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Abundance and Strength of M−H···H−C (M = Al, Ga, In) Dihydrogen Bonds Jorge Echeverría* Departament de Química Inorgànica i Orgànica and Institut de Química Teòrica i Computacional (IQTC-UB), Universitat de Barcelona, Martí i Franquès 1-11, 08028 Barcelona, Spain S Supporting Information *

ABSTRACT: Dihydrogen bonds involving carbon and metals of group 13, M−H···H−C (M = Al, Ga, In), were analyzed theoretically. A structural survey of the Cambridge Structural Database revealed the surprising abundance of these interactions in the solid state, where they are often accompanied by weaker C−H···H−C homopolar contacts. Furthermore, cooperative effects were observed to reinforce both interactions in the case of bifurcated short contacts. To study the energetics of the interaction, a comprehensive computational benchmarking was first carried out to find the most suitable calculation method. Dispersion corrected functionals (DFT-D) give good results in terms of both intermolecular distance and binding energies. Interaction energies were then calculated for systems involving terminal and bridging hydrogen atoms, obtaining values in the range 1−2.5 kJ/mol. For dimers of Lewis acid−base adducts, binding energies increase up to 10 kJ/mol per H···H contact due to the redistribution of the electron density of the monomers, which eventually leads to an enhancement of the electrostatic character of the interacting unit.

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INTRODUCTION

calculated to be 1.8 kJ/mol with two C−H···H−N and C−H··· H−B distances at 2.47 and 2.93 Å, respectively.10 Focusing on group 13, the lower electronegativity of the metals of the group with respect to boron would expectedly lead to stronger interactions with C−H or N−H groups via the Hδ+ atom. There exist a few theoretical papers in the literature about the participation of group 13 metals Al and Ga in short H···H contacts. The (NH3MH3)2 (M = Al, Ga) dimers were investigated at the MP2/cc-pVDZ level, giving binding energies of −25.1 and −20.9 kJ/mol for Al and Ga, respectively, with M−H···H−N distances close to 1.8 Å.11 Other theoretical studies at the MP2 level have dealt with MH4−···HO−CH3 (M = Al, Ga) interactions reporting energies of about −42 kJ/mol with very short H···H distances (1.62 Å).12 Also, the AlH3···H− ArF dimer has been analyzed, showing a lengthening of the 1.085 Å H···H distance upon halogen substitution in the alane molecule.13 In another work, intramolecular Al−H···H−C contacts were studied with the atoms in molecules (AIM) method showing bond paths between the H atoms with electron density values of 0.007−0.008 au at the bond critical points.14 However, there is a surprising scarcity of information about Al−H···H−C short intermolecular contacts or the analogous contacts with the heavier elements of the group, i.e., Ga, In, and Tl. To our knowledge, there is no work in the literature devoted to study comprehensively this particular type of dihydrogen bonding. This is more shocking considering that a quick structural search returns 350 hits with Al−H···H−C

The term dihydrogen bond encompasses a series of X−H···H− Y short contacts between protic and hydridic hydrogen atoms at distances shorter than the sum of the van der Waals radii (2.4 Å).1 It is known nowadays that these unconventional interactions might determine the molecular architecture, supramolecular arrangements, and reactivity of many compounds.2 A comprehensive review on the implications of dihydrogen bonds in the reactions of metal hydrides was published very recently,3 also pointing out some potential applications such as the development of hydrogen-storage materials. In a dihydrogen bond, it is usual that the negatively charged H atom is attached to a metal atom, resulting in an interaction of the type M−Hδ−···δ+H−Y. Since the first report of very short Re−H···H−N contacts by Wessel et al.4 in 1995, an increasing number of M−H···H−Y bonds were identified, involving different transition metals (M = Ta, W, Fe, Ru, Os, Co, Rh, and Ir; Y = C).5,6 On the other hand, dihydrogen interactions with main group metal hydrides have been studied less than those with transition metals probably because most interest was attracted by the more abundant B−H···H−C and B−H···H−N short contacts. Among the latter, perhaps the most studied model was the prototypical (NH3BH3)2 dimer, whose crystal structure determined by neutron diffraction presents N−H···H−B intermolecular distances of 2.02 Å.7 The binding energy was estimated in −25.5 kJ/mol at the PCI-80/B3LYP level of theory,8 and more recently, the value of −17.8 kJ/mol was obtained by means of MP2 calculations.9 For comparison, the B3LYP dissociation energy of the NH3BH3···CH4 dimer was © XXXX American Chemical Society

Received: January 16, 2017 Revised: February 9, 2017

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DOI: 10.1021/acs.cgd.7b00069 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

Table 1. Number of Structures Containing M−H···H−C Contacts and Averaged Angular Parameters with the Corresponding Standard Deviationsa

a

M

no. structures

% structures with H···H

avg. α

avg. β

Al Ga In Tl

195 [433] 84 [139] 8 [16] 1 [1]

45 60 50 100

139.3 ± 21.6 136.8 ± 21.7 137.5 ± 22.7 76.7

147.6 ± 15.8 144.4 ± 17.1 147.4 ± 16.4 162.2

The total number of potential structures that have at least one M−H and one C−H bond are given in square brackets.

aluminum in any form and with any coordination number present short Al−H···H−C contacts. It seems that if these contacts are not as abundant as, for instance, B−H···H−C ones, it is because of the limited number of potential structures in which they can occur compared to those with B−H and C−H bonds. Regarding the topology of M−H···H−C contacts, a similar interaction pattern appears for all metals (1). The average value of the angle α is in all cases slightly smaller than that of β (Table 1). It is worth noting that those angles are not modified even in the case of bifurcated (2) or trifurcated interactions. The average angles must be considered with prudence due to the relatively large values of the standard deviations. In any case, the angles associated with M−H···H−C (M = Al, Ga, In) contacts are in the same range as those found for homopolar B−H···H−B and C−H···H−C ones in boranes17 and alkanes,18 respectively. The shortest Al−H···H−C contact between nonfixed H atoms occurs at 2.26 Å (lipral),19 whereas the shortest Ga−H···H−C and In−H···H−C ones are found at 2.41 (kukkac)20 and 2.30 Å (keqdep),21 respectively. However, the latter example presented fixed alkyl H atoms at a C−H distance of 0.97 Å because no structure was found with In−H··· H−C short contacts between refined hydrogens. There are in total 54 Al−H···H−C, 19 Ga−H···H−C, and 5 In−H···H−C contacts shorter than 2.4 Å.

contacts shorter than 2.8 Å (with some H···H distances as short as 2.2 Å), which is a considerable number of examples, excluding this interaction of being considered as merely testimonial. The intermediate character of Al−H···H−C contacts between B−H···H−C and TM−H···H−C (TM = transition metal) as well as its apparent easiness to be established make these interactions an appealing subject of investigation. In this paper, we studied in detail the abundance, topology, and energies associated with M−H···H−C (M = Al, Ga, In, Tl) short intermolecular interactions by means of a combined structural and computational analysis. First, we searched structural databases to identify the geometrical features of such contacts. Then, we attempted to establish a robust DFT methodology, cheaper than post-Hartree−Fock methods in terms of computational cost, which allows the study of large systems. Finally, several hypothetical and existing dimers connected via M−H···H−C interactions were theoretically analyzed. Also, the existence of possible cooperative effects in the solid state will be taken into account.

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STRUCTURAL ANALYSIS We performed systematic searches in the Cambridge Structural Database15 (CSD) to establish the abundance of intermolecular M−H···H−C (M = Al, Ga, In, Tl) contacts. A threshold of 2.65 Å was chosen for the H···H distance, which is the sum of twice the van der Waals radius of H (1.20 Å)16 plus 10%. When undertaking a structural analysis involving H···H contacts, one must pay close attention to how the positions of H atoms were assigned in the crystal structures. It is known that the most reliable data come from neutron diffraction structures. However, we have not found any neutron resolved structure containing M−H···H−C (M = Al, Ga, In, Tl) short contacts. On the other hand, in X-ray structures, the position of the H atoms can be refined (or Fourier mapped) or assigned to fixed positions according to characteristic bond distance values. In the present analysis, the positions of all hydrogen atoms attached to the group 13 metals were refined to guarantee representative H···H distances. For the H atoms at the other side of the interacting unit, i.e., those attached to a C atom, we also tried to stay confined to refined data, but fixed H positions were allowed in some examples of interest (see Table 2). The H···H distances associated with these fixed cases must be taken with caution and should not be used for statistical purposes. The M−H···H and C−H···H angles, however, are not significantly affected by the positioning method of H atoms. Focusing on the structural analysis, we compared the number of structures showing short M−H···H−C contacts with the number of existing structures having at least one M−H and one C−H bond to put our results in context. Remarkably, about half of the time, there is the possibility of establishing a M−H··· H−C contact; such contact is found in the crystal structure (Table 1). Furthermore, the 4.1% of all structures containing

In the crystal structures where they are found, M−H···H−C contacts are not usually the only intermolecular interaction. In a vast majority of the cases (95% for Al, 80% for Ga, and 100% for In and Tl), they are accompanied by C−H···H−C contacts also shorter than 2.65 Å. These homopolar dihydrogen contacts can involve the CH unit participating in the M−H···H−C contact or another one from a different part of the molecule. Of course, other types of interactions (e.g. CO···H−C in sondoq and sonduw)22 can be present, sometimes involving different neighboring molecules; but surprisingly, this situation is not common, and only a handful of such examples are found among the whole set of structures. In general, M−H···H−C (M = Al, Ga, In) interactions coexist only with C−H···H−C ones in crystal structures. However, there are a few cases in which Al−H···H−C and Ga−H···H−C contacts are the only interactions between two molecules in a given crystal structure. We found five examples for Al and seven for Ga of these unsupported M−H···H−C contacts (Table 2). Most of them occur between Lewis acid− base adducts in which the donor atom is N or P and the metal B



Article

According to our structural analysis, M−H···H−C (M = Al, Ga, In) short contacts, often accompanied by other noncovalent interactions such as C−H···H−C, seem to be the “glue” that holds together a significant number of structures in the solid state. As explained in the next section, we conducted a computational study on the nature and energetics of this unexplored dihydrogen interaction, focusing on the most abundant metals Al and Ga.

Table 2. Unsupported M−H···H−C (M = Al, Ga) Contacts Shorter Than 2.65 Å As Found in the CSDa M

CSD refcode

ref

compound

Al

casnep03

27

[H2Al(NMe2)]3

xickav

26

Me2HN·AlH3

albmam11

24

Me3N·Al(η2-BH4)3

tarjeb

25

[(η2-tbutoxo)·AlH2]2

gilpia

30

[(η2-Et(Me)N·AlH2]2

jodfen01

31

[−CH2Me2N·GaH3]2

kawdoc

28

MeH2N·GaH3

naszir01

32

Me3P·GaH2Cl

2.53, 2.63 2.58, 2.63 2.59, 2.62 2.62

tarjol

25

[(η2-tbutoxo)·GaH2]2

2.43

tmegal02 uleyit

23 29

Me3N·GaH3 Me3P·GaH3

xickid01

26

Me2HN·GaH3

2.58 2.61, 2.64 2.50

xickoj

26

[H2Ga(NMe2)]3

Ga

H···H (Å) 2.53− 2.64 2.62, 2.64 2.25, 2.45 2.57

2.41− 2.63

H-C position refined fixed (0.98) refined

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ENERGETICS OF MH···HC INTERACTIONS The H3CH···HAlH2 Dimer. A set of benchmark calculations was first carried out on the simplest neutral dimer with an Al− H···H−C short contact (i.e. H3CH···HAlH2) to assess the performance of different post-Hartree−Fock and DFT methods (Table 3). We selected a 1:1 interaction topology (3) to avoid

fixed (0.96) refined refined fixed (0.98) fixed (0.98) fixed (0.96) refined refined

Table 3. Binding Energies (kJ/mol) with and without Correction of the BSSE and H···H Distances in CH4···H3Al Dimers with 1:1 Topology (3) at Different Levels of Theorya

fixed (0.98) fixed (0.98)

a The position of the fixed H-C atoms in the corresponding crystal structures is given in parentheses as the C−H bond distance (Å). The H-M atoms have all been refined.

center is tetracoordinated. In this kind of molecule, for instance (CH3)3N·AlH3 (tmegal02),23 both the N and Al atoms are sterically protected from the establishment of intermolecular interactions, and it is precisely in this context where H···H short contacts predominate. Moreover, intuition says that interactions of heteropolar nature will be favored over homopolar ones, which is in good agreement with the observed prevalence of Al−H···H−C contacts over C−H···H−C ones in this type of compound. A very short H···H distance (2.25 Å) is found in albmam11,24 involving one bridging H atom from a bidentate tetrahydroborato ligand coordinated to the Al center. In this case, the nature of the bridging H atom is affected not only by the Al but also the B atom. In the same crystal structure, there is also a longer B···HC contact at 2.93 Å (sum of the vdW radii = 3.11 Å). In two Al-containing structures, there are also somewhat long C−H···H−C contacts at 2.94 (tarjeb)25 and 3.03 Å (xickav)26 that do not seem to drive the formation of the shorter Al−H···H−C interactions. In casnep03,27 one of the molecules involved in H···H interactions establishes lateral Al··· H contacts at 3.67 Å (sum of the vdW radii = 3.70 Å) with another neighboring molecule. For Ga compounds, we also find very short H···H distances at 2.41 (xickoj)26 and 2.43 Å (tarjol).25 Both crystal structures also present C−H···H−C contacts longer than 2.75 Å. In kawdoc28 and xickid01,26 there are short Ga−H···H−N contacts (2.14−2.21 Å), but they do not support the Ga− H···H−C ones because they are located in a different region of the unit cell. Remarkably, in the crystal structure (determined at 150 K) of uleyit,29 the Me3P·GaH3 units are connected to each other by means of Ga−H···H−C short contacts as the only intermolecular interaction.

method

H···H (Å)

ΔE

ΔEBSSE

CCSD(T)/CBS CCSD(T)/aug-cc-pVQZ CCSD(T)/aug-cc-pVTZ MP2 M06-2X M06-2X-D3 B3LYP-D3 PBE0-D3 ωB97xD LC-ωPBE-D3BJ

2.594 2.588 2.531 2.553 3.062 3.053 2.519 2.500 2.509 2.660

−1.492 −1.547 −2.006 −1.881 −0.961 −1.174 −1.630 −2.215 −1.588 −1.379

−1.379 −1.338 1.129 −0.711 −0.920 −1.254 −1.881 −1.212 −1.045

a

The aug-cc-pVTZ basis set was used for all atoms unless otherwise specified.

any cooperative effect that might complicate the interpretation of the calculated energies and geometrical parameters. Due to the lack of experimental references, the results were compared to high level CCSD(T)/CBS calculations performed on the MP2/aug-cc-pTZV optimized geometries of the methane and alane molecules. In the dimer calculation, the interacting Al−H and C−H bonds as well as the intermolecular H···H distance were optimized, while the rest of variables were kept frozen. The use of different basis set sizes has not been evaluated here; however, in a previous work on C−H···H−C short contacts,33 it was seen that, despite the fact that larger basis sets tend to approach to the CCSD(T)/CBS limit, a triple-ζ with polarization and diffuse functions gives a good compromise between computational cost and accuracy. Although MP2 seems to work reasonably well for Al, further exploratory calculations show that this method tends to overbind the CH4···H3Ga and CH4···H3In dimers, giving H··· H equilibrium distances of 2.196 and 2.166 Å for Ga and In, respectively. Accordingly, the binding energies are also overestimated (−5.267 and −8.736 kJ/mol for Ga and In, respectively), with unacceptable BSSE energies (almost 100% of the binding energy). On the other hand, DFT methods C



Article

than that of the dialane···methane one with both interaction topologies. The increase in the binding energy is more pronounced if we compare the interaction through the terminal and bridging H atoms. In this case, the binding energy for the latter is 50 and 62% larger for Al and Ga, respectively. We performed an NBO analysis of these dimeric systems to gain further insight into the nature of M−H···H−C interactions. The lower electronegativity of Al with respect to Ga is reflected in the charge distribution of dialane and digallane molecules. Atomic charges are 1.009 and 0.699 for Al and Ga, respectively. Moreover, H atoms have more hydridic character in dialane than in digallane. It is also interesting to observe how atomic charges evolve upon dimerization. In all cases, there is a charge transfer in the atoms involved in the interaction, from the metal to the hydridic hydrogen and from the protic hydrogen to the carbon atom, with an amount of transferred charge of 0.012 and 0.015 for the Hterm and Hbridg topologies, respectively, which results in an electrostatically enhanced M−Hδ‑···δ+H−C interaction. Also, the charge difference between the two H atoms is larger for the Hbridg case than for the Hterm one, which could explain the higher binding energies observed for the former. Dimers of Lewis Acid−Base Adducts: (R3P·MR3)2. Dimers from crystal structures in which molecules are held together by means of Al−H···H−C and Ga−H···H−C short interactions were analyzed. DFT calculations were done on the crystallographic coordinates without further optimization. In this way, we quantified the binding energies of experimental structures to test our theoretical predictions from model systems. We selected one alane (xickav)26 and one gallane (tmegal0223) adduct with a Lewis base resulting in a tetracoordinated environment in which the metal has practically sp3 hybridization and the originally planar MH3 moiety is distorted toward a tetrahedron (Figure 1). Our calculated binding energy for the dimer of dimethylaminealane (−22.03 kJ/mol) with two Al−H···H−C contacts at 2.64 Å is very similar to that of the (Me3N·BH3)2 dimer, which was previously calculated to be −22 kJ/mol at the MP2 level with two bifurcated C−H···H−B short contacts at 2.13 and 2.31 Å.34 It is worth noticing the much higher binding energy of the dimer of trimethylaminegallane (−6.56 kJ/mol) with respect to gallane···methane (−1.26 kJ/mol), both with the same 1:1 interaction topology, and also of the dimer of dimethylamineallane (−22.03 kJ/mol) with respect to alane···methane (−1.25 kJ/mol). To understand this behavior, we mapped the molecular electrostatic potential (MEP) of alane and trimethylaminealane (Figure 2). The two molecules present regions of positive electrostatic potential around the three H atoms bound to the Al center, which exhibits the characteristic

reproduce the reference values relatively well. Also, for Ga and In dimers, DFT methods seem to give results more reasonable than those of MP2 (complete benchmarking tables can be found in the Supporting Information). If we compare the three elements of group 13, the binding energies of Al and Ga are similar (−1.254 and −1.296 kJ/mol at the B3LYP-D3 level, respectively), whereas that of In is larger (1.463 kJ/mol at the same level of theory). This behavior is also seen for the rest of the functionals. The DTF calculated H···H distances are also in very good agreement with the experimental values shown in Table 2. However, the M06-2X hybrid functional, especially without empirical dispersion, gives a longer distance and a lower binding energy. On the other hand, the PBE0-D3 distance is the shortest among all methods, which results in a slightly overbound dimer. Note that, in general, the BSSE energies are relatively small yet not negligible. On the basis of the present benchmarking, we consider that the B3LYP-D3 functional combined with the aug-cc-pVTZ basis set gives reasonably good values both of intermolecular distance and binding energy. Thus, this calculation method was employed throughout the next sections. M−H···H−C Contacts Involving M−H−M Bridging Hydrogen atoms. The interaction of dialane and digallane with methane was also analyzed. Two different 1:1 interaction topologies were taken into account, the first one involving a terminal H atom in the metal hydride, whereas the second one involved a bridging μ2-H atom. Only the intermolecular M− H···H−C distances were optimized in the dimers, calculated on the geometry of the fully optimized monomers. We are aware that those are not minima of the corresponding potential energy surfaces, but our interest here was to reproduce interaction patterns that can be found in the solid state rather than to explore a hypothetical gas phase scenario. The results are presented in Table 4. All calculated H···H distances are very Table 4. BSSE-Corrected Binding Energies and Intermolecular Distances for the M2H6···H4C (M = Al, Ga) Dimers with Interaction Topologies M−Hterm···H−C and M−Hbridg···H−C Calculated at the DFT-D level metal

interacting H

H···H (Å)

ΔEBSSE (kJ/mol)

Al Al Ga Ga

terminal bridging terminal bridging

2.491 2.474 2.450 2.438

−1.338 −2.006 −1.421 −2.300

close to each other in the range 2.43−2.49 Å. The shortest distances are associated with M−Hbridg···H−C interactions. Larger differences are seen, however, in the binding energies. The digallane···methane dimer shows binding energy higher

Figure 1. Short Al−H···H−C and Ga−H···H−C contacts (Å) in the crystal structures of (a) xickav26 and (b) tmegal0223 with the corresponding calculated binding energies. The H···H distance values are given in Å. Colors codes: Al = brown; Ga = pink; N = blue; C = gray; H = white. D



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structure of uleyit), obtaining values of −25.66 and −41.21 kJ/ mol, respectively. Thus, the binding energy per contact lies in a range of 8.55−10.30 kJ/mol, which is also in very good agreement with the calculated values for the dimers in Figure 1. We also analyzed the electron density of the two dimers in Figure 1 by means of the atoms in molecules (AIM) methodology. In the dimer of trimethylaminegallane, there is a bond path between the two H atoms located at a distance of 2.58 Å with a bond critical point (bcp) of 0.0051 for the electron density. For the dimer of dimethylamineallane, 4 different bond paths were identified, 2 with H···H distances of 2.64 Å and two of 2.99 Å (electron density value at the bcp of 0.0039 and 0.0022, respectively). These values are similar to those found for other dihydrogen bonds18 but are still below the typical values for covalent interactions (0.2−0.4).

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COOPERATIVE EFFECTS In about one-third of all M−H···H−C contacts, the interacting C−H unit also establishes a C−H···H−C short contact with another C−H group. This quite common situation seems to take benefit from a cooperative effect between both interactions. As seen above, there is some charge transfer in the C−H group when interacting with the M−H, which leads to a more positive H atom attached to C. This hydrogen is able to interact then more strongly with another CH unit, reinforcing in this way the electrostatic component of the C− Hδ+···Hδ+−C contact, now happening between two differently charged hydrogen atoms (yet both positive). The charge difference, however, is not as large as between Al−H and H−C and, in consequence, the C−H···H−C distances are in general slightly longer (around 0.1−0.3 Å) than those of the Al−H··· H−C ones. An experimental example of this behavior is provided in Figure 4.

Figure 2. MEP surface of AlH3 (left) and Me3N·AlH3 (right) on the 0.001 au contour with two different views. The Vs,min values are given in kJ/mol.

π-hole with a region of positive MEP. However, in the case of trimethylaminealane, the presence of an electron donor group attached to the AlH3 framework is reflected in a more negative MEP around the hydrogen atoms. Consequently, the Vs,min is more negative for trimethylaminealane than for alane (−109 and −41 kJ/mol, respectively). Interestingly, the Hδ+ atoms of the methyl groups (in blue in Figure 2, right) point exactly to these Vs,min regions when forming the M−H···H−C interactions, as can be seen in Figure 1. It seems thus plausible that an enhancement of the electrostatic character of the dihydrogen bond is responsible for the aforementioned large energy differences. An interesting example of interactions between regions of positive and negative electrostatic potential was found in the crystal structure of trimethylphosphinegallane (uleyit)29 (Figure 3). There, trimethylphosphinegallane molecules are

Figure 4. C−H···H−C (2.79 Å) short contacts mediated by Al−H··· H−C (2.62 Å) interactions in the crystal structure of bis(η2diethylamide)-dichloro-dihydrido-dialuminum (sudlag). 35 Color codes: Al = brown; Cl = green; N = blue; C = gray; H = white.

The cooperativity energy, defined by Alkorta et al.36 as Ecoop = ΔE BSS E (ABC) − [ΔE BSSE (AB) + ΔE B SSE (AC) + ΔEBSSE(BC)], has proved to be a useful tool to quantify cooperative effects in systems with multiple coexisting interactions.37 To corroborate our hypothesis, we built a model system consisting of a dialane···methane···methane trimer with one Al−Hbridg···H−C and one C−H···H−C short contact, as depicted in Figure 5. The calculated Ecoop for this trimer is 0.9 kJ/mol, which confirms that the establishment of C−H···H−C interactions associated with the Al−H···H−C ones is not only driven by geometric factors but also favored by an energetic stabilization. Furthermore, the binding energy of B and C is ΔEB−C = −1.88 kJ/mol, increasing in the presence of A up to ΔEAB‑C = −5.31 kJ/mol, both with correction of the BSSE.

Figure 3. Intermolecular Ga−H···H−C interactions in the crystal structure of trimethylphosphinegallane (uleyit).29 Color codes: Ga = pink; P = yellow; C = gray; H = white.

arranged in a head-to-tail fashion that favors the establishment of chains via Hδ+···Hδ‑ short contacts (2.63 Å). Remarkably, these chains interact with each other side-to-side through slightly longer H···H contacts (2.70 Å), which creates a 3D network of multiple Ga−H···H−C interactions. We calculated the binding energy of the head-to-tail and side-to-side interacting dimers (with the geometries from the crystal E



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COMPUTATIONAL DETAILS

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ASSOCIATED CONTENT

Article

All DFT, MP2, and CCSD(T) calculations were done with Gaussian09.39 The aug-cc-pVTZ basis set was used for all atoms, including the associated relativistic pseudopotential for In (aug-ccpVTZ-PP). CBS limit was estimated by extrapolation from aug-ccpVTZ and aug-cc-pVQZ basis sets at the CCSD(T) level. After the benchmarking, all calculations were performed at the B3LYP-D3/augcc-pVTZ level. Partial geometry optimizations of dimers on the fully optimized monomer geometries allowed the relaxation of the atoms involved in the interacting unit M−H···H−C, whereas the rest of the atoms were kept frozen. None of the calculated dimers were characterized as real minima of the potential energy surface because our final goal here was to analyze interaction patterns existing in condensed phases rather than to reproduce a gas phase scenario. This approximation was successfully applied in previous theoretical studies dealing with different dihydrogen interactions.18 All binding energies were corrected for the BSSE with the Counterpoise method. Atomic charges were calculated with the NBO method implemented in Gaussian09. Bader’s AIM analysis of the electron density was done by means of the AIMAll software.40 Structural searches were performed in the Cambridge Structural Database15 (version 5.37, November 2015 + 3 updates). Only structures with coordinates determined, not disordered, and with R factors smaller than 0.1 were allowed in searches. Furthermore, only three significant figures were given for experimental H···H distances throughout the text. CSD refcodes of illustrative examples are given in parentheses as a six-letter combination (abcdef). For the structural analysis, we used the van der Waals radii proposed by Alvarez.16

Figure 5. Dialane···methane···methane trimer (A−B−C) used as a model to study cooperative effects with intermolecular distances given in Å.

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CONCLUSIONS We carried out a combined structural and computational study of M−H···H−C short contacts, M being a group 13 metal (Al, Ga, In, Tl). Analysis of this unexplored type of dihydrogen bond has drawn several interesting conclusions that we summarize next. On the basis of our structural analysis, we discovered that if they can be established, i.e., if C−H and M−H groups are present, M−H···H−C (M = Al, Ga, In) interactions are surprisingly common. In a large number of cases, they are accompanied by weaker homopolar interactions such as C−H··· H−C contacts. However, M−H···H−C (M = Al, Ga) are practically the only short intermolecular contacts in Lewis acid−base adduct derivatives. Before the interaction energetics were analyzed, a computational methodology was established based on benchmark calculations on a simple model. Several post-Hartree−Fock and DFT methods were tested and compared to high level CCSD(T)/CBS reference values. We concluded that the B3LYP functional with the empirical Grimme dispersion38 and the original damping function (B3LYP-D3) combined with a large basis set (aug-cc-pVTZ) can give better results than those obtained at the more expensive MP2 level. In general, the M−H···H−C interaction strengthens when descending down the group 13, but not very large energy differences were found between the different metals. It has also been seen that larger binding energies are obtained when bridging hydrogen atoms are involved. In terms of strength, M−H···H−C contacts are more energetic than C−H···H−C or B−H···H−B homopolar contacts and also the heteropolar B− H···H−C ones. Binding energies can be as large as −22 kJ/mol in the dimer of dimethylaminealane or −41 kJ/mol in that of trimethylphosphinegallane. The binding energies per Al−H··· H−C contact are in the range of 1−1.5 kJ/mol for terminal··· terminal interactions in small systems (CH4···AlH3), 2−2.5 kJ/ mol when a bridging H atom is involved (Al2H6···CH4), and 6− 11 kJ/mol for dimers of Lewis acid−base adducts. Finally, we also observed that M−H···H−C and C−H···H−C interactions can be significantly enhanced due to cooperative effects with an increase of 12% in the binding energy in the case of bifurcated contacts (Figure 5). Our results indicate that M−H···H−C (M = Al, Ga, In) are not negligible in terms of the forces that drive the solid-state packing of molecules as confirmed, for instance, by the crystal structure of trimethylphosphinegallane. Intermolecular Al−H··· H−C and Ga−H···H−C interactions can be thus employed and also combined with other weak interactions, to design packing motifs in the solid state, becoming a useful tool in supramolecular chemistry and crystal engineering.

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.7b00069. Benchmark calculations on C−H···H−M contacts in Ga and In hydrides (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Jorge Echeverría: 0000-0002-8571-0372 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author thanks the Spanish MINECO for a Juan de la Cierva research fellowship (IJC-2014-20097) and CSUC for the allocation of computational facilities. J. Jover is gratefully acknowledged for his constructive comments on the manuscript.

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