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Post Calculation Addition of Empirical Dispersion – Fixing interaction energies


Calculation of interaction energies is one of those things people are more concerned with and is also something mostly done wrong. The so called ‘gold standard‘ according to Pavel Hobza for calculating supramolecular interaction energies is the CCSD(T)/CBS level of theory, which is highly impractical for most cases beyond 50 or so light atoms. Basis set extrapolation methods and inclusion of electronic correlation with MP2 methods yield excellent results but they are not nonetheless almost as time consuming as CC. DFT methods in general are terrible and still are the most widely used tools for electronic structure calculations due to their competitive computing times and the wide availability of schemes for including  terms which help describe various kinds of interactions. The most important ingredients needed to get a decent to good interaction energies values calculated with DFT methods are correlation and dispersion. The first part can be recreated by a good correlation functional and the use of empirical dispersion takes care of the latter shortcoming, dramatically improving the results for interaction energies even for lousy functionals such as the infamous B3LYP. The results still wont be of benchmark quality but still the deviations from the gold standard will be shortened significantly, thus becoming more quantitatively reliable.

There is an online tool for calculating and adding the empirical dispersion from Grimme’s group to a calculation which originally lacked it. In the link below you can upload your calculation, select the basis set and functionals employed originally in it, the desired damping model and you get in return the corrected energy through a geometrical-Counterpoise correction and Grimme’s empirical dispersion function, D3, of which I have previously written here.

The gCP-D3 Webservice is located at: http://wwwtc.thch.uni-bonn.de/

The platform is entirely straightforward to use and it works with xyz, turbomole, orca and gaussian output files. The concept is very simple, a both gCP and D3 contributions are computed in the selected basis set and added to the uncorrected DFT (or HF) energy (eq. 1)

eq1 (1)

If you’re trying to calculate interaction energies, remember to perform these corrections for every component in your supramolecular assembly (eq. 2)

eq2(2)

Here’s a screen capture of the outcome after uploading a G09 log file for the simplest of options B3LYP/6-31G(d), a decomposed energy is shown at the left while a 3D interactive Jmol rendering of your molecule is shown at the right. Also, various links to the literature explaining the details of these calculations are available in the top menu.

Figure1

I’m currently writing a book chapter on methods for calculating ineraction energies so expect many more posts like this. A special mention to Dr. Jacinto Sandoval, who is working with us as a postdoc researcher, for bringing this platform to my attention, I was apparently living under a rock.

 

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The Local Bond Order, LBO (Barroso et al. 2004)


I don’t know why I haven’t written about the Local Bond Order (LBO) before! And a few days ago when I thought about it my immediate reaction was to shy away from it since it would constitute a blatant self-promotion attempt; but hell! this is my blog! A place I’ve created for my blatant self-promotion! So without further ado, I hereby present to you one of my own original contributions to Theoretical Chemistry.

During the course of my graduate years I grew interested in weakly bonded inorganic systems, namely those with secondary interactions in bidentate ligands such as xanthates, dithiocarboxylates, dithiocarbamates and so on. Description of the resulting geometries around the central metallic atom involved the invocation of secondary interactions defined purely by geometrical parameters (Alcock, 1972) in which these were defined as present if the interatomic distance was longer than the sum of their covalent radii and yet smaller than the sum of their van der Waals radii. This definition is subject to a lot of constrictions such as the accuracy of the measurement, which in turn is related to the quality of the monocrystal used in the X-ray difraction experiment; the used definition of covalent radii (Pauling, Bondi, etc.); and most importantly, it doesn’t shed light on the roles of crystal packing, intermolecular contacts, and the energetics of the interaction.

This is why in 2004 we developed a simple yet useful definition of bond order which could account for a single molecule in vacuo the strength and relevance of the secondary interaction, relative to the well defined covalent bonds.

Barroso-Flores, J. et al. Journal of Organometallic Chemistry 689 (2004) 2096–2102
http://dx.doi.org/10.1016/j.jorganchem.2004.03.035,

Let a Molecular Orbital be defined as a wavefunction ψi which in turn may be constructed by a linear combination of Atomic Orbitals (or atom centered basis set functions) φj

We define ζLBO in the following way, where we explicitly take into account a doubly occupied orbital (hence the multiplication by 2) and therefore we are assuming a closed shell configuration in the Restricted formalism.

The summation is carried over all the orbitals which belong to atom A1 and those of atom A2.
Simplifying we yield,

where Sjk is the overlap integral for the φj and φk functions.

By summing over all i MOs we have accomplished with this definition to project all the MO’s onto the space of those functions centered on atoms A1 and A2. This definition is purely quantum mechanical in nature and is independent from any geometric requirement of such interacting atoms (i.e. interatomic distance) thus can be used as a complement to the internuclear distance argument to assess the interaction between them. This definition also results very simple and easy to calculate for all you need are the coefficients to the LCAO expansion and the respective overlap integrals.

Unfortunately, the Local Bond Order hasn’t found much echo, partly due to the fact that it is hidden in a missapropriate journal. I hope someone finds it interesting and useful; if so, don’t forget to cite it appropriately 😉

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