A new paper is coming out! These are always good news for someone whose productivity is evaluated by the number of his/her publications, and in my case the pleasure is double. It turns out that despite the fact a scientist is continuously working, there isn’t always the possibility of having results put “out there”. Back in Mexico we have the “National Researchers System” in which the National Council for Science and Technology encourages us to keep on working by providing economical stimuli and evaluating our productivity by, yes, the number of papers published each year. For three years I worked for a private research center in which fundamental science was tackled as far as it was economically possible and cost effective. Practically all of the work carried out there was confidential since the company it belonged to is leader in its market, not only in Mexico but in Latin America and southern USA!  At this facility some papers were published from time to time (most of them came from research in molecular modeling) but not without struggle against the administrators. We can thank for most of the struggle (and the papers!) to Dr. Armando Gama-Goicochea, a great physicist as well as a great friend of mine.

Anyway, the bottom line here is that I’m excited about having a new paper coming out again, even if I’m nowhere close to being first author. This three year paper fastening seems to be over and let us hope it’s only the first of various now that I’m holding a postdoc position here in Romania.

In this paper we tackled the bonding properties of some Aluminum complexes with three chalcogeno triazoles. The electrostatic potential mapped onto a density surface of one of those compounds is currently shown in the header of this blog, btw. We concluded that the bonding in such compounds is mainly covalent as opposed to the more conventional electrostatic notion prevailing for such hard atoms. In order to get this information we resorted to Natural Bonding Analysis calculations with the RHF method and somewhat large basis sets in order to get a full description of the electronic density.

I very much like these systems in which several bonding possibilities occur. The fact that nature is chosing one out of many has always a reason which can be assessed by our models and may serve us to learn how to modify it’s behaviour.

Coordination Diversity of Aluminum Centers Molded by Triazole Based Chalcogen Ligands

Jocelyn Alcántara-García, Vojtech Jancik, Joaquín Barroso, Sandra Hidalgo-Bonilla, Raymundo Cea-Olivares, Rubén A. Toscano and Mónica Moya-Cabrera

This is the second post on a series which will try to address common technical questions in computational chemistry that recursively appear on the CCL.

The Natural Bond Orbitals analysis is a powerful tool in population analysis calculations which is more robust than the traditional Mulliken approach, if for no better reason because its almost insensitive to the change of basis set while Mulliken’s P.A. is highly sensitive to basis set effects. Another advantage of the NBO analysis is that it provides a localized depiction of the electron density over a molecule, making it more related to chemists intuition. So far I have only worked with Gaussian 98, Gaussian 03 and only recently with Gaussian 09 in calculating NBO’s although it is possible also to perform them with GAMESS and the standalone NBO5.0 program created by Frank Weinhold. Visualizing them, however is never a straightforward process, and quite often we see more questions on the CCL than answers trying to address the matter. Most of the answers are concerned with what visualization programs to use but they seldom provide step by step instructions, furthermore most manuals are a bit cryptic about the procedure to plot this orbitals.

In Molekel 4.3

http://molekel.cscs.ch/wiki/pmwiki.php

Make sure that the route section in your input file includes the following options: pop=nboread; gfoldprint (in case you are using G03 or even G09) or gfprint (in case you are still running G98), e.g.:

#P opt rhf/6-31G(d,p) pop=(full,nboread) gfoldprint geom=connectivity

This calculation requests a geometry optimization followed by a Natural Bond Orbital population analysis (with keywords to be read) using the Restricted Hartree-Fock method with the split valence basis set 6-31G(d,p)

NOTE: I have my own issues and concerns about the use of DFT along with NBO but maybe that will be treated in another post.

At the end of the input file, after the infamous blank line type the following:

$NBO PLOT $END

You may include other keywords such as BNDIDX which generates a Wiberg bond index (order) matrix; or BOAO which generates the same matrix but in the Natural Atomic Orbitals basis. The PLOT option will generate a series of files with numerical extensions. The one you want to pay attention to is filename.47

If you are using Gaussian 03 or Gaussian 09 and STILL want to use Molekel 4.3 then you probably already know you have to change 03 for 98 on the header of the output file:

****************…              ****************
Gaussian 03:  x86…  –>       Gaussian 98:  x86-
2-Feb-2009                               2-Feb-2009
***************…                ****************

That aside, load your output file (filename.out or filename.log) on Molekel 4.3 as usual. Then go to Load -> nbo orb and load filename.47. Now, go to Compute -> Orbital and now select the Natural Bond Orbital you are interested in. This should do it! As an interesting exercise try computing the same orbitals (lets say HOMO and HOMO-1) with and without loading filename.47 in order to observe the difference between the shape of the MO’s and NBO’s. Molekel 4.3, though, is filled with bugs that will make it close unexpectedly, specially when running under Windows Vista. Sometimes the window closes because some sort of resolution problem, specially when taking snapshots (interestingly enough this happened to me when the background color was set to white) decrease the resolution of your monitor before taking the snapshot to prevent this problem. Some people complain about the look and feel of the latest molekel version so they stick to this old bugged one, so that is why I’m posting this method.

In Gasusview 3.0

This is the gaussview version I currently work with. When performing the NBO analysis on Gaussian (by the way, Gaussian 09 cannot be visualized with gaussview 3.x) use the savenbo option in the rout section, for example:

#P opt HF/6-31G(d) freq=noraman pop=(ful,nboread,savenbo) geom=connectivity

This will save the NBO coefficients into the checkpoint file. Load the output file with gaussview normally and then click on the Molecular Orbital icon (or go to Edit -> MO’s). This will open a new window with four tabs at the bottom of the molecule image. Click on the ‘New’ tab and load your checkpoint file. Gaussview will automatically format the chk file (this can cause some troubles when crossing architectures or platforms, so be careful to generate the proper formatted chk file!) Once load select the orbital you need to visualize and go to the ‘Visualize’ tab and click update; the orbital displayed is the Natural Bond Orbital. In this tab you can also adjust certain parameters like the isovalue (which is set to 0.02 by default) or the cube grid which controls how smooth the surface looks. UPDATE: According to John Keller from Alaska you can use this methodology when calculating with G09 and using Gview3.x, this also allows to visualize vibrations when this same software combination is used.

As usual, this post will be updated whenever I find some more useful information about the matter. Rate this post or leave a comment, just to know if you found it useful. Thanks!

I’m posting this white paper “as is” but I will keep on coming back to update it; the thing is that I haven’t had the time to post anything else lately and if I don’t do it like this then I will never get it out. Please be kind on your comments and ratings!

For a more thorough discussion of NBO analysis please check out the references.

Requesting an NBO population analysis on the route section of a Gaussian job (via the simplest option pop=nbo) generates a lot of information on the output file which sometimes is not too straightforward to read. Please refer to previous posts in this blog (all under the NBO category) for more info on NBO calculations. The first part of this post deals with the analysis of the default information obtained from an NBO calculation; the second part deals with some useful/popular options of the NBO analysis which are controlled through the pop=nboread keyword available in NBO3.1 which is the version incorporated in Gaussian.

pop=nbo

Perhaps the most common issue when reading NBO results is making sense of the hybridization shown. Take the example below as taken from the NBO manual for Methylamine:

(Occupancy)   Bond orbital/ Coefficients/ Hybrids

————————————————————-

1. (1.99858)  BD  (1)  C 1 – N 2

(40.07%)    0.6330*  C1 s(21.71%)p 3.61(78.29%)

-0.0003  -0.4653  -0.0238  -0.8808  -0.0291

-0.0786  -0.0110  -0.0000  -0.0000

(50.93%)     0.7742* N  2  s(30.88%)p 2.24(69.12%)

-0.0001  -0.5557  0.0011  0.8302  0.0004

0.0443  -0.0098  0.0000 0.0000

The first line shows the occupancy (between 0.00 and 2.00 electrons), then the label of the NBO (BD = Bonding (2 centers); CR = Core (1 center); LP = Lone pair; RY = Rydberg; BD* = Antibond), after that a ‘serial number‘ which corresponds to the connectivity (or idealized bond index between the atoms, i.e., single double triple bond), and finally the atom(s) to which the NBO belongs.

The next line describes the natural atomic hybrids of which the NBO is composed, giving the percentage (100|cA|^2) of the NBO on each hybrid (40% the C hybrid orbital and 60% the N hybrid orbital), the polarization coefficient cA (Nitrogen is more electronegative than Carbon, hence the polarization coefficients look like 0.633 for C and 0.7742 for N, i.e. this NBO is more polarized towards N), the atom label (self explanatory) , and a hybrid label showing the sp^x composition: for the C hybrid orbital it is sp^3.61 while for the one on N is sp^2.24. The number in parenthesis is just the percentage in composition of the hybrid (75%p and 25%s corresponds to an ideal sp^3 hybridization) Now, for the tricky part: Sometimes you’ll get numbers larger than 3 for an sp^x hybrid or even s^yp^x hybrids (for y>1 and x>3), this has to do with the basis set employed and the number of functions used to describe each atomic orbital. (EXAMPLE SOON, IM LAZY)

Below the hybridization we find the set of coefficients that specify how the NHO is written as a linear combination of Natural Atomic Orbitals. The previous NHO for C has the largest coefficients from the second (-0.4653) and fourth (-0.8808) natural atomic orbitals, corresponding to a rough description like: NHOc = -0.4653(2s)c -0.8808(2px)c

pop=nboread

To control the options in the Natural Bond Orbital population analysis the line $NBO keywords $END must be included at the end of the input file (after the infamous blank line located after the molecule specification)

Wiberg bond indexes

This is a feature I use a lot when dealing with adducts with closed shell molecules. It is achieved through the BNDIDX keyword. Two indexes are obtained: The Wiberg bond index which is presented as a matrix; and the Wiberg bond index total which is the summation of all Wiberg indexes for every atom. The latter index roughly resembles the number of covalent bonds each atom forms. When analyzing this total index on a given atom, it should be compared to a well defined one in another part of the molecule just to make sure that all numbers are reflecting the same trends. Wiberg’s is not the only bond index provided by NBO analysis: the BOAO keyword generates bond index on the basis of the natural atomic orbitals.

Some common errors and possible solutions

->> Concerning NBO Deletion analysis

***** WARNING ***** The variational principle has been violated and the above deletion energy is invalid!!

This usually caused by one of the following:

1) Wavefunction symmetry breaking: Use the Nosymm option on the route section of your input file.

2) The use of DFT methods: Strong deletions often lead to densities that derail the density functional.  Safest is to use HF, where the variational theorem can be counted on, and
DFT artifacts are averted.  The FIXDM keyword (available only in NBO 5.0) may also correct some numerical problems associated with large basis sets

3) Deletion of some degenerated orbitals which breaks the symmetry of the wavefunction. Sometimes it could be that although there are no formal degenerate states accidental degeneracies might occur, deletion of which will cause this error.

->> Also on NBO Deletion Analysis

************************************************
** ERROR IN INITNF. NUMBER OF VARIABLES ( 57) **
**  INCORRECT (SHOULD BE BETWEEN 1 AND 50)  **
************************************************

This is one weird error. I have solved it by changing the molecule specification from Z-Matrix to Cartesian coordinates. Also, if you are running a DFT calculation in an older revision of Gaussian 03, try using the IOp(5/48=10000). Later revisions of Gaussian 03 and the more recent Gaussian 09 claim to have fixed this problem.

->> NBO Analysis

WARNING: Population inversion found on atom X#

This is not a problem! NBO lists orbitals within each atom according to their energy and their population afterwards. This warning only states that some low energy lying orbitals are less populated than others with higher energy. It cannot be “fixed” since this is a natural consequence of the orthonormalization process of the NBO generation.

References

NBO5.0 Home. Site of the creator of NBO and NBOView (Dr. Frank Weinhold)

FAQ‘s on NBO Home. I can’t recommend it enough!!!

Population Analysis Keyword in Gaussian

The Natural Bond Orbitals Deletion analysis provides an excellent approach to the assessment of bonding energy within a single molecular fragment or between many. It deletes specific elements of the Fock matrix (this means it sets their values to 0.000) and then re-diagonalizes it in order to find the difference in energy respect to the original matrix. About nine different kinds of deletions are available, which will be briefly summarized in the following section.

One of the main strengths of the NBO derived methods is their almost complete basis set independence, which allows us to obtain comparable numbers under different levels of theory.

Both G03 and G09 use the NBO3.1 program. The 5.0 version is sold separately by their creators, namely prof. Frank Weinhold, who can be contacted through their website. It’s not available for geometry optimizations (gradients), some people insist on trying to get a different geometry by eliminating a certain interaction and that is just not possible directly with the NBODel method It is indeed possible to perform NBODeletions along with optimizations in G09 (Thanks to prof. Weinhold for his clarifying message) but there are some restrictions: molecular coordinates should be in Z-Matrix format and the number of variables to be optimized should not exceed 50; prof. Weinhold also recommends to use print=0 in the $NBO keylist in order to prevent the output files to become too big. Be sure to start with a proper geometry (close to the desired minimum) since given the nature of this analysis some apretiable geometry effects are to be expected.

The general syntax for its usage includes the string pop=NBODel in the route section of the GaussianX input file. Then, at the end of the file, the following is required:

--End of Input File--
--blank line--
$NBO $END
$DEL
Interactions to be deleted
$END

ENTIRE BLOCKS OF ATOMS

In this kind of deletion one is able to delete all the elements between specific groups of atoms, as if their orbitals (and hence their common Fock elements) did not overlap.

--End of Input File--
--blank line--
$NBO $END
$DEL
ZERO 2 ATOM BLOCKS
2 BY 3
1 2
3 4 5
3 BY 2
3 4 5
1 2
$END
--blank line--

The first line after $DEL indicates how many groups of atoms will be set to zero and the following lines indicate how many atoms belong to each group (i.e. the size of each block which in this case are 2 and 3, respectively). After this line the groups of atoms are listed, in this example all elements from atoms 1 and 2 with those of atoms 3, 4 and 5 will become zero. The next three lines are used for symmetry, so all the interactions from (1,2)->(3,4,5) are deleted along with (3,4,5)->(1,2)

DELETIONS BETWEEN ENTIRE MOLECULAR FRAGMENTS (Intermolecular deletions)

If we want to assess the interaction energy between two molecules, the previous method would consume a lot of time in declaring the size of each block with every atom of each molecule in it, plus there seems to be a limit to the size of the block. In this kind of deletion one is able to delete all the elements between two or more molecular fragments.

--End of Input File--
--blank line--
$NBO $END
$DEL
ZERO 2 DELOC FROM 1 TO 2 FROM 2 TO 1
$END
--blank line--

The delocalizations can also be calculated only in one direction (FROM 1 to 2), in the case above both interactions 1->2 and 2->1 have been deleted. The input for a trimer in which all three fragments interacted with each other would look like this:

ZERO 6 DELOC FROM 1 TO 2 FROM 2 TO 1 FROM 2 TO 3 FROM 3 TO 2 FROM 1 TO 3 FROM 3 TO 1

In short, the number of bilateral delocalizations to be deleted is equal to twice the number of edges in a graph depicting the intermolecular interactions (A post on topology in chemistry is now due).

Reading the output file

Almost at the very end of the output file the following section can be found:

>>>>>>>>>> Convergence criterion not met.
SCF Done:  E(RHF) =  -4728.57245403     A.U. after    2 cycles
Convg  =    0.2354D-03             -V/T =  2.0012
——————————————————————————
Energy of deletion :      -4728.572454034
Total SCF energy :      -4728.604640956
——————-
Energy change :          0.032187 a.u.,          20.198 kcal/mol
——————————————————————————

The warning about the convergence can be disregarded without any concern about the accuracy of the outcome and it will show in every $DEL calculation. The SCF energy displayed in the second line is the energy corresponding to the modified Fock Matrix, which is the same as the one labeled as Energy of deletion. The Total SCF energy corresponds to the original Fock Matrix; the difference between them is labeled as Energy change and the value is reported in both atomic units as well as kcal/mol.

Some common errors and possible solutions

–> Sometimes you get the following error message at the beginning of the calculation making it crash:

************************************************
** ERROR IN INITNF. NUMBER OF VARIABLES ( 57) **
**  INCORRECT (SHOULD BE BETWEEN 1 AND 50)  **
************************************************

I have found that changing the molecule specification section from Z-matrix to Cartesian coordinates, or vice versa, overcomes this difficulty. Also, if the Opt keyword appears in the route section the previous message will be shown. Opt is not available under the NBODel method (read the first paragraph for the proper correction).

–> Possible conflicts between NBODel and the usage of DFT methods:

In some revisions of Gaussian 03 there is a conflict when using NBODel and DFT methods. The IOp(5/48=10000) should be included to repair such conflict. This issue was solved in some revision of Gaussian 03 but I don’t know which, so try this if you have problems. Gaussian09 has taken care of the issue although still the usage of DFT to obtain NBODel calculations is not advised.

–> The following error is not self-explanatory:

NtrOpn-Old failed
Error termination via Lnk1e in ‘/../../path’

This particular error arises from the absence of the ‘$NBO $END’ line before the $DEL instruction. The previous line may or may not include additional keywords. If you are interested in computing some kind of deletion energy just leave the line as presented above in all previous examples. My guess is that the $DEL instruction does not calculate the corresponding NBO’s from which to make the deletion but it rather takes all the results from the $NBO instruction and works from there. Bottom line: don’t forget this line!

As with other posts tagged as ‘white papers’, this one will be updated and expanded every time new information is found. In the mean time, thanks to everyone for reading, commenting and rating, this keeps me going with the blog. Have you encountered problems with NBODel methods? share your experiences and solutions with the rest in the comments section.

Have a nice day!

A new paper has been published and that is always good news. The paper entitled “Synthesis of new γ-lactones from preactivated monosubstituted pyrazines and TMS–ketene acetals” coauthored by Azucena Garduño-Alva, M. Carmen Ortega-Alfaro, José G. López-Cortés, Isabel Chávez, Joaquin Barroso-Flores, Rubén A. Toscano, Henri Rudler and Cecilio Álvarez-Toledano was a fruitful collaboration between several researchers from within the UNAM Institute of Chemistry and from other labs.

Therein, the lactone formation from pyrazines is analyzed, with some resulting orientations not quite in accordance with the common orientation patterns yield by electrondonor and electronwithrdawing groups. In order to assess the electronic structure of the intermediates and its influence on the resulting orientations, I performed a Fukui analysis based on the Natural Population formalism.

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
http://dx.doi.org/10.1016/j.jorganchem.2004.03.035,

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 ;-)

Today is truly a landmark in our lab because on this day, María Eugenia “Maru” Sandoval-Salinas has defended her thesis and has thus obtained her B. Sc. in Chemistry. She is the first student under my supervision to achieve this goal, and I hope it won’t be long until we get some more, although now the bar has been set quite high. For the time being, Maru is pursuing a career in the pharmaceutical industry but has every intention of coming back to the lab for her Masters degree; she has a reserved spot here with us at CCIQS.

Hard work pays off – We wait for you to come back for your Masters Degree!

Maru’s thesis deals mainly, but not exclusively, with calculating the interaction energies of calix- and thia-calix[n]arenes with the tyrosine kinase inhibitor Imatinib, which is widely used in the treatment of Chronic Myeloid Leukemia (CML), in order to rationally design a drug delivery agent for this drug. Her work is (a huge) part of an article currently under revision that I only wish had been published before her defense. Still, we await for that paper to be published in the next few weeks.

Throughout her stay at our lab, Maru was a dedicated student willing to learn new skills every time. As she replied today to one of the questions: “it’s not so much how many calculations I got right, but how many I got wrong!“. I find deep meaning in this sentence, perhaps deep enough as to consider it an aphorism, because indeed the more we try the more we fail, and the more we fail the more we learn and the closer we get to success.

Congratulations, Maru! I personally thank you for all the hard work invested in your thesis, all the long hours in front of the computer and your disposition to learn and work during the last 1.5 years. I’m certain you’ll find success in any venture you undertake; and I’m certain of it because you never stop trying.

Taking the Oath after being unanimously approved

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 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

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.

It is with great pleasure that I announce the graduation of another member of our research group: Luis Enrique “Kike” Aguilar defended his BSc thesis yesterday and is now counting the days left for the Autumn when he’ll move to the Netherlands for a masters in computational chemistry.

Luis Enrique, Kike, calculated the interaction energies of 144 different inclusion complexes where calix and thia-calix[n]arenes were once again the chosen hosts (36 of them) and two drugs for the treatment of chronic myeloid leukemia (CML), namely Sorafenib and Bosutinib, were the guests.

The publication of the corresponding article in which we once again were fortunate enough to count with the collaboration of Dr. Rodrigo Galindo from Utah University in the molecular dynamics section, is still pending but we’re confident enough that it wont take much longer until it’s out there.

Kike is a very diligent student with great learning skills, I’m sure he’ll succeed in any enterprise he sets himself off.  Congratulations, Kike! Thanks for being a part of our research but more importantly for being a part of our community.

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

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

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.

One of the most popular posts in this blog has to do with calculating Fukui indexes, however, when dealing with a large number of molecules, our described methodology can become cumbersome since it requires to manually extract the population analysis from two or three different output files and then performing the arithmetic on them separately with a spreadsheet or something.

Our new team member Ricardo Loaiza has written a python script that takes the three aforementioned files and yields a .csv file with the calculated Fukui indexes, and it even points out which of the atoms exhibit the largest values so if you have a large molecule you don’t have to manually check for them. We have also a batch version which takes all the files in any given directory and performs the Fukui calculations for each, provided it can find file triads with the naming requirements described below.

Output files must be named filename.log (the N electrons reference state), filename_plus.log (the state with N+1 electrons) and filename_minus.log (the N-1 electrons state). Another restriction is that so far these scripts only work with NBO population analysis as provided by the NBO3.1 program available in the various versions of Gaussian. I imagine the listing is similar in NBO5.x and NBO6.x and so it should work if you do the population analysis with them.

The syntax for the single molecule version is:

python fukui.py filename.log filename_minus.log filename_plus.log

For the batch version is:

./fukuiPorLote.sh

(Por Lote means In Batch in Spanish.)

These scripts are available via GitHub. We hope you find them useful, and you do please let us know whether here at the comments section or at our GitHub site.

Chemically actuating a molecule is a very cool thing to do and the Weak Link Approach (WLA) allows us to do precisely that through the reversible coordination of one or various organometallic centers to a longer ligand that opens or closes a macrocyclic cavity. All this leads to an allosteric effect so important in biological instances available in inorganic molecules. Once again, the Mirkin group at Nortwestern University in Evanston, Illinois, has given me the opportunity to contribute with the calculations to the energetic properties of these actuators as well as their electronic properties for their use as molecular scavengers or selective capsules for various purposes such as drug delivery agents.

As in the previous WLA work (full paper), the NBODel procedure was used at the B97D/LANL2DZ level of theory, only this time the macrocycle consisted of two organometallic centers and for the first time the asymmetric opening of the cavity was achieved, as observed by NMR. With the given fragments, all possibilities shown in scheme 1 were obtained. The calculated bond energies for the Pt – S bonds are around 60 – 70 kcal/mol whereas for the Pt – Cl bonds the values are closer to 90 kcal/mol. This allows for a selective opening of the cavity which can then be closed by removing the chlorine atoms with the help of silver salts.

For the case of complex mixture 4a, 4b, and 4c, the thermochemistry calculations show they are all basically isoenergetic with differences in the thousandths of kcal/mol. The possibilities for the groups in the weakly bonded ligands are enormous; currently, there is work being done about substituting those phenyl rings for calix[4]arenes in order to have a macrucyclic capsule made by macrocylic capusules.

Thanks to Andrea D’Aquino for taking me into her project, for all the stimulating discussions and her great ideas for expanding WLA into new avenues; I’m sure she’ll succeed in surprising us with more possibilities for these allosteric macrocycles.

The full paper is published in Inorganic Chemistry from the ACS (DOI: 10.1021/acs.inorgchem.7b02745). Thanks for reading and -if you made it this far into the post- happy new year!

The canonical molecular orbital depiction of an electronic transition is often a messy business in terms of a ‘chemical‘ interpretation of ‘which electrons‘ go from ‘which occupied orbitals‘ to ‘which virtual orbitals‘.

Natural Transition Orbitals provide a more intuitive picture of the orbitals, whether mixed or not, involved in any hole-particle excitation. This transformation is particularly useful when working with the excited states of molecules with extensively delocalized chromophores or multiple chromophoric sites. The elegance of the NTO method relies on its simplicity: separate unitary transformations are performed on the occupied and on the virtual set of orbitals in order to get a localized picture of the transition density matrix.

[1] R. L. Martin, J. Chem. Phys., 2003, DOI:10.1063/1.1558471.

In Gaussian09:
After running a TD-DFT calculation with the keyword TD(Nstates=n) (where n = number of states to be requested) we need to take that result and launch a new calculation for the NTOs but lets take it one step at a time. As an example here’s phenylalanine which was already optimized to a minimum at the B3LYP/6-31G(d,p) level of theory. If we take that geometry and launch a new calculation with the TD(Nstates=40) in the route section we obtain the UV-Vis spectra and the output looks like this (only the first three states are shown):

Excitation energies and oscillator strengths:

Excited State 1: Singlet-A 5.3875 eV 230.13 nm f=0.0015 <S**2>=0.000
42 -> 46 0.17123
42 -> 47 0.12277
43 -> 46 -0.40383
44 -> 45 0.50838
44 -> 47 0.11008
This state for optimization and/or second-order correction.
Total Energy, E(TD-HF/TD-KS) = -554.614073682
Copying the excited state density for this state as the 1-particle RhoCI density.

Excited State 2: Singlet-A 5.5137 eV 224.86 nm f=0.0138 <S**2>=0.000
41 -> 45 -0.20800
41 -> 47 0.24015
42 -> 45 0.32656
42 -> 46 0.10906
42 -> 47 -0.24401
43 -> 45 0.20598
43 -> 47 -0.14839
44 -> 45 -0.15344
44 -> 47 0.34182

Excited State 3: Singlet-A 5.9254 eV 209.24 nm f=0.0042 <S**2>=0.000
41 -> 45 0.11844
41 -> 47 -0.12539
42 -> 45 -0.10401
42 -> 47 0.16068
43 -> 45 -0.27532
43 -> 46 -0.11640
43 -> 47 0.16780
44 -> 45 -0.18555
44 -> 46 -0.29184
44 -> 47 0.43124

The oscillator strength is listed on each Excited State as “f” and it is a measure of the probability of that excitation to occur. If we look at the third one for this phenylalanine we see f=0.0042, a very low probability, but aside from that the following list shows what orbital transitions compose that excitation and with what energy, so the first line indicates a transition from orbital 41 (HOMO-3) to orbital 45 (LUMO); there are 10 such transitions composing that excitation, visualizing them all with canonical orbitals is not an intuitive picture, so lets try the NTO approach, we’re going to take excitation #10 for phenylalanine as an example just because it has a higher oscillation strength:

%chk=Excited State 10: Singlet-A 7.1048 eV 174.51 nm f=0.3651 <S**2>=0.000
41 -> 45 0.35347
41 -> 47 0.34685
42 -> 45 0.10215
42 -> 46 0.17248
42 -> 47 0.13523
43 -> 45 -0.26596
43 -> 47 -0.22995
44 -> 46 0.23277

Each set of NTOs for each transition must be calculated separately. First, copy you filename.chk file from the TD-DFT result to a new one and name it after the Nth state of interest as shown below (state 10 in this case). NOTE: In the route section, replace N with the number of the excitation of interest according to the results in filename.log. Run separately for each transition your interested in:

#chk=state10.chk

#p B3LYP/6-31G(d,p) Geom=AllCheck Guess=(Read,Only) Density=(Check,Transition=N) Pop=(Minimal,NTO,SaveNTO)

0 1
--blank line--

By requesting SaveNTO, the canonical orbitals in the state10.chk file are replaced with the NTOs for the 10th excitation, this makes it easier to plot since most visualizers just plot whatever set of orbitals they read in the chk file but if they find the canonical MOs then one would need to do some re-processing of them. This is much more straightforward.

Now we format our chk files into fchk with the formchk utility:

formchk -3 filename.chk filename.fchk
formchk -3 state10.chk state10.fchk

If we open filename.fchk (the file where the original TD-DFT calculation is located) with GaussView we can plot all orbitals involved in excited state number ten, those would be seven orbitals from 41 (HOMO-3) to 47 (LUMO+2) as shown in figure 1.

If we now open state10.fchk we see that the numbers at the side of the orbitals are not their energy but their occupation number particular to this state of interest, so we only need to plot those with highest occupations, in our example those are orbitals 44 and 45 (HOMO and LUMO) which have occupations = 0.81186; you may include 43 and 46 (HOMO-1 and LUMO+1, respectively) for a much more complete description (occupations = 0.18223) but we’re still dealing with 4 orbitals instead of 7.

The NTO transition 44 -> 45 is far easier to conceptualize than all the 10 combinations given in the canonical basis from the direct TD-DFT calculation. TD-DFT provides us with the correct transitions, NTOs just paint us a picture more readily available to the chemist mindset.

NOTE: for G09 revC and above, the %OldChk option is available, I haven’t personally tried it but using it to specify where the excitations are located and then write the NTOs of interest into a new chk file in the following way, thus eliminating the need of copying the original chk file for each state:

%OldChk=filename.chk
%chk=stateN.chk

NTOs are based on the Natural Hybrid orbitals vision by Löwdin and others, and it is said to be so straightforward that it has been re-discovered from time to time. Be that as it may, the NTO visualization provides a much clearer vision of the excitations occurring during a TD calculation.

Thanks for reading, stay home and stay safe during these harsh days everyone. Please share, rate and comment this and other posts.

This is a guest post by our very own Gustavo “Gus” Mondragón whose work centers around the study of excited states chemistry of photosynthetic pigments.

When you’re calculating excited states (no matter the method you’re using, TD-DFT, CI-S(D), EOM-CCS(D)) the analysis of the orbital contributions to electronic transitions poses a challenge. In this post, I’m gonna guide you through the CI-singles excited states calculation and the analysis of the electronic transitions.

I’ll use adenine molecule for this post. After doing the corresponding geometry optimization by the method of your choice, you can do the excited states calculation. For this, I’ll use two methods: CI-Singles and TD-DFT.

The route section for the CI-Singles calculation looks as follows:

%chk=adenine.chk
%nprocshared=8
%mem=1Gb

#p CIS(NStates=10,singlets)/6-31G(d,p) geom=check guess=read scrf=(cpcm,solvent=water)

adenine excited states with CI-Singles method

0 1
--blank line--

I use the same geometry from the optimization step, and I request only for 10 singlet excited states. The CPCP implicit solvation model (solvent=water) is requested. If you want to do TD-DFT, the route section should look as follows:

%chk=adenine.chk
%nprocshared=8
%mem=1Gb

#p FUNCTIONAL/6-31G(d,p) TD(NStates=10,singlets) geom=check guess=read scrf=(cpcm,solvent=water)

adenine excited states with CI-Singles method

0 1
--blank line--

Where FUNCTIONAL is the DFT exchange-correlation functional of your choice. Here I strictly not recommend using B3LYP, but CAM-B3LYP is a noble choice to start.

Both calculations give to us the excited states information: excitation energy, oscillator strength (as f value), excitation wavelength and multiplicity:

Excitation energies and oscillator strengths:

 Excited State   1:      Singlet-A      6.3258 eV  196.00 nm  f=0.4830  <S**2>=0.000
      11 -> 39        -0.00130
      11 -> 42        -0.00129
      11 -> 43         0.00104
      11 -> 44        -0.00256
      11 -> 48         0.00129
      11 -> 49         0.00307
      11 -> 52        -0.00181
      11 -> 53         0.00100
      11 -> 57        -0.00167
      11 -> 59         0.00152
      11 -> 65         0.00177

The data below corresponds to all the electron transitions involved in this excited state. I have to cut all the electron transitions because there are a lot of them for all excited states. If you have done excited states calculations before, you realize that the HOMO-LUMO transition is always an important one, but not the only one to be considered. Here is when we calculate the Natural Transition Orbitals (NTO), by these orbitals we can analyze the electron transitions.

For the example, I’ll show you first the HOMO-LUMO transition in the first excited state of adenine. It appears in the long list as follows:

35 -> 36         0.65024

The 0.65024 value corresponds to the transition amplitude, but it doesn’t mean anything for excited state analysis. We must calculate the NTOs of an excited state from a new Gaussian input file, requesting from the checkpoint file we used to calculate excited states. The file looks as follows:

%Oldchk=adenine.chk
%chk=adNTO1.chk
%nproc=8
%mem=1Gb

#p SP geom=allcheck guess=(read,only) density=(Check,Transition=1) pop=(minimal,NTO,SaveNTO)

I want to say some important things right here for this last file. See that no level of theory is needed, all the calculation data is requested from the checkpoint file “adenine.chk”, and saved into the new checkpoint file “adNTO1.chk”, we must use the previous calculated density and specify the transition of interest, it means the excited state we want to analyze. As we don’t need to specify charge, multiplicity or even the comment line, this file finishes really fast.

After doing this last calculation, we use the new checkpoint file “adNTO1.chk” and we format it:

formchk -3 adNTO1.chk adNTO1.fchk

If we open this formatted checkpoint file with GaussView, chemcraft or the visualizer you want, we will see something interesting by watching he MOs diagram, as follows:

We can realize that frontier orbitals shows the same value of 0.88135, which means the real transition contribution to the first excited state. As these orbitals are contributing the most, we can plot them by using the cubegen routine:

cubegen 0 mo=homo adNTO1.fchk adHOMO.cub 0 h

This last command line is for plotting the equivalent as the HOMO orbital. If we want to plot he LUMO, just change the “homo” keyword for “lumo”, it doesn’t matter if it is written with capital letters or not.

You must realize that the Natural Transition Orbitals are quite different from Molecular Orbitals. For visual comparisson, I’ve printed also the molecular orbitals, given from the optimization and from excited states calculations, without calculating NTOs:

These are the molecular frontier orbitals, plotted with Chimera with 0.02 as the isovalue for both phase spaces:

The frontier NTOs look qualitatively the same, but that’s not necessarily always the case:

If we analyze these NTOs on a hole-electron model, the HOMO refers to the hole space and the LUMO refers to the electron space.

Maybe both orbitals look the same, but both frontier orbitals are quite different between them, and these last orbitals are the ones implied on first excited state of adenine. The electron transition will be reported as follows:

If I can do a graphic summary for this topic, it will be the next one:

NTOs analysis is useful no matter if you calculate excited states by using CIS(D), EOM-CCS(D), TD-DFT, CASSCF, or any of the excited states method of your election. These NTOs are useful for population analysis in excited states, but these calculations require another software, MultiWFN is an open-source code that allows you to do this analysis, and another one is called TheoDORE, which we’ll cover in a later post.

Compound 2 represents the first structural example of a 12 e− auride complex, with a pseudohalide/hydride nature in bonding. According to our NBO calculations, this electron deficient gold center is stabilized by weak intramolecular interactions between Au p orbitals and σC−C and σC−H bonds of adjacent aromatic rings together with a Ga−Au−Ga 3 centers−2 electrons bond (I like the term ‘banana bond‘, don’t you?).

I was invited to participate in this wonderful venture by my good friend and colleague Dr. José Oscar Carlos Jiménez-Halla, from the University of Guanajuato, Mexico, with whom we’re now working with Prof. Rong Shang at the Hiroshima University. Prof. Shang has synthesized this portentous Auride complex and over the last year, Leonardo “Leo” Lugo has worked with Oscar and I in calculating their electronic structure and bonding properties.

Gold catalysis is an active area of research but low valent Au compounds are electron deficient and therefore highly reactive and elusive; that’s why researchers prefer to synthesize these compounds in situ, to harness their catalytic properties before they’re lost. Power’s digalladeltacyclane was used as a ligand framework to bind to a Au(I) center, which became reduced after the addition and breaking of the Ga−Ga bond while the opposite face of the metallic center became blocked by the bulky aromatic groups on the main ligand. NBO calculations at the M05-2X/[LANL2TZ(f),6-311G(d,p)] and QTAIM BCP analysis show the main features of Au bonding in 2, noteworthy features are the 3c−2e bond (banana) and the σC−C and σC−H donations (See figure 2).

One of the most interesting features of this compound is the fact that Au(PPh₃)Cl reacts differently to the digallane ligand than it does to analogous B−B, Si−Si, or Sn−Sn bonds. The Au−Cl bond does not undergo metathesis as with B−B, nor does it undergo an oxidative addition, so to further understand the chemistry of−and leading to−compound 2, the reaction mechanism energy profile was calculated in a rather painstakingly effort (Kudos, Leo, and a big shoutout to my friend Dr. Jacinto Sandoval for his one on one assistance). Figure 3 shows the energy profile for the reaction mechanism for the formation of 2 from Power’s digallane reagent and Au(PPh₃)Cl.

You can read more details about this research in Organometallics DOI:10.1021/acs.organomet.0c00557. Thanks again to Profs. Rong Shang and Óscar Jiménez-Halla for bringing me on board of this project and to Leo for his relentless work getting those NBO calculations done; this is certainly the beginning of a golden opportunity for us to collaborate on a remarkable field of chemistry, it has certainly made me go bananas over Aurides chemistry. OK I’ll see myself out.

The Grignard addition is one of those reactions you learn during your first year of Organic chemistry and probably the last you forget when you become a computational chemist. It was Victor Grignard who became one of the earliest Nobel Laureate in Chemistry ever, and I know it took me a while to recognize it as an organometallic reaction. But the Grignard reaction is far from simple and its versatility keeps it as a rich source of study.

This new study demonstrates that alkylmagnesium iodide (RMgI) reagents exhibit markedly higher diastereoselectivity compared to their chloride (RMgCl) or bromide (RMgBr) counterparts whenever preorganization is possible as is the case with the β-hydroxy ketones under study. Our DFT calculations at the M06-2X(SMD=CH₂Cl₂)/def2-TZVPP//M06-2X/6-31+G(d) level of theory, reveal that this halide effect is attributed to the ability of the iodide-bound magnesium species to form more Lewis acidic chelates, which in turn guide the addition reaction with greater selectivity. The resulting modified nucleosides are of great interest in medicinal chemistry, as they play crucial roles in the development of antiviral agents (e.g., against HIV and hepatitis B) and anticancer therapies. This approach could provide a high-yield pathway for producing these bioactive molecules with high diastereocontrol.

According to our energy decomposition studies, the iodide anion, more than chloride or bromide, stabilizes the key transition states via stronger electrostatic interactions, effectively lowering the activation energy of the diastereoselective pathway. Additionally, transition state geometry optimizations indicate that the iodide-bound magnesium complexes adopt a more rigid and preorganized structure, which favors selective addition on one side of the carbonyl. Population-based energy decomposition analysis confirms that electronic and steric effects synergistically contribute to the observed selectivity trends.

For more details, check out our full article in Nature Communications: “Unmasking the halide effect in diastereoselective Grignard reactions applied to C4´ modified nucleoside synthesis” DOI: https://doi.org/10.1038/s41467-025-56895-7. I’m deeply thankful to my friend Dr. Guillermo Caballero for bringing me on board of this wonderful study; I look forward to new collaborations with the group of Robert Britton at Simon Fraser University.