The energy of your calculated transition state (TS) is lower than that of the reagents. That’s gotta be an error right? Well, maybe not.
Typically, in classical transition state theory, we associate the reaction barrier to the energy difference between the reaction complex and the TS, in other words, we associate the reaction barrier to the relative energy of the TS. However, this isn’t always the case, since the TS isn’t always located at the barrier, which simply may not exist or may be a submerged one, i.e. the TS relative energy is negative with respect to the reaction complex. This leads to negative activation energies, but one must bear in mind that the activation energy is not equal to the relative energy of the TS but rather to the slope of the Arrhenius plot, which in turn comes from the Arrhenius equation given below.
k = Aexp(Ea/RT) or in logarithmic form Lnk = LnA + (Ea/RT) The Arrhenius plot is then the plot of Lnk vs T-1, with slope Ea
Caution is advised since the apparent presence of such a barrier may be due to a computational artifact rather than to the real kinetics taking place, that’s why an IRC calculation must follow a TS optimization in order to verify the truthfulness of the TS; keep in mind that in classical transition state theory, we’re ‘slicing‘ a multidimensional map along a carefully chosen reaction coordinate but this choice might not entirely be the right one, or even an existing one for that matter. I also recommend to change the level of theory, reconsider the reaction complex structure (because a hidden intermediate or complex may be lurking between reactants and TS, see figure 1) and fully verifying the thermochemistry of all components involved before asserting that any given reaction under study has one of these atypical barriers.
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.
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.
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!
It is with great pleasure that I’d like to announce the thesis defense of Guillermo “Memo” Caballero and Howard Diaz who in past days became the second and third students, respectively, to get their B.Sc. degrees with theses completed at our lab. I want to publicly thank them for their hard work which hasn’t only contributed with a thesis to our library but will soon contribute with research papers to our count.
Guillermo “Memo” Caballero worked on the calculation of a reaction mechanism that cannot happen. He started as a synthetic chemist and when he hit a wall at the lab he thought computational chemistry might help him get synthesis on the right direction. He has proven now that the aromatization process of a substituted glutarimide into the corresponding pyridine can only proceed only if substituents with a very strong electron withdrawing effect are used. For two reaction mechanisms proposed, both of them intramolecular rearrangements and only one of them concerted, the calculated energy barriers to reach for the corresponding transition states (QST2 and QST3 methods used) are higher than a pyrolitic decomposition. Memo found also that the delocalization of the pi electron system and its extent goes a long way into the stabilization of the non-aromatic analogue. At first we wanted to treat this problem as a tautomeric equilibrium but since we cannot observe the aromatic tautomer there is no equilibrium and hence no tautomerism. We are still thinking how to name this correspondence between the two compounds when we submit the corresponding paper. It must be said that Guillermo graduated with the highest honors in a most deserved way.
Howard Diaz worked on the design of molecular blockers for the entrance process of the HIV-1 virus into lymphocytes through the GP120 protein. Six known blockers based on phenyl-indoyl-urea were assessed through docking, the binding site of the GP120 protein was described in terms of the interactions formed with each on these compounds and that served as the basis for what in the end came up to be a 36 compound library of blockers, whose structures were first optimized at the B3LYP/6-31G** level of theory. All the 42 blockers were docked in the binding site of the protein and a thorough conformational search was performed. From this set, lead compounds were selected in terms of their binding energies (first calculated heuristically) and further studied at the Density Functional Theory, B97D/cc-pVTZ in order to study the electronic structure of the blocker when interacting with a selection of residues at the binding site. Interaction energies calculated at the quantum level are consistent with the complex formation but since we had to cut the protein to only a few residues little correlation is found with the first calculation; this is fine and still publishable, I just wish we had a more seamless transition between heuristics and quantum chemical calculations. Wiberg indexes were very low, as consistent with a hydrophobic cavity, and delocalization energies calculated with second order perturbation theory analysis on the Natural Bond Orbitals revealed that the two most important interactions are C-H…π and Cl…π, these two were selected as key parameters in our design of new drugs for preventing the HIV-1 virus to bind lymphocytes-T; now we only need to have them synthesized and tested (anyone interested?).
Thank you guys for all your hard work, it has truly payed off. I’m completely certain that no matter what you do and where you go you will be very successful in your careers and I wish you nothing but the very best. This lab’s doors will always remain open for you.
So many events going on and so little time to blog about.
Two weeks ago, four members of this group traveled to Morelia in southern Mexico to present their research at the XIII Mexican Physical Chemistry Meeting. The next week after that, they all brought their posters back to Toluca for the internal symposium at CCIQS, where a masters student, María Eugenia, gave a small talk about her research project concerning photosynthesis in bacteria. Below, a short description of their projects is presented in order of seniority.
María Eugenia “Maru” Sandoval
Maru is working in photosynthesis of green sulfur bacteria. Her research deals with the excited states calculations at the Time Dependent DFT level for describing the first stages of photon interaction in antennae complexes of the photosystem II, namely the Fenna-Matthews-Olsen (FMO) complex, which was selected due to its relative structural simplicity over that of more evolved organisms. Maru also gave a talk at the internal Symposium back in Toluca the very next week where she got a positive feedback which will be used in her project.
One of the many strategies out there for treatment of HIV-1 infections is to block those proteins used to anchor the virus to a healthy cell. Sort of getting the virus’ hands busy so they can’t attach to a host. 60+ new compounds derived from thiourea were screened and assessed in their interactions with protein GP120, the protein to which the attachment is made, through docking and DFT calculations. Lead compounds are reported. It must be stressed that Howard got an award at CCIQS for having one of the best posters out of 70 in the entire symposium. Kudos and thanks to you, Howard! We now have some MD simulations in order.
Guillermo “Memo” Caballero
His project has some nice philosophical implications if you ask me. Memo started as an experimental chemist and when he ran into a wall trying to obtain a pyridine from the non-aromatic analogue (glutarimide), he came to our group to run some calculations and find out how to force the aromatization process, or at least rationalize if it could be performed at all. Two mechanisms were proposed and now we know that even when the reaction should be quite exothermic, the reaction barriers are too high to be overcome by conventional methods. We now need to find a way to decrease those barriers (cue transition metal simulations). So in a way we are dealing here with the mechanism of a reaction that never happens (at least in an intramolecular way), leading to a reverse reductio ad absurdum reasoning – we assumed the reaction(s) did happen and we found out why is it impossible for them to happen.
No pic. available as of yet
Luis Enrique “Kike” Aguilar
Luis continues to work with calix(n)arenes, this lab’s first love, in drug delivery systems. He is working with two drugs at once: Bosutinib and Sorafenib, second generation drugs for the treatment of Chronic Myeloid Leukemia in cases were resistance to Imatinib has been developed. One of his main goals is to find a calixarene system which is able to discriminate between Bosutinib and pseudo-bosutinib, a commercial isomer which has incorrectly been available for a few years now.
reers and the advancement of our research group. Now back to work, guys!
Theoretical evaluation of a reaction mechanism is all about finding the right transition states (TS) but there are no guarantees within the available methods to actually find the one we need. Chemical intuition in the proposal of a mechanism is paramount. Let’s remember that a TS is a critical point on a Potential Energy Surface (PES) that is a minimum in every dimension but one. For a PES with more than two degrees of freedom, a hyper-surface, envisioning the location of a TS is a bit tricky, in the case of a three dimensional PES (two degrees of freedom) the saddle point constitutes the location of the TS as depicted in figure 1 by a section of a revolution hyperboloid.
The following procedure considers gas phase calculations. Nevertheless, the use of the SCRF keyword activates the implicit solvent calculation of choice in order to evaluate to some degree the solvent influence on the reaction energetics at different temperatures with the use of the temperature keyword.
The first step consists of a high level optimization of all minimums involved, such as reagents, products and intermediates, with a subsequent frequency analysis that includes no imaginary eigenvalues.
In order to find the structures of the transition states we use in Gaussian the Synchronous Transit-guided Quasi-Newton method  through the keywords QST2 or QST3. In the former case, coordinates for the reagents and products are needed as input; for the latter keyword, coordinates for the TS structure guess is needed also.
#p opt=(qst2,redundant) m062x/6-31++G(d,p) freq=noraman Temperature=373.15 SCRF=(Solvent=Water)
Title card for reagents
Cartesian Coordinates for reagents
Title card for products
Cartesian Coordinates for products
#p opt=(qst3,redundant) m062x/6-31++G(d,p) freq=noraman Temperature=373.15 SCRF=(Solvent=Water)
Title Card for reagents
Cartesian Coordinates for reagents
Title card for products
Cartesian Coordinates for products
Title card for TS
Cartesian Coordinates for TS
NOTE: It is fundamental that the numbering order is kept constant throughout the molecular specifications of all two, or three, input structures. Hence, I recommend to build a set of molecules, save their structure, and then modified the coordinates on the same file to produce the following structure, that way the number for every atom will remain the same for every step.
As I wrote above, there are no guarantees of finding the right TS so many attempts are probably needed. Once we have the optimized structures for all the species involved in our mechanistic proposal we can plot their energies very simply with MS Excel the way we’ve previously described in this blog (reblogged from eutactic.wordpress.com)
Once we’ve succeeded in finding the structure of our TS we may run an Internal Reaction Coordinate (IRC) calculation. This calculation will connect the TS structure to those of the products and the reagents. Initial constant forces are required and these are commonly retrieved from the TS calculation checkpoint file through the RCFC keyword.
#p m062x/6-31++G(d,p) IRC=(Maxpoints=50,RCFC,phase=(2,1))Temperature=373.15 SCRF=(Solvent=Water) geom=allcheck
Finally, the IRC path can be visualized with GaussView from the Results menu. A successful IRC will link both structures along a single reaction coordinate proving that both reagents and products are linked by the obtained TS.
Hat tip to Howard Diaz who has become quite skillful in calculating these mechanisms as proven by his recent poster at the XII RMFQT a couple of weeks back. And as usual thanks to everyone who reads, comments, likes, recommends, rates and shares my silly little posts.