials outside of the initial training set is tested through calculations of 35Cl, 17O, and 14

N, EFG tensors from a wide array of organic solids. The results of the calculations are

illustrated in Figure 2, and statistical analysis is provided in Tables 3 and 4. The largest variation in calculated EFG tensor parameters between different structure types is observed for 35Cl sites. Considering all of the principal elements of the 35Cl EFG tensors together, rmse values of 1.51 MHz and 1.30 MHz were observed for the XRD-derived structures and rPBE refined structures, respectively. The errors for the rPBE structures are highly



systematic; the relationship between calculated and experimental values is modeled with a linear function with a slope of 1.32. This systematic overestimation of the magnitude of EFG tensor principal elements has been observed in previous work.83 We believe that the source of this error is related to the underestimation of H···Cl- contacts in the crystal structures when a proper treatment of dispersion is not included in the geometry optimization (vide supra). In extreme cases, calculated values of CQ for rPBE structures differ from experiment by over 3.5 MHz. In contrast, structural refinement at the rPBE-D2* level leads to a rmse of only 0.40 MHz, which is ca. 3 times smaller than the value obtained for rPBE-refined structures. The variation in calculated 35Cl EFG tensors is also observed in each of the three principal elements individually, with the best agreement with experiment obtained by calculations on rPBE-D2* structures (Table 4). Calculations of 17O EFG tensors are strongly influenced by the type of structure used in the calculation. Because all of the 17O SSNMR studies cited here involve oxygen atoms involved in covalent bonding, the variability in computed EFG tensor parameters is significantly smaller than observed for 35Cl sites. For XRD-derived structures, rPBE refined structures, and rPBE-D2* refined structures, the rmse values are 0.58 MHz, 0.49 MHz, and 0.36 MHz, respectively. Refinement at the rPBE level leads to notably worse predictions of eQV22/h than is predicted by either XRD structures or structures refined at the rPBE-D2* level. This difference is present throughout the majority of systems studies here, independent of the type of 17Ocontaining moiety, including oxygen sites that do not participate in hydrogen bonding. It is worth comparing the 17O EFG tensors reported herein to those from an earlier study.85 Previously, an rmse of 0.28 MHz was reported for 17O sites based on calculations using dispersion-corrected DFT, which is slightly lower than the rmse of 0.36 MHz reported herein.


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Three facts about the previous study should be noted: (i) the xc functional PW91 was used rather than rPBE; (ii) it employed a version of the DFT-D2 model parameterized using only 17O EFG tensor parameters, rather than the heteronuclear parameterization used here; (iii) it was based on a smaller number of materials, exhibiting a limited diversity of moieties. Based on these observations, it is possible that the introduction of a set of distinct values for the damping parameter, for all possible types of atomic pairs, will further improve upon the results obtained using a global damping parameter (i.e., a single value of d for all atomic-pairwise corrections). This is beyond the scope of the current study. Calculated 14N EFG tensor parameters appear to be the least sensitive to structural refinement (in terms of rmse) of the three nuclides discussed herein. The rmse for XRD-derived structures is 0.33 MHz. This quantity is reduced to 0.17 MHz and 0.15 MHz following structural refinement at the rPBE and rPBE-D2* levels, respectively. Differences in calculated 14N EFG tensor parameters between rPBE and rPBE-D2* refined structures are largest for the principal element eQV22/h. rPBE errors in 14N EFGs are most strongly pronounced for V22 of pseudotetrahedral nitrogen sites with 0.31 ≤ ηQ ≤ 0.70. There are nine 14N-containing materials with an experimentally-determined asymmetry parameter in this range (Table 5). In contrast, refinement at the rPBE-D2* level results in superior agreement with experimental values (Figure 3). Pseudotetrahedral 14N sites with ηQ in this range are indicative of species with NH3+ groups that act as hydrogen bond donors to nearby oxygen sites. Analysis of the rPBE-D2* refined structures reveals greater variation in N-H bond lengths in NH3+ groups than species with low values of ηQ (0.00 ≤ ηQ ≤ 0.30), in agreement with previous observations.43 The greater variation in N-H bond lengths results from the greater variation in O···H hydrogen bonding distances.



When the N-H and O···H bond lengths are similar, the 14N site exhibits higher axial symmetry (lower ηQ). Comparison with Neutron Diffraction Structures. Structures derived from neutron diffraction are often considered superior to those derived from XRD due to the ability of the former to determine the positions of hydrogen atoms with a greater degree of precision.26-29 Proper positioning of hydrogen atoms is critical for accurate prediction of EFG tensor parameters, particularly those of 35Cl EFG tensors of chloride ion sites involved in hydrogen bonds. Comparison of calculation of 35Cl EFG tensor parameters between neutron-diffraction derived structures and rPBE or rPBE-D2* refinements of XRD-derived structures provides a robust method of assessing structural refinements. The crystal structures of glycine HCl, L-valine HCl, L-glutamic acid HCl, L-histidine HCl·H2O, L-lysine HCl·2H2O, and L-phenylalanine HCl have been determined from neutron diffraction,104-109 and are used here as a final figure of merit for assessing structural refinement by the rPBE-D2* model (Table 6). For each material, calculations of 35Cl EFG tensor parameters for rPBE-D2* refined structures results in superior agreement with experiment than calculations on models based on structures derived from neutron diffraction (Figure 4). The poorest agreement with experimental 35Cl EFG tensor parameters is obtained from rPBE-refined structures in each case. H···Cl- contacts determined by rPBE-D2* refinement are longer than those determined by neutron diffraction or rPBE refinement (Table 7), by an average of 0.046 Å and 0.078 Å, respectively. Neutron-diffraction-derived H···Cl- contacts are longer than rPBE contacts by an average of 0.032 Å. These observations points to the longer H···Cl- contacts determined by rPBE-D2* refinements being better models to the true intermolecular structure of the


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hydrochloride salts since the best agreement with experimental 35Cl EFG tensor parameters is achieved for structures refined with this model chemistry.

CONCLUSIONS Calculated nuclear EFG tensors are sensitive probes of molecular-level structure. Not only are these tensor parameters useful in assessing the quality of models representing the structures of solids, but experimental determinations of nuclear EFG tensor parameters can be used to inform ab initio structural refinements. Plane-wave DFT calculations of nuclear EFG tensor parameters were used here as a basis for refining the positions of atoms in crystal structures determined initially through scXRD. The analysis was based on predictions of 14N, 17

O, and 35Cl EFG tensor parameters in 86 organic solids (17 and 69 molecules in the training set

and test set, respectively). Calculations on models of solid materials were carried out using plane-wave DFT with the inclusion of empirical force fields. The success of these calculations was predicated upon parameterization of the damping function in Grimme’s two-body dispersion force field86 to aid in structural refinements, by assessing the quality of the resulting structures through calculations of nuclear EFG tensor parameters. By adjusting the value of a single term in the force field (specifically, the damping parameter), one is able to achieve significantly improved agreement with experimental values for a large variety of organic solids. Calculations of nuclear EFG tensors on crystal structures optimized through this protocol are able to predict experimental values with a higher accuracy than those obtained through calculations on models representing XRD-derived structures, DFT refinements of XRD-derived structures, and even neutron diffraction structures (when such data are available for comparison).



The structural refinement protocol described here produces structures that differ from XRD-derived structures, structures obtained with conventional DFT refinements of diffraction structures, and even neutron diffraction structures. The most significant structural differences are observed for H···Cl- hydrogen bonds, which can vary by more than 0.2 Å between different types of structural data/refinements. In contrast, bond lengths between non-hydrogen atoms are generally shortened by 0.012 Å, relative to XRD-derived structures. 35

Cl SSNMR has proven to be one of the most sensitive structural probes of chloride

anions in organic HCl or metal chloride salts. The variation in calculated quadrupolar coupling constants among different types of structural data can be a large as 4 MHz, which is ca. 50% as large as the largest values typically observed for these sites. The extraordinary sensitivity of 35Cl EFG tensors to local structure should prove to be a powerful tool in future NMR crystallography investigations, as this technique may be the only method able to determine the geometry H···Clbonding environments with a level of precision rivaling neutron diffraction. We note that the methodology developed herein has focused exclusively on organic solids; however, the introduction of an appropriate training set could allow for the extension of this work to include extended network solids. Additionally, these protocols may be expanded to include types of atoms or bond (e.g., covalently bound chlorine atoms) that were not considered in the present study. Finally, there are advanced computational methods that may be applied, such as the D3 correction and vdW-DFT;110 however, the former has not yet been implemented in CASTEP, and the latter requires the adjustment of a larger parameter set. Nonetheless, these may be good candidates for future explorations in crystal structure refinement utilizing EFG tensors. There are exciting prospects for this generalized method to be used for the refinement and prediction of new crystal structures utilizing EFG tensor parameters derived from this method, either


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independently or alongside of additional computations of chemical shift tensors and/or experimentally derived X-ray and neutron diffraction data.



ASSOCIATED CONTENT Supporting Information Practical implementation of the force field model in Materials Studio; list of CCSD codes for relevant crystal structures; plane-wave DFT benchmark calculations; additional structural analysis of energy-minimized structures; summary of calculated nuclear EFG tensor parameters. Crystallographic Information Crystallographic information files for each of the refined structures discussed in this article.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]; Tel: (519) 253-3000 x3548; Fax: (519) 973-7098 Notes The authors declare no competing financial interests.

ACKNOWLEDGEMENTS We thank both Genentech and the Natural Sciences and Engineering Research Council of Canada (NSERC) for funding this research (NSERC in the form of a Discovery Grant). R.W.S. is also grateful for a 50th Anniversary Golden Jubilee Chair from the University of Windsor. This work was made possible, in part, by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca). We are grateful to Prof. Maria Baias (New York University Abu Dhabi) and Prof. Oded Hod (Tel Aviv University) for very helpful discussions.


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104. Al-Karaghouli, A. R.; Cole, F. E.; Lehmann, M. S.; Miskell, C. R.; Verbist, J. J.; Koetzle, T. F., Precision neutron diffraction structure determination of protein and nucleic acid components. xvii. molecular and crystal structure of the amino acid glycine hydrochloride. J. Chem. Phys. 1975, 63, 13601366. 105. Koetzle, T. F.; Golic, L.; Lehmann, M. S.; Verbist, J. J.; Hamilton, W. C., Precision neutron diffraction structure determination of protein and nucleic acid components. xv. crystal and molecular structure of the amino acid L-valine hydrochloride. J. Chem. Phys. 1974, 60, 4690-4696. 106. Sequeira, A.; Rajagopal, H.; Chidambaram, R., A neutron diffraction study of the structure of Lglutamic acid·HCl. Acta Crystallogr., Sect. B 1972, 28, 2514-2519. 107. Koetzle, T. F.; Lehmann, M. S.; Verbist, J. J.; Hamilton, W. C., Precision neutron diffraction structure determination of protein and nucleic acid components. vii. the crystal and molecular structure of the amino acid L-lysine monohydrochloride dihydrate. Acta Crystallogr., Sect. B 1972, 28, 3207-3214. 108. Al-Karaghouli, A. R.; Koetzle, T. F., Neutron diffraction study of L-phenylalanine hydrochloride. Acta Crystallogr., Sect. B 1975, 31, 2461-2465. 109. Fuess, H.; Hohlwein, D.; Mason, S. A., Neutron diffraction study of L-histidine hydrochloride monohydrate. Acta Crystallogr., Sect. B 1977, 33, 654-659. 110. Kristian, B.; Valentino, R. C.; Kyuho, L.; Elsebeth, S.; Thonhauser, T.; Per, H.; Bengt, I. L., van der Waals forces in density functional theory: a review of the vdW-DF method. Rep. Prog. Phys. 2015, 78, 066501.


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Table 1. Statistical data associated with the prediction of EFG tensors for the training set organic solids, as calculated on XRD-derived structures and on rPBE, rPBE-D2, or rPBE-D2* refined structures. a Structure rmsre b rmse (MHz) c max(+) (MHz) d max(-) (MHz) e 14 N XRD 0.267 0.33 0.88 -0.21 rPBE 0.112 0.17 0.40 -0.08 rPBE-D2 0.089 0.15 0.44 -0.07 rPBE-D2* 0.077 0.10 0.21 -0.11 17 O XRD 0.071 0.54 1.34 -0.80 rPBE 0.055 0.44 0.79 -0.72 rPBE-D2 0.054 0.42 0.76 -0.74 rPBE-D2* 0.036 0.28 0.55 -0.39 35 Cl XRD 0.364 1.86 5.49 -3.66 rPBE 0.314 1.65 3.54 -0.43 rPBE-D2 0.307 1.63 3.56 -0.57 rPBE-D2* 0.055 0.23 0.61 -0.46 All XRD 0.233 rPBE 0.175 rPBE-D2 0.168 rPBE-D2* 0.053 a All calculations were performed using the rPBE plane wave DFT method, as implemented in the CASTEP module of Materials Studio. b Root mean square relative error. c Root mean square error. d Maximum positive error. e Maximum negative error.



Table 2. The shortest H⋯Cl- contacts for several amino acid hydrochlorides as determined via energy minimization and geometry optimization with DFT plane wave calculations. H···Cl- contacts (Å) b XRD rPBE rPBE-D2* Glycine HCl ROOH···Cl 1.974 1.981 2.071 + RNH3 ···Cl 2.159 2.114 2.186 RNH3+···Cl2.264 2.119 2.201 + RNH3 ···Cl 2.721 2.619 2.604 L-alanine HCl ROOH···Cl2.043 1.967 2.074 RNH3+···Cl2.205 2.126 2.197 RNH3+···Cl2.227 2.138 2.208 L-valine HCl ROOH···Cl 2.103 1.969 2.071 RNH3+···Cl2.277 2.153 2.238 + RNH3 ···Cl 2.325 2.220 2.261 RNH3+···Cl2.393 2.353 2.414 ROOH···Cl 2.206 1.986 2.093 L-cysteine HCl·H2O HOH···Cl2.394 2.157 2.224 HOH···Cl 2.395 2.237 2.304 RNH3+···Cl2.536 2.356 2.348 RNH3+···Cl2.165 2.142 2.215 L-histidine HCl·H2O HOH···Cl2.389 2.157 2.263 + RNH3 ···Cl 2.404 2.210 2.291 a Indicates the functional group contributing to the H⋯Cl contacts (i.e., ROOH⋯Cl-, RNH3+⋯Cl-, and HOH⋯Cl- denote carboxylic-, positively charged primary ammonia-, and water-type hydrogen contacts, respectively). b The shortest H⋯Cl- contacts (< 2.64 Å) as determined via XRD or geometry optimization at the rPBE and rPBE-D2* levels. Material

Contact type a


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Table 3. Statistical data associated with the prediction of EFG tensors for the test set organic solids, as calculated on XRD-derived structures, and on rPBE or rPBE-D2* refined structures. Structure rmse (MHz) b max(+) (MHz) c max(-) (MHz) d 14 N XRD 0.33 0.92 -1.06 rPBE 0.17 0.46 -0.61 rPBE-D2* 0.15 0.42 -0.44 17 O XRD 0.58 2.01 -2.50 rPBE 0.49 1.39 -1.15 rPBE-D2* 0.36 1.09 -1.33 35 Cl XRD 1.51 5.49 -3.66 rPBE 1.30 3.54 -0.99 rPBE-D2* 0.40 0.80 -1.21 a b c Root mean square relative error. Root mean square error. Maximum positive error. d Maximum negative error.



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Table 4. Root mean square errors in calculated EFG tensor principal elements based on model structures obtained from XRD, or structures refined at the rPBE and rPBE-D2* levels. Structure

All principal values (MHz)

eQV₁₁/h (MHz)

eQV₂₂/h (MHz)

eQV₃₃/h (MHz)

ηQ

0.33 0.17 0.15

0.23 0.14 0.14

0.36 0.17 0.11

0.39 0.19 0.19

0.17 0.10 0.07

0.58 0.49 0.36

0.66 0.44 0.34

0.33 0.58 0.32

0.67 0.45 0.41

0.09 0.09 0.05

1.51 1.30 0.40

0.92 0.57 0.32

1.42 1.33 0.40

1.99 1.73 0.46

0.19 0.10 0.10

14

N XRD rPBE rPBE-D2* 17 O XRD rPBE rPBE-D2* 35 Cl XRD rPBE rPBE-D2*


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Table 5. Experimental and calculated values of eQV22/h for all pseudotetrahedral 14N sites with 0.31 ≤ ηQ ≤ 0.70. Material L-isoleucine L-leucine L-lysine HCl·2H2O L-methionine L-threonine L-valine α-glycine β-glycine γ-glycine

Exp (MHz) -0.74 -0.74 -0.71 -0.87 -0.76 -0.74 -0.90 -0.90 -0.82

X-ray (MHz) -1.00 -1.23 -0.78 -1.68 -1.31 -1.11 -0.96 -1.17 -0.95

rPBE (MHz) -1.06 -1.10 -0.93 -1.16 -0.85 -1.03 -1.10 -1.13 -0.97

rmse (MHz) a 0.41 0.25 max(+) (MHz) b 0.82 0.36 max(-) (MHz) c a b c Root mean square error. Maximum positive error. Maximum negative error.


rPBE-D2* (MHz) -0.79 -0.83 -0.71 -0.86 -0.84 -0.78 -0.91 -0.87 -0.83 0.04 0.09 -0.03


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Table 6. Experimental and calculated 35Cl EFG tensor parameters for six HCl salts, as determined for several types of structural data. Material

Glycine HCl L-valine HCl L-glutamic acid HCl L-histidine HCl·H2O L-lysine HCl·2H2O L-phenylalanine HCl

Exp CQ (MHz) 6.42 5.89 3.61 1.80 2.49 6.08

ηQ 0.61 0.51 0.65 0.72 0.42 0.52

rPBE CQ (MHz) -9.13 -8.22 5.47 2.77 4.23 -8.45

ηQ 0.82 0.53 0.69 0.60 0.50 0.43

Neutron CQ ηQ (MHz) -8.35 0.82 -8.15 0.54 3.89 0.30 2.71 0.64 3.45 0.41 -7.92 0.54

rmse (MHz) a 1.63 1.24 max(+) (MHz) b 3.14 2.43 max(-) (MHz) c -0.43 -0.50 a b c Root mean square error. Maximum positive error. Maximum negative error.


rPBE-D2* CQ ηQ (MHz) -6.57 0.76 -5.76 0.59 3.72 0.39 1.65 0.69 3.05 0.68 -6.07 0.48 0.35 0.80 -0.46

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Table 7. The shortest H⋯Cl- contacts for several amino acid hydrochlorides as determined by neutron diffraction or via energy minimization and geometry optimization at the rPBE-D2* level. H···Cl contacts (Å) b rPBE Neutron rPBE-D2* Glycine HCl ROOH···Cl 1.981 2.008 2.071 RNH3+···Cl2.114 2.123 2.186 RNH3+···Cl2.119 2.160 2.201 RNH3+···Cl2.619 2.593 2.604 L-valine HCl ROOH···Cl 1.969 1.990 2.071 RNH3+···Cl2.153 2.161 2.238 RNH3+···Cl2.220 2.263 2.261 RNH3+···Cl2.353 2.355 2.414 L-glutamic acid HCl ROOH···Cl 2.008 2.073 2.118 RNH3+···Cl2.068 2.107 2.137 RNH3+···Cl2.154 2.137 2.190 + RNH3 ···Cl 2.142 2.215 2.165 L-histidine HCl·H₂O HOH···Cl 2.157 2.233 2.263 RNH3+···Cl2.210 2.265 2.291 L-lysine HCl·2H2O RNH3+···Cl2.103 2.150 2.198 RNH3+···Cl2.211 2.196 2.262 HOH···Cl2.211 2.273 2.278 HOH···Cl 2.267 2.329 2.384 L-phenylalanine HCl ROOH···Cl1.941 2.004 2.065 RNH3+···Cl2.090 2.142 2.201 RNH3+···Cl2.300 2.302 2.368 + RNH3 ···Cl 2.304 2.361 2.385 a Indicates the functional group contributing to the H⋯Cl contacts (i.e., ROOH⋯Cl-, RNH3+⋯Cl-, and HOH⋯Cl- denote carboxylic-, positively charged primary ammonia-, and water-type hydrogen contacts, respectively). b The shortest H⋯Cl- contacts (< 2.64 Å) as determined via neutron diffraction or geometry optimization at the rPBE and rPBE-D2* levels. Material

Contact type a



ToC Graphic


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Figure 1. Root mean square relative errors (rmsre) in the principal elements of computed EFG tensors of the training set organic solids as a function of the damping parameter, 2.5 ≤ d ≤ 10.0. By default, the value of d is set to 20 in CASTEP.



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Figure 2. Relationship between the principal elements of calculated and experimental nuclear EFG tensors. Panels illustrate the results for 35Cl sites (a - c), 17O sites (d – f), and 14N sites (g – i). Computed EFG tensor parameters are derived from calculations on XRD-derived structures (green), and structures with atomic coordinates refined at the rPBE (orange) or rPBE-D2* (blue) levels. The dashed lines represent perfect agreement between calculated and experimental values. The dotted red line in (b) represents the best fit between calculated and experimental values.


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Figure 3. Errors in calculated eQV22/h in pseudotetrahedral 14N sites with 0.31 ≤ ηQ ≤ 0.70. Calculations were performed on X-ray structures (green), rPBE structures (orange), and rPBE-D2* structures (blue). The materials are L-isoleucine (1), L-leucine (2), L-lysine HCl·2H2O (3), L-methionine (4), L-threonine (5), L-valine (6), -glycine (7), -glycine (8), and -glycine (9).

Figure 4. Root mean square error in the calculated principal elements of 35Cl EFG tensors based on structures obtained by rPBE refinement of X-ray diffraction structures (orange), neutron diffraction (grey), or rPBE-D2* refinement of X-ray diffraction structures. The materials are glycine HCl (1), L-valine HCl (2), L-glutamic acid HCl (3), L-histidine HCl·H2O (4), L-lysine HCl·2H2O (5), and L-phenylalanine HCl (6).


Refining Crystal Structures with Quadrupolar NMR ... - ACS Publications

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