In addition to studying the mechanistic details of chemical reactions, ORCA can also be used to calculate precise energy barriers and thus predict reaction rates with some accuracy.
It should be clear here that it is quite difficult to compare the absolute values of the experimental energy barriers with the calculated ones. First, because these "experimental" values are never measured directly, but are obtained from measured data only after a series of assumptions.
Second, there is always a relatively large error associated with solvation unless you explicitly model the solvent. And that's to say the least if you don't also take into account conformational entropy, transfer coefficients, etc.
Case study: the Diels-Alder reaction
Still, it makes sense to comparerelativebarriers and reaction energy rates, and we show here how this can be done for a classical Diels-Alder (DA) reaction between cyclopentadiene and some dieneophiles:
This is an important reaction that preserves all atoms in the reactants and is particularly useful for synthesizing chiral compounds. Its reaction rate varies dramatically with the nature of the reactants.\(10^{-8}\)one\(10^{2}s^{-1}\) [Guo2012], and the electron-withdrawing groups on the dieneophile are known to accelerate the formation of the cyclic products:
Let's try to study the relative barrier heights for the reaction between cyclopentadiene and the above cyanide compounds usingNEB-TSMethod for finding the transition states and studying the effect of additioncorrelation energyPlease, ask.
First the transition state.
The transition state (TS) for DA reactions is not uncommon, apart from the fact that three double bonds are broken and two single bonds are formed simultaneously, which is sometimes more difficult to track with TS search algorithms than relying on a single coordinated search.
Using ORCANEB-TSmethod, the search for TS becomes much easier, with just the structures of the reactants and products. For example, to optimize them with B3LYP and a good DEF2-TZVP base, you can use:
!B3LYP D4 DEF2-SVP OPT FREC CPCM(TOLUENO)* XYZFILE 0 1 4CN_reactant.xyz
Here we use correction D4[Grimme2017]consider the scattering interaction which is crucial in this case and the CPCM solution model[Truhlar2009]include solvation effects to some extent.
After verifying that both the reactant and the product are true minima, without anynegative frequencies, the NEB-TS calculation can now be started with the optimized structures:
!B3LYP D4 DEF2-SVP NEB-TS FREQ CPCM(TOLUOL)%NEB NEB_END_XYZFILE "4CN_product_optimized.xyz"END* XYZFILE 0 1 4CN_reactant_optimized.xyz
The new keywords here are NEB-TS and FREQ in the main entry and the name of the file containing the product geometry in %NEB. If all goes well, a TS will have a single negative frequency of about\(-368cm^{-1}\)automatically finds:
Calculation of the energy barrier
With the TS and the reagent in hand, you can calculate the\(\Delta G^{\terra} = G^o_{TS} - G^o_{Reagens}\)doGibbs free energydifference between them. Here is a table summarizing the results for the three cyanides shown above:
connection | b3lyp | One acre. |
|---|---|---|
2CN | 9,90 | 17.7 |
3CN | 10.69 | 16.2 |
4C | 21.10 | 13.6 |
Well, that's not very helpful as there's no clear trend! No clear trends emerge from the B3LYP calculation, but the geometries look good and the transition states are indeed saddle points on the potential energy surface. Can we improve?
Using DLPNO-CCSD(T) to correct electronic energy
In general, DFT is known to reproduce geometries and frequencies with reasonable quality for its low cost, but the energies are definitely a weak point. And they are even worse when the system under study is outside the functional training set, which normally does not contain transition states or atypical connection situations.
There is the top levelFrom the startMethods must be used to calculate the electronic energy of these systems. Correlated methods such as CCSD(T) are non-parameterized, are based on real physical principles and must faithfully reproduce experimental results.
Using these methods along with theThe DLPNO schemedeveloped by the ORCA team allows these barriers to be calculated quickly and accurately. To calculate an accurate electron energy in this case, we could take the DFT geometry and run:
!DLPNO-CCSD(T) DEF2-TZVPP DEF2-TZVPP/C* XYZFILE 0 1 4CN_reactant_optimized.xyz
for both the reagent and the TS.
changed\(It's the}\)one\(G^o\)
Convert Electronic Energy DLPNO-CCSD(T) (\(It's the}\)) that is real\(G^o\), we need to include the vibration fixes already discussed inthermodynamicsSection. As the DFT predicts frequencies relatively well, we can use the correction obtained earlier here.
To account for solvation, we can also consider the\(\Delta G_{solv}\)presented inImplicit Solution ModelsSection calculated with DFT and add them to get a better final result\(\Delta G^{\ddaga}\):
\[\Delta G^{\ddagger}_{solv} = E_{el}(DLNPO-CC) + \Delta G_{Correction} (DFT) + \Delta G^{o_{solv} (DFT)\]
Using these results, our updated table is now:
connection | b3lyp | CCSD(T) | One acre. |
|---|---|---|---|
2CN | 9,90 | 14.71 | 17.7 |
3CN | 10.69 | 12.73 | 16.2 |
4CN | 31.10 | 9.48 | 13.6 |
And the pattern is clearly there. We can even plot a graph to show that there is indeed a linear correlation between the calculated and experimental energy barriers:
That is, we could now, in principle, use this model to predict, calculate and fit experimental reaction barriers quite accurately for unknown compounds.
Important
Again, it is highly unlikely that the predicted and measured energy barriers are the same, unless by chance. We are not necessarily calculating the same size that was measured, but there should be relationships like the one shown above.
initial structures
react 2 CN
C -3.69069 -0,24255 -3.05179C -3,57337 -0,78190 -1,82588C -4.57294 -0,54798 -0,84072norte -5.39811 -0,33921 -0,05153C -2.43977 -1,57564 -1.49371norte -1,51125 -2.22351 -1.23872C -2.11514 2,97164 -2.46395C -2.75801 2,94686 -1.10748C -1.82097 2.05962 -0,34096H -3.76291 2.51806 -1.15405H -2.80319 3,94828 -0,67099C -0,81416 1.66412 -1.13627C -0,99670 2.22898 -2.45201H -2,92766 -0,38759 -3.81222H -4.53742 0,38354 -3.32077H -1,94095 1,79488 0,69929H -2.49714 3.51913 -3.31237H -0,32049 2.07163 -3.27893H 0,01334 1.02833 -0,85638
2CN product
C -3.20025 0,72134 -2,78548C -3.00842 0,13368 -1.34492C -4.31274 -0,11620 -0,70067norte -5.34079 -0,28100 -0,18784C -2.20903 -1.10215 -1.36536norte -1.58073 -2.07860 -1.39072C -2,57948 2.13393 -2.67804C -2,95544 2.53312 -1,25252C -2.28011 1.30743 -0,61598H -4.03779 2,57885 -1.09093H -2,51589 3,48780 -0,93519C -0,88730 1.50339 -1.17636C -1,08955 1,99428 -2.51692H -2.70739 0,12618 -3.56413H -4.26210 0,80563 -3.04971H -2.31744 1.29698 0,47604H -2,88251 2.84043 -3,45175H -0,33630 2.05640 -3.28724H 0,03572 1.09522 -0,79171
3 CN react
C -3,69898 -0,23681 -3.01835C -3,57195 -0,75519 -1.78419C -4.80664 0,54628 -3,43654C -4.55433 -0,56516 -0,77237norte -5.70215 1.19542 -3,78131norte -5.35261 -0,39983 0,05254C -2.39886 -1,49200 -1,46183norte -1,42999 -2,08557 -1.22834C -2.16113 2.90081 -2.48911C -2,79788 2.88278 -1.12904C -1,84985 2.00691 -0,36196H -3.80037 2.44838 -1.16469H -2,84751 3,88655 -0,69946C -0,83661 1,62434 -1.15570C -1.03013 2.17737 -2.47476H -2,91467 -0,37452 -3,75726H -1,96469 1,74575 0,68017H -2.55493 3.43897 -3.33913H -0,34955 2.03081 -3.30051H 0,00267 1,00519 -0,87184
3CN product
C -3.21165 0,73346 -2,79907C -3.05715 0,14686 -1,35153C -4,59355 0,81756 -3.28802C -4.33041 -0,09422 -0,64696norte -5.67828 0,90014 -3,68685norte -5.32012 -0,26103 -0,06541C -2.26700 -1.09612 -1.38224norte -1.63017 -2.06502 -1.43179C -2,59535 2.15521 -2.66873C -2,94766 2.54448 -1.23191C -2.28872 1.30023 -0,62078H -4.02563 2.61090 -1.05062H -2.48524 3,48659 -0,90886C -0,89880 1,47289 -1.19641C -1.10174 2.00115 -2.52318H -2,63399 0,15306 -3.53289H -2.30987 1,27987 0,47185H -2,89272 2.88862 -3.42118H -0,36528 1,99552 -3.31368H 0,01318 1.01032 -0,84542
react 4 CN
C -3.76429 -0,37684 -3.05298C -3.60332 -0,85967 -1,80350C -4,84674 0,48726 -3.38148C -2.83647 -0,67438 -4.09120C -4.50871 -0,52662 -0,75671norte -5,72595 1.19981 -3.63289norte -2.07298 -0,91406 -4,92930norte -5.24903 -0,23911 0,08783C -2,49977 -1,69300 -1,46447norte -1,59559 -2.36605 -1.19547C -2.03189 2.63992 -2,56556C -2.72195 2.85001 -1.24813C -1,92245 1,95807 -0,34275H -3,76788 2,53469 -1.29212H -2.66422 3.89444 -0,93118C -0,93044 1.37401 -1,03374C -0,99859 1,79618 -2.41214H -2.10952 1,83559 0,71465H -0,18080 0,70157 -0,64011H -0,30576 1,47983 -3.17969H -2.31440 3.12647 -3.48834
4CN product
C -3.23690 0,57004 -2.84697C -3.10513 0,02214 -1.37198C -4.63139 0,84698 -3.24961C -2.62174 -0,28568 -3,87624C -4.40033 -0,15824 -0,68769norte -5.71978 1.10212 -3,55657norte -2.13314 -0,94274 -4.69748norte -5.40972 -0,27525 -0,12983C -2.34560 -1.23731 -1.26251norte -1.73491 -2.21857 -1.16631C -2.48050 1,94339 -2.75503C -2,88270 2.43329 -1.35852C -2.33206 1.18899 -0,65239H -3.96105 2.57301 -1.23004H -2.38120 3.36434 -1.06181C -0,90638 1.26474 -1.14799C -1,00346 1.72997 -2.50778H -2.41730 1.22638 0,43690H -0,03865 0,78453 -0,71547H -0,22189 1.63333 -3.24983H -2.68691 2,66265 -3,55212