Category Archives: DFT
The canonical molecular orbital depiction of an electronic transition is often a messy business in terms of a ‘chemical‘ interpretation of ‘which electrons‘ go from ‘which occupied orbitals‘ to ‘which virtual orbitals‘.
Natural Transition Orbitals provide a more intuitive picture of the orbitals, whether mixed or not, involved in any hole-particle excitation. This transformation is particularly useful when working with the excited states of molecules with extensively delocalized chromophores or multiple chromophoric sites. The elegance of the NTO method relies on its simplicity: separate unitary transformations are performed on the occupied and on the virtual set of orbitals in order to get a localized picture of the transition density matrix.
 R. L. Martin, J. Chem. Phys., 2003, DOI:10.1063/1.1558471.
After running a TD-DFT calculation with the keyword TD(Nstates=n) (where n = number of states to be requested) we need to take that result and launch a new calculation for the NTOs but lets take it one step at a time. As an example here’s phenylalanine which was already optimized to a minimum at the B3LYP/6-31G(d,p) level of theory. If we take that geometry and launch a new calculation with the TD(Nstates=40) in the route section we obtain the UV-Vis spectra and the output looks like this (only the first three states are shown):
Excitation energies and oscillator strengths: Excited State 1: Singlet-A 5.3875 eV 230.13 nm f=0.0015 <S**2>=0.000 42 -> 46 0.17123 42 -> 47 0.12277 43 -> 46 -0.40383 44 -> 45 0.50838 44 -> 47 0.11008 This state for optimization and/or second-order correction. Total Energy, E(TD-HF/TD-KS) = -554.614073682 Copying the excited state density for this state as the 1-particle RhoCI density. Excited State 2: Singlet-A 5.5137 eV 224.86 nm f=0.0138 <S**2>=0.000 41 -> 45 -0.20800 41 -> 47 0.24015 42 -> 45 0.32656 42 -> 46 0.10906 42 -> 47 -0.24401 43 -> 45 0.20598 43 -> 47 -0.14839 44 -> 45 -0.15344 44 -> 47 0.34182 Excited State 3: Singlet-A 5.9254 eV 209.24 nm f=0.0042 <S**2>=0.000 41 -> 45 0.11844 41 -> 47 -0.12539 42 -> 45 -0.10401 42 -> 47 0.16068 43 -> 45 -0.27532 43 -> 46 -0.11640 43 -> 47 0.16780 44 -> 45 -0.18555 44 -> 46 -0.29184 44 -> 47 0.43124
The oscillator strength is listed on each Excited State as “f” and it is a measure of the probability of that excitation to occur. If we look at the third one for this phenylalanine we see f=0.0042, a very low probability, but aside from that the following list shows what orbital transitions compose that excitation and with what energy, so the first line indicates a transition from orbital 41 (HOMO-3) to orbital 45 (LUMO); there are 10 such transitions composing that excitation, visualizing them all with canonical orbitals is not an intuitive picture, so lets try the NTO approach, we’re going to take excitation #10 for phenylalanine as an example just because it has a higher oscillation strength:
%chk=Excited State 10: Singlet-A 7.1048 eV 174.51 nm f=0.3651 <S**2>=0.000 41 -> 45 0.35347 41 -> 47 0.34685 42 -> 45 0.10215 42 -> 46 0.17248 42 -> 47 0.13523 43 -> 45 -0.26596 43 -> 47 -0.22995 44 -> 46 0.23277
Each set of NTOs for each transition must be calculated separately. First, copy you filename.chk file from the TD-DFT result to a new one and name it after the Nth state of interest as shown below (state 10 in this case). NOTE: In the route section, replace N with the number of the excitation of interest according to the results in filename.log. Run separately for each transition your interested in:
#chk=state10.chk #p B3LYP/6-31G(d,p) Geom=AllCheck Guess=(Read,Only) Density=(Check,Transition=N) Pop=(Minimal,NTO,SaveNTO) 0 1 --blank line--
By requesting SaveNTO, the canonical orbitals in the state10.chk file are replaced with the NTOs for the 10th excitation, this makes it easier to plot since most visualizers just plot whatever set of orbitals they read in the chk file but if they find the canonical MOs then one would need to do some re-processing of them. This is much more straightforward.
Now we format our chk files into fchk with the formchk utility:
formchk -3 filename.chk filename.fchk
formchk -3 state10.chk state10.fchk
If we open filename.fchk (the file where the original TD-DFT calculation is located) with GaussView we can plot all orbitals involved in excited state number ten, those would be seven orbitals from 41 (HOMO-3) to 47 (LUMO+2) as shown in figure 1.
If we now open state10.fchk we see that the numbers at the side of the orbitals are not their energy but their occupation number particular to this state of interest, so we only need to plot those with highest occupations, in our example those are orbitals 44 and 45 (HOMO and LUMO) which have occupations = 0.81186; you may include 43 and 46 (HOMO-1 and LUMO+1, respectively) for a much more complete description (occupations = 0.18223) but we’re still dealing with 4 orbitals instead of 7.
The NTO transition 44 -> 45 is far easier to conceptualize than all the 10 combinations given in the canonical basis from the direct TD-DFT calculation. TD-DFT provides us with the correct transitions, NTOs just paint us a picture more readily available to the chemist mindset.
NOTE: for G09 revC and above, the %OldChk option is available, I haven’t personally tried it but using it to specify where the excitations are located and then write the NTOs of interest into a new chk file in the following way, thus eliminating the need of copying the original chk file for each state:
NTOs are based on the Natural Hybrid orbitals vision by Löwdin and others, and it is said to be so straightforward that it has been re-discovered from time to time. Be that as it may, the NTO visualization provides a much clearer vision of the excitations occurring during a TD calculation.
Thanks for reading, stay home and stay safe during these harsh days everyone. Please share, rate and comment this and other posts.
Calculating the pKa value for a Brønsted acid is very hard, like really hard. A full thermodynamic cycle (fig. 1) needs to be calculated along with the high-accuracy solvation free energy for each of the species under consideration, not to mention the use of expensive methods which will be reviewed here in another post in two weeks time.
Finding descriptors that help us circumvent the need for such sophisticated calculations can help great deal in estimating the pKa value of any given acid. We’ve been interested in the reactivity of σ-hole bearing groups in the past and just like Halogen, Tetrel, Pnicogen and Chalcogen bonds, Hydrogen bonds are highly directional and their strength depends on the polarization of the O-H bond. Therefore, we suggested the use of the maximum surface electrostatic potential (VS,max) on the acid hydrogen atom of carboxylic acids as a descriptor for the strength of their interaction with water, the first step in the deprotonation process.
We selected six basis sets; five density functionals; the MP2 method for a total of thirty-six levels of theory to optimize and calculate VS,max on thirty carboxylic acids for a grand total of 1,080 wavefunctions, which were later passed onto MultiWFN (all calculations were taken with PCM = water). Correlation with the experimental pKa values showed a great correlation across the levels of theory (R2 > 0.9), except for B3LYP. Still, the best correlations were obtained with LC-wPBE/cc-pVDZ and wB97XD/cc-pVDZ. From this latter level of theory the linear correlation yielded the following equation:
pKa = -0.2185(VS,max) + 16.1879
Differences in pKa turned out to be less than 0.5 units, which is remarkable for such a straightforward method; bear in mind that calculation of full thermodynamic cycles above chemical accuracy (1.0 kcal/mol) yields pKa differences above 1.0 units.
We then took this equation for a test with 10 different carboxylic acids and the prediction had a correlation of 98% (fig. 2)
I think this method can really catch on for a quick way to predict the pKa values of any carboxylic acid imaginable. We’re now working on the model extension to other groups (i.e. Bronsted bases) and putting together a black-box workflow so as to make it even more accessible and straightforward to use.
We’ve recently published this work in the journal Molecules, an open access publication. Thanks to Prof. Steve Scheiner for inviting us to participate in the special issue devoted to tetrel bonding. Thanks to Guillermo Caballero for the inception of this project and to Dr. Jacinto Sandoval for taking the time from his research in photosynthesis to work on this pet project of ours and of course the rest of the students (Gustavo Mondragón, Marco Diaz, Raúl Torres) whose hard work produced this work.
The video below is a sad recount of the scientific conditions in Mexico that have driven an enormous amount of brain power to other countries. Doing science is always a hard endeavour but in developing countries is also filled with so many hurdles that it makes you wonder if it is all worth the constant frustration.
That is why I think it is even more important for the Latin American community to make our science visible, and special issues like this one from the International Journal of Quantum Chemistry goes a long way in doing so. This is not the first time IJQC devotes a special issue to the Comp.Chem. done south of the proverbial border, a full issue devoted to the Mexican Physical Chemistry Meetings (RMFQT) was also published six years ago.
I believe these special issues in mainstream journals are great ways of promoting our work in a collected way that stresses our particular lines of research instead of having them spread a number of journals. Also, and I may be ostracized for this, but I think coming up with a new journal for a specific geographical community represents a lot of effort that takes an enormous amount of time to take off and thus gain visibility.
For these reasons I’ve been cooking up some ideas for the next RMFQT website. I don’t pretend to say that my colleagues need any shoutouts from my part -I could only be so lucky to produce such fine pieces of research myself- but it wouldn’t hurt to have a more established online presence as a community.
¡Viva la ciencia Latinoamericana!
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)
If you’re trying to calculate interaction energies, remember to perform these corrections for every component in your supramolecular assembly (eq. 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.
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.
Today’s science is published mostly in English, which means that non-English speakers must first tackle the language barrier before sharing their scientific ideas and results with the community; this blog is a proof that non-native-English speakers such as myself cannot outreach a large audience in another language.
For young scientists learning English is a must nowadays but it shouldn’t shy students away from learning science in their own native tongues. To that end, the noble effort by Dr. José Cerón-Carrasco from Universidad Católica San Antonio de Murcia, in Spain, of writing a DFT textbook in Spanish constitutes a remarkable resource for Spanish-speaking computational chemistry students because it is not only a clear and concise introduction to ab initio and DFT methods but because it was also self published and written directly in Spanish. His book “Introducción a los métodos DFT: Descifrando B3LYP sin morir en el intento” is now available in Amazon. Dr. Cerón-Carrasco was very kind to invite me to write a prologue for his book, I’m very thankful to him for this opportunity.
Así que para los estudiantes hispanoparlantes hay ahora un muy valioso recurso para aprender DFT sin morir en el intento gracias al esfuerzo y la mente del Dr. José Pedro Cerón Carrasco a quien le agradezco haberme compartido la primicia de su libro
¡Salud y olé!
One of the most popular posts in this blog has to do with calculating Fukui indexes, however, when dealing with a large number of molecules, our described methodology can become cumbersome since it requires to manually extract the population analysis from two or three different output files and then performing the arithmetic on them separately with a spreadsheet or something.
Our new team member Ricardo Loaiza has written a python script that takes the three aforementioned files and yields a .csv file with the calculated Fukui indexes, and it even points out which of the atoms exhibit the largest values so if you have a large molecule you don’t have to manually check for them. We have also a batch version which takes all the files in any given directory and performs the Fukui calculations for each, provided it can find file triads with the naming requirements described below.
Output files must be named filename.log (the N electrons reference state), filename_plus.log (the state with N+1 electrons) and filename_minus.log (the N-1 electrons state). Another restriction is that so far these scripts only work with NBO population analysis as provided by the NBO3.1 program available in the various versions of Gaussian. I imagine the listing is similar in NBO5.x and NBO6.x and so it should work if you do the population analysis with them.
The syntax for the single molecule version is:
python fukui.py filename.log filename_minus.log filename_plus.log
For the batch version is:
(Por Lote means In Batch in Spanish.)
These scripts are available via GitHub. We hope you find them useful, and you do please let us know whether here at the comments section or at our GitHub site.
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).
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.
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!
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.
Select your WFN/WFX file on which the calculation is to be run. (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).
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).
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.