No, seriously, why can’t orbitals be observed?

The concept of electronic orbital has become such a useful and engraved tool in understanding chemical structure and reactivity that it has almost become one of those things whose original meaning has been lost and replaced for a utilitarian concept, one which is not bad in itself but that may lead to some wrong conclusions when certain fundamental facts are overlooked.

Last week a wrote -what I thought was- a humorous post on this topic because a couple of weeks ago a viewpoint in JPC-A was published by Pham and Gordon on the possibility of observing molecular orbitals through microscopy methods, which elicited a ‘seriously? again?‘ reaction from me, since I distinctly remember the Nature article by Zuo from the year 2000 when I just had entered graduate school. The article is titled “direct observation of d-orbital holes.” We discussed this paper in class and the discussion it prompted was very interesting at various levels: for starters, the allegedly observed d-orbital was strikingly similar to a dz2, which we had learned in class (thanks, prof. Carlos Amador!) that is actually a linear combination of d(z2-x2) and d(z2-y2) orbitals, a mathematical -lets say- trick to conform to spectroscopic observations.

Pham and Gordon are pretty clear in their first paragraph: “The wave function amplitude Ψ*Ψ is interpreted as the probability density. All observable atomic or molecular properties are determined by the probability and a corresponding quantum mechanical operator, not by the wave function itself. Wave functions, even exact wave functions, are not observables.” There is even another problem, about which I wrote a post long time ago: orbitals are non-unique, this means that I could get a set of orbitals by solving the Schrödinger equation for any given molecule and then perform a unit transformation on them (such as renormalizing them, re-orthonormalizing them to get a localized version, or even hybridizing them) and the electronic density derived from them would be the same! In quantum mechanical terms this means that the probability density associated with the wave function internal product, Ψ*Ψ, is not changed upon unit transformations; why then would a specific version be “observed” under a microscope? As Pham and Gordon state more eloquently it has to do with the Density of States (DOS) rather than with the orbitals. Furthermore, an orbital, or more precisely a spinorbital, is conveniently (in math terms) separated into a radial, an angular and a spin component R(r)Ylm(θ,φ)σ(α,β) with the angular part given by the spherical harmonic functions Ylm(θ,φ), which in turn -when plotted in spherical coordinates- create the famous lobes we all chemists know and love. Zuo’s observation claim was based on the resemblance of the observed density to the angular part of an atomic orbital. Another thing, orbitals have phases, no experimental observation claims to have resolved those.

Now, I may be entering a dangerous comparison but, can you observe a 2? If you say you just did, well, that “2” is just a symbol used to represent a quantity: two, the cardinality of a set containing two elements. You might as well depict such quantity as “II” or “⋅⋅” but still cannot observe “a two”. (If any mathematician is reading this, please, be gentle.) I know a number and a function are different, sorry if I’m just rambling here and overextending a metaphor.

Pretending to having observed an orbital through direct experimental methods is to neglect the Born interpretation of the wave function, Heisenberg’s uncertainty principle and even Schrödinger’s cat! (I know, I know, Schrödinger came up with this gedankenexperiment in order to refute the Copenhagen interpretation of quantum mechanics, but it seems like after all the cat is still not out of the box!)

So, the take home message from the viewpoint in JPC is that molecular properties are defined by the expected values of a given wave function for a specific quantum mechanical operator of the property under investigation and not from the wave function itself. Wave functions are not observables and although some imaging techniques seem to accomplish a formidable task the physical impossibility hints to a misinterpretation of facts.

I think I’ll write more about this in a future post but for now, my take home message is to keep in mind that orbitals are wave functions and therefore are not more observable (as in imaging) than a partition function is in statistical mechanics.

#CompChem – Can Orbitals Be Directly Observed?


The Gossip Approach to Scientific Writing

Communication of scientific findings is an essential skill for any scientist, yet it’s one of those things some students are reluctant to do partially because of the infamous blank page scare. Once they are confronted to writing their thesis or papers they make some common mistakes like for instance not thinking who their audience is or not adhering to the main points. One of the the highest form of communication, believe it or not, is gossip, because gossip goes straight to the point, is juicy (i.e. interesting) and seldom needs contextualization i.e. you deliver it just to the right audience (that’s why gossiping about friends to your relatives is almost never fun) and you do it at the right time (that’s the difference between gossips and anecdotes). Therefore, I tell my students to write as if they were gossiping; treat your research in a good narrative way, because a poor narrative can make your results be overlooked.

I’ve read too many theses in which conclusions are about how well the methods work, and unless your thesis has to do with developing a new method, that is a terrible mistake. Methods work well, that is why they are established methods.

Take the following example for a piece of gossip: Say you are in a committed monogamous relationship and you have the feeling your significant other is cheating on you. This is your hypothesis. This hypothesis is supported by their strange behavior, that would be the evidence supporting your hypothesis; but be careful because there could also be anecdotal evidence which isn’t significant to your own as in the spouse of a friend had this behavior when cheating ergo mine is cheating too. The use of anecdotal evidence to support a hypothesis should be avoided like the plague. Then, you need an experimental setup to prove, or even better disprove, your hypothesis. To that end you could hack into your better half’s email, have them followed either by yourself or a third party, confronting their friends, snooping their phone, just basically about anything that might give you some information. This is the core of your research: your data. But data is meaningless without a conclusion, some people think data should speak for itself and let each reader come up with their own conclusions so they don’t get biased by your own vision and while there is some truth to that, your data makes sense in a context that you helped develop so providing your own conclusions is needed or we aren’t scientists but stamp collectors.

This is when most students make a terrible mistake because here is where gossip skills come in handy: When asked by friends (peers) what was it that you found out, most students will try to convince them that they knew the best algorithms for hacking a phone or that they were super conspicuous when following their partners or even how important was the new method for installing a third party app on their phones to have a text message sent every time their phone when outside a certain area, and yeah, by the way, I found them in bed together. Ultimately their question is left unanswered and the true conclusion lies buried in a lengthy boring description of the work performed; remember, you performed all that work to reach an ultimate goal not just for the sake of performing it.

Writers say that every sentence in a book should either move the story forward or show character; in the same way, every section of your scientific written piece should help make the point of your research, keep the why and the what distinct from the how, and don’t be afraid about treating your research as the best piece of gossip you’ve had in years because if you are a science student it is.


Some Comp.Chem. Tweeps

Out of some +1000 twitter accounts I follow about a quarter are related computational chemistry. The following public list isn’t comprehensive and prone to errors and contains researchers, programmers, students, journals, products and companies who gravitate around the use of in silico methods for the understanding and design of chemical and biochemical compounds.


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 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 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:


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





DSD-PBEP86 (double hybrid, DFT-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.




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.

Is #OpenAccess a first world problem?

The goal of any scientist is to generate new knowledge and then it would be a fair assumption that most scientists are inclined to share that knowledge with as many people as possible in a noble effort to improve the world in which we live; in fact, that is the very -underlying- reason why we publish articles of all our research, so every bit of knowledge generated in our labs goes not only on record but is available for testing and questioning. The Open Access (OA) supporters rightfully wish that all publications were accessible to anyone interested without having a middleman such as a big publisher controlling access and making a profit along the way.

A while ago there was a rather noble initiative in Mexico to have all publicly funded research fully available to everybody; sounds reasonable but here is the catch: Our research would have to be published in a public online platform created, managed and operated by the state with public money. This means the Mexican tax payers would have to pay not only for research to be done but to be stored and curated also. On top of that, this platform would require to become somehow visible to other researchers in other countries in order for it not only to gather attention and recognition from the larger scientific community but also to get their proper scrutiny; and that might not a be task that the state is good at doing. Furthermore, once our research is made public through this platform we might have a copyright problem when submitting it to a mainstream traditional journal with a quantifiable IF and whether we like it or not – whether we believe in it or not – IF is a quick go-to measure with which researchers are qualified by current and future employers, in fact, permanence in certain institutions as well as organizations rely on the continuous publishing of peer reviewed indexed articles.

When I started doing research here at IQ-UNAM dollars were about eleven pesos each, they are now over twenty yet my budget is still pretty much the same and is always in pesos, not dollars, so a larger gap keeps building up. So to me, paying for an OA is becoming more and more expensive everyday and although there are very prestigious, legitimate, peer reviewed, indexed OA journals the publication fee is an important factor to consider. If I indeed have the money available I may better think twice about saving it by going to a traditional journal and use it for other purposes. And in the end, fair or not, does everybody really want to read about my calculations? I really doubt so. My personal take is to publish in a traditional journal* and then blog about it in a more relaxed way here, plus making it visible in several platforms such as Mendeley, or ResearchGate and share it with others whenever possible.

It would be fairly easy to assume from the title and previous line that I oppose Open Access publications but then again that would be a wrong assumption. The broader answer is that I am for OA but that I don’t think the current scientific landscape makes it a terrific idea. First, employers would have to stop fixating in IFs and prestigious titles and then there would have to be enough money for paying OA’s or making the decision between paying the fee or using the money for other things; and that right there is what makes it a First World problem to me.

%d bloggers like this: