ARTICLE pubs.acs.org/JPCA
Importance of Accurate Spectral Simulations for the Analysis of Terahertz Spectra: Citric Acid Anhydrate and Monohydrate Matthew D. King, Eric A. Davis, Tiffany M. Smith, and Timothy M. Korter* Department of Chemistry, Syracuse University, 1-014 Center for Science & Technology, Syracuse, New York 13244-4100, United States
bS Supporting Information ABSTRACT: The terahertz (THz) spectra of crystalline solids are typically uniquely sensitive to the molecular packing configurations, allowing for the detection of polymorphs and hydrates by THz spectroscopic techniques. It is possible, however, that coincident absorptions may be observed between related crystal forms, in which case careful assessment of the lattice vibrations of each system must be performed. Presented here is a THz spectroscopic investigation of citric acid in its anhydrous and monohydrate phases. Remarkably similar features were observed in the THz spectra of both systems, requiring the accurate calculation of the low-frequency vibrational modes by solid-state density functional theory to determine the origins of these spectral features. The results of the simulations demonstrate the necessity of reliable and rigorous methods for THz vibrational modes to ensure the proper evaluation of the THz spectra of molecular solids.
1. INTRODUCTION Lattice vibrations of molecular crystals occur at terahertz (THz) frequencies and are incredibly sensitive to the intermolecular contacts of the crystal system.1 Variations in crystalline materials composed of identical molecules, such as polymorphs and hydrates, typically exhibit unique THz vibrational spectra due to their distinct three-dimensional structures, contrary to that observed in the mid-IR spectra where vibrations are dependent on intramolecular geometries.2,3 This makes THz spectroscopy a valuable technique for analyzing crystalline solids for the detection of changes in crystal phase. In some instances, however, it is possible that similar systems may give rise to coincident spectral features. Presented in this study is such an example where the anhydrous and hydrated forms of crystalline citric acid produce quite similar THz absorption spectra. In such occurrences, it is necessary to possess the capability to accurately calculate these low-frequency vibrational motions in order to discern the proper chemical identities of the systems by determining the underlying physical origins of the absorption features. Solid-state density functional theory (DFT) has been proven to be a dependable approach for the accurate determination of THz vibrational frequencies for a variety of molecular crystals.4 11 The high-quality results of DFT methods are unparalleled by other computational approaches, such as rigid molecule and force-field calculations.12,13 Although other methods may be adequate for the approximation of lattice vibrational energies, they lack the chemical accuracy to correctly represent the complex physical interactions responsible for absorptions in the THz region. In order to replicate the mixed intra- and intermolecular motions of lattice vibrations, molecules must be allowed full conformational freedom and possess the appropriate r 2011 American Chemical Society
intermolecular forces that are relevant to the system under investigation. The generalized models used for rigid molecule and force field calculations lack the necessary flexibility and specificity to properly model these critical intermolecular interactions. Solid-state DFT accommodates these necessary requirements and offers a more complete physical model of periodic crystalline systems. The conventional DFT model, which is unable to adequately model dispersion interactions, can be enhanced by the incorporation of corrections for London-type dispersion forces.14 17 The inclusion of these forces has been shown to increase the reliability of structural and THz spectral simulations for chemical identification. Presented here is a comparative investigation of citric acid (CA) and citric acid monohydrate (CM) by THz spectroscopy and solid-state DFT. CA is a well-known biological molecule that is important as an intermediate in metabolic processes. This weak organic acid is also a commonly used commercial additive in food products and cleaning agents. CA crystallizes from aqueous solution in one of two stable forms depending on the crystallization conditions: as the anhydrous phase in the monoclinic P21/c space group, or as an orthorhombic monohydrate form in the P212121 space group.18,19 The different spatial arrangements of the citric acid molecules in these two crystal forms suggest that each should have a distinct THz spectrum. In fact, the CM spectrum consists of multiple features, several of which coincide with the primary features of the CA spectrum. Without a definitive treatment of these two systems by computational methods, Received: May 22, 2011 Revised: August 25, 2011 Published: September 16, 2011 11039
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Table 1. Observed Experimental THz Absorptions (in cm 1) for CA and CM at 293 and 78 K CA
CM
293 K
78 K
293 K
78 K
56.4
57.2
42.9
46.7
77.0
74.0
74.4
57.5
79.9
73.9 79.7a 82.4 88.0
a
Peak center determined by line shape analysis.
it would not be clear whether the analogous absorptions originate from lattice vibrations of the CM solid, or if the CM sample contains some quantity of the anhydrous CA phase due to dehydration of the CM crystals. DFT methods allowed for comprehensive analyses of both the CA and CM crystal structures and THz spectra to be achieved. The THz spectra of CA and CM were recorded from 10 to 90 cm 1 at 293 and 78 K (Table 1), and the spectra were simulated using solid-state DFT with periodic boundary conditions. The room temperature spectra of both CA and CM have been separately reported; however, no attempts were made to compare the systems or analyze the THz vibrational modes.20,21 Analysis of the spectra by DFT methods showed that all absorptions in the CM spectra could be accounted for by the normal mode calculations. These two systems containing citric acid represent a unique case in which two different crystal structures produced similar THz spectra. The results demonstrate the need for robust computational methods in the analysis of THz spectral data and the ability of solid-state DFT to provide the required level of accuracy.
2. EXPERIMENTAL PROCEDURE CA (no. 251275) and CM (no. C7129) were purchased from Sigma-Aldrich and used without further purification. Single-crystal X-ray crystallographic measurements of CM at 90 K were performed on a Bruker-AXS SMART-CCD diffractometer using a graphite monochromated Mokα radiation source (λMokα = 0.71073 Å). Corrections for Lorentz and polarization effects and absorption were made using SADABS.22 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.23 All calculations were performed using SHELXTL crystallographic software packages.24,25 The crystallographic data for CM at 90 K are available as Supporting Information. Powder X-ray diffraction (PXRD) measurements of CA and CM were obtained using a Rigaku D2000 Bragg Brentano diffractometer equipped with a copper rotating anode, a diffracted beam monochromator tuned to Cukα radiation, and a scintillation detector. Data were collected over a range of 2 50°
2θ as a continuous scan of 2° 2θ min 1. The resulting diffraction data were analyzed using MDI Jade 9.0 software.26 Experimental THz spectra were obtained using a time-domain pulsed THz spectrometer based on an amplified Ti:Sapphire femtosecond near-infrared laser system. ZnTe crystals were used for generation of THz radiation by optical rectification27 and detection by free-space electro-optic sampling.28 A detailed description of the THz spectrometer has been reported elsewhere.9 Samples for THz measurements were mixed with polytetrafluoroethylene (PTFE) powder at a concentration of approximately 2% by mass and pulverized using a stainless-steel ball mill (Dentsply Rinn 3110 3A) to minimize particle size. Approximately 0.55 g of the sample mixtures were pressed into pellets under a measured pressure of 2000 psi (∼10,000 psi at sample) 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 zeropadded 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. Fourier transforms were performed using a Hanning window. 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 were performed using the CRYSTAL09 software package.29,30 Calculations utilized the PBE density functional31 with the atom-centered cc-pVDZ basis set.32 Calculations incorporated an empirical dispersion correction term of the form C6/R6, and are denoted as PBE-D throughout.33,34 Initial atomic positions and lattice parameters were taken from experimentally determined crystal structures. All lattice dimensions were allowed to relax during structural optimizations within the constraint of preserving imposed space group symmetry. Parameters for the dispersion correction term were taken from ref 32 and modified according to Civalleri et al.35 for the application of dispersion corrections in the calculations of molecular crystals. The functional-dependent global dispersion scalar (s6) of the dispersion term was modified for each system to best reproduce the experimental lattice dimensions. This approach has been demonstrated in previous studies to be a reliable method for the accurate reproduction of both crystal structures and THz vibrational frequencies.15,36 An s6 value of 0.54 was used for the CA system, and 0.14 for the CM calculations. Total energy convergence criteria of ΔE < 10 8 hartree was used for geometry optimizations and ΔE < 10 11 hartree for normal mode calculations. Shrinking factors for reciprocal lattice vectors were set to values of 6 to specify the sampling rate as a function of k points in defining the Pack-Monkhorst and Gilat nets.37,38 The number of grid points varied between the calculations of CA and CM depending on their initial optimization 11040
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Figure 2. THz spectra from 10 to 90 cm 1 of (a) CA and (b) CM obtained at 78 K (solid line) and 293 K (dashed line). (c) Overlay of anhydrous CA (red) and CM (blue) THz spectra showing the coincident absorptions between the two different systems. The spectra in panel c are arbitrarily scaled to better show the positions of coincident absorptions.
Figure 1. (a) Molecular structure of CA. Unit cell representations of (b) anhydrous CA and (c) CM.
geometries. The radial and angular distribution of points was 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.39 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.40 The IR intensities for normal modes were calculated from the dipole moment derivatives (dμ/dQ) determined using the Berry phase approach to calculate the Born charge tensors.41
4. RESULTS AND DISCUSSION 4.1. X-ray Crystallography. Input crystal structures for the solid-state DFT calculations were taken from experimentally
determined structures. In order to accurately calculate THz spectra, it is necessary to use lattice dimensions of the crystal structure at a temperature near that which the spectra were recorded. Since no low-temperature crystal structures of CM have been reported, the crystal structure at 90 K was determined by single-crystal X-ray crystallography. The structure was found to be isostructural to the published room-temperature structure, with lattice vectors slightly contracted along all axes due to decreased thermal contributions.19 The crystal system was orthorhombic in space group P212121. The lattice dimensions were a = 6.2343 Å, b = 9.2882 Å, c = 15.246 Å, and α = β = γ = 90°. Additional crystallographic data for CM at 90 K is available as Supporting Information. A low-temperature crystal structure for CA (CCDC 635772) was obtained from the Cambridge Crystallographic Database.42 The lattice parameters of CA at 150 K are a = 11.438 Å, b = 5.580 Å, c = 12.664 Å, β = 111.45°, and α = γ = 90° in space group P21/c. Representations of the CA molecule and the unit cells for CA and CM are shown in Figure 1. PXRD measurements of CA and CM were taken to examine whether dehydration of CM might occur due to mechanical grinding during preparation of the samples for THz measurements. The ground CA and CM samples were shown to be pure, with no evidence of dehydration of the CM. This was also verified 11041
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The Journal of Physical Chemistry A by thermal gravimetric analysis, confirming a 1:1 molar ratio of citric acid to water in the CM sample. The PXRD patterns for both CA and CM could be completely indexed, which showed that each contained only a single crystal phase. The PXRD patterns of CA and CM are available as Supporting Information. 4.2. THz Spectroscopy. The THz spectra from 10 to 90 cm 1 of CA and CM were obtained at 293 and 78 K (Figure 2). The room temperature spectrum of CA showed two absorptions centered at 56.4 and 77.0 cm 1 (Figure 2a). The absorption at 77.0 cm 1 is quite broad and asymmetric resulting from multiple overlapping absorptions made apparent in the spectrum collected at 78 K. At low temperature, the line widths are narrowed as a result of the reduction of sequence bands due to thermally populated vibrational states, revealing underlying spectral features. In the CA spectra, the absorption at 77.0 cm 1 splits into two peaks located at 74.0 and 79.9 cm 1. The absorption at 56.4 cm 1 in the room temperature spectrum is shifted to 57.2 cm 1 in the 78 K spectrum. A possible fourth feature became noticeable at about 40 cm 1, although this weak absorption could not be accurately located by peak fitting due to its low signal-to-noise ratio. The resolvable features are observed to shift to higher energies upon cooling due to the constriction of lattice dimensions between these temperatures. The THz spectrum of CM is similar to that of CA at room temperature, displaying two broad absorptions at 42.9 and 74.4 cm 1 (Figure 2b). The spectrum is consistent with the previously reported room-temperature THz spectrum of CM.21 Decreasing the sample temperature revealed several additional spectral features. Four features at 73.9, 79.7, 82.4, and 88.0 cm 1 are uncovered from the single absorption at 74.4 cm 1 in the room-temperature spectrum. The asymmetry of the high intensity peak is due to the nearly coincident absorptions at 79.7 and 82.4 cm 1 as determined by least-squares fitting of the spectrum with Lorentzian line shapes. A peak is also observed at 57.5 cm 1 that is not apparent at room temperature. The two different crystal systems displayed marked similarities in their THz spectra. The three spectra features observed in the 78 K CA spectrum can seemingly be easily correlated, albeit incorrectly, by location and intensity to features present in the CM spectrum (Figure 2c). The initial comparison of the experimental THz spectra raises suspicions concerning the purity of the CM sample, that it may contain some quantity of CA due to dehydration during sample preparation. It cannot be determined based solely on experimental evidence that the THz spectrum of CM is in fact a product of lattice vibrations within the CM crystals. Therefore, proper analysis of the CA and CM THz spectra is dependent on the ability to accurately simulate these THz spectra by computational methods. Without knowledge of the origins of these similar absorption features, one might also assume they are a product of similar molecular motions of the CA molecules contained in both systems. These absorptions, however, result from different lattice vibrational motions, and the analogous locations and intensities are merely a coincidence. 4.3. Theoretical. 4.3.1. Structural Analysis. The crystal structures used for normal mode calculations were first optimized within the total energy convergence criteria. The qualities of structural reproductions by the DFT methods were evaluated by examining the root-mean-squared deviations (RMSDs) of bond lengths, bond angles, and hydrogen bond distances between the calculated and experimental crystal structures. The full-geometry optimizations using PBE-D yielded unit cell geometries for CA and CM in high agreement with the experimentally determined
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Figure 3. Simulation of the terahertz spectra of anhydrous CA. Lorentzian line shapes with an empirically determined full width at half-maximum (fwhm) of 2.5 cm 1 were convolved into the calculated vibrational modes.
Table 2. Frequencies, Intensities, and Vibrational Characters of the Calculated IR-Active Vibrational Modes (
