In my opinion, the best way to estimate the strength of H-bonds is looking for their effects on the vibrational spectra.

For example, you have an organic molecule solvated by water, haven't you?

Well, you could:

• perform a frequency calculation on the isolated organic molecule, and then...
• ...perform the same calculation including the H-bonded water molecules.

The N-R stretching frequencies should be redshifted somewhat, and that redshift depends on the strength of the H-bonds.

A related reference:

Bridging QTAIM with vibrational spectroscopy: the energy of intramolecular hydrogen bonds in DNA-related biomolecules

http://pubs.rsc.org/en/content/articlelanding/2012/cp/c2cp40176b

Thanks Bipin, I will go through it.

Thanks again, I've been through the article and registered for a copy of AIMAll. In my pursuit of further information on this particular subject, I came upon a suggestion of using counterpoise=n for systems of intermolecular interactions. Must this always be the case? I have two sets of systems, organic+metal and organic+water-cluster. Both sets optimise to a very tight convergence using a very high basis set without failure and they display the desired distance and orientation of intermolecular bonding. Would my system benefit further to using the counterpoise key word?

Thanks

Both counterpoise and QTAIM gave same value of interaction energy. If you sum all values of interaction energy, it will be equal to the binding energy by counterpoise method if Basis set superposition error is considered. NBO analysis also helps in understanding the hydrogen bonding.

In my opinion, the best way to estimate the strength of H-bonds is looking for their effects on the vibrational spectra.

For example, you have an organic molecule solvated by water, haven't you?

Well, you could:

• perform a frequency calculation on the isolated organic molecule, and then...
• ...perform the same calculation including the H-bonded water molecules.

The N-R stretching frequencies should be redshifted somewhat, and that redshift depends on the strength of the H-bonds.

Hi Francesco, 

Thanks that great suggestions. It certainly gives me more to look into. 

Thanks again. 

Aim analizis show the bond critical points, and you can download http://www.aim2000.de/  with tutorials...

To evaluate the strength of H-bonding you can use the Iogansen’s rules for vibrational frequencies and its intensities. Please look at our paper “How Strong Is Hydrogen Bonding in Ionic Liquids? Combined X-ray Crystallographic, Infrared/Raman Spectroscopic, and Density Functional Theory Study” and references cited in.

If you tried the ADF package, you'd find there the ETS-NOCV scheme which gives you the binding energy between two molecular fragments into which you have divided your molecule (in your case it would probably be the molecule itself and the water molecules, or the molecule and all water but one as the first fragment, and this single molecules as the second fragment). The ETS-NOCV scheme gives you the binding energy decomposed into several components and the natural orbitals for the differential density matrix that picture different channels of electron flow associated with the bond formation together with their individual energetic contributions.

Would using symmetry adapted perturbation theory be appropriate for you problem?

Energy of hydrogen bond may be calculated from potential energy density at bond critical point as described in:

Hydrogen bond strengths revealed by topological analyses of experimentally observed electron densities / E. Espinosa, E. Molins, C. Lecomte // Chem. Phys. Lett. - 1998. - Vol. 285, N 3–4. - P. 170-173.

Besides vibrational shifts and topological analysis, energy decomposition analyses are useful in quantifying H-Bonding (more generally: intermolecular interactions).

The Morokuma analysis is described here:

The origin of hydrogen bonding. An energy decomposition study, H. Umeyama & K. Morokuma, J. Am. Chem. Soc., 1977, 99 (5), pp 1316–1332

and a newer method based on "absolutely localized molecular orbitals"  here:

R. Z. Khaliullin, E. A. Cobar, R. C. Lochan, A. T. Bell, M. Head-Gordon, Unravelling the Origin of Intermolecular Interactions Using Absolutely Localized Molecular Orbitals , J. Phys. Chem. A, 2007, 111, 8753–8765.

This way one can isolate different energetic components due to polarization and charge transfer.

Hi all, 

Thanks for the posts. I've now completed the opt+freq at wb97xd/6-311++g**. Comparing the IR vibrational spectra to a control i.e., no explicit water, I am seeing quite a shift to a lower frequency in the OH bond vibrations. I am also seeing an increase in the O-H bond distance i.e., (R-O-H....OH2). I have a similar set of structure currently optimising, but they are in the gas phase as I am not sure how the PCM for a solvent would affect the IR vib spectra.

I am now looking into the NBO properties, already I see an increase in occupancy in the sigma(O-H)* orbital. 

Then I am going to move on topological analysis using multifwn. 

I'm not sure about this, but I think that PCM has only very small effects on the vibrational spectra.

I would agree with my predecessor that PCM would only weakly affect most vbrational frequencies. If you have a protic solvent, however, explicit inclusion of several solvent molecules in the vicinity of the H-bond (apart from the PCM) could result in a significant changes.

Exactly, Marcin in very right: PCM changes almost nothing, yet the explicit solvent can redshift vibrational frequencies a lot.

The fact is that H-Bonding is a directional interaction with a small (but non-vanishing!) covalent character.

To model such an interaction, PCM is not enough.

Anyway, PCM greatly enhances the accuracy of optical spectra within the TD-DFT framework.

Regarding PCM and Hydrogen bonding in ground state, I like to share my current experience, where an amino acid water interaction was studied in different solvents using PCM. The effect of PCM with different dielectric media is almost negligible in terms of change in bond order, electron density, bond length etc.,

Hi Debashree, thank you for that reply. That is very useful to know. What difference have you encountered in comparison to the gas phase?

The above-mentioned parameters are distinctly different in gas phase from the PCM calculations in any of the solvents. We have scanned solvents with dielectric media ranging from 4 to 80.

Hi,

I have worked on that same problem. I compared several descriptors and their usefulness in prediction of hydrogen bond energies and it turned out that the density at the bond critical point in Bader's theory of atoms in molecules is the best. I also used it to estimate hydrogen bond energies in a macromolecule using hybrid QM/MM. Please consult the following two papers:

http://link.springer.com/article/10.1007%2Fs00214-014-1520-7

http://www.ncbi.nlm.nih.gov/pubmed/25099813

Regards,

Ahmed Ayoub