Article pubs.acs.org/crystal
Symmetry Influence on the Rotation of Molecules in Crystals Daut R. Islamov,*,† Valery G. Shtyrlin,† Nikita Yu. Serov,† Ivan V. Fedyanin,‡ and Konstantin A. Lyssenko‡ †
A. M. Butlerov Chemistry Institute, Kazan Federal University, Kremlevskaya str. 18, 420008 Kazan, Russia Institute of Organoelement Compounds of Russian Academy of Sciences, Vavilova str. 28, 119334 Moscow, Russia
‡
ABSTRACT: It was shown that rotational mobility of molecules in crystals is affected by the symmetry of their surroundings. A hypothesis was proposed for the discovered correlation. Three cases are possible for the location of the molecules with respect to the crystallographic symmetry elements: I − the location in a general position; II − the location in special positions without symmetry disordering; III − the location in special positions with symmetry disordering. According to the experimental data, the rotation barrier heights at the location of the molecules in cases I and III are lower than in case II. This fact is explained by the amplitude and phase shifts of the rotational energy profiles of two parts of the molecule in case I and by increasing the number of minima on the rotation barrier profile at disordering the molecules by symmetry in case III. The way is proposed for lowering the rotational barrier of molecules in crystals.
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INTRODUCTION Crystal design is becoming one of the fastest growing fields in chemistry and physics today.1−5 In these fields, rotation of molecules in crystals has long attracted the attention of researchers. The rotation of molecules in crystals is investigated, in particular, for the creation of molecular rotors. Chemists who envisioned and built machines on the molecular scale have won the 2016 Nobel Prize in Chemistry. It is not surprising that many reviews are devoted to the topic of molecular rotation, for example, see refs 6−11. It is well-known that controlled molecular motion is the heart of the molecular rotor and is a decisive parameter in the operation of molecular machines which are capable of tuning the bulk physical properties of materials.12−17 Consequently, this requirement prompted us to explore correlation between the rotation of molecules and symmetry. One of the early successes in this field was Linus Pauling’s work in 193018 where it was shown that the rotational barrier function in the crystal may be presented in the first approximation as a cosine wave with a period equal to θ/n, where θ is angle of rotational axis relative to the equilibrium position and n is the order of the symmetry axis of the molecule having the rotational axis. In the words of Dunitz and co-workers,5 “In a sense, one can say that spectroscopy sees the rate at which molecules cross the barrier, while diffraction sees the bottom of the potential well; we derive roughly the same barrier height as long as the potential is approximately sinusoidal.” This approach allowed us to estimate the height of the barrier of rotation based on the analysis of thermal vibrations in the X-ray structures in the framework of the theory of translation/libration/screw (TLS) in numerous papers.19−21 As expected by the shape-conforming nature of the short-range forces responsible for close-packing interactions © 2017 American Chemical Society
of molecular crystals, the rotational frequencies and activation energies for a set of crystalline rotors correlate well with the molecular symmetry of their corresponding rotational axes.22 Previously in our study23 the correlation between the environment symmetry of coronene and its rotational mobility was supposed. The purpose of this paper is to solidify this correlation and provide a hypothesis for the previously discovered correlation that will allow us to expand analysis to more classes of compounds and symmetry operations.
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EXPERIMENTAL SECTION
Calculations. The initial coordinates of the structure of the coronene−F4TCNQ 2:1 complex were taken from crystallographic data determined by X-ray diffraction.23 During the course of the geometry optimization the positions of the heavy atoms were frozen, while the hydrogen atoms were optimized by semiempirical method PM6 implemented in Gaussian package.24 The nearest 15 neighbors of coronene were chosen as species located within the distance equal to the sum of vdW radii plus 1 Å with respect to the reference coronene molecule. The dependences of energy versus angle rotation for coronene fragment in the coronene−F4TCNQ 2:1 structure were obtained by scanning the angle from 0° to 60° with the 2° step, with only hydrogen atoms optimized by the PM6 method. First, the energy profiles were obtained separately for each neighbor. Then, the optimization was performed taking into account all 15 coronene neighbors. Received: April 25, 2017 Revised: June 30, 2017 Published: July 20, 2017 4703
DOI: 10.1021/acs.cgd.7b00588 Cryst. Growth Des. 2017, 17, 4703−4709
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Article
RESULTS AND DISCUSSION Experimental Data on the Rotation of Molecules in the Crystals Depending upon Their Position on the Crystallographic Symmetry. Obviously, the height of the rotation barrier of the molecules in the crystal depends on the intermolecular interactions.25 However, numerous attempts to define generally intermolecular contacts impeding rotation have not always been successful. As for the objects in this study, crystals containing molecules of benzene, cyclopentadienyl ring in metallocenes (Cp ring), and coronene as ones of the most studied objects against rotation molecules in crystals were selected. Let us consider the effect of the location of the rotating molecule (the rotating part of the molecule) on the height of the rotation barrier. With this purpose Tables 1, 2, and 3
height of the rotational barrier for the orthorhombic modification only. The rotation barrier of benzene in the structure of benzene clathrate28 was defined by us with the cosine approximation5 by the formula B = RT/(1 − cos(nφ)), own value of the tensor L1 0.0081 (Rij = 0.0268) is obtained using XP program.32 In this structure the location of the benzene in the general positions promotes to the lowest value of the rotation barrier we found in the literature for the benzene molecules in crystals. In the benzene cyclamer structure,29 the benzene molecule is located on the crystallographic 3-fold axis and on the center of symmetry in a way that only one-sixth of benzene remains independent, and the location of molecules in special positions leads to the high rotation barriers. Because of lack of data on the height of the rotation barrier of the benzene molecules in various crystals we consider the rotation barrier height of the sandwich molecules. The rotation relative to the molecular 6-fold axis in the (η6-C6H6)2Cr molecule practically is free so the height of the rotation barrier of benzene in the crystal (η6-C6H6)2Cr depends mainly on the intermolecular interactions.25 In this structure, the benzene moiety is located on the crystallographic 3-fold axis which coincides with the molecular 6-fold axis. As will be shown below, the rotation barrier height of benzene should be the lowest in the case of phase V31 among all polymorphs because there is only general position of benzene in known polymorphs. Let us consider rotation of the Cp rings in the metallocene (Figure 2) relatively to the molecular 5-fold axis in the crystals (Table 2). Ferrocene forms three polymorphs for each of them in the paper,33 and the rotation barrier heights were determined by a cosine approximation based on TLS analysis. The values found are in good agreement with the results of investigations by NMR34,36 and incoherent quasi-elastic neutron scattering (IQENS)37 methods. Table 2 shows that, as in the previous cases, the position of the molecules in a general position (ferrocene−triclinic) leads to a much lower rotation barrier in comparison with the position of the molecules in special positions (ferrocene−orthorhombic). However, in the monoclinic ferrocene molecules are arranged in special positions at the center of inversion, and the value of the rotation barrier for this case is the lowest in the series of the presented polymorphs. It should be clarified that in orthorhombic ferrocene the molecule is located on the plane of symmetry so that two halves of different Cp rings are independent. On the other hand, in the case of the monoclinic structure the inversion center is located on the iron atom, and it leaves one Cp ring fully independent. Crystallization of ferrocene in chiral groups gives naturally to the absence of crystallographic planes and the centers of
Table 1. Selected Crystal Parameters for the Crystals Containing Benzene Molecules crystal benzene clathrate28 benzene26 (η6-C6H6)2Cr25 benzene cyclamer29
space group
Z′ of benzenea
P1̅
1
Pbca Pa3̅ R3̅
0.5 1/3 1/6
special position
i 3 3+i
rotational barrier, kJ/mol 5.8 (our estimation) 17.627 28.725 2530
case I II II II
a Z′ is the number of formula units in the unit cell divided by the number of independent general positions.
summarize data on the barrier height of the molecule rotation relative to the axis of symmetry of the highest order and crystallographic parameters of the selected compounds under consideration. It should be noted that three cases may be realized for the location of a molecule relative to the crystallographic symmetry: (1) Case I − the location in a general position; (2) Case II − the location in a special position without disordering by symmetry; (3) Case III − the location in a special position with disordering by symmetry. Such classification will be used in this article. Let us consider the rotation of the benzene (Figure 1) in the crystal relative to the molecular 6-fold axis (Table 1). Seven polymorphs of benzene are already known, two of which were experimentally determined. The structure of the remaining five polymorphs were predicted theoretically.31 In all of these structures benzene is located in special positions except theoretically predicted phase V31 with space group P21. To the best of our knowledge, the literature contains data on the
Table 2. Selected Crystal Parameters for Crystals Containing Metallocene Molecules crystal
space group
Z′ of Cp ring
ferrocene−triclinic33 ferrocene−monoclinic33 ferrocene−deoxycholic acid38 trans-bis(μ2-carbonyl)-dicarbonyl-bis(η5-cyclopentadienyl)-di-iron40 nickelocene42 titanocene dichloride47 ferrocene−orthorhombic33 ruthenocene45,46
P1̅ P21/c P212121 P21/c P21/c P1̅ Pnma Pnma
4 1 1 1 1 4 0.5 + 0.5 0.5 + 0.5
4704
special position
rotational barrier, kJ/mol
case
m m
6−1033−37 2.7−5.433,36,37 krot > 108 s−139 12.541 5−6.533,43,44 2.134 24.833,36 9.6−5033−35
I I I I I I II II
DOI: 10.1021/acs.cgd.7b00588 Cryst. Growth Des. 2017, 17, 4703−4709
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Table 3. Selected Crystal Parameters for the Crystals Containing Coronene Molecules
a
crystal
space group
Z′ of coronene
coronene−F4TCNQ 2:123a coronene−TCNQ 3:150 coronene−[Ni(mnt)2] 2.5:150b coronene23 coronene−F4TCNQ−MeCN 1:1:123 coronene−F4TCNQ 1:149 coronene−TCNQ 1:151 coronene−Me2TCNQ49 coronene−(MeO)2TCNQ49 coronene−Mo6Cl142−52
C2/c P1̅ P1̅ P21/n P21/n P1̅ P21/c P21/n P1̅ Pm3̅m
1 1.5 2.5 0.5 0.5 0.5 0.5 0.5 0.5 1/8
special position
rotational barrier, kJ/mol
case
i i i i i i 4
8.3−1423,48 13.750 750 2749 65−7723 3049 1749 2449 2349 1552
I I I II II II II II II III
TCNQ − tetracyanoquinodimethane. bmnt − maleonitriledithiolate.
Figure 1. Benzene rotation around the 6-fold axis of molecular symmetry.
Figure 3. Coronene rotation around the six order molecular symmetry axis.
shows three structures that contain molecules of coronene arranged in general position; all of them have lower values of the rotation barrier than the other structures. The rotation barrier of coronene in the coronene−Mo6Cl142− structure is much lower than in other cases with coronene in a special position. In this case, the coronene molecule is located at the 4fold crystallographic axis (case III), resulting in disordering of coronene. According to a search in the CCDC six more structures are already known containing coronene in a general position,53−59 but for them information about the rotation barrier height is absent. On the basis of the given article this barrier should be lower than in crystals where the coronene occupies a special position. From Tables 1−3 it is clear that there is a relationship between the arrangement symmetry and rotation barrier height of molecule (moiety). Apparently, the presence of benzene in a special position on the inversion center in both experimentally confirmed polymorphs is the main cause of the absence of noticeable rotation of the benzene molecules in these crystals. Working Hypothesis. At this stage, the authors offer a hypothesis description of the observed qualitative correlation. When the molecule is removed from the stationary state, the symmetry of the environment of the molecule leads to the cooperation of forces from the opposite sides of the molecule. Further, this will be discussed in terms of the influence of individual forces on the rotational barrier. Let us analyze the rotational barriers on the example of the coronene. In the first approximation, we can consider the profile of rotational barrier in the crystal as the cosine. Energy of the rigid molecule rotation barrier depends only on the intermolecular interactions that are complex (Figure 4a). However, one can analyze the contribution of a certain contact to the energy profile of rotational barrier removing all but one of the intermolecular contacts (Figure 4b). As well, we can leave to analyze two or more contacts, for example, all the contacts of half coronene (Figure 4c).
Figure 2. Cp ring rotation around the five order molecular symmetry axis in metallocenes.
symmetry. Below we will show that this fact leads to low rotational barrier, for example, in the structure of the ferrocene−deoxycholic acid crystal.38 Unfortunately, the literature does not provide an accurate value of the rotation barrier height for the case, but in the work39 it was shown that this barrier should be low. Let us consider the data on the rotation of the coronene (Figure 3) in the crystals with reference to the molecular symmetry axis of the six order (Table 3). In the coronene−TCNQ 3:1 structure two symmetrically nonequivalent coronene molecules are present. The paper50 reported that one of these molecules has significantly less rotation barrier, and Table 3 shows data for this particular coronene molecule. The second coronene molecule, which has a much higher barrier of rotation, is located in a special position. A similar circumstance is realized in the complex coronene−[Ni(mnt)2] 2.5:1 where there are three independent coronene molecules, two of which are located in the general position and have similar values of the rotation barrier height, 7 kJ/mol,50 while the molecule which is located in a special position has a significantly higher rotation barrier.50 Table 3 4705
DOI: 10.1021/acs.cgd.7b00588 Cryst. Growth Des. 2017, 17, 4703−4709
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Figure 4. Intermolecular interactions of coronene in a hypothetical crystal. From the left to the right: all intermolecular interactions; one intermolecular interaction; all the intermolecular interactions of one-half of coronene.
barrier is equal to the sum of the amplitudes (see Figure 5, black line). Case III. A molecule is located in a special position on disproportionate symmetry and disordered by symmetry (for example, complex coronene−Mo6Cl142−52). Disordering molecule by symmetry leads to a new equilibrium states as well as to increase of number of minima in the rotational profile. This leads to decreasing the rotation barriers (see Figure 6 and more information in ref 22).
After an attempt to estimate the presence of a phase shift and new minima on the profile of the rotation barrier by enumeration of various operations of crystallographic symmetry on molecules of various symmetry, we distinguish three cases: I − when a molecule is in a general position; II − when a molecule is in a specific position and not disordered by symmetry; III − when a molecule is in a special position on disproportionate symmetry and disordered by symmetry. Case I. A molecule is in a general position (for example, complex coronene−F4TCNQ 2:123). Let us divide molecule into two identical parts and consider the contribution to the rotational profile of the two parts of the molecule. Since the two identical parts of the molecule have a different environment, the rotational profile will be different in the starting phase and in amplitude but with the same period. Because the initial phase will not be the same, the value of the total barrier obtained by summing up the rotational profiles is less than the sum of two amplitudes (see Figure 5). In the case considered by us, at a maximum of the rotation profile on one side of the molecule there is a minimum on the other side (see below).
Figure 6. Potential energy surfaces calculated in cosine approximation (E = 1/2E0(1 − cos(nφ)) for rotators with axial symmetry C2 (n = 2), C4 (n = 4), C6 (n = 6), and C∞ (n = ∞) (see ref 22).
The above consideration means that the rotational barrier will be higher when the molecule is located in case II as compared with cases I and III. Let us consider rotational barrier of the coronene−F4TCNQ 2:1 complex23 in more detail. The coronen molecule here is in a general position. The height of the rotational barrier of coronene in the crystal coronene−F4TCNQ 2:123 is estimated by us to be 6.5 kJ/mol with quantum chemical computations. Figure 7 shows the calculation results of the rotational profiles taking into account 15 neighboring molecules simultaneously and separately are about the same. Figure 8 shows the environment of the coronene molecule highlighted in red in the coronene−F4TCNQ 2:1 complex on opposite sides of the molecule. Figure 9 shows two calculated rotational profiles of coronene: the red line corresponds to the accounting effect on the rotation of surrounding molecules on
Figure 5. Sum of two cosine waves with the same amplitude and period at the various shifts of their phases (Δ). Emax is the height of barrier in a.u.
Case II. A molecule is located in a special position (for example, complex coronene−F4TCNQ−MeCN 1:1:123). The location of coronene on the crystallographic symmetry center leads to two parts that have the same environment, and then the rotational profile will be the same at the initial phase and amplitude. Consequently, the total value of the rotational 4706
DOI: 10.1021/acs.cgd.7b00588 Cryst. Growth Des. 2017, 17, 4703−4709
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(Part 2, Figure 8b). The rotation profile of the two parts of surroundings is obtained by summing the rotation profiles obtained by the influence of individual neighboring molecules. Obviously, when the coronene is positioned at the center of the inversion as in crystals coronene−F4TCNQ−MeCN 1:1:1,23 the influence of the environment on the rotation profiles of the opposite parts will coincide to increasing the rotational barrier high. As is evident from Figure 9, the calculated rotational profiles, that take into account the intermolecular interaction with the two sides of the coronene, do not match either in magnitude or in the initial phase, in contrast to the case when the coronene is at the crystallographic inversion center (see Table 3). Thus, on the basis of a hypothesis relative to the discovered correlation, it was possible to distinguish three cases of position of molecules relative to symmetry in the aspect of the influence on rotation in crystals, despite the rare empirical data on the III type of position. Moreover, since the regularities are related only to the principal trend of the intermolecular interactions, these regularities are applicable for comparison of crystals with similar energy of intermolecular interactions (the E amplitude). It should be noted that the high mobility of the molecules is not conducive to crystalline state. In an extreme case, crystals with a high mobility of the molecules are transformed into liquid. On the basis of patterns described in this article, it may be assumed that the molecules tend to occupy a special position to reduce mobility. It is well-known that the strongest intermolecular bonds (e.g., hydrogen bonds) formed on the symmetry elements (in the case of carboxylic acids on the inversion center). Through strong intermolecular interactions molecules form oligomeric and polymeric structures, dimers in the case of carboxylic acids. This behavior of chiral carboxylic acids often causes the crystallization with Z′ ≥ 2. Such dimers can be considered as individual particles. In the crystals such dimers are often located on the crystallographic symmetry. In our opinion, this tendency is due to a decrease of the particle mobility at a special position. Enthalpy factor contributes to the arrangement of the molecules in a special position, while the entropy factor−in a general position. It should be mentioned that this article is limited only to the conceptual consideration of the effect of the directionality of weak intermolecular interactions on the rotation barriers. Strong intermolecular interactions such as hydrogen bonding are not analyzed here. As follows from the presented results, in all the cases considered, the factor of the directionality of weak interactions prevails over other factors.
Figure 7. Rotational barriers of coronene in the coronene−F4TCNQ 2:1 crystal according to quantum chemical computations. The red line corresponds to the sum of the rotational barrier profiles at the interaction of one coronene molecule with 15 neighboring molecules separately, and the black line refers to the rotational barrier profile taking into account the interaction of one coronene molecule with 15 neighboring molecules simultaneously.
Figure 8. Surroundings of the coronene molecule (red color) in the coronene−F4TCNQ 2:1 crystal:23 (a) Part 1 left; (b) Part 2 right.
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CONCLUSIONS The correlations in the dependences of the rotation barriers height of molecules on their location in the crystal packing were established. According to the location of the molecule with respect to the crystallographic symmetry elements three cases are possible: I − the location of the molecules in a general position; II − the location of the molecules in special positions without symmetry disordering; III − the location of the molecules in special positions with symmetry disordering. On the basis of the experimental data and theoretical analysis, it was shown that the rotation barrier height at the location of the molecules in the cases I and III is lower than in the case II. The reasons for this phenomenon are the amplitude and phase shift of the rotational energy profiles of two parts of the molecule in the case I and increasing the number of minima on the rotation
Figure 9. Calculated contributions to the coronene rotational barrier profile in the coronene−F4TCNQ 2:1 crystal from the intermolecular interactions with two different sides around the coronene (Part 1− black line; Part 2 − red line; see Figure 8).
the one hand (Part 1, Figure 8a) and black line corresponds accounting all surrounding molecules on the opposite sides 4707
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barrier profile at disordering the molecules by symmetry in the case III. The regularities revealed lead, in particular, to the following predictive conclusions: (1) The lowest rotational barrier among polymorphs of benzene should occur in the benzene V crystals. (2) At the cocrystallization of ferrocene with enantio-pure compounds the barrier height of the Cp ring rotation is lower than for the orthorhombic polymorphs and comparable with the barrier height of the Cp ring rotation in the triclinic and monoclinic polymorphs of ferrocene.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
Daut R. Islamov: 0000-0002-5988-1012 Valery G. Shtyrlin: 0000-0003-4820-884X Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The reported study was funded by RFBR according to the Research Project No. 16-33-00641 and by the Russian Government Program of Competitive Growth of Kazan Federal University.
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REFERENCES
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Crystal Growth & Design
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DOI: 10.1021/acs.cgd.7b00588 Cryst. Growth Des. 2017, 17, 4703−4709
