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.
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).
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)
(1)
If you’re trying to calculate interaction energies, remember to perform these corrections for every component in your supramolecular assembly (eq. 2)
(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.
The Mental Health Problem in Grad School
Mental health problems in graduate students have existed for ages. The constant and ever-increasing competition both in and out of the academic realm puts an extra toll on young students who already must deal with harsh economic conditions, an uncertain future, and the general unrecognition from society, not to mention sometimes a bullying environment from advisors. Back in the old days, struggling students were said to be ‘cracking under pressure‘, only for the heightening of thriving students who, in comparison, were deemed superior.
The story of Jason Altom is an extreme example of how a highly competitive environment may transform into an abusive one. Jason took his life in 1998 by ingesting potassium cyanide during his final years at Harvard. He was 26. The molecule he was trying to synthesize was completed the following year, and the corresponding report in JACS listed him as a co-author. It was also dedicated to his memory in the acknowledgements section. He was also not the first in the lab to take his life but his suicide note, as reported by The Crimson, suggested some policy changes like having not one but three supervisors per student.
Research institutions outside the top highest in the world, have also a lot of pressure put on students and young researchers even if the stakes are not Nobel-Prize-high. At the same time there are more graduate students now than ever before; the high demand for higher qualifications without the proper emotional development led to a critical mass of frustrated students who become bitter against the same activity they were first drawn to.
Getting a PhD, a real one, is tremendously hard, no question about it, but it shouldn’t be something you lose your mind for. Nothing should. One of my dearest mentors, Prof. Raymundo Cea-Olivares whom I’ve quoted many times before in this blog, often said that any human activity is hard, especially if you try to push its limits, yet PhD students are six-times more prone to suffer some kind of mental issue than a person the same age in the general population. To me, getting a PhD -or doing research for that matter- means you are trying to solve a question nobody else has been able to answer with methods you first need to master before even knowing whether they’re entirely suitable or not. A recurring theme in troubled students is not fully understanding what they are doing or why things are not going out the way they’re supposed to, which only increases the ‘impostor syndrome’ we all feel at some point or another. By definition, you are only an impostor if you’re working unethically, faking or stealing data, otherwise you’re welcome to my lab always; in fact, I prefer to deal with colleagues suffering from impostor syndrome than Dunning-Kruger‘s any day of the week. Here is the bottom line: superior or inferior its a relative term that only exists when you compare yourself to others. Don’t. Ever. The amount of time you devote to comparing yourself to others or indulging in self pity is wasted time you could well be using in doing something for yourself, whether it is studying, working or living.
If I should say something to struggling students is this: You are better than you think. That’s it. Seriously. You got into grad school and more importantly you will come out of it.
Nature has recently curated a collection of articles and essays addressing the mental-health problem in academia. Also, Prof. Christopher J. Cramer has a popular video on the matter, and somewhat tangentially so does Dr. Neil deGrasse Tyson. There are many other resources at your local university to help you cope with your PhD-derived anxiety, because remember: You are not alone.
Mg²⁺ Needs a 5th Coordination in Chlorophylls – New paper in IJQC
Photosynthesis, the basis of life on Earth, is based on the capacity a living organism has of capturing solar energy and transform it into chemical energy through the synthesis of macromolecules like carbohydrates. Despite the fact that most of the molecular processes present in most photosynthetic organisms (plants, algae and even some bacteria) are well described, the mechanism of energy transference from the light harvesting molecules to the reaction centers are not entirely known. Therefore, in our lab we have set ourselves to study the possibility of some excitonic transference mechanisms between pigments (chlorophyll and its corresponding derivatives). It is widely known that the photophysical properties of chlorophylls and their derivatives stem from the electronic structure of the porphyrin and it is modulated by the presence of Mg but its not this ion the one that undergoes the main electronic transitions; also, we know that Mg almost never lies in the same plane as the porphyrin macrocycle because it bears a fifth coordination whether to another pigment or to a protein that keeps it in place (Figure 1).
Figure 1 The UV-Vis spectra of BCHl-a changes with the coordination state
During our calculations of the electronic structure of the pigments (Bacteriochlorophyll-a, BChl-a) present in the Fenna-Matthews-Olson complex of sulfur dependent bacteria we found that the Mg²⁺ ion at the center of one of these pigments could in fact create an intermolecular interaction with the C=C double bond in the phytol fragment which lied beneath the porphyrin ring.
Figure 2 Mg points ‘downwards’ upon optimization, hinting to the interaction under study
This would be the first time that a dihapto coordination is suggested to occur in any chlorophyll and that on itself is interesting enough but we took it further and calculated the photophysical implications of having this fifth intramolecular dihapto coordination as opposed to a protein or none for that matter. Figure 3 shows that the calculated UV-Vis spectra (calculated with Time Dependent DFT at the CAM-B3LYP functional and the cc-pVDZ, 6-31G(d,p) and 6-31+G(d,p) basis sets). A red shift is observed for the planar configuration, respect to the five coordinated species (regardless of whether it is to histidine or to the C=C double bond in the phytyl moiety).
Figure 3 CAMB3LYP UV-VIS spectra. Basis set left to right cc-PVDZ, 6-31G(d,p) and 6-31+G(d,p)
Before calculating the UV-Vis spectra, we had to unambiguously define the presence of this observed interaction. To that end we calculated to a first approximation the C-Mg Wiberg bond indexes at the CAM-B3LYP/cc-pVDZ level of theory. Both values were C(1)-Mg 0.022 and C(2)-Mg 0.032, which are indicative of weak interactions; but to take it even further we performed a non-covalent interactions analysis (NCI) under the Atoms in Molecules formalism, calculated at the M062X density which yielded the presence of the expected critical points for the η²Mg-(C=C) interaction. As a control calculation we performed the same calculation for Magnoscene just to unambiguously assign these kind of interactions (Fig 4, bottom).
Figure 4 (a), (b) NCI analysis for Mg-(C=C) interaction compared to Magnesocene (c)
This research is now available at the International Journal of Quantum Chemistry. A big shoutout and kudos to Gustavo “Gus” Mondragón for his work in this project during his masters; many more things come to him and our group in this and other research ventures.
I’m done with Computational Studies
I’ve lately reviewed a ton of papers whose titles begin with some version of “Computational studies of…“, “Theoretical studies of…” or even more subtly just subtitled “A theoretical/computational study” and even when I gotta confess this is probably something I’ve done once or twice myself, it got me thinking about the place and role of computational chemistry within chemistry itself.
As opposed to physicists, chemists are pressed to defend a utilitarian view of their work and possibly because of that view some computational chemists sometimes lose sight of their real contribution to a study, which is far from just performing a routine electronic structure calculation. I personally don’t like it when an experimental colleague comes asking for ‘some calculations’ without a clear question to be answered by them; Computational Chemistry is not an auxiliary science but a branch of physical chemistry in its own right, one that provides all the insight experiments -chemical or physical- sometimes cannot.
I’m no authority on authoring research papers but I encourage my students to think about the titles of their manuscripts in terms of what the manuscript most heavily relies on; whether it’s the phenomenon, the methodology or the object of the study, that should be further stressed on the title. Papers titled “Computational studies of…” usually are followed by ‘the object of study’ possibly overlooking the phenomenon observed throughout such studies. It is therefore a disservice to the science contained within the manuscript, just like experimental papers gain little from titles such as “Synthesis and Characterization of…“. It all comes down to finding a suitable narrative for our work, something that I constantly remind my students. It’s not about losing rigor or finding a way to oversell our results but instead to actually drive a point home. What did you do why and how. Anna Clemens, a professional scientific writer has a fantastic post on her blog about it and does it far better than I ever could. Also, when ranting on Twitter, the book Houston, we have a narrative was recommended to me, I will surely put it my to-read list.
While I’m on the topic of narratives in science, I’m sure Dr. Stuart Cantrill from Nature Chemistry wouldn’t mind if I share with you his deconstruction of an abstract. Let’s play a game and give this abstract a title in the comments section based on the information vested in it.
Error for Gaussian16 .log files and GaussView5
There’s an error message when opening some Gaussian16 output files in GaussView5 for which the message displayed is the following:
ConnectionGLOG::Parse_Gauss_Coord(). Failure reading oriented atomic coordinates. Line Number
We have shared some solutions to the GaussView handling of *chk and *.fchk files in teh past but never for *.log files, and this time Dr. Davor Šakić from the University of Zagreb in Croatia has brought to my attention a fix for this error. If “Dipole orientation” with subsequent orientation is removed, the file becomes again readable by GaussView5.
Here you can download a script to fix the file without any hassle. The usage from the command line is simply:
˜$ chmod 777 Fg16TOgv5 ˜$ ./Fg16TOgv5 name.log
The first line is to change and grant all permissions to the script (use at your discretion/own risk), which in turn will take the output file name.log and yield two more files: gv5_name.log and and name.arch; the latter archive allows for easy generation of SI files while the former is formatted for GaussView5.x.
Thanks to Dr. Šakić for his script and insight, we hope you find it useful and if indeed you do please credit him whenever its due, also, if you find this or other posts in the blog useful, please let us know by sharing, staring and commenting in all of them, your feedback is incredibly helpful in justifying to my bosses the time I spent curating this blog.
Thanks for reading.
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.
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!
Our first dabble in #MedChem through #CompChem
We’ve expanded the scope of our research interests from quantum mechanical calculations to docking and MedChem for over a year now; it has been a very interesting ride and a very rich avenue of research to explore. Durbis Castillo has led -out of his own initiative- this project and today he presents us with a guest post on the nuances of his project. Bear in mind that the detail of the calculations and a small -very targeted- tutorial on MAESTRO will be provided later in further posts and that making all this decisions required a long process of trial and error, we can only thank Dr. Antonio Romo for his help in minimizing the time this process took.
HIV is a tricky virus, and even though many of the steps included in its lifecycle are druggable, the chemical machinery making it work has been quite elusive since research groups started studying it. Highly Active Antiretroviral Therapy (HAART) works thanks to the combination of several drugs targeting different proteins such as the HIV protease or reverse transcriptase.
In 1998 the elucidation of the gp120 envelope glycoprotein crystal structure introduced a new step in the drug discovery race: HIV entry. Since drugs targeting gp120 have not been widely explored or developed, we decided to use common methodologies like docking (rigid and fit-induced) and ADME predictions to address the following question: How can we easily discover a molecule that inhibits gp120 binding to the lymphocyte CD4 receptor without having to synthesize it first? The answer was to perform a virtual screening with a bottleneck methodology based on docking calculations.
Docking methodologies are often looked as insufficient, careless or even unscientific, since the algorithms they are founded upon are not as accurate or descriptive as the ones that support DFT or ab initio calculations, for example. But there is a huge advantage to simpler operations: less computational resources are required. Then, following Russia’s example when making tanks during the WWII, why not make thousands or millions of docking calculations to quickly explore an entire chemical space and find which molecules are more likely to bind the protein?
And this is exactly what we did. We built a piperazine-based dataset of 16.3 million compounds, all of them including fragments that are reported in the medicinal chemistry literature, thus having two main characteristics, synthetic accessibility and pharmacological activity. These 16.3 million compounds were thoroughly filtered through several docking steps, each one of them being more accurate and comprehensive than the previous one, abruptly eliminating poorly fitted molecules, leaving us with a total of 275 candidates that were redocked in a different crystal structure and a different program (consensus docking).
After analyzing the ADME properties of the candidates, with descriptors such as human oral absorption and possible metabolic reactions, as well as the Induced-Fit Docking score of these molecules, ten ligands were selected as the best ones inside the analyzed chemical space. You can see ligand 255 (figure 1) as an example of the molecules that obtained the best scores throughout the docking steps.
Figure 1
Many of the colleague researchers related to this kind of topics asked “Why didn’t you download a set of molecules from Zinc or Maybridge?” And the answer to this question includes three aspects: first we wanted to test a combinatorial approach to drug design, second, we wanted to test whether including a piperazine as the core of the set of molecules would immediately grant them activity and high potency, and finally, a built database will always confer a higher degree of novelty to the possible hits when compared to commercially available compounds whose synthesis has already been developed. However, this last point needs to be addressed by an organic chemist since none of the molecules from our database have ever been synthesized (any takers?).
Right now, we are trying to explore further through molecular dynamics simulations using Desmond and Amber. Other future goals for this project include screening large databases of commercial and novel compounds with gp120 and other proteins involved in the HIV lifecycle. Also, we remain open to collaborate with anyone interested in taking the challenge to synthesize our molecules, as well as performing the biochemical assays to get an idea of their activity.
More details on MD simulations and the path of our first virtual hits to follow. Anyone interested in reading my thesis work can contact me through my linkedin profile at https://www.linkedin.com/in/durbisjaviercp/. An article is under preparation and will soon be submitted, stay tuned!
A new paper on the Weak Link Approach
Chemically actuating a molecule is a very cool thing to do and the Weak Link Approach (WLA) allows us to do precisely that through the reversible coordination of one or various organometallic centers to a longer ligand that opens or closes a macrocyclic cavity. All this leads to an allosteric effect so important in biological instances available in inorganic molecules. Once again, the Mirkin group at Nortwestern University in Evanston, Illinois, has given me the opportunity to contribute with the calculations to the energetic properties of these actuators as well as their electronic properties for their use as molecular scavengers or selective capsules for various purposes such as drug delivery agents.
As in the previous WLA work (full paper), the NBODel procedure was used at the B97D/LANL2DZ level of theory, only this time the macrocycle consisted of two organometallic centers and for the first time the asymmetric opening of the cavity was achieved, as observed by NMR. With the given fragments, all possibilities shown in scheme 1 were obtained. The calculated bond energies for the Pt – S bonds are around 60 – 70 kcal/mol whereas for the Pt – Cl bonds the values are closer to 90 kcal/mol. This allows for a selective opening of the cavity which can then be closed by removing the chlorine atoms with the help of silver salts.
For the case of complex mixture 4a, 4b, and 4c, the thermochemistry calculations show they are all basically isoenergetic with differences in the thousandths of kcal/mol. The possibilities for the groups in the weakly bonded ligands are enormous; currently, there is work being done about substituting those phenyl rings for calix[4]arenes in order to have a macrucyclic capsule made by macrocylic capusules.
Thanks to Andrea D’Aquino for taking me into her project, for all the stimulating discussions and her great ideas for expanding WLA into new avenues; I’m sure she’ll succeed in surprising us with more possibilities for these allosteric macrocycles.
The full paper is published in Inorganic Chemistry from the ACS (DOI: 10.1021/acs.inorgchem.7b02745). Thanks for reading and -if you made it this far into the post- happy new year!
