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Dealing with Spin Contamination


Most organic chemistry deals with closed shell calculations, but every once in a while you want to calculate carbenes, free radicals or radical transition states coming from a homolytic bond break, which means your structure is now open shell.

Closed shell systems are characterized by having doubly occupied molecular orbitals, that is to say the calculation is ‘restricted’: Two electrons with opposite spin occupy the same orbital. In open shell systems, unrestricted calculations have a complete set of orbitals for the electrons with alpha spin and another set for those with beta spin. Spin contamination arises from the fact that wavefunctions obtained from unrestricted calculations are no longer eigenfunctions of the total spin operator <S^2>. In other words, one obtains an artificial mixture of spin states; up until now we’re dealing only with single reference methods. With each step of the SCF procedure the value of <S^2> is calculated and compared to s(s+1) where s is half the number of unpaired electrons (0.75 for a radical and 2.0 for triplets, and so on); if a large deviation between these two numbers is found, the then calculation stops.

Gaussian includes an annihilation step during SCF to reduce the amount of spin contamination but it’s not 100% reliable. Spin contaminated wavefunctions aren’t reliable and lead to errors in geometries, energies and population analyses.

One solution to overcome spin contamination is using Restricted Open Shell calculations (ROHF, ROMP2, etc.) for which singly occupied orbitals is used for the unpaired electrons and doubly occupied ones for the rest. These calculations are far more expensive than the unrestricted ones and energies for the unpaired electrons (the interesting ones) are unreliable, specially spin polarization is lost since dynamical correlation is hardly accounted for. The IOP(5/14=2) in Gaussian uses the annihilated wavefunction for the population analysis if acceptable but since Mulliken’s method is not reliable either I don’t advice it anyway. 

The case of DFT is different since rho.alpha and rho.beta can be separated (similarly to the case of unrestricted ab initio calculations), but the fact that both densities are built of Kohn-Sham orbitals and not true canonical orbitals, compensates the contamination somehow. That is not to say that it never shows up in DFT calculations but it is usually less severe, of course for the case of hybrid functional the more HF exchange is included the more important spin contamination may become. 

So, in short, for spin contaminated wavefunctions you want to change from restricted to unrestricted and if that doesn’t work then move to Restricted Open Shell; if using DFT you can use the same scheme and also try changing from hybrid to pure orbitals at the cost of CPU time. There is a last option which is using spin projection methods but I’ll discuss that in a following post. 

Grimme’s Dispersion DFT-D3 in Gaussian #CompChem


I was just asked if it is possible to perform DFT-D3 calculations in Gaussian and my first answer was to use the following  keyword:

EmpiricalDispersion=GD3

which is available in G16 and G09 only in revision D, apparently.

There are also some overlays that can be used to invoke the use dispersion in various scenarios:

IOp(3/74=x) Exchange and Correlation Potentials

-77

-76

-60

-59

DSD-PBEP86 (double hybrid, DFT-D3).

PW6B95-D3.

B2PLYP-D3 (double hybrid, DFT-D3).

B97-D (DFT-D3).

IOp(3/76=x) Mixing of HF and DFT.

-33 PW6B95 and PW6B95-D3 coefficients.

IOp(3/124=x) Empirical dispersion term.

30

40

50

Force dispersion type 3 (Grimme DFT-D3).

Force dispersion type 4 (Grimme DFT-D3(BJ)).

Force dispersion type 5 (Grimme D3, PM7 version).

 

The D3 correction method of Grimme defines the van der Waals energy like:

$\displaystyle E_{\rm disp} = -\frac{1}{2} \sum_{i=1}^{N_{at}} \sum_{j=1}^{N_{at...
...{6ij}} {r_{ij,{L}}^6} +f_{d,8}(r_{ij,L})\,\frac{C_{8ij}} {r_{ij,L}^8} \right ),$

where coefficients $ C_{6ij}$ are adjusted depending on the geometry of atoms i and j. The damping D3 function for is:

$\displaystyle f_{d,n}(r_{ij}) = \frac{s_n}{1+6(r_{ij}/(s_{R,n}R_{0ij}))^{-\alpha_{n}}},$

where the values of s are adjustable parameters fit for the exchange-correlation functionals used in each calculation.

Fluorescent Chemosensors for Chloride in Water – Sensors and Actuators B: Chemical


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.

Sensors

A quick look to the Frontier Molecular Orbitals (FMO’s) show that the chloride anion acts as an electron donor to the sensor.

Frontier Molecular Orbitals

Frontier Molecular Orbitals

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.

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.

jpca

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.

The Nobel Prize in Chemistry 2013


I’m quite late to jump on this wagon but nonetheless I’m thrilled about this year’s Nobel Prize in Chemistry being awarded to three awesome computational chemists: Martin Karplus (Harvard), Michael Levitt (Stanford) and Arieh Warshel (USC) for the development of computational models at the service of chemistry; most prominently, the merging of computations both at the classical . and quantum levels, the former allows for a computationally feasible calculation while the latter provides the needed accuracy for the description of a chemical process.

Nobel Laureates in Chemistry 2013 (source: NBC.com)

Nobel Laureates in Chemistry 2013 (source: NBC.com)

As a computational chemist myself I must say that, at some level, it feels as some sort of vindication of the field, which makes me wonder if it indeed needs it, I don’t think so but maybe some might. Last week, Nobel week, I attended a symposium on the Advances in Quantum Chemical Topology where big names such as Paul Ayers, Paul Popelier and Chérif Matta among many others participated along with my friends and colleagues from CCIQS, Fernando Cortés (whom actually organized the whole thing! Kudos, Fer!) and Vojtech Jancik who contributed to the experimental (X-ray diffraction methods) part of the symposium. Surprisingly nobody at the conferences mentioned the Nobel Prize! Not even during the round table discussion titled “The Future of Quantum Chemical Topology“. At some point during this discussion the issue of usefulness came out. I  pointed out chemists have this inherent need of feeling useful, including computational chemists, as opposed to physicists of any denomination. Computational or theoretical chemists try to be like physicists yet still have chemistry behavior baggage. Even more baffling is the fact that at such an abstract conference usefulness is discussed, yet those theoretical chemists who do not develop new methods, nor dwell into equations or propose new Hamiltonians, but rather make use of well established methodologies for tackling and solving particular problems in chemistry become somewhat ostracized by the theoretical chemistry community*.

Much controversy among the comp.chem. community was aroused by this much deserved award (try reading the comment section on this post by the great Derek Lowe at In The Pipeline). Here in Mexico we have a saying: “Ni son todos los que están ni están todos los que son” which is hard to translate given the two different meanings of the verb To Be, but it can be roughly translated as “Not all the ones who should be are present, nor the ones that are present are all that should be“, or something like that. Of course there are many other computational chemists that are left behind from this prestigious prize, but the contributions of Karplus, Levitt and Warshel to chemistry through the use of computational chemistry can be denied. In fact this does vindicate the field of comp.chem. by acknowledging the importance of modelling in molecular design and reactivity understanding.

Congratulations from a Mexican fan to Professors Karplus, Levitt and Warshel for the most deserved Nobel Prize in Chemistry 2013!

PS a much better post on this topic can be found at the curious wavefunction.

Thanks for reading, liking, rating and commenting

*Of course this is just my opinion and views (which is redundant to state since this is my very own blog!)

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