DOI: 10.1002/chem.201500296

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& Quantum Chemistry

Probing Ionic Crystals by the Invariom Approach: An Electron Density Study of Guanidinium Chloride and Carbonate Yulia V. Nelyubina* and Konstantin A. Lyssenko[a] Dedicated to Professor V. I. Minkin on the occasion of his 80th birthday

Abstract: A comparative study of two guanidinium salts, chloride and carbonate, is carried out to test the performance of the invariom approach for ionic crystals. Although treating them as formed by isolated ions with no charge transfer between them, the invariom approach

Introduction Electron density studies from X-ray diffraction are very helpful in addressing many important chemical problems in modern material and biosciences.[1] They, however, require accurate datasets to be collected at the lowest temperature possible for a single crystal of excellent quality and reflective power, which is a challenge for most of the crystalline materials. In those cases, a recent concept of invarioms (aspherical atomic scattering factors)[2] may be of use. Introduced to replace an independent atom model (IAM)[3] in crystal structure refinement, it is steadily emerging as a simple and convenient tool in experimental electron density studies[1] of small and large organic molecules.[4] By using database entries[5] of multipolar parameters computed at a high level of theory[6] within the Hansen– Coppens formalism[7] for each atom in a given covalent environment, it performs as fast as IAM[6, 8] and provides results that are as informative as those from conventional multipole refinement of high-resolution X-ray diffraction data.[8] Although the invariom approximation is based on pseudo-atoms derived from isolated molecules and thus does not take crystal environment into account, it reproduces features of covalent bonds with the accuracy of a full multipole refinement[8–10] and gives a rather adequate description of intermolecular interactions in crystals formed by hydrogen bonds[3, 10–13] and an even better one for those formed by weak van der Waals contacts.[14] It also has an advantage of providing experimental electron densities (as they are still based on X-ray diffraction data) for systems that are not accessible otherwise; those of

[a] Dr. Y. V. Nelyubina, Prof. K. A. Lyssenko A. N. Nesmeyanov Institute of Organoelement Compounds Russian Academy of Sciences, 119991, Vavilova Str., 28, Moscow (Russia) E-mail: [email protected] Supporting information for this article is available on the WWW under http://dx.doi.org/10.1002/chem.201500296. Chem. Eur. J. 2015, 21, 9733 – 9741

provides features of interionic contacts that are amazingly similar to those obtained from conventional charge density analysis of high-resolution X-ray diffraction data, thus emerging as an easy way towards reliable description of chemical bonding peculiarities in ionic crystals.

a larger size,[4, 15] having poor reflective power,[4, 6, 12, 16] suffering from disorder[15] or twinning,[17] and so on. The invariom concept is generally applicable to any organic compound (as new invarioms for atoms in other covalent environments may be easily calculated[18]); however, it has been tried almost only on molecular crystals with an exception being one example of the invariom modeling of an organic chloride.[16] This may be in part due to this approach allowing no charge transfer between molecules even if the symmetry of a crystal does not forbid it, such as in systems with several independent molecules in a asymmetric part of the unit cell (Z’ > 1).[16, 17] Applying the procedure of achieving electroneutrality as in the above salt[16] (see the Experimental Section) implies that net charges of ionic species do not deviate from their formal values, although they should because of cation–anion interactions.[19] Thus, the chloride anion[16] involved in hydrogen bonding with a ciprofloxacin cation was treated as having a net charge of ¢1 e; the features of cation–anion interactions resulted from such a treatment were not, however, evaluated in that study.[16] To confirm the applicability of the invariom concept to ionic crystals of organic compounds, these features should be accessed and compared with those obtained from a full multipole refinement of high-resolution X-ray diffraction data that do account for charge redistribution between the species. Also, note that the invariom entry for the chloride anion describes its electron density as spherically symmetric (since it forms no covalent bonds), whereas it is not so in a crystal environment (see Figure 3, below), and the observed deformation of electron density of the chloride anion is clearly governed by interionic (as Cl¢···Cl¢ contacts are also possible)[20] interactions. In this case, one could expect the cation–anion interactions to be rather poorly described by the invariom approximation as compared, for example, with those involving an anion that has covalent bonds in it (such as nitrate, carbonate, etc.), if at all.

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Full Paper The motivation for our study is to provide evidence on how the invariom approach would perform for ionic systems if it does not account for charge transfer, and how it would (or would not) reproduce parameters of interionic interactions for species that have their electron densities defined by covalent bonds and those governed by crystal environment. For this purpose, we have chosen two salts sharing the same biologically relevant[21] guanidinium cation, that is, chloride[22] [C(NH2)3]Cl and carbonate[23] [C(NH2)3]2CO3 (hereinafter referred as GuaCl and GuaCO3 ; Figure 1). To compare the features of the guanidinium cation (which should show transferability, the central concept of the invariom approach) and of interionic interactions it forms with different counterions as revealed from two models of electron density distribution, we have performed a high-resolution X-ray diffraction investigation of these salts.

Figure 1. General views (top) and fragments of the crystal packing, showing the environment of the anions (bottom), in GuaCl (left) and GuaCO3 (right).

Four electron densities resulted from the full multipole and invariom refinements of the data obtained for GuaCl and GuaCO3. These were analyzed by using Bader’s “Atoms in Molecules” (AIM) theory.[24] The latter is very useful for identifying all bonding (stabilizing) interactions in a crystal by the presence of bond critical points (bcps) and then quantifying them by the values of electron density and its derivatives, as many descriptors used in search for structure–property relations[25] are based on them. In particular, the value of local potential energy v(r) in a bcp provides an estimate for the energy of an interaction (Eint);[26, 27] a semi-qualitative relation between these two parameters was initially observed for H-bonds[26, 27] and later successfully applied to other types of intermolecular and interionic interactions[28] (it is also the best choice for estimating the energy of binding between ionic species, for which Chem. Eur. J. 2015, 21, 9733 – 9741

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classical “energy difference-based” approach in quantum chemistry predicts destabilizing character[29]). This methodology proved very helpful for revealing a good performance of the invariom approximation for molecular crystals, with a sum of the interaction energies thus estimated quite nicely reproducing the energy of a crystal lattice.[14]

Results and Discussion In the two crystalline salts, the guanidinium cation adopts a very similar geometry whether chloride or carbonate anion is present (Figure 1). In agreement with previous X-ray diffraction data[22, 23] and theoretical studies,[30] its CN3 fragment is planar (within 0.003(1) æ) with C¢N bond lengths falling within a narrow range (1.3249(3)–381(4) æ); the lowest and largest of these values are found in GuaCO3. Its hydrogen atoms are slightly out of plane, and their deviation from the CN3 mean plane is larger in GuaCO3 (up to 0.18 æ) than in GuaCl (0.10 æ). The carbonate moiety, which occupies a special position in GuaCO3 (a 2-fold axis that passes through O(1) and C(2) atoms), is perfectly planar; its C¢O bond lengths are close (1.2853(3) and 1.2910(4) æ) and typical for a carbonate moiety. With a geometry resembling that of an isolated anion (C¢O 1.307 æ), it should be rather well described by the invariom approximation (see also the Experimental Section) despite being involved in moderate H-bonds (Figure 1). Each oxygen atom is an acceptor of four H-bonds (N···O 2.7739(3)–664(4) æ, NHO 165(1)–177(1) 8), none of which is in the plane of the carbonate moiety. This makes in total twelve H-bonds that are formed with six cationic species arranged around the carbonate anion in such a manner that three of them are above and three below its plane. All the hydrogen atoms of the guanidinium cation are involved in H-bonds, and the resulting supramolecular motif in GuaCO3 is a three-dimensional H-bonded framework. In GuaCl, the chloride anion forms six H-bonds (N···Cl 3.2325(3)–058(3) æ, NHCl 147(1)–158(1) 8) with three guanidinium species, two of which are in one plane and the third one being perpendicular to it (Figure 1). By using all of the hydrogen atoms of the cation, these H-bonds result in interpenetrating 3D frameworks linked by an anion···p interaction (Cl···C 3.5643(3) æ, ClCN 84.71(3)–100.00(3) 8; Figure 1); the latter being crucial for many important chemical and biological processes.[31] Two different types of cation–anion interactions observed in GuaCl and their influence on the electron density distribution of the chloride anion may also be compared, thus expanding the list of comparisons to be made in this study: those between the two guanidinium salts and between the two experimental models of electron density. Four electron density distributions thus available for the guanidinium cation in GuaCl and GuaCO3 make it a good starting point for assessing how well (or how bad) the invariom approximation may reproduce the features of ionic species from the full multipole refinement of high-resolution X-ray diffraction data. In all cases, the deformation electron densities for the guanidinium cation (Figure S2 in the Supporting Information) are very much alike: all have an approximate

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Full Paper C3v symmetry with the expected maxima along the covalent bonds. Topological analysis within the AIM approach (Table 1) also provides identical sets of bond critical points (bcps): those are closer to the least electronegative atom being nitrogen in N¢H or carbon in C¢N bonds. The largest difference in the corresponding 1(r) values for all the C¢N bonds is however small (0.13 e æ¢3) and may be accounted for their “natural spread” (0.1 e æ¢3).[32] The r21(r) values in these bcps vary by approximately 4 e æ¢5 from one salt to the other, which is well within the reported “transferability index” (3–4 e æ¢5);[32] a twice as large difference (up to 8 e æ¢5) between the two models reveals a deficiency of the invariom approach in describing electron density in ionic crystals.

Table 1. Topological parameters of 1(r) in bcps for covalent C¢N and C¢O bonds in GuaCl (top) and GuaCO3 (bottom) from full multipole and invariom refinements.[a] Interaction

D [æ]

1(r) [e æ¢3]

r21(r) [e æ¢5]

e[b]

C(1)-N(1)

1.3339(4) 1.3381(4) 1.3303(3) 1.3249(3) 1.3323(3) 1.3324(4) – 1.2910(4) – 1.2853(3)

2.48//2.40 2.44//2.39 2.46//2.42 2.52//2.41 2.46//2.41 2.44//2.41 – 2.73//2.52 – 2.59//2.51

27.19//20.98 24.58//20.57 25.63//21.69 25.85//22.36 27.92//21.40 28.79//21.32 – 40.06//30.92 – 37.91//29.59

0.23//0.26 0.15//0.25 0.19//0.26 0.29//0.25 0.23//0.26 0.25//0.25 – 0.07//0.17 – 0.09/0.21

C(1)-N(2) C(1)-N(3) O(1)-C(2) O(2)-C(2)

[a] The first//second entry denotes the values from multipole//invariom refinement; [b] e stands for bond ellipticity, which reflects a contribution of the p component to a bond.

Note that bond ellipticities obtained from the full multipole refinement show the inequality of the C¢N bonds that is not included in the invariom model, although they agree on significant electron delocalization over the guanidinium moiety (0.15–0.29 vs. 0.25–0.26). Therefore, the electron density for the guanidinium cation can be safely transferred between the two salts (although the net charge of this species should be different, as judged by different cation–anion interactions it is involved in), but the match is not as good between the invariom and full multipole models. The same is observed for the carbonate anion in GuaCO3. Although in this case the distinction between the two electron density distributions is more pronounced (Figure 2), their main features are still preserved, such as maxima along the covalent bonds and near the oxygen atoms. The latter are associated with the lone pairs of the oxygen atoms; those are exactly in the CO3 plane in the invariom density but slightly deviate from it in the full multipole one. The largest difference in electron density values in the bcps of the C¢O bonds as obtained from the two models (the values for the two symmetry-independent bonds within the same model are quite similar; Table 1) is higher than that observed for the C¢N bonds (0.21 vs. 0.13 e æ¢3); the r21(r) values vary by approximately 9 versus 8 e æ¢5 above. Chem. Eur. J. 2015, 21, 9733 – 9741

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Figure 2. Deformation electron density (DED) maps in the plane of the carbonate anion as obtained by invariom (left) and full multipole (right) refinements of GuaCO3. Contours are drawn through 0.1 e æ¢3, the negative contours are dashed.

Note that the ellipticities of the two C¢O bonds are also close (0.02–0.04) and agree with the electron density delocalization over the carbonate anion to the extent that is much lower in the case of the multipole model (0.07–0.09 vs. 0.17–0.21). However, overall agreement between the invariom and full multipole modeling of experimental data for the species that have covalent bonds is satisfactory (deformation electron density (DED) maps similar, topological parameters not very much different), which is much better than for the chloride anion. For the chloride anion in GuaCl, even the deformation electron density maps differ dramatically, showing spherical distribution of electron density around Cl(1) from the invariom refinement and a significantly distorted one from the full multipole modeling (Figure 3). The latter features four maxima attributed to four localized lone pairs of the chloride anion; their positions cannot be guessed a priori for a pointcharge ion such as Cl¢ . According to the analysis of ¢r21(r) topology, mutual arrangement of its lone pairs may be described as a flattened tetrahedron with vertices directed (although to a different extent) towards areas of electron density depletion near hydrogen atoms as typical for H-bonds (Figure 3). Those H-bonds are clearly responsible for the asphericity of electron density around the chloride anion in GuaCl; them being ignored (as in the invariom approximation) resulted in no such deformation. The same (i.e., the chloride anion being described differently in the two models) is also true for its net parameters such as charge and volume (Table 2), which are estimated by integrating over atomic basins defined according to the AIM formalism.[24] The charge for Cl(1) thus obtained from the invariom electron density approaches its formal value of ¢1, but it is twice as low in the case of the full multipole refinement (¢0.53 e) as a result of charge transfer through cation–anion interactions in GuaCl. Note that an even lower value (¢0.28 e) has been observed for the chloride anion in a previously studied crystal of [NH3OH]Cl,[20] which was involved in similar but stronger N¢H···Cl bonds (N···Cl 3.1780(5)–138(4) æ, NHCl 158(1)–160(1) 8). The latter agrees with the volume of the chloride anion being lower in [NH3OH]Cl[20] (27.91 æ3 vs. 32.44 æ3 in average); the difference in its volumes between the two electron density models for GuaCl being approximately 1.3 æ3.

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Figure 3. DED maps in the plane of N(1)¢H(1A)···Cl and N(2)¢H(2B)···Cl H-bonds showing the distribution of electron density around the chloride anion as obtained by invariom (left) and full multipole (right) refinements of GuaCl. Contours are drawn through 0.1 e æ¢3, the negative contours are dashed.

Table 2. Selected characteristics of the ionic species in GuaCl and GuaCO3 from multipole and invariom refinements.[a] Gua + q [e] V [æ3]

GuaCl Cl¢

+ 0.53// + 0.98 79.97//78.71

Gua +

¢0.53//¢0.99 31.81//33.07

GuaCO3 CO32¢

+ 0.29// + 0.99 93.44//90.01

¢0.57//¢1.98 48.98//55.35

[a] The first//second entries denote the values from multipole//invariom refinements. In all cases, the charge leakage as a result of numerical integration was less than 0.01 e, and the sum of atomic volumes (111.78 æ3 in GuaCl and 235.38–235.86 æ3 in GuaCO3) reproduced well the volume of an independent part of the unit cell (111.99 and 236.32 æ3) with a relative error not more than 0.4 %. Although integrated Langrangian (L(r) = ¢1/4r21(r)) for every atomic basin has to be exactly zero, a reasonably small value averaging to 0.1 Õ 10¢3 a.u. was obtained.

For the carbonate anion in GuaCO3, the difference between the models is even larger. Its charge from the full multipole refinement (¢0.57 e) is nearly a fourth of its formal value (¢2 e) and of its invariom charge (¢1.98 e). Although no experimental electron density data for an organic carbonate are available, a similar value of the net charge (¢0.69 e) was found in azurite [Cu3(CO3)2(OH)2] featuring an H-bond with the carbonate anion.[33] The latter also has very distinct volumes in GuaCO3 as revealed from the multipole and invariom electron densities: the difference is six times higher than for the chloride anion in GuaCl; these values (48.98 and 55.35 æ3) are comparable with the one in azurite (44.3 æ3). The distinction between GuaCl and GuaCO3 in terms of net ionic parameters appears clearly for the guanidinium cation. In the case of the multipole electron density, the guanidinium moiety has a net charge that varies from + 0.29 to + 0.53 e and a volume from 79.97 to 93.44 æ3 depending on the crystal environment; so little transferability of these parameters is observed between the salts as well as between the models (compare with the invariom charge for the guanidinium cation equal to + 0.98 to + 0.99 e and the volume of 78.71 to 90.01 æ3). Note that such a decrease in charge of ionic species is an important effect in crystal structure formation, as it may result in new types of supramolecular interactions.[34] Chem. Eur. J. 2015, 21, 9733 – 9741

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Charges and volumes for individual atoms of the guanidinium cation from the multipole and invariom refinements (Tables S1 and S2 in the Supporting Information) are more persistent for hydrogen atoms, which are involved in H-bonds with the anion, rather than for others, which are not. The largest difference for the former is 0.07 e and 0.6 æ3 only, whereas for the latter it reaches the values of approximately 0.30 e and 1.7 æ3 (for the atom N(2) with the shortest C¢N bond in both cases) that are comparable with those found for Cl(1) above (ca. 0.45 e, 1.3 æ3). Estimated from the multipole electron density, both these parameters have higher values for the guanidinium’s nitrogen atoms and lower for its carbon as well as for hydrogen atoms in GuaCl; for those in GuaCO3, the variation between the models seems random. The highest relative difference in charge (volume) for the non-hydrogen atoms in GuaCl and GuaCO3 is observed for the same nitrogen atom N(2) (the carbon atom C(1)). If, however, the variation is calculated relative to electronic population of an atom rather than its charge, the largest difference for the carbon and nitrogen atoms is twice as low as for hydrogens. Given much higher electron population of the chlorine atom, the corresponding decrease in its charge on going from the invariom to the full multipole electron density is rather minor and only slightly below that for the nitrogen atoms. Very similar differences between the two models are obtained for the atoms of the carbonate anion in GuaCO3. Their charges and volumes decrease by 0.33–0.41 e and 1.6–1.7 æ3, with the largest variation observed for the carbon atom. If compared between the two salts, the atomic charges for the guanidinium cation are the same within 0.01 e in the invariom model, but in the case of the full multipole refinement there is a ten-fold variation (up to 0.10 e) for hydrogen atoms. A rather small difference in the charge of the carbon atom (0.07 e) suggests only minor influence of the anion···p interaction (which involves this atom in GuaCl) on the electron density distribution within the ionic species, as expected for it being much weaker than the H-bonds with a much lower charge transfer to the guanidinium cation. The atomic volumes for this ion in the two salts, however, vary by approximately 4 æ3 for nitrogen, about 2 æ3 for carbon and 0.7 æ3 for hydrogen atoms, whether obtained from the full multipole or invariom models. The nitrogen atoms are more negatively charged and more compact in GuaCl; the opposite is true for charges of carbon and most of hydrogens, whereas no obvious trend is observed in the volumes of the hydrogen atoms. Added up, these atomic parameters result in the above charges and volumes of the ions, showing their little transferability between the salts and between the models but nevertheless giving neutral crystals of GuaCl and GuaCO3 with volumes of their unit cells quite nicely reproduced (Table 2). Variation of chemical bonding features within the ionic species in GuaCl and GuaCO3 is, of course, the result of interionic interactions, as is the difference between them from the two models of electron density, since these interactions are not accounted for in the invariom approximation. The question is how the latter affects qualitative peculiarities of electron

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Full Paper density distribution in the interionic areas and quantitative parameters of the interionic interactions. Topological analysis performed for this purpose has revealed the expected H-bonds in GuaCl and GuaCO3 as well as the anion···p interaction and additional Cl···N and N¢H···N ones in GuaCl (the latter being the only type of interactions between the like-charged ions in the two salts), all identified by the presence of bcps (Figure 4). Identical sets of these bcps, as of all other critical points (3, + 1) and (3, + 3), were found in the invariom and full multipole models.

electron density depletion area at the central carbon atom of the guanidinium cation. Topological parameters in the bcps of all the cation–anion interactions show the expected difference of the interionic bonding in the two salts but also its amazing similarity in the two electron density models (Tables 3 and 4). In GuaCl, the Hbonds (N···Cl 3.2325(3)–058(3) æ, NHCl 147(1)–158(1) 8) are closed-shell interactions with rather low 1(r), positive r21(r) and electron energy density (he(r)) values at bcps, which vary in narrow ranges of 0.08–0.12 e æ¢3, 1.15–1.88 e æ¢5, and 0.0016–0.0042 a.u., respectively. Note that the observed variation in 1(r) and r21(r) by up to 0.03 e æ¢3 and 0.39 e æ¢5 arising from the use of the invariom approximation is very much below the above “transferability indexes” (0.1 e æ¢3 and 3–4 e æ¢5).[32]

Table 3. Topological parameters of 1(r) in bcps for interionic interactions in GuaCl from multipole and invariom refinements.[a] Interaction

1(r) [e æ¢3]

r21(r) [e æ¢5]

he(r) [a.u.]

¢v(r) [a.u.]

Eint [kcal mol¢1]

Cl(1)···H(1A)[b]

0.08 0.09 0.08 0.09 0.09 0.10 0.09 0.12 0.10 0.12 0.09 0.11 0.03 0.04 0.03 0.03 0.04 0.04 0.03 0.03 0.03 0.03

1.32 1.15 1.35 1.17 1.49 1.24 1.88 1.49 1.88 1.50 1.73 1.42 0.35 0.39 0.39 0.34 0.48 0.45 0.44 0.39 0.38 0.33

0.0029 0.0018 0.0029 0.0019 0.0032 0.0018 0.0042 0.0016 0.0038 0.0017 0.0037 0.0018 0.0087 0.0088 0.0010 0.0009 0.0012 0.0011 0.0012 0.0010 0.0011 0.0009

0.0079 0.0083 0.0083 0.0085 0.0091 0.0093 0.0101 0.0122 0.0120 0.0122 0.0105 0.0112 0.0019 0.0022 0.0018 0.0017 0.0026 0.0025 0.0021 0.0021 0.0018 0.0017

2.5 2.6 2.6 2.7 2.9 2.9 3.5 3.8 3.8 3.8 3.3 3.5 0.6 0.7 0.6 0.6 0.8 0.8 0.7 0.7 0.6 0.6

Cl(1)···H(1B)[b] Cl(1)···H(2A)[b] Cl(1)···H(2B)[b] Cl(1)···H(3A)[b] Cl(1)···H(3B)[b] Cl(1)···C(1) Cl(1)···N(1)[c] Cl(1)···N(2)[c] N(2)···H(1A)[d] N(3)···H(1B)[d] Figure 4. Cation–anion interactions in GuaCl (top) and GuaCO3 (bottom) identified by bcps (orange spheres) and bond paths (orange lines) in the electron density from both the multipole and invariom refinements. Interatomic distances for cation–anion interactions in GuaCl and GuaCO3 [æ]: N(1)···Cl(1) 3.3366(3) and 3.3207(3), N(2)···Cl(1) 3.3058(3) and 3.2419(3), N(3)···Cl(1) 3.2325(3) and 3.2558(3), Cl(1)···C(1) 3.5643(3), Cl(1)···N(1) 3.7381(3), Cl(1)···N(2) 3.5280(3); N(1)···O(1) 2.9499(3) and N(1)···O(2) 3.1664(4), N(2)···O(1) 2.8847(3) and N(2)···O(2) 2.7739(3), N(3)···O(2) 2.7732(4) and 3.0822(4).

[a] The first and second entries denote the values from multipole and invariom refinement. [b] Atoms H(1A) and H(2B), H(1B) and H(3A), H(2A) and H(3B) are obtained from the basic ones by symmetry operations ¢x + 1, y¢1, ¢z; x¢0.5, y, ¢z¢0.5; x, ¢y¢0.5, z¢0.5, respectively. [c] Atoms N(1) and N(2) are obtained from the basic ones by symmetry operations x¢1, y, z, and x¢1, ¢y + 0.5, z¢0.5. [d] Atoms H(1A) and H(1B) are obtained from the basic ones by symmetry operation: ¢x + 1.5, y + 0.5, z.

Note that in all cases the H-bonds involving the anions display an electron density distribution that is of a peak-to-hole type (as in Figure 3), although oxygen’s lone pair domains of the carbonate anion in GuaCO3 are not directed exactly towards the corresponding hydrogen atoms (Figure S3 in the Supporting Information). The same type of electron density distribution is observed for the anion···p interaction in GuaCl (Figure S3, the Supporting Information); the latter may also be described as a lone pair of the chloride anion pointing at an

Energy of the H-bonds estimated by Espinosa’s relation based on the v(r) value at a bcp[26, 27] found in either full multipole or invariom electron density (Eint) is 2.5 to 3.8 kcal mol¢1 (Table 3). For comparison, the interaction energies in the range of 4.4–4.7 kcal mol¢1 were signed to H-bonds in [NH3OH]Cl[20] (N···Cl 3.1780(5)–138(4) æ, NHCl 158(1)–160(1) 8); the difference agrees with the anion-to-cation charge transfer, as estimated from the full multipole electron densities, being 1.5 times lower in GuaCl (see above). The largest difference in the Eint

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Full Paper values for the H-bonds obtained from the invariom and full multipole refinements for GuaCl is below 0.3 kcal mol¢1. The energy estimated for the anion···p interaction from the two models is even closer (0.6 vs. 0.7 kcal mol¢1), as in the case of other cation–anion and cation–cation interactions; being weak, those are better described by the invariom approximation.[14]

Table 4. Topological parameters of 1(r) in bcps for interionic interactions in GuaCO3 from multipole and invariom refinements.[a] Interaction

1(r) [e æ¢3]

r21(r) [e æ¢5]

he(r) [a.u.]

¢v(r) [a.u.]

Eint [kcal mol¢1]

O(1)···H(1A)

0.11 0.16 0.08 0.10 0.16 0.18 0.17 0.24 0.22 0.23 0.10 0.12

2.95 2.10 1.76 1.22 3.25 2.47 4.78 3.29 4.25 3.25 2.10 1.51

0.0074 0.0018 0.0042 0.0015 0.0059 0.0019 0.0103 0.0004 0.0055 0.0009 0.0049 0.0018

0.0158 0.0182 0.0099 0.0097 0.0219 0.0219 0.0290 0.0334 0.0332 0.0319 0.0121 0.0121

5.0 5.7 3.1 3.0 6.9 6.9 9.1 10.5 10.4 10.0 3.8 3.8

O(2)···H(1B)[b] O(1)···H(2A)[b] O(2)···H(2B) O(2)···H(3A)[b] O(2)···H(3B)[b]

[a] The first and second entries denote the values from multipole and invariom refinement. [b] Atoms H(1B), H(2A), H(3A), and H(3B) are obtained from the basic ones by symmetry operations: y, x¢1, ¢z; y + 0.5, ¢x + 0.5, z¢0.25; x, y¢1, z and x + 0.5, ¢y + 0.5, z¢0.25, respectively.

Note that according to quantum chemical modeling of cation–anion bonding in GuaCl,[30] two dimers formed by pincer-like interactions were found to be at an energy minimum. Those formed through H-bonds and a Cl···C orthogonal interaction (Figure 1); the former being stronger as in our case. Both types of cation–anion bonding were strong closed-shell interactions with a pronounced charge transfer and 1(r) values in their bcps of the same order of magnitude as estimated from the invariom and full multipole refinement of X-ray diffraction data that we have acquired for GuaCl. In GuaCO3, the only interactions present (Figure 4) are the above cation–anion H-bonds (N···O 2.7739(3)–664(4) æ, NHO 165(1)–177(1) 8). These are also strong closed-shell interactions with the 1(r), r21(r), and he(r) values varying in the ranges of 0.08–0.23 e æ¢3, 1.22–4.78 e æ¢5 and 0.0004–0.0103 a.u., respectively. The difference in the 1(r) and r21(r) values obtained from the two electron density models (0.08 e æ¢3 and 1.49 e æ¢5) is two- and five-times that in GuaCl but still falls well below the “transferability indexes” (0.1 e æ¢3 and 3– 4 e æ¢5).[32] The Espinosa’s interaction energies (Eint) for these Hbonds vary from 3.1 to 10.5 kcal mol¢1 (Table 4), following the trends in their structural parameters. Unlike with GuaCl, the values obtained for the H-bonds involving the carbonate anion cannot be directly compared with those for other carbonate salts, as these data are scarce. Thus, an H-bond in the abovementioned [Cu3(CO3)2(OH)2],[33] which is not so short and directional (O···O 2.9817(8) æ, OHO 150 8) and occurs between two like-charged species, has a much lower energy of 1.7 kcal mol¢1, and an Eint value of 2.1 kcal mol¢1 has been assigned to Chem. Eur. J. 2015, 21, 9733 – 9741

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a N¢H···O bond in the above [NH3OH]Cl[20] (N···O 2.9780(4) æ, NHO 105(1) 8). The estimated energies for GuaCO3 agree, however, with those in molecular systems, such as polymorphs of paracetamol with similar N¢H···O bonds (N···O 2.9040(4) and 2.9354(4) æ, NHO 163(1) and 162(1) 8, 6.0 and 4.6 kcal mol¢1); the accuracy of energy evaluation for the latter has been proved by a good agreement between total interaction energies and experimental sublimation enthalpies of the two polymorphs.[35] For GuaCO3, the largest difference between the interaction energies from the full multipole and invariom refinements is 1.4 kcal mol¢1 (Table 4) and observed for the H-bond N(2)¢H(2B)···O(2) that is the second to the strongest one N(3)¢H(3A)···O(2) (its energy from the two models varying by 0.4 kcal mol¢1 only). The better match of these values for the latter agrees with the lone pair (lp) domains of the oxygen atoms occupying ideal positions in the case of the invariom density: according to the analysis of ¢r21(r) topology, the corresponding maxima are exactly in the CO3 plane with an angle lpOC of approximately 120 8. The relevant angles formed between the NH groups and the CO3 mean plane for the above H-bonds N(2)¢H(2B)···O(2) (9.1/10.5 kcal mol¢1) and N(3)¢ H(3A)···O(2) (10.4/10.0 kcal mol¢1) are 56 and 49 8, respectively, with the HO(2)C(2) angles being 114 and 130 8. For other H-bonds (as no other types of interionic interactions are found in GuaCO3), the difference between the interaction energies from the two models may be as low as 0.1 kcal mol¢1 (similar to GuaCl). Differences in strength of interionic interactions in GuaCl and GuaCO3 agree with the charge transfer (as obtained from the full multipole electron density) that is two times higher in the carbonate salt: total energy of all the cation–anion interactions per one guanidinium moiety is 20.5 kcal mol¢1 in GuaCl and 38.3 kcal mol¢1 in GuaCO3, and the corresponding charge transfer is 0.45 and 0.71 e; both in line with a correlation found[34] between these parameters in other ionic salts. Although this charge redistribution in GuaCl and GuaCO3 is not accounted for in the invariom approximation, the quantitative features of interionic interactions are reproduced amazingly well. Note that despite the well-recognized “importance of promolecule”,[36] if the electron densities in the two salts are composed from non-interacting overlapping spherical atoms (a pro-crystal model),[37] the number and type of interionic interactions in these crystals remain unchanged, but their topological parameters vary greatly (Table S3, the Supporting Information). Even though 1(r) in intermolecular regions should be close to that produced by the pro-crystal model, and so should be the values of v(r) in bcps and consequently Eint, the energy of H-bonds thus obtained for GuaCl and GuaCO3 is much higher; the variation from the Eint values estimated in the same way but based on the full multipole or invariom density is up to 70 %. The use of aspherical pseudo-atoms within the invariom approach gives a much better agreement with the full multipole modeling in GuaCl and GuaCO3 : the difference in the energies of the H-bonds is at most 6 and 15 %, respectively. This emphasizes the deficiency of the pro-molecule model in describing electron density distribution in ionic crys-

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Full Paper tals as compared with the invariom approximation, although it is nearly as easy to employ.

Conclusion Already a useful tool in electron density studies of molecular crystals, the invariom approach now emerges as an easy way to get insight into chemical bonding in ionic crystals as well. Although it describes them as composed of isolated ions, our comparative study showed this approach to produce a reliable electron density distribution within ionic species and between them. In the latter case, it provides exactly the same set of interionic interactions with their features closely matching those obtained from a conventional multipole refinement of highresolution X-ray diffraction data. Such similarity of electron density distributions constructed from ions with their net charges fixed at formal values in the invariom approximation and those refined freely to significantly lower values in the full multipole refinement shows how Bader’s concept of transferability of molecular fragments,[24] the basis for the invariom approach,[2] works for ionic systems: it gives similar parameters of chemical bonding within charged species and amazingly similar between them, even though full charge transfer is assumed. The invariom approximation was found to better describe interionic interactions with the chloride anion than with the carbonate anion, although the electron density distribution of the former is governed by the crystal environment around it and that of the latter is well defined by covalent bonds within it. This, however, agrees with an excellent performance of the invariom approximation in the case of weaker contacts in molecular crystals.[14] If there are no extremely strong interionic interactions such as in polyiodides, the invariom approach is a very convenient tool (as standard resolution X-ray diffraction datasets will do) for reliable and accurate description of chemical bonding peculiarities in ionic crystals, thus contributing to our understanding of many crystalline materials, those having ferroelectric, piezoelectric, conductive, triboluminescent, and other important properties.

Experimental Section Crystals of GuaCl (CH6ClN3, M = 95.54) were orthorhombic, space group Pbca: a = 7.61440(10), b = 9.01530(10), c = 13.0516(2) æ, V = 895.94(2) æ3, Z = 8 (Z’ = 1), 1calcd = 1.417 g cm¢3 (see Table S4, the Supporting Information). Crystals of GuaCO3 (C3H12N6O3, Mw = 180.19) were tetragonal, space group P41212: a = 6.95610(10), c = 19.5353(2) æ, V = 945.26(2) æ3, Z = 4 (Z’ = 0.5), 1calcd = 1.266 gcm¢3. High-resolution X-ray diffraction data were collected at 100 K with a Bruker APEX2 DUO diffractometer [l(MoKa) = 0.71072 æ, w-scans, 2q < 110 8] in three batches, a low-angle (2q = ¢32 8), a middleangle (2q = ¢628), and a high-angle batch (2q = ¢92 8), in an omega-scan mode (Dw = 0.5 8) with a detector to a sample distance of 4.1 cm at exposure times of 2 s for low-angle reflections, 5 s for middle-angle reflections, and 10 s for high-angle reflections, respectively. Raw data were integrated by using the program SAINT and then scaled, merged and corrected for Lorentz-polarizaChem. Eur. J. 2015, 21, 9733 – 9741

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tion effects using the SADABS package; semi-empirical absorption correction from equivalents was applied using SADABS.[38] The structures were solved by direct method and refined by the full-matrix least-squares technique against F2 in anisotropic-isotropic approximation. Hydrogen atoms were located from difference Fourier synthesis of electron density and refined in the isotropic approximation. For GuaCl, the refinement converged to wR2 = 0.0685 and GOF = 1.002 for all the independent reflections (R1 = 0.0198 was calculated against F for 4826 observed reflections with I > 2s(I)). For GuaCO3, the refinement converged to wR2 = 0.0809 and GOF = 1.004 for all the independent reflections (R1 = 0.0288 was calculated against F for 5715 observed reflections with I > 2s(I)). All calculations were performed using SHELXTL PLUS 5.0.[39] CCDC-1044692 (GuaCl) and CCDC-1044693 (GuaCO3) contain the supplementary crystallographic data for this paper. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif. Experimental dataset was modeled using the Hansen–Coppens formalism[7] as implemented in the program package XD.[40] Input files were generated with the program InvariomTool.[41] Multipolar populations (up to hexadecapolar level) and kappa parameters from the invariom library[5] were assigned to all atoms of GuaCl and those of guanidinium cation in GuaCO3 ; the monopole populations were adjusted to keep the net charges of guanidinium, chloride and carbonate species equal to their formal values of + 1, ¢1 and ¢2 as implemented in the program InvariomTool.[41] An alternative procedure of achieving electroneutrality has been also tested for GuaCl, in which the difference from electroneutrality (the sum of the monopoles of all but the chloride atom) was manually assigned to a database entry for chloride. Taking monopole populations of invarioms automatically assigned for nitrogen (N1.5c[1.5n1.5n]1h1h), carbon (C1.5n[1h1h]1.5n[1h1h]1.5n[1h1h]) and hydrogen (H1n[1.5c1h]) atoms of the guanidinium cation produced a monopole population for the chloride anion of 8.4598 (it should be 8, if full charge transfer is assumed), resulting in its Bader’s charge of ¢1.41 e (it should be no less than ¢1; otherwise, a reverse charge transfer is observed). So the initial procedure of achieving electroneutrality (with atomic monopole populations adjusted to keep the net charges of ions equal to + 1, ¢1 and ¢2) has been adopted in the invariom modelling of GuaCl and GuaCO3. The multipolar populations and kappa parameters for carbon and oxygen atoms of the CO32¢ moiety occupying a two-fold axis in the crystal that passes through O(1) and C(2) atoms were calculated by using computational tools kindly provided by Dr. Habil. Birger Dittrich’s group. A straightforward use of entries available in the invariom library[5] for CO32¢ moiety with no two-fold site symmetry imposed upon it yielded totally unrealistic results (see Figure S1 in the Supporting Information). This issue is a result of site symmetry restrictions on multipolar parameters, which need to be imposed for atoms (with an appropriate local coordinate system) occupying special positions in a crystal;[40] they are not so frequent in molecular crystals (except for center of symmetry) but are common for small, highly symmetric ions (such as borate, nitrate, carbonate, etc.). The corresponding symmetry restrictions that should be assigned in the multipole refinement may thus conflict with those used for creating an invariom entry; however, an additional quantum chemical calculation of the model system with the same site symmetry as observed for the atom in a crystal under study allows easily resolving this issue and provides a “symmetrycorrected” invariom to be used in further refinement. In the following invariom refinement, positional and displacement parameters of non-hydrogen atoms together with a scale factor

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Full Paper were refined against F for all the experimental data (sin q/l up to 1.1 æ¢1) using statistical weights based on 1/s(Fobs). The N¢H bond lengths were fixed at the values of 1.01589 æ from the invariom database;[5] hydrogen ADPs were estimated with the SHADE server.[42] The invariom refinements converged to R = 0.0141 and 0.0189, Rw = 0.0112 and 0.0163, GOF = 1.32 and 2.08 for 4811 and 3338 merged reflections with I > 3s(I) for GuaCl and GuaCO3, respectively. For the conventional multipole refinements, the order of multipole expansion included hexadecapoles for all non-hydrogen atoms and dipoles for hydrogens; those were adjusted against measured data using statistical weights based on 1/s(Fobs). The N¢H bond lengths were fixed at the values of 1.01589 æ from the invariom database;[5] hydrogen ADPs were estimated with the SHADE server.[42] The refinement of atomic coordinates and ADPs of non-hydrogen atoms was preformed against high-angle data (sin q/l = 0.7– 1.1 æ¢1), and the refinement of all other parameters was performed up to sin q/l = 1.0 æ¢1. At the beginning, coordinates + ADPs were refined to obtained accurate positional coordinates and thermal parameters for all atoms, followed with the refinement of multipoles; both steps were repeated until R stopped decreasing. Then monopoles, first-order kappas, and second-order kappas were introduced, all preceded and followed by “coordinates + ADPs and multipoles” refinement cycle, until repeating of any of these steps stopped leading to deviation from obtained parameters and/or to decrease of R. In all cases, the residual electron density maps were flat, with the largest and lowest values of 0.10 and ¢0.27 e æ¢3 only. The latter was found in the invariom model near the Cl(1) nucleus, suggesting either too high charge imposed on it or improper description of electron density distribution around it by the invariom approximation or both. In all cases, the Hirshfeld test[43] yielded a highest difference in mean square displacement amplitudes along covalent bonds of 3 Õ 10¢4 æ2, indicating a proper deconvolution of thermal motion and electron density. Topological analysis of the resulting functions 1(r) was carried out by using the WINXPRO program package.[44] Potential energy density v(r) was evaluated through the Kirzhnits’s approximation[45] for kinetic energy density function g(r). Accordingly, the g(r) function is described as: (3/10)(3p2)2/3[1(r)]5/3 + (1/72) j r1(r) j 2/1(r) + 1/6r21(r), giving in conjunction with the virial theorem (2 g(r) + n(r) = 1/4r21(r))[24] the expression for v(r). Interaction energies were estimated by means of Espinosa’s correlation scheme, a semi-quantitative relation between the energy of an interaction and the value of the potential energy density function v(r) in its bcp.[26, 27] Having a very simple form as 0.5v(r), it has been repeatedly shown to give accurate estimates in many cases (those are succinctly summarized in[28]), including weak interactions such as H···H and C¢H···O[46] or C¢H···N,[14] Mg···C and Ca···C strong and intermediate H-bonds,[49] interactions,[47, 48] [50] [51, 52] Ca¢O(carbonate), Au¢PPh3 and Gd¢OH2 bonds, and so on.[28] The interaction energies thus obtained have been shown to accurately reproduce the energy of a crystal lattice;[14, 46, 50, 53, 54] the discrepancy between the crystal lattice energies estimated in such a manner from X-ray diffraction data and those measured experimentally can be as small as 0.2 kcal mol¢1.[35, 46]

Acknowledgements This study was financially supported by Russian Science Foundation (Project 14-13-00884). The authors would like to thank Chem. Eur. J. 2015, 21, 9733 – 9741

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Dr. I. V. Taydakov (Lebedev Institute of Physics, Moscow, Russia) for providing high-quality crystals of GuaCl and GuaCO3. Keywords: ionic crystals · invariom approach · quantum chemistry · topological analysis · X-ray diffraction [1] C. Gatti,C. F. Matta, Modern Charge-Density Analysis, Springer, Heidelberg, 2012. [2] B. Dittrich, T. S. Koritsansky, P. Luger, Angew. Chem. Int. Ed. 2004, 43, 2718 – 2721; Angew. Chem. 2004, 116, 2773 – 2776. [3] B. Dittrich, M. Weber, R. Kalinowski, S. Grabowski, C. B. Hubschle, P. Luger, Acta Crystallogr. Sect. B 2009, 65, 749 – 756. [4] B. Dittrich, T. Koritsanszky, A. Volkov, S. Mebs, P. Luger, Angew. Chem. Int. Ed. 2007, 46, 2935 – 2938; Angew. Chem. 2007, 119, 2993 – 2996. [5] B. Dittrich, C. B. Hubschle, K. Propper, F. Dietrich, T. Stolper, J. J. Holstein, Acta Crystallogr. Sect. B 2013, 69, 91 – 104. [6] C. J. Schìrmann, K. Propper, T. Wagner, B. Dittrich, Acta Crystallogr. Sect. B 2012, 68, 313 – 317. [7] N. K. Hansen, P. Coppens, Acta Crystallogr. Sect. A 1978, 34, 909 – 921. [8] J. J. Holstein, C. B. Hubschle, B. Dittrich, CrystEngComm 2012, 14, 2520 – 2531. [9] B. Dittrich, M. A. Spackman, Acta Crystallogr. Sect. A 2007, 63, 426 – 436. [10] R. Kalinowski, B. Dittrich, C. B. Hubschle, C. Paulmann, P. Luger, Acta Crystallogr. Sect. B 2007, 63, 753 – 767. [11] M. Weber, S. Grabowski, A. Hazra, S. Naskar, S. Banerjee, N. B. Mondal, P. Luger, Chem. Asian J. 2011, 6, 1390 – 1397. [12] P. Luger, M. Weber, C. Hubschle, R. Tacke, Org. Biomol. Chem. 2013, 11, 2348 – 2354. [13] J. Bacsa, M. Okello, P. Singh, V. Nair, Acta Crystallogr. Sect. C 2013, 69, 285 – 288. [14] Y. V. Nelyubina, A. A. Korlyukov, K. A. Lyssenko, Chem. Eur. J. 2014, 20, 6978 – 6984. [15] J. J. Holstein, P. Luger, R. Kalinowski, S. Mebs, C. Paulmann, B. Dittrich, Acta Crystallogr. Sect. B 2010, 66, 568 – 577. [16] B. Dittrich, C. B. Hubschle, J. J. Holstein, F. P. A. Fabbiani, J. Appl. Crystallogr. 2009, 42, 1110 – 1121. [17] Y. V. Nelyubina, A. A. Korlyukov, K. A. Lyssenko, Mendeleev Commun. 2014, 24, 286 – 289. [18] C. B. Hìbschle, P. Luger, B. Dittrich, J. Appl. Crystallogr. 2007, 40, 623 – 627. [19] M. Meot-Ner Mautner, Chem. Rev. 2005, 105, 213 – 284. [20] Y. V. Nelyubina, M. Y. Antipin, K. A. Lyssenko, J. Phys. Chem. A 2007, 111, 1091 – 1095. [21] M. D. Best, S. L. Tobey, E. V. Anslyn, Coord. Chem. Rev. 2003, 240, 3 – 15. [22] J. M. Adams, R. W. H. Small, Acta Crystallogr. Sect. B 1974, 30, 2191 – 2193. [23] D. J. Haas, D. R. Harris, H. H. Mills, Acta Crystallogr. 1965, 19, 676 – 679. [24] R. F. W. Bader, Atoms in Molecules. A Quantum Theory, Clarendron, Oxford, 1990. [25] C. F. Matta, A. A. Arabi, Future Med. Chem. F 2011, 3, 969 – 994. [26] E. Espinosa, E. Molins, C. Lecomte, Chem. Phys. Lett. 1998, 285, 170 – 173. [27] E. Espinosa, I. Alkorta, I. Rozas, J. Elguero, E. Molins, Chem. Phys. Lett. 2001, 336, 457 – 461. [28] K. A. Lyssenko, Mendeleev Commun. 2012, 22, 1 – 7. [29] Y. V. Nelyubina, M. Y. Antipin, K. A. Lyssenko, J. Phys. Chem. A 2009, 113, 3615 – 3620. [30] I. Rozas, P. E. Kruger, J. Chem. Theory Comput. 2005, 1, 1055 – 1062. [31] B. L. Schottel, H. T. Chifotides, K. R. Dunbar, Chem. Soc. Rev. 2008, 37, 68 – 83. [32] L. Checinska, S. Mebs, C. B. Hìbschle, D. Fçrster, W. Morgenroth, P. Luger, Org. Biomol. Chem. 2006, 4, 3242 – 3251. [33] Y. V. Nelyubina, M. Y. Antipin, E. L. Belokoneva, K. A. Lyssenko, Mendeleev Commun. 2007, 17, 71 – 73. [34] Y. V. Nelyubina, P. Y. Barzilovich, M. Y. Antipin, S. M. Aldoshin, K. A. Lyssenko, ChemPhysChem 2011, 12, 2895 – 2898. [35] Y. V. Nelyubina, I. V. Glukhov, M. Y. Antipin, K. A. Lyssenko, Chem. Commun. 2010, 46, 3469 – 3471. [36] M. A. Spackman, Chem. Phys. Lett. 1999, 301, 425 – 429.

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Full Paper [37] V. Tsirelson, Y. Abramov, V. Zavodnik, A. Stash, E. Belokoneva, J. Stahn, U. Pietsch, D. Feil, Struct. Chem. 1998, 9, 249 – 254. [38] SMART, SAINT, and SADABS, Siemens Analytical X-ray Instruments Inc., Madison, Wisconsin USA, 1999. [39] G. M. Sheldrick, Acta Crystallogr. Sect. A 2008, 64, 112 – 122. [40] A. Volkov, P. Macchi, L. J. Farrugia, C. Gatti, P. Mallinson, T. Richter,T. Koritsanszky in XD2006: A computer program for multipole refinement, topological analysis of charge densities and evaluation of intermolecular energies from experimental or theoretical structure factors, Vol. 2006. [41] C. B. Hìbschle, B. Dittrich, J. Appl. Crystallogr. 2011, 44, 238 – 240. [42] A. O. Madsen, J. Appl. Crystallogr. 2006, 39, 757 – 758. [43] F. L. Hirshfeld, Acta Crystallogr. Sect. A 1976, 32, 239 – 244. [44] A. Stash, V. Tsirelson, J. Appl. Crystallogr. 2002, 35, 371 – 373. [45] D. A. Kirzhnits, Sov. Phys. JETP 1957, 5, 64 – 72. [46] K. A. Lyssenko, A. A. Korlyukov, M. Y. Antipin, Mendeleev Commun. 2005, 15, 90 – 92. [47] E. A. Pidko, R. A. van Santen, ChemPhysChem 2006, 7, 1657 – 1660.

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www.chemeurj.org

[48] E. A. Pidko, J. Xu, B. L. Mojet, L. Lefferts, I. R. Subbotina, V. B. Kazansky, R. A. van Santen, J. Phys. Chem. B 2006, 110, 22618 – 22627. [49] L. Sobczyk, S. J. Grabowski, T. M. Krygowski, Chem. Rev. 2005, 105, 3513 – 3560. [50] Y. V. Nelyubina, K. A. Lyssenko, Chem. Eur. J. 2012, 18, 12633 – 12636. [51] A. O. Borissova, A. A. Korlyukov, M. Y. Antipin, K. A. Lyssenko, J. Phys. Chem. A 2008, 112, 11519 – 11522. [52] L. N. Puntus, K. A. Lyssenko, M. Y. Antipin, J.-C. G. Bunzli, Inorg. Chem. 2008, 47, 11095 – 11107. [53] K. A. Lyssenko, A. A. Korlyukov, D. G. Golovanov, S. Y. Ketkov, M. Y. Antipin, J. Phys. Chem. A 2006, 110, 6545 – 6551. [54] I. V. Glukhov, K. A. Lyssenko, A. A. Korlyukov, M. Y. Antipin, Faraday Discuss. 2007, 135, 203 – 215.

Received: January 22, 2015 Revised: April 21, 2015 Published online on May 26, 2015

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