DOI: 10.1002/cphc.201402673
Articles
Experimental Charge Density Evidence for Pnicogen Bonding in a Crystal of Ammonium Chloride Yulia V. Nelyubina,*[a] Alexander A. Korlyukov,[a, b] and Konstantin A. Lyssenko[a] Dedicated to the memory of Professor Oleg V. Shishkin
experimental evidence for weak s-hole bonds (1.5 kcal mol1) that involve ammonium cations in a crystal. Our results show this type of supramolecular interaction to be more numerous than has been found to date by using gas-phase calculations or statistical analysis of CSD.
Chemical binding in crystalline ammonium chloride, a simple inorganic salt with an unexpectedly complex bonding pattern, was studied by using a topological analysis of electron density function derived from high-resolution X-ray diffraction. Supported by periodic quantum chemical calculations, it provided
1. Introduction Of the wide range of intermolecular interactions, hydrogen bonds are clearly the most important;[1] they are strong, directional, and selective, and thus provide the best control over molecular aggregation processes,[2] so they are a powerful tool in supramolecular chemistry. During the last decades, however, other types of noncovalent interactions that are competitive with hydrogen bonds[3] have been (re)recognized as important supramolecular linkers. Those include halogen,[4] chalcogen,[5] pnicogen,[6] and (most recently)[7] tetrel[8] bonds that involve the elements of groups IV–VII, which all share the same feature of a s-hole (Figure 1).[9] The s-hole is a region of positive electrostatic potential on the outer surface of a covalently bonded atom that can interact with a negative site, for example, a lone pair, a p system, or an anion, to give rise to highly directional s-hole interactions[10] (more specifically named by referring to the group in the Periodic Table the atom belongs to).[11] Like hydrogen bonds, which are sometimes regarded as a special case of s-hole bonding,[10, 12] these interactions occur widely from simple inorganic to biological systems[13] and are already used in crystal engineering.[14] Given their importance in crystal structures,[10] s-hole bonds with the elements of groups IV–VII were thoroughly investigated by using computational methods to provide insights into their nature and energetics, including theoretical electrostatic potential[15] and electron density analysis,[16, 17] NBO partitioning,[18] and other energy decomposition schemes;[19, 20] the ap-
Figure 1. Computed electrostatic potential on the 0.001 a.u. molecular surface of NH4 + . Blue color corresponds to the maximum and red corresponds to the minimum electrostatic potential. Black points designate the extremes of electrostatic potential at H and N atoms, which are 0.286 and 0.263 a.u., respectively.[33] (Reprinted with permission from Ref. [33].)
plicability of the latter was, however, questioned.[10] This led to rationalization of s-hole bonds as electrostatically driven interactions (with some contribution from polarization and dispersion)[10] that are more frequently found for heavier atoms in a more electron-withdrawing covalent environment,[21] although they still may be observed for the first-row elements (Figure 1).[18, 22] These studies have been generally focused on molecular complexes between the two species linked by a s-hole bond, whereas its features are clearly affected by other interactions,[9] sometimes dramatically.[23] In a crystalline environment in which the latter are in abundance, the s-hole bonds are mostly identified by statistical analysis of crystal structures available in the Cambridge Structural Database (CSD);[7, 19, 24–26] those with longer interatomic distances, however, may be easily missed by doing so. For halogen and chalcogen bonding, experimental evidence was also obtained from electron density studies (see Refs. [27, 28], which are among the latest) based on high-resolution X-ray diffraction. Assisted by R. Bader’s Atoms in Mole-
[a] Dr. Y. V. Nelyubina, Prof. A. A. Korlyukov, Prof. K. A. Lyssenko X-ray Diffraction Centre and Quantum Chemistry Department A.N. Nesmeyanov Institute of Organoelement Compounds of Russian Academy of Sciences 119991, Vavilova Str. 28, Moscow (Russia) E-mail: [email protected] [b] Prof. A. A. Korlyukov Pirogov Russian National Research Medical University 117997, Ostrovitianov str. 1, Moscow (Russia) Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402673.
ChemPhysChem 0000, 00, 0 – 0
These are not the final page numbers! ÞÞ
1
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
&
Articles cules (AIM) theory,[29] this approach provides a full set of bonding interactions in a crystal, all unambiguously revealed by a bond critical points (bcps; 3, 1) search and characterized by the values of electron density, its laplacian, etc. A semi-quantitative relation between the potential energy density at a bcp and the energy of an interaction, which was proposed by Espinosa’s group for hydrogen bonds[30, 31] and then shown to perform well for others,[32] allows a comparison of different types of interatomic interactions (however weak they may be) and an estimation of the contribution each of them makes to the stabilization of a given crystal structure. Here we provide experimental charge density evidence for pnicogen bonds in the crystal of ammonium chloride (NH4Cl; Figures S1, 2 in the Supporting Information); these were theoretically predicted to form between the ammonium cation (which seemed unlikely, given the trends in s-hole strengths) and HCN or N2 molecules but only after all its hydrogen atoms were involved in hydrogen bonding.[25, 33] The choice of ammonium chloride, a classic example of an order–disorder phase transition in a crystal[34] and the first ferroelastoelectric confirmed by experiment,[35] as a model compound is due to its very simple unit-cell composition with the NH4 + cation involved in hydrogen and pnicogen bonds only.
2. Results and Discussion The cubic crystal structure of NH4Cl resembles that of CsCl, with hydrogen atoms lying along the body diagonals that form NH···Cl hydrogen bonds; however, two orientations of the ammonium cation are possible, with hydrogen atoms along the blue or orange lines in Figure 2, top. They are both randomly populated at room temperature but only one of them persists below the transition point (30 8C).[36, 37] The accompanying change in the space group from Pm3m to P4¯3m agrees well with the piezoelectric effect that is experimentally observed only in the ordered phase of NH4Cl.[35] Note that in both cubic phases of NH4I[38] and in NH4Br, which is isostructural with NH4Cl at high temperature but has a tetragonal crystal structure (space group P4/nmm[39]) at low temperatures, the ammonium cation is disordered. Given that no such disorder is observed in NH4Cl at a low temperature, it is a rare case of N···X lengths being equal for hydrogen and pnicogen bonds (N···Cl 3.3177(1) , NHCl and HNCl 1808); although long, these pnicogen bonds still may contribute to the order–disorder transition in crystalline NH4Cl. Based on the separation between neighboring chloride anions in NH4Cl (3.8314(1) ), Cl···Cl bonding interactions also may be expected[40] (Figure 2) similar to those found in NaCl[41] or hydroxylammonium chloride NH3OHCl.[42] Therefore, the full set of interionic contacts here should include NH···Cl hydrogen bonds, Cl···NH pnicogen bonds, and Cl···Cl interactions; the latter cannot be described by the s-hole concept because they form no covalent bonds and thus have no s-holes, but they resemble its “like attracting like” cases. To quantify all these types of interactions in crystalline NH4Cl (with NH as the only covalent bonds), we performed a topological analysis of electron densities obtained by using multi-
&
ChemPhysChem 0000, 00, 0 – 0
www.chemphyschem.org
Figure 2. Top: General view of NH4Cl showing the environment of the ammonium cation (atoms are given as thermal ellipsoids at p = 90 %) and bottom: bond paths (orange spheres represent bond critical points) for the interionic interactions it forms in a crystal.
pole refinement against experimental X-ray diffraction data and theoretical structure factors (issued from the calculated wavefunction in both static and dynamic models) and straightforwardly derived from periodic quantum chemistry (with and without geometry optimization). Theoretical calculations provide a reference with no contribution from extinction effects suffered by the crystal of NH4Cl because electron density features are very sensitive to experimental pitfalls; even the smallest ones that can be easily overlooked[43] may result in totally unrealistic parameters for interatomic interactions or charge distribution between the species. If successfully corrected for extinction, X-ray diffraction data should provide results that are consistent between all the models, as has been observed for molecular crystals.[44] By using the AIM partitioning of a molecule into nonspherical atomic regions by zero-flux surfaces,[45] we estimated atomic volumes and charges in the crystalline NH4Cl based on the electron densities from experimental and theoretical structure factors and from periodic quantum chemistry (Table 1). Optimization of atomic positions in a cubic unit cell of NH4Cl 2
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ÝÝ These are not the final page numbers!
Articles be quantified from the topological analysis of an electron density distribution by using the above-mentioned Espinosa’s correlation.[30, 31] Topological analysis of the total of five electron densities (Table 2) within the AIM theory[29] gives much more consistent results than was observed for the net atomic properties (charges and volumes). In each case, all the expected types of bond-
Table 1. Atomic charges and volumes in crystalline NH4Cl.
N(1)
H(1)
Cl(1)
qat [e]
Vat [3]
1.43//1.20 (1.05)[a] 1.11//1.11[b] + 0.57// + 0.46 (+ 0.44)[a] + 0.47// + 0.47[b] 0.83//0.62 (0.70)[a] 0.76//0.77[b]
15.38//14.90 (14.52)[a] 14.26//14.06[b] 2.24//3.09 (2.93)[a] 2.92//2.84[b] 31.85//28.83 (29.83)[a] 30.30//30.80[b]
Table 2. Interatomic distances and topological parameters of electron density in bcps for all bonding interactions in NH4Cl.[a]
[a] The upper entry denotes the values from multipole refinements against experimental//calculated static (dynamic) structure factors. In all cases, the charge leakage was below 0.01 e; the sum of atomic volumes per NH4Cl moiety (56.08–56.18 3) reproduced the volume of the unit cell (56.245(1) 3) with a relative error of not more than 0.2 %. Although integrated Langrangian (L(r) = 1/4r21(r)) for every atomic basin has to be exactly zero, a reasonably small value that averaged to 0.1 103 a.u. was obtained. [b] The lower entry stands for the theoretical values from periodic quantum chemical calculations with//without geometry optimization.
www.chemphyschem.org
These are not the final page numbers! ÞÞ
H(1)···Cl(1)
N(1)···Cl(1)
Cl(1)···Cl(1)
1.030 1.042//1.030
3.3178 3.3178
3.8314 3.8314
1(r) [e 3]
2.08//1.78 (1.86) 2.20//2.40 37.59// 17.62 (18.59) 45.08// 56.80 0.5834// 0.3736 (0.3991) 0.6143// 0.7253 0.6775//0.5646 (0.6054) 0.7187//0.8080
2.288 2.276// 2.288 0.19//0.13 (0.14) 0.16//0.15 1.50//1.24 (1.19) 1.09//1.06
0.05//0.06 (0.06) 0.05//0.05 0.66//0.71 (0.72) 0.61//0.61
0.02//0.03 (0.03) 0.04//0.04 0.30//0.34 (0.36) 0.32//0.32
0.0066// 0.0001 (0.0002) 0.0013// 0.0007 0.0148// 0.0127 (0.0127) 0.0149// 0.0135 4.7//4.0 (4.0) 4.7//4.2
0.0016// 0.0014 (0.0014) 0.0015// 0.0014 0.0037// 0.0045 (0.0047) 0.0038// 0.0038 1.2//1.4 (1.5) 1.2//1.2
0.0008// 0.0008 (0.0009) 0.0007// 0.0007 0.0015// 0.0018 (0.0020) 0.0022// 0.0022 0.5//0.6 (0.6) 0.7//0.7
r21(r) [e 5]
(high symmetry allows only hydrogen atoms to be shifted during the computation) has resulted in minor differences in these parameters; yet they are quite different from those obtained by using multipolar modeling, which also display a rather wide dispersion. For hydrogen and chlorine atoms, the extreme values correspond to multipolar densities from experimental and theoretical structure factors, with the latter giving more similar results to the topological analysis of the computed electron densities. In all cases, however, the net volumes of the counterions show the same tendency to be higher for the Cl species (28.8–31.8 vs. 24.33–27.33 3), which thus supports the occurrence of bonding halide–halide interactions in NH4Cl.[46] Overall, the estimated volumes vary up to 10 % but their sum coincides nicely with the volume of the unit cell (Table 1). This is also true for the atomic charges: the largest difference of 0.4 e is found for the nitrogen atom, the lowest (0.13 e) is observed for hydrogen atoms, but the net charges of the counterions vary by only 0.2 e (0.63–0.83 e), which thus matches the difference earlier reported for a crystal with no signs of extinction.[44] Although the chosen models do not provide a consistent charge distribution within the NH4 + moiety (with straightforward quantum chemical calculations seeming superior to others in this respect, providing a value for the nitrogen atom’s charge close to one found in the above clusters of NH4 + with Lewis bases from 1.15 to 1.05 e), its features in the interionic areas may still be well reproduced. In all cases, the ammonium cation displays a net charge that is significantly reduced from its formal value of + 1, with the experimental electron density giving the best match to the calculated limit value of approximately + 0.87 e in its clusters.[33] Even when aware of a known fallacy of atomic charges, especially in relation to s-hole interactions,[10] one can still view the modest charge transfer from the chloride anion to the ammonium cation in NH4Cl ( 0.2–0.4 e) as an indicator of rather weak hydrogen bonds between them,[47] which may ChemPhysChem 0000, 00, 0 – 0
N(1)H(1) D []
he(r) [a.u.]
v(r) [a.u.]
Eint [kcal mol1]
–
[a] In each column, the upper entries denotes the values from multipole refinements against experimental//calculated static (dynamic) structure factors and the lower entry gives the theoretical values from periodic quantum chemical calculations with//without geometry optimization.
ing in NH4Cl feature bcps and associated bond paths (Figure 2); topological parameters in these bcps classify the N H bonds as being of a shared type of interatomic interaction with high 1(r), negative r21(r), and he(r) values (he(r) is the electron energy density) and all others as of a closed-shell type with low 1(r), positive r21(r), and he(r). The largest difference in these parameters, as retrieved from the five different models, is found for the covalent NH bonds (Table 2): electron density and the absolute value of laplacian in their bcps vary greatly as compared with their natural spread[48] of 0.1 e 3 and 3 to 4 e 5, owing mainly to the calculated structure factors. The latter agrees with these values being statistically smaller for the theoretical multipolar model (improved by the use of dynamic structure factors but only to a minor extent) than for the experimental one,[44] which in our case shows the best agreement with quantum chemistry (the variation that is still observed is a result of different radial dependences between the electron densities obtained from periodic quantum chemistry and from multipolar modeling). 3
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
&
Articles 3. Conclusions
All the electron densities gathered for NH4Cl, however, demonstrate very similar features in the interionic areas: the corresponding differences (0.06 e 3 and 0.44 e 5 at most) are significantly below the above transferability indices (0.1 e 3 and 3–4 e 5).[48] The energy of these interactions as estimated through the Espinosa’s correlation[30, 31] varies the most for N H···Cl hydrogen bonds from 4.0 to 4.7 kcal mol1, with the largest value observed for the experimental and quantum chemical data and the lowest for the multipolar modeling against theoretical structure factors. Given an average charge transfer of 0.3 e in NH4Cl (see above), the total energy of hydrogen bonds between the counterions of 16 to 19 kcal mol1 agrees well with an estimated value of around 20 kcal mol1 from a semi-quantitative relation between these parameters obtained by Bader partitioning and topological analysis for a series of organic and inorganic salts.[49] The variation between the models in the case of weaker Cl···N and Cl···Cl interactions is twice as small (Table 2). The energy of the pnicogen bonds is 1.2 to 1.5 kcal mol1, so they account for 20 to 25 % of the interaction energy per one NH4 + moiety in NH4Cl, which totals to 21.6 to 23.6 kcal mol1. Although hydrogen bonds enable the existence of the pnicogen bonds with the ammonium cation, there is a clear interplay between these two types in crystal structure stabilization (and, possibly, in phase transition behavior and ferroelastoelectric and other properties) of NH4Cl, as demonstrated by singlepoint calculations of the (NH4)8Cl7 + clusters starting from the experimental geometry and then replacing one Cl···N bond with a hydrogen bond (making use of their equal N···Cl distances and ClHN/ClNH angles). Although the difference in the energies of the two systems favors one with fewer Cl···N interactions by 0.76 kcal mol1 (the cluster with all eight hydrogen bonds being the most energetically preferable), two out of five hydrogen bonds that are now trans two each other become weaker (4.74 kcal mol1 as estimated by Espinosa’s correlation[30, 31]) and those that are trans to the remaining pnicogen bonds become stronger (4.81 kcal mol1). The observed variation seems too infinitesimal to draw any meaningful conclusions; however, the tendency of a Cl···NH interaction to strengthen a NH···Cl interaction it is in line with persists in all clusters with a number of pnicogen bonds from one to four. It is also the case in the cluster NH4Cl43 expanded by one more chloride anion that forms a pnicogen bond; the hydrogen bond that is opposite to this bond has slightly higher energy (4.39 kcal mol1) than the three others (4.21 kcal mol1). Note that the number of hydrogen bonds in a cluster affects the energy of pnicogen bonds even less because it is equal to 1.39 to 1.41 kcal mol1 in all cases. The interactions between the chloride anions in the crystal of NH4Cl, also identified as stabilizing by the AIM approach, are the weakest of all the three types of interatomic bonding and have energy values of below 1 kcal mol1. The estimated energy values for Cl···N (3.3178 ) and Cl···Cl (3.8314 ) bonding in NH4Cl also coincide nicely with the values reported earlier for NH3OHCl:[42] those with interatomic separations of 3.18 and 3.8 to 3.9 were assigned energies of 1.5 and 0.6 to 0.7 kcal mol1, respectively.
&
ChemPhysChem 0000, 00, 0 – 0
www.chemphyschem.org
The experimental electron density derived from X-ray diffraction data provides an accurate description for interionic bonding in NH4Cl that is very consistent with quantum-chemistrybased approaches, which all support the occurrence of a Cl···N pnicogen bond with highly reproducible features. Although similar Cl···N interactions have been observed before in crystals,[42] they were not recognized as pnicogen bonds because they are not easily identifiable based on interatomic distances that are not as small as usually associated with s-hole interactions. However, they interplay with other supramolecular interactions in contributing to crystal structure formation and thus the properties of solids; even though going to real periodic systems (if high-resolution X-ray diffraction data for a crystal are unavailable then periodic quantum chemistry will do equally well for this purpose) is needed to ascertain their existence and significance. Found in abundance in many crystals from simple inorganic to complex biological systems, s-hole interactions are even more numerous than suggested by gasphase calculations of molecular complexes or statistical analysis of CSD and the protein databank.
Experimental Section Crystals of NH4Cl (Mr = 53.49) are cubic; space group P¯43m at 120 K; a = 3.83143(5) ; V = 56.245(1) 3 ; Z = 1 (Z’ = 1/24); 1calcd = 1.579 g cm3 ; m(MoKa) = 12.45 cm1; F(000) = 28. Intensities of 10 262 reflections were measured by using a Bruker SMART APEX2 CCD diffractometer (l(MoKa) = 0.71072 , w scans, 2q < 1208), and 196 independent reflections (Rint = 0.0171) were used in further refinement. These data were collected in three batches, a low-angle (2q = 328), a middle-angle (2q = 628), and a high-angle batch (2q = 928), in an omega-scan mode (Dw = 0.58) with a detectorto-sample distance of 4.1 cm at exposure times of 1 s for the lowangle reflections, 2 s for the middle-angle reflections, and 5 s for the high-angle reflections, respectively, to give a high-resolution dataset (sinq/l up to 1.2 1). Raw data were integrated by using the SAINT program and then scaled, merged, and corrected for Lorentz polarization effects by using the SADABS package (BrukerAXS Inc., Madison, WI-53719, USA, 1999); face-index numerical absorption correction was applied. The structure was solved by using direct methods and refined by the full-matrix least-squares technique against F2 in the anisotropic–isotropic approximation. Hydrogen atoms were located from the difference Fourier synthesis of the electron density and refined in the isotropic approximation. An extinction correction was made during the refinement to give an extinction parameter equal to 0.70(9).[50] The refinement converged to wR2 = 0.0175 and GOF = 1.012 for all the independent reflections (R1 = 0.0073 was calculated against F for 196 observed reflections with I > 2s(I)). All calculations were performed by using SHELXTL PLUS 5.0.[51] CSD 428519 contains the supporting crystallographic data for this paper. These data can be obtained free of charge from Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (e-mail: [email protected], http:// www.fiz-karlsruhe.de/ecid/Internet/en/DB/icsd/depot_anforderung. html). The multipole refinement against experimental structure factors was carried out within the Hansen–Coppens formalism[20] as implemented in the program package XD;[21] the input reflection file
4
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ÝÝ These are not the final page numbers!
Articles with absorption-weighted path length was generated with the SADABS program to allow for extinction refinement in XD. The NH bond distance was fixed at a value of 1.03 from a neutron diffraction study of NH4Cl.[36, 37] Multipole expansion was truncated at the hexadecapole level for chlorine and nitrogen atoms (because those occupy the special positions with a site symmetry of 43m, cubic harmonics were refined as a linear combinations of spherical harmonics),[52] and at the quadrupole level for hydrogen atoms. Together with a scale factor, kappa and thermal parameters, the multipole populations were adjusted against measured highresolution data. An isotropic extinction correction[53] of type I with a Lorentzian mosaic distribution was applied, with the g’ value refined to 0.023(2). The refinement was carried out against F and converged to R = 0.0051, Rw = 0.0065, and GOF = 4.3646 for 126 merged reflections with I > 3s(I). The residual electron density maps were flat and the highest and lowest values were as high as 0.07 e 3 and as low as 0.09 e 3, both features are located in the vicinity of the Cl(1) nucleus.
PW-DFT calculations were carried out by using the VASP 5.3.3 program;[68–71] exchange and correlation parts of the total energy were described by means of PBE functional.[54] Optimization of atomic positions (when applicable) has been started from the experimental data by using a plane wave basis set (with a kinetic energy cutoff of 1360 eV). Residual forces on atoms were less than 102 mdyn 2 and energy variations near the end of geometry optimization were less than 103 eV. To account for core electrons, projected augmented wave (PAW) potentials were used.[72] Periodic quantum chemical calculations were carried out with cell parameters fixed to experimental values. Electron density functions were obtained in separate single-point calculations for both the optimized and nonoptimized structures by using the same kinetic energy cut-off and dense fast Fourier transformation grid (432 432 432 points). Topological analysis of 1(r) functions directly issued from these calculations were carried out by using the AIM program[73] implemented in the ABINIT program package. Single-point DFT calculations for the isolated clusters (NH4)8Cl7 + and (NH4)Cl53 were performed by using the Gaussian 09 program[74] package with the M06-2x functional[75] and cc-pVTZ basis set. The topological analysis of the resulting electron densities was performed by using AIMall program package.[76]
Theoretical structure factors were calculated within the periodical DFT approach with atom-centered Gaussian-type functions basis sets as implemented in the Crystal09 software package.[29] We have used the combination of PBE0 functional[54] with TZVP basis set specially fitted for solid-state calculations.[31] The wave function was optimized in the experimental geometry, and static structure factors were calculated for 5898 independent reflections up to the resolution d = 0.355 (sinq/l up to 1.419 1). Dynamic structure factors were then generated by multiplying static structure factors by a Debye–Waller term with isotropic atomic displacement parameter chosen as an average of the equivalent isotropic displacement parameters obtained in the experimental data modeling.[44] Multipole refinement against static and dynamic structure factors was performed by using the XD program package (with the same sinq/l cutoffs as used for the refinement against experimental structure factors)[26] with thermal parameters being fixed at zero and refined during the multipole refinement against the calculated dataset; a unit-weighting scheme was used in both cases.[55] The refinements were carried out against F and converged to R = 0.0115, GOF = 0.06 for 196 reflections and to R = 0.0019, GOF = 0.01 for 196 reflections. Going from static to dynamic structure factors resulted in a dramatic decrease in R factor and in electron density residuals being 0.44/0.18 and 0.02/0.02 e 3.[44]
Acknowledgements This study was financially supported by the Russian Science Foundation (grant 14-13-00884). Keywords: electron density distribution · pnicogens · sigmahole interactions · topological analysis · X-ray diffraction
[1] T. Steiner, Angew. Chem. Int. Ed. 2002, 41, 48 – 76; Angew. Chem. 2002, 114, 50 – 80. [2] G. R. Desiraju, J. Chem. Soc. Dalton Trans. 2000, 3745 – 3751. [3] P. Politzer, J. S. Murray, P. Lane, Int. J. Quantum Chem. 2007, 107, 3046 – 3052. [4] P. Politzer, P. Lane, M. C. Concha, Y. G. Ma, J. S. Murray, J. Mol. Model. 2007, 13, 305 – 311. [5] W. Z. Wang, B. M. Ji, Y. Zhang, J. Phys. Chem. A 2009, 113, 8132 – 8135. [6] S. Zahn, R. Frank, E. Hey-Hawkins, B. Kirchner, Chem. Eur. J. 2011, 17, 6034 – 6038. [7] A. Bauz, T. J. Mooibroek, A. Frontera, Angew. Chem. Int. Ed. 2013, 52, 12317 – 12321; Angew. Chem. 2013, 125, 12543 – 12547. [8] S. Grabowski, Phys. Chem. Chem. Phys. 2014, 16, 1824 – 1834. [9] J. S. Murray, P. Lane, P. Politzer, J. Mol. Model. 2009, 15, 723 – 729. [10] P. Politzer, J. S. Murray, T. Clark, Phys. Chem. Chem. Phys. 2013, 15, 11178 – 11189. [11] G. Cavallo, P. Metrangolo, T. Pilati, G. Resnati, G. Terraneo, Cryst. Growth Des. 2014, 14, 2697 – 2702. [12] T. Clark, WIREs Comput. Mol. Sci. 2013, 3, 13 – 20. [13] J. S. Murray, K. E. Riley, P. Politzer, T. Clark, Aust. J. Chem. 2010, 63, 1598 – 1607. [14] P. Metrangolo, H. Neukirch, T. Pilati, G. Resnati, Acc. Chem. Res. 2005, 38, 386 – 395. [15] A. Bundhun, P. Ramasami, J. S. Murray, P. Politzer, J. Mol. Model. 2013, 19, 2739 – 2746. [16] I. Alkorta, G. Sanchez-Sanz, J. Elguero, J. E. Del Bene, J. Phys. Chem. A 2013, 117, 183 – 191. [17] J. Ji, Y. Zeng, X. Zhang, L. Meng, J. Mol. Model. 2013, 19, 4887 – 4895. [18] D. Mani, E. Arunan, Phys. Chem. Chem. Phys. 2013, 15, 14377 – 14383. [19] S. Scheiner, Int. J. Quantum Chem. 2013, 113, 1609 – 1620. [20] M. Solimannejad, V. Ramezani, C. Trujillo, I. Alkorta, G. Sanchez-Sanz, J. Elguero, J. Phys. Chem. A 2012, 116, 5199 – 5206.
Topological analysis of the resulting functions 1(r) was carried out by using the WINXPRO program package.[22, 23] Potential energy density v(r) was evaluated through the Kirzhnits’s approximation[56] 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), which in conjunction with the virial theorem (2g(r) + n(r) = 1/4r21(r))[29] gives the expression for v(r). Interaction energies were estimated through a semiquantitative relation between the energy of an interaction and the value of the potential energy density function v(r) at its bcp.[30, 31] With a very simple form as 0.5v(r), it was repeatedly shown to give accurate estimates in many cases (those are succinctly summarized in Ref. [32]), including weak interactions, such as H···H and CH···O[57] or CH···N,[58] Mg···C, and Ca···C interactions,[59, 60] strong and intermediate hydrogen bonds,[61] CaO(carbonate),[62] AuPPh3, and GdOH2 bonds,[63, 64] etc.[32] The interaction energies thus obtained were shown to accurately reproduce the energy of a crystal lattice,[57, 58, 62, 65, 66] 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 mol1.[57, 67]
ChemPhysChem 0000, 00, 0 – 0
www.chemphyschem.org
These are not the final page numbers! ÞÞ
5
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
&
Articles [21] J. S. Murray, P. Lane, T. Clark, K. E. Riley, P. Politzer, J. Mol. Model. 2012, 18, 541 – 548. [22] P. Metrangolo, J. S. Murray, T. Pilati, P. Politzer, G. Resnati, G. Terraneo, CrystEngComm 2011, 13, 6593 – 6596. [23] Y. V. Nelyubina, M. Y. Antipin, D. S. Dunin, V. Y. Kotov, K. A. Lyssenko, Chem. Commun. 2010, 46, 5325 – 5327. [24] A. Bauz, D. Quinonero, P. M. Deya, A. Frontera, CrystEngComm 2013, 15, 3137 – 3144. [25] S. Grabowski, Chem. Eur. J. 2013, 19, 14600 – 14611. [26] A. Gavezzotti, Mol. Phys. 2008, 106, 1473 – 1485. [27] M. E. Brezgunova, E. Aubert, S. Dahaoui, P. Fertey, S. Lebegue, C. Jelsch, J. G. Angyan, E. Espinosa, Cryst. Growth Des. 2012, 12, 5373 – 5386. [28] M. E. Brezgunova, J. Lieffrig, E. Aubert, S. Dahaoui, P. Fertey, S. Lebegue, J. G. Angyan, M. Fourmigue, E. Espinosa, Cryst. Growth Des. 2013, 13, 3283 – 3289. [29] R. F. W. Bader, Atoms In molecules. A Quantum Theory, Clarendron Press, Oxford, 1990. [30] E. Espinosa, E. Molins, C. Lecomte, Chem. Phys. Lett. 1998, 285, 170 – 173. [31] E. Espinosa, I. Alkorta, I. Rozas, J. Elguero, E. Molins, Chem. Phys. Lett. 2001, 336, 457 – 461. [32] K. A. Lyssenko, Mendeleev Commun. 2012, 22, 1 – 7. [33] S. Grabowski, ChemPhysChem 2014, 15, 876 – 884. [34] F. Simon, Ann. Phys. 1922, 373, 241 – 280. [35] E. Mohler, R. Pitka, Solid State Commun. 1974, 14, 791 – 794. [36] G. H. Goldschmidt, D. G. Hurst, Phys. Rev. 1951, 83, 88 – 94. [37] H. A. Levy, S. W. Peterson, Phys. Rev. 1952, 86, 766 – 770. [38] A. Skjeltorp, A. V. Belushkin, Forces, Growth and Form in Soft Condensed Matter: At the Interface between Physics and Biology, Springer, New York, 2004. [39] J. A. A. Ketelaar, Nature 1934, 134, 250 – 251. [40] Y. V. Nelyubina, M. Y. Antipin, K. A. Lyssenko, Russ. Chem. Rev. 2010, 79, 167 – 187. [41] V. Tsirelson, Y. Abramov, V. Zavodnik, A. Stash, E. Belokoneva, J. Stahn, U. Pietsch, D. Feil, Struct. Chem. 1998, 9, 249 – 254. [42] Y. V. Nelyubina, M. Y. Antipin, K. A. Lyssenko, J. Phys. Chem. A 2007, 111, 1091 – 1095. [43] Y. V. Nelyubina, A. A. Korlyukov, K. A. Lyssenko, Mendeleev Commun. 2014, 24, 286 – 289. [44] E. Aubert, S. Lebegue, M. Marsman, T. T. T. Bui, C. Jelsch, S. Dahaoui, E. Espinosa, J. G. Angyan, J. Phys. Chem. A 2011, 115, 14484 – 14494. [45] R. F. W. Bader, C. F. Matt, J. Phys. Chem. A 2004, 108, 8385 – 8394. [46] A. M. Pends, V. LuaÇa, A. Costales, J. Phys. Chem. B 1998, 102, 6937 – 6948. [47] M. Meot-Ner, Chem. Rev. 2005, 105, 213 – 284. [48] L. Checinska, S. Mebs, C. B. Hubschle, D. Forster, W. Morgenroth, P. Luger, Org. Biomol. Chem. 2006, 4, 3242 – 3251. [49] Y. V. Nelyubina, P. Y. Barzilovich, M. Y. Antipin, S. M. Aldoshin, K. A. Lyssenko, ChemPhysChem 2011, 12, 2895 – 2898. [50] A. C. Larson in The Inclusion of Secondary Extinction in Least-Squares Refinement of Crystal Structures (Eds.: F. R. Ahmed, S. R. Hall, C. P. Huber), Munksgaard, Copenhagen, 1970, pp. 291 – 294. [51] G. M. Sheldrick, Acta Crystallogr. Sect. A 2008, 64, 112 – 122. [52] K. Kurki-Suonio, Isr. J. Chem. 1977, 16, 124 – 131. [53] P. J. Becker, P. Coppens, Acta Crystallogr. Sect. A 1974, 30, 129 – 147.
&
ChemPhysChem 0000, 00, 0 – 0
www.chemphyschem.org
[54] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865 – 3868. [55] H. Bruning, D. Feil, Acta Crystallogr. Sect. A 1992, 48, 865 – 872. [56] D. A. Kirzhnits, Sov. Phys. JETP-USSR 1957, 5, 64 – 72. [57] K. A. Lyssenko, A. A. Korlyukov, M. Y. Antipin, Mendeleev Commun. 2005, 15, 90 – 92. [58] Y. V. Nelyubina, A. A. Korlyukov, K. A. Lyssenko, Chem. Eur. J. 2014, 20, 6978 – 6984. [59] E. A. Pidko, R. A. van Santen, ChemPhysChem 2006, 7, 1657 – 1660. [60] 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. [61] L. Sobczyk, S. J. Grabowski, T. M. Krygowski, Chem. Rev. 2005, 105, 3513 – 3560. [62] Y. V. Nelyubina, K. A. Lyssenko, Chem. Eur. J. 2012, 18, 12633 – 12636. [63] A. O. Borissova, A. A. Korlyukov, M. Y. Antipin, K. A. Lyssenko, J. Phys. Chem. A 2008, 112, 11519 – 11522. [64] L. N. Puntus, K. A. Lyssenko, M. Y. Antipin, J.-C. G. Bunzli, Inorg. Chem. 2008, 47, 11095 – 11107. [65] K. A. Lyssenko, A. A. Korlyukov, D. G. Golovanov, S. Y. Ketkov, M. Y. Antipin, J. Phys. Chem. A 2006, 110, 6545 – 6551. [66] I. V. Glukhov, K. A. Lyssenko, A. A. Korlyukov, M. Y. Antipin, Faraday Discuss. 2007, 135, 203 – 215. [67] Y. V. Nelyubina, I. V. Glukhov, M. Y. Antipin, K. A. Lyssenko, Chem. Commun. 2010, 46, 3469 – 3471. [68] G. Kresse, J. Hafner, Phys. Rev. B 1993, 47, 558. [69] G. Kresse, J. Hafner, Phys. Rev. B 1994, 49, 14251. [70] G. Kresse, J. Furthmller, Comput. Mater. Sci. 1996, 6, 15. [71] G. Kresse, J. Furthmller, Phys. Rev. B 1996, 54, 11169. [72] G. Kresse, D. Joubert, Phys. Rev. B 1999, 59, 1758. [73] X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Cote, T. Deutsch, L. Genovese, P. Ghosez, M. Giantomassi, S. Goedecker, D. R. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, M. J. T. Oliveira, G. Onida, Y. Pouillon, T. Rangel, G.-M. Rignanese, D. Sangalli, R. Shaltaf, M. Torrent, M. J. Verstraete, G. Zerah, J. W. Zwanziger, Comput. Phys. Commun. 2009, 180, 2582 – 2615. [74] Gaussian 09, Revision B01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, . Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian, Inc., Wallingford CT, 2009. [75] Y. Zhao, D. G. Truhlar, Theor. Chem. Acc. 2008, 120, 215 – 241. [76] T. A. Keith, AIMAll (Version 10.12.13), 2010, http://aim.tkgristmill.com. Received: September 26, 2014 Published online on && &&, 2014
6
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ÝÝ These are not the final page numbers!
ARTICLES The ties that bind: Chemical binding in crystalline ammonium chloride was studied by using a topological analysis of electron density function derived from high-resolution X-ray diffraction. Supported by periodic quantum chemical calculations, it provided experimental evidence for weak s-hole bonds (1.5 kcal mol1) that involve ammonium cations in a crystal (see figure). This type of supramolecular interaction is even more numerous than now appears.
ChemPhysChem 0000, 00, 0 – 0
www.chemphyschem.org
These are not the final page numbers! ÞÞ
Y. V. Nelyubina,* A. A. Korlyukov, K. A. Lyssenko && – && Experimental Charge Density Evidence for Pnicogen Bonding in a Crystal of Ammonium Chloride
7
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
&
Articles
Experimental Charge Density Evidence for Pnicogen Bonding in a Crystal of Ammonium Chloride Yulia V. Nelyubina,*[a] Alexander A. Korlyukov,[a, b] and Konstantin A. Lyssenko[a] Dedicated to the memory of Professor Oleg V. Shishkin
experimental evidence for weak s-hole bonds (1.5 kcal mol1) that involve ammonium cations in a crystal. Our results show this type of supramolecular interaction to be more numerous than has been found to date by using gas-phase calculations or statistical analysis of CSD.
Chemical binding in crystalline ammonium chloride, a simple inorganic salt with an unexpectedly complex bonding pattern, was studied by using a topological analysis of electron density function derived from high-resolution X-ray diffraction. Supported by periodic quantum chemical calculations, it provided
1. Introduction Of the wide range of intermolecular interactions, hydrogen bonds are clearly the most important;[1] they are strong, directional, and selective, and thus provide the best control over molecular aggregation processes,[2] so they are a powerful tool in supramolecular chemistry. During the last decades, however, other types of noncovalent interactions that are competitive with hydrogen bonds[3] have been (re)recognized as important supramolecular linkers. Those include halogen,[4] chalcogen,[5] pnicogen,[6] and (most recently)[7] tetrel[8] bonds that involve the elements of groups IV–VII, which all share the same feature of a s-hole (Figure 1).[9] The s-hole is a region of positive electrostatic potential on the outer surface of a covalently bonded atom that can interact with a negative site, for example, a lone pair, a p system, or an anion, to give rise to highly directional s-hole interactions[10] (more specifically named by referring to the group in the Periodic Table the atom belongs to).[11] Like hydrogen bonds, which are sometimes regarded as a special case of s-hole bonding,[10, 12] these interactions occur widely from simple inorganic to biological systems[13] and are already used in crystal engineering.[14] Given their importance in crystal structures,[10] s-hole bonds with the elements of groups IV–VII were thoroughly investigated by using computational methods to provide insights into their nature and energetics, including theoretical electrostatic potential[15] and electron density analysis,[16, 17] NBO partitioning,[18] and other energy decomposition schemes;[19, 20] the ap-
Figure 1. Computed electrostatic potential on the 0.001 a.u. molecular surface of NH4 + . Blue color corresponds to the maximum and red corresponds to the minimum electrostatic potential. Black points designate the extremes of electrostatic potential at H and N atoms, which are 0.286 and 0.263 a.u., respectively.[33] (Reprinted with permission from Ref. [33].)
plicability of the latter was, however, questioned.[10] This led to rationalization of s-hole bonds as electrostatically driven interactions (with some contribution from polarization and dispersion)[10] that are more frequently found for heavier atoms in a more electron-withdrawing covalent environment,[21] although they still may be observed for the first-row elements (Figure 1).[18, 22] These studies have been generally focused on molecular complexes between the two species linked by a s-hole bond, whereas its features are clearly affected by other interactions,[9] sometimes dramatically.[23] In a crystalline environment in which the latter are in abundance, the s-hole bonds are mostly identified by statistical analysis of crystal structures available in the Cambridge Structural Database (CSD);[7, 19, 24–26] those with longer interatomic distances, however, may be easily missed by doing so. For halogen and chalcogen bonding, experimental evidence was also obtained from electron density studies (see Refs. [27, 28], which are among the latest) based on high-resolution X-ray diffraction. Assisted by R. Bader’s Atoms in Mole-
[a] Dr. Y. V. Nelyubina, Prof. A. A. Korlyukov, Prof. K. A. Lyssenko X-ray Diffraction Centre and Quantum Chemistry Department A.N. Nesmeyanov Institute of Organoelement Compounds of Russian Academy of Sciences 119991, Vavilova Str. 28, Moscow (Russia) E-mail: [email protected] [b] Prof. A. A. Korlyukov Pirogov Russian National Research Medical University 117997, Ostrovitianov str. 1, Moscow (Russia) Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402673.
ChemPhysChem 0000, 00, 0 – 0
These are not the final page numbers! ÞÞ
1
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
&
Articles cules (AIM) theory,[29] this approach provides a full set of bonding interactions in a crystal, all unambiguously revealed by a bond critical points (bcps; 3, 1) search and characterized by the values of electron density, its laplacian, etc. A semi-quantitative relation between the potential energy density at a bcp and the energy of an interaction, which was proposed by Espinosa’s group for hydrogen bonds[30, 31] and then shown to perform well for others,[32] allows a comparison of different types of interatomic interactions (however weak they may be) and an estimation of the contribution each of them makes to the stabilization of a given crystal structure. Here we provide experimental charge density evidence for pnicogen bonds in the crystal of ammonium chloride (NH4Cl; Figures S1, 2 in the Supporting Information); these were theoretically predicted to form between the ammonium cation (which seemed unlikely, given the trends in s-hole strengths) and HCN or N2 molecules but only after all its hydrogen atoms were involved in hydrogen bonding.[25, 33] The choice of ammonium chloride, a classic example of an order–disorder phase transition in a crystal[34] and the first ferroelastoelectric confirmed by experiment,[35] as a model compound is due to its very simple unit-cell composition with the NH4 + cation involved in hydrogen and pnicogen bonds only.
2. Results and Discussion The cubic crystal structure of NH4Cl resembles that of CsCl, with hydrogen atoms lying along the body diagonals that form NH···Cl hydrogen bonds; however, two orientations of the ammonium cation are possible, with hydrogen atoms along the blue or orange lines in Figure 2, top. They are both randomly populated at room temperature but only one of them persists below the transition point (30 8C).[36, 37] The accompanying change in the space group from Pm3m to P4¯3m agrees well with the piezoelectric effect that is experimentally observed only in the ordered phase of NH4Cl.[35] Note that in both cubic phases of NH4I[38] and in NH4Br, which is isostructural with NH4Cl at high temperature but has a tetragonal crystal structure (space group P4/nmm[39]) at low temperatures, the ammonium cation is disordered. Given that no such disorder is observed in NH4Cl at a low temperature, it is a rare case of N···X lengths being equal for hydrogen and pnicogen bonds (N···Cl 3.3177(1) , NHCl and HNCl 1808); although long, these pnicogen bonds still may contribute to the order–disorder transition in crystalline NH4Cl. Based on the separation between neighboring chloride anions in NH4Cl (3.8314(1) ), Cl···Cl bonding interactions also may be expected[40] (Figure 2) similar to those found in NaCl[41] or hydroxylammonium chloride NH3OHCl.[42] Therefore, the full set of interionic contacts here should include NH···Cl hydrogen bonds, Cl···NH pnicogen bonds, and Cl···Cl interactions; the latter cannot be described by the s-hole concept because they form no covalent bonds and thus have no s-holes, but they resemble its “like attracting like” cases. To quantify all these types of interactions in crystalline NH4Cl (with NH as the only covalent bonds), we performed a topological analysis of electron densities obtained by using multi-
&
ChemPhysChem 0000, 00, 0 – 0
www.chemphyschem.org
Figure 2. Top: General view of NH4Cl showing the environment of the ammonium cation (atoms are given as thermal ellipsoids at p = 90 %) and bottom: bond paths (orange spheres represent bond critical points) for the interionic interactions it forms in a crystal.
pole refinement against experimental X-ray diffraction data and theoretical structure factors (issued from the calculated wavefunction in both static and dynamic models) and straightforwardly derived from periodic quantum chemistry (with and without geometry optimization). Theoretical calculations provide a reference with no contribution from extinction effects suffered by the crystal of NH4Cl because electron density features are very sensitive to experimental pitfalls; even the smallest ones that can be easily overlooked[43] may result in totally unrealistic parameters for interatomic interactions or charge distribution between the species. If successfully corrected for extinction, X-ray diffraction data should provide results that are consistent between all the models, as has been observed for molecular crystals.[44] By using the AIM partitioning of a molecule into nonspherical atomic regions by zero-flux surfaces,[45] we estimated atomic volumes and charges in the crystalline NH4Cl based on the electron densities from experimental and theoretical structure factors and from periodic quantum chemistry (Table 1). Optimization of atomic positions in a cubic unit cell of NH4Cl 2
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ÝÝ These are not the final page numbers!
Articles be quantified from the topological analysis of an electron density distribution by using the above-mentioned Espinosa’s correlation.[30, 31] Topological analysis of the total of five electron densities (Table 2) within the AIM theory[29] gives much more consistent results than was observed for the net atomic properties (charges and volumes). In each case, all the expected types of bond-
Table 1. Atomic charges and volumes in crystalline NH4Cl.
N(1)
H(1)
Cl(1)
qat [e]
Vat [3]
1.43//1.20 (1.05)[a] 1.11//1.11[b] + 0.57// + 0.46 (+ 0.44)[a] + 0.47// + 0.47[b] 0.83//0.62 (0.70)[a] 0.76//0.77[b]
15.38//14.90 (14.52)[a] 14.26//14.06[b] 2.24//3.09 (2.93)[a] 2.92//2.84[b] 31.85//28.83 (29.83)[a] 30.30//30.80[b]
Table 2. Interatomic distances and topological parameters of electron density in bcps for all bonding interactions in NH4Cl.[a]
[a] The upper entry denotes the values from multipole refinements against experimental//calculated static (dynamic) structure factors. In all cases, the charge leakage was below 0.01 e; the sum of atomic volumes per NH4Cl moiety (56.08–56.18 3) reproduced the volume of the unit cell (56.245(1) 3) with a relative error of not more than 0.2 %. Although integrated Langrangian (L(r) = 1/4r21(r)) for every atomic basin has to be exactly zero, a reasonably small value that averaged to 0.1 103 a.u. was obtained. [b] The lower entry stands for the theoretical values from periodic quantum chemical calculations with//without geometry optimization.
www.chemphyschem.org
These are not the final page numbers! ÞÞ
H(1)···Cl(1)
N(1)···Cl(1)
Cl(1)···Cl(1)
1.030 1.042//1.030
3.3178 3.3178
3.8314 3.8314
1(r) [e 3]
2.08//1.78 (1.86) 2.20//2.40 37.59// 17.62 (18.59) 45.08// 56.80 0.5834// 0.3736 (0.3991) 0.6143// 0.7253 0.6775//0.5646 (0.6054) 0.7187//0.8080
2.288 2.276// 2.288 0.19//0.13 (0.14) 0.16//0.15 1.50//1.24 (1.19) 1.09//1.06
0.05//0.06 (0.06) 0.05//0.05 0.66//0.71 (0.72) 0.61//0.61
0.02//0.03 (0.03) 0.04//0.04 0.30//0.34 (0.36) 0.32//0.32
0.0066// 0.0001 (0.0002) 0.0013// 0.0007 0.0148// 0.0127 (0.0127) 0.0149// 0.0135 4.7//4.0 (4.0) 4.7//4.2
0.0016// 0.0014 (0.0014) 0.0015// 0.0014 0.0037// 0.0045 (0.0047) 0.0038// 0.0038 1.2//1.4 (1.5) 1.2//1.2
0.0008// 0.0008 (0.0009) 0.0007// 0.0007 0.0015// 0.0018 (0.0020) 0.0022// 0.0022 0.5//0.6 (0.6) 0.7//0.7
r21(r) [e 5]
(high symmetry allows only hydrogen atoms to be shifted during the computation) has resulted in minor differences in these parameters; yet they are quite different from those obtained by using multipolar modeling, which also display a rather wide dispersion. For hydrogen and chlorine atoms, the extreme values correspond to multipolar densities from experimental and theoretical structure factors, with the latter giving more similar results to the topological analysis of the computed electron densities. In all cases, however, the net volumes of the counterions show the same tendency to be higher for the Cl species (28.8–31.8 vs. 24.33–27.33 3), which thus supports the occurrence of bonding halide–halide interactions in NH4Cl.[46] Overall, the estimated volumes vary up to 10 % but their sum coincides nicely with the volume of the unit cell (Table 1). This is also true for the atomic charges: the largest difference of 0.4 e is found for the nitrogen atom, the lowest (0.13 e) is observed for hydrogen atoms, but the net charges of the counterions vary by only 0.2 e (0.63–0.83 e), which thus matches the difference earlier reported for a crystal with no signs of extinction.[44] Although the chosen models do not provide a consistent charge distribution within the NH4 + moiety (with straightforward quantum chemical calculations seeming superior to others in this respect, providing a value for the nitrogen atom’s charge close to one found in the above clusters of NH4 + with Lewis bases from 1.15 to 1.05 e), its features in the interionic areas may still be well reproduced. In all cases, the ammonium cation displays a net charge that is significantly reduced from its formal value of + 1, with the experimental electron density giving the best match to the calculated limit value of approximately + 0.87 e in its clusters.[33] Even when aware of a known fallacy of atomic charges, especially in relation to s-hole interactions,[10] one can still view the modest charge transfer from the chloride anion to the ammonium cation in NH4Cl ( 0.2–0.4 e) as an indicator of rather weak hydrogen bonds between them,[47] which may ChemPhysChem 0000, 00, 0 – 0
N(1)H(1) D []
he(r) [a.u.]
v(r) [a.u.]
Eint [kcal mol1]
–
[a] In each column, the upper entries denotes the values from multipole refinements against experimental//calculated static (dynamic) structure factors and the lower entry gives the theoretical values from periodic quantum chemical calculations with//without geometry optimization.
ing in NH4Cl feature bcps and associated bond paths (Figure 2); topological parameters in these bcps classify the N H bonds as being of a shared type of interatomic interaction with high 1(r), negative r21(r), and he(r) values (he(r) is the electron energy density) and all others as of a closed-shell type with low 1(r), positive r21(r), and he(r). The largest difference in these parameters, as retrieved from the five different models, is found for the covalent NH bonds (Table 2): electron density and the absolute value of laplacian in their bcps vary greatly as compared with their natural spread[48] of 0.1 e 3 and 3 to 4 e 5, owing mainly to the calculated structure factors. The latter agrees with these values being statistically smaller for the theoretical multipolar model (improved by the use of dynamic structure factors but only to a minor extent) than for the experimental one,[44] which in our case shows the best agreement with quantum chemistry (the variation that is still observed is a result of different radial dependences between the electron densities obtained from periodic quantum chemistry and from multipolar modeling). 3
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
&
Articles 3. Conclusions
All the electron densities gathered for NH4Cl, however, demonstrate very similar features in the interionic areas: the corresponding differences (0.06 e 3 and 0.44 e 5 at most) are significantly below the above transferability indices (0.1 e 3 and 3–4 e 5).[48] The energy of these interactions as estimated through the Espinosa’s correlation[30, 31] varies the most for N H···Cl hydrogen bonds from 4.0 to 4.7 kcal mol1, with the largest value observed for the experimental and quantum chemical data and the lowest for the multipolar modeling against theoretical structure factors. Given an average charge transfer of 0.3 e in NH4Cl (see above), the total energy of hydrogen bonds between the counterions of 16 to 19 kcal mol1 agrees well with an estimated value of around 20 kcal mol1 from a semi-quantitative relation between these parameters obtained by Bader partitioning and topological analysis for a series of organic and inorganic salts.[49] The variation between the models in the case of weaker Cl···N and Cl···Cl interactions is twice as small (Table 2). The energy of the pnicogen bonds is 1.2 to 1.5 kcal mol1, so they account for 20 to 25 % of the interaction energy per one NH4 + moiety in NH4Cl, which totals to 21.6 to 23.6 kcal mol1. Although hydrogen bonds enable the existence of the pnicogen bonds with the ammonium cation, there is a clear interplay between these two types in crystal structure stabilization (and, possibly, in phase transition behavior and ferroelastoelectric and other properties) of NH4Cl, as demonstrated by singlepoint calculations of the (NH4)8Cl7 + clusters starting from the experimental geometry and then replacing one Cl···N bond with a hydrogen bond (making use of their equal N···Cl distances and ClHN/ClNH angles). Although the difference in the energies of the two systems favors one with fewer Cl···N interactions by 0.76 kcal mol1 (the cluster with all eight hydrogen bonds being the most energetically preferable), two out of five hydrogen bonds that are now trans two each other become weaker (4.74 kcal mol1 as estimated by Espinosa’s correlation[30, 31]) and those that are trans to the remaining pnicogen bonds become stronger (4.81 kcal mol1). The observed variation seems too infinitesimal to draw any meaningful conclusions; however, the tendency of a Cl···NH interaction to strengthen a NH···Cl interaction it is in line with persists in all clusters with a number of pnicogen bonds from one to four. It is also the case in the cluster NH4Cl43 expanded by one more chloride anion that forms a pnicogen bond; the hydrogen bond that is opposite to this bond has slightly higher energy (4.39 kcal mol1) than the three others (4.21 kcal mol1). Note that the number of hydrogen bonds in a cluster affects the energy of pnicogen bonds even less because it is equal to 1.39 to 1.41 kcal mol1 in all cases. The interactions between the chloride anions in the crystal of NH4Cl, also identified as stabilizing by the AIM approach, are the weakest of all the three types of interatomic bonding and have energy values of below 1 kcal mol1. The estimated energy values for Cl···N (3.3178 ) and Cl···Cl (3.8314 ) bonding in NH4Cl also coincide nicely with the values reported earlier for NH3OHCl:[42] those with interatomic separations of 3.18 and 3.8 to 3.9 were assigned energies of 1.5 and 0.6 to 0.7 kcal mol1, respectively.
&
ChemPhysChem 0000, 00, 0 – 0
www.chemphyschem.org
The experimental electron density derived from X-ray diffraction data provides an accurate description for interionic bonding in NH4Cl that is very consistent with quantum-chemistrybased approaches, which all support the occurrence of a Cl···N pnicogen bond with highly reproducible features. Although similar Cl···N interactions have been observed before in crystals,[42] they were not recognized as pnicogen bonds because they are not easily identifiable based on interatomic distances that are not as small as usually associated with s-hole interactions. However, they interplay with other supramolecular interactions in contributing to crystal structure formation and thus the properties of solids; even though going to real periodic systems (if high-resolution X-ray diffraction data for a crystal are unavailable then periodic quantum chemistry will do equally well for this purpose) is needed to ascertain their existence and significance. Found in abundance in many crystals from simple inorganic to complex biological systems, s-hole interactions are even more numerous than suggested by gasphase calculations of molecular complexes or statistical analysis of CSD and the protein databank.
Experimental Section Crystals of NH4Cl (Mr = 53.49) are cubic; space group P¯43m at 120 K; a = 3.83143(5) ; V = 56.245(1) 3 ; Z = 1 (Z’ = 1/24); 1calcd = 1.579 g cm3 ; m(MoKa) = 12.45 cm1; F(000) = 28. Intensities of 10 262 reflections were measured by using a Bruker SMART APEX2 CCD diffractometer (l(MoKa) = 0.71072 , w scans, 2q < 1208), and 196 independent reflections (Rint = 0.0171) were used in further refinement. These data were collected in three batches, a low-angle (2q = 328), a middle-angle (2q = 628), and a high-angle batch (2q = 928), in an omega-scan mode (Dw = 0.58) with a detectorto-sample distance of 4.1 cm at exposure times of 1 s for the lowangle reflections, 2 s for the middle-angle reflections, and 5 s for the high-angle reflections, respectively, to give a high-resolution dataset (sinq/l up to 1.2 1). Raw data were integrated by using the SAINT program and then scaled, merged, and corrected for Lorentz polarization effects by using the SADABS package (BrukerAXS Inc., Madison, WI-53719, USA, 1999); face-index numerical absorption correction was applied. The structure was solved by using direct methods and refined by the full-matrix least-squares technique against F2 in the anisotropic–isotropic approximation. Hydrogen atoms were located from the difference Fourier synthesis of the electron density and refined in the isotropic approximation. An extinction correction was made during the refinement to give an extinction parameter equal to 0.70(9).[50] The refinement converged to wR2 = 0.0175 and GOF = 1.012 for all the independent reflections (R1 = 0.0073 was calculated against F for 196 observed reflections with I > 2s(I)). All calculations were performed by using SHELXTL PLUS 5.0.[51] CSD 428519 contains the supporting crystallographic data for this paper. These data can be obtained free of charge from Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (e-mail: [email protected], http:// www.fiz-karlsruhe.de/ecid/Internet/en/DB/icsd/depot_anforderung. html). The multipole refinement against experimental structure factors was carried out within the Hansen–Coppens formalism[20] as implemented in the program package XD;[21] the input reflection file
4
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ÝÝ These are not the final page numbers!
Articles with absorption-weighted path length was generated with the SADABS program to allow for extinction refinement in XD. The NH bond distance was fixed at a value of 1.03 from a neutron diffraction study of NH4Cl.[36, 37] Multipole expansion was truncated at the hexadecapole level for chlorine and nitrogen atoms (because those occupy the special positions with a site symmetry of 43m, cubic harmonics were refined as a linear combinations of spherical harmonics),[52] and at the quadrupole level for hydrogen atoms. Together with a scale factor, kappa and thermal parameters, the multipole populations were adjusted against measured highresolution data. An isotropic extinction correction[53] of type I with a Lorentzian mosaic distribution was applied, with the g’ value refined to 0.023(2). The refinement was carried out against F and converged to R = 0.0051, Rw = 0.0065, and GOF = 4.3646 for 126 merged reflections with I > 3s(I). The residual electron density maps were flat and the highest and lowest values were as high as 0.07 e 3 and as low as 0.09 e 3, both features are located in the vicinity of the Cl(1) nucleus.
PW-DFT calculations were carried out by using the VASP 5.3.3 program;[68–71] exchange and correlation parts of the total energy were described by means of PBE functional.[54] Optimization of atomic positions (when applicable) has been started from the experimental data by using a plane wave basis set (with a kinetic energy cutoff of 1360 eV). Residual forces on atoms were less than 102 mdyn 2 and energy variations near the end of geometry optimization were less than 103 eV. To account for core electrons, projected augmented wave (PAW) potentials were used.[72] Periodic quantum chemical calculations were carried out with cell parameters fixed to experimental values. Electron density functions were obtained in separate single-point calculations for both the optimized and nonoptimized structures by using the same kinetic energy cut-off and dense fast Fourier transformation grid (432 432 432 points). Topological analysis of 1(r) functions directly issued from these calculations were carried out by using the AIM program[73] implemented in the ABINIT program package. Single-point DFT calculations for the isolated clusters (NH4)8Cl7 + and (NH4)Cl53 were performed by using the Gaussian 09 program[74] package with the M06-2x functional[75] and cc-pVTZ basis set. The topological analysis of the resulting electron densities was performed by using AIMall program package.[76]
Theoretical structure factors were calculated within the periodical DFT approach with atom-centered Gaussian-type functions basis sets as implemented in the Crystal09 software package.[29] We have used the combination of PBE0 functional[54] with TZVP basis set specially fitted for solid-state calculations.[31] The wave function was optimized in the experimental geometry, and static structure factors were calculated for 5898 independent reflections up to the resolution d = 0.355 (sinq/l up to 1.419 1). Dynamic structure factors were then generated by multiplying static structure factors by a Debye–Waller term with isotropic atomic displacement parameter chosen as an average of the equivalent isotropic displacement parameters obtained in the experimental data modeling.[44] Multipole refinement against static and dynamic structure factors was performed by using the XD program package (with the same sinq/l cutoffs as used for the refinement against experimental structure factors)[26] with thermal parameters being fixed at zero and refined during the multipole refinement against the calculated dataset; a unit-weighting scheme was used in both cases.[55] The refinements were carried out against F and converged to R = 0.0115, GOF = 0.06 for 196 reflections and to R = 0.0019, GOF = 0.01 for 196 reflections. Going from static to dynamic structure factors resulted in a dramatic decrease in R factor and in electron density residuals being 0.44/0.18 and 0.02/0.02 e 3.[44]
Acknowledgements This study was financially supported by the Russian Science Foundation (grant 14-13-00884). Keywords: electron density distribution · pnicogens · sigmahole interactions · topological analysis · X-ray diffraction
[1] T. Steiner, Angew. Chem. Int. Ed. 2002, 41, 48 – 76; Angew. Chem. 2002, 114, 50 – 80. [2] G. R. Desiraju, J. Chem. Soc. Dalton Trans. 2000, 3745 – 3751. [3] P. Politzer, J. S. Murray, P. Lane, Int. J. Quantum Chem. 2007, 107, 3046 – 3052. [4] P. Politzer, P. Lane, M. C. Concha, Y. G. Ma, J. S. Murray, J. Mol. Model. 2007, 13, 305 – 311. [5] W. Z. Wang, B. M. Ji, Y. Zhang, J. Phys. Chem. A 2009, 113, 8132 – 8135. [6] S. Zahn, R. Frank, E. Hey-Hawkins, B. Kirchner, Chem. Eur. J. 2011, 17, 6034 – 6038. [7] A. Bauz, T. J. Mooibroek, A. Frontera, Angew. Chem. Int. Ed. 2013, 52, 12317 – 12321; Angew. Chem. 2013, 125, 12543 – 12547. [8] S. Grabowski, Phys. Chem. Chem. Phys. 2014, 16, 1824 – 1834. [9] J. S. Murray, P. Lane, P. Politzer, J. Mol. Model. 2009, 15, 723 – 729. [10] P. Politzer, J. S. Murray, T. Clark, Phys. Chem. Chem. Phys. 2013, 15, 11178 – 11189. [11] G. Cavallo, P. Metrangolo, T. Pilati, G. Resnati, G. Terraneo, Cryst. Growth Des. 2014, 14, 2697 – 2702. [12] T. Clark, WIREs Comput. Mol. Sci. 2013, 3, 13 – 20. [13] J. S. Murray, K. E. Riley, P. Politzer, T. Clark, Aust. J. Chem. 2010, 63, 1598 – 1607. [14] P. Metrangolo, H. Neukirch, T. Pilati, G. Resnati, Acc. Chem. Res. 2005, 38, 386 – 395. [15] A. Bundhun, P. Ramasami, J. S. Murray, P. Politzer, J. Mol. Model. 2013, 19, 2739 – 2746. [16] I. Alkorta, G. Sanchez-Sanz, J. Elguero, J. E. Del Bene, J. Phys. Chem. A 2013, 117, 183 – 191. [17] J. Ji, Y. Zeng, X. Zhang, L. Meng, J. Mol. Model. 2013, 19, 4887 – 4895. [18] D. Mani, E. Arunan, Phys. Chem. Chem. Phys. 2013, 15, 14377 – 14383. [19] S. Scheiner, Int. J. Quantum Chem. 2013, 113, 1609 – 1620. [20] M. Solimannejad, V. Ramezani, C. Trujillo, I. Alkorta, G. Sanchez-Sanz, J. Elguero, J. Phys. Chem. A 2012, 116, 5199 – 5206.
Topological analysis of the resulting functions 1(r) was carried out by using the WINXPRO program package.[22, 23] Potential energy density v(r) was evaluated through the Kirzhnits’s approximation[56] 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), which in conjunction with the virial theorem (2g(r) + n(r) = 1/4r21(r))[29] gives the expression for v(r). Interaction energies were estimated through a semiquantitative relation between the energy of an interaction and the value of the potential energy density function v(r) at its bcp.[30, 31] With a very simple form as 0.5v(r), it was repeatedly shown to give accurate estimates in many cases (those are succinctly summarized in Ref. [32]), including weak interactions, such as H···H and CH···O[57] or CH···N,[58] Mg···C, and Ca···C interactions,[59, 60] strong and intermediate hydrogen bonds,[61] CaO(carbonate),[62] AuPPh3, and GdOH2 bonds,[63, 64] etc.[32] The interaction energies thus obtained were shown to accurately reproduce the energy of a crystal lattice,[57, 58, 62, 65, 66] 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 mol1.[57, 67]
ChemPhysChem 0000, 00, 0 – 0
www.chemphyschem.org
These are not the final page numbers! ÞÞ
5
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
&
Articles [21] J. S. Murray, P. Lane, T. Clark, K. E. Riley, P. Politzer, J. Mol. Model. 2012, 18, 541 – 548. [22] P. Metrangolo, J. S. Murray, T. Pilati, P. Politzer, G. Resnati, G. Terraneo, CrystEngComm 2011, 13, 6593 – 6596. [23] Y. V. Nelyubina, M. Y. Antipin, D. S. Dunin, V. Y. Kotov, K. A. Lyssenko, Chem. Commun. 2010, 46, 5325 – 5327. [24] A. Bauz, D. Quinonero, P. M. Deya, A. Frontera, CrystEngComm 2013, 15, 3137 – 3144. [25] S. Grabowski, Chem. Eur. J. 2013, 19, 14600 – 14611. [26] A. Gavezzotti, Mol. Phys. 2008, 106, 1473 – 1485. [27] M. E. Brezgunova, E. Aubert, S. Dahaoui, P. Fertey, S. Lebegue, C. Jelsch, J. G. Angyan, E. Espinosa, Cryst. Growth Des. 2012, 12, 5373 – 5386. [28] M. E. Brezgunova, J. Lieffrig, E. Aubert, S. Dahaoui, P. Fertey, S. Lebegue, J. G. Angyan, M. Fourmigue, E. Espinosa, Cryst. Growth Des. 2013, 13, 3283 – 3289. [29] R. F. W. Bader, Atoms In molecules. A Quantum Theory, Clarendron Press, Oxford, 1990. [30] E. Espinosa, E. Molins, C. Lecomte, Chem. Phys. Lett. 1998, 285, 170 – 173. [31] E. Espinosa, I. Alkorta, I. Rozas, J. Elguero, E. Molins, Chem. Phys. Lett. 2001, 336, 457 – 461. [32] K. A. Lyssenko, Mendeleev Commun. 2012, 22, 1 – 7. [33] S. Grabowski, ChemPhysChem 2014, 15, 876 – 884. [34] F. Simon, Ann. Phys. 1922, 373, 241 – 280. [35] E. Mohler, R. Pitka, Solid State Commun. 1974, 14, 791 – 794. [36] G. H. Goldschmidt, D. G. Hurst, Phys. Rev. 1951, 83, 88 – 94. [37] H. A. Levy, S. W. Peterson, Phys. Rev. 1952, 86, 766 – 770. [38] A. Skjeltorp, A. V. Belushkin, Forces, Growth and Form in Soft Condensed Matter: At the Interface between Physics and Biology, Springer, New York, 2004. [39] J. A. A. Ketelaar, Nature 1934, 134, 250 – 251. [40] Y. V. Nelyubina, M. Y. Antipin, K. A. Lyssenko, Russ. Chem. Rev. 2010, 79, 167 – 187. [41] V. Tsirelson, Y. Abramov, V. Zavodnik, A. Stash, E. Belokoneva, J. Stahn, U. Pietsch, D. Feil, Struct. Chem. 1998, 9, 249 – 254. [42] Y. V. Nelyubina, M. Y. Antipin, K. A. Lyssenko, J. Phys. Chem. A 2007, 111, 1091 – 1095. [43] Y. V. Nelyubina, A. A. Korlyukov, K. A. Lyssenko, Mendeleev Commun. 2014, 24, 286 – 289. [44] E. Aubert, S. Lebegue, M. Marsman, T. T. T. Bui, C. Jelsch, S. Dahaoui, E. Espinosa, J. G. Angyan, J. Phys. Chem. A 2011, 115, 14484 – 14494. [45] R. F. W. Bader, C. F. Matt, J. Phys. Chem. A 2004, 108, 8385 – 8394. [46] A. M. Pends, V. LuaÇa, A. Costales, J. Phys. Chem. B 1998, 102, 6937 – 6948. [47] M. Meot-Ner, Chem. Rev. 2005, 105, 213 – 284. [48] L. Checinska, S. Mebs, C. B. Hubschle, D. Forster, W. Morgenroth, P. Luger, Org. Biomol. Chem. 2006, 4, 3242 – 3251. [49] Y. V. Nelyubina, P. Y. Barzilovich, M. Y. Antipin, S. M. Aldoshin, K. A. Lyssenko, ChemPhysChem 2011, 12, 2895 – 2898. [50] A. C. Larson in The Inclusion of Secondary Extinction in Least-Squares Refinement of Crystal Structures (Eds.: F. R. Ahmed, S. R. Hall, C. P. Huber), Munksgaard, Copenhagen, 1970, pp. 291 – 294. [51] G. M. Sheldrick, Acta Crystallogr. Sect. A 2008, 64, 112 – 122. [52] K. Kurki-Suonio, Isr. J. Chem. 1977, 16, 124 – 131. [53] P. J. Becker, P. Coppens, Acta Crystallogr. Sect. A 1974, 30, 129 – 147.
&
ChemPhysChem 0000, 00, 0 – 0
www.chemphyschem.org
[54] J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865 – 3868. [55] H. Bruning, D. Feil, Acta Crystallogr. Sect. A 1992, 48, 865 – 872. [56] D. A. Kirzhnits, Sov. Phys. JETP-USSR 1957, 5, 64 – 72. [57] K. A. Lyssenko, A. A. Korlyukov, M. Y. Antipin, Mendeleev Commun. 2005, 15, 90 – 92. [58] Y. V. Nelyubina, A. A. Korlyukov, K. A. Lyssenko, Chem. Eur. J. 2014, 20, 6978 – 6984. [59] E. A. Pidko, R. A. van Santen, ChemPhysChem 2006, 7, 1657 – 1660. [60] 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. [61] L. Sobczyk, S. J. Grabowski, T. M. Krygowski, Chem. Rev. 2005, 105, 3513 – 3560. [62] Y. V. Nelyubina, K. A. Lyssenko, Chem. Eur. J. 2012, 18, 12633 – 12636. [63] A. O. Borissova, A. A. Korlyukov, M. Y. Antipin, K. A. Lyssenko, J. Phys. Chem. A 2008, 112, 11519 – 11522. [64] L. N. Puntus, K. A. Lyssenko, M. Y. Antipin, J.-C. G. Bunzli, Inorg. Chem. 2008, 47, 11095 – 11107. [65] K. A. Lyssenko, A. A. Korlyukov, D. G. Golovanov, S. Y. Ketkov, M. Y. Antipin, J. Phys. Chem. A 2006, 110, 6545 – 6551. [66] I. V. Glukhov, K. A. Lyssenko, A. A. Korlyukov, M. Y. Antipin, Faraday Discuss. 2007, 135, 203 – 215. [67] Y. V. Nelyubina, I. V. Glukhov, M. Y. Antipin, K. A. Lyssenko, Chem. Commun. 2010, 46, 3469 – 3471. [68] G. Kresse, J. Hafner, Phys. Rev. B 1993, 47, 558. [69] G. Kresse, J. Hafner, Phys. Rev. B 1994, 49, 14251. [70] G. Kresse, J. Furthmller, Comput. Mater. Sci. 1996, 6, 15. [71] G. Kresse, J. Furthmller, Phys. Rev. B 1996, 54, 11169. [72] G. Kresse, D. Joubert, Phys. Rev. B 1999, 59, 1758. [73] X. Gonze, B. Amadon, P.-M. Anglade, J.-M. Beuken, F. Bottin, P. Boulanger, F. Bruneval, D. Caliste, R. Caracas, M. Cote, T. Deutsch, L. Genovese, P. Ghosez, M. Giantomassi, S. Goedecker, D. R. Hamann, P. Hermet, F. Jollet, G. Jomard, S. Leroux, M. Mancini, S. Mazevet, M. J. T. Oliveira, G. Onida, Y. Pouillon, T. Rangel, G.-M. Rignanese, D. Sangalli, R. Shaltaf, M. Torrent, M. J. Verstraete, G. Zerah, J. W. Zwanziger, Comput. Phys. Commun. 2009, 180, 2582 – 2615. [74] Gaussian 09, Revision B01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, . Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, D. J. Fox, Gaussian, Inc., Wallingford CT, 2009. [75] Y. Zhao, D. G. Truhlar, Theor. Chem. Acc. 2008, 120, 215 – 241. [76] T. A. Keith, AIMAll (Version 10.12.13), 2010, http://aim.tkgristmill.com. Received: September 26, 2014 Published online on && &&, 2014
6
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ÝÝ These are not the final page numbers!
ARTICLES The ties that bind: Chemical binding in crystalline ammonium chloride was studied by using a topological analysis of electron density function derived from high-resolution X-ray diffraction. Supported by periodic quantum chemical calculations, it provided experimental evidence for weak s-hole bonds (1.5 kcal mol1) that involve ammonium cations in a crystal (see figure). This type of supramolecular interaction is even more numerous than now appears.
ChemPhysChem 0000, 00, 0 – 0
www.chemphyschem.org
These are not the final page numbers! ÞÞ
Y. V. Nelyubina,* A. A. Korlyukov, K. A. Lyssenko && – && Experimental Charge Density Evidence for Pnicogen Bonding in a Crystal of Ammonium Chloride
7
0000 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
&
