Category Archives: Articles

Tribology – New paper in JPC A

Tribology isn’t exactly an area with which us chemists are most familiar, yet chemistry has a great impact on this branch of physics of high industrial importance. Tribology is basically the science which studies the causes and consequences of friction between surfaces. 

The plastic bag industry requires the use of chemical additives to reduce the electrostatic adherence between sheets of plastic. My good old friend Dr. Armando Gama has studied through Dissipative Particle Dynamics (DPD) coarse-grained simulations the friction coefficients of having two slightly different molecules: erukamide and behenamide, which only differ in the presence of a double bond between carbon atoms 12 and 13 (Fig1).


Fig 1

In order to study the electronic aspects that give rise to different tribological effects in these very similar molecules, four chains of each kind were bounded to a frozen graphene surface (four bonds apart to prevent steric crowding) and were optimized at the B97D/6-31G(d,p) level of theory.



Double bonds in erukamide pile together through pi-pi stacking interactions (Fig2) which are absent in behenamide which is why these last ones are able to slide better between each other (Fig3). Interaction energies calculated for the inner chains at the same level of theory are 44.21 and 34.46 kcal/mol for erukamide and behenamide, respectively. As per the suggestion of a referee we extended the calculations to a 2D system by placing seven molecules on graphene, which once again was kept at the optimized geometry of its isolated state, at four bonds of separation in order to prevent steric crowding (Fig 4).


Fig 4

This calculations clearly represent a limit case with a high density covering of the surface, but they nevertheless reflect the observed trend that behenamide works better than erukamide in reducing the static friction coefficient between sheets.

The paper is now available at JPC-A. Thanks to Dr. Gama for this great opportunity to work with his team, I know it wont be the last.

New paper in Tetrahedron #CompChem “Why U don’t React?”

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.

New Paper in JIPH – As(V)@calix[n]arenes

As part of an ongoing collaboration with the University of Arizona (UA) and the Center for Advanced Research and Studies (CINVESTAV – Saltillo), we are looking into the use of calix[n]arenes for bio-remediation agents capable to extract Arsenic (V) and (III) species from water. Water contamination by arsenic is a pressing issue in northern Mexico and the southern US, therefore any efforts aiming to their elimination has strong social and health repercussions.

As in previous studies, all calixarenes were optimized along with their corresponding guests within the cavity, namely H3AsO4, H2AsO4 and HAsO42- at the DFT level with the so-called Minnesota functionals by Truhlar and Cao, M06-2X/6-31G(d,p) level of theory. Interaction energies were calculated through the NBODel procedure. Calixarenes with R = SO3H and PO3H are the most promising leads. This study is now publishes in the Journal of Inclusion Phenomena and Macrocyclic Chemistry (DOI 10.1007/s10847-016-0617-0) as an online first article.

This article is also the first to be published by our undergraduate (and almost grad student in a month) Gustavo Mondragón who took this project on a side to his own research on photosynthesis.

Now my colleagues in Arizona and Saltillo, Prof. Reyes Sierra and Dr. Eddie López, respectively, will work on the experimental side of the project. Further calculations are being undertaken to extend this study to As(III) and to the use of other potential extracting materials such as metallic nanoparticles to which calixarenes could be covalently linked.

Simulation of Raman Spectroscopy and crystal cell effects – Selenium Carboxylate Eur. J. Inorg. Chem.

Computing spectroscopic features of molecules is always an interesting challenge, specially when intermolecular contacts are into play. Take vibrational spectroscopy for instance, all the non-covalent interactions present in a solid will have an important effect on the the calculated frequencies and their intensities. However calculating the spectroscopical properties of a solid quickly becomes a daunting task.

My colleague and friend Dr. Vojtech Jancik asked me to calculate the Raman frequencies for a new compound: Selenoyl bis-carboxylate, which according to him was very hard to obtain due to the very nature of selenium. So we performed various calculations on the isolated molecule to reproduce the measured Raman spectrum but we soon realized that a calculation on the crystal cell was needed if we wanted to get a more thorough picture of the experiment.

The level of theory used was PBEPBE/LANL2DZ. Optimization of the title structure pointed to a low coordination capacity by carboxylate groups as evidenced by the longer Se -O-C=O distances and reduced Wiberg bond indexes. A blue shift was observed for all bands and so we calculated the Raman frequencies at the crystal structure which gave us a better correspondence between spectra. Finally we computed the Raman spectra for the full unit cell comprised of four molecules with which an excellent agreement was obtained (a scaling factor of 0.8 was used).

Unfortunately we failed to further extend this calculation to a larger system with four unit cells and 32 molecules apparently due to insufficient memory; the calculation just stalled and stopped without error after consuming its time in the queue. I’ll try to take a look into it some day.

You can read the whole story in: Synthesis and Crystal Structure of the First Selenonyl Bis(carboxylate) SeO2(O2CCH3)2
Lukas Richtera · Vojtech Jancik · Joaquín Barroso‐Flores · Petr Nykel · Jiri Touzin · Jan Taraba

European Journal of Inorganic Chemistry 06/2015; 2015(18):2923–2927. DOI:10.1002/ejic.201500271

Thanks for reading!

New paper in JPC-A

As we approach to the end of another year, and with that the time where my office becomes covered with post-it notes so as to find my way back into work after the holidays, we celebrate another paper published! This time at the Journal of Physical Chemistry A as a follow up to this other paper published last year on JPC-C. Back then we reported the development of a selective sensor for Hg(II); this sensor consisted on 1-amino-8-naphthol-3,6-disulphonic acid (H-Acid) covalently bound to a modified silica SBA-15 surface. H-Acid is fluorescent and we took advantage of the fact that, when in the presence of Hg(II) in aqueous media, its fluorescence is quenched but not with other ions, even with closely related ions such as Zn(II) and Cd(II). In this new report we delve into the electronic reasons behind the quenching process by calculating the most important electronic transitions with the framework laid by the Time Dependent Density Functional Theory (TD-DFT) at the PBE0/cc-pVQZ level of theory (we also included an electron core potential on the heavy metal atoms in order to decrease the time of each calculation). One of the things I personally liked about this work is the combination of different techniques that were used to assess the photochemical phenomenon at hand; some of those techniques included calculation of various bond orders (Mayer, Fuzzy, Wiberg, delocalization indexes), time dependent DFT and charge transfer delocalizations. Although we calculated all these various different descriptors to account for changes in the electronic structure of the ligand which lead to the fluorescence quenching, only delocalization indexes as calculated with QTAIM were used to draw conclusion, while the rest are collected in the SI section.


Thanks a lot to my good friend and collaborator Dr. Pezhman Zarabadi-Poor for all his work, interest and insight into the rationalization of this phenomenon. This is our second paper published together. By the way, if any of you readers is aware of a way to finance a postdoc stay for Pezhman here at our lab, please send us a message because right now funding is scarce and we’d love to keep bringing you many more interesting papers.

For our research group this was the fourth paper published during 2014. We can only hope (and work hard) to have at least five next year without compromising their quality. I’m setting the goal to be 6 papers; we’ll see in a year if we delivered or not.

I’d like to also take this opportunity to thank all the readers of this little blog of mine for your visits and your live demonstrations of appreciation at various local and global meetings such as the ACS meeting in San Francisco and WATOC14 in Chile, it means a lot to me to know that the things I write are read; if I were to make any New Year’s resolutions it would be to reply quicker to questions posted because if you took the time to write I should take the time to reply.

I wish you all the best for 2015 in and out of the lab!

New paper in JACS

Well, I only contributed with the theoretical section by doing electronic structure calculations, so it isn’t really a paper we can ascribe to this particular lab, however it is really nice to see my name in JACS along such a prominent researcher as Prof. Chad Mirkin from Northwestern University, in a work closely related to my area of research interest as macrocyclic recognition agents.

In this manuscript, a calix[4]arene is allosterically opened and closed reversibly by coordinating different kinds of ligands to a platinum center linked to the macrocycle. (This approach has been referred to as the weak link approach.) I recently visited Northwestern and had a great time with José Mendez-Arroyo, the first author, who showed me around and opened the possibility for further work between our research groups.

(Ligands: Green = Chloride; Blue = Cyanide)

Closed, semi-open and fully open conformations; selectivity is modulated through cavity size. (Ligands: Green = Chloride; Blue = Cyanide)

Here at UNAM we calculated the interaction energies for the two guests that were successfully inserted into the cavity: N-methyl-pyridinium (Eint = 57.4 kcal/mol) and Pyridine-N-oxide (Eint = +200.0 kcal/mol). Below you can see the electrostatic potential mapped onto the electron density isosurface for one of the adducts. Relative orientation of the hosts within the cavity follows the expected (anti-) alignment of mutual dipole moments. At this level of theory, we could easily be inclined to assert that the most stable interaction is indeed the one from the semi-open compound and that this in turn is due to the fact that host and guest are packed closer together but there is also an orbital issue: Pyridine Oxide is a better electron acceptor than N-Me-pyridinium and when we take a closer look to the (Natural Bonding) orbitals interacting it becomes evident that a closer location does not necessarily yields a stronger interaction when the electron accepting power of the ligand is weaker (which is, in my opinion, both logic and at the same time a bit counterintuitive, yet fascinating, nonetheless).

Electrostatic potential mapped onto the electron density surface of one of the aducts under study

Electrostatic potential mapped onto the electron density surface of one of the adducts under study

All calculations were performed at the B97D/LANL2DZ level of theory with the use of Gaussian09 and NBO3.1 as provided within the former. Computing time at UNAM’s supercomputer known as ‘Miztli‘ is fully acknowledged.

The full citation follows:

A Multi-State, Allosterically-Regulated Molecular Receptor With Switchable Selectivity
Jose Mendez-Arroyo Joaquín Barroso-Flores §,Alejo M. Lifschitz Amy A. Sarjeant Charlotte L. Stern , and Chad A. Mirkin *

J. Am. Chem. Soc., Article ASAP
DOI: 10.1021/ja503506a
Publication Date (Web): July 9, 2014

 Thanks to José Mendez-Arroyo for contacting me and giving me the opportunity to collaborate with his research; I’m sure this is the first of many joint projects that will mutually benefit our groups. 


New paper in Journal of Chemical Theory and Computation

Happy new year to all my readers!

Having a new paper published is always a matter of happiness for this computational chemist but this time I’m excedingly excited about anouncing the publishing of a paper in the Journal of Chemical Theory and Computation, which is my highest ranked publication so far! It also establishes the consolidation of our research group at CCIQS as a solid and competitive group within the field of theoretical and computational chemistry. The title of our paper is “In Silico design of monomolecular drug carriers for the tyrosine kinase inhibitor drug Imatinib based on calix- and thiacalix[n]arene host molecules. A DFT and Molecular Dynamics study“.

In this article we aimed towards finding a suitable (thia-) calix[n]arene based drug delivery agent for the drug Imatinib (Gleevec by Novartis), which is a broadly used powerful Tyrosine Kinase III inhibitor used in the treatment of Chronic Myeloid Leukaemia and, to a lesser extent, Gastrointestinal Stromal Tumors; although Imatinib (IMB) exhibits a bioavailability close to 90% most of it is excreted, becomes bound to serum proteins or gets accumulated in other tissues such as the heart causing several undesired side effects which ultimately limit its use. By using a molecular capsule we can increase the molecular weight of the drug thus increasing its retention, and at the same time we can prevent Imatinib to bind, in its active form, to undesired proteins.

We suggested 36 different calix and thia-calix[n]arenes (CX) as possible candidates; IMB-CX complexes were manually docked and then optimized at the B97D/6-31G(d,p) level of theory; Stephan Grimme’s B97D functional was selected for its inclusion of dispersion terms, so important in describing π-π interactions. Intermolecular interaction energies were calculated under the Natural Bond Order approximation; a stable complex was needed but a too stable complex would never deliver its drug payload! This brings us to the next part of the study. A monomolecular drug delivery agent must be able to form a stable complex with the drug but it must also be able to release it. Molecular Dynamics simulations (+100 ns) and umbrella sampling methods were used to analyse the release of the drug into the aqueous media.

Optimized geometries for all complexes under study (B97D/6-31G*)

Optimized geometries for the 20 most stable complexes under study (B97D/6-31G*)

Potential Mean Force profiles for the four most stable complexes for position N1 and  N2 from the QM simulations are shown below (Red, complexes in the N1 position, blue, N2 position). These plots, derived from the MD simulations  give us an idea of the final destination of the drug respect of the calixarene carrier. In the next image, the three preferred structures (rotaxane-like; inside; released) for the final outcome of the delivery process are shown. The stability of the complexes was also assessed by calculating the values of ΔG binding through the use of the Poisson equations.

PMF for the most stable compounds

PMF for the most stable compounds

General MD simulation final structures

General MD simulation final structures

Thanks to my co-authors Maria Eugenia Sandoval-Salinas and Dr. Rodrigo Galindo-Murillo for their enormous contributions to this work; without their hard work and commitment to the project this paper wouldn’t have been possible.

New paper in J. Phys. Chem. C

Having a new paper out is always fun and this week we got the wonderful news from the Journal of Physical Chemistry C that a paper I co authored with Prof. Alireza Badiei at the University of Tehran in Iran and his student, who actually got us all in touch, Dr. Pezhman Zarabadi-Poor, was accepted for publication.

The paper is titled “Selective Optical Sensing of Hg(II) in Aqueous Media by H-Acid/SBA-15: A Combined Experimental and Theoretical Study“; in it we explored the fluorescence quenching mechanism for a Hg(II) complex which forms the basis of a novel selective mercury detector. Geometry optimizations were carried out at the PBE0/6-31++G** PCM level of theory (along with the aug-cc-pVDZ-PP basis set and corresponding ECP for Hg), also the electronic spectrum of both the free acid and the Hg(II) complex was calculated.

(Frontier orbitals were depicted using Chemcraft)

Higher laying orbitals for Hg(II) complex

Higher laying orbitals for Hg(II) complex

We can observe that HOMO and LUMO+1 are mainly located on the naphtalene ring allowing for the S0 -> S1 transition and back, which accounts for the molecular fluorescence. Other internal conversion processes were also assessed and discussed in the paper which accounts for the quenching effect. In short, we have obtained a full quantum description of the mechanism by which coordination of the free acid to Hg(II) alters the ligand’s electronic structure converting its emisive lowest-lying excited state to a dark state, i.e., quenching! Pretty cool stuff!

Once again thanks to both Dr. Zarabadi-Poor and Prof. Badiei for thinking about me for collaborating with them in this joint endeavor which hopefully wont be our last. A PDF copy of the article is available by direct request through this post.

Thanks for reading, sharing, rating and commenting.

Article in ‘Ciencia y Desarrollo’ (Science and Development)

Here is a link to an article I was invited to write by my good old friend, Dr. Eddie López-Honorato from CINVESTAV – Saltillo; Mexico, for the latest issue of the journal ‘Ciencia y Desarrollo’ (Science and Development) to which he was a guest editor. ‘Ciencia y Desarrollo’ is a popular science magazine edited by the National Council for Science and Technology (CONACyT) of which I’ve blogged before.

This magazine is intended for people interested in science with a general knowledge of it but not necessarily specialized in any field. With that in mind, I decided to write about the power of computational chemistry in predicting some phenomena while shedding light in certain aspects of chemistry that are not that readily available through experiments. The article is titled ‘Chemistry without flasks: Simulating chemical reactions‘. The link will take you to the magazine’s website which is in Spanish, as is the article itself, and only to the first page; so, below I translated the piece for anyone who could be interested in reading it (Hope I’m not infringing any copyright laws!). Don’t forget to also check out Dr. López-Honorato’s blog on nuclear energy research and the development of materials for nuclear waste containment! Encourage him to blog more often by liking and following his blog.


Chemistry without flasks?
Typically we think of a chemist as a scientist who, dressed in a white robe and protected with safety glasses and latex gloves, busily working within a laboratory, surrounded by measurement equipment, glassware and bottles with colored substances; pours one substance onto other substance, transforming them into new substances while noting that the chemical reaction occurs through color changes, heat release , perhaps gas, and occasionally even an explosion.
Thus chemistry, the study of the material processing involves active experimentation to accomplish chemical reactions subsequently confirmed, although indirectly, that the changes have been conducted in the microscopic world, moreover, in the molecular and atomic world. The chemist plans these changes based on the knowledge he has of the chemical properties of the substances of which he started and, like any other substance, are due to its molecular structure, i.e., the spatial arrangement of the atoms that form it.
Under this archetypal image just posed, then it’s at least funny to think that there is a branch of chemistry named Theoretical Chemistry.

What is theoretical chemistry?
Theoretical chemistry is a kind of bridge between chemistry and physics; using laws and equations that govern the subatomic world, to calculate the molecular structure of a substance, more specifically calculate the distribution of electrons surrounding the molecule forming a cloud, which interact with the electron cloud of another molecule to form a new substance. It is based on the knowledge of the electron density cloud or we can understand and predict the chemical properties of any substance. We can then define theoretical chemistry as the set of physical theories that describe the distribution and properties of the electron cloud belonging to a molecule, in this particular mathematical description we call electronic structure and this is the starting point for descriptions and chemical predictions.

What is it good for?
Through theoretical chemistry we can find answers to fundamental questions about the structure of matter. Consider a molecule of water, which has the chemical formula H2O. This formula implies that there are two hydrogen atoms attached to an oxygen atom But what spacial structure does a water molecule have? The simplest geometry it could take would be a linear structure, in which the angle formed by the three atoms is 180 °. However, the water molecule has an angle of 109 °, far from a linear structure. In Figure 2 we can see the result of the calculation of the electronic structure of H2O, it observed that the electron cloud that exists on the oxygen atom also has a place in space and thus push the hydrogen atoms bringing them together instead of allowing them to take a  more comfortable conformation.
Figure 2. Oxygen remaining electrons (red cloud around the oxygen atom) that are not chemically push the hydrogen atoms towards each other.

The industrial area currently impacted by the application of theoretical chemistry is the pharmacist, as they generate a new drug involves significant investment in financial and human resources, so predicting the properties of a molecule with pharmacological activity before synthesizing is highly attractive. Therefore it has been generated within the theoretical chemistry field, otherwise known as branch Rational Drug Design.
Drugs acting on our organism when active molecules interact directly with the various proteins which are distributed in the tissue cells. If the structure of the protein is known and we attack is known also a drug which acts on it, then we can design similar drugs having greater efficacy in the treatment of diseases. But it is not only fit one molecule to another, but to calculate the energy of interaction, the energy of dissolution and the probability that this interaction can be observed experimentally (Figure 3). The calculation of the interaction energy between the drug and the protein tells how strongly attract each other, a weak attraction drug will result in a low efficiency, while a greater attraction involve a more effective drug.
How do you calculate a molecule?

All matter exists in the universe is made of atoms, which in turn are composed of a nucleus of protons and neutrons surrounded by a cloud of electrons. When two or more atoms combine to form a molecule combining do their electron clouds and how do these combinations are best described by the equations of quantum mechanics, the branch of physics that describes the behavior of the subatomic world. However, due to its complexity, the equations of quantum mechanics can only be accurately resolved in the simplest cases such as the hydrogen atom, which consists of a single electron orbiting a proton. We must therefore resort to a range of methods and approaches to tackle cases of chemical interest and even biological.
For years the only available computers could solve the approximate equations for small molecules, no later than thirty atoms, which which can be interesting, but not entirely useful. Today modern supercomputing equipment (which may amount to up to tens or even hundreds of powerful computers connected together to work cooperatively) allow us to make models with hundreds of atoms molecules such as proteins or DNA fragments.
While the software available to perform these calculations is developed continuously for the last thirty years has been the progress in the design of computer systems able to perform thousands of operations per second the cornerstone that has made the theoretical chemistry a predictive tool commonly used. Today the branch known as Molecular Dynamics, which studies the interactions between molecules over time, has benefited from the development of the latest game consoles, as their processors, known as graphics processing units (GPUs , for its acronym in English) are able to perform calculations in parallel: Many of the images seen in our video games are actually calculated, not animated, this means that the console must calculate how to answer each item on the screen According to each stimulus we introduce. Conversely, if the images were animated, the answers would be always the same and the game would become unrealistic. Each game event should be calculated almost immediately to maintain its fluidity and emotion, in such a way that these GPUs have to be able to perform several mathematical operations simultaneously.
Traditionally molecular dynamics is based on the equations of classical physics, which only see the time evolution of molecules like solid objects collide, hundreds of molecules floating in water or other solvent. With the advent of GPUs can include dynamic calculating the electronic structure so we can peek into biological processes such as DNA replication or the passage of nutrients through a channel protein embedded in the membrane of a cell.
Since the fundamental understanding of the distribution of electrons in a molecule, its structure and properties to rational drug design, new materials based on molecular modeling theoretical chemistry is a powerful tool which is constantly progressing. The development of computer systems increasingly powerful detail allows us to meet the electronic processes involved in a chemical reaction while we can predict the real-time progress of molecular transformations. All this brings us ever closer to the dream of modern alchemists: transform matter to obtain substances with properties designed to pleasure.
In the nineteenth century, the American philosopher Ralph Waldo Emerson, wrote: “Chemistry was born from the dream of the alchemists to turn cheap metals into gold. By failing to do so, they have accomplished much more important things. ” And yes. Today we delve into the innermost secrets of nature not only to understand how it works but also to modify its operation on our behalf.

The Local Bond Order, LBO (Barroso et al. 2004)

I don’t know why I haven’t written about the Local Bond Order (LBO) before! And a few days ago when I thought about it my immediate reaction was to shy away from it since it would constitute a blatant self-promotion attempt; but hell! this is my blog! A place I’ve created for my blatant self-promotion! So without further ado, I hereby present to you one of my own original contributions to Theoretical Chemistry.

During the course of my graduate years I grew interested in weakly bonded inorganic systems, namely those with secondary interactions in bidentate ligands such as xanthates, dithiocarboxylates, dithiocarbamates and so on. Description of the resulting geometries around the central metallic atom involved the invocation of secondary interactions defined purely by geometrical parameters (Alcock, 1972) in which these were defined as present if the interatomic distance was longer than the sum of their covalent radii and yet smaller than the sum of their van der Waals radii. This definition is subject to a lot of constrictions such as the accuracy of the measurement, which in turn is related to the quality of the monocrystal used in the X-ray difraction experiment; the used definition of covalent radii (Pauling, Bondi, etc.); and most importantly, it doesn’t shed light on the roles of crystal packing, intermolecular contacts, and the energetics of the interaction.

This is why in 2004 we developed a simple yet useful definition of bond order which could account for a single molecule in vacuo the strength and relevance of the secondary interaction, relative to the well defined covalent bonds.

Barroso-Flores, J. et al. Journal of Organometallic Chemistry 689 (2004) 2096–2102,

Let a Molecular Orbital be defined as a wavefunction ψi which in turn may be constructed by a linear combination of Atomic Orbitals (or atom centered basis set functions) φj

We define ζLBO in the following way, where we explicitly take into account a doubly occupied orbital (hence the multiplication by 2) and therefore we are assuming a closed shell configuration in the Restricted formalism.

The summation is carried over all the orbitals which belong to atom A1 and those of atom A2.
Simplifying we yield,

where Sjk is the overlap integral for the φj and φk functions.

By summing over all i MOs we have accomplished with this definition to project all the MO’s onto the space of those functions centered on atoms A1 and A2. This definition is purely quantum mechanical in nature and is independent from any geometric requirement of such interacting atoms (i.e. interatomic distance) thus can be used as a complement to the internuclear distance argument to assess the interaction between them. This definition also results very simple and easy to calculate for all you need are the coefficients to the LCAO expansion and the respective overlap integrals.

Unfortunately, the Local Bond Order hasn’t found much echo, partly due to the fact that it is hidden in a missapropriate journal. I hope someone finds it interesting and useful; if so, don’t forget to cite it appropriately ;-)

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