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The HOMO-LUMO Gap in Open Shell Calculations. Meaningful or meaningless?


The HOMO – LUMO orbitals are central to the Frontier Molecular Orbital (FMO) Theory devised by Kenichi Fukui back in the fifties. The central tenet of the FMO theory resides on the idea that most of chemical reactivity is dominated by the interaction between these orbitals in an electron donor-acceptor pair, in which the most readily available electrons of the former arise from the HOMO and will land at the LUMO in the latter. The energy difference between the HOMO and LUMO of any chemical species, known as the HOMO-LUMO gap, is a very useful quantity for describing and understanding the photochemistry and photophysics of organic molecules since most of the electronic transitions in the UV-Vis region are dominated by the electron transfer between these two frontier orbitals.

But when we talk about Frontier Orbitals we’re usually referring to their doubly occupied version; in the case of open shell calculations the electron density with α spin is separate from the one with β spin, therefore giving rise to two separate sets of singly occupied orbitals and those in turn have a α-HOMO/LUMO and β-HOMO/LUMO, although SOMO (Singly Occupied Molecular Orbital) is the preferred nomenclature. Most people will then dismiss the HOMO/LUMO question for open shell systems as meaningless because ultimately we are dealing with two different sets of molecular orbitals. Usually the approach is to work backwards when investigating the optical transitions of a, say, organic radical, e.g. by calculating the transitions with such methods like TD-DFT (Time Dependent DFT) and look to the main orbital components of each within the set of α and β densities.

To the people who have asked me this question I strongly suggest to first try Restricted Open calculations, RODFT, which pair all electrons and treat them with identical orbitals and treat the unpaired ones independently. As a consequence, RO calculations and Unrestricted calculations vary due to variational freedom. RO calculations could yield wavefunctions with small to large values of spin contamination, so beware. Or just go straight to TDDFT calculations with hybrid orbitals which include a somewhat large percentage of HF exchange and polarized basis sets, but to always compare results to experimental values, if available, since DFT based calculations are Kohn-Sham orbitals which are defined for non-interacting electrons so the energy can be biased. Performing CI or CASSCF calculations is almost always prohibitive for systems of chemical interest but of course they would be the way to go.

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Calculating NMR shifts – Short and Long Ways


Nuclear Magnetic Resonance is a most powerful tool for elucidating the structure of diamagnetic compounds, which makes it practically universal for the study of organic chemistry, therefore the calculation of 1H and 13C chemical shifts, as well as coupling constants, is extremely helpful in the assignment of measured signals on a spectrum to an actual functional group.

Several packages offer an additive (group contribution) empirical approach to the calculation of chemical shifts (ChemDraw, Isis, ChemSketch, etc.) but they are usually only partially accurate for the simplest molecules and no insight is provided for the more interesting effects of long distance interactions (vide infra) so quantum mechanical calculations are really the way to go.

With Gaussian the calculation is fairly simple just use the NMR keyword in the route section in order to calculate the NMR shielding tensors for relevant nuclei. Bear in mind that an optimized structure with a large basis set is required in order to get the best results, also the use of an implicit solvation model goes a long way. The output displays the value of the total isotropic magnetic shielding for each nucleus in ppm (image taken from the Gaussian website):

Magnetic shielding (ppm):
  1  C    Isotropic =    57.7345   Anisotropy =   194.4092
   XX=    48.4143   YX=      .0000   ZX=      .0000
   XY=      .0000   YY=   -62.5514   ZY=      .0000
   XZ=      .0000   YZ=      .0000   ZZ=   187.3406
  2  H    Isotropic =    23.9397   Anisotropy =     5.2745
   XX=    27.3287   YX=      .0000   ZX=      .0000
   XY=      .0000   YY=    24.0670   ZY=      .0000
   XZ=      .0000   YZ=      .0000   ZZ=    20.4233

Now, here is why this is the long way; in order for these values to be meaningful they need to be contrasted with a reference, which experimentally for 1H and 13C  is tetramethylsilane, TMS. This means you have to perform the same calculation for TMS at -preferably- the same level of theory used for the sample and substract the corresponding values for either H or C accordingly. Only then the chemical shifts will read as something we can all remember from basic analytical chemistry class.

GaussView 6.0 provides a shortcut; open the Results menu, select NMR and in the new window there is a dropdown menu for selecting the nucleus and a second menu for selecting a reference. In the case of hydrogen the available references are TMS calculated with the HF and B3LYP methods. The SCF – GIAO plot will show the assignments to each atom, the integration simulation and a reference curve if desired.

The chemical shifts obtained this far will be a good approximation and will allow you to assign any peaks in any given spectrum but still not be completely accurate though. The reasons behind the numerical deviations from calculated and experimental values are many, from the chosen method to solvent interactions or basis set limitations, scaling factors are needed; that’s when you can ask the Cheshire Cat which way to go

If you don’t know where you are going any road will get you there.

Lewis Carroll – Alice in Wonderland

Well, not really. The Chemical Shift Repository for computed NMR scaling factors, with Coupling Constants Added Too (aka CHESHIRE CCAT) provides with straight directions on how to correct your computed NMR chemical shifts according to the level of theory without the need to calculate the NMR shielding tensor for the reference compound (usually TMS as pointed out earlier). In a nutshell, the group of Prof. Dean Tantillo (UC Davis) has collected a large number of isotropic magnetic shielding values and plotted them against experimental chemical shifts. Just go to their scaling factors page and check all their linear regressions and use the values that more closely approach to your needs, there are also all kinds of scripts and spreadsheets to make your job even easier. Of course, if you make use of their website don’t forget to give the proper credit by including these references in your paper.

We’ve recently published an interesting study in which the 1H – 19F coupling constants were calculated via the long way (I was just recently made aware of CHESHIRE CCAT by Dr. Jacinto Sandoval who knows all kinds of web resources for computational chemistry calculations) as well as their conformational dependence for some substituted 2-aza-carbazoles (fig. 1).

1-s2.0-S0022286018310330-fx1_lrg

Journal of Molecular Structure Vol 1176, 15 January 2019, Pages 562-566

The paper is published in the Journal of Molecular Structure. In this study we used the GIAO NMR computations to assign the peaks on an otherwise cluttered spectrum in which the signals were overlapping due to conformational variations arising from the rotation of the C-C bond which re-orients the F atoms in the fluorophenyl grou from the H atom in the carbazole. After the calculations and the scans were made assigning the peaks became a straightforward task even without the use of scaling factors. We are now expanding these calculations to more complex systems and will contrast both methods in this space. Stay tuned.

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.

 

DFT Textbook in Spanish by Dr. José Cerón-Carrasco


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.

test

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!

Another Great Year at the Lab! 2017


2017 was a complicated year for various reasons here in Mexico (and some personal health issues) but nonetheless I’m very proud of the performance of everyone at the lab whose hard work and great skills keep pushing our research forward.

Four new members joined the team and have presented their work at the national meeting for CompChem for the first time. Also, for the first time, one of my students, Gustavo Mondragón, gave a talk at this meeting with great success about his research on the Fenna Matthews Olson complex of photosynthetic bacteria.

The opportunity to attend WATOC at Munich presented me the great chance to meet wonderful people from around the world and was even kindly and undeservingly invited to write the prologue for an introductory DFT book by Prof. Pedro Cerón from Spain. I hope to Jeep up with the collaborations abroad such as the one with the Mirkin group at Nortgwestern and the one with my dear friend Kunsagi-Mate Sándor at Pecsi Tudomanyegyetem (Hungary), among many others; I’m thankful for their trust in our capabilities.

Two members got their BSc degrees, Marco an Durbis, the latter also single handedly paved the way for us to develop a new research line on the in silico drug developing front; his relentless work has also been praised by the QSAR team at the Institute of Chemistry with which he has collaborated by performing toxicity calculations for the agrochemical industry as well as by designing educational courses aimed to the dissemination of our work and QSAR in general among regulatory offices and potential clients. We’re sad to see him go next fall but at the same time we’re glad to know his scientific skills will further develop.

I cannot thank the team enough: Alejandra Barrera, Gustavo Mondragón, Durbis Castillo, Fernando Uribe, Juan Guzman, Alberto Olmedo, Eduardo Cruz, Ricardo Loaiza and Marco Garcia; may 2018 be a great year for all of you.

And to all the readers thank you for your kind words, I’m glad this little space which is about to become nine years old is regarded as useful; to all of you I wish a great 2018!

 

Python scripts for calculating Fukui Indexes


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:

./fukuiPorLote.sh

(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.

XVI Mexican Meeting on Phys.Chem.


A yearly tradition of this Comp.Chem. lab and many others throughout our nation is to attend the Mexican Meeting on Theoretical Physical Chemistry to share news, progress and also a few drinks and laughs. This year the RMFQT was held in Puebla and although unfortunately I was not able to attend this lab was proudly represented by its current members. Gustavo Mondragón gave a talk about his progress on his photosynthesis research linking to the previous work of María Eugenia Sandoval already presented in previous editions; kudos to Gustavo for performing remarkably and thanks to all those who gave us their valuable feedback and criticism. Also, five posters were presented successfully, I can only thank the entire team for representing our laboratory in such an admirable way, and a special mention to the junior members, I hope this was the first of many scientific events they attend and may you deeply enjoy each one of them.

Among the invited speakers, the RMFQT had the honor to welcome Prof. John Perdew (yes, the P in PBE); the team took the opportunity of getting a lovely picture with him.

Here is the official presentation of the newest members of our group:

Alejandra Barrera (hyperpolarizabilty calculations on hypothetical poly-calyx[n]arenes for the search of NLO materials)

img_8255

Fernando Uribe (Interaction energy calculations for non-canonical nucleotides)

img_8254

Juan Guzmán (Reaction mechanisms calculations for catalyzed organic reactions)

img_8259

We thank the organizing committee for giving us the opportunity to actively participate in this edition of the RMFQT, we eagerly await for next year as every year.

 

Chemistry Makes the Chemical


The compound shown below in figure 1 is listed by Aldrich as 4,5,6,7-tetrahydroindole, but is it really?

tetrahydroindole

Fig 1. An indole?

To a hardcore organic chemist it is clear that this is not an indole but a pyrrole because  the lack of aromaticity in the fused ring gives this molecule the same reactivity as 2,3-diethyl pyrrole.  If you search the ChemSpider database for ‘tetrahydroindole’ the search returns the following compound with the identical chemical formula C8H11N but with a different hydrogenation pattern: 2,3,3a,4-Tetrahydro-1H-indole

14650657

Fig 2. Also listed as an indole

The real indole, upon an electrophilic attack, behaves as a free enamine yielding the product shown in figure 3 in which the substitution occurs in position 3. This compound cannot undergo an Aromatic Electrophilic Susbstitution since that would imply the formation of a sigma complex which would disrupt the aromaticity.

indole_reaction

On the contrary, the corresponding pyrrole is substituted in position 2

pyrole_reaction

These differences in reactivity towards electrophiles are easily rationalized when we plot their HOMO orbitals (calculated at the M062X/def2TZVP level of theory):

If we calculate the Fukui indexes at the same level of theory we get the highest value for susceptibility towards an electrophilic attack as follows: 0.20 for C(3) in indole and 0.25 for C(2) in pyrrole, consistent with the previous reaction schemes.

So, why is it listed as an indole? why would anyone search for it under that name? Nobody thinks about cyclohexane as 1,3,5-trihydrobenzene. According to my good friend and colleague Dr. Moisés Romero most names for heterocyles are kept even after such dramatic chemical changes due to historical and mnemonic reasons even when the reactivity is entirely different. This is only a nomenclature issue that we have inherited from the times of Hantzsch more than a century ago. We’ve become used to keeping the trivial (or should I say arbitrary) names and further use them as derivations but this could pose an epistemological problem if students cannot recognize which heterocycle presents which reactivity.

So, in a nutshell:

Chemistry makes the chemical and not the structure.

A thing we all know but sometimes is overlooked for the sake of simplicity.

WATOC 2017


Last week the WATOC congress in Munich was a lot of fun. Our poster on photosynthesis had a great turnout and got a lot of positive feedback as well as many thought provoking questions. One of the highlights of my time there was seeing my former students and knowing they’re all leading successful and happy grad-student lives in Europe, I’m so very proud of them. It was great to connect with old friends and making new ones; a big thank you to all the readers of this little blog who took the time to come and say hi, I’m very glad the blog has been helpful to you.

Better recounts of WATOC 2017 can be found in the great Rzepa’s blog here and here.

Below there is an image of our poster (some typos persist).

Imagen1

See you all in 2020!

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).

Imagen1

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

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

Imagen2

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!

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