Supramolecular Synthons and Crystal Structure Prediction of Organic

Supramolecular Synthons and Crystal Structure Prediction of Organic Compounds Detlef W. M.

Hofmann,†

Ludmila N.

Kuleshova,*,‡

and Mikhail Yu.

Antipin‡

University of Frankfurt, Marie-Curie Street 11, Frankfurt on Main, 60439, Germany, and Institute of Organoelement Compounds, Russian Academy of Sciences, 28 Vavilov Street, Moscow, 119991, Russia Received January 15, 2004;

CRYSTAL GROWTH & DESIGN 2004 VOL. 4, NO. 6 1395-1402

Revised Manuscript Received August 12, 2004

ABSTRACT: The strategy taking into account regularities of crystal structure formation and results of theoretical crystal structure prediction has been proposed as a tool for crystal engineering. The role of the symmetry of the supramolecular associates (synthons) in the symmetry of the crystal structure is suggested. As an example, the design of a polar (acentric) crystal structure is demonstrated. To establish the factors leading to acentric structure formation, the structural analysis of the polymorphic centric-acentric pairs derived from CSD has been performed. It was found that such pairs very often are formed from the identical stable acentric supramolecular synthons and crystallized under the same kinetic conditions (concomitant polymorphism). It was shown that crystal structure prediction with Hofmann’s potential function can reproduce typical hydrogen-bonded synthons even in the case of relatively weak hydrogen bonds. As a successful example of the suggested approach, the engineering of the acentric crystal structure of N′-(2-phenyl-1H-indole-3-aldehyde)-4-nitrophenylhydrazone has been demonstrated. 1. Introduction Crystal structure symmetry determines many physical properties of the solid state, i.e., electrical, magnetic, linear and nonlinear optical (NLO), electron and ionic conductivity, and many others. The aim of crystal engineeringsa field of modern material sciencesis to predict and to control formation of crystal packing arrays with desired symmetry that will be responsible for a physical property of interest. Because crystal structure formation depends on not only thermodynamic, but kinetic factors as well (temperature, type of the solvent, concentration, the speed of crystallization), the successful strategy of crystal structure prediction must take into account the enthalpy of the proposed packing and dynamic processes in solution. In principle, a computer simulation of these processes is possible,1 but these calculations are difficult and time-consuming. Therefore, an actual problem is to take into consideration kinetic factors in the theoretical and experimental design of the crystal symmetry. An easy and fast approach to take into account kinetic factors is an analysis of a large amount of structural information accumulated in structural databases. Of course, crystal structure itself cannot provide information about kinetics of the seed formation and crystal growth, but it is, nevertheless, the final result of these processes. It is possible to suggest that if some structural array is rather abundant in a database, it may reflect thermodynamic stability of a given crystal packing array, as well as a kinetic preference of its formation. Therefore, structural databases (in particular CSD2) play an important role in the crystal structure prediction.3,4 Earlier, successful attempts5-11 were made in a search of main features of crystal structure formation, namely, * Corresponding author. Fax: +(095)135-50-85. E-mail: lukul@ xrlab.ineos.ac.ru. † University of Frankfurt. ‡ Russian Academy of Sciences.

the search of typical stable supramolecular ensembles which molecules form in crystals. Thus, G. Desiraju was the first who mentioned about the opportunity of using these ensembles (synthons) in crystal engineering.12,13 Gavezzotti and Filippini14 used the CSD to understand the processes of crystal structure formation. They mentioned that the identical chemical composition in parent pairs of centric and acentric crystals allows one to analyze structural aspects and to find regularities in molecular packing arrays, which can be used for a further crystal structure design. Recently, Kuleshova and Antipin15,16 performed a systematic study of the main features of the crystal structure of compounds forming both centric and acentric polymorphic modifications. In the literature,17 several strategies of crystal structure prediction including CSD search procedure are described. In particular, in studies by D. Hofmann et al.18,19 the data mining was applied to the CSD. This powerful technique allows the extraction of predictive information from large databases. In refs 18 and 19, data mining was used to derive a physically reasonable trained atom-pair potential. This potential was applied and tested for prediction of sublimation energies, ligandprotein-docking, crystal structure prediction, and crystal structure determination. The potential was able to identify the “truth” crystal structure among many predicted (and ranked by energy) possible packing arrays in 93% cases for space group P1 and in 37% cases for the space group P1 h . Because the accuracy of this trained potential depends on the number of corresponding structures in the CSD (which is increased day-byday), it is possible to expect that this approach could be an appropriate tool to solve some crystal packing problems including crystal structure prediction. In the present paper, the results of the systematic study15,16 of the crystal structure of compounds, forming both centric and acentric polymorphic modifications, and the strategy of crystal structure prediction18,19 were

10.1021/cg049969f CCC: $27.50 © 2004 American Chemical Society Published on Web 10/08/2004

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combined for design of materials with a desired (polar) symmetry of the crystal. 2. Experimental Procedures Choice of the Polymorphs. We selected all polymorphs with identical REFCODEs, but different numerical indexes in the Cambridge Structural Database (Version 2000). Theoretically, centric and acentric crystalline modifications of the same compound can be formed upon crystallization either from a racemic mixture of enantiomers containing an asymmetric atom or from a solution of achiral molecules with a low barrier to racemization. The former enantiomers are referred to as resolved enantiomers and can have different REFCODEs. The second group of enantiomers are termed unresolved (or rapidly inverted) enantiomers and, as a rule, are described in the CSD by an identical literal REFCODE but with a different numerical index. According to McCrone,20 polymorphic modifications are the crystals which being melted or dissolved result in the same compound. In the strict sense, polymorphic modifications are the crystals forming with the second group of molecules. Since the potential nonlinear optically active molecules of interest belongs mainly to the second group, we have restricted ourselves to the search for polymorphic modifications with identical REFCODEs. To obtain statistically sufficient information, we considered only the most commonly encountered space groups,21 namely, the centrosymmetric space groups P1 h , P21/c, and Pbca; the chiral space groups P212121, P21, and P1; and the racemic, but acentric space groups Pc, Pna21, and Pca21. For each of these space groups, we created a file containing the REFCODEs of all the compounds specified by the attribute “polymorph” in the “All Text” Build Quires. All the possible settings (including nonstandard ones) for these groups were taken into consideration. Then, for the purpose of revealing different structures with the same literal REFCODE, the files of centrosymmetric space groups were compared with the files of acentric space groups. A total of 122 pairs of centric and acentric modifications were found. It should be noted that the pairs in which a crystal with the space group P21/c serves as a centrosymmetric counterpart are considerably more frequent (92 pairs) in the Cambridge Structural Database as compared to those with the space groups P1 h (22 pairs) or Pbca (8 pairs). This stems from the fact that the P21/c group is most often encountered in organic compounds. For the REFCODEs obtained in such a manner, all the data available in the Cambridge Structural Database were extracted through the database query QUEST3D. A number of polymorphic modifications were rejected because the available data were either incomplete or invalid: errors in the determination of the space group and atomic coordinates, the absence of atomic coordinates, etc. Energy Calculations. The energy calculations for polymorphs derived from CSD were done with the program FlexCryst.19 This program is very fast in its calculations and is parametrized for all kinds of atoms contained in the CSD. The parameters are derived by data mining. This technique allows one to derive an optimal set for parameters from the database. The program calculates the sublimation energy of crystal structures as sum of intermolecular interaction. For two molecules I and J with nI and nJ atoms the energy is nI

E)

∑(i,j,r ) ij

i)1

The energy function  is a distance- and atom-type-dependent potential. The atom-type corresponds to the atom number of the atom. For hydrogen atoms bonded to carbon, nitrogen, and oxygen an additional atom type was introduced to describe hydrogen bonds as accurately as possible. As an example, we give the potential for N-H‚‚‚O interaction (Figure 1). The potential is defined by the auxiliary points and between these points the energy is linear interpolated. During data mining, the position of the auxiliary points is shifted until the potential finally can discriminate between experimental and distorted structures. We can assume that the experimental structure

Figure 1. The trained potential for N-H‚‚‚O interaction.

Figure 2. The plot of the calculated energies versus measured sublimation energies. should be a local minimum. Therefore, a correct force field should assign always to the experimental structure a lower energy as to an slightly distorted structure. Therefore, we optimize during training our parameters to fulfill this condition as well as possible. In our type of approximation, the functional form is not predetermined, and we end up with potentials, which differ significantly from common approaches, e.g., the given potential clearly indicates two different minimum, one corresponds to the van der Waals interaction at 3.7 Å, and the second at 1.6 Å reflects the hydrogen bond. Therefore, the selected program was adapted for our purpose to predict correctly synthons formed by hydrogen bonds. To check the accuracy of the potentials, we predicted the sublimation energies of 230 substances and compared them to the experiment22 (Figure 2). The mean error was 9.1 kJ/ mol. If it is considered that sublimation energies are difficult to measure, the result is near the experimental accuracy. For our purposes of the energetical investigation of polymorphs, the accuracy is good enough because we are not interested in the absolute sublimation energy, but in the difference between two polymorphic forms.

3. Results and Discussion General Structural Features of Pairs of the Centric and Acentric Polymorphic Modifications. Here we will consider the main structural features which have been found earlier15,16 in the detailed

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Table 1. Total Number of Pairs of Centric and Acentric Modifications Available in the Cambridge Structural Database Version 2000 P21/c - P212121 P21/c - P21 P21/c - Pna21 P21/c - Pca21 P21/c - Pc P21/c - P1

41 17 16 3 11 4

P1 h - P212121 P1 h - P21 P1 h - Pna21 P1 h - Pca21 P1 h - Pc P1 h - P1

9 4 2 2 2 3

Pbca - P212121 Pbca - P21 Pbca - Pna21 Pbca - Pca21 Pbca - Pc Pbca -P1

2 2 2 2

analysis of the crystal structures of compounds forming both centric and acentric polymorphic modifications. The parent 122 polymorphic pairs have been found in the CSD version 2000 (Table 1), and 85 of them have been used in further analysis. In analysis of polymorphic modifications, the following factors were taken into account: crystal formation conditions, molecular geometry, the type of the molecular associate (synthon) in crystal, and unit cell parameters. All needed information was extracted from the CSD. Because the crystal conditions for growth was only rarely reported there, we retrieved this information from the original papers. The main results obtained are as follows. More than half of the considered pairs of polymorphs were obtained at the same kinetic conditions in the same solvent (concomitant polymorphism23). Very often such polymorphic pairs are built with the molecules, which form strong intermolecular hydrogen bonds in crystals. We have found that in this case the centric and acentric modifications are formed from similar supramolecular associates built via intermolecular hydrogen bonds. The list of considered REFCODEs and main results derived in15,16 are summarized in Table 2 and are discussed in detail in the following section. Energy Calculations and Density Correlation for Centric and Acentric Packing. In Table 2, the densities and thermodynamic stability for polymorphic pairs considered are summarized. To estimate the influence of the molecular association on the character of the distribution ∆d, the values taken from Table 2 have been divided in two groups. The first one was formed by polymorphs built from similar synthons (more than half of these were mostly concomitant polymorphs). All other polymorphs obtained at different conditions were included in the second group. As it can be seen from Figure 3a,b, the ∆d (where ∆d ) (dc - dac) × 2 × 100/(dc + dac)) distribution is noticeably different for these groups. In the first group of polymorphs, built from similar synthons, the average ∆dm value was found to be -0.639 ( 0.479%. In this group the acentric polymorphic modifications are denser then their centrosymmetric counterpairs. In the second group of polymorphs, built from different synthons, the average difference density value were found to be ∆dm ) 0.087 ( 0.389%. This result is in line with conclusions made in ref 24 for rapidly interconverted enantiomers where no significant difference between the density packing for racemic and chiral crystals was found. Distributions of the crystal packing energy differences ∆E (where ∆E ) -(Ec - Eac) × 2 × 100/(Ec + Eac)) for the centric and acentric polymorphs build from similar and different synthons are presented in Figure 4. The energy was calculated with the program FlexCryst19 in accordance with procedure described in the experimen-

tal section. It is clearly seen from this figure that in the list of selected compounds the centric crystals are obviously energetically preferable in both groups. The average value of the ∆Em for polymorphs built from similar synthons is 2.145 ( 1.264% (Figure 4a). For pairs of modifications built from different synthons the ∆Em value is 2.117 ( 5.731%. As the statistical data for the ∆E values is not quite sufficient, the characteristics of the distribution in the last case are rather pure, and no reliable conclusion can be made. It is clear, however, that centrosymmetric modifications are more energetically favorable in general for both groups of modification. This result corresponds to data obtained by Gavezzotti and Filippini,14 where 80% of centrosymmetric crystals are stabilized by 1-3%. For first group of polymorphs with similar hydrogenbonded synthons acentric polymorphs have a larger density, but are less energetically favorable than centrosymmetric ones. The possible explanation was made by a detailed analysis of the very short intermolecular (hydrogen-bonded) atom-atom contacts in the crystals one of the polymorphs. The MNPHOL25,26 has two modifications: P212121, Eac ) -65.80 kJ/mol, d ) 1.542 g/cm3; P21/n, Ec ) -70.10 kJ/mol, d ) 1.478 g/cm3. In these modifications, molecules form the same hydrogenbonded contacts (Figure 5). In Table 3 the characteristics of the most representative contacts corresponding to this hydrogen bonding are shown. It is seen that the more dense acentric structure P212121 has shorter contacts than the centric P21/n one. Although the character (attractive or repulsive) of the interactions between corresponding atoms in different modifications is the same, the values of repulsive contribution are stronger in the more dense structure. As a result, the summary energy of hydrogen-bonding in pairs of molecules is by 0.898 kJ/mol stronger in centric modifications in spite of (or owing to) shorter contacts in the acentric one. This example confirms the importance to investigate the synthons in detail in crystal structure formation. The Role of Synthons in Crystal Structure Formation. In the design of crystal structures with desirable symmetry, the important consideration above (as well as in refs 12 and 13) should be noted. The conservation of the type of synthons in centric and acentric polymorphs obtained in refs 15 and 16 give us a better understanding of the crystal growth process. Namely, we can consider that crystal structure is formed from supramolecular assembles existing already in a mother solution, but not from the separated molecules. It allows us to assume that the symmetry of the molecular associate formed by intermolecular hydrogen bonds plays a key role in formation of a final symmetry of a crystal. Two scenarios are possible in formation the centric or acentric crystal. If molecules form an acentric associate via intermolecular hydrogen bonds, both acentric and centrosymmetric crystals can be formed. If molecules form an centrosymmetric associate, in general, a centrosymmetric crystal is formed. Only in rare cases an acentric crystal structure also can be formed. These cases are characterized by a pseudo-symmetry and the presence of a several independent molecules in the unit cell (Z′ > 1).27

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Table 2. List of Compounds Forming Both Centric and Acentric Polymorphic Modificationsa REFCODE

1

2

dc

dac

∆db

CLBZAM DMFUSC DPGUAN DTBPTP FABFUJ FABFUJ MNPHOL COYMOS JAMLUE HAMNEO GLYCIN EMPIPP MBZYAN FAJTIT ATSPEN MOPBZA LAVMOK LAVMOK BANGOM FOVYOE DUVZOJ DUVZOJ DGLYCN SILXUG DHNAPH SLFNMF BESKAL PYRZIN PEGVAY PEZBOL ACTOLD AMBACO LEZJAB TOLSAM DMFUSC TALJIZ DOGWOL BIXGIU MABZNA POFLAX NOVRIZ DLMSU_ TETROL NMBYAN PYRZIN HABJUP DCLNAP BOPSAA HETPAL MABZNA FIKFIO VAWWEV FESKAP CUMTAF BUNKOK BARWUM VISSOF DEFDUN SECZAB BIGTIU CIVTUM NOSWAT PUMVIC CHAPEP CLPHTE ZEPFAB HPTHEL FAHVOZ HOQABS GAXLEW CLBZNT CAXMOD NOJHEZ NOJHEZ MBYINO MBYINO

S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S S D D D D D D D D D D D D D D D D D D D D D D D D D D D

C C C C C C C C C C C C C C C C C C NC NC NC NC C C C NC NC NC C C C NC NC NC NC NC NC NC NC NC C NC C C NC NC NC NC NC C C C C C C C C C NC NC NC NC NC NC NC C NC C C NC NC C NC NC NC NC

1.640 1.191 1.205 1.162 1.457 1.457 1.478 1.376 1.587 1.877 1.609 1.304 1.130 1.246 1.326 1.477 1.400 1.339 1.667 1.387 1.396 1.396 1.595 1.341 1.562 1.421 1.578 1.460 2.434 1.327 1.221 1.387 1.581 1.453 1.191 1.096 1.280 1.410 1.301 1.084 1.593 1.420 1.262 1.310 1.460 1.343 1.677 1.289 1.415 1.327 1.279 1.266 1.969 1.317 1.635 1.471 1.277 1.478 1.202 1.420 1.640 1.345 1.497 1.357 2.315 1.237 1.299 1.407 1.300 1.718 1.429 1.441 1.389 1.382 1.334 1.318

1.702 1.198 1.207 1.114 1.465 1.445 1.542 1.369 1.577 1.886 1.584 1.256 1.147 1.216 1.333 1.474 1.377 1.377 1.671 1.405 1.443 1.429 1.611 1.342 1.637 1.363 1.542 1.485 2.546 1.328 1.231 1.409 1.555 1.397 1.197 1.127 1.270 1.510 1.334 1.064 1.675 1.408 1.282 1.248 1.460 1.476 1.694 1.297 1.430 1.334 1.208 1.295 2.010 1.298 1.575 1.418 1.267 1.542 1.250 1.424 1.702 1.370 1.479 1.360 2.364 1.238 1.288 1.403 1.347 1.736 1.441 1.345 1.362 1.362 1.331 1.331

-3.710 -0.586 -0.166 4.218 -0.548 0.827 -4.238 0.510 0.632 -0.478 1.566 3.750 -1.493 2.437 -0.527 0.203 1.656 -2.798 -0.240 -1.289 -3.311 -2.336 -0.998 -0.075 -4.698 4.167 2.308 -1.698 -4.498 -0.075 -0.816 -1.574 1.658 3.930 -0.503 -2.789 0.784 -6.849 -2.505 1.862 -5.018 0.849 -1.572 4.848 0.0 -9.436 -1.009 -0.619 -1.054 -0.526 5.710 -2.265 -2.061 1.453 3.738 3.669 0.786 -4.238 -3.915 -0.281 -3.710 -1.842 1.210 -0.221 -2.094 -0.081 0.850 0.285 -3.551 -1.042 -0.836 6.892 1.963 1.458 0.225 -1.056

∆Ec

Ec

Eac

-121.57 -112.18

-118.47 -108.61

2.583 3.234

-123.08 -123.08 -68.59 -115.02

-132.74 -125.14 -66.95 -106.67

-7.552 -1.660 2.420 7.533

-53.99 -73.12 -111.01 -108.56 -75.17 -150.41

-54.39 -62.51 -112.17 -106.06 -73.71 -139.84

-0.738 15.646 -1.040 2.330 1.961 7.283

-144.92 -124.86 -89.09 -89.09

-140.92 -137.64 -86.17 -81.76

2.799 -9.737 3.332 8.580

-75.36

-73.90

1.956

-81.93 -72.28

-82.01 -69.49

-0.098 3.936

-121.57

-117.46

3.439

-79.79 -123.45

-77.59 -132.67

2.798 -7.200

-125.78

-117.89

6.476

-119.36

-115.11

3.625

-96.67 -124.41

-95.150 -118.46

1.585 4.900

-137.01

-115.30

17.209

-134.90 -118.22

-133.58 -112.61

0.983 4.861

-91.32

-94.67

-3.602

-110.42

-107.06

3.090

-112.81 -112.05 -84.35

-105.53 -105.64 -75.90

6.668 5.889 10.546

-138.45

-135.82

1.918

-118.72

-119.24

-0.437

-138.01

-163.17

-16.708

-80.91

-74.11

8.773

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Table 2 (Continued)

a

dac)

REFCODE

1

2

dc

dac

∆db

Ec

Eac

∆Ec

FAHNOR BAAANL NOETNA PNEOSI PUBMUU REWPUE HPTSIO HEYHUO NOTLAJ SIWDEH BIXGIY CERLOA CUMHUN SESHUT

D D D D D D D D D D D D D D

C C NC NC NC NC C C NC C NC C C NC

1.455 1.580 1.954 1.367 1.916 2.339 1.270 1.236 1.292 1.327 1.509 1.309 1.640 1.370

1.459 1.580 1.918 1.361 1.958 2.335 1.220 1.233 1.308 1.345 1.499 1.295 1.643 1.370

-0.275 0.000 1.860 0.440 -2.168 0.171 4.016 0.243 -1.231 -1.347 0.665 1.075 -0.183 0.0

-138.91

-130.51

6.236

-76.65 -195.82

-87.83 -195.07

-13.594 0.384

-177.90 -99.22

-170.59 -100.53

4.195 -1.312

-155.77 -159.00

-177.29 -132.67

-12.923 18.055

1, type of synthons: S, similar; D, different; 2, crystal formation conditions: C, concomitant; NC, different conditions. 2 × 100/(dc + dac). c ∆E ) -(Ec - Eac) × 2 × 100/(Ec + Eac).

×

b ∆d

) (dc -

Table 3. Comparison of Intermolecular Contacts and Their Energies in Modifications of MNPHOL

Figure 3. Histograms for the ∆d values in centric-acentric pairs of polymorphic modifications: (a) for polymorphs built from similar synthons, and (b) for polymorphs built from different synthons.

Figure 4. Histograms for ∆E packing energy for centricacentric pairs of polymorphic modifications: (a) for polymorphs built from similar synthons, and (b) for polymorphs build from different synthons.

Figure 5. Scheme of hydrogen bonding in polymorphic modifications of the MNPHOL.

Therefore, from the structural point of view, we may consider an appearance of polymorphs as a result of multivariant superposition of the similar supramolecular fragments (layers in most cases). These arguments may be used in a strategy for design of acentric crystal structures that is based on the next conclusion: if molecules may form stable acentric supramolecular synthons via intermolecular hydrogen bonds, there is a

contact

Rac(Å) P212121

Rc (Å) P21/n

Eac (kJ/mol) P212121

Ec (kJ/mol) P21/n

Eac - Ec

O2‚‚‚H O1‚‚‚O2 O3‚‚‚H O1‚‚‚O3 N‚‚‚H O1‚‚‚N

1.91 2.89 2.53 3.25 2.53 3.46

1.95 2.94 2.65 3.32 2.62 3.52 total

-0.16 0.859 0.799 -0.904 1.291 -0.814 1.071

-0.031 0.459 0.629 -0.975 0.875 -0.784 0.173

-0.129 0.400 0.170 0.071 0.416 -0.030 0.898

good chance to obtain a stable acentric crystal by an appropriate choosing of crystallization conditions. The opportunity of acentric synthon formation may be confirmed by via theoretical estimation (crystal structure prediction), or from experimental data (the presence of acentric associates in known centrosymmetric crystal structures). Theoretical Prediction of Crystal Structure. As a first step to a crystal structure prediction, it was worth demonstrating that the Hofmann’s approach based on a trained potential function may generate real supramolecular packing fragments (synthons) for compounds able to form hydrogen bonds. As a test example, we took into account the meta-nitrophenol structure (MNPHOL) already considered above, which forms two concomitant polymorphs (P21/c, Z ) 4, and P212121, Z ) 4) characterizing with close unit cell parameters and similar layered crystal packing motif (Figure 6). The layers are formed by infinite chains via the OH‚‚‚O hydrogen bonds linked together by more weak CH‚‚‚O interactions. The energetically most favorable predicted structure of MNPHOL as well as the two experimental ones have a layered character. The layers formed by the intermolecular hydrogen bonds OH‚‚‚O and CH‚‚‚O in the predicted structure have very similar topology (Figure 6c). The symmetry of the predicted crystal is orthorhombic, space group Pbca, and unit cell parameters a and b are close to those found in the experimental structures, and the c parameter has a multiple value (Table 4). The similarity of the predicted and experimental characteristics gives an opportunity to consider the predicted structure as one of the possible but nonrealized polymorphic modifications. As another test example, we generated crystal packing of 3,4-dihydroxy-2-oxo-1-methyl-4-piperidine (TOMYEZ),28 which is also able to form a developed system of hydrogen bonds. In the experimental crystal

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Figure 8. Comparison of the predicted (grey) and experimental (black) crystal structures of TOMYEZ.

Figure 6. Packing of hydrogen bonded synthons of MNPHOL in (a) polymorph with space group P21/n, (b) polymorph with space group P212121, and (c) predicted structure with space group Pbca.

Figure 7. Supramolecular hydrogen-bonded synthon of the TOMYEZ. Table 4. Unit Cell Parameters of the MNPHOL Polymorphs and Predicted Crystal Structure space group, Z

a, Å

b, Å

c, Å

R, deg

β, deg

γ, deg

P21/c, Z ) 4 P212121, Z ) 4 Pbca, Z ) 8

11.240 11.136 12.011

6.891 6.649 6.554

8.154 8.091 15.546

90 90 90

98.05 90 90

90 90 90

structure, the molecules form double chains of centrosymmetric dimers (Figure 7). In this case, the predicted structure was found to be fully identical to the experimental one, including a reproducing unit cell parameters and types of the supramolecular associates. Figure 8 demonstrates the similarity of the experimental and predicted structures. The presented results show that the Hofmann’s force field can reproduce typical hydrogen-bonded packing motives, even in the case of relatively weak hydrogen bonds, and it can be used as an instrument of crystal generation in an approach taking into account the symmetry of supramolecular synthon.

Design of the Acentric Crystal Structure of N′(2-phenyl-1H-indole-3-aldehydo-4-nitrophenylhydrazone). The possibilities of application of the combined approach for future engineering of the desired crystal structure we will illustrate by the design of the acentric crystal structure of N′-(2-phenyl-1H-indole-3aldehydo-4-nitrophenylhydrazone) (I).29 Donor-acceptor (D-A) derivatives of hydrazones possess relatively high values of the molecular hyperpolarizability and represent therefore an interest as compounds for nonlinear optics. They may be easily obtained by a condensation reaction of different donor derivatives of aromatic aldehydes (D) with nitrophenylhydrazine (A). These compounds are very suitable models for crystal engineering because in this case it is possible to control crystal structure formation by varying crystallization conditions.30-32 In addition, hydrazone molecules form stable acentric supramolecular associates (the λ-type plane chains) (Figure 9a) due to hydrogen bonds of the central amino-group with one of the oxygen atoms of the nitro-group, and, in addition, more weak interactions between the C-H group of azomethyne fragment with the same oxygen atom. The compound (I) was synthesized in a search of new prospective NLO-active compounds through the condensation of 2-phenyl-indole 3-aldehyde with 4-nitrophenylhydrazine in acetic acid. Theoretical estimation33 of the molecular first-order hyperpolarizability (β) of this compound resulted in a rather high value (β ) 66.68 × 10-51 cm3/V2), but the substance previously crystallized from dioxane was found to possess the centrosymmetric space group P21/c excluding NLO activity in the solid state. Analysis of the crystal structure has shown that crystals of I are built from acentric λ-type planar chains, which are typical for hydrazones (Figure 9a). This may allow one to obtain stable acentric crystal structure of this compound by varying crystallization conditions. Both the theoretical and experimental attempts to obtain other crystal structures of I were performed. An attempt to calculate optimal crystal packing of this compound using the Hofmann’s program19 resulted to the acentric crystal (space group Cc) with a stable acentric associate different from that in the experimental structure (Figure 9b). The λ-chains in the predicted structure are formed via the N-H groups of the indole fragment of molecules but not via the N-H group of the hydrazone fragment as was found in the experiment. Estimation of the crystal first-order hyperpolarizability

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crystal grown from acetone, participates in formation of the supramolecular synthon (Figure 9d). However, due to phenyl ring rotation in the indole group, there is no above-mentioned CH‚‚‚O contacts stabilizing the planar structure of the λ-chain. Therefore, the chain is not planar and molecules in the chain are rotated by 70.0 degrees (the angle between the mean-squared molecular planes). This results in a decrease in the value of the crystal NLO response (d31 ) -8.9 pm/V, d32 ) 7.9 pm/V, d33 ) 23.2 pm/V) of real crystals in comparison to predicted optimal crystal packing. The details of X-ray analysis are presented in ref 28. The importance of supramolecular association in formation of final symmetry of a crystal structure has been demonstrated as with structural systematic investigations with the crystal structural prediction method. We believe that the combination of structural analysis and molecular modeling in crystal engineering will be a successful tool in the construction of crystal structures of compounds of interesting physical properties. Acknowledgment. This work was supported by the Russian Foundation for Basic Research, Project Nos. 0303-32716 and German Forschergruppe “Spin- and Charge-Correlations in Low-Dimensional Organometallic Solids”. References

Figure 9. Supramolecular synthons of N′-(2-phenyl-1Hindole-3-aldehydo-4-nitrophenylhydrazone) in crystals: (a) polymorph with space group P21/c, grown from acetone, (b) predicted with space group Cc, (c) polymorph with space group P1 h , grown from pyridine, and (d) polymorph with space group Pca21, grown from acetonitrile.

(d) of the predicted structure resulted to quite good results (dxxx ) 90.8 pm/V, dzzx ) 28.6 pm/V); therefore, we made further attempts to obtain other crystal modifications of this compound by changing solvents. As a result, two new crystal phases were obtained: the dark red, small-sized, needle-shaped crystal grown by slow evaporation from pyridine and dark red prismatic crystals grown by slow evaporation from acetonitrile. X-ray-analysis of single crystal from pyridine has shown the centrosymmetric space group P1 h . It is important to note that molecules in this crystal, as well as in the predicted structure (Figure 9b), form acentric chains via hydrogen bonds of the NH group of the indole fragment and oxygen atom of the nitro-group (Figure 9c). In crystals, these chains are packed in the antiparallel manner forming a centrosymmetric structure. Because of rotation of the phenyl group, there is no short CH‚‚‚O contacts stabilizing the planar structure of the λ-chains. X-ray-analysis of single crystal from acetonitrile has shown finally the desired acentric structure with the space group Pna21. In this structure, the hydrogen atom of the central amino-group, as well as in the case of

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