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Investigating the Anharmonicity of Lattice Vibrations in Water-Containing Molecular Crystals through the Terahertz Spectroscopy of L-Serine Monohydrate Matthew D. King, William D. Buchanan, and Timothy M. Korter* Department of Chemistry, Syracuse UniVersity, 1-014 Center for Science and Technology, Syracuse, New York 13244-4100 ReceiVed: June 11, 2010; ReVised Manuscript ReceiVed: August 2, 2010
The influence of cocrystallized H2O molecules on the terahertz (THz) spectra and corresponding computational treatment of hydrated molecular crystals was investigated in the study of protonated and deuterium-substituted L-serine · H2O. The THz spectra of both solids have been measured in the range of 10 to 90 cm-1, with simulations of the crystalline structure and THz vibrational modes performed using solid-state density functional theory. Significant and systematic overestimations of the predicted vibrational frequencies were observed in all calculations. Evidence provided by the comparison of the experimental and calculated vibrational frequencies for both the protonated and deuterated L-serine · H2O solids indicates the presence of significant anharmonicity in the observed lattice vibrations. The results suggest that vibrational anharmonicity may play a much larger role in the interpretation of the THz spectra of hydrates in contrast to their corresponding anhydrous forms. 1. Introduction Terahertz (THz) spectroscopy is remarkably sensitive to the three-dimensional arrangement of molecules in crystalline solids.1,2 The features observed in THz spectra are the result of the low-frequency intermolecular vibrational motions (e.g., hindered translations and rotations) of the molecules in the solid state and therefore are direct measures of the interactions that are present between the crystal constituents. This sensitivity has played a central role in the development of THz spectroscopy as an analytical tool for the detection and identification of crystalline polymorphs with particular attention drawn to pharmaceutical applications.3-6 Variations in structure can be affected by factors such as temperature, humidity, and solvent conditions and can lead to changes in the physicochemical properties of the material, which are of utmost importance to the pharmaceutical industry.7-9 The rapid detection of these structural changes can be readily accomplished with THz spectroscopy. Hydrates are common variations of solid-state structures in which water molecules are explicitly incorporated into the periodic crystal structure. The incorporation of water molecules into the crystal structure of pharmaceuticals must be monitored since the hydrate form can be easily created or destroyed during the manufacturing process, and the crystalline hydrate often has drastically different physical properties in comparison to the anhydrous form.10 Detection of cocrystallized waters is not easily accomplished since many analytical techniques (e.g., midinfrared spectroscopy) are unable to differentiate between cocrystallized waters and those that are simply surface wetting the sample. However, these cocrystallized waters will typically greatly alter the crystal structure thereby completely changing the lattice vibrations that form the basis of solid-state THz spectroscopy, making THz techniques particularly responsive to crystalline hydrates. While the hydration and relaxation dynamics of water in large biosystems studied by THz spectroscopy has recently gained * To whom correspondence should be addressed. E-mail: tmkorter@ syr.edu.
interest,11-14 small molecular solids containing cocrystallized water have been the focus of only a few studies.15-18 The inclusion of water molecules in a molecular solid alters the intermolecular contacts and the hydrogen bonding strengths governing lattice vibrations, as well as the possibility for additional low-energy vibrational modes arising from purely external motions of the water molecules. It is important to understand the behavior of these intermolecular interactions through networked H2O molecules in order to properly evaluate the underlying vibrational motions contributing to the observed THz spectra. The understanding of these lattice vibrations can be accomplished by combining experimental THz spectroscopic results with first-principles solid-state simulations of molecular structure and vibrations.19-21 This comparative approach also reveals the varying computational treatments required between hydrated and anhydrous systems, as the vibrational frequencies in solid-state simulations are typically calculated within the harmonic limit, whereas the true vibrational motions of some systems, such as hydrates, may be quite anharmonic in nature. In this study, the influence on the THz spectrum from water molecules cocrystallized with the small biomolecule L-serine was investigated. The THz absorption spectra of L-serine · H2O and deuterium-substituted L-serine · H2O were measured in the range of 10 to 90 cm-1. These experimental results were then compared with the detailed computational simulations of the solid-state structure and THz vibrational frequencies performed using solid-state density functional theory (DFT) with periodic boundary conditions. Comparisons of equivalent computational treatments between the hydrated and anhydrous forms of L-serine can be made using the previously reported THz study of anhydrous L-serine.22 While some DFT studies on the THz spectra of water-containing molecular crystals have been reported,18,19,23 little consideration has been given to the influence of the relatively large contributions of the H2O molecules to the total vibrational motions. The systematic overestimation of vibrational frequencies of L-serine · H2O in the DFT simulations as compared to the accurate prediction of the anhydrous L-serine THz spectrum can be attributed to significantly increased anharmonicity of lattice vibrations involving motions of coc-
10.1021/jp105384x 2010 American Chemical Society Published on Web 08/17/2010
Terahertz Spectroscopy of L-Serine Monohydrate
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TABLE 1: Crystallographic Data Summary for L-Serine · H2O at 97 K empirical formula f.w. crystal system space group a (Å) b (Å) c (Å) R (deg) β (deg) γ (deg) V (Å3) Z µ (mm-1) T (K) λ (Å) R1a wR2b
C3H7NO3 · H2O 123.11 orthorhombic P212121 4.7987(4) 9.3063(9) 12.1460(11) 90 90 90 542.42(8) 4 0.140 97(2) 0.71073 0.0277 0.0758
a R1 ) ∑|F0| - |Fc|/∑|F0|. b wR2 ) ∑[w(F02 - Fc2)2]/∑[w(F02)2]1/2; w ) 1/[σ2(F02) + (aP)2 + bP]; P ) [max(F02,0) + 2Fc2]/3.
rystallized H2O molecules. Analogous results were obtained in the comparative DFT investigations of solid-state oxalic acid and oxalic acid dihydrate, where the vibrational frequencies of the dihydrate form were similarly overestimated by a variety of density functionals.15 Additional evidence of vibrational anharmonicity can be found in the analysis of the THz spectrum of deuterated L-serine · H2O. The discrepancies between the experimental and calculated shifts in vibrational energies upon isotopic substitution provide insight into the anharmonicity in the lattice vibrations of these strongly hydrogen bonded systems. 2. Experimental Procedure Experimental spectra were recorded using a home-built timedomain pulsed THz spectrometer based on an amplified Ti:Sapphire femtosecond laser system. ZnTe crystals were used for generation of THz radiation by optical rectification24 and detection by free-space electro-optic sampling.25 A detailed description of the THz spectrometer has been reported elsewhere.26 L-Serine (g99%) was purchased from Sigma-Aldrich and used without further purification. L-Serine monohydrate crystals were grown from a saturated H2O solution cooled to 5 °C. Deuterium substitution was performed by successively recrystallizing L-serine in D2O (Sigma-Aldrich, 99.9%) five times in the same manner. All crystal structures were verified by singlecrystal X-ray diffraction crystallography. X-ray crystallographic measurements of L-serine · H2O at 97 K were performed on a Bruker-AXS SMART-CCD diffractometer using a graphite monochromated MoκR radiation source (λMoκR ) 0.71073 Å).27 Corrections for Lorentz and polarization effects and absorption were made using SADABS.28 The structures were solved by direct methods. All non-hydrogen atoms were refined anisotropically. After locating all heavy atoms, the model was refined against F2 using both isotropic and anisotropic thermal displacement parameters. Non-hydrogen bonding hydrogen atoms were introduced in calculated positions and refined isotropically, while hydrogen atoms involved in hydrogen bonding were located on the difference map and refined isotropically. Neutral atom scattering coefficients and anomalous dispersion corrections were taken from the International Tables for Crystallography, Vol. C.29 All calculations were performed using SHELXTL crystallographic software packages.30,31 The crystallographic details are summarized in Table 1.
Figure 1. Atomic labeling scheme for L-serine · H2O.
The degree of deuterium substitution of L-serine · H2O was examined by mid-IR spectroscopy, which showed the carbonbound hydrogen atoms did not transfer as evident by the presence of adsorptions in the C-H stretching and bending regions. These nonsubstituted hydrogen atoms are labeled H1, H5, and H6 in Figure 1, which shows the atomic labeling scheme adopted for descriptions throughout. All other protons of the serine and H2O molecules were exchanged. Only having partial deuteration of the serine molecule (referred to as d6-Lserine · H2O hereafter) is of lesser importance in the investigation into the affects of isotopic substitution on lattice vibrations, as this leads to less than a 3% difference in mass of the serine molecule. However, deuterium-substituted H2O molecules constitute an 11% increase in mass over protonated water molecules. This larger modification of molecular mass makes the significance of isotopic substitution more apparent in lattice vibrations involving substantial external motions of water molecules. Serine samples were mixed with polytetrafluoroethylene (PTFE) powder at a concentration of approximately 3% by mass and pulverized using a stainless-steel ball mill (Dentsply Rinn 3110-3A) to minimize particle size and reduce both Mie scattering and crystal anisotropy. Approximately 0.55 g of the sample mixtures were pressed into pellets under a pressure of 2000 psi using a hydraulic press (ICL EZ-Press 12) equipped with a 13-mm stainless steel die, giving final pellet dimensions of 13 mm × 2.2 mm. Pure PTFE pellets for use as “blank” references were prepared in the same manner. The samples and blanks for measurement were held in a cryostat (Janis Research Systems) equipped with 3-mm thick polymethylpentene windows. Data was acquired at 293 and 78 K with samples under vacuum. Samples and blanks were scanned 32 times and data averaged for each individual data set. A 32 ps scan window consisting of 3200 data points was used to capture the THz waveform, which was then symmetrically zero-padded to a total of 6000 data points for the data transforms. The effective instrument resolution arising from the 32 ps scan length was approximately 1.0 cm-1. The ratio of the power spectra obtained from the Fourier-transformed data sets of the sample and blank yields the THz absorption spectrum. Each THz spectrum presented in this work is the average of four individual THz spectra, each representing a complete set of sample and blank measurements. 3. Theoretical All DFT calculations on solid-state L-serine · H2O were performed using the CRYSTAL06 software package.32 Calculations were performed utilizing the B3LYP33,34 and PW9135
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Figure 2. (a) Unit cell and (b) crystal packing arrangement of L-serine · H2O.
density functionals with the atom-centered triple-ζ 6-311G(d,p) basis set.36 Atomic positions used for subsequent normal mode calculations were optimized within the constraints of fixed unit cell parameters and space group symmetries determined by X-ray crystallographic measurements. To meet the total energy convergence criteria of ∆E < 10-8 hartree for geometry optimizations and ∆E < 10-11 hartree for normal mode calculations, a shrinking factor of 6 was used to specify the sampling rate as a function of k points used for calculating the density matrix and the commensurate grid in reciprocal space.37,38 A total of 387 253 grid points were used in each calculation, with the radial and angular distribution defined by a pruned (75 974) integration grid. Truncation tolerances used for Coulomb and HF exchange integral series were set to 10-6, 10-6, 10-6, 10-6, and 10-12 hartree. Frequencies of normal modes were calculated within the harmonic approximation by numerical differentiation of the analytical gradient of the potential energy with respect to atomic position.39 The IR intensities for normal modes were calculated from the dipole moment derivatives (dµ/dQ) determined using well-localized Wannier functions of the unit cell to calculate the Born charge tensors.39,40 Vibrational mode descriptions were based on visual inspection of the atomic displacements for each normal mode and reported with 25% precision. Percent contributions from mixed internal and external motions cannot be determined at higher precision using numerical methods given the nature of the rectilinear displacements reported for the normal mode calculations. Percent contributions from motions of H2O molecules to the total atomic displacements within each mode were calculated from the sums of the displacement vectors for both the H2O and serine molecules and reported with 1% precision. 4. Results and Discussion 4.1. Experimental Section. 4.1.1. X-ray Crystallography. The X-ray crystallographic data for crystalline L-serine · H2O at 97 K are given in Table 1. The unit cell and crystal packing arrangement of L-serine · H2O are depicted in Figure 2. The unit cell was determined to be orthorhombic with space group P212121, matching that of previously published room-temperature structures.41,42 The unit cell dimensions are slightly contracted from those of the room-temperature cell, with a ) 4.7987 Å, b ) 9.3063 Å, c ) 12.1460 Å. There is no indication of a phase transition upon cooling. X-ray structural determination of deuterium-substituted d6-L-serine · H2O confirmed a crystal structure that was isomorphous to the protonated L-serine · H2O crystal. Supplemental crystallographic data for L-serine · H2O (CCDC 780565) can be obtained free of charge from The Cambridge Crystallographic Database.43
Figure 3. Terahertz spectra of (a) L-serine · H2O and (b) d6-Lserine · H2O at 78 K (solid) and 293 K (dashed).
4.1.2. Terahertz Spectroscopy. The experimental THz spectra from 10 to 90 cm-1 of L-serine · H2O at 78 and 293 K are shown in Figure 3a. In the 293 K spectrum, only one fully resolved absorption feature centered at 66.9 cm-1 is present, with an additional absorption at higher frequency that cannot be fully resolved within the experimental bandwidth. Upon cooling to 78 K, five absorption features become evident. The most intense absorption at 67.5 cm-1 correlates with the single resolved peak seen in the room-temperature spectrum shifted to slightly higher energy. The decrease in populated vibrational states leads to the narrowing of the observed peaks. This decrease in line width enables the observation of the additional peaks at 51.5, 75.7, 82.5, and 88.1 cm-1 which are now clearly resolved. The origins of the most notable additional feature at 82.5 cm-1 may be due to the red-shifting of this mode upon cooling, which is typically not observed between room temperature and cryogenic temperatures, or may be due to a large variation in absorption
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TABLE 2: Terahertz Vibrational Frequencies of L-Serine · H2O and d6-L-Serine · H2O Observed at 78 K in the Experimental Range of 10 to 90 cm-1, and the Observed Frequency Shift (∆ν)
TABLE 3: Calculated Bond Lengths (Å), Bond Angles (deg), and RMSD Values for L-Serine · H2O Compared to Experimental X-ray Values exp
vibrational frequencies (cm-1) L-serine · H2O
d6-L-serine · H2O
∆ν
51.5 67.5 75.7 82.5 88.1
51.1 66.7 75.3 82.0 87.0
-0.4 -0.8 -0.4 -0.5 -1.1
intensity resulting from temperature-induced changes in unit cell dimensions and hence alterations in charge localization and normal coordinates. Likewise for the feature observed at 88.1 cm-1, where there is an apparent red-shift of this mode from the broad absorption band seen in the room temperature spectrum. The small feature at 51.5 cm-1 appears in the 78 K spectrum as a result of the narrowing of the primary absorption band at 67.5 cm-1. Similar results were observed in the THz spectra of d6-Lserine · H2O (Figure 3b). Both the 78 K and the 293 K spectra resemble that of L-serine · H2O with the absorptions shifted to lower energies due to the increased molecular masses. The most notable exception to this trend is the shoulder on the high-energy absorption in the 293 K spectrum, which gives rise to either the 82.0 or 87.0 cm-1 feature in the 78 K spectrum. An additional shoulder at the base of the highest intensity peak at 66.7 cm-1 is also present in the d6-L-serine · H2O spectrum which is not present in the L-serine · H2O spectrum. Comparison between the vibrational frequencies observed in the 78 K spectra of L-serine · H2O and d6-L-serine · H2O is given in Table 2. Only the highest-energy feature exhibits a mass-induced shift greater than 1.0 cm-1. Accurate estimations of the smaller shifts were accomplished by determining peak centers through least-squares fitting of Lorentzian lineshapes to the spectral features. The overlay of the 78 K THz spectra of L-serine · H2O and d6-Lserine · H2O is shown in Figure 4. There is noticeable asymmetry in the highest-intensity absorption feature in both the protonated and deuterated L-serine · H2O, although more pronounced in the protonated L-serine · H2O. Although less evident in the d6-Lserine · H2O spectrum, analysis of the line shape demonstrates slight asymmetry on the higher-energy side of the peak. This
Figure 4. Overlay of the THz spectra of L-serine · H2O (solid) and d6-L-serine · H2O (dashed) at 78 K.
B3LYP
PW91
C1-C2 C1-O1 C1-O2 C2-C3 C2-N C3-O3
Bond Lengths 1.5300 1.53243 1.2558 1.25948 1.2556 1.25590 1.5243 1.52807 1.4926 1.49040 1.4219 1.42072 RMSD 0.0026
1.53413 1.27009 1.26496 1.52996 1.49221 1.42370 0.0076
C1-C2-C3 C1-C2-N C2-C1-O1 C2-C1-O2 C2-C3-O3 C3-C2-N O1-C1-O2
Bond Angles 111.0930 111.52048 110.5187 111.26521 118.7320 119.08045 115.8944 115.85634 111.1157 112.69578 111.5460 112.78929 125.3683 125.05038 RMSD 0.8457
111.54279 111.77948 119.36348 115.89746 112.94953 112.76175 124.72733 1.0311
asymmetry may be a result of anharmonicity in the vibrational motion or due to the additive combination of nearly coincident vibrational modes. 4.2. Theoretical. 4.2.1. Structural Analysis. The calculated bond lengths and bond angles for L-serine · H2O obtained from solid-state DFT calculations are provided in Table 3 and compared with those of the experimental X-ray structure. Rootmean-squared deviations (RMSDs) are given for a quantitative evaluation of the performances of each functional to reproduce the experimentally determined molecular structure. Structure optimizations were performed for L-serine · H2O within the constraints of fixed unit cell parameters supplied by the X-ray crystallographic data. Structure optimizations for d6-Lserine · H2O were not performed as isotope-induced changes to the electronic structure are negligible, and the optimized L-serine · H2O structures were therefore used in subsequent normal mode calculations for both the protonated and deuterated solids. The B3LYP calculations performed best in reproducing the molecular structure of L-serine · H2O in terms of both bond lengths and angles. This same outcome was obtained in the previously published anhydrous L-serine structural optimizations performed using the 6-311G(d,p) basis set.22 The RMSD of the L-serine · H2O bond lengths was 0.0026 Å for the B3LYP calculations, compared to 0.0076 Å for the PW91 calculations. The bond lengths were generally overestimated in calculations by both functionals. The largest deviations occurred in the C1-O1 and C1-O2 double bonds of the carboxylate group in the PW91 calculations, with overestimations of 0.0143 Å and 0.0094 Å, respectively. The L-serine · H2O bond angle RMSDs were 0.8457° and 1.0311° for the B3LYP and PW91 functionals, respectively. The majority of bond angles were overestimated in both calculations with the largest deviations occurring in the C2-C3-O3 bond angle involved in the positioning of the hydroxyl side group of the serine molecule. The RMSD values obtained for L-serine · H2O are nearly double those calculated for anhydrous L-serine at the same level of theory, although similarly large overestimations of the C2-C3-O3 bond angle were also observed.22 The discrepancies between bond angle RMSDs of anhydrous L-serine and L-serine · H2O may be attributed to the increased conformational freedoms of the hydrogen bonding network through the cocrystallized H2O molecules, such that the intramolecular structure of the serine
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TABLE 4: Calculated Hydrogen Bond Heavy Atom Distances (Å) and RMSDs for Crystalline L-Serine · H2O Compared with Experimental X-ray Values hydrogen bonda
exp
B3LYP
PW91
O1 · · · N(H3) O1 · · · N(H4) O2 · · · O3(H7) O2 · · · OW(HW1) O3 · · · OW(HW2) OW · · · N(H2) OW · · · N
2.8901 2.7438 2.7468 2.8059 2.8358 2.8782 2.9346 RMSD
2.90590 2.74572 2.79429 2.74654 2.80028 2.84804 2.95387 0.0333
2.90961 2.73421 2.71354 2.79469 2.79471 2.80303 3.03258 0.0450
a Hydrogen bond heavy atoms. Hydrogen atom involved in H-bond given in parentheses next to donor atom.
molecules is influenced by the intermolecular hydrogen bonding interactions that may be less accurately reproduced by the theory. As the THz spectrum is primarily influenced by hydrogen bonding contacts within the crystal structure of strongly hydrogen-bonded systems such as L-serine · H2O, it is important to evaluate the structural reproduction of these intermolecular contacts. Provided in Table 4 are the heavy-atom hydrogen bond distances and RMSDs compared with the experimental X-ray values. Calculated hydrogen bond distances and angles, however, cannot be directly compared to the experimental structure, as hydrogen positions are not accurately determined by X-ray crystallography. Each serine molecule is involved in ten hydrogen bonds, six of which are unique, with both H2O molecules and neighboring serine molecules. There exists two of each O1 · · · H3-N, O1 · · · H4-N, and O2 · · · H7-O3 hydrogen bonds per serine molecule, one with the molecule acting as the hydrogen donor and for the other as a hydrogen acceptor. These six hydrogen bonds involve only serine-serine contacts. The remaining four hydrogen bonds listed in Table 4 involve serine-H2O contacts and occur only once per molecule. The OW · · · N contact is not a direct hydrogen bond involving a single hydrogen but the collective interaction of an H2O oxygen atom with three approximately equidistant amine hydrogens. The molecules are arranged in the unit cell in alternating layers of serine and H2O molecules, with layers lying in the a-b plane (Figure 2b). The RMSDs for the calculated hydrogen bond heavy atom distances show that the B3LYP functional performed best overall in the reproduction of intermolecular geometry with a value of 0.0333 Å, compared to 0.0450 Å produced in the PW91 optimization. In the B3LYP calculations, all serine-serine contacts were overestimated while the serine-H2O hydrogen bonds were underestimated. The PW91 calculation underestimated all but two heavy atom separations as compared to the experimental structure, with the largest deviations involving serine-H2O contacts. The contrasting capacities for the reproduction of intermolecular geometry by the B3LYP and PW91 functionals is evident in the L-serine · H2O system and stems from the variations in the ability to model long-range van der Waals interactions. While strong static hydrogen-bonding interactions are effectively represented by both functionals, weaker van der Waals interactions contributing to the overall attractive forces are not. It has been shown in studies of van der Waals complexes that the PW91 functional may exhibit false attractive interactions, while B3LYP demonstrates the inability to model weak long-range intermolecular contacts.44,45 In the L-serine · H2O system, these tendencies lead to the overestimation of the majority of hydrogen
TABLE 5: Changes in Unit Cell Dimensions (Å), Volume (Å3), and Total Unit Cell Energy (kJ mol-1) for Full Geometry Optimizations of L-Serine · H2O Compared To Experimental X-ray Crystallographic Data a b c V E
B3LYP
PW91
0.0470 0.0530 0.4543 29.07 -6.81
0.0120 -0.0261 0.4822 21.37 -2.59
bond distances in the B3LYP calculations, and the general underestimation of hydrogen bond distances in the PW91 calculations due to the additional artificial lowering of the potential energy minima describing the intermolecular bonding interactions. 4.2.2. Unit Cell Optimizations. Complete optimizations of the L-serine · H2O unit cell were performed that allow for all lattice constants to freely optimize within the constraints of the preservation of space group symmetry. This allows for the comparison of total unit cell energies between fixed-geometry and full-geometry optimizations in order to evaluate the deficiencies in long-range van der Waals interactions in the DFT models applied to molecular crystals. The neglect of appropriate van der Waals interactions leads to potential energy surfaces with greater repulsive character, resulting in the net expansion of the unit cell upon full optimization. An absolute determination of these deficiencies in interaction energies is not obtainable in these calculations, as some basis set superposition error (BSSE) is present in calculations using the 6-311G(d,p) basis set.46 However, comparison of the full unit cell optimizations may provide useful insight into performances of the exchange and correlation functionals in modeling intermolecular interactions despite small BSSE contributions. Percent changes in unit cell dimensions and volume, and total changes in unit cell energy for the full unit cell optimizations, are given in Table 5. In the calculation using the B3LYP functional, expansion of the unit cell occurred along all axes. The largest expansion was observed along the c-axis, which underwent a 3.74% change corresponding to a change of only 0.4493 Å. Much smaller relative changes were seen along the a- and b-axes with increases in length of 0.98% and 0.57%, respectively. The PW91 calculation yielded similar results with an expansion of 3.97% along the c-axis and 0.25% along the a-axis. However, a slight contraction of 0.28% was observed along the b-axis in the PW91 optimization. The relatively small changes in cell dimensions along the a- and b-axes are due to the hydrogen bonding configuration. The majority of hydrogen bonding interactions are serine/serine contacts along the a and b coordinates of the unit cell. Less hydrogen bonding interactions are present between molecules along the c-axis, resulting in the larger increase in cell length along that coordinate given the deficiencies of van der Waals forces in the calculations. The results for both the B3LYP and PW91 calculations demonstrated the overall increase in unit cell volume. Correlated to the increase in volume is the decrease in total unit cell energy. Increases in L-serine · H2O unit cell volume upon full optimization were 5.36 and 3.94% for the B3LYP and PW91 calculations, respectively. This corresponds to decreases in total unit cell energies of 6.81 and 2.59 kJ mol-1 for the respective functionals. The difference in energies between the hybrid and GGA functionals arises from the varying abilities of the functionals to treat long-range interactions as previously mentioned. This same trend in full-optimization unit cell energies
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TABLE 6: Frequencies (cm-1), Intensities (km mol-1), and Symmetries of Calculated IR-Active Vibrational Modes for L-Serine · H2O and d6-L-Serine · H2O L-serine · H2O
B3LYP
d6-L-serine · H2O PW91
B3LYP
frequency shifta
PW91
mode
symmb
expc
freq
intend
freq
inten
exp
freq
inten
freq
inten
exp, ∆cm-1
B3LYP, ∆cm-1
PW91, ∆cm-1
a b c d e f g h i
B1 B3 B2 B3 B1 B3 B2 B1 B3
51.5 67.5 75.7 82.5 88.1 -
61.0 72.9 80.1 82.3 91.5 98.9 101.5 105.8 107.6
0.34 20.24 0.29 4.80 35.98 5.66 4.64 16.59 32.14
60.6 71.0 73.3 81.9 88.5 96.2 99.2 101.4 109.5
0.45 22.68 0.18 2.86 33.50 4.65 5.69 20.25 36.76
51.1 66.7 75.3 82.0 87.0 -
59.6 70.9 78.8 81.3 89.7 96.4 98.4 102.3 103.7
0.36 19.23 0.18 4.60 34.66 8.12 6.24 13.62 26.61
59.1 69.1 72.0 80.8 86.8 93.6 96.6 98.1 105.6
0.49 21.48 0.13 2.87 32.23 6.31 7.99 18.00 31.17
-0.4 -0.8 -0.4 -0.5 -1.1 -
-1.4 -2.0 -1.3 -1.0 -1.9 -2.5 -3.1 -3.5 -3.9
-1.4 -1.8 -1.2 -1.0 -1.7 -2.6 -2.6 -3.3 -3.9
RMSD RMSD (scalede)
8.6 2.9
7.0 3.4
7.7 3.0
6.0 3.4
a Shift in frequency for d6-L-serine · H2O compared with frequencies for L-serine · H2O. b Symmetry. c Experimental. d Intensity. e RMSDs with applied frequency scalars for L-serine · H2O of 0.925 and 0.950 for B3LYP and PW91 calculations, respectively, and for d6-L-serine · H2O of 0.941 and 0.965 for B3LYP and PW91, respectively.
has been observed in previous studies of hydrogen-bonded molecular crystals employing both hybrid and GGA functionals.15,22 The contraction of the b-axis in the PW91 full optimizations, in contrast to the expansion along this coordinate in the B3LYP full optimization, further shows the difference in the modeling of van der Waals interactions by hybrid and GGA functionals. The small changes in unit cell energies seen in the full optimizations demonstrates that hydrogen bonding, which is effectively modeled by DFT methods, is the dominant interaction governing the packing arrangement of the molecules within the unit cell. The relatively minor changes along all axes suggest that hydrogen bonding interactions are well represented within the unit cell despite the underestimation of weaker van der Waals interactions. However, these small changes in unit cell dimensions can have a large influence on calculated vibrational frequencies and intensities. Without the accurate prediction of all intermolecular interactions, full optimizations provide unit cell geometries that are not physically reasonable; thus, fixedcell optimizations were used for subsequent normal mode calculations. 4.2.3. Simulated THz Spectra and Vibrational Mode Assignment. The experimental (10-90 cm-1) and calculated (
