Identification and Quantification of Polymorphism in the

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ARTICLE pubs.acs.org/ac

Identification and Quantification of Polymorphism in the Pharmaceutical Compound Diclofenac Acid by Terahertz Spectroscopy and Solid-State Density Functional Theory 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, United States

bS Supporting Information ABSTRACT: Polymorph detection and quantification in crystalline materials is a principle interest of the pharmaceutical industry. Terahertz (THz) spectroscopy can be used for such analytical applications since this technique is sensitive to the intermolecular interactions of molecules in the solid state. Understanding the fundamental nature of the lattice vibrational motions leading to absorptions in THz spectra is challenging, but may be achieved through computational approaches. In this study, the THz spectra of two diclofenac acid polymorphs were obtained by THz spectroscopy, and the vibrational characters of the observed absorptions were analyzed using solid-state density functional theory (DFT). The results demonstrate the quantitative capacity of THz spectroscopy and the reliability and utility of solid-state DFT in the calculation of low-frequency vibrational motions.

T

he rapid identification of polymorphs in crystalline solids is a primary concern of the pharmaceutical industry as the matter of polymorphism carries with it many implications in product development, marketing, and patent legalities.1
3 Nearly all pharmaceutical compounds exhibit polymorphism, and the associated physicochemical properties, such as solubility, stability, and bioavailability, are influenced by these variations in crystal structure.4 The engineering of high-volume synthesis procedures in drug manufacturing processes often poses challenges for maintaining the production of the target polymorph, and therefore, continuous analysis of the synthesis products is required. Developing better techniques to monitor these products and to reliably detect the presence of undesired polymorphs or impurities at low concentrations is a persistent focus of the industry. One such analytical technique that is gaining considerable attention as a promising method for polymorph detection is terahertz (THz) spectroscopy. The THz region of the electromagnetic spectrum is considered the frequencies ranging from 0.1 to 10 THz (3 to 333 cm
1). The majority of crystalline solids contain characteristic lattice vibrations within this frequency range, making THz spectroscopy a powerful analytical tool for probing the intermolecular interactions of molecular crystals.5,6 Potential applications of THz spectroscopy in the pharmaceutical industry have been demonstrated in studies regarding the quantification of drug dosage forms,7,8 the identification of polymorphs and racemic mixtures,9
13 the monitoring of phase transitions and dehydration processes,14
16 and the analysis of drug tablet coatings.17,18 Despite the expansion of research in these areas, understanding r 2011 American Chemical Society

the THz spectra of crystalline solids and uncovering the complex vibrational motions giving rise to absorptions in this region remains a daunting task. In order to utilize THz spectroscopy for the identification of crystal variants, there must be a fundamental understanding of the physical origins of the THz spectra. Computational methods have been demonstrated to be reliable approaches for the simulation of THz spectra, particularly in revealing the chemical basis of these low-frequency vibrational motions. Technological innovation has increased the accessibility of high-level computational resources for the study of increasingly complicated systems. Many theoretical methodologies have been applied in the attempt to interpret the THz spectra of molecular systems, only few of which are sufficient for adequately representing solid-state systems and describing the complex dynamics of lattice vibrations. Some of these methods include rigidmolecule approximations,19 isolated-molecule calculations,20 empirical force field methods,21 and solid-state density functional theory (DFT).21
23 Although far less computationally demanding, it has been clearly demonstrated that isolated-molecule calculations cannot dependably reproduce THz spectra due to the neglect of all intermolecular interactions that are the primary contributors to absorptions in this region.24,25 Rigid-molecule approaches may be able to accurately calculate vibrational modes strictly intermolecular in nature, but are unable to predict Received: February 1, 2011 Accepted: April 11, 2011 Published: April 11, 2011 3786

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Analytical Chemistry energies of vibrations containing mixed internal and external motions, such as most vibrational motions observed at THz frequencies. For large molecular systems, it has been shown that THz spectra may be reasonably calculated using force field methods, although this approach has many downfalls due to the overgeneralization and limited transferability of computational parameters.26 A more robust theoretical treatment that better represents the intermolecular and intramolecular contributions governing lattice vibrational motions is that of solidstate DFT. Although requiring greater computational resources, solid-state DFT has been shown to reproduce crystalline structures and THz spectra with accuracy unparalleled by other methods.13,24,25,27 With continued refinement of the application of DFT to molecular crystals, these methodologies serve as a valuable analytical tool in conjunction with experimental approaches. In this study, two monoclinic polymorphs of the commonly used nonsteroidal anti-inflammatory drug diclofenac acid were analyzed by THz spectroscopy and solid-state DFT with periodic boundary conditions. The sensitivity of THz spectroscopy for the identification and quantification of crystalline samples containing one or more polymorphs is demonstrated. The THz spectra showed distinct differences between the polymorphs due to the differences in crystal packing arrangements and intermolecular interactions. Using the spectra of the individual polymorphs, the THz spectra of samples containing a mixture of polymorphs could be quantified to determine the relative abundances of each crystal form. The THz spectra were also simulated using solidstate DFT to obtain descriptions of the vibrational motions leading to the observed THz absorptions. The simulated spectra were in excellent agreement with the experimental THz spectra. This research demonstrates the potential application of THz spectroscopy in an analytical pharmaceutical setting and provides important information to the ongoing evaluation of the application of computational methods in the detailed analyses of the lattice dynamics of molecular solids.

ARTICLE

Figure 1. (a) Atomic labeling scheme for diclofenac acid. (b) Hydrogen-bonded diclofenac acid dimer.

’ RESULTS AND DISCUSSION X-ray Crystallography. The Form I unit cell at 99 K was found to be monoclinic with the space group P21/c. Lattice dimensions were a = 8.3229(13) Å, b = 10.7529(17) Å, c = 14.717(1) Å, β = 92.872(3)°, and R = γ = 90°. Four molecules make up the unit cell (Z = 4), with one molecule in the asymmetric unit (Z0 = 1). The diclofenac acid molecules form dimers that are hydrogen bonded through the carboxyl moieties (Figure 1). The two molecules making up the dimer are constitutional isomers that are mirror images of one another. The dimers are bound in the solid state by dipole
dipole and dispersion interactions. The unit cell of Form II at 98 K was also monoclinic, but with Z = 8 (Z0 = 1) and space group C2/c. Dimensions of the unit cell were determined to be a = 20.0965(14) Å, b = 6.8944(5) Å, c = 19.8443(14) Å, β = 109.7390(10)°, and R = γ = 90°. The same dimer conformation as in Form I was also present in Form II, however, with a different packing arrangement of the dimers in the C-centered Form II unit cell. These data agree with previously reported room temperature structures28 but show contraction along all lattice dimensions for the cryogenic structures. The X-ray crystallographic data and unit cell representations for the diclofenac acid polymorphs Forms I and II are available in the Supporting Information.

Figure 2. (a) Terahertz spectra of diclofenac acid Form I at 78 K (solid) and 293 K (dashed). (b) Terahertz spectra of diclofenac acid Form II at 78 K (solid) and 293 K (dashed).

Terahertz Spectroscopy. The 78 and 293 K THz spectra from 10 to 90 cm
1 of Forms I and II are shown in Figure 2. The observed vibrational frequencies for the 293 and 78 K spectra of both polymorphs are given in Table 1, with peak centers determined by least-squares fitting of the experimental features with Lorentzian line shapes. Each polymorph produced a distinct 3787

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Analytical Chemistry

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Table 1. Experimental Terahertz Absorption Frequencies (cm
1) between 10 and 90 cm
1 for Diclofenac Acid Forms I and II Form I

Form II

293 K

78 K

293 K

78 K

26.7

29.6

24.6

26.2

34.7

36.1

37.9

41.2

40.0

43.5

47.2

50.6

44.7

48.5

57.1 70.1a

57.4 66.6

62.8 71.8

74.4

80.4

84.3

70.3

79.7 86.5 a

88.7

Peak center determined by line shape analysis.

THz vibrational spectrum as a result of the differences in intramolecular forces governing the crystalline packing arrangement. While the room temperature spectra are adequate to differentiate between the two polymorphs, not all THz vibrational modes contributing to these spectra can be resolved due to the broad absorptions. Narrowing of the absorption features is achieved by cooling the samples to 78 K, which reduces the spectral linewidths by reducing excited vibrational state populations and sequence band transition intensities and reveals the presence of underlying vibrational modes otherwise undetectable in the room temperature spectra. Obtaining THz spectra at cryogenic temperatures is not only important for a more accurate differentiation between polymorphic forms, but also necessary for the proper assignment of vibrational modes and the thorough evaluation of the quality of THz spectral simulations. The different diclofenac acid polymorphs displayed characteristic THz spectra both at room temperature and at 78 K. The 293 K THz spectrum of Form I revealed five apparent absorptions located at 26.7, 37.9, 47.2, 70.3, and 86.5 cm
1 (Figure 2a). Other spectral features are noticeable, but their low signal-tonoise ratio prevents the confirmation of these absorptions as distinguishable vibrational modes. The 78 K THz spectrum reveals a total of seven prominent peaks at 29.6, 41.2, 50.6, 57.1, 74.4, 79.7, and 88.7 cm
1 resulting from the reduced baseline and peak width. Two additional features are evident as a shoulder on the low-frequency side of the peak centered at 70.1 cm
1, and a very low-intensity peak at 34.7 cm
1. There is a notable blue shift of the vibrational frequencies between the room temperature and 78 K spectra as a result of the contraction of the unit cell volume upon cooling. The blue shifting of lattice vibrational frequencies with reduced temperature has been well documented in previous THz studies, with very few exceptions.23,27,29 In the room temperature spectrum of Form II, there are six easily distinguishable features located at 24.6, 40.0, 44.7, 57.4, 66.6, and 80.4 cm
1 (Figure 2b). These vibrational modes are shifted to higher energies in the 78 K spectrum with frequencies centered at 26.2, 43.5, 48.5, 62.8, 71.8, and 84.3 cm
1. An additional spectral feature becomes visible at 36.1 cm
1 in the 78 K spectrum as the baseline is reduced. The apparent absorption intensities of the vibrational modes in the spectra of both polymorphs are increased at cryogenic temperatures due to the narrowing of the peaks; however, the integrated intensities of the peaks are nearly conserved between the room

Figure 3. Overlay of the 78 K terahertz spectrum of a polymorph mixture of diclofenac acid with the spectra of diclofenac acid Forms I and II. The dashed line indicates the residual of the polymorph mixture THz spectrum minus those of the individual polymorphs.

temperature and 78 K spectra. In both the Form I and Form II THz spectra, the broad features observed below 20 cm
1 are attributed to sampling artifacts resulting from the low dynamic range of the instrument in this low-frequency range. Crystallization procedures for diclofenac acid, as with most pharmaceutical compounds, can often lead to mixtures of the multiple polymorphs. Shown in Figure 3 is the THz spectrum obtained from a single-batch mixture of both Form I and Form II polymorphs overlaid with the THz spectra of the individual polymorphs. In comparing this spectrum to the THz spectra of the individual polymorphs, it is clear that the THz spectrum of the mixture is a linear combination of the individual spectra of the two polymorphs. The dashed line in Figure 3 represents the residual of the THz spectrum of the polymorph mixture after subtraction of the individual polymorph spectra. This suggests that the Form I and Form II polymorphs crystallize independently and are not involved in any significant cross-interactions that would influence the observed THz spectra. Because the THz spectra of mixed polymorphs are additive of the individual components, the relative quantities of the different polymorphic forms in a mixture can readily be determined analytically. In order for the relative peak intensities to be accurately estimated between spectra, a reasonable method for baseline subtraction must be adopted. The rising baseline present in all THz spectra is in large part due to scattering of radiation.30
33 Given the typically unknown distribution of particle sizes in a sample after preparation, and the broad distribution of radiation wavelengths in the target THz bandwidth, a definitive equation for the precise scattering processes at work cannot be properly expressed. However, fitting the experimental spectra with Lorentzian line shapes on an arbitrary exponential background of form I = Aνb was shown to produce quality fits of the HD spectra. In this equation, I is the scattering intensity, A is a scalar accounting for the particle size distribution, ν is the radiation frequency, and b is the exponential factor influencing the frequency dependence of the scattering intensity. The value for b of 3.3 was found to produce the highest-quality fit of the spectra for both polymorphs and the mixture. This value cannot be explicitly described by any one physical scattering process; however, this represents a composite value of all scattering 3788

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Analytical Chemistry

Figure 4. Overlay of experimental 78 K terahertz spectrum of diclofenac acid polymorph I (Form I) with the spectrum simulated using solidstate DFT. (a) Simulation of THz spectrum with vibrational frequencies as calculated. (b) Simulation with applied frequency scalar of 0.955.

processes (i.e., Rayleigh, Mie) simultaneously occurring for all samples without regard for the particles size distribution. The same optimal exponent value of 3.3 was obtained in a detailed study by Shen et al.30 on the THz scattering effects of granulated materials. The THz spectra in Figure 3 were analyzed by performing least-squares routines that fit Lorentzian line shapes to the experimental spectral features while simultaneously fitting an exponential baseline. The procedure was completed independently for the THz spectra of the individual polymorphs and for the mixture. By this method, it was determined that the relative quantities of each polymorph giving rise to the THz spectrum of the polymorph mixture were approximately 57% (( 6.2%) of Form I and 45% (( 4.8%) of Form II. For this approach to be applicable, it is necessary to have high-quality THz spectra of each pure polymorphic form. The accuracy of the quantification of polymorph mixtures will be dependent on several factors including the number of possible polymorphs contained in the mixture, the complexity of each polymorph spectrum, and the proximity of the absorptions (i.e., coincident absorptions by two or more polymorphs). Any of these factors may influence the quality of the fitting procedure and the associated errors. In addition, the possibility of unknown polymorphs may lead to further difficulties in quantifying polymorph mixtures. In such cases, it may be possible to reveal the presence of unknown polymorphs through the computational simulations of the THz spectra of known polymorphic components. Simulated THz Spectra and Mode Assignments. The THz spectra for the diclofenac acid polymorphs Forms I and II simulated by solid-state DFT are shown in Figures 4 and 5, respectively. The frequencies and intensities of the calculated modes (