The 20th Mexican Meeting on Theoretical Physical Chemistry (RMFQT) just occurred last week and it was a special edition for various reasons: The fact this meeting has been organized for two decades speaks volumes about a thriving national scientific community; being the 20th anniversary, the comitee saw fit to hold it at the very same place where it first began, Cuernavaca, an idyllic warm town just an hour south of Mexico City. And last, but certainly not least, it also served as a frame for a homage to one of the great minds in the field of DFT and electronic structure research, Dr. Alberto Vela-Amieva.
Prof. Vela was born in Mexico City in 1956. As an undergraduate he worked with the late Prof. Andoni Garritz at UNAM, his dissertation was titled “Atomic Charge Distribution in Molecular Calculations by Multiple Dispersion“. He then got a PhD from Prof. José Luis Gázquez with a thesis titled “Time Independent Response Coefficients in Atoms and Molecules“, which was awarded the Weuznann Best Thesis Award (1990) from the Mexican Academy of Sciences. His contributions to theoretical chemistry are too many to list in this post, but some of the most relevant are his development of Exchange and Correlation functionals, Chemical Reactivity within the frame of DFT (a name he very much prefers over ‘conceptual DFT’), and the development of deMon from his days back in Montreal. Prof. Alberto Vela is now a full Professor at the Center for Research and Advanced Studies (CINVESTAV) where he continues inspiring the new generation of scientists in the field.
Endowed with a great sense of humor, he shared one of his pet peeves with the audience during his speech at the RMFQT: The use and abuse of B3LYP, and he did so through a collection of memes found mostly on Twitter where he constantly lurks from behind the curtains. Indeed, B3LYP has become a laughing stock for Comp Chemists worldwide since it is usually regarded as an Ehrlich’s silver bullet of sorts, a one-size-fits-all solutions to electronic structure. Inevitably, every time someone mentions it with him in the audience, we all turn our heads to watch for his reaction, even if it’s just a small twinkle in his eye.
These meetings are great opportunities to establish collaborations, learning new things, and to catch up with old friends, it’s great to have them back after three years (2020 was suspended by COVID-19 and 2021 took place online.)
Long life to Pro. Alberto Vela and to the RMFQT! Check out some of the talk titles in their Twitter feed RMFQT.
Regarding my lab, my students had an outstanding participation with their posters! Samantha Martínez has developed a python based tool to quickly assess the size of a large library of molecules. Miguel Porras laid out his research plan and first results for the inclusion of a library of molecules into an abasic site for a short DNA strand and evaluate their interaction energies. Cristian works also with exogenous DNA and showed his Eint calculations for natural and unnatural nucleotides. Humberto showed his results on Singlet Fission for carotenoids, whereas Emanuel worked a TD-DFT benchmark for their excited states. Ricardo Padilla is on the verge of publishing his work on a method to calculate polarons and bipolarons in PEDOT oligomers. Leo presented his work we recently published in Chem. Science. Finally, Gustavo Mondragón gave a talk on his last results published in JCTC and some unpublished results soon to be submitted.
To calculate what the bonding properties of a molecule are in a particular excited state we can run any population analysis following the root of interest. This straightforward procedure takes two consecutive calculations since you don’t necessarily know before hand which excited state is the one of interest.
The regular Time Dependent Density Functional Theory (TD-DFT) calculation input with Gaussian 16 looks as follows (G09 works pretty much the same), let us assume we’ve already optimized the geometry of a given molecule:
%OldChk=filename.chk %nprocshared=16 %chk=filename_ES.chk #p TD(NStates=10,singlets) wb97xd/cc-pvtz geom=check guess=read Title Card Required 0 1 --blank line--
This input file retrieves the geometry and wavefunction from a previous calculation from filename.chk and doesn’t write anything new into it (that is what %OldChk=filename.chk means) and creates a new checkpoint where the excited states are calculated (%chk=filename_ES.chk)
In the output you search for the transition which peeks your interest; most often than not you’ll be interested in the one with the highest oscillator strength, f. The oscillator strength is a dimensionless number that represents the ratio of the observed, integrated, absorption coefficient to that calculated for a single electron in a three-dimensional harmonic potential [Harris & Bertolucci, Symmetry and Spectroscopy]; in other words, it is related to the probability of that transition to occur, and therefore it takes values from 0.0 to 1.0 (for single photon absorption processes.)
The output of this calculation looks as follows, the value of f for every excitation is reported together with its energy and the orbital transitions which comprise it.
Excitation energies and oscillator strengths: Excited State 1: Singlet-A 3.1085 eV 398.86 nm f=0.0043 <S**2>=0.000 56 -> 59 -0.11230 58 -> 59 0.69339 This state for optimization and/or second-order correction. Total Energy, E(TD-HF/TD-DFT) = -1187.56377917 Copying the excited state density for this state as the 1-particle RhoCI density. Excited State 2: Singlet-A 4.0827 eV 303.68 nm f=0.0016 <S**2>=0.000 52 -> 59 0.46689 52 -> 64 -0.20488 53 -> 59 0.19693 54 -> 59 0.40414 54 -> 64 -0.16261 ... ... Excited State 8: Singlet-A 5.2345 eV 236.86 nm f=0.8063 <S**2>=0.000 52 -> 60 0.17162 53 -> 59 0.47226 53 -> 60 -0.11771 54 -> 59 -0.27658 54 -> 60 -0.22006 55 -> 59 0.20496 56 -> 59 0.15029
Now we’ve selected excited state #8 because it has the largest value of f from the lot, we use the following input to read in the geometry from the old checkpoint file and we generate a new one in case we need it for something else. The input file for doing all this looks as follows (I’ve selected as usual the Natural Bond Orbital population analysis):
%oldchk=a_ES.chk %nprocshared=16 %chk=a_nbo.chk #p TD(Read,Root=8) wb97xd/cc-pvtz geom=check density=current guess=read pop=NBORead Title Card Required 0 1 $NBO BOAO BNDIDX E2PERT $END --blank line--
The flags at the bottom request the calculation of Wiberg Bond Indexes (BNDIDX) as well as Bond Order in the Atomic Orbital basis (BOAO) and a second order perturbation theory for the electronic delocalization (E2PERT). Now we can compare the population analysis between ground and the 8th excited state; check figure 1 and notice the differences in Wiberg’s bond order for this complex made of two molecules and one Na+ cation.
In this example we can observe that in the ground state we have a neutral and a negative molecule together with a Na+ cation, but when we analyze the population in the 8th excited state both molecules acquire a similar charge, ca. 0.46e, which means that some of the electron density has been transferred from the negative one to the neutral molecule, forming an Electron Donor-Acceptor complex (EDA) in the excited state.
This procedure can be extended to any other kind of population analysis and their derived combination, e.g. one could calculate their condensed fukui functions in the Nth excited state; but beware! These calculations yield vertical excitations, should the excited state of interest have a minimum we can first optimize the ES geometry and then perform the population analysis on said geometry; just add the opt keyword to perform both jobs in one go, but bear in mind that the NBO population analysis is performed before and after the optimization process so look for the tables and values closer to the end of the output file.
In the case of open shell systems the procedure is the same but one should be extremely careful in searching for the total population analysis since the output file contains this table for the alpha and beta populations separately as well as the added values for the total number of electrons.
Photosynthetic organisms are so widespread around the globe they have adapted to various solar lighting conditions to thrive. The bacteria Blastochloris viridis absorbs light in the near infrared region of the electromagnetic spectrum, in fact, it holds the record for the longest wavelength (~1015 nm) absorbing organism whose Light Harvesting complex 1 (LHC1) has been elucidated. Despite their adaptation to a wide number of light conditions, photosynthetic organism can only make use of so many pigments or chromophores; the LHC1 (Figure 1) in B. viridis in fact is made up of Bacteriochlorophyll-b (BChl-b) molecules, one of the most abundant photosynthetic pigments on Earth, whose main absorption in solution (MeOH) is observed at 795 nm.
So, how can B. viridis use BChl-b molecules to absorb near IR radiation and how does it achieve this remarkable red-shifting effect? The LHC1 structure was solved in 2018 by Qian et al. through Cryo-EM at a 2.9 Å resolution; it is comprised of 17 protein subunits surrounding the so called photosynthetic pigments special pair. Each of these subunits is made up of three α-helix structures surrounding two BChl-b and one dihydroneurosporene (DHN) molecule for a total of 34 of these photosynthetic pigments inside the LHC and 17 DHN molecules interacting between the protein structures and the
main BChl-b pigments.
It was Dr. Jacinto Sandoval and Gustavo “Gus” Mondragón who brought this facts to our attention during their survey of potential candidates for calculating exotic exciton transfer mechanisms in photosynthetic organisms, part of Gustavo’s PhD thesis. To them, it was clear from the start that some sort of cooperative effect between pigments was operating and possibly leading to the red-shifted absorption, therefore a careful dissection of all possible pigments combinations was carried out and their UV-Vis spectra were calculated at the CAMB3LYP/cc-pVDZ on PBE0/6-31G(d) optimized geometries, leading to the systems shown below in figure 2.
System B7 reproduced the red-shifted absorption at 1026 nm, but since the original structure was fitted from the Cryo-EM with a 2.9 Å resolution, “Gus” suggested reaching out to the group of Prof. Andrés Gerardo Cisneros and Dr. Jorge Nochebuena at UT Dallas for carrying out QM/MM calculations; this optimization included the proteins surrounding the pigments in the MM layer and the interacting residues (Hys coordinated to Mg2+ ions in BChl-b) along the chromophores were incorporated into the QM layer, however the thus obtained minima for the B7 system lost the main absorption in the near-IR region, therefore, Dr. Nochebuena suggested running an MD simulation (45 ns) and took a random sampling of ten structures (Figure 3).
All structures in the sampling reproduced the red-shifted absorption (~1000 nm) successfully proving that cooperative and dynamic effects allow B. viridis to perform photosynthesis with low energy radiation (Figure 4). Therefore, close intermolecular interactions along with thermal/dynamical fluctuations allow for a regular pigment such as BChl-b to form near-IR absorbing photosystems for organisms to thrive in low conditions of solar light.
If you want to read further details, this work is now published in the Journal of Chemical Theory and Computation of the American Chemical Society. I’ll talk about this and other ventures in photosynthesis next week at the WATOC conference in Vancouver, swing by to talk CompChem!
Canonical Molecular Orbitals are–by construction–delocalized over the various atoms making up a molecule. In some contexts it is important to know how much of any given orbital is made up by a particular atom or group of atoms, and while you could calculate it by hand given the coefficients of each MO in terms of every AO (or basis set function) centered on each atom there is a straightforward way to do it in Gaussian.
If we’re talking about ‘dividing’ a molecular orbital into atomic components, we’re most definitely talking about population analysis calculations, so we’ll resort to the pop keyword and the orbitals option in the standard syntax:
#p M052x/cc-pVDZ pop=orbitals
This will produce the following output right after the Mulliken population analysis section:
Atomic contributions to Alpha molecular orbitals: Alpha occ 140 OE=-0.314 is Pt1-d=0.23 C38-p=0.16 C31-p=0.16 C36-p=0.16 C33-p=0.15 Alpha occ 141 OE=-0.313 is Pt1-d=0.41 Alpha occ 142 OE=-0.308 is Cl2-p=0.25 Alpha occ 143 OE=-0.302 is Cl2-p=0.72 Pt1-d=0.18 Alpha occ 144 OE=-0.299 is Cl2-p=0.11 Alpha occ 145 OE=-0.298 is C65-p=0.11 C58-p=0.11 C35-p=0.11 C30-p=0.11 Alpha occ 146 OE=-0.293 is C58-p=0.10 Alpha occ 147 OE=-0.291 is C22-p=0.09 Alpha occ 148 OE=-0.273 is Pt1-d=0.18 C11-p=0.12 C7-p=0.11 Alpha occ 149 OE=-0.273 is Pt1-d=0.18 Alpha vir 150 OE=-0.042 is C9-p=0.18 C13-p=0.18 Alpha vir 151 OE=-0.028 is C7-p=0.25 C16-p=0.11 C44-p=0.11 Alpha vir 152 OE=0.017 is Pt1-p=0.10 Alpha vir 153 OE=0.021 is C36-p=0.15 C31-p=0.14 C63-p=0.12 C59-p=0.12 C38-p=0.11 C33-p=0.11 Alpha vir 154 OE=0.023 is C36-p=0.13 C31-p=0.13 C63-p=0.11 C59-p=0.11 Alpha vir 155 OE=0.027 is C65-p=0.11 C58-p=0.10 Alpha vir 156 OE=0.029 is C35-p=0.14 C30-p=0.14 C65-p=0.12 C58-p=0.11 Alpha vir 157 OE=0.032 is C52-p=0.09 Alpha vir 158 OE=0.040 is C50-p=0.14 C22-p=0.13 C45-p=0.12 C17-p=0.11 Alpha vir 159 OE=0.044 is C20-p=0.15 C48-p=0.14 C26-p=0.12 C54-p=0.11
Alpha and Beta densities are listed separately only in unrestricted calculations, otherwise only the first is printed. Each orbital is listed sequentially (occ = occupied; vir = virtual) with their energy value (OE = orbital energy) in atomic units following and then the fraction with which each atom contributes to each MO.
By default only the ten highest occupied orbitals and ten lowest virtual orbitals will be assessed, but the number of MOs to be analyzed can be modified with orbitals=N, if you want to have all orbitals analyzed then use the option AllOrbitals instead of just orbitals. Also, the threshold used for printing the composition is set to 10% but it can be modified with the option ThreshOrbitals=N, for the same compound as before here’s the output lines for HOMO and LUMO (MOs 149, 150) with ThreshOrbitals set to N=1, i.e. 1% as occupation threshold (ThreshOrbitals=1):
Alpha occ 149 OE=-0.273 is Pt1-d=0.18 N4-p=0.08 N6-p=0.08 C20-p=0.06 C13-p=0.06 C48-p=0.06 C9-p=0.06 C24-p=0.05 C52-p=0.05 C16-p=0.04 C44-p=0.04 C8-p=0.03 C15-p=0.03 C17-p=0.03 C45-p=0.02 C46-p=0.02 C18-p=0.02 C26-p=0.02 C54-p=0.02 N5-p=0.01 N3-p=0.01 Alpha vir 150 OE=-0.042 is C9-p=0.18 C13-p=0.18 C44-p=0.08 C16-p=0.08 C15-p=0.06 C8-p=0.06 N6-p=0.04 N4-p=0.04 C52-p=0.04 C24-p=0.04 N5-p=0.03 N3-p=0.03 C46-p=0.03 C18-p=0.03 C48-p=0.02 C20-p=0.02
The fragment=n label in the coordinates can be used as in BSSE Counterpoise calculations and the output will show the orbital composition by fragments with the label "Fr", grouping all contributions to the MO by the AOs centered on the atoms in that fragment.
As always, thanks for reading, sharing, and rating. I hope someone finds this useful.
Stabilizing Gold in low oxidation states is a longstanding challenge of organometallic chemistry. To do so, a fine tuning of the electron density provided to an Au atom by a ligand via the formation of a σ bond. The group of Professor Rong Shang at the University of Nagasaki has accomplished the stabilization of an aurate complex through the use of a boron, nitrogen-containing heterocyclic carbene; DFT calculations at the wB97XD/(LANL2TZ(f),6-311G(d)) level of theory revealed that this ligand exhibits a high π-withdrawing character of the neutral 4π B,N-heterocyclic carbene (BNC) moiety and a 6π weakly aromatic character with π-donating properties, implying that this is the first cyclic carbene ligand that is able to be tuned between π-withdrawing (Fischer-type)- and π-donating (Schrock-type) kinds.
A π-withdrawing character on part of the ligand is important to allow the electron-rich gold center back donate some of its excess electron density, this way preventing its oxidation. A modification of Bertrand’s cyclic (alkyl)(amino)carbene (CAAC) has allowed Shang and co-workers to perform the two electrons Au(I) reduction to form the aurate shown in figure 1 (CCDC 2109027). This work also reports on the modular synthesis of the BNC-1 ligand and the mechanism was calculated once again by Leonardo “Leo” Lugo.
The ability of the BNC-1 ligand to accept gold’s back donation is reflected on the HOMO/LUMO gap as shown in Figure 2; while BNC-1 has a gap of 7.14 eV, the classic NHC carbene has a gap of 11.28 eV, furthermore, in the case of NHC the accepting orbital is not LUMO but LUMO+1. Additionally, the NBO delocalization energies show that the back donation from Au 5d orbital to the C-N antibonding π* orbital is about half that expected for a Fischer type carbene, suggesting an intermediate character between π accepting and π donating carbene. On the other hand, the largest interaction corresponds to the carbanion density donated to Au vacant p orbital (ca. 45 kcal/mol). All these observations reveal the successful tuning of the electron density on BNC-1.
This study is available in Dalton Transactions. As usual, I’m honored to be a part of this international collaboration, and I’m deeply thankful to the amazing Prof. José Oscar Carlos Jiménez-Halla for inviting me to be a part of it.
Yoshitaka Kimura, Leonardo I. Lugo-Fuentes, Souta Saito, J. Oscar C. Jimenez-Halla, Joaquín Barroso-Flores, Yohsuke Yamamoto, Masaaki Nakamoto and Rong Shang* “A boron, nitrogen-containing heterocyclic carbene (BNC) as a redox active ligand: synthesis and characterization of a lithium BNC-aurate complex”, Dalton Trans., 2022,51, 7899-7906 https://doi.org/10.1039/D2DT01083F
Molecules. Atoms glued by bonds; nuclei incarcerated by electrons; electrons forming an inhomogeneous gas contained not by outer walls but by an electrostatic potential in its interior ironically named ‘external potential’. Molecules. The study object of chemists. The fundamental construct on which the chemical understanding of the universe relies.
Ten electrons, ten protons, and ten neutrons, giving rise to various electronic densities, various chemical properties: CH4, NH3, H2O, HF; which is it?
Atoms are letters, molecules are words; Chemistry, their unabashed poetry.
Density Functional Theory is by far the most successful way of gaining access to molecular properties starting from their composition. Calculating the electronic structure of molecules or solid phases has become a widespread activity in computational as well as in experimental labs not only for shedding light on the properties of a system under study but also as a tool to design those systems with taylor-made properties. This level of understanding of matter brought by DFT is based in a rigorous physical and mathematical development, still–and maybe because of it–DFT (and electronic structure calculations in general for that matter) might be thought of as something of little use outside academia.
Prof. Juan Carlos Sancho-García from the University of Alicante in Spain, encouraged me to talk to his students last month about the reaches of DFT in the industrial world. Having once worked in the IP myself I remembered the simulations performed there were mostly DPD (Dissipative Particle Dynamics), a coarse grained kind of molecular dynamics, for investigating the interactions between polymers and surfaces, but no DFT calculations were ever on sight. It is widely known that Docking, QSAR, and Molecular Dynamics are widely used in the pharma industry for the development of new drugs but I wasn’t sure where DFT could fit in all this. I thought patent search would be a good descriptor for the commercial applicability of DFT. So I took a shallow dive and searched for patents explicitly mentioning the use of DFT as part of the invention development process and protection. The first thing I noticed is that although they appear to be only a few, these are growing in numbers throughout the years (Figure 1). Again, this was not an exhaustive search so I’m obviously overlooking many.
The second thing that caught my attention was that the first hit came from 1998, nicely coinciding with the rise of B3LYP (Figure 2). This patent was awarded to Australian inventors from the University of Wollongong, South New Wales to determine trace gas concentrations by chromatography by means of calculating the FT-IR spectra of sample molecules (Figure 3), so DFT is used as part of the invention but I ignore if this is a widespread method in analytical labs.
While I’m mentioning the infamous B3LYP functional, a search about it in patents yields the following graph (Figure 4), most of which relate to the protection of photoluminescent or thermoluminescent molecules for light emitting devices; it appears that DFT calculations are used to provide the key features of their protection, such as HOMO-LUMO gap etc.
So what about software? Most of the more recent patents in Figure 1 (2018 – 2022) lie in the realm of electronics, particularly the development of semiconductors, ceramical or otherwise, so it was safe to assume VASP could be a popular choice to that end, right? turns out that’s not necessarily the case since a patent search for VASP only accounts for about the 10% of all awarded patents (Figure 5).
I guess it’s safe to say by now that DFT has a significant impact in the industrial development, one could only expect it to keep on rising, however the advent of machine learning techniques and other artificial intelligence related methods promise an accelerated development. I went again to the patents database and this time searched for ‘machine learning development materials‘ (the term ‘development’ was deleted by the search engine, guess found it too obvious) and its rise is quite notorious, surpassing the frequency of DFT in patents (Figure 6), particularly in the past 5 years (2018 – 2022).
I’m guessing in some instances DFT and ML will tend to go hand in hand in the industrial development process, but the timescales reachable by ML will only tend to grow, so I’m left with the question of what are we waiting for to make ML and AI part of the chemistry curricula? As computational chemistry teachers we should start talking about this points with our students and convince the head of departments to help us create proper courses or we risk our graduates to become niche scientists in a time when new skills are sought after in the IP.
Thanks again to Prof. Juan Carlos Sancho García at the University of Alicante, Spain, who asked me talk about the subject in front of his class, and to Prof. José Pedro Cerón-Carrasco from Cartagena for allowing me to talk about this and other topics at Centro Universitario de la Defensa. Thank you, guys! I look forward to meeting you again soon.
I’m very honored to have been invited to this edition of this long standing event, the Virtual Winter School of Computational Chemistry. In this talk I walk through the basics of what are excitons and how do they move or transfer across matter; and of course, a primer on how to calculate the energy transfer with Gaussian.
This is a very basic introduction but I hope someone finds it useful. Thanks to Henrique Castro for inviting me to take part of this experience and to all the professors and students involved in the organization. Don’t forget to go and check all the other fantastic talks, including one by Nobel Laureate and chemistry legend Prof. Roald Hoffmann, at the Virtual Winter School’s website: https://winterschool.cc/
I’m very excited and honored to participate in this year’s Virtual Winter School on #CompChem. This event started back in 2015 and this year the list of participants includes Nobel Laureate and legend Roald Hoffmann. The topics will range from drug design to quantum chemistry on quantum computers. Additionally, two workshops will be given for ADF and Gaussian.
Aside from the teaching sessions there will also be some virtual social gatherings that promise to be a lot of fun. So don’t miss it next 21—25 of February 2022. Register here.
I will teach the tools to model Exciton Energy Transfer processes, a handy set of skills to work on the fields of photophysics, photosynthesis, or photochemistry of materials. We’ll review the concepts of excitons and the basic mechanisms by which they are originated and transferred.
Thanks to Henrique Castro from Rio de Janeiro for inviting me to be a part of this event which is a direct heir from the first electronic conferences organized by Profs. Bacharach and Rzepa. Here is the program.
The word ‘umpolung‘ is not used often enough in my opinion, and that’s a shame since this phenomenon refers to one of the most classic tropes or deus ex machina used in sci-fi movies—prominently in the Dr. Who lore*—and that is ‘reversing the polarity‘. Now, reversing the polarity only means that for any given dipole the positively charged part now acquires a negative charge, while the originally negatively charged part becomes positively charged, and thus the direction of the dipole moment is, well, reversed.
In chemistry, reversing the polarity of a bond is an even cooler matter because it means that atoms that typically behave as positively charged become negatively charged and react with other molecules accordingly. Such is the case of this new research conducted experimentally by Prof. Rong Shang at Hiroshima University and theoretically elucidated by Leonardo “Leo” Lugo, who currently works jointly with me and my good friend the always amazing José Oscar Carlos Jimenez-Halla at the University of Guanajuato, Mexico.
Production of molecular hydrogen from water splitting at room temperature is a remarkable feat that forms the basis of fuel cells in the search for cleaner sources of energy; this process commonly requires a metallic catalyst, and it has been achieved via Frustrated Lewis Pairs from Si(II), but so far the use of an intramolecular electron relay process has not been reported.
Prof. Rong Shang and her team synthesized an ortho-phenylene linked bisborane functionalized phosphine (Figure 1), and proved their stoichiometric reaction with water yielding H2 and phosphine oxide quantitatively at room temperature. During the reaction mechanism the umpolung occurs when a proton from the captured water molecule forms a hydride centered on the borane moiety of BPB. The reaction mechanism is shown in Figure 2.
According to the calculated mechanism, a water molecule coordinates to one of the borane groups via the oxygen atom, and the phosphorus atom later forms a hydrogen bond via their lone pair separating the water molecule into OH– and H+, this latter migrates to the second borane and it is during this migration (marked TSH2 in Figure 2) where the umpolung process takes place; the natural charge of the hydrogen atom changes from positive to negative and stays so in the intermediate H3. This newly formed hydride reacts with the hydrogen atom on the OH group to form the reduction product H2, the final phosphine oxide shows a PO…B intramolecular forming a five membered ring which further stabilizes it.
This results are now available in Chemical Science, 2021, 12, 15603 DOI:10.1039/d1sc05135k. As always, I deeply thank Prof. Óscar Jiménez-Halla for inviting me to participate on this venture.
* Below there’s a cool compilation of the Reverse the Polarity trope found in Dr. Who: