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.
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:
Prof. Mario Molina was awarded the Nobel Prize in Chemistry in 1995, the same year I started my chemistry education at the chemistry school from the National Autonomous University of Mexico, UNAM, the same school from where he got his undergraduate diploma. To be a chemistry student in the late nineties in Mexico had Prof. Molina as a sort of mythical reference, something to aspire to, a role model, the sort of representation the Latinx and other underrepresented communities still require and seldom get.
I saw him several times at UNAM, where he’d pack any auditorium almost once a year to talk about various research topics, but I remember distinctly the first time I sort of interacted with him. It was 1997 and I attended my first congress, the 5th North America Chemistry Congress. Minutes before the official inauguration which he was supposed to preside, I caught a glimpse of him in the hallways near the main conference room. Being only 19 years old, I thought it’d be a good idea to chase him, ask for his autograph and a picture. He was kind enough not to brush me off and took just a minute to shake my hand, sign my book of abstracts, and get his picture taken with me. But cameras back then relied on the user to place a roll of film correctly. I did not; so the picture, although it happened, it doesn’t exist. Because of this and other anecdotes, that congress cemented my love for chemistry. I never asked for a second picture in the few subsequent occasions I had the pleasure to hear him talk.
Prof. Molina was an advocate of green and sustainable sources of energies. His work predicted the existence of a hole in the ozone layer and his struggle brought change into the banning of CFCs and other substances which interfere with the replenishment of ozone in the sub-stratosphere. Today, his legacy remains but also do his pending battles in the quest for new policies that favor the use of green alternative forms of energy. May he rest in peace and may we continue his example.
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!
The compound shown below in figure 1 is listed by Aldrich as 4,5,6,7-tetrahydroindole, but is it really?
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
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.
On the contrary, the corresponding pyrrole is substituted in position 2
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.
Literature in synthetic chemistry is full of reactions that do occur but very little or no attention is payed to those that do not proceed. The question here is what can we learn from reactions that are not taking place even when our chemical intuition tells us they’re feasible? Is there valuable knowledge that can be acquired by studying the ‘anti-driving force’ that inhibits a reaction? This is the focus of a new manuscript recently published by our research group in Tetrahedron (DOI: 10.1016/j.tet.2016.05.058) which was the basis of Guillermo Caballero’s BSc thesis.
It is well known in organic chemistry that if a molecular structure has the possibility to be aromatic it can somehow undergo an aromatization process to achieve this more stable state. During some experimental efforts Guillermo Caballero found two compounds that could be easily regarded as non-aromatic tautomers of a substituted pyridine but which were not transformed into the aromatic compound by any means explored; whether by treatment with strong bases, or through thermal or photochemical reaction conditions.
These results led us to investigate the causes that inhibits these aromatization reactions to occur and here is where computational chemistry took over. As a first approach we proposed two plausible reaction mechanisms for the aromatization process and evaluated them with DFT transition state calculations at the M05-2x/6-31+G(d,p)//B3LYP/6-31+G(d,p) levels of theory. The results showed that despite the aromatic tautomers are indeed more stable than their corresponding non-aromatic ones, a high activation free energy is needed to reach the transition states. Thus, the barrier heights are the first reason why aromatization is being inhibited; there just isn’t enough thermal energy in the environment for the transformation to occur.
But this is only the proximal cause, we went then to search for the distal causes (i.e. the reasons behind the high energy of the barriers). The second part of the work was then the calculation of the delocalization energies and frontier molecular orbitals for the non-aromatic tautomers at the HF/cc-pVQZ level of theory to get insights for the large barrier heights. The energies showed a strong electron delocalization of the nitrogen’s lone pair to the oxygen atom in the carbonyl group. Such delocalization promoted the formation of an electron corridor formed with frontier and close-to-frontier molecular orbitals, resembling an extended push-pull effect. The hydrogen atoms that could promote the aromatization process are shown to be chemically inaccessible.
Further calculations for a series of analogous compounds showed that the dimethyl amino moiety plays a crucial role avoiding the aromatization process to occur. When this group was changed for a nitro group, theoretical calculations yielded a decrease in the barrier high, enough for the reaction to proceed. Electronically, the bonding electron corridor is interrupted due to a pull-pull effect that was assessed through the delocalization energies.
The identity of the compounds under study was assessed through 1H, 13C-NMR and 2D NMR experiments HMBC, HMQC so we had to dive head long into experimental techniques to back our calculations.
A new publication is now available in which we calculated the binding properties of a fluorescent water-soluble chemosensor for halides which is specially sensitive for chloride. Once again, we were working in collaboration with an experimental group who is currently involved in developing all kinds of sustainable chemosensors.
The electronic structure of the chromophore was calculated at the M06-2X/6-311++G(d,p) level of theory under the SMD solvation model (water) at various pH levels which was achieved simply by changing the protonation and charges upon the ligand. Wiberg bond indexes from the Natural Population Analysis showed strong interactions between the chloride ion and the chromophore. Also, Fukui indexes were calculated in order to find the most probable binding sites. A very interesting feature of this compound is its ability to form a cavity without being a macrocycle! I deem it a cavity because of the intramolecular interactions which prevent the entrance of solvent molecules but that can be reversibly disrupted for the inclusion of an anion. In the figure below you can observe the remarkable quenching effect chloride has on the anion.
A quick look to the Frontier Molecular Orbitals (FMO’s) show that the chloride anion acts as an electron donor to the sensor.
If you are interested in more details please check: Bazany-Rodríguez, I. J., Martínez-Otero, D., Barroso-Flores, J., Yatsimirsky, A. K., & Dorazco-González, A. (2015). Sensitive water-soluble fluorescent chemosensor for chloride based on a bisquinolinium pyridine-dicarboxamide compound. Sensors and Actuators B: Chemical, 221, 1348–1355. http://doi.org/10.1016/j.snb.2015.07.031
Thanks to Dr. Alejandro Dorazco from CCIQS for asking me to join him in this project which currently includes some other join ventures in the realm of molecular recognition.