Hello there,
I have completed dynamic 1H NMR experiments to study a reaction in DMSO. I have obtained my rates and rate constants for various temperatures and calculated the thermodynamic parameters for my second order reaction which is an SN2 reaction.
I have computed at DFT/B3LYP/6-311++g(d,p)/GD3 in DMSO (PCM) in Gaussian a scan which follows the reactants through the TS to the product. From this I have :
i) separate reagents, A and B
ii) the pre-reactive complex, A+B
iii) the TS, AB‡ (using QST3 and berny optimization, followed by IRC to confirm the reactants and products)
I calculated the rate constant using the following equation:
k=(kb·T)/h * EXP (-ΔG‡/RT)
I have two issues. The first is the above equation has units of s-1 and not M-1 s-1 for a second order reaction. Often it is stated in textbooks to include a unit conversion of 1/c0 where c0 has units of M using the equation below
k=(kb·T)/h *1/c0* EXP (-ΔG‡/RT)
But I'm not sure if this c0 was suppose to carry a value different from 1M.
The second issue is that the calculated rate constant I obtain is larger than my experimental value of 7.3 × 10−3 M-1 s-1. I have tried using the ΔG‡ as the difference between:
i) the TS and pre-reactive complex, but this results in an extremely large rate constant (1.33 × 102),
ii) the TS and separate reagents, much better approximation but still larger (1.24 × 10−2).
How do I match the theoretically calculated rate constant to experimental value with units of M-1 s-1. Is there a conversion I need to do or a different equation I need to use?
I’d appreciate any help, thank you in advance
Dear Dominique,
Note that the second-order rate constant for a bimolecular reaction reads:
Gas phase: K=[KbT/h](RT/P0) [exp(-deltaG/RT)]; P0=1atm
Solution phase: K=[KbT/hC0][exp(-deltaG/RT); C0=1mol/l
So, your formula is correct.
In addition, we can never expect that a computational quantity becomes quite identical with an experimental one. We should try to be close to the experimental quantity as much as possible with the improve the level of computations.
1- Since electronic energy has the most contribution in G, I suggest you to improve value of delta_E(ele) through single point calculation employing more accurate levels. For example: DLPNO-CCSD(T)/aug-cc-pVTZ. This level of computation is not available in Gaussian but you can perform that using Orca. If, due to presence specific elements, you cannot employ this basis set, you can try def2-TZVPP which cover almost the whole periodic table.
2- Moreover, there is a very important point which, unfortunately, is not considered by the most researchers. Indeed, in a solution phase, a correcting term should be added to the G. This correcting term which corresponds to the change in G due to variation of concentration from gas phase standard state (1atm) to the solution phase standard state (1M) is: RTln(RT/P). This value at 298.15K becomes 3.012*10^-3 a.u. or 1.89 kcal/mol. Thus, for a bimolecular reaction, when you calculate ΔG‡ using data extracted from Gaussian output files, you should correct this value as:
ΔG‡-1.89
Note that 1.89 is in kcal/mol; thus, ΔG‡ should also be computed in kcal/mol. This correction can considerably affect value of ΔG‡!
I hope you find these explanations helpful.
Sincerely,
Saeed
Dear Saeedreza Emamian and Morteza Jamshidi
Thank you both for your input, I really appreciate it.
Saeedreza Emamian, I'm aware of the 1 atm standard state in the Gaussian calculation and I was wondering if this would be of concern, followed by the contribution of low vibrational frequencies, which I have tried to correct for as well by setting those below 100 cm-1 to 100 cm-1. Both have not lead to great improvement of my calculated values. I will try Orca as you have suggested. I have never used the program before, but always keen to learn something new especially if might help. Thank you for also giving insight into the basis sets I can test.
Morteza Jamshidi, I will try go though the IOP's. That is completely new to me, and thank you for pointing it out!
Thank you again to both of you for answering my question!
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