Published as part of a special issue of selected papers presented at the 8th International Workshop on the Crystal Growth of Organic Materials (CGOM8), Maastricht, Netherlands, September 15-17, 2008
CRYSTAL GROWTH & DESIGN 2009 VOL. 9, NO. 6 2713–2718
Spotting Conglomerates by Second Harmonic Generation Arnaud Galland,† Valerie Dupray,*,† Benjamin Berton,† Sandrine Morin-Grognet,† Morgane Sanselme,‡ Hassan Atmani,† and Ge´rard Coquerel‡ La2B, EA 3233 Centre UniVersitaire d’EVreux, 1 rue du 7e`me Chasseurs - BP 281, F-27002 EVreux Cedex, France, and Unite´ de Croissance Crystalline et Mode´lisation Mole´culaire, EA3233 UniVersite´ de Rouen, F-76821 Mont-Saint-Aignan Cedex, France ReceiVed December 14, 2008; ReVised Manuscript ReceiVed March 9, 2009
ABSTRACT: Detection of conglomerates by using second harmonic generation (SHG) effect is comprehensively reviewed. The fundamentals together with the possibilities and the limitations are detailed. An experimental set up is described and the application of this high throughput prescreening technique is exemplified using (()-trans-1,2-diaminocyclohexane salts. Introduction In the past two decades, the demand of the pharmaceutical industry for pure enantiomers has been in constant development. The main reason is the increasing pressure of regulatory authorities for chiral drugs to be administered in an enantiomerically pure form. Besides enantioselective synthesis, crystallization techniques are commonly used to achieve the resolution of racemic mixtures. The conventional Pasteurian method1 is the most popular way, but the resolution can also be carried out by preferential crystallization2 if the racemic mixture or accessible derivatives such as salts solvated or not crystallize as a stable conglomerate (i.e., a mechanical mixture of single crystals containing homochiral molecules only). However, this condition is a serious limitation to the application of preferential crystallization since it is admitted that only 5%-10% of molecular compounds crystallize as conglomerates.2 Spotting a conglomerate is even more beneficial since (i) an optimized recrystallization can “virtually” be carried out without any loss of enantiomeric excess.3,4 (ii) When coupled to racemization, almost pure enantiomers can be obtained by attrition from the racemic mixture.5 Various methods are commonly used to identify conglomerates (X-ray diffraction, IR spectroscopy, Raman spectroscopy, solid-state CD,6 CD microscopy7), but they are often time-consuming and require access to the pure enantiomer. Indeed, they consist of comparing spectroscopic data obtained with the racemic mixture and the pure enantiomer. Consequently, there is a need for a faster and cheaper method of screening compatible with a combinatorial approach of crystallization of derivatives (salts, solvates, cocrystals, etc.). For this purpose, nonlinear optics and especially second harmonic generation (SHG) seem promising. In this work, we present the principle of conglomerate detection by using SHG. The potential of a prescreening via SHG and the advantages and drawbacks of this technique are discussed. An example is treated with the prescreening of conglomerates on (() trans* To whom correspondence should be addressed. Phone: +33 (2) 32 39 90 82. E-mail:
[email protected]. † La2B, EA 3233 Centre Universitaire d’Evreux. ‡ UC2M2, EA3233 Universite´ de Rouen.
1,2-diaminocyclohexane (DACH) salts. One enantiomer of DACH is of interest for pharmaceutical applications since it is a key component of an anticancer drug.8 This molecule can also be used as a ligand9 and in numerous asymmetric syntheses. It has been found that DACH crystallizes as a conglomerate10 below -10 °C (space group P21212). Nevertheless, a derivative offering also a complete chiral discrimination in the solid state but with a higher melting (or decomposition) point will be more suitable in terms of resolution. Principle of Conglomerate Prescreening Using SHG. To understand how SHG can be used to detect conglomerates, let us first recall some facts about packing of chiral molecules. Dealing with this subject implies making a distinction between the chirality of the molecule itself and the chirality of the crystal structure in which the molecule crystallizes. Indeed, the chirality of a crystal structure depends on its symmetry group. It is also important to distinguish between non-centrosymmetry and chirality. If a chiral object is obviously non-centrosymmetric, the opposite is not necessarily true. Recall that chiral crystals belong to point groups that contain only symmetry operations of the first kind (rotation, translation). Non-centrosymmetric crystals belong to point groups that can also contain symmetry operations of the second kind (rotoinversion). Usually, crystal structures can be classified into three types: CA, NA, and NC: 11
Type CA: centrosymmetric (achiral) structures (point groups: 1j, 2/m, mmm, 4/m, 4/mmm, 3j, 3jm, 6/m, 6/mmm, m3, and m3m) Type NA: non-centrosymmetric achiral structures (point groups: m, mm2, 4j, 4mm, 4j2m, 3m, 6j, 6 mm, 6jm2, and 4j3m) Type NC: non-centrosymmetric chiral structures (point groups 1, 2, 222, 4, 422, 3, 32, 6, 622, 23 and 432) A racemic mixture can crystallize in three different types of packing: (i) The racemic compound (formerly called racemate) is a mixture of crystals that contain both enantiomers in equal proportion. Racemic compounds are the most common racemic species and represent 90-95% of them. They can crystallize in any space group (CA, NA, or NC), but 95% of the known racemic compounds crystallize in centrosymmetric space groups
10.1021/cg801356m CCC: $40.75 2009 American Chemical Society Published on Web 05/14/2009
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Table 1. Formation of Crystalline Structures from Racemic Mixtures achiral structure
racemic compound 90-95% conglomerate 5-10% solid solution less than 1%
structure proportion predominant space groups structure proportion predominant space groups structure
CA centrosymmetric achiral
NA non-centrosymmetric achiral
NC non-centrosymmetric chiral
permitted ∼95% P21/c, C2/c, Pbca and P1j forbidden 0%
permitted 4.5-5% Pna21, Pca21, Cc, and Pc forbidden 0%
permitted
permitted
permitted 0.02% P212121 and P21 permitted 100% P212121, P21, C2 and P1 permitted
(CA).12 The most popular space groups are P21/c, C2/c, Pbca, and P1j (98% of the centrosymmetric racemic compounds).12 Non-centrosymmetric racemic compounds (NA) represent a proportion of almost 4.5-5%, predominantly in space groups Pna21, Pca21, Cc, and Pc. This is the case for example of DLallyglycine.12 Only in rare occasions11 (0.02%), racemic compounds crystallize in chiral space groups (mainly P212121 and P21), like ortho-thyrosine, R-methylsuccinic acid, or camphoroxime.2,13,14 (ii) The conglomerate (5-10% of the racemic species) is an equimolar mechanical mixture of crystals; each one contains only a single enantiomer. The chiral nature of the molecules imposes restriction on the construction of the crystalline structure, so it is impossible to form achiral crystal structures by crystallization of enantiomerically pure chiral molecules.2,15 Consequently, conglomerates crystallize only in one of the 65 chiral space groups (spaces groups P212121, P21, C2, and P1 represent 95% of the known conglomerates).16 (iii) The racemic solid solution is the rarest type (below 1% of the racemic species). It is a solid solution containing an equal number of molecules of each enantiomer, but contrary to the racemic compound, the arrangement is a random distribution. The three crystal types are permitted, but no data seem available about the predominant space groups in the case of racemic solid solution. These possibilities for the crystallization of racemic mixtures are summarized in Table 1. Considering the low occurrence of racemic compounds crystallizing in non-centrosymmetric structures (less than 5% for NA + NC) a method that would detect the absence of center of symmetry in crystals obtained from racemic mixtures will be able in most cases to detect conglomerates. This is why SHG is of great interest. In the following, we will describe the principle of SHG. Propagation of light into any medium is driven by dielectric properties and response to an electromagnetic field. When an electromagnetic field (light) is applied to a molecule, the shape of the electronic cloud is modified. Consequently, an induced electric dipole moment is generated. On a macroscopic scale, the term polarization (dipole moment per unit volume) is used. It is defined as
P ) ε0χ(1)E
(1)
with E, the applied electric field, ε0 is the vacuum permittivity, and χ(1) the linear (first order) susceptibility of the material. The linear susceptibility is a second rank tensor related to the permittivity ε and the refractive index n of the material:
ε ) n2)ε0(1 + χ(1))
chiral structure
(2)
Such a linear response can only occur if the electric field remains weak. When the intensity of light becomes greater than 1 MW/cm2, the polarization becomes a nonlinear function of
the applied electric field and can be described as a power series expansion of the macroscopic field:
P ) ε0(χ(1)E + χ(2)E2 + χ(3)E3 + ...) ) ε0χ(1)E + PNL (3) with χ(2) and χ(3) the second and the third order susceptibility tensors respectively and PNL, the nonlinear polarization. This equation means that during the propagation of light at a frequency ω, nonlinear components of the polarization at frequencies 2ω and 3ω are generated giving rise to harmonics of the original optical field at 2ω and 3ω. Note that the susceptibility coefficients decrease rapidly with increasing order. Consequently, in most cases the nonlinear polarization PNL can be approximated by the quadratic term ε0 χ(2) E2. Neglecting terms higher than two, consider the case of a beam of frequency ω propagating through a crystal. The associated electromagnetic field is
1 E ) E0 exp[j(ωt - k·r)] + c.c 2
(4)
where E0 is the amplitude and k is the wave vector, and c.c is the complex conjugate of the formula. The electric field gives rise to a polarization:
P ) ε0χ(1)E + ε0χ(2)E2 P)
{
(5)
1 ε χ(2)E20 + ε0χ(1)E0 exp[j(ωt - k·r)] + 2 0 1 (2) 2 ε χ E0 exp[2j(ωt - k·r)] + c.c (6) 2 0
}
Finally, the net polarization has three components: a continuous component corresponding to the phenomenon of optical rectification,17 a component at frequency ω (optical polarizability), and a second harmonic term (frequency 2ω) corresponding to the phenomenon known as SHG.18 In SHG, a fundamental wave of amplitude Eω, angular frequency ω (wavelength λ), and wave vector kω passing through a crystal generates a second harmonic wave of amplitude E2ω, angular frequency 2ω (wavelength λ/2), and wave vector k2ω. The second harmonic amplitude varies with the distance traveled through the crystal. So the amount of second harmonic generated can be determined by solving the propagation equation given by
∇2E - µ0ε0
∂ 2E ∂ 2P ) µ0 2 2 ∂t ∂t
(7)
where µ0 is the permeability of free space. The average intensity of an electromagnetic wave of amplitude E is I ) (E · E*)/(2 ε0 c) where c is the velocity of light. Assuming that the waves are traveling in the z direction and that the conversion efficiency is low (so amplitude of the
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fundamental is almost unchanged), the second harmonic intensity after a distance l through the crystal is given by Armstrong: 19
ω2(χ(2))2l2 I2ω(l) ) 2ε0c3nω2 n2ω
( ∆kl2 ) I ( ∆kl2 )
sin2
2
2 ω
(8)
where nω is the refractive index of the crystal at angular frequency ω; n2ω is the refractive index of the crystal at angular frequency 2ω; and ∆k is the phase mismatch: ∆k ) k2ω 2 kω ) (2 ω)/(c) (n2ω - nω); Among other parameters, I2ω depends on ∆k. Under certain conditions and for particular materials called “phase-matchable materials”, ∆k can be equal to zero. In this case, the longer the distance traveled inside the crystal, the greater the SHG intensity (i.e., large particles will generate a better SHG signal). A wellknown example of phase-matchable material is potassium diphosphate (KDP) which is used for doubling high power lasers or as a nonlinear standard. But most materials are “non phasematchable” (i.e., ∆k * 0) meaning that the intensity is an oscillating function of l. This function reaches a maximum for the particular value given by
lc )
π λ ) ∆k 4(n2ω - nω)
Figure 1. SHG activity among the 32 crystallographic classes.
(9)
lc is called the “coherence length”. This implies that the SHG intensity will be optimized for particles of size equal to lc or equal to an odd multiple of lc. The consequence of the coherence length will be discussed later, but the most interesting point for the detection of conglomerates is the dependence of I2ω with χ(2), the second order nonlinear susceptibility. χ(2) is a third rank tensor that exhibits 27 electro-optic components, but the number of independent coefficients can be reduced. Indeed, in the particular case of SHG, if the absorption of the material is negligible at ω and 2ω, the tensor is invariant by circular permutation of its three indices20 and the number of independent components is reduced to 10. Moreover, considering the 32 crystallographic classes and their symmetry elements, it is possible to determine the number of independent coefficients non equal to zero. In particular, crystals with a center of inversion will have a null χ(2). Thus, in centrosymmetric structures all the elements of the χ(2) tensor are zero. Consequently, these types of crystals cannot generate a SHG signal. Note that if the symmetry rules of Kleinman are applicable,20 three chiral point groups (NC) present also a null χ(2) (422, 622, and 432). However and fortunately, it has been shown that Kleinman symmetry presents some failures.21 These different possibilities are schematized in Figure 1. Finally, the detection of a SHG signal can be used as a test for the absence of center of symmetry.22-24 Consequently, it was chosen in this study as a prescreening method for spotting conglomerates. The experimental set up proposed by Kurtz and Perry23 gives quick information about the SHG activity of a powder sample. Because the majority of the pharmaceutical crystalline samples are available in the form of powders, we chose to adapt this setup to the predetection of conglomerates. Experimental Section Second Harmonic Generation Setup. Figure 2 shows the experimental setup used for the SHG measurements. The laser is a Nd:YAG Q-switched laser (Quantel) operating at 1.06 µm. It delivers 360 mJ pulses of 5 ns duration with a repetition rate of 10 Hz. An energy adjustment device is made up of two polarizers (P) and a half-wave
Figure 2. Second harmonic generation setup. plate (λ/2). It allows the incident energy to vary from 0 to ca. 200 mJ per pulse. A RG1000 filter is situated after the energy adjustment device to remove light from laser flash lamps. The samples (powdered crystals confined between two microscope slides in sample holders of 8 mm diameter and 1.6 mm depth) were irradiated with 60 mJ pulses with a beam diameter of 4 mm. The signal generated by the sample (diffused light) is collected into an optical fiber (500 µm of core diameter) and directed onto the entrance slit of a spectrometer (Ocean Optics). A boxcar integrator allowed an average spectrum (spectral range 250-700 nm with a resolution of ( 2 nm) to be recorded over 1 s (10 pulses). X-ray Powder Diffraction. Crystalline solid phases were analyzed at room temperature by means of X-ray powder diffraction (XRPD) on a Siemens D5005 apparatus (θ-θ set, fixed slits 1.6 mm) with Cu KR radiation (1.54056 Å) (Kβ filter) under 40 kV and 30 mA and collected on a scintillation detector. The θ angle calibrations were carried out by using Siemens slits and a quartz sample (secondary standard). Preparation of Salts. (() trans-1,2-Diaminocyclohexane was purchased from Acros Organics with a purity grade better than 98% and was used without further purification. (()-DACH salts were obtained from acid-base reactions by addition of an achiral acid and (()-DACH in a solvent. Experiments were performed with 23 acids, stoichiometries 1:1, 1:2, and 2:1 (moles of DACH/mole of acid) and with four different solvents (water, acetone, methyl alcohol, or ethyl alcohol). Acids and solvents were obtained as reagent grade materials and were used without further purification. After a 15 min stirring, homogeneous solutions were left to crystallize by slow evaporation at room temperature. Then, the solutions were filtered to extract the powder and crystals were washed with the chosen solvent and left to dry at room temperature.
Results Two hundred and seventeen experiments have been performed in order to produce DACH-salts. In some cases, crystallization
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Table 2. Detailed Results of SHG Activity for the Salts Obtained with Citric Acid and Oxalic Acida acid
stoichiometry (mole of DACH/mole of acid)
water
ethanol
methanol
citric acid
1:1 1:2 2:1 1:1 1:2 2:1
conglomerate glass glass (I) (II) (III)
conglomerate conglomerate
conglomerate conglomerate
(VI) (VII) (VI)
(VI) (VII) (VI)
oxalic acid
a Data in bold mean SHG signal detected; glass: glassy material (i.e., no crystallization). after the crystallization.
did not occur, so only 181 powders have been collected and submitted to the SHG tests. Fifty-one powders have generated a second harmonic signal with of course a certain redundancy (See Table S1, Supporting Information). Results are detailed below for two particular counterions. Salts obtained with citric and oxalic acids (for several stoichiometries and solvents) have exhibited a high level of positive responses (see Table 2). Consequently, the salts formed with these two acids have been studied preferentially. To conclude on the conglomerate nature of the SHG active crystals, a study of the samples by conventional methods such as a comparison between the XRPD patterns of the racemic salt and that of the corresponding enantiomeric salt is required. In the case of citric acid, a perfect match has been observed between the XRPD patterns of the racemic and the enantiomeric salts (Figure S1, Supporting Information). The hypothesis of a conglomerate formation with citric acid has since been confirmed by single crystal X-ray diffraction. Indeed, the DACH-citrate monohydrate formed in water, methanol, and ethanol crystallizes in the chiral space group P21212 (submitted to Tetrahedron Asymmetry). The thermal dehydration takes place at 180 °C showing the great stability of this hydrate. During the crystallization processes, evaporation of methanol or ethanol under ambient conditions has probably led to an uptake of a sufficient amount of moisture to permit the crystallization of the monohydrate. In the case of oxalic acid, using the three stoichiometries and the four solvents, 12 attempts have been performed by addition of racemic DACH. The XRPD analysis on these salts has demonstrated the existence of seven different phases (labeled I-VII in Table 2). Consequently, one can suspect polymorphism or solvates or more complicated situations described in ref 25. Among these seven different solids, three have generated a SHG signal (III, VI, and VII). X-ray diffractograms obtained for the (+)-DACH oxalates have led to the characterization of two different phases. Thus, in that case, the identification of the conglomerate is complex. Moreover, we have no guarantee that the SHG positive phases are stable. However, the systematic comparison of the XRPD patterns leads us to suspect a conglomerate in the case of phase VI. Discussion Owing to the proportion of conglomerates, it is not crippling to have a limited number of false positive responses. Conversely, it would be extremely awkward to miss one conglomerate. As a consequence, the accuracy of the SHG method will be discussed, and then the influence of the operative conditions of crystallization will be considered. The situations encountered during the SHG tests are reported in the decision diagram in Figure 3. The first part of the diagram (panel a) deals with the samples for which a signal is detected at λ/2. Case 1 corresponds to false positive responses. For some samples, it is possible to observe a “non SHG” signal at λ/2
b
acetone b b b (IV) (IV) (V)
Crystals isolated and submitted to SHG test immediately
Figure 3. (a, b) Detection of conglomerate by using prescreening SHG test: decision diagram.
resulting from optical phenomena such as two-photon fluorescence (TPF) or other photoluminescent processes. For example, a TPF signal could be centered at 532 nm, thus at the same wavelength as the expected SHG signal but its spectral bandwidth will be much broader than that of the SHG signal (cf. Figure 4). A baseline correction around the SHG wavelength (532 nm) allows the distinction between light resulting from the SHG process itself (signal of interest) and “spurious” light.26 So after the acquisition of the spectrum, it is possible to extract the effective value of the SHG signal. Case 2 concerns racemic compounds crystallizing in noncentrosymmetric space groups (NA) which represent a proportion of almost 5% of the crystallized organic compounds.12 Because one cannot totally exclude a tendency of a given racemic mixture to crystallize in non-centrosymmetric space groups, systematic study by conventional methods of the samples that have generated SHG activity has to be pursued. It is worth mentioning that slightly disordered racemic structures also fall into this category.27–29 In the second part of the diagram (panel b), samples that do not present any signal at λ/2 are considered. Case 3 corresponds
Spotting Conglomerates by SHG
Figure 4. Extraction of the effective SHG signal.
to nondetected conglomerates. This can be due to a SHG effect too weak to be detected because of low nonlinear coefficients (i.e., low hyperpolarizability of the molecule) or an inappropriate crystal size distribution. Indeed, the second harmonic field generated by a crystalline powder is the sum of the contribution of each individual particle (electromagnetic fields are uncorrelated). Since each particle is assumed to have arbitrary orientation and the fundamental beam passes through a large number of particles, the intensity of the SHG beam is not easy to optimize and strongly depends on the particle size (especially in nonphase matchable materials where I2ω depends on the coherence length). For most materials, coherence length is on the order of magnitude of several microns; therefore, to preserve the reliability of the method, it is not suitable to work with too fine particles (in particular, submicronic or nanocrystalline powders should be avoided). However, the number of nondetected conglomerates should be limited as the level of detection of the SHG setup is at present close to 1/100 of the SHG signal generated by the quartz powder (standard nonphase-matchable material for SHG measurements). This value is usually considered as an acceptable “zero” reference.22 Another critical situation is materials presenting absorption at the wavelength of irradiation (1064 nm) or at the wavelength of the re-emitted radiation (532 nm) associated or not to a decomposition of the sample during the exposure to the laser beam. In these cases, the use of a tunable laser source, or at least a laser source emitting at an alternative wavelength, will be required. The last case (Case 4) concerns chiral crystals related to point groups 422, 622, and 432 which are SHG inactive24 if Kleinman permutation rules are applicable. Our experience refutes the general applicability of these rules. Indeed, a significant SHG activity has been observed in N-acetylmethylbenzylamine which crystallizes as a conglomerate in space group P41212.30 A last case has to be considered carefully: a SHG signal has already been observed in some solid solutions, but it is difficult to determine the influence of parameters such as the degree of disorder (or pseudosymmetry) of the structure and its consequence on the χ(2) coefficients. As far as the length traveled through the crystal is concerned, the length of local order and the associated crystal space group will probably influence the results. However, the detection of partial solid solutions can be of interest since some of them can be potentially adequate for preferential crystallization.31 Considering all these situations, the SHG test is consequently proposed as a prescreening method only.
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Once a SHG active phase is detected, its identification as member of NA or NC subsets needs to be determined. Even if it is a conglomerate, this mirror image mixture of phases can be of a metastable character. To speed up the detection of a stable conglomerate, it would be beneficial to control the crystallization conditions. This implies control of (i) the nature of the counterion or cocrystal former (ii) the stoichiometry (iii) the temperature (during the crystallization but also during the SHG detection) (iv) the nature of the solvent. Interesting conglomerates may exist only in equilibrium with their mother liquor (because of one or several of the following reasons: noncongruent solubility, solvates with an efflorescent character, solvates that are hydrolyzed by moistures, CO2 sensitive solid, etc.).32 The improvement of the SHG setup has to be pursued to analyze the solid phases in contact with their mother liquors. The confinement will isolate the studied suspensions from moisture and CO2; moreover, it will prevent evaporation of the solvent and thus allow the conglomerate detection of effluorescent solvates. Conclusion SHG already appears as a promising prescreening technique for detection of conglomerates. Among numerous benefits one can list the following points: (i) Only a small quantity of the racemic mixture is necessary (ca. 20 mg typically) (ii) There is at this first stage of prescreening no need for comparison between results of SHG tests on the racemic mixture and the pure enantiomer. The screening can be undertaken even when the pure enantiomer is not available and thus can be carried out at an early stage of the development of the molecule. (iii) The response is instantaneously delivered; it is thus conceived to be a true high throughput prescreening method. (iv) It is a priori a nondestructive method. (v) It is cheap and can be fully automated: a high throughput device including motorized sample holders and a computer assisted treatment of the spectra should allow in a realistic way selection of the “good” candidates with a 50% probability or more. Further developments are carried out to enlarge the possibility of detection of the best situation of chiral discrimination in the solid state (i.e., the conglomerate) to moisture or CO2 sensitive salts as well as noncongruent solubility phases. Nevertheless, this will not prevent some drawbacks of the technique which will always require complementary analyses to make conclusions about the genuine nature of the solid phase: chiral (NC) or non-centrosymmetric and achiral (NA). Acknowledgment. Sanofi-Aventis (Paris, France) is gratefully acknowledged for its support during this study. Supporting Information Available: Results of SHG activity for the salts obtained with various acids (Table S1); XRPD patterns of (a) (()-DACH-citrate (1:1), (b) (+)-DACH-citrate (1:1) (Figure S1). This information is available free of charge via Internet at http://pubs.acs.org.
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CG801356M
