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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:
 |
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.
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.
New paper in Tetrahedron #CompChem “Why U don’t React?”
Literature in synthetic chemistry is full of reactions that do occur but very little or no attention is payed to those that do not proceed. The question here is what can we learn from reactions that are not taking place even when our chemical intuition tells us they’re feasible? Is there valuable knowledge that can be acquired by studying the ‘anti-driving force’ that inhibits a reaction? This is the focus of a new manuscript recently published by our research group in Tetrahedron (DOI: 10.1016/j.tet.2016.05.058) which was the basis of Guillermo Caballero’s BSc thesis.
It is well known in organic chemistry that if a molecular structure has the possibility to be aromatic it can somehow undergo an aromatization process to achieve this more stable state. During some experimental efforts Guillermo Caballero found two compounds that could be easily regarded as non-aromatic tautomers of a substituted pyridine but which were not transformed into the aromatic compound by any means explored; whether by treatment with strong bases, or through thermal or photochemical reaction conditions.
These results led us to investigate the causes that inhibits these aromatization reactions to occur and here is where computational chemistry took over. As a first approach we proposed two plausible reaction mechanisms for the aromatization process and evaluated them with DFT transition state calculations at the M05-2x/6-31+G(d,p)//B3LYP/6-31+G(d,p) levels of theory. The results showed that despite the aromatic tautomers are indeed more stable than their corresponding non-aromatic ones, a high activation free energy is needed to reach the transition states. Thus, the barrier heights are the first reason why aromatization is being inhibited; there just isn’t enough thermal energy in the environment for the transformation to occur.
But this is only the proximal cause, we went then to search for the distal causes (i.e. the reasons behind the high energy of the barriers). The second part of the work was then the calculation of the delocalization energies and frontier molecular orbitals for the non-aromatic tautomers at the HF/cc-pVQZ level of theory to get insights for the large barrier heights. The energies showed a strong electron delocalization of the nitrogen’s lone pair to the oxygen atom in the carbonyl group. Such delocalization promoted the formation of an electron corridor formed with frontier and close-to-frontier molecular orbitals, resembling an extended push-pull effect. The hydrogen atoms that could promote the aromatization process are shown to be chemically inaccessible.
Further calculations for a series of analogous compounds showed that the dimethyl amino moiety plays a crucial role avoiding the aromatization process to occur. When this group was changed for a nitro group, theoretical calculations yielded a decrease in the barrier high, enough for the reaction to proceed. Electronically, the bonding electron corridor is interrupted due to a pull-pull effect that was assessed through the delocalization energies.
The identity of the compounds under study was assessed through 1H, 13C-NMR and 2D NMR experiments HMBC, HMQC so we had to dive head long into experimental techniques to back our calculations.
The “art” of finding Transition States Part 2
Last week we posted some insights on finding Transitions States in Gaussian 09 in order to evaluate a given reaction mechanism. A stepwise methodology is tried to achieve and this time we’ll wrap the post with two flow charts trying to synthesize the information given. It must be stressed that knowledge about the chemistry of the reaction is of paramount importance since G09 cannot guess the structure connecting two minima on its own but rather needs our help from our chemical intuition. So, without further ado here is the remainder of Guillermo’s post.
METHOD 3. QST3. For this method, you provide the coordinates of your reagents, products and TS (in that order) and G09 uses the QST3 method to find the first order saddle point. As for QST2 the numbering scheme must match for all the atoms in your three sets of coordinates, again, use the connection editor to verify it. Here is an example of the input file.
link 0 --blank line-- #p b3lyp/6-31G(d,p) opt=(qst3,calcfc) geom=connectivity freq=noraman --blank line-- Charge Multiplicity Coordinates of reagents --blank line— Charge Multiplicity Coordinates of products --blank line-- Charge Multiplicity Coordinates of TS --blank line---
As I previously mentioned, it happens that you find a first order saddle point but does not correspond to the TS you want, you find an imaginary vibration that is not the one for the bond you are forming or breaking. For these cases, I suggest you to take that TS structure and manually modify the region that is causing you trouble, then use method 2.
METHOD 4. When the previous methods fail to yield your desired TS, the brute force way is to acquire the potential energy surface (PES) and visually locate your possible TS. The task is to perform a rigid PES scan, for this, the molecular structure must be defined using z-matrix. Here is an example of the input file.
link 0 --blank line-- #p b3lyp/6-31G(d,p) scan test geom=connectivity --blank line-- Charge Multiplicity Z-matrix of reagents (or products) --blank line--
In the Z-matrix section you must specify which variables (B, A or D) you want to modify. First, locate the variables you want to modify (distance B, angle A, or dihedral angle D). Then modify those lines within the Z-matrix, here is an example.
B1 1.41 3 0.05 A1 104.5 2 1.0
What you are specifying with this is that the variable B1 (a distance) is going to be stepped 3 times by 0.05. Then variable A1 (an angle) is going to be stepped 2 times by 1.0. Thus, a total of 12 energy evaluations will be performed. At the end of the calculation open the .log file in gaussview and in Results choose the Scan… option. This will open a 3D surface where you should locate the saddle point, this is an educated guess, so take the structure you think corresponds to your TS and use it for method 2.
I have not fully explored this method so I encourage you to go to Gaussian.com and thoroughly review it.
Once you have found your TS structure and via the imaginary vibration confirmed that is the one you are looking for the next step is to verify that your TS connects both your reagents and products in the potential energy surface. For this, an Intrinsic Reaction Coordinate (IRC) calculation must be performed. Here is an example of the input file for the IRC.
link 0 --blank line-- #p b3lyp/6-31G(d,p) irc=calcfc geom=connectivity --blank line-- Charge Multiplicity Coordinates of TS --blank line--
With this input, you ask for an IRC calculation, the default numbers of steps are 20 for each side of your TS in the PES; you must specify the coordinates of your TS or take them from the .chk file of your optimization. In addition, an initial force constant calculation must be made. It often occurs that the calculation fails in the correction step, thus, for complicated cases I hardly suggest to use irc=calcall, this will consume very long time (even days) but there is a 95% guaranty. If the number of points is insufficient you can put more within the route section, here is such an example for a complicated case.
link 0 --blank line-- #p b3lyp/6-31G(d,p) irc=(calcall,maxpoints=80) geom=connectivity --blank line-- Charge Multiplicity Coordinates of TS --blank line--
With this route section, you are asking to perform an IRC calculation with 80 points on each side of the PES, calculating the force constants at every point. For an even complicated case try adding the scf=qc keyword in the route section, quadratic convergence often works better for IRC calculations.
The ‘art’ of finding Transition States Part 1
Guillermo Caballero, a graduate student from this lab, has written this two-part post on the nuances to be considered when searching for transition states in the theoretical assessment of reaction mechanisms. He’s been quite successful in getting beautiful energy profiles for organic reaction mechanisms, some of which have even explained why some reactions do not occur! A paper in Tetrahedron has just been accepted but we’ll talk about it in another post. I wanted Guillermo to share his insight into this hard practice of computational chemistry so he wrote the following post. Enjoy!
Yes, finding a transition state (TS) can be one of the most challenging tasks in computational chemistry, it requires both a good choice of keywords in your route section and all of your chemical intuition as well. Herein I give you some good tricks when you have to find a transition state using Gaussian 09 Rev. D1
METHOD 1. The first option you should try is to use the opt=qst2 keyword. With this method you provide the structures of your reagents and your products, then the program uses the quadratic synchronous transit algorithm to find a possible transition state structure and then optimize it to a first order saddle point. Here is an example of the input file.
link 0 --blank line-- #p b3lyp/6-31G(d,p) opt=qst2 geom=connectivity freq=noraman --blank line-- Charge Multiplicity Coordinates of reagents --blank line-- Charge Multiplicity Coordinates of products --blank line---
It is mandatory that the numbering must be the same in the reagents and the products otherwise the calculation will crash. To verify that the label for a given atom is the same in reagents and products you can go to Edit, then Connection. This opens a new window were you can manually modify the numbering scheme. I suggest you to work in a split window in gaussview so you can see at the same time your reagents and products.
The keyword freq=noraman is used to calculate the frequencies for your optimized structure, it is important because for a TS you must only observe one imaginary frequency, if not, then that is not a TS and you have to use another method. It also occurs that despite you find a first order saddle point, the imaginary frequency does not correspond to the bond forming or bond breaking in your TS, thus, you should use another method. I will give you advice later in the text for when this happens. When you use the noraman in this keyword you are not calculating the Raman frequencies, which for the purpose of a TS is unnecessary and saves computing time. Frequency analysis MUST be performed AT THE VERY SAME LEVEL OF THEORY at which the optimization is performed.
The main advantage for using the qst2 option is that if your calculation is going to crash, it generally crashes at the beginning, in the moment of guessing your transition state structure. Once the program have a guess, it starts the optimization. I suggest you to ask the algorithm to calculate the force constants once, this generally improves on the convergence, it will take slightly more time depending on the size of your structure but it pays off. The keyword in the route section is opt=(qst2,calcfc). Indeed, I hardly encourage you to use the calcfc keyword in any optimization you want to run.
METHOD 2. If method 1 does not work, my next advice is to use the opt=ts keyword. For this method, the coordinates in your input file are those for the TS structure. Here is an example of the input file.
link 0 --blank line-- #p b3lyp/6-31G(d,p) opt=ts geom=connectivity freq=noraman --blank line-- Charge Multiplicity Coordinates of TS --blank line--
The question that arises here is how should I get the coordinates for my TS? Well, honestly this is not a trivial task, here is where you use all the chemistry you know. For example, you can start with the coordinates of your reagents and manually get them closer. If you are forming a bond whose length is to be 1.5Å, then I suggest you to have that length in 1.6Å in your TS. Sometimes this becomes trial and error but the most accurate your TS structure is, based on your chemical knowledge, the easiest to find your TS will be. As another example, if you want to find a TS for a [1,5]-sigmatropic reaction a good TS structure will be putting the hydrogen atom that migrates in the middle point through the way. I have to insist, this method hardly depends on your imagination to elucidate a TS and on your chemistry background.
Most of the time when you use the opt=ts keyword the calculations crashes because of an error in the number of eigenvalues, you can avoid it adding noeigen to the route section; here is an example of the input file, I encourage you to use this method.
link 0 --blank line-- #p b3lyp/6-31G(d,p) opt=(ts,noeigen,calcfc) geom=connectivity freq=noraman --blank line-- Charge Multiplicity Coordinates of TS --blank line--
If you have problems in the optimization steps I suggest you to ask the algorithm to calculate the force constants in every step of the optimization opt=(ts,noeigen,calcall) this is quite a harsh method because will consume long computing time but works well for small molecules and for complicated TSs to find.
Another ‘tricky’ way to get your coordinates for your TS is to run the qst2 calculation, then if it fails, take the second- or the third-step coordinates and used them as a ‘pre-optimized’ set of coordinates for this method.
By the way, here is another useful trick. If you are evaluating a group of TSs, let’s say, if you are varying a functional group among the group, focus on finding the TS for the simplest case, then use this optimized TS as a template where you add the moieties and use this this method. This works pretty well.
For this post we’ll leave it up to here and post the rest of Guillermo’s tricks and advice on finding TS structures next week when we’ll also discuss the use of IRC calculations and some considerations on energy corrections when plotting the full energy profile. In the mean time please take the time to rate, like and share this and other posts.
Thanks for reading!
New Paper in JIPH – As(V)@calix[n]arenes
As part of an ongoing collaboration with the University of Arizona (UA) and the Center for Advanced Research and Studies (CINVESTAV – Saltillo), we are looking into the use of calix[n]arenes for bio-remediation agents capable to extract Arsenic (V) and (III) species from water. Water contamination by arsenic is a pressing issue in northern Mexico and the southern US, therefore any efforts aiming to their elimination has strong social and health repercussions.
As in previous studies, all calixarenes were optimized along with their corresponding guests within the cavity, namely H3AsO4, H2AsO4– and HAsO42- at the DFT level with the so-called Minnesota functionals by Truhlar and Cao, M06-2X/6-31G(d,p) level of theory. Interaction energies were calculated through the NBODel procedure. Calixarenes with R = SO3H and PO3H are the most promising leads. This study is now publishes in the Journal of Inclusion Phenomena and Macrocyclic Chemistry (DOI 10.1007/s10847-016-0617-0) as an online first article.
This article is also the first to be published by our undergraduate (and almost grad student in a month) Gustavo Mondragón who took this project on a side to his own research on photosynthesis.
Now my colleagues in Arizona and Saltillo, Prof. Reyes Sierra and Dr. Eddie López, respectively, will work on the experimental side of the project. Further calculations are being undertaken to extend this study to As(III) and to the use of other potential extracting materials such as metallic nanoparticles to which calixarenes could be covalently linked.
Comparing the Relative Stability of Non-Equivalent Molecules
How do you compare the stability of two or more compounds which differ in some central atom(s)?
If you simply calculate the energy of both compounds you get a misleading answer since the number of electrons is different from one to the next -in fact, the answer is not so much misleading as it is erroneous. Take compounds 1 and 2 shown in figure 1, for example. Compound 1 was recently synthesized characterized through X-Ray crystallography by my friend Dr. Monica Moya’s group; compound 2 doesn’t exist and we want to know why – or at least know if it is relatively unstable respect to 1.
Figure 1. Compound 1 exists but compound 2 is apparently less stable. Is it?
Although stoichiometry is the same, varying only by the substitution of Ga by Al the number of electrons is quite different. We then made the following assumption: Since the atomic radii of Ga and Al are quite similar (according to the CCDC their respective covalent radii are 122[4] and 121[3] pm), relative stability must rely on the bonding properties rendering 2 harder to obtain, at least through the method used for 1. The total energy for compound 1 was calculated at the M06-2X/6-31G(d,p) level of theory; then both Al atoms were changed by Ga and the total energy was calculated again at the same level. Separately, the energy of isolated Ga and Al atoms were calculated. Compensating the number of electrons was now a simple algebraic problem:
ΔE = E(MnBxOy) – nEM + nEM’ – E(M’nBxOy)
The absolute energy difference E1 – E2 is staggering due to the excess of 36 electrons in 2. But after this compensation procedure we now have a more reliable result of ΔE value of ca. 81 kcal/mol in favor of compound 1. In strict sense, we performed geometry optimizations at various stages: first on compound 1 to remove the distorsions due to the crystal field and then on the substituted compound 2 to make sure Ga atoms would find a right fit in the molecule but since their covalent radii are similar, no significant changes in the overall geometry were observed confirming the previous assumption.
We now have the value of the energy difference between 1 and 2 and other similar cases, the next step is to find the distal causes of the relative stability which may rely on the bonding properties of the Ga-O bond respect to the Al-O bonds.
What do you think? Is there another method you can share for tackling this problem? Please share your thoughts on the comments section.
Thanks for reading.
Singlet Fission in the Fenna-Matthews-Olson Complex – A Talk
Last week at the congress of the Mexican Society of Chemistry I presented some of our results in the study of photosynthesis. Below I embeded the talk. Unfortunately for the wider audience of this blog, the talk is in Spanish (if anyone out there is willing to make subtitles for it I’ll hire you on the spot!)
The slides are also in Spanish although they should be easier to follow for non-Spanish speakers and they are uploaded in SlideShare at this link.
A big thank you to Maria Eugenia “Maru” Sandoval for all the hard work and time invested in this project!
Thanks for clicking!
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.
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
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.
