Dynamics and Thermodynamics of Crystalline Polymorphs: α-Glycine

Article pubs.acs.org/JPCA

Dynamics and Thermodynamics of Crystalline Polymorphs: α‑Glycine, Analysis of Variable-Temperature Atomic Displacement Parameters Thammarat Aree*,† and Hans-Beat Bürgi‡ †

Department of Chemistry, Faculty of Science, and Center for Petroleum, Petrochemicals and Advanced Materials, Chulalongkorn University, Phyathai Road, Pathumwan, Bangkok 10330, Thailand ‡ Department of Chemistry and Biochemistry, University of Berne, Freiestrasse 3, CH-3012 Bern, and Institute of Organic Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8050 Zürich, Switzerland S Supporting Information *

ABSTRACT: Multitemperature synchrotron diffraction data to 0.5 Å resolution in the temperature range 10−298 K and neutron data at 18 K of the α-glycine polymorph have been collected at the KEK photon factory (PF), SPring-8 and the Institut Laue Langevin (ILL) for the study of molecular motion in the crystal and of the associated thermodynamic functions. Atomic displacement parameters (ADPs) of non-H atoms are obtained from refinements based on nonspherical atomic scattering factors (invariom model) to minimize correlation between parameters describing thermal motion and valence electron density. The ADPs in the temperature range 50−298 K from SPring-8 connect smoothly with those from neutron diffraction at 18 K and 288−323 K. The combined ADPs from both sources covering the temperature range 18−323 K are used for a normal-mode analysis in the molecular mean field approximation. The lattice vibration frequencies from the ADP analysis and the internal vibration frequencies from an ONIOM (B3LYP/6-311+G(2d,p):PM3) calculation together with the Einstein, Debye, and Nernst−Lindemann models of heat capacity are used to calculate Cp, Hvib, and Svib values that are in good agreement with those from calorimetry. diffraction data have been reported.11,12 Kozhin has measured unit cell constants only and determined thermal expansion tensors in the range from 77 to 415 K.13 Boldyreva and coworkers have studied structural distortions on cooling α-glycine from 294 to 150 K using sealed-tube X-ray data.11 Langan and co-workers have studied anomalous electrical behavior based on neutron data in the temperature range from 288 to 427 K.12 The X-ray multitemperature studies are limited in resolution to 0.7 Å rather than the 0.5 Å necessary for obtaining accurate atomic displacement parameters (ADPs) and minimizing the influence of valence electron density in the case of X-ray studies. In addition, the high dispersion of the beam from a sealed X-ray tube causes ADPs from sealed tube radiation to be systematically larger by ∼6 × 10−4 Å2 compared with those from synchrotron radiation.14 Finally the data reported so far do not cover the temperature range from the quantum to classic regimes that is required for normal-mode analysis.15 We have therefore embarked on a multitemperature synchrotron Xray study with the aim of obtaining accurate ADPs, interpreting them by a molecular normal-mode analysis and calculating thermodynamical functions.

1. INTRODUCTION Glycine, NH2CH2COOH, the smallest member of the amino acid family, functions as a neurotransmitter and is commonly found in proteins, enzymes, and hormones. In the gas phase glycine exists as a neutral molecule, whereas in aqueous solution it mainly appears as a zwitterion +NH3CH2COO−. In the solid state it exhibits three polymorphic forms at ambient pressure with relative stabilities: γ > α > β.1 The three glycine polymorphs differ in the packing of the zwitterions.2,3 In the αform (monoclinic, P21/n) and the β-form (monoclinic, P21), zwitterions are connected via NH···O hydrogen bonds into chains which are stabilized by additional, longer hydrogen bonds and van der Waals interactions. In the γ-form (trigonal, P31), zwitterions form polar helices linked with each other via extra NH···O hydrogen bonds. Differences in crystal packing of the three glycine polymorphs result in differences in their physical and chemical properties. The β- and γ-phases exhibit piezoelectric properties,2,3 whereas the α-phase shows pyroelectricity near room temperature.4 α-Glycine has been extensively studied by X-ray and neutron diffraction. Here we mentioned only the structural studies done under atmospheric pressure after 1950. Most diffraction data of α-glycine were collected at a single temperature, e.g. with sealed-tube X-rays5−7 or neutrons8,9 at room temperature or combining X-ray and neutron diffraction for a charge density study at 120 K.10 Thus far three sets of multitemperature © 2012 American Chemical Society

Received: May 19, 2012 Revised: June 26, 2012 Published: June 29, 2012 8092

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evaporation and big crystals of 3 mm were used for neutron diffraction. 2.2. Diffraction Data Collection. 2.2.1. Synchrotron. Synchrotron data to 0.5 Å resolution of α-glycine were collected between 10 and 298 K at beamline 1B of KEK Photon Factory (PF) and at beamline 2B1 of SPring-8, Japan in order to compare the ADPs measured from both sources. One to three single crystals of 0.1−0.3 mm were mounted on twocircle diffractometers in two orientations to gain better coverage of reciprocal space and diffraction intensities measured with a cylindrical imaging plate detector. However, due to limited beamtime and inappropriate orientation of mounted crystals, the completeness of the merged data is relatively low (82−91%) though sufficiently good for normalmode analysis (see section 4.2). 2.2.2. Neutron. A rod-like crystal of 1.3 × 1.3 × 3.0 mm3 was chosen for data collection at 18 K, using the four-circle diffractometer of the hot neutron beamline D9 at the Institut Laue−Langevin (ILL), Grenoble, France. Unit cell constants at 18 and 100 K and a workable data set at 18 K with a resolution of 0.54 Å and a completeness of 90% could be obtained. The experimental conditions used for data collection at synchrotron and neutron beamlines are summarized in Table 1S of the Supporting Information. 2.3. Data Processing. The multitemperature synchrotron diffraction data obtained from KEK-PF and SPring-8 were indexed and integrated by using Rapid Auto ver. 2.40 (ref 27) and Denzo/Scalepack (HKL System ver. 1.98.7),28 respectively. Multiscan absorption corrections were applied with ABSCOR29 or Denzo/Scalepack.28 Data were then scaled and merged with XPREP.30 The structures were refined with SHELXL97.31 The values of completeness, redundancy, Rint, and R1 are as follows: 88−91%, 2.6−3.9, 0.013−0.036, and 0.030−0.055 for the KEKPF data and 82−84%, 3.4−3.9, 0.029−0.036, and 0.039−0.049 for the SPring-8 data (Supporting Information, Tables 2S and 3S). Data statistics from both sources indicate reasonable data quality (Table 1). The unit cell parameters of α-glycine from the synchrotron experiments are comparable to those from sealed tube ones11 (Figure 1S in Supporting Information). The SPring-8 ADPs are depicted as ORTEP32 plots in Figure 1 and compared with the KEK ones in Figure 2 for O(2) and N(1). Comparisons for the other non-hydrogen atoms look similar. Over the entire temperature range, the ADPs from both experiments show the expected continuous increase with temperature. The increase is noticeably and significantly larger, however, for the KEK ADPs than for the SPring-8 ones. It is unlikely that this difference is due only to the different crystals used for data collection; the different software programs for data processing seem a more likely cause for the discrepancy. The SPring-8 ADPs at 20 K are larger than those of 50 K. We think that this is due to the ice that formed during data collection and affected the measured scattering intensities, particularly at high scattering angles. Therefore, the 20 K data have been excluded from further data analysis. For neutron diffraction, the data collected in three different resolution shells (low, medium, high) were integrated with standard in-house software. No absorption correction was applied. Data were scaled and merged with XPREP.30 The unit cell constants of α-glycine from neutron diffraction (18−200 and 288−427 K12) are consistent with those from X-ray diffraction (10−298 and 150−294 K11), see Figure 1S in the Supporting Information. All hydrogen atoms were located from a difference Fourier map and all atoms were refined

According to the normal mode model proposed by Bürgi and Capelli,15 the ADPs may be expressed as: Σx(T ) = AgVδ(T )VTg T AT + εx

(1)

where δ(T) is a diagonal matrix of temperature-dependent normal mode displacements with elements δi(T ) =

⎛ hν ⎞ h coth⎜ i ⎟ 2 8π νi ⎝ 2kBT ⎠

(2)

The matrices g and A transform the normal modes with frequencies νi and eigenvectors V into atomic displacements Σx(T); ADPs are the 3 × 3 diagonal blocks of Σx; εx is a temperature-independent term accounting for the highfrequency intramolecular vibrations, which are not significantly excited in the temperature range of the diffraction experiments; h is the Planck constant; and kB is the Boltzmann constant. The vibrational motion of molecules in the crystal is parametrized by the model of motion, i.e. the frequencies νi, the independent elements of the orthonormal matrix V representing molecular displacement coordinates, and the six independent elements of each of the 3 × 3 diagonal blocks of εx (one per atom). Anharmonicity associated with the thermal expansion of the crystal may be taken into account by Grüneisen parameters16 (eq 3) derived from the ratio of the frequency change to the cell-volume change with temperature.15 γG , i = −

V (0) Δνi(T ) · ΔV (T ) νi(0)

(3)

This technique leads to estimates of averages over the Brillouin zone of (mostly) lattice vibrations. It has been successfully applied to analyze the zero-point vibrational amplitudes of benzene,17,18 isotope effects in crystalline benzene and perdeuterobenzene,19 the librational and translational motions of naphthalene,20,21 anthracene,20 and hexamethylenetetramine (HMT),22 and the out-of-plane deformation of the peptidic NH2 groups of urea.17 For naphthalene, anthracene, and HMT, the specific heat Cv has been estimated with Einstein23 and Debye24 models from the 6 predominantly external frequencies derived by ADP analysis and from the 3n − 6 internal frequencies calculated ab initio.21,22 Taking into account compressibility by the Nernst−Lindemann relation,25 the corresponding specific heat Cp of naphthalene, anthracene, and HMT has also been calculated.26 In the present work, we collected multitemperature synchrotron diffraction data to obtain ADPs of the α-glycine polymorph, used normal-mode analysis to obtain average lattice vibration frequencies, performed ab initio calculations to deduce internal vibration frequencies, and combined all the vibration frequencies for an estimate of the thermodynamic parameters of the α-glycine polymorph. In future work this approach will be applied to the β- and γ-polymorphs for insight into their relative stabilities.

2. DIFFRACTION EXPERIMENTS 2.1. Crystal Preparation. White powdered glycine purchased from Fluka was used as received. Rod-like, colorless single crystals of the α-glycine polymorph (monoclinic, P21/n) were obtained by evaporation of a saturated aqueous solution at room temperature. Smaller crystals up to 0.3 mm in size were selected for synchrotron diffraction, whereas much larger crystals, up to 1.2 cm long, could be obtained from very slow 8093

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Table 1. Refinement Statistics from Independent Atom Model with SHELXL97 and Multipole Atom Model with XD of α-Glycine Data from KEK, SPring-8, and ILL temp (K)

R1(F)_IAMa (%)

10c 70 130 190 250 298

3.39 4.12 3.47 3.31 4.40 4.46

50d 100 150 200 250 298

4.09 4.12 4.54 4.62 4.50 4.68

18

4.04

R1(F)_INVb (%) KEK 2.75 3.27 2.90 2.46 3.09 3.60 SPring-8 3.56 3.73 4.29 4.39 4.33 4.47 ILL

Δρ_IAM (e Å−3)

Δρ_INV (e Å−3)

0.69/−0.52 0.68/−0.66 0.51/−0.43 0.45/−0.39 0.48/−0.56 0.58/−0.30

0.32/−0.48 0.33/−0.61 0.43/−0.31 0.17/−0.36 0.17/−0.34 0.38/−0.30

0.58/−0.50 0.47/−0.50 0.54/−0.54 0.43/−0.46 0.47/−0.43 0.41/−0.35

0.31/−0.45 0.34/−0.50 0.30/−0.53 0.28/−0.52 0.24/−0.51 0.33/−0.41

1.60/−1.56e

a

Independent atom model for spherical refinement with SHELXL97.31 Invariom refinement34 with XD.33 cExamples of the residual electron density and deformation electron density maps for 10 K KEK data are given in Figure 3a-d. dExamples of the residual electron density and deformation electron density maps for 50 K SPring-8 data are given in Figure 3e,f. eHigh residual electron densities ca. 5 times the standard errors are similar to those of KEK and SPring-8 data at low temperatures. b

Figure 2. Variable-temperature ADPs of α-glycine (a) O(2) and (b) N(1) atoms from IAM and invariom refinements of KEK and SPring-8 data in comparison with those from 18 K and high-temperature neutron diffraction.12 The standard errors are 2 × 10−4 Å2, or ca. the line thickness.

unchanged provided the immediate environment of the atom in different molecules is the same. The deformation electron density of α-glycine as parametrized by the invariom multipole parameters are depicted in Figure 3c,d. The selected statistics before and after invariom refinements are summarized in Table 1. In general, it is expected that an invariom refinement should improve the R-value by ∼1% for Mo Kα data sets.35 While the KEK data have ΔR1 ≈ 0.6−1.3%, the SPring-8 data have ΔR1 ≈ 0.2−0.5%. After invariom refinements of the KEK data residual electron densities (Δρ_INV) are still found on three bonds although overall the difference density is slightly flatter by 0.1− 0.2 e Å−3 than the one from the SPring-8 data, see Table 1 and Figure 3a,b,e,f. The comparison of KEK and SPring-8 ADPs is displayed in Figure 2. For the spherical refinement, the ADPs (U11 in particular) from KEK are larger than those from SPring-8 by up to 3 × 10−3 Å2 or ∼10 times the standard errors at 298 K. After invariom refinements, the ADPs from both sources decrease slightly, ∼3 times the standard errors or about 6 × 10−4 Å2; while this difference is not very important around room temperature, its effect (together with the sealed tube vs synchrotron difference of similar magnitude as mentioned in section 1) is significant at temperatures around absolute zero.

Figure 1. ORTEP32 plots (rmsd scale 2.50) of α-glycine data from ILL (18 K) and SPring-8 (50−298 K). The H-atoms of SPring-8 data are omitted for clarity.

anisotropically with SHELXL97,31 giving R1 = 0.040 (Table 1) at 18 K. 2.4. Deconvolution of Thermal Motion from Valence Bonding Density. ADPs of non-H atoms minimally biased by valence electron density may be obtained by refining the diffraction data with nonspherical atomic form factors with the program XD.33 We adopted the invariom model34 based on the approximation that the multipole parameters of an atomic electron density fragment are transferable, i.e. remain essentially

3. THEORETICAL CALCULATIONS The zwitterionic form of glycine is unstable in the gas phase, but is stabilized by the crystal field in the solid phase. The crystal field was mimicked by a 15-molecule cluster with the central molecule in a hydrogen bonding network of the 14 8094

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Figure 3. Residual electron density and deformation electron density maps of α-glycine (a−d) 10 K KEK data and (e, f) 50 K SPring-8 data on the N(1)−C(1)−C(2) and C(2)−O(1)−O(2) planes; solid, dotted, and dashed lines represent positive (peak), negative (hole), and zero contours, respectively (0.1 e Å−3 level).

ADPs at the higher temperatures indicates positive anharmonic motion (Figure 2) and thus a positive Grüneisen parameter in the normal mode model. The ADP curves of KEK are steeper than those of SPring-8; this feature is absorbed by an increased Grüneisen parameter in the normal-mode analysis (see section 4.2). Note that neither a significant discontinuity in the ADP curves nor a change in orientation of the ADP principal axes of the N-atom were observed in the whole temperature range, even at 150 K, contrary to results from incoherent inelastic neutron scattering39 and NMR spectroscopy.40,41 4.1.2. Combination of X-ray and Neutron Data. The ADPs from neutron diffraction at 18 and 288−323 K12 are compared with those from KEK and SPring-8 in Figures 1 and 2. Given the discrepancy between the two X-ray data sets (Figure 2) the question arises as to which one is more reliable. The ADPs reported in refs 5−11 are generally larger than or about equal to those from the KEK data. The neutron data measured at 18

surrounding neighbors. The cluster was built by using the atomic coordinates of the α-glycine neutron structure at 18 K from ILL-D9. A two-layer ONIOM(B3LYP/6-311+G(2d,p):PM3) method was employed to estimate the vibration frequencies of the glycine molecule in its crystalline environment with program Gaussian03.36 The central molecule was treated at the B3LYP/6-311+G(2d,p) level of theory, the 14 surrounding molecules with the semiempirical PM3 method. This ab initio crystal field approach with a cluster size of 15 molecules has been successfully applied to model the structures of the three glycine polymorphs.37 The cluster size is consistent with Kitaigorodski’s rule of molecular close packing.38

4. RESULTS AND DISCUSSION 4.1. Variable-Temperature ADPs. 4.1.1. General Features of the ADPs. Overall, the ADPs vary smoothly and continuously as expected. The steeper-than-linear increase of 8095

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Table 2. Normal Mode Analysis of Multitemperature ADPs of α-Glycine from SPring-8 and Neutron Diffraction ADP Set 1: Invariom; Model rbeg

Lx Ly Lz Tx Ty Tz

f req (ν̅, cm−1), Grüneisen and Eigenvector 67.0(0.8) 75.1(1.1) 83.5(1.1) 120.1(2.6) 2.35(0.59) 2.35(0.59) 2.35(0.59) 0.242(17) −0.084(30) −0.683(9) −0.498(19) 0.445(9) −0.237(19) −0.150(17) −0.287(15) −0.321(14) −0.343(13) −0.019(13) −0.034(20) −0.062(13) 0.168(29) −0.676(13) 0.684(13) 0.672(14) −0.451(24) 0.190(30) 0.446(9) −0.430(23) −0.766(17) −0.130(34) 0.046(13)

ϵ (×10−4) N1 C1 C2 O1 O2 −10(1)

H1 H2 −91(37)

H3 H4 H5 −56(30)

2(1) −3(1)

2(1) 1(1) 6(2)

−2(0) 4(37)

5(0) 12(0) 20(37)

2(0) 40(30)

−2(0) −4(0) −8(30)

GooF

R (%)

2.90

5.04

Observations: 210 Restraints: 12 Parameters: 49

ADP Set 2: Invariom + Neutron; Model rbegb

Lx Ly Lz Tx Ty Tz U1 U2

f req (ν,̅ cm−1), Grüneisen and Eigenvector 71.3(0.9) 77.9(1.2) 86.7(1.2) 120.9(2.0) 3.19(0.41) 3.19(0.41) 3.19(0.41) 0.197(17) −0.145(27) −0.688(10) −0.557(22) 0.399(12) −0.251(15) −0.079(17) −0.157(26) −0.337(10) −0.306(15) 0.070(17) 0.087(27) −0.086(12) 0.139(26) −0.686(12) 0.683(10) 0.685(15) −0.461(23) 0.141(24) 0.395(18) −0.457(25) −0.746(15) −0.068(31) 0.007(12) 0.062(10) 0.070(15) 0.071(9) −0.105(19) −0.003(4) 0.041(9) 0.122(13) 0.153(21)

ϵ (×10−4) N1 C1 C2 O1 O2 −3(1)

1(1) 0(1)

3(1) 1(1) 11(2)

−2(5) 154(7)

5(5) 12(5) 170(9)

2(4) 170(7)

−2(4) −4(7) 122(6)

H1 H2 59(7)

H3 H4 H5 74(5)

GooF

R (%)

2.65

5.74

Observations: 570 Restraints: 12 Parameters: 57

Figure 4. PEANUT45 plots showing difference displacement parameters 10 × (Uobs − Ucalc) of α-glycine from SPring-8 (50−298 K) and neutron diffraction (18 and 288−323 K); positive differences shown with solid lines and negative differences with dashed lines. Axes shown are the molecular coordinate system for normal-mode analysis, see text for more details.

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Table 3. Lattice Vibration Frequencies of α-Glycine from Various Techniques lattice vib freq (ν̅, cm−1) 71.3, 77.9, 86.7, 121 147, 157, 169 53, 74, 109, 164, 183, 199 52, 73, 109, 162, 190 50, 69, 107, 154, 190 51, 73, 109, 160, 190 53, 75, 111,182 56, 75, 118, 150 52, 74, 110, 163, 180, 198 92, 150, 186 90, 143, 172 71, 101, 119, 136, 149, 170, 190 75, 98, 114, 140, 147, 162, 184 42, 76, 100, 115, 129, 146, 160, 176

technique

T (K)

sample

ref

ADP-analysis on X-ray (SPring-8) and neutron ONIOM(B3LYP/6-311+G(2d,p):PM3) Raman spectroscopy polarized Raman polarized Raman (N-deuterated) Raman spectroscopy polarized Raman Raman spectroscopy Raman spectroscopy far-IR far-IR neutron scattering neutron scattering (C-deuterated) neutron scattering (N-deuterated)

18−323

single crystal cluster model single crystal single crystal single crystal single crystal single crystal single crystal polycrystalline powder powder polycrystalline polycrystalline polycrystalline

this work this work 46 47 47 48 49 50 51 52 52 53 53 53

298 298 298 298 298 60 300 76 298 20 20 20

C, N, and O atoms, but similar differences for the H atoms at the higher temperatures. Glycine is a relatively small molecule with substantial hydrogen bonding and limited mobility in the crystal lattice. Thus only four normal modes have a frequency low enough to be significantly excited in the temperature range covered by the diffraction data and to be reasonably determined from the temperature dependence of the ADPs. On the whole the four lattice frequencies obtained from SPring-8−neutron ADPs (71.3, 77.9, 86.7, 121 cm−1) agree with those from spectroscopies46−53 (Table 3). The comparison has to be taken with a grain of salt though, because for the spectroscopic frequencies an assignment in terms of eigenvectors is not available in contrast to the normal modes from ADPs which are characterized by both frequencies and eigenvectors. ADPs from IAM and invariom refinements of the KEK data were also tested against the four normal mode models mentioned above. All four models explain the ADPs from KEK less well than those from SPring-8. The fitting results of model rbeg to the KEK invariom ADPs are given as Supporting Information. 4.3. Internal Vibration Frequencies from ONIOM Calculation. The ONIOM(B3LYP/6-311+G(2d,p):PM3) method applied to the 15-molecule cluster provides 30 vibrational frequencies (147−3304 cm−1), mostly internal modes. Averaging the ratios of observed to calculated vibrational frequencies from the 24 highest energy modes gives a scaling factor of 0.982 that is similar to the values proposed by Scott and Radom.54 Although the calculated frequencies agree reasonably well with those from spectroscopy55 (see the Supporting Information, Table 4S), the caveat mentioned in section 4.2 applies here as well. 4.4. Thermodynamic Functions. The four temperaturedependent vibration frequencies from normal-mode analysis of combined X-ray−neutron data and the 26 highest (mostly internal) vibration frequencies from the ONIOM calculation are used together with the Einstein23 and Debye24 models of heat capacity to estimate the specific heat Cv. In the absence of information on the temperature-dependent compressibility, the difference between Cp(T) and Cv(T) has been approximated with the Nernst−Lindemann relation,25 which is based on two quantities, namely the melting point (182 °C for glycine) and a universal constant (1.63 × 10−2 K mol cal−1). This relation has been successfully applied to polymers and macromolecules.56 Clearly, Cp, Svib, and Hvib from ADP analysis are in good

and 288−323 K fall into line smoothly with the SPring-8 data. Furthermore, both the ADPs and unit cell constants from the SPring-8 experiment vary more smoothly with temperature. We therefore prefer the SPring-8 results. The combined X-ray data from SPring-8 and neutron data covering 18−323 K are subsequently used for normal-mode analysis. 4.2. Dynamics in the Crystal from Normal Mode Analysis. Four simple models of motion were fitted to two sets of multitemperature ADPs for normal-mode analysis with the program NKA:42 Model 1 (rb), a simple rigid body model corresponding to a multitemperature TLS analysis;43,44 model 2 (rbe), which includes internal vibration effects (in terms of 3 ϵ tensors, one for non-H atoms; one for the methylene hydrogen atoms H1, H2, and one for the ammonium hydrogen atoms H3, H4, H5; the local coordinate systems of these tensors are given in the Supporting Information); model 3 (rbeg), which includes anharmonic effects accounted for by a single Grüneisen constant; and model 4 (rbegb), which includes torsional oscillations of the NH3 and CO2 groups (U2 and U1 in Table 2). The two sets of ADPs that were tested and reported here are the following: set 1, the ADPs from invariom refinement of the SPring-8 data; and set 2, the ADPs from the neutron diffraction data and from the invariom refinement of the SPring-8 data. The molecular coordinate system for normalmode analysis is defined with the x-axis along the vector O1··· N1, the z-axis orthogonal to the plane defined by the vectors along the vectors O1···N1 and C2···C1, and the y-axis orthogonal to the x- and z-axes and completing a right-handed system (Figure 4). Table 2 shows results of the normal-mode analyses. Whereas the ADPs from invariom refinements are best fitted by the model rbeg, the combined ADPs from SPring-8 and neutron diffraction are best fitted by the model rbegb. Clearly, the presence of neutron data not only improves the data/parameter ratio and the goodness of fit, but also provides a more reasonable Grüneisen constant and well-defined ϵ of the Hatoms that are consistent with those from ONIOM calculations: 58, 142, 159 × 10−4 Å2 for H1, H2; and 69, 248, 158 × 10−4 Å2 for H3, H4, H5 (diagonal elements). The value of 248 × 10−4 Å2 for H3, H4, H5 is significantly larger than that derived by normal-mode analysis (170 × 10−4 Å2) where a significant part of the torsional motion is found in the third and fourth normal mode of Table 2. The PEANUT plots45 in Figure 4 show small magnitudes and random distribution of the difference displacement parameters for the 8097

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agreement with those from calorimetric measurements,1 particularly in the temperature range 80−260 K (Figure 5). The present findings compare well with analogous results for molecular crystals of HMT, naphthalene, and anthracene.26

Hvib, and Svib, all of them in satisfactory agreement with calorimetric measurement. Variable-temperature diffraction data of the β- and γ-glycine modifications have also been collected and data analysis is in progress. Normal mode analysis of the multitemperature ADPs from all three glycine polymorphs will hopefully enable us to gain a better understanding of the differences in molecular motion between the polymorphs and its influence on their relative thermodynamic stabilities. The present results of α-glycine also show that while it is now straightforward to determine accurate molecular geometries reproducibly, it is still quite difficult to do the same for ADPs, even at state-of-the-art synchrotron sources. For the common temperatures of 250 and 298 K the non-H bond lengths from the experiments at KEK-PF and SPring-8 are very comparable; the maximum difference is 3.7 ± 0.8 × 10−3 Å for the O1−C2 bond. In contrast most of the differences in the ADPs are significant.

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ASSOCIATED CONTENT

S Supporting Information *

Information on data processing and normal-mode analysis. This material is available free of charge via the Internet at http:// pubs.acs.org. Crystallographic information files (CIFs) have been deposited with the Cambridge Crystallographic Data Centre, CCDC nos. 849660−849671 (synchrotron) and 865358 (neutron). Copies of this information may be obtained free of charge from the Director, Cambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK (fax +44-1223-336033; e-mail [email protected] or via: www. ccdc.cam.ac.uk).

Figure 5. Thermodynamic functions of the α-glycine polymorph: (a) molar heat capacity and (b) vibrational entropy and enthalpy (without zero point contributions).

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AUTHOR INFORMATION

Corresponding Author

*Tel.: + 66-2-2187584. Fax: + 66-2-2541309. E-mail: [email protected].

5. SUMMARY High-resolution, multitemperature synchrotron and neutron diffraction in the temperature range 10−298 K of the α-glycine polymorph have been collected at the KEK photon factory (PF), SPring-8, and ILL. The aim of the experiments was to study molecular motion in the crystal and to subsequently derive thermodynamic functions of the α-glycine polymorph. We summarize this study as follows: The non-H atom ADPs are slightly improved by employing multipole refinement based on an invariom model to deconvolute thermal motion from the nonspherical part of the valence electron density. Combining the ADPs from neutron diffraction (18 and 288−323 K) with those from SPring-8 (50−298 K) provides useful additional information for the normal-mode analysis, anisotropic H-atom ADPs in particular. The dynamics of the α-glycine polymorph in the temperature range of 10−323 K observed by diffraction experiments are sufficiently parametrized with a model (rbegb) of four (mostly) rigid-body modes including a Grüneisen correction (γ) for anharmonic motion, three temperature-independent terms (ε’s) and torsional oscillations of the NH3 and CO2 groups. The vibration frequencies from ADP analysis and the (mostly) internal vibration frequencies from an ONIOM(B3LYP/6311+G(2d,p):PM3) calculation generally agree with those from spectroscopy. They are used with the Einstein, Debye, and Nernst−Lindemann models of heat capacity to calculate Cp,

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the Synchrotron Light Research Institute of Thailand (GRANT 1-2550/PS07), the National Research University Project (FW657B) from the Office of the Higher Education Commission, Ministry of Education and the Thai Government Stimulus Package 2 (TKK2555). We thank Dr. Akiko Nakao at KEK-PF, Dr. Yoshiki Osawa at SPring-8, and Dr. Silvia Capelli at ILL for help in data collection and processing.

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