Category Archives: DFT

Photosynthesis and Singlet Fission – #WATOC2017 PO1-296

If you work in the field of photovoltaics or polyacene photochemistry, then you are probably aware of the Singlet Fission (SF) phenomenon. SF can be broadly described as the process where an excited singlet state decays to a couple of degenerate coupled triplet states (via a multiexcitonic state) with roughly half the energy of the original singlet state, which in principle could be centered in two neighboring molecules; this generates two holes with a single photon, i.e. twice the current albeit at half the voltage (Fig 1).


Jablonski’s Diagram for SF

It could also be viewed as the inverse process to triplet-triplet annihilation. An important requirement for SF is that the two triplets to which the singlet decays must be coupled in a 1(TT) state, otherwise the process is spin-forbidden. Unfortunately (from a computational perspective) this also means that the 3(TT) and 5(TT) states are present and should be taken into account, and when it comes to chlorophyll derivatives the task quickly scales.

SF has been observed in polyacenes but so far the only photosynthetic pigments that have proven to exhibit SF are some carotene derivatives; so what about chlorophyll derivatives? For a -very- long time now, we have explored the possibility of finding a naturally-occurring, chlorophyll-based, photosynthetic system in which SF could be possible.

But first things first; The methodology: It was soon enough clear, from María Eugenia Sandoval’s MSc thesis, that TD-DFT wasn’t going to be enough to capture the whole description of the coupled states which give rise to SF. It was then that we started our collaboration with SF expert, Prof. David Casanova from the Basque Country University at Donostia, who suggested the use of Restricted Active Space – Spin Flip in order to account properly for the spin change during decay of the singlet excited state. A set of optimized bacteriochlorophyll-a molecules (BChl-a) were oriented ad-hoc so their Qy transition dipole moments were either parallel or perpendicular; the rate to which SF could be in principle present yielded that both molecules should be in a parallel Qy dipole moments configuration. When translated to a naturally-occurring system we sought in two systems: The Fenna-Matthews-Olson complex (FMO) containing 7 BChl-a molecules and a chlorosome from a mutant photosynthetic bacteria made up of 600 Bchl-d molecules (Fig 2). The FMO complex is a trimeric pigment-protein complex which lies between the antennae complex and the reaction center in green sulfur dependent photosynthetic bacteria such as P. aestuarii or C. tepidium, serving thus as a molecular wire in which is known that the excitonic transfer occurs with quantum coherence, i.e. virtually no energy loss which led us to believe SF could be an operating mechanism. So far it seems it is not present. However, for a crystallographic BChl-d dimer present in the chlorosome it could actually occur even when in competition with fluorescence.


FMO Complex. Trimer (left), monomer (center), pigments (right)


BChQRU chlorosome. 600 Bchl-d molecules

I will keep on blogging more -numerical and computational- details about these results and hopefully about its publication but for now I will wrap this post by giving credit where credit is due: This whole project has been tackled by our former lab member María Eugenia “Maru” Sandoval and Gustavo Mondragón. Finally, after much struggle, we are presenting our results at WATOC 2017 next week on Monday 28th at poster session 01 (PO1-296), so please stop by to say hi and comment on our work so we can improve it and bring it home!


Grimme’s Dispersion DFT-D3 in Gaussian #CompChem

I was just asked if it is possible to perform DFT-D3 calculations in Gaussian and my first answer was to use the following  keyword:


which is available in G16 and G09 only in revision D, apparently.

There are also some overlays that can be used to invoke the use dispersion in various scenarios:

IOp(3/74=x) Exchange and Correlation Potentials





DSD-PBEP86 (double hybrid, DFT-D3).


B2PLYP-D3 (double hybrid, DFT-D3).

B97-D (DFT-D3).

IOp(3/76=x) Mixing of HF and DFT.

-33 PW6B95 and PW6B95-D3 coefficients.

IOp(3/124=x) Empirical dispersion term.




Force dispersion type 3 (Grimme DFT-D3).

Force dispersion type 4 (Grimme DFT-D3(BJ)).

Force dispersion type 5 (Grimme D3, PM7 version).


The D3 correction method of Grimme defines the van der Waals energy like:

$\displaystyle E_{\rm disp} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at...
...{6ij}} {r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}} {r_{ij,L}^8} \right ),$

where coefficients $ C_{6ij}$ are adjusted depending on the geometry of atoms i and j. The damping D3 function for is:

$\displaystyle f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}},$

where the values of s are adjustable parameters fit for the exchange-correlation functionals used in each calculation.

Atoms in Molecules (QTAIM) – Flash lesson

As far as population analysis methods goes, the Quantum Theory of Atoms in Molecules (QTAIM) a.k.a Atoms in Molecules (AIM) has become a popular option for defining atomic properties in molecular systems, however, its calculation is a bit tricky and maybe not as straightforward as Mulliken’s or NBO.

Personally I find AIM a philosophical question since, after the introduction of the molecule concept by Stanislao Cannizzaro in 1860 (although previously developed by Amadeo Avogadro who was dead at the time of the Karlsruhe congress), the questions of whether or not an atom retains its identity when bound to others? where does an atom end and the next begins? What are the connections between atoms in a molecule? are truly interesting and far deeper than we usually consider because it takes a big mental leap to think about how matter is organized to give rise to substances. Particularly I’m very interested with the concept of a Molecular Graph which in turn is concerned with the way we “draw lines” to form conceptual molecules. Perhaps in a different post we can go into the detail of the method, which is based in the Laplacian operator of the electron density, but today, I just want to collect the basic steps in getting the most basic AIM answers for any given molecule. Recently, my good friend Pezhman Zarabadi-Poor and I have used rather extensively the following procedure. We hope to have a couple of manuscripts published later on. Therefore, I’ve asked Pezhman to write a sort of guest post on how to run AIMALL, which is our selected program for the integration algorithm.

The first thing we need is a WFN or WFX file, which contains the wavefunction in a Fortran unformatted file on which the Laplacian integration is to be performed. This is achieved in Gaussian09 by incluiding the keyword output=wfn or output=wfx in the route section and adding a name for this file at the bottom line of the input file, e.g.


(NOTE: WFX is an eXtended version of  WFN; particularly necessary when using pseudopotentials or ECP’s)

Analyzing this file requires the use of a third party software such as AIMALL suite of programs, of which the standard version is free of charge upon registration to their website.

OpenAIMStudio (the accompanying graphical interface) and select the AIMQB program from the run menu as shown in figure 1.


Figure 1

Figure 1

Select your WFN/WFX file on which the calculation is to be run. (Figure 2)


Figure 2

Figure 2

You can control several options for the integration of the Laplacian of the electron density as well as other features. If your molecules are simple enough, you may go through with a successful and meaningful calculation using the default settings. After the calculation is finished, several result files are obtained. We’ll work in this tutorial only with *.mpgviz (which contains information about the molecular graph, MG) and *.sum (which contains all of  needed numerical data).

Visualization of the MG yields different kinds of critical points, such as: 1) Nuclear Attractor Critical Points (NACP); 2) Bond Critical Points (BCP); 3) Ring CP’s (RCP); and 4) Cage CP’s (CCP).

Of the above, BCP are the ones that indicate the presence of a chemical bond between two atoms, although this conclusion is not without controversy as pointed out by Foroutan-Njead in his paper: C. Foroutan-Nejad, S. Shahbazian and R. Marek, Chemistry – A European Journal, 2014, 20, 10140-10152. However, at a first approximation, BCP’s can help us to explore chemical interactions.

Now, let’s go back to visualizing those MGs (in our examples we’ve used methane and ethylene and acetylene). We open the corresponding *.mpgviz file in AIMStudio and export the image from the file menu and using the save as picture option (figure 3).

Figure 3

Figure 3

The labeled atoms are NACP’s while the green dots correspond to BCP’s. Multiplicity of a bond cannot be discerned within the MG; in order to find out whether a bond is a single, double or triple bond we have to look into the *.sum file, in which we’ll take a look at the bond orders between pairs of atoms in the section labeled “Diatomic Electron Pair Contributions and Delocalization Data” (Figure 4).

Figure 4

Figure 4

Delocalization indexes, DI’s, show the approximate number of electrons shared between two atoms. From the above examples we get the following DI(C,C) values: 1.93 for C2H4 and 2.87 for C2H2; on the other hand, DI(C,H) values are  0.98 for CH4, 0.97 in C2H4 and 0.96 in C2H2. These are our usual bond orders.

This is the first part of a crash tutorial on AIM, in my opinion this is the very basics anyone needs to get started with this interesting and widespread method. Thanks to all who asked about QTAIM, now you have your long answer.

Thanks a lot to my good friend Dr Pezhman Zarabadi-Poor for providing this contribution to the blog, we hope you all find it helpful. Please share and comment.

New paper in JACS

Well, I only contributed with the theoretical section by doing electronic structure calculations, so it isn’t really a paper we can ascribe to this particular lab, however it is really nice to see my name in JACS along such a prominent researcher as Prof. Chad Mirkin from Northwestern University, in a work closely related to my area of research interest as macrocyclic recognition agents.

In this manuscript, a calix[4]arene is allosterically opened and closed reversibly by coordinating different kinds of ligands to a platinum center linked to the macrocycle. (This approach has been referred to as the weak link approach.) I recently visited Northwestern and had a great time with José Mendez-Arroyo, the first author, who showed me around and opened the possibility for further work between our research groups.

(Ligands: Green = Chloride; Blue = Cyanide)

Closed, semi-open and fully open conformations; selectivity is modulated through cavity size. (Ligands: Green = Chloride; Blue = Cyanide)

Here at UNAM we calculated the interaction energies for the two guests that were successfully inserted into the cavity: N-methyl-pyridinium (Eint = 57.4 kcal/mol) and Pyridine-N-oxide (Eint = +200.0 kcal/mol). Below you can see the electrostatic potential mapped onto the electron density isosurface for one of the adducts. Relative orientation of the hosts within the cavity follows the expected (anti-) alignment of mutual dipole moments. At this level of theory, we could easily be inclined to assert that the most stable interaction is indeed the one from the semi-open compound and that this in turn is due to the fact that host and guest are packed closer together but there is also an orbital issue: Pyridine Oxide is a better electron acceptor than N-Me-pyridinium and when we take a closer look to the (Natural Bonding) orbitals interacting it becomes evident that a closer location does not necessarily yields a stronger interaction when the electron accepting power of the ligand is weaker (which is, in my opinion, both logic and at the same time a bit counterintuitive, yet fascinating, nonetheless).

Electrostatic potential mapped onto the electron density surface of one of the aducts under study

Electrostatic potential mapped onto the electron density surface of one of the adducts under study

All calculations were performed at the B97D/LANL2DZ level of theory with the use of Gaussian09 and NBO3.1 as provided within the former. Computing time at UNAM’s supercomputer known as ‘Miztli‘ is fully acknowledged.

The full citation follows:

A Multi-State, Allosterically-Regulated Molecular Receptor With Switchable Selectivity
Jose Mendez-Arroyo Joaquín Barroso-Flores §,Alejo M. Lifschitz Amy A. Sarjeant Charlotte L. Stern , and Chad A. Mirkin *

J. Am. Chem. Soc., Article ASAP
DOI: 10.1021/ja503506a
Publication Date (Web): July 9, 2014

 Thanks to José Mendez-Arroyo for contacting me and giving me the opportunity to collaborate with his research; I’m sure this is the first of many joint projects that will mutually benefit our groups. 


New paper in Computational and Theoretical Chemistry

I always get very happy to have a new paper out there! I find it exciting but most of all liberating since it makes you feel like your work is going somewhere but most of all that it is making its way ‘out there’; there is a strong feeling of validation, I guess.

Two very different families of calix[n]arenes (Fig 1) were tested as drug carriers for a very small molecule with a huge potential as a chemotherapeutic agent against Leukemia, namely, 3-phenyl-1H-[1]benzofuro[3,2-c]pyrazole a.k.a. GTP which has proven to be an effective in vitro Tyrosine Kinase III inhibitor. Having such a low molecular weight it is expected to have a very high excretion rate therefore the use of a carrier could increase its retention time and hence its activity. This time we considered n = 4, 5, 6 and 8 for the size of the cavities and R = -SO3H and -OEt as functional groups on the upper rim as to evaluate only a polar coordinating group and a non-polar non-coordinating one since GTP offers two H-bond acceptor sites and one H-bond donor one along the π electron density that could form π – π stacking interactions between the aromatic groups on GTP and the walls of the calixarene.

Fig 1. Calixarenes under study and their complexes with GTP

Fig 1. Calixarenes under study and their complexes with GTP

Once again calculations were carried out at the B97D/6-31G(d,p) level of theory along with molecular dynamics simulations for over 100 ns of production runs. NBO Deletion interaction energies were computed in order to discern which hosts formed the most stable complexes.

NBO Del interaction energies B97D/6-31G(d,p)

NBO Del interaction energies B97D/6-31G(d,p)

You may find a link to the ScienceDirect website for downloading the paper from this link. Last, but certainly not least, I’d like to thank all coauthors for their contributions and patience in getting this study published: Dr. Rodrigo Galindo-Murillo; Alberto Olmedo-Romero; Eduardo Cruz-Flores; Dr. Petronela M. Petrar and Prof. Dr. Kunsági-Máté Sándor. Thanks a lot for everything!


Donor and acceptor H-bond sites increases the probability of keeping the drug in place for a higher retention rate

Donor and acceptor H-bond sites increases the probability of keeping the drug in place for a higher retention rate

New paper in Journal of Chemical Theory and Computation

Happy new year to all my readers!

Having a new paper published is always a matter of happiness for this computational chemist but this time I’m excedingly excited about anouncing the publishing of a paper in the Journal of Chemical Theory and Computation, which is my highest ranked publication so far! It also establishes the consolidation of our research group at CCIQS as a solid and competitive group within the field of theoretical and computational chemistry. The title of our paper is “In Silico design of monomolecular drug carriers for the tyrosine kinase inhibitor drug Imatinib based on calix- and thiacalix[n]arene host molecules. A DFT and Molecular Dynamics study“.

In this article we aimed towards finding a suitable (thia-) calix[n]arene based drug delivery agent for the drug Imatinib (Gleevec by Novartis), which is a broadly used powerful Tyrosine Kinase III inhibitor used in the treatment of Chronic Myeloid Leukaemia and, to a lesser extent, Gastrointestinal Stromal Tumors; although Imatinib (IMB) exhibits a bioavailability close to 90% most of it is excreted, becomes bound to serum proteins or gets accumulated in other tissues such as the heart causing several undesired side effects which ultimately limit its use. By using a molecular capsule we can increase the molecular weight of the drug thus increasing its retention, and at the same time we can prevent Imatinib to bind, in its active form, to undesired proteins.

We suggested 36 different calix and thia-calix[n]arenes (CX) as possible candidates; IMB-CX complexes were manually docked and then optimized at the B97D/6-31G(d,p) level of theory; Stephan Grimme’s B97D functional was selected for its inclusion of dispersion terms, so important in describing π-π interactions. Intermolecular interaction energies were calculated under the Natural Bond Order approximation; a stable complex was needed but a too stable complex would never deliver its drug payload! This brings us to the next part of the study. A monomolecular drug delivery agent must be able to form a stable complex with the drug but it must also be able to release it. Molecular Dynamics simulations (+100 ns) and umbrella sampling methods were used to analyse the release of the drug into the aqueous media.

Optimized geometries for all complexes under study (B97D/6-31G*)

Optimized geometries for the 20 most stable complexes under study (B97D/6-31G*)

Potential Mean Force profiles for the four most stable complexes for position N1 and  N2 from the QM simulations are shown below (Red, complexes in the N1 position, blue, N2 position). These plots, derived from the MD simulations  give us an idea of the final destination of the drug respect of the calixarene carrier. In the next image, the three preferred structures (rotaxane-like; inside; released) for the final outcome of the delivery process are shown. The stability of the complexes was also assessed by calculating the values of ΔG binding through the use of the Poisson equations.

PMF for the most stable compounds

PMF for the most stable compounds

General MD simulation final structures

General MD simulation final structures

Thanks to my co-authors Maria Eugenia Sandoval-Salinas and Dr. Rodrigo Galindo-Murillo for their enormous contributions to this work; without their hard work and commitment to the project this paper wouldn’t have been possible.

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