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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.
Stability of Unnatural DNA – @PCCP #CompChem
As is the case of proteins, the functioning of DNA is highly dependent on its 3D structure and not just only on its sequence but the difference is that protein tertiary structure has an enormous variety whereas DNA is (almost) always a double helix with little variations. The canonical base pairs AT, CG stabilize the famous double helix but the same cannot be guaranteed when non-canonical -unnatural- base pairs (UBPs) are introduced.
Figure 1
When I first took a look at Romesberg’s UBPS, d5SICS and dNaM (throughout the study referred to as X and Y see Fig.1) it was evident that they could not form hydrogen bonds, in the end they’re substituted naphtalenes with no discernible ways of creating a synton like their natural counterparts. That’s when I called Dr. Rodrigo Galindo at Utah University who is one of the developers of the AMBER code and who is very knowledgeable on matters of DNA structure and dynamics; he immediately got on board and soon enough we were launching molecular dynamics simulations and quantum mechanical calculations. That was more than two years ago.
Our latest paper in Phys.Chem.Chem.Phys. deals with the dynamical and structural stability of a DNA strand in which Romesberg’s UBPs are introduced sequentially one pair at a time into Dickerson’s dodecamer (a palindromic sequence) from the Protein Data Bank. Therein d5SICS-dNaM pair were inserted right in the middle forming a trisdecamer; as expected, +10 microseconds molecular dynamics simulations exhibited the same stability as the control dodecamer (Fig.2 left). We didn’t need to go far enough into the substitutions to get the double helix to go awry within a couple of microseconds: Three non-consecutive inclusions of UBPs were enough to get a less regular structure (Fig. 2 right); with five, a globular structure was obtained for which is not possible to get a proper average of the most populated structures.
X and Y don’t form hydrogen bonds so the pairing is pretty much forced by the scaffold of the rest of the DNA’s double helix. There are some controversies as to how X and Y fit together, whether they overlap or just wedge between each other and according to our results, the pairing suggests that a C1-C1′ distance of 11 Å is most stable consistent with the wedging conformation. Still much work is needed to understand the pairing between X and Y and even more so to get a pair of useful UBPs. More papers on this topic in the near future.
I’m putting a new blog out there
As if I didn’t have enough things to do I’m launching a new blog inspired by the #365papers hashtag on Twitter and the naturalproductman.wordpress.com blog. In it I’ll hopefully list, write a femto-review of all the papers I read. This new effort is even more daunting than the actual reading of the huge digital pile of papers I have in my Mendeley To-Be-Read folder, the fattest of them all. The papers therein wont be a comprehensive review of Comp.Chem. must-read papers but rather papers relevant to our lab’s research or curiosity.
Maybe I’ll include some papers brought to my attention by the group and they could do the review. The whole endeavor might flop in a few weeks but I want to give it a shot; we’ll see how it mutates and if it survives or not. So far I haven’t managed to review all papers read but maybe this post will prompt to do so if only to save some face. The domain of the new blog is compchemdigest.wordpress.com but I think it should have included the word MY at the beginning so as to convey the idea that it is only my own biased reading list. Anyway, if you’re interested share it and subscribe, those post will not be publicized.
Unnatural DNA and Synthetic Biology
Ever since I read the highly praised article by Floyd Romesberg in Nature back in 2013 I got really interested in synthetic biology. In said article, an unnatural base pair (UBP) was not only inserted into a DNA double strand in vivo but the organism was even able to reproduce the UBPs present in subsequent generations.
Romesberg’s Nucleosides. No Hydrogen bonding is formed between them!
Inserting new unnatural base pairs in DNA works a lot like editing a computer’s code. Inserting a couple UBPs in vitro is like inserting a comment; it wont make a difference but its still there. If the DNA sequence containing the UBPs can be amplified by molecular biology techniques such as PCR it means that a polymerase enzyme is able to recognize it and place it in site, this is equivalent to inserting a ‘hello world’ section into a working code; it will compile but it’s pretty much useless. Inserting these UBPs in vivo means that the organism is able to thrive despite the large deformation in a short section of its genetic code, but having it replicated by the chemical machinery of the nucleus is an amazing feat that only a few molecules could allow.
The ultimate goal of synthetic biology would be to find a UBP which codes effectively and purposefully during translation of DNA.This last feat would be equivalent to inserting a working subroutine in a program with a specific purpose. But not only could the use of UBPs serve for the purposes of expanding the genetic code from a quaternary (base four) to a senary (base six) system: the field of DNA origami could also benefit from having an expansion in the chemical and structural possibilities of the famous double helix; marking and editing a sequence would also become easier by having distinctive sections with nucleotides other than A, T, C and G.
It is precisely in the concept of double helix that our research takes place since the available biochemical machinery for translation and replication can only work on a double helix, else, the repair mechanisms get activated or the DNA will just stop serving its purpose (i.e. the code wont compile).
My good friend, Dr. Rodrigo Galindo and I have worked on the simulation of Romesberg’s UBPs in order to understand the underlying structural, dynamical and electronic causes that made them so successful and to possibly design more efficient UBPs based on a set of general principles. A first paper has been accepted for publication in Phys.Chem.Chem.Phys. and we’re very excited for it; more on that in a future 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:
 |
where coefficients 
are adjusted depending on the geometry of atoms i and j. The damping D3 function for is:
 |
where the values of s are adjustable parameters fit for the exchange-correlation functionals used in each calculation.
Women in #CompChem and the rest of STEM
In the past I’ve avoided this topic for various reasons. First, because I strongly believe that focusing on labels perpetuates them, and as scientists, we should always rise above them, for is science and not scientists what’s important. I remember my former PhD advisor, Prof. Cogordan, saying that “Liberties are exercised, not demanded“. Take Rosa Parks, for instance, her refusal to move to the back of the bus was an exercise of her liberty, and one that moved to a profound change, alas not without turmoil. But should I really call it a label? since it applies to roughly half the potential brain power available in the planet it then becomes a relevant question. Are equality and political correctness mutually exclusive terms?
It could be argued that I talk from a privileged position being a male scientist but since I’m a Mexican, non-white, non-US-based, male scientist those privileges are only so many.
I first began drafting this post way back before November 2016, when the misogyny displayed by a presidential candidate was in everyone’s mind to such a large extent that even when it even seemed prone to cause his demise it didn’t. The women’s march in D.C. has proven the topic to be still quite relevant though, and next April 22nd, Earth Day, a scientists march will take place to protest against policies that put science -and therefore mankind- in jeopardy. Some particular issues associated with the march will be the communication gag orders against scientific federal agencies; the consequences of the travel-ban to scientists from black-listed countries and, of course, the threat of having a misogynistic environment on the status of women in STEM careers.
Fact: There is a clear selection bias since there is still a large number disparity between men and women in academia throughout the world and since the number of academic position is growing at a much lower rate than the number of scientists competing for such positions, the race has become tighter and usually women take the worst part of the deal. There is a leaking pipeline in which women don’t reach the end of the race. I imagine in some cases it may have to do with maternity as it is still conservatively perceived by most countries but issues like harassment and condescension are not to be ignored.
Fact: Scientific curiosity is innate to all human beings -which confirms the above mentioned bias- therefore talking about encouraging young women to pursuit a career in STEM is plain stupid; they don’t need to be encouraged they must stop being discouraged somewhere along the path. The playing field for both genders should be leveled or science risks loosing half the population in these dire times in which all the brain power available is much needed. Also, I fear the continuous talk about these disadvantages could be off-putting for future generations of women who might be interested in undertaking STEM careers. Leveling the field for female and male scientists should be done and not just demanded but details about the mechanisms to accomplish it are still unclear and vary from one institution to another. Here in Mexico, for instance, all public universities have collective contracts, therefore every scientist in a given level earns as much as another in the same level. In other countries salaries are personally negotiated and therefore each scientists earnings vary, which has led to women earning less on average. Now, the ease with which levels are climbed within an institution are also a matter for debate. Does this mean that earnings and positions are the main problems women face in academia? Could they be the best starting points? Is the rate of enrollment the root of the problem? If so, are us teachers and professors to blame?
Another reason why I avoided this topic was because it would seem so patronizing on my part to give a shout-out to women whose work in computational chemistry I so much admire when I myself could only aspire to one day have work of their quality. They definitely don’t need my praises because they have well earned all our admiration. Nonetheless, here is a link to a great directory of women working in computational chemistry in which some great names are found such as Anna Krylov, Gloria Tabacchi, Romelia Salomón, Patricia Hunt, and so many more great scientists from all over the world. Here in Mexico we count with names such as Margarita Bernal, Patrizia Calaminici, Annia Galano, Estela Mayoral and so many other. It is hard to make a comprehensive list, and as I said before I could only aspire to have work with the same quality as theirs. The importance of recognizing and promoting women to take a career in computational chemistry will in short be addressed by the FemEx-NL-2017 conference next June 22nd in the Netherlands; their motto is “Promoting female excellence in theoretical and computational chemistry”, certainly a worthy and noble endeavor for a problem far from solved.
Perhaps another good reason for writing this post lies in the image below. It is a true statement but we should analyze the causality for it and fix whatever it is we’re doing wrong because it is certainly not the plumbing:
Comp. Chem. problems: no line for women’s restroom but men’s is out the door. 😦 #drugalchemy pic.twitter.com/BFlxXvd7H6
— David Mobley (@davidlmobley) May 17, 2016
I have a daughter. I want her to be able to do whatever she wants when she grows up without deterrence from unfairness. I want a world for her without labels so she never has the option of playing ‘The Woman Card’. It wouldn’t be fair for anyone around her.
This wont be the last post on this topic. Please share your views in the comments and criticism section. They are all welcome.
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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
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.
Back in Pécsi Tudomanyegyetem (Hungary)
I’m so glad to be back in Pécs, Hungary, at the lab of my good old friend Prof. Dr. Sándor Kunsági. It has been seven years since I was last here and so many things have happened and yet it feels like yesterday I was walking through these halls.
As part of an agreement between the science councils of both Mexico and Hungary, our research proposal on the development of macrocyclic-based therapeutic agents for capturing micotoxins and other molecules was selected for financing. As before, the theoretical section will be handled by us, namely to some extent by Marco Diaz as part of his BSc thesis, while the experimental part will be handled by the group from Prof. Kunsagi’s lab and Dr. Lemli Beáta‘s. I’m very excited about living for a month here in Pécs but also about having a close friend, to whom I owe so much, working with me in an experimental-theoretical project that will further advance both our researches and careers. It was in fact the work of Profs. Kunsagi here in Pécs and Silaghi in Cluj, Romania, which got me interested in the supramolecular chemistry of calixarenes.
Lets hope we can manage to keep this collaboration between our labs going on for many years to come. For the sake of humor here are some old and new photographs.
New paper in PCCP: CCl3 reduced to CH3 through σ-holes #CompChem
I found it surprising that the trichloromethyl group could be chemically reduced into a methyl group quite rapidly in the presence of thiophenol, but once again a failed reaction in the lab gave us the opportunity to learn some nuances about the chemical reactivity of organic compounds. Even more surprising was the fact that this reduction occured through a mechanism in which chlorine atoms behave as electrophiles and not as nucleophiles.
We proposed the mechanism shown in figure 1 to be consistent with the 1H-NMR kinetic experiment (Figure 2) which shows the presence of the intermediary sulfides and leads to the observed phenyl-disulfide as the only isolable byproduct. The proposed mechanism invokes the presence of σ-holes on chlorine atoms to justify the attack of thiophenolate towards the chlorine atom leaving a carbanion behind during the first step. The NMR spectra were recorded at 195K which implies that the energy barriers had to be very low; the first step has a ~3kcal/mol energy barrier at this temperature.
Figure 1 – Calculated mechanism BMK/6-31G(d,p) sigma holes are observed on Cl atoms
1H NMR of the chemical reduction of the trichloromethyl group. Sulfide 4 is the only observed byproduct
To calculate these energy barriers we employed the BMK functional as implemented in Gaussian09. This functional came highly recommended to this purpose and I gotta say it delivered! The optimized geometries of all transition states and intermediaries were then taken to an MP2 single point upon which the maximum electrostatic potential on each atom (Vmax) was calculated with MultiWFN. In figure 3 we can observe the position and Vmax value of σ-holes on chlorine atoms as suggested by the mapping of electrostatic potential on the electron density of various compounds.
We later ran the same MP2 calculations on other CCl3 groups and found that the binding to an electron withdrawing group is necessary for a σ-hole to be present. (This fact was already present in the literature, of course, but reproducing it served us to validate our methodology.)
Figure 3 – Sigma holes found on other CCl3 containing compounds
We are pleased to have this work published in PhysChemChemPhys. Thanks to Dr. Moisés Romero for letting us into his laboratory and to Guillermo Caballero for his hard work both in the lab and behind the computer; Guillermo is now bound to Cambridge to get his PhD, we wish him every success possible in his new job and hope to see him again in a few years, I’m sure he will make a good job at his new laboratory.
Quick note on WFN(X) files and MP2 calculations #G09 #CompChem
A few weeks back we wrote about using WFN(X) files with MultiWFN in order to find σ-holes in halogen atoms by calculating the maximum potential on a given surface. We later found out that using a chk file to generate a wfn(x) file using the guess=(read,only) keyword didn’t retrieve the MP2 wavefunction but rather the HF wavefunction! Luckily we realized this problem very quickly and were able to fix it. We tried to generate the wfn(x) file with the following keywords at the route section
#p guess=(read,only) density=current
but we kept retrieving the HF values, which we noticed by running the corresponding HF calculation and noticing that every value extracted from the WFN file was exactly the same.
So, if you want a WFN(X) file for post processing an MP2 (or any other post-HartreFock calculation for that matter) ask for it from the beginning of your calculation in the same job. I still don’t know how to work around this or but will be happy to report it whenever I do.
PS. A sincere apology to all subscribers for getting a notification to this post when it wasn’t still finished.
