CRYSTAL GROWTH & DESIGN 2008 VOL. 8, NO. 8 2589–2594
PerspectiVes Molecular Design Strategies for Optimizing the Nonlinear Optical Properties of Chiral Crystals Ronald D. Wampler, Nathan J. Begue, and Garth J. Simpson* Department of Chemistry, Purdue UniVersity, West Lafayette, Indiana 47907 ReceiVed August 3, 2007; ReVised Manuscript ReceiVed April 2, 2008
ABSTRACT: A simple theoretical framework is presented to identify the key molecular properties and macromolecular arrangements leading to high second-order nonlinear optical (NLO) activity of chiral crystals. In chiral materials, maximum second harmonic generation (SHG) efficiency is predicted for an antiparallel molecular arrangement of Λ-like chromophores. This prediction is in stark contrast to the majority of previous crystal engineering efforts for second-order NLO materials, which have been focused almost exclusively on the construction of crystals exhibiting high degrees of polar order. Methods for possible rational electrostatic control of crystal structure by appropriate molecular design are considered. Introduction The most common crystal classes of achiral materials are centrosymmetric, leaving only a relatively small subset of inorganic materials that exhibit strong second-order nonlinear optical (NLO) activity and are simultaneously sufficiently optically transparent. Consequently, interest has grown in the use of organic materials for NLO applications. Such materials have the distinct advantage of allowing for rational optimization of the molecular structure to maximize the NLO activity. Much of the early effort in organic NLO materials has focused on the development of molecular systems with large hyperpolarizabilities.1–3 However, the net NLO activity is a function of both the molecular structure and the degree of orientation within the final product. As the field has evolved, the focus has increasingly shifted toward strategies for assembly of NLO chromophores into highly oriented structures that retain the engineered second harmonic generation (SHG) activity of the individual molecules. Although there are numerous other strategies for developing NLO materials such as poled polymers,4 multilayer films,5–7 and liquid crystals,8,9 single crystals offer many attractive features. First, the degree of orientational order and stability in order within crystalline materials is unmatched. Second, the chromophore density can be very high, fostered by the absence of a diluting host medium. Furthermore, the relatively rigid lattice structure allows for fast modulation of the electro-optic properties, which is an essential requirement for some applications of such materials.10 In light of these potential advantages, a host of different crystal engineering strategies have been developed for the * To whom correspondence should be addressed. E-mail: gsimpson@ purdue.edu.
rational design of molecules that will self-assemble into NLOactive crystalline forms. These efforts are generally complicated by electrostaticssthe chromophores most often used for NLO materials exhibit large permanent dipoles, which tend to produce antiparallel orientation within crystal lattices. Three general strategies have been developed to combat this complication: (1) the use of competing interactions to overcome the unfavorable dipole-dipole electrostatic interactions, (2) minimization of the molecular dipole through the use of octupolar chromophores, and (3) modification of the effective molecular “aspect ratio” to make coparallel packing energetically favorable.11,12 An alternative approach that has until recently received considerably less attention is the use of chiral molecules and macromolecular assemblies for crystalline NLO materials.11,13 Chiral crystals have the distinct advantage of necessarily lacking inversion symmetry and therefore always exhibiting symmetry-allowed SHG. However, symmetry alone does not necessarily provide a direct indication of the efficiency of SHG-activity, suggesting the need for a rational design framework. A excellent treatise of relationships connecting molecular orientation and macroscopic crystal NLO properties was prepared over 20 years ago by Zyss and Oudar.14 However, that foundational work focused primarily on achiral crystals classes containing rod-like chromophores. In this work, we revisit this basic approach, focusing primarily on chiral crystal classes. Theory Approximately 89% of chiral molecules for which crystal structures are known to crystallize into either the orthorhombic P212121 or the monoclinic P21 space groups, which are both noncentrosymmetric and SHG-active.15 The initial focus will
10.1021/cg700732n CCC: $40.75 2008 American Chemical Society Published on Web 06/28/2008
2590 Crystal Growth & Design, Vol. 8, No. 8, 2008
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Figure 1. Hyper-ellipsoid representation of the χ(2) tensor for the P212121 space group.
be on the P212121 crystal class, as it the most common chiral crystal structure (∼55%) and results in a lattice with no polar order or permanent dipole. From this starting point, P21 crystals (∼34%) can also be treated using many of the same arguments. The P212121 crystal class has an orthorhombic unit cell containing improper C2 operations about each orthogonal crystallographic axis. Consequently, only three unique χ(2) tensor elements remain: χXYZ ) χXZY, χYZX ) χYXZ, and χZXY ) χZYX.16 From inspection of these tensor elements, a single incident beam propagating along any crystallographic axis cannot generate a symmetry-allowed copropagating SHG beam. However, other crystal orientations can potentially exhibit significant SHG activity. Consistent with all octupolar systems, a P212121 crystal exhibits no permanent dipole, contributing to its energetic stability. This fact is reflected in the shape of the hyperellipsoid representation of the χ(2) tensor which consists of two interwined tetrahedra of opposite sign (Figure 1). The magnitude of the hyperellipsoid in any given direction represents the efficiency of generating an SHG polarization along that coordinate when driven by coparallel incident fields, with the color indicating the sign of the resulting SHG polarization (green ) positive, red ) negative).17 Additional information on hyperellipsoid representations of molecular and macromolecular tensors can be found in previous publications.17,18 For the relatively simple planar or rod-like molecular tensors considered in this work, these hyperellipsoids are complete and quantitative representation of the bulk χ(2) tensor in the weak coupling limit when the distance from the origin is expressed in appropiate units.18 The SHG efficiency of a P212121 crystal structure is given by the projection of the molecular tensor onto the hyperellipsoid shown in Figure 1. The simplest starting point for bridging the molecular and macroscopic NLO activities is through consideration of the weak-coupling limit, in which the net NLO tensor of the bulk material is approximated by coherent addition of the independent molecular tensors through orientational averages.
χIJK = Nb
∑
〈RIiRJjRKk 〉βijk
(1.1)
ijk)x,y,z
In eq 1.1, each R refers to an element of the Euler rotation matrix
describing the coordinate transformation between the molecular and macroscopic frames. Under resonance-enhanced conditions, the weak-coupling limit is valid provided that the energy splitting associated with coupling is much less than the line width of the transition.17,19 Far from resonance, the weakcoupling limit can be expected to hold even with strong energy splittings as long as the coupled electronic states are significantly higher in energy than the doubled frequency. In any case, eq 1.1 can be assumed to reliably recover the major contributions to the macroscopic NLO activity in chiral crystals. Obviously, the two key parameters dictating the bulk tensor are the properties of the molecular β(2) tensor and the monomer orientation within the lattice. In a P212121 crystal, the orientational averages are relatively straightforward to evaluate. If the molecular tensor is expressed in the crystal coordinate system, each rotation matrix becomes the identity matrix, and the nonzero χ(2) tensor elements correspond one-to-one with the identical molecular tensor elements (i.e., χXYZ = Nbβxyz). However, in practice the crystal coordinate system is not necessarily the most convenient for expressing the molecular tensor. Although chiral molecules are generally of quite low symmetry, many of the organic chromophores currently under development for NLO materials routinely exhibit relatively high symmetry or pseudosymmetry. The presence of pseudosymmetry often results in a relatively small number of tensor elements dominating the NLO activity of the chromophore, significantly reducing the complexity of the orientational averages connecting the molecular and crystal frames. In these limiting cases, the connections between the molecular and macromolecular frames become quite important for the development of rational design strategies. Some of the most common pseudosymmetry classes of chromophore structures currently under consideration for NLO materials are considered explicitly in the next sections. Case 1: Rod-like βzzz-Dominated NLO Chromophores. Rod-like chromophores easily comprise the overwhelming majority of molecules historically considered for NLO applications. Since a molecular tensor dominated by the element βzzz is clearly achiral (i.e., it is not affected by a mirror-plane operation containing the z-axis), it may not be immediately obvious how to interpret the NLO properties of a chiral crystal comprised of exclusively achiral, rod-like chromophores. Given that the nonzero χ(2) tensor elements in P212121 crystals all contain three unique coordinates, it may be tempting to initially correlate chirality within the molecular tensor with macroscopic SHG-activity.20,21 However, eq 1.1 provides a proper context for interpreting the bulk SHG-activity of such systems. In these cases, the macroscopic chiral activity is given by the combined projections of the molecular z axis onto each of the bulk X, Y, and Z axes (Figure 2). The hyperellipsoid representations shown in Figure 2 provide a visual aid for interpreting the nonzero values of the bulk χ(2) tensor in a chiral crystal. For a rod-like βzzz-dominated chromophore, the hyperellipsoid is shaped like a dumbbell (Figure 1). The greatest collective projection will arise when the molecular z-axis trisects all three coordinates (e.g., θ ) (54.7° and φ ) (45° for a orthorhombic lattice) with a projection of 1⁄ √3 along each crystallographic axis.
χXYZ ) χYZX ) χZXY )
1 Nbβzzz 3√3
(1.2)
For an individual rod-like chromophore, the βzzz tensor can only project onto one of the four possible lobes of the bulk hyperellipsoid. Consequently, in the limit of a rod-like chro-
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Figure 2. Hyper-ellipsoid representation of a βzzz dominated chromophore (a). The optimal projection of the βzzz dominated hyperellipsoid (b) on to the hyper-ellipsoid of the P212121 space group (c) in Cartesian coordinates.
mophore, the maximum value of any χ(2) tensor element is less than 20% (i.e., 1/33) of what it would be if all the chromophores were oriented exactly coparallel along a Cartesian coordinate. This result has already been demonstrated previously by Zyss and Ouder,14 but is presented here again to illustrate the analysis approach. Since the SHG intensity scales with the square of this value, the per-molecule efficiency of frequency doubling in terms of intensity is at most 4% of that expected from a perfectly coparallel assembly. In practice, this value may be difficult to achieve, as local electrostatic interactions within the unit cell will generally be expected to drive rod-like chromophores to assemble in largely antiparallel orientations rather than along the (111) and related faces. The >96% reduction in SHG intensity conversion is admittedly disheartening. It suggests that the benefits of incorporating rod-like chromophores into chiral crystalline materials is generally not likely to yield substantial improvements in the NLO efficiency compared to more traditional methods such as electric field poling within a polymer matrix. Moreover, local electrostatic interactions are often likely to favor SHG-inactive antiparallel orientations within rod-like assemblies of chromophores with large permanent dipoles due to dipole-dipole electrostatic interactions, further exacerbating these already unfavorable conditions. Fortunately, βzzz-dominated chromophores arguably represent the worst-case situation for chiral NLO materials, with substantial improvements possible through the use of alternative chromophore architectures. Case 2: Λ-Like βxxz ) βxzx-Dominated Chromophores. Several classes of “Λ-like” chromophores are dominated by the βxxz element under common experimental conditions (i.e., with the dominant transitions lying at energies close to or higher than 2pω).22–25 Such chromophores are often characterized by transition moments oriented perpendicular to the charge-transfer axis. In this limiting case, the maximum net projection of the molecular tensor onto the remaining crystal tensor elements
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Figure 3. Hyper-ellipsoid representation of a βxxz ) βxzx dominated chromophore (a) and the optimal orientation to maximize projection on to the P212121 hyper-ellipsoid representation (b).
arises when the z-axis of the molecule lies along one of the crystallographic axes (e.g., Z, corresponding to θ ) 0°), with the x-axis bisecting the remaining crystal axes, as shown in Figure 3 (for a tilt angle of 0°, rotation about φ and ψ become equivalent). In this configuration, the following relationships hold for the macroscopic χ(2) tensor elements:
1 χXYZ ) χYZX = Nbβxxz ; χZXY = 0 2
(1.3)
If instead the molecular tensor is dominated by the βzxx element, the same optimal orientation leads to the following relationships
1 χXYZ ) χYZX = 0; χZXY = Nbβzxx 2
(1.4)
Interestingly, these relations predict a maximum SHG activity for an antiparallel arrangement of chromophores exhibiting no polar order. The improper C2 symmetry operations along the X and Y axes invert the orientation of the molecular z-axis within the lattice, such that the z axes of neighboring chromophores are perfectly antiparallel when aligned along a crystallographic axis. Nevertheless, the bulk crystal is predicted to retain up to 50% of the SHG activity of a perfectly coparallel assembly, corresponding to an intensity-conversion efficiency as high as 25% relative to a comparable δ-function assembly of perfectly coparallel chromophores. Interestingly, this same class of Λ-like chromophores has been suggested for maximizing the NLO activity of uniaxial (i.e., noncrystalline) chiral assemblies of chromophores, primarily through orientational effects quite similar to those described here for chiral crystals.21,23,24,26–28 This initially counter-intuitive behavior (optimal SHG for an antiparallel orientation) can also be understood through inspection of the hyper-ellipsoid representations (Figure 3). A mirrorplane reflection results in two molecules with antiparallel orientations and complete cancelation of all SHG-activity. However, a nonzero twist angle of the molecular z-axis about
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Figure 4. Crystal structure of urea. Adapted from ref 30.
the laboratory Z-axis yields a configuration in which the C2 operation about either X or Y inverts the molecular z-axis, but rotates the molecular axes to produce a nonzero projection onto the hyperellipsoid representation of the crystal tensor. For example, a twist of 45° (i.e., the optimal value) would result in good initial overlap between the monomer tensor and four of the eight lobes in the octupolar hyperellipsoid of the crystal. Furthermore, the C2 operations about either the X or Y crystallographic axes rotates the molecular tensor to provide good overlap with the remaining four lobes. From inspection of Figure 1 describing the hyperellipsoid representation of the crystal χ(2) tensor and Figure 3b for the βxxz-dominated tensor, this C2 operation does, indeed, optimize the projection of the molecular tensor onto the macroscopic tensor of the crystal. In contrast to the overwhelming majority of nonlinear optical materials, this class of chromophores within chiral crystals has the distinct practical advantage of working with, rather than against, electrostatic interactions. In most instances, dipole-dipole interactions favoring antiparallel orientation between neighboring chromophores are considered difficult energetic obstacles to overcome when constructing a bulk material with a high NLO activity. However, in this case, the NLO response is actually optimized when these dipole-dipole interactions result in a bulk crystalline material exhibiting antiparallel orientation. Although the particular 3D structure arising upon crystallization is often quite difficult to predict from first principles, electrostatic interactions such as these are arguably among the most reliable predictors for macroscopic crystal structure.29 Consequently, it stands to reason that Λ-like chromophores with strong permanent dipoles may very well serve as excellent building blocks for the rational design of crystalline materials exhibiting large second order NLO-activity. Arguably the most familiar NLO-active molecular crystal exploiting these structural advantages is that of urea, in which each unit cell contains a pair of antiparallel monomers twisted 90° relative to each other (Figure 4).14,30 The P4j21m crystal lattice of urea is not chiral, containing a mirror plane running 45° between the a and b axes. Nevertheless, the only nonzero tensor elements in crystalline urea are χXYZ ) χYXZ, χXZY ) χYZX, and χZXY ) χZYX (in SHG, χXYZ ) χXZY). The relatively high symmetry of the P4j21m crystal structure of urea is fairly rare,
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representing less than 0.3% of known crystals in the Cambridge Structural Database,31 which may be one reason this structural motif has not been pursued with greater vigor. Consequently, it would appear that the close connections between the P4j21m crystal structure of urea and the P212121 structure most commonly encountered in chiral crystals has not been widely recognized or exploited in a manner comparable to other molecular design strategies, despite the ubiquitous use of urea as a reference material for comparisons of NLO activities. Case 3: Planar Octopolar βxxz = βzxx = -βzzz Dominated Chromophores. Octupolar chromophores represent another interesting class of NLO-active compounds. Octupolar chromophores have attracted considerable attention recently,32–35 as their absence of a permanent dipole significantly minimizes the unfavorable electrostatic interactions that often complicate the construction of highly oriented polar materials using “rod-like” chromophores. By effectively turning off dipolar electrostatic interactions, octupolar chromophores generally have a greater tendency to form noncentrosymmetric SHG-active bulk materials. However, they also have some limitationssif assembly into polar crystals does not occur spontaneously, the absence of a permanent dipole no longer provides a convenient “handle” to induce polar order by other means (e.g., by electric field poling). Two different classes of octupolar chromophores have been considered in detail within the literature; tridentate systems exhibiting nominal C3 or D3 symmetry,36,37 and to a lesser extent tetradentate systems of nominal Td tetrahedral symmetry.38,39 In this section, discussion will be limited to the more common tridentate classes. Within chiral crystals, octupolar chromophores share many similarities with Λ-like chromphores. As in the βxxz-dominated system, the optimal orientation within the crystal lattice arises for an antiparallel orientation with the z-axis coparallel with a crystal axis and an azimuthal angle φ (or ψ) of (45°. Under these conditions, the following relationships emerge for the macroscopic tensors (Figure 5).
1 χXYZ ) χYZX ) χZXY = Nbβxxz 2
(1.5)
Again, the maximum SHG activity is as high as 50% of that expected for a perfectly coparallel orientation (expressed with respect to electric field). Indeed, it would appear that the addition of the third chromophore to transition from a bidentate Λ-like chromophore to a tridentate octupolar chromophore provides no significant advantage with respect to chiral crystals. In fact, the opposite may very well be true, as the favorable dipolar electrostatic interactions leading to antiparallel orientations in assemblies of Λ-like chromophores are no longer present in assemblies of octupolar chromophores, leaving only higher-order multipolar interactions. Extension to the P21 Crystal Class. The P21 crystal structure contains only a single 2-fold screw axis and falls in the monoclinic crystal class. As a result, the number of nonzero unique tensor elements for the crystal increases from 3 in P212121 to 8 in P21, namely, χZXY ) -χZYX, χXXZ ) χXZZ, χXYZ ) χXZY, χYXZ ) χYZX, χYYZ ) χYZY, χZXX, χZYY, χZZZ (assuming a 2-fold axis along the Z-axis). In principle, these new elements can result in new sets of orientational averages and new possibilities for optimal molecular orientations within the lattice. Most significantly, a P21 crystal can exhibit polar order and a permanent electric dipole. However, in practice, the energetic cost associated with formation of a material with a large permanent electric dipole still generally favors a largely antiparallel orientation in the lattice. Consequently, the basic guidelines developed in this
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Crystal Growth & Design, Vol. 8, No. 8, 2008 2593
linear optical properties ultimately dictating the phase-matching requirements in bulk crystalline materials. Conclusion
Figure 5. Hyper-ellipsoid of an octupolar chromophore (a) and the optimal projection onto the hyper-ellipsoid for the P212121 space group (b).
work for interpreting P212121 crystals will also be qualitatively reliable for describing P21 crystals with structures reasonably similar to orthorhombic (i.e., with angles of ∼90° between crystallographic axes). Limitations of the Calculations. Those experienced with NLO materials are intimately familiar with the fact that the linear optical properties of the material often matter just as much as the NLO properties when it comes to the macroscopic efficiency for frequency conversion. Phase-matching within bulk crystalline materials is dictated by dispersion, generally requiring birefringence in refractive index along different crystallographic axes. Fortunately, all chiral crystals are also necessarily birefringent, and will generally exhibit significant differences in refractive index along the different crystallographic axes. The degree of birefringence may or may not be sufficient to allow for favorable phase-matching conditions within bulk crystalline materials. If phase-matching conditions cannot be satisfied by the bulk crystal structure, alternative pseudo-phase matching strategies can be employed, but at the expense of additional complexity.40 Another caveat relates to limitations of the hyperellipsoid representations. The magnitude of the ellipsoid describes the efficiency of generating SHG when all of the incident and exigent electric fields are coparallel. However, several irreducible representations of rank 3 tensors do not contribute to the hyperellipsoid magnitude. In effect, the hyperellipsoids qualitatively describe just one type of phase-matching condition (fully coparallel type I), which may not be the most favorable for a given crystal when considering the linear optical properties as well.41 Nevertheless, for the purposes of this paper, the hyperellipsoids provide a visual means to qualitatively understand the overall magnitudes of the net crystal tensors. At the molecular level, the magnitudes associated with alternative phase-matching conditions will often track those described by the magnitudes of the hyperellipsoids, with the
The present analysis predicts that large permanent dipoles and antiparallel orientations can actually be advantageous in the design of NLO-active crystalline materials when comprised of Λ-like chromophores. This approach runs contrary to the most widely used current architectures, in which two strategies have been most commonly taken: (1) optimization of assembly conditions exhibiting polar order from molecules with large dipoles, and (2) construction and polar orientation of octupolar chromophores with no permanent dipole. Ultimately, full experimental implementation of the tools described in this work hinge on two key steps: (1) rational design of Λ-like chromophores with exceptionally large NLO activity, and (2) successful identification of strategies for constructing crystal structures exhibiting favorable chromophore orientations. Efforts on the first front will involve relatively straightforward extension of the existing methods designed to produce polar (rod-like) and octupolar NLOchromophores. On the second front, accurate a priori predictions of crystal structures from molecular structures (i.e., crystal engineering) is nontrivial, particularly in chiral systems, due to the relatively weak intermolecular interactions driving crystallization.29,42,43 However, progress in this area continues at a rapid pace.44,45 The objectives of the present work are simply to define what those favorable conditions are to optimize the bulk NLO activity in the most common crystal classes. Acknowledgment. The authors gratefully acknowledge financial support from the National Science Foundation (CHE-0640549), the Research Corporation (Cottrell Teacher-Scholar Award), and the Beckman Foundation (Young Investigator Award).
References (1) Williams, D. J. Angew. Chem. Inter. Ed. Engl. 1984, 23, 703. (2) Kang, H.; Facchetti, A.; Zhu, P.; Jiang, H.; Yang, Y.; Cariati, E.; Righetto, S.; Ugo, R.; Zuccaccia, C.; Macchioni, A.; Stern, C.; Liu, Z.; Ho, S.; Marks, T. Angew. Chem. Inter. Ed. Engl. 2005, 44, 7925. (3) Marder, S. R.; Perry, J. W.; Yakymyshyn, C. P. Chem. Mater. 1994, 6, 1137. (4) Dalton, L. R. AdV. Polym. Sci. 2002, 158, 1. (5) Kang, H.; Evmenenko, G.; Dutta, P.; Clays, K.; Song, K.; Marks, T. J. J. Am. Chem. Soc. 2006, 128, 6194. (6) Ashwell, G. J. J. Mater. Chem. 1999, 9, 1991. (7) Marks, T. J.; Ratner, M. A. Angew. Chem., Int. Ed. Engl. 1995, 34, 155. (8) Koike, M.; Yen, C.; Yuqing, L.; Tsuchiya, H.; Tokita, M.; Kawauchi, S.; Takezoe, H.; Watanabe, J. Macromolecules 2007, 40, 2524. (9) Soldera, A.; Theberge, R. Liq. Cryst. 2003, 30, 1251. (10) Singer, K. D.; Lalama, S. L.; Sohn, J. E.; Small, R. D. In Nonlinear Optical Properties Of Organic Molecules and Crystals; Chemia, D. S., Zyss, J., Eds.; Academic Press: New York, 1987; pp 437-467. (11) Wong, M. S.; Bosshard, C.; Gu¨nter, P. AdV. Mater. 1997, 9, 837. (12) Evans, O. R.; Lin, W. Acc. Chem. Res. 2002, 35, 511. (13) Verbiest, T.; Elshoct, S. V.; Kauranen, M.; Hellemans, L.; Snauwaert, J.; Nuckolls, C.; Katz, T. J.; Persoons, A. Science 1998, 282, 913. (14) Zyss, J.; Oudar, J. L. Phys. ReV. A 1982, 26, 2028. (15) Clegg, W.; Blake, A. J.; Gould, R. O.; Main, P. Crystal Structure Analysis: Principles and Practice; Oxford University Press: New York, 2001. (16) Butcher, P. N.; Cotter, D. The Elements of Nonlinear Optics; Cambridge University Press: New York, 1990. (17) Perry, J. M.; Moad, A. J.; Begue, N. J.; Wampler, R. D.; Simpson, G. J. J. Phys. Chem. B 2005, 109, 20009. (18) Wampler, R. D.; Moad, A. J.; Moad, C. W.; Heiland, R.; Simpson, G. J. Acc. Chem. Res. 2007, 40, 953.
2594 Crystal Growth & Design, Vol. 8, No. 8, 2008 (19) Simpson, G. J.; Perry, J. M.; Moad, A. J.; Wampler, R. D. Chem. Phys. Lett. 2004, 390, 8. (20) Wampler, R. D.; Zhou, M.; Thompson, D. H.; Simpson, G. J. J. Am. Chem. Soc. 2006, 128, 10994. (21) Simpson, G. J. ChemPhysChem 2004, 5, 1301. (22) Ostroverkhov, V.; Petschek, R. G.; Singer, K. D.; Twieg, R. J. Chem. Phys. Lett. 2001, 340, 109. (23) Ostroverkhov, V.; Singer, K. D.; Petschek, R. G. J. Opt. Soc. Am. B 2001, 18, 1858. (24) Ostroverkhov, V.; Ostroverkhova, O.; Petschek, R. G.; Singer, K. D.; Sukhomlinova, L.; Twieg, R. J.; Wang, S.; Chien, L. C. Chem. Phys. 2000, 257, 263. (25) Moad, A. J.; Simpson, G. J. J. Phys. Chem. B 2004, 108, 26. (26) Ostroverkhov, V.; Petschek, R. G.; Singer, K. D.; Sukhomlinova, L.; Twieg, R. J.; Wang, S. X.; Chien, L. C. J. Opt. Soc. Am. B 2000, 17, 1531. (27) Ostroverkhov, V.; Petschek, R. G.; Singer, K. D.; Twieg, R. J. Chem. Phys. Lett. 2001, 340, 109. (28) Simpson, G. J. J. Chem. Phys. 2002, 117, 3398. (29) Seddon, K. R.; Zaworotko, M. Crystal Engineering: The Design and Application of Functional Solids; Kluwer Academic Publishers: Boston, 1999. (30) Morrell, J. A.; Albrecht, A. C.; Levin, K. H.; Tang, C. L. J. Chem. Phys. 1979, 71, 5063. (31) Clegg; W. Blake, A. J.; Gould, R. O.; Main, P. Crystal Structure Analysis: Principles and Practice; Oxford University Press Inc.: New York, 2001.
Perspectives (32) Le Bozec, H.; Maury, O. Acc. Chem. Res. 2005, 38, 691. (33) Thalladi, V. R.; Brasselet, S.; Weiss, H.; Blaser, D.; Katz, A. K.; Carrell, H. L.; Boese, R.; Zyss, J.; Nangia, A.; Desiraju, G. R. J. Am. Chem. Soc. 1998, 120, 2563. (34) Cho, B. R.; Lee, S. J.; Lee, S. H.; Son, K. H.; Kim, Y. H.; Doo, J.-Y.; Lee, G. J.; Kang, T. I.; Lee, Y. K.; Cho, M.; Jeon, S. -J. Chem. Mater. 2001, 13, 1438. (35) Hennrich, G.; Asselberghs, K. C.; Persoons, A. J. Org. Chem. 2004, 69, 5077. (36) Zyss, J.; Dhenaut, C.; Chauvan, T.; Ledoux, I. Chem. Phys. Lett. 1993, 206, 409. (37) Maury, O.; Viau, L.; Senechal, K.; Corre, B.; Guegan, J.; Renouard, T.; Ledoux, I.; Zyss, J.; Le Bozec, H. Chem. Eur. J. 2004, 10, 4454. (38) Renouard, T.; Le Bozec, H.; Brasselet, S.; Ledoux, I.; Zyss, J. Chem. Commun. 1999, 871. (39) Cho, M.; An, S.-Y.; Lee, H.; Ledoux, I.; Zyss, J. J. Chem. Phys. 2002, 116, 9165. (40) Boyd, R. W. Nonlinear Optics; Academic Press: San Diego, 2003. (41) Dick, B. Chem. Phys. 1985, 96, 199. (42) Braga, D.; Grepioni, F.; Orpen A. G. Crystal Engineering: From Molecules and Crystals to Materials; Kluwer Academic Publishers: Boston, 1999. (43) Gavezzotti, A. Model. Sim. Mater. Sci. Eng. 2002, 10, R1. (44) Datta, S.; Grant, D. J. W. Nat. ReV. Drug Disc. 2004, 3, 42. (45) Price, S. AdV. Drug DeliVery ReV. 2004, 56, 301.
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