Blog Archives
Estimation of pKa Values through Local Electrostatic Potential Calculations
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.
- Fig 1. Thermodynamic Cycle for the pKa calculation of any given Bronsted acid, HA
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)
- fig 2. calculated v experimental pKa values for a test set of 10 carboxylic acids from equation above
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.
Dr. Gabriel Merino wins The Walter Kohn Prize 2018
Just as I was thinking about the state of Mexican scientific environment in the global scale, Prof. Dr. Gabriel Merino from CINVESTAV comes and gets this prize awarded by the International Center for Theoretical Physics (ICTP) and the Quantum ESPRESSO Foundation, showing us all that great science is possible even under pressing circumstances.
This prize is awarded biennially to a young scientist for outstanding contributions in the field of quantum-mechanical materials and molecular modeling, performed in a developing country or emerging economy,and in the case of Dr. Merino it is awarded not only for his contributions to theory and applications but also by his contributions to the prediction of novel systems that violate standard chemical paradigms, broadening the scope of concepts like aromaticity, coordination and chemical bond. The list of his contributions is very long despite his young age and there are barely any topic in chemistry or materials science that escapes his interest.
Gabriel is also one of the leading organizers of the Mexican Theoretical Physical Chemistry Meeting, an unstoppable mentor with many of his former students now leading research teams of their own. He is pretty much a force of nature.
Congratulations to Dr. Gabriel Merino, his team, CINVESTAV and thanks for being such an inspiration and a good friend at the same time.
¡Felicidades, Gabriel!
Computational Chemistry from Latin America
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!
XVII Mexican Meeting on Theoretical Physical Chemistry
The RMFQT meeting is a long standing tradition within the Mexican Comp.Chem. community; a tradition that is now transcending our borders as more and more foreign students and researchers take part of this party, for it is a festive occasion indeed. This was the first time the RMFQT was held at a private institute, The Monterrey Institute of Technology.
As in previous years, our lab contributed with a four posters and one talk by yours truly. The posters presented by Raul Torres, Raúl Márquez, Gustavo Mondragón and Dr. Jacinto Sandoval whose pictures you can spot below in the gallery.
My talk was on the collaborative nature of Comp.Chem. and our particular interactions with the organic synthesis lab of Dr. Moisés Romero. The published papers discussed in the talk can be found in Tetrahedron (post), PCCP (post), and some unpublished results that can be read as a preprint in preprints.org.
I had the pleasure to meet and interact with old friends and make new ones like Dr. Julio Palma from Penn State, whose work on molecular rectifiers is very interesting. Also, I got to interact with many wonderful students who apparently are aware of the existence of this blog. (A big shoutout to M. Joaquina Beltrán and Plinio Cantero, from Chile whose work on DNA mismatch sensors is quite interesting, I look forward to further interacting with their team of research.)
A particular reason for this meeting to be special for me is the fact that I have been now announced as part of the local organizing committee for the next edition in 2019 in Toluca. I was also asked to develop a centralized website and coordinate the social media communication related to the this and other events, starting with the creation of the official Twitter account for our network and the meeting. I’m working on a few ideas, but if you have any suggestions please send them in the comments section.
See you next year in Toluca!
Calculation of Intermolecular Interactions for Sensors with Biological Applications
Two new papers on the development of chemosensors for different applications were recently published and we had the opportunity to participate in both with the calculation of electronic interactions.
A chemosensor requires to have a measurable response and calculating either that response from first principles based on the electronic structure, or calculating another physicochemical property related to the response are useful strategies in their molecular design. Additionally, electronic structure calculations helps us unveil the molecular mechanisms underlying their response and efficiency, as well as providing a starting point for their continuous improvement.
In the first paper, CdTe Quantum Dots (QD’s) are used to visualize in real time cell-membrane damages through a Gd Schiff base sensitizer (GdQDs). This probe interacts preferentially with a specific sequence motif of NHE-RF2 scaffold protein which is exposed during cell damage. This interactions yields intensely fluorescent droplets which can be visualized in real time with standard instrumentation. Calculations at the level of theory M06-2X/LANL2DZ plus an external double zeta quality basis set on Gd, were employed to characterize the electronic structure of the Gd³⁺ complex, the Quantum Dot and their mutual interactions. The first challenge was to come up with the right multiplicity for Gd³⁺ (an f⁷ ion) for which we had no experimental evidence of their magnetic properties. From searching the literature and talking to my good friend, inorganic chemist Dr. Vojtech Jancik it was more or less clear the multiplicity had to be an octuplet (all seven electrons unpaired).
As can be seen in figure 1a the Gd-N interactions are mostly electrostatic in nature, a fact that is also reflected in the Wiberg bond indexes calculated as 0.16, 0.17 and 0.21 (a single bond would yield a WBI value closer to 1.0).
PM6 optimizations were employed in optimizing the GdQD as a whole (figure 1f) and the MM-UFF to characterize their union to a peptide sequence (figure 2) from which we observed somewhat unsurprisingly that Gd³⁺interacts preferently with the electron rich residues.
This research was published in ACS Applied Materials and Interfaces. Thanks to Prof. Vojtech Adam from the Mendel University in Brno, Czech Republic for inviting me to collaborate with their interdisciplinary team.
The second sensor I want to write about today is a more closer to home collaboration with Dr. Alejandro Dorazco who developed a fluorescent porphyrin system that becomes chiefly quenched in the presence of Iodide but not with any other halide. This allows for a fast detection of iodide anions, related to some gland diseases, in aqueous samples such as urine. This probe was also granted a patent which technically lists yours-truly as an inventor, cool!
The calculated interaction energy was huge between I⁻ and the porphyrine, which supports the idea of a ionic interaction through which charge transfer interactions quenches the fluorescence of the probe. Figure 3 above shows how the HOMO largely resides on the iodide whereas the LUMO is located on the pi electron system of the porphyrine.
This research was published in Sensors and Actuators B – Chemical.
Redox Allosteric Control – New communication in JACS
The Weak Link Approach (WLA) is a successful strategy for allosterically controlling the formation of cavities¹ and the access to them² through the action of reversible hemilabile-bond formation around an organometallic center. Thus far, the WLA has been used to mimic biological cavities whose access is controlled chemically as in the scheme shown below which belongs to a previous WLA work published in 2014, my first time involved in the calculation of bond energies for hemilabile groups.
Mendez-Arroyo et al. JACS (2014) 136, 10340-10348
Chiefly developed by the Chad Mirkin group at Northwestern, the WLA has now reached a new milestone in which the allosteric control is further coupled to a redox equilibrium which alters the strength of the hemilabile bonds. These findings are reported in JACS as a communication (DOI: 10.1021/jacs.8b09321). Previous efforts were unsuccessful due to the instability of the oxidized species, which makes regulation challenging. A ferrocenyl (Fc) group was attached to the hemilabile ligand to provide the redox center which can further assist and control the ring opening via an increment in the electrostatic repulsion of the two metallic centers. Thus, the weak-link is displaced by exogenous ligands only after the Fc group was oxidized.
Bond strengths for the hemilabile bonds were calculated at the ω-B97XD/lanl2dz level of theory upon optimized structures. Relative energies were calculated through the thermochemistry analysis (freq=noraman) made by Gaussian09 and the bond strengths were calculated with the NBODel procedure included in NBO3.1. In the open configurations we found that upon oxidation of Fc the exogenous ligand bond to Pt(II) strengthens by a few kcal/mol (2 – 10), however the Fe(III)-P distance increases and that can be observed via ³¹P NMR spectroscopy.
For the non-oxidized complexes, the HOMO’s are largely composed of the ferrocene highest energy orbitals, which is susceptible of being oxidized, whereas the LUMO’s are located throughout the organometallic fragment. When Ferrocene is oxidized to Ferrocenium, the situation is reversed and now HOMO’s are found spread over the organometallic fragment and the LUMO’s over ferrocenium; all of which is coherent with the idea of Fc now being able to be reduced. Plots for the HOMO LUMO orbitals for compound (6) in the Reduced (Fe2) and Oxidized (Fe3) states are shown (alpha and beta density are shown separately in the latter case).
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- (6) Reduced HOMO
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- (6) Reduced LUMO
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- (6) Oxidized HOMO
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- (6) Oxidized LUMO alpha
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- (6) Oxidized LUMO beta
Thanks to Prof. Chad Mirkin, Dr. Andrea d’Aquino, and Edmund Cheng for letting me be a part of this project.
[1] D’Aquino, A. I., Cheng, H. F., Barroso-Flores, J., Kean, Z. S., Mendez-Arroyo, J., McGuirk, C. M., & Mirkin, C. A. (2018). An Allosterically Regulated, Four-State Macrocycle. Inorganic Chemistry, 57(7), 3568–3578.
[2] Mendez-Arroyo, J., Barroso-Flores, J., Lifschitz, A. M., Sarjeant, A. a., Stern, C. L., & Mirkin, C. a. (2014). A multi-state, allosterically-regulated molecular receptor with switchable selectivity. Journal of the American Chemical Society, 136(29), 10340–10348.
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.
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.
