# Monthly Archives: July 2010

## The Chemical blogspace (Cb) has ranked this blog!

I just recently found out this very blog of mine was found and ranked by the Chemical blogspace as number **96** (out of about 250, before you ask). I still don’t know how do they do the math but it seems it has to do with the number of clicks a blog gets over a certain period of time and relating that somehow to the number of new posts over that same period. The Chemical blogspace is a blog which retrieves information from other chemistry blogs on the Internet and gathers it in a way that allows one to search by author, blog, topic or even molecule. The following link is to the ranking of my blog within Cb.

Why isn’t it retrieving my photo or why do all posts appear in the feed without the proper title but with my *fullname *instead? I have no idea!

Be that as it may, I’m very happy to know this rather neglected hobby is out there, is getting read and has even become a small Internet resource. I call it neglected because my posting rate is about 1 post/month. Some posts have become very popular, such as the ones on NBO analysis and their visualization and the one on PCM calculations and troubleshooting. Some have never amounted to much like the one on my thoughts about baseball or the relationship between knots -through graph theory- and chemistry. Some rants I like a lot like the one on the invention of the wheel and some got posted without proofing (and they remain shamefully so) like that on basis sets. During the first few months the number of visitors was somewhere between 40 to 60 visitors per month, now I don’t have less than 1700 a month! I now get a lot of questions from -mostly- students worldwide, and although I can’t always help them -sometimes not even reply soon!- I’m glad to be taken into consideration. It’s interesting to get these questions since in the vast majority of them you can tell they actually read the posts first; this means this is people actually trying to get something done! I don’t think I’ve ever had a question that requires an **RTFM **answer, thank goodness!

This ranking makes me think it could be worth the while to post things more often about my own work; also a good redesigning of the site is due in order to make it a site and not just a blog. Who knows? maybe I can climb higher in the ranking by the end of this year š

Thanks to everyone who has ever clicked, read, rated and commented the entries!

Cheers!

## How to calculate Fukui indices

It seems a bit weird that there isn’t much information on this topic on the internet. Recently I’ve had to calculate some of these indices to explain an anomalous behaviour in lactones formation and out of curiosity I ran a small search on the net about how to calculate them. Most of the information I retrieved were papers dealing with calculated Fukui and condensed Fukui indices, but unless you count with electronic subscriptions to the corresponding journals you were left in the dark. Moreover, even if you get to read the paper they will tell you as much about how to calculate Fukui indices as they tell you about the Hartree-Fock procedure details.

Therefore here I post this information specifically under “*how to calculate Fukui indices*” so others might find it. It seems to me this blog is taking a rather educational turn which was not its original intention. Still, if I can atract people to read about my work while finding useful information I’m glad to do it.

Fukui indices are, in short, reactivity indices; they give us information about which atoms in a molecule have a larger tendency to either loose or accept an electron, which we chemist interpret as which are more prone to undergo a nucleophilic or an electrophilic attack, respectively. This in turn has to do with a molecule’s tendency of becoming polarized in the presence of an external field or upon the change of electron density. The key word here is *electron density*, the whole idea behind Fukui’s lies in the realm of **conceptual DFT.**

Fukui functions are defined as the functional derivative of the chemical potential respect to the external potential (the one produced by the nuclei) at a constant electron number. Since the chemical potential is defined as the derivative of the density functional respect to the electron density, fukui functions are also defined as the derivative of the electron density respect to the number of electrons at a constant potential, and this latter definition is what we want to work with because it means that we can calculate how the density changes at every point (since it is already different at every point **r**) when adding or removing an electron while keeping the potential constant (that is the position of the nuclei, in other words mantaining the molecular geometry). The name fukui function stems from the fact that these added/removed electrons go into the frontier or Fukui orbitals HOMO/LUMO, but the reality is that the definition was conceived by Yang and Parr (like almost everything in conceptual DFT).

To practically perform these calculations the finite differences method is employed and so the **condensed to atom fukui index **is obtained.

Electrophilicity of atom A in molecule M (of N electrons)

f_{A}^{+} = P_{A}(N+1)-P_{A}(N)

Nucleophilicity of atom A in molecule M (of N electrons)

f_{A}^{–} = P_{A}(N)-P_{A}(N-1)

Radical attack susceptibility of atom A in molecule M (of N electrons)

f_{A}^{0} = 1/2[P_{A}(N+1)-P_{A}(N-1)]

where P stands for the population of atom A in molecule M. If you want to analyze the fukui function at an ionized species the procedure is the same but most people need to beware that N is the number of electrons of the original ion! (i.e. the species you are trying to analyze), sometimes it may be confusing if you are trying to analyze the nucleophilicity (f-) of an atom in a cationic species (M+).

The population analysis on the + or – system has to be performed at the **same **equilibrium geometry as the original molecule! If we optimize again the system then we are letting the system relax and therefore we loose information on the polarization of the electron density upon the change in number of electrons.

“Negative indices are meaningless and should be disregarded” This is a common statement that ever since the definition of Fukui indices has been regarded as true; however there have been a couple of recent publications (see below) that defy to some extent such notion.

Major drawback: Since we are ultimately dealing with occupation numbers on each atom these indices are very sensitive towards changes in basis sets and population analysis paradigm. I strongly recomend never to take those numbers as absolutes, only as comparative parameters within the same system! I also find useful to compute them using more than just one method and one level of theory in order to further confirm or even to dismiss the trends observed. Natural population analysis and AIM are much more robust than simple Mulliken PA.

Hopefully this will be helpful to people trying to calculate fukui functions and also to understand what they mean. Subscribe to this post for further updates (you never know). Rates and comments are always most welcome specially if you found this post interesting or useful. Cheers!

**Further reading.**-Computational Chemistry by Errol Lewars

-Bultinck et al. **Negative Fukui functions: New insights based on electronegativity
equalization**

*J.Chem.Phys*118 (10) 4349-4356 (2003)

-Melin J, Ayers PW, Ortiz JV.

**Removing electrons can increase the electron density: a computational study of negative Fukui functions**.

*J Phys Chem A*. 2007 111(40):10017-9

-Bultnick & Cabo-Dorca

**Negative and Infinite Fukui Functions: The Role of Diagonal Dominance in the Hardness Matrix**

*J. Mat. Chem.*34 (2003) 67-74