Winter school – Exploring reactions using static methods
Michaël addition
Date: January 2024
C. Michel
Our aim is to investigate the enantioselective Michael Addition of cyclic Ketones to nitroalkenes. This practical session refers to the experimental work published by Lu et al. in 2011 in the Journal of Organic Chemistry (here), especially regarding the numbering of the molecules.
We will use the software Gaussian (online manual). To start, our calculations will be performed at the PM6 level for the sake of efficiency. We will use B3LYP-D3 as a refinement level. The protocol to submit a calculation will be provided during the practical session. The preparation of input files and the visualisation of results can be done using Avogadro, GaussView or Molden for instance as a Graphical User Interface (GUI).
The sequence is split in four steps and is expected to take 4h00. Working as a team is encouraged.
1. Geometry Optimization of reactants and products
We start by studying the reactants and the product of the Michael addition using acetone (3) and the trans-nitrostyrene (7a) as the Michael acceptor.
- Build a possible structure for acetone (3) using a GUI (Avogadro, Molden., GaussView)
- Optimize its structures at the PM6 level using Gaussian and compute frequencies to get Gibbs free energies. Here is a typical input file structure:
#n PM6 Opt Freq [blanck line] [Title] Optimization of nitrostyren [blanck line] [Charge,Multiplicity] 0,1 [xyz formated coordinates] [blank line]
- Check the absence of an imaginary frequency using a GUI (e.g. Molden) or reading the .log file, or using a grep command) (NImag=).
- Measure few charateristic bonds and angles using a GUI. You can also find some in the .log file.
- Build at least two possible conformers of the enol of the acetone. Optimize the corresponding geometries. Measure few charateristic bonds and angles. Compare with the ones measured in acetone and discuss.
- Identify which conformer is the most stable using the electronic energy provided at the end of the .log file.
- Compute the equilibrium constant of the ceton-enolic equilibrium. Comment on the large excess of acetone that is used experimentally. The Gibbs energy is reported in the - Thermochemistry - paragraph of the .log file as the Sum of electronic and thermal Free Energies= in Hartree/particle.
- [Optionnal – work as a group] Determine the most stable conformers of the trans-nitrostyrene (7a).
- For selected cases, repeat using the redundant internal coordinates (default of Gaussian, opt) vs. cartesian coordinates (Opt=Cartesian) and compare the efficiency with the previous geometry optimization in term of number of steps and CPU usage.
- [Optionnal – work as a group] Determine the most conformer of the Michael addition product (8a).
- Determine the reaction energy of the Michael addition. Discuss the experimental results reported in Table 1 (entry 1 and entry 5).
2. Transition State search
We move to the transition state search in absence of any catalyst. We will first perform a scan along a well-chosen coordinate and consider that the structure at the highest energy is a good approximation of the TS structure, close enough to switch to a eigen-follow method to optimize the TS.
- Identify the best Michael adduct conformer in order to split the C-C bond and build the O-H bond.
- Identify the labels of the carbon atoms of the C-C bond to split, the C-H bond to split and the O-H bond to form. Be carefull, Avogadro starts counting at 0, Gaussian and Molden at 1.
- To start, we hypothesize that the reaction proceed in one step, with the H transfer being concomittant with the C-C. We also assume that it is governed by the C-C splitting. Thus, we first set a linear transit by increasing stepwise the C-C distance. You can follow this exemple that corresponds to stirring the C1-C8 distance using 2 steps of 0.15 Å. Adapt the atom labels, the number of steps and the step size! As a rule of thumb, the C-C distance will be roughly 50% longer in the TS.
#n PM6 Opt=ModRedundant C-H splitting 0,1 [bloc of xyz coordinates] 1 8 S 2 0.15
- In the .log file, you will find a summury of the linear transit providing the energy of each optimized contrained structure and the internal coordinates. You can plot the energy in function of the coordinate. You can also use Molden as a GUI to visualize the scan. Do you observe other rearrangements during the scan? Is our hypothesis correct?
- Select the structure the closest to the maximum and optimize the transition state using the TS option in opt. The calcfc option allows to compute the hessian prior starting the optimization, the calcall option allows to compute the hessian at each step. The noeigentest allows to perform the optimisation even if more than one imaginary frequency is found in the starting hessian. You can try with and without those keywords.
#n PM6 Opt=(TS,calcfc,noeigentest) freq
- Check that the structure has been optimized. Measure the C-C distance, but also the C-H and O-H bond distance. Check the number of imaginary frequencies. Visualize the corresponding mode of vibration. Does it correspond to the reaction coordinate?
- During the C-C splitting, a H should also be able to transit from the CH2 in alpha to the NO2 group to the O of the carbonyl to generate the enol. This is not described in the approximative reaction coordinate we were using here and generally not observed during the C-C scan. Consider now the C-H splitting/O-H bond formation in a linear transit starting from the Michael adduct. Do you observe a concomittent C-C? If not, you may have an intermediate. Optimize it. Find the two transition states corresponding to the C-H and the C-C splitting in a two-steps mechanism. Conclude about the mechanism.
- Determine the Gibbs free energy of activation of the Michaël addition.
3. [Optionnal] Including the catalyst
We now aim at understanding the contrasted impact of the primary amine-thiophosphoramide catalyst 2. Thanks to this amine, the ketone is turned into an enamine intermediate. A possible transition state is provided by the authors in Figure 1.
- Propose a model of 2, m2, with a limited number of atoms and degree of freedom.
- Identify the most stable conformer of the enamine intermediate using m2. Compute the Gibbs energy of reaction to generate this enamine.
- Optimize the product of the C-C coupling resulting from the addition of the enamine on the trans-nitrostyrene. Evaluate the Gibbs Energy of reaction of this coupling.
- Evaluate the activation energy of the C-C coupling in presence of the catalyst m2. Compare with the one found previously.
4. [Optionnal] Refinement
Previous calculations were using a low level of theory, sometimes a simplified model. We will investigate here how those results can be refined.
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- To refine the quality of the energies we obtained, we can start from the optimized geometries at the PM6 level and climb to the DFT level, for instance using B3LYP-D3. Here is a typical input file structure using a low quality basis set:
#n B3LYP EmpiricalDispersion=GD3 3-21G Opt Freq [blanck line] [Title] Optimization of nitrostyren [blanck line] [Multiplicity,Charge] 0,1 [xyz formated coordinates] [blank line]
- To refine the model, you can replace m2 by 2, first at the PM6 level, then at the B3LYP-D3.
- To further refine the energetic, you may also include the solvent using a polarisable continuum model adding the keyword SCRF=(Solvent=toluene) for toluene. You can also explore the effect of the solvent reported in Table 1 (entry 3 vs. 4).
- To refine the quality of the energies we obtained, we can start from the optimized geometries at the PM6 level and climb to the DFT level, for instance using B3LYP-D3. Here is a typical input file structure using a low quality basis set:
Some optimized structures in .xyz format
28 A conformer of the Michael Adduct C -2.59344 -0.95125 0.06459 C -1.36103 -1.28322 -0.76323 O -2.56951 -0.92228 1.27305 H -1.39298 -0.76402 -1.74158 C -3.84141 -0.68288 -0.72282 H -4.72864 -0.68073 -0.06950 H -3.80128 0.30807 -1.19900 H -4.01659 -1.42002 -1.51457 C -0.06641 -0.92300 -0.01005 H -1.39212 -2.36710 -0.99813 H -0.17425 -1.27046 1.06072 H -0.75739 0.80459 1.94495 C 1.12322 -1.68354 -0.62821 H 1.30711 -1.36871 -1.68034 N 2.38816 -1.46523 0.17697 H 0.91366 -2.77651 -0.64877 C 0.85857 2.63525 -1.08111 C 0.70389 1.24612 -1.11007 C 0.13256 0.57946 -0.01754 C -0.29549 1.31744 1.09706 C -0.14121 2.70546 1.12129 C 0.43799 3.36702 0.03347 H -0.47071 3.27166 1.99168 H 1.31272 3.14691 -1.92836 H 1.04010 0.68921 -1.98257 H 0.56357 4.44798 0.05604 O 3.36102 -1.07743 -0.44139 O 2.35051 -1.71597 1.36463
28 TS C-C split C -1.86606 -1.48784 0.53297 C -0.47451 -1.46107 0.52957 O -2.56932 -0.82648 1.46521 H 0.06644 -2.20416 -0.05638 C -2.75428 -2.13357 -0.44682 H -3.76073 -2.34594 -0.04523 H -2.93269 -1.42128 -1.29583 H -2.34445 -3.05703 -0.87570 C 0.01858 0.11728 -0.40846 H 0.05737 -1.25622 1.45947 H -0.31083 -0.25694 -1.40175 H 1.85883 -0.86789 -2.11379 C -0.71968 1.19519 0.11399 H -0.32553 1.85978 0.87396 N -1.97869 1.52499 -0.41672 H -2.01028 -0.19922 2.02731 C 3.48071 0.53593 1.12681 C 2.09295 0.57864 0.97189 C 1.49565 0.07308 -0.19385 C 2.30726 -0.47783 -1.20053 C 3.69474 -0.51607 -1.04276 C 4.28373 -0.01127 0.12100 H 4.31872 -0.93775 -1.82985 H 3.93803 0.93466 2.03156 H 1.47424 1.01581 1.75539 H 5.36564 -0.04094 0.24209 O -2.55727 2.53422 -0.02819 O -2.48570 0.74568 -1.24665
28 TS H transfer C 1.75077 -1.17184 0.14616 C 0.71328 -0.74000 1.17254 O 1.39972 -1.16047 -1.10364 H 1.19347 -0.55993 2.15370 C 2.85096 -2.09718 0.54392 H 3.19879 -2.69375 -0.31680 H 3.73374 -1.52867 0.89730 H 2.56301 -2.78700 1.34584 C -0.02940 0.54027 0.70414 H -0.00268 -1.57140 1.33756 H -0.02445 1.27043 1.55429 H -2.30823 1.59613 1.77177 C 0.70283 1.17146 -0.47748 H 0.15918 1.95449 -1.00703 N 2.09081 1.35954 -0.30942 H 0.74513 -0.04249 -1.29847 C -3.07018 -0.94947 -1.06377 C -1.74652 -0.67790 -0.71297 C -1.46210 0.23831 0.31128 C -2.51460 0.87993 0.97839 C -3.83942 0.60463 0.62441 C -4.11973 -0.30920 -0.39527 H -4.65384 1.10603 1.14524 H -3.28534 -1.66048 -1.86042 H -0.92689 -1.17881 -1.23667 H -5.15118 -0.52156 -0.67012 O 2.70736 2.32712 -0.68715 O 2.73145 0.35413 0.21100
28 intermediate C 1.79560 -1.02815 -0.07568 C 0.75975 -0.99735 1.04662 O 1.23050 -1.18471 -1.35471 H 1.27761 -1.15763 2.01511 C 2.88470 -2.07824 0.04001 H 3.33314 -2.26971 -0.95085 H 3.69842 -1.74272 0.69862 H 2.49549 -3.03226 0.41212 C -0.04750 0.31282 1.11661 H 0.07575 -1.86513 0.93281 H -0.20728 0.54506 2.20929 H -2.42077 -0.20026 2.34723 C 0.68917 1.48754 0.54686 H 0.17436 2.45194 0.62047 N 1.89585 1.45284 0.02481 H 0.44660 -0.59680 -1.51080 C -2.83693 0.12702 -1.50243 C -1.57383 0.27185 -0.92349 C -1.41096 0.15761 0.46381 C -2.52939 -0.10889 1.26786 C -3.79226 -0.25557 0.68704 C -3.94960 -0.13649 -0.69747 H -4.65719 -0.46163 1.31665 H -2.95411 0.22072 -2.58164 H -0.70530 0.47639 -1.55825 H -4.93464 -0.24825 -1.14712 O 2.59168 2.36516 -0.37994 O 2.57463 0.21924 -0.11482
41 2m S -3.07793 -0.88554 1.64283 P -3.12673 -0.00059 -0.09874 N -1.60542 0.77225 -0.56558 N -0.74437 -2.17513 -0.60882 C -4.34885 1.41763 -0.14081 C -3.60405 -1.08134 -1.53186 C 1.23099 1.72434 1.32043 C 2.17919 2.75066 1.35989 C 2.57227 3.39029 0.18017 C 2.01533 3.00055 -1.04226 C 1.06879 1.97382 -1.08627 C 0.67334 1.33020 0.09590 C -0.36569 0.21857 0.06980 C 0.15572 -0.99629 -0.76804 C 1.58727 -1.33040 -0.37088 C 2.61639 -1.20945 -1.31443 C 3.92972 -1.54137 -0.96807 C 4.22262 -1.99597 0.32110 C 3.19780 -2.11503 1.26581 C 1.88458 -1.78370 0.92297 H -4.30130 1.97495 -1.08164 H -5.37574 1.04259 -0.02160 H -4.17696 2.11526 0.69019 H -4.54540 -1.60922 -1.33827 H -3.68933 -0.51299 -2.46336 H -2.82269 -1.85302 -1.69109 H -1.61637 1.80858 -0.48402 H -0.54007 -0.13643 1.12817 H 0.93188 1.22886 2.24391 H 2.61319 3.05031 2.31248 H 3.31163 4.18809 0.21292 H 2.32165 3.49589 -1.96185 H 0.63554 1.66982 -2.03892 H 0.11207 -0.71352 -1.85603 H -0.30306 -3.00657 -0.99545 H -0.93757 -2.37419 0.37414 H 1.09445 -1.87369 1.66737 H 2.39808 -0.84996 -2.31852 H 4.72552 -1.44320 -1.70435 H 5.24477 -2.25411 0.58996 H 3.42353 -2.46508 2.27181
66 2m TS CC S -2.73388 -2.48499 2.63126 P -1.75174 -2.87816 1.00023 N -0.92293 -1.46032 0.34885 N 0.49223 0.87812 0.81777 C 1.42190 2.91570 -0.22833 C 2.85027 1.21822 0.93929 C -2.80374 -3.59171 -0.36714 C -0.35334 -4.09663 1.20733 C -4.17179 -0.11792 -0.27514 C -5.19381 -0.15990 -1.22872 C -4.88443 -0.31692 -2.58290 C -3.54905 -0.43466 -2.98453 C -2.52475 -0.39338 -2.03625 C -2.83476 -0.23026 -0.67756 C -1.73502 -0.21218 0.37242 C 1.59934 1.65068 0.54495 C -0.81227 1.03518 0.12003 C -1.55235 2.27410 0.59639 C -2.19790 3.08641 -0.34767 C -2.89661 4.22237 0.06927 C -2.95419 4.55318 1.42707 C -2.31531 3.74113 2.36933 C -1.61790 2.60197 1.95770 H 3.68201 1.89904 1.00657 H 2.99343 0.34727 1.55656 H 0.60774 3.54366 0.16804 H 2.32893 3.53434 -0.22793 H 1.17760 2.69922 -1.28670 H -2.22148 -3.81691 -1.26727 H -3.30297 -4.51378 -0.04048 H -3.60128 -2.88731 -0.65676 H -0.72805 -5.06275 1.57269 H 0.18766 -4.26658 0.26944 H 0.36926 -3.72963 1.95188 H -0.49127 -1.60929 -0.59740 H -2.18307 -0.08865 1.40556 H -4.41906 -0.00317 0.78216 H -6.23202 -0.07019 -0.91260 H -5.68073 -0.34759 -3.32421 H -3.30535 -0.55800 -4.03886 H -1.48216 -0.49202 -2.36008 H -0.60056 1.12046 -0.98937 H -1.12676 1.96865 2.69703 H -2.16643 2.82760 -1.40625 H -3.39998 4.84860 -0.66567 H -3.49895 5.43834 1.75000 H -2.36422 3.99249 3.42789 C 3.57443 0.28020 -0.91013 C 4.91977 -0.00958 -0.37257 C 2.69029 -0.73637 -1.21754 H 3.44064 1.26334 -1.39166 H 2.85081 -1.76892 -0.90610 H 0.60514 0.01442 1.36138 N 1.49316 -0.49867 -1.92632 O 0.72688 -1.45047 -2.13407 O 1.20507 0.64413 -2.29990 C 5.97467 0.86914 -0.68262 C 7.26318 0.61432 -0.20946 C 7.51066 -0.51091 0.58440 C 6.46508 -1.38282 0.90373 C 5.17493 -1.13570 0.42849 H 5.79048 1.74931 -1.29814 H 8.07708 1.29451 -0.45785 H 8.51643 -0.70652 0.95424 H 6.65595 -2.25714 1.52502 H 4.36259 -1.81567 0.68587
66 2m TS Htransfer S -1.59383 -4.63479 -0.76530 P -0.78305 -3.05431 0.03106 N -1.35063 -1.65916 -0.90939 N 0.29884 0.85553 -1.23820 C 0.69859 -0.58430 -3.22740 C 2.57949 0.33216 -1.72333 C 1.07173 -2.98476 -0.11048 C -1.15138 -2.78081 1.83008 C -3.23255 0.03513 1.64711 C -4.54166 0.16634 2.11841 C -5.62084 0.05278 1.23625 C -5.38768 -0.18808 -0.12143 C -4.07986 -0.31722 -0.59746 C -2.99712 -0.21015 0.28656 C -1.56741 -0.37202 -0.19821 C 1.10748 0.21351 -2.04389 C -1.18289 0.77359 -1.21017 C -1.70071 2.13363 -0.78195 C -2.49490 2.86565 -1.67771 C -2.98003 4.12494 -1.31506 C -2.67278 4.66185 -0.06072 C -1.88139 3.93346 0.83241 C -1.39622 2.67151 0.47661 H 3.17137 -0.41777 -2.28683 H 2.95266 1.32014 -2.07275 H -0.05411 -0.07337 -3.84722 H 1.53597 -0.84557 -3.88941 H 0.23178 -1.54181 -2.91297 H 1.47247 -2.03281 0.30200 H 1.53280 -3.80489 0.45814 H 1.39417 -3.08401 -1.15326 H -0.95205 -3.69279 2.41315 H -0.51864 -1.98165 2.26229 H -2.20523 -2.52070 1.99980 H -2.16592 -1.89527 -1.51907 H -0.86613 -0.29178 0.68477 H -2.39683 0.13210 2.34229 H -4.71970 0.35855 3.17600 H -6.64025 0.15224 1.60552 H -6.22662 -0.27636 -0.81033 H -3.91098 -0.50006 -1.65671 H -1.59245 0.51055 -2.22140 H -0.78799 2.11661 1.19497 H -2.74254 2.45724 -2.65536 H -3.59971 4.68831 -2.01109 H -3.05095 5.64337 0.22053 H -1.64030 4.34582 1.81270 C 2.87752 0.16533 -0.20313 C 4.36644 0.32066 0.03553 C 2.07123 1.12608 0.64267 H 2.56386 -0.88876 0.07647 H 2.47342 2.13523 0.74417 H 0.90861 1.37475 -0.23639 N 1.42100 0.61855 1.79481 O 1.01673 1.40508 2.65002 O 1.14691 -0.59455 1.85459 C 5.09591 -0.75758 0.55757 C 6.46953 -0.63261 0.78532 C 7.12439 0.56768 0.49406 C 6.39899 1.64680 -0.02138 C 5.02588 1.52589 -0.24941 H 4.59384 -1.69349 0.79884 H 7.02896 -1.47264 1.19451 H 8.19337 0.66397 0.67257 H 6.90466 2.58560 -0.24149 H 4.46729 2.37495 -0.63806
Last update : November 2023