# What's the bonding in the diborane(6)- hydrogen chloride dimer?

Then I faced a very interesting structure, something that I have never seen before. Something that turns up lesser than 50 results in Google, most of which are behind paywalls, and thus leave me in pain of not understanding this species. I'm talking about diborane - hydrogen chloride.

Source

So, I'd like to understand this species better.

The bonding certainly doesn't seem ionic. What is the attraction force between $\ce{HCl}$ and $\ce{B2H6}$? There must be one or they wouldn't have written these two compounds together.

Edit: I'm specifically looking for the hydrogen chloride - diborane(6) dimer you can see in the image. And the Cl is pointing towards the H in diborane, so this isn't about dipole/induced dipole interactions. You can find more info about it in here. Interestingly, in calculating molar mass, both the $M$s of $\ce{HCl}$ and $\ce{B2H6}$ are taken into account.

• I am currently running SAPT2+3(CCD) on this to determine the attractive and repulsive contributions to the interaction energy. I will post the results once completed. It is clear, however, that this would be a non-covalent interaction. – LordStryker Jun 10 '15 at 18:42
• This paper calls it a hydrogen bond, this one provides structural information – ron Jun 10 '15 at 18:58
• I would imagine that it would be a dipole/induced-dipole judging by the second paper that ron posted (with the hydrogen on HCl pointing toward the diborane). The first paper shows HCl pointing up toward the centroid of diborane which is completely different than the geometry presented in paper 2. – LordStryker Jun 10 '15 at 19:09
• @Lord The first paper Ron linked to speaks about diborane (4), while I'm looking for the diborane (6) "version". There's some info here. The interesting part is that in computing molecular mass, it takes both HCl and B2H6 into account. – It's Over Jun 10 '15 at 19:16
• Any chance an H2O-HX (where X is a halogen) dimer system has been examined? That would be a very analogous model system to your diborane-HCl dimer assuming an appropriate orientation. – LordStryker Jun 10 '15 at 19:29

I find this question to be quite interesting as it clearly pertains to non-covalent interactions.

I have analyzed two conformations of the diborane-HCl dimer system, one with the chlorine on HCl orientated toward diborane (HCl-Dib) and one with the chlorine oriented away from the diborane (ClH-Dib). For comparison, I have similarly analyzed the Water-HCl dimer with the chlorine oriented toward the two hydrogens on water.

Methodology

Full geometry optimizations and corresponding harmonic vibrational frequency computations were performed with Gaussian 09 using Grimme's B97D density functional along with the 6-31+G(d',p') basis set. All geometries were characterized to C$_{2V}$ symmetry. Symmetry adapted perturbation theory (SAPT) was implemented at the SAPT2+3(CCD) level using the Psi4 software package. These computations implemented Dunning's heavy-aug-cc-pVTZ (haTZ) basis set (i.e. aug-cc-pVTZ for non-hydrogen atoms and cc-pVTZ for all hydrogen atoms). Finally, natural charges were quantified using the Natural Bond Orbital (NBO) analysis routine available in Gaussian 09 (see http://nbo6.chem.wisc.edu/ for more details).

Results

Both diborane-containing complexes were minima on the B97D potential energy surface. The H$_2$O-HCl dimer is a higher order saddle point exhibiting two imaginary modes of vibration. The interaction energy ($E_{\mathrm{int}}$) can be quantified by attractive and repulsive contributions, the former consisting of electrostatics ($E_{\mathrm{elst}}$), induction ($E_{\mathrm{ind}}$), and dispersion ($E_{\mathrm{disp}}$) and the latter consisting of exchange ($E_{\mathrm{exch}}$). The table below summarizes the SAPT results.

Clearly, the dominant attractive force in each case is dispersion. The ClH-Dib complex exhibits the strongest interaction energy and contains a dipole that points from the diborane monomer to the chlorine. The HCl-Dib complex has an interaction energy that is about 1 kcal mol$^{-1}$ smaller in magnitude and exhibits a dipole pointing toward the diborane monomer. The analogous H$_2$O-HCl system is qualitatively similar to the HCl-Dib complex in terms of the magnitudes of the components to the interaction energy. Surprisingly, this dipole-dipole interaction is slightly weaker (by about 0.1 kcal mol$^{-1}$) than that seen in the dipole/induced-dipole system of HCl-Dib.

I have included below figures for the HCl-Dib, ClH-Dib, and H$_2$O-HCl complexes, respectively, with corresponding natural atomic charges shown on each atom.

Figure 1 - HCl-Dib

Figure 2 - ClH-Dib

Figure 3 - H$_2$O-HCl

Interestingly, when chlorine is pointed toward diborane (Figure 1), the natural atomic charges for diborane remain rather symmetrical and diborane barely exhibits an individual dipole moment. The H$\cdots$Cl separation between the two monomers is about 3.4 Angstroms, a long-range interaction. However, when chlorine is pointed away from diborane (Figure 2), the H$\cdots$H interaction is much smaller, exhibiting a separation of about 2.2 Angstroms. When considering water, the separation increases once again (Figure 3) to about 3.2 Angstroms.

Conclusions

The dominate attractive force to the interaction energy for these dimer systems is dispersion, though we see a competing contribution from electrostatics in ClH-Dib (Figure 2). Surprisingly, the orientation of the halogen significantly affects the geometry and energetics of these systems. When chlorine is oriented toward the two hydrogens, a weaker interaction and a larger inter-monomer separation is seen. However, when hydrogen is oriented toward the two hydrogens, the interaction energy increases in magnitude and the inter-monomer separation decreases.

Q/A

I find it more convenient to address some of Martin's comments within the answer itself (sometimes responses can become quite long).

Which compound is lower in energy?

• Based on absolute energies, H$_2$O-Cl is the lowest in energy of the three dimers (by about 23 Hartrees).

How stable are they wrt decomposition?

• The interaction energy will give you this information (defined as the energy difference between the interacting monomers in an optimized dimer geometry and infinitely separated monomers adopting the geometry they have in the dimer complex). Given that the magnitude of $E_{\mathrm{int}}$ is less than 2 kcal mol$^{-1}$, I would say that these are not very 'stable'.

Have you tried asymmetric states?

• No. I do not believe breaking symmetry in the diborane-containing complexes will change the energy/geometry appreciably.

I find it quite surprising, that the BH--ClH distance is much longer (0.6A) than the sum of the respective vdW radii, while the BH--HCl distance is about the sum of the vdW radii. Still, in both cases there should be (about) no contribution from the orbitals. How do the bond lengths change in the two conformations?

• In the diborane-containing complexes, the bond lengths deviate by about 0.01 Angstroms (so... no change).

Can you make a rough comparison between the B--Cl distance in the two cases? They appear to be quite similar.

• In HCl-Dib, the B$\cdots$Cl separation is about 3.79 Angstroms. In ClH$\cdots$Dib, the B$\cdots$Cl separation is about 3.86 Angstroms. Similar they are indeed.
• I have so many questions about this, but first things first: Congratulations on your choice of functional ;) Secondly but not lesser: This is good work as usual. Thirdly: I am curious, so I am pretty sure I will come up with a terrible lot of questions. (Probably also due to my lack of knowledge in SAPT. I'll do some reading.) Let's start with the obvious. Which compound is lower in energy? How stable are they wrt decomposition? Have you tried asymmetric states? – Martin - マーチン Jun 12 '15 at 5:50
• I find it quite surprising, that the BH--ClH distance is much longer (0.6A) than the sum of the respective vdW radii, while the BH--HCl distance is about the sum of the vdW radii. Still, in both cases there should be (about) no contribution from the orbitals. How do the bond lengths change in the two conformations? Can you make a rough comparison between the B--Cl distance in the two cases? They appear to be quite similar. – Martin - マーチン Jun 12 '15 at 6:02
• @Martin-マーチン I thank you for your insightful questions and I've responded to them in the body of the answer. Are you happy with B97D for these complexes or should we look for method effects on these geometries? I could always implement B3LYP. ;) – LordStryker Jun 12 '15 at 12:45