COLOCACIÓN Y NEGOCIACIÓN DE LOS VDF

More limited set of methods and basis sets employed to study the product structures. These included G3B3, B3LYP/6-31G*, B3LYP/6-31+G**, CBS-QB3, CCSD(T)/6-311+G**, CCSD(T)/aug-cc-pvdz, MP4(sdq)/aug-cc-pvdz, MP4(sdtq)/cc- pvtz,. The more limited sets of calculations was because the stabilities of the products were of lower importance for the purpose of the study. A summary of all the predicted enthalpies and free energies is organized in all the tables with a variety of gas-phase computational approaches expressed in kcal/mol can be found in Tables 4.11,4.12, and 4.13 contains the structures located for the products with the methyl in the equatorial position and axial position, respectively. To better understand these tables the reader should refer to diagram 1.

Subsequent to determining the barriers from complexes for the formation of all potential products in the hydroboration of 3-methylcyclohexene, we want to explore in detail other possibilities to explain the experimental selectivity. So far the kinetic selectivity in hydroboration is view as the result of the two differing transition state barriers that lead to the alternative reaction products. This does not consider the fact that an exothermic association process and an entropic barrier might be involved. This was applied to this case without considering the fact that an exothermic association process with an entropic barrier might be involved.

Table 4.8. Calculated enthalpies and free energy values for 3-methylcyclohexene with methyl in axial position relative to the methyl in equatorial position.

Table 4.9. Calculated enthalpies and free energies for all structures located for the complexes formed from combining BH3 with 3-methylcyclohexene.

Table 4.10. Calculated enthalpies and free energies for transition state structures located for the reaction of BH3 with 3-methylcyclohexene with the methyl in the equatorial

Table 4.11. Calculated enthalpies and free energies for transition structures located for the products of the reaction of BH3 with 3-methylcyclohexene with the methyl in the

Table 4.12. Calculated enthalpies and free energies for product structures located for the reaction of BH3 with 3-methylcyclohexene with the methyl in the equatorial position.

Table 4.13. Calculated enthalpies and free energies for structures located for the products of the reaction of BH3 with 3-methylcyclohexene with the methyl in the axial position.

As previously found with other alkenes, there is no enthalpic barrier for formation of any of the olefin – BH3 π-complexes (4e-3 to 4e-6) from separate 3-

variational transition states for the association of BH3 with 3-methylcyclohexene to

afford the π-complexes were located by an adaptation of the "nosaddle" procedure of Truhlar and coworkers83,84. The starting point for the location of 4e-23‡ and 4e-24‡ were the lowest-energy structures found in a scan of positions with BH3 and 3- methylcyclohexene associated by separated by 5 Å (Table 4.14). From these structures, with the program PROGDYN,84 the steepest-descent paths in mass-weighted coordinates were followed in each case as described for other alkenes. The structures 4e-23‡ and 4e- 24‡ were the free-energy maximum along these paths when the free energy is graph against the B-C1 and B-C2 distance.

Table 4.14. Calculated enthalpies and free energies for the variational transition state structures located for the reaction of BH3 with 3-methylcyclohexene with the methyl in

the equatorial position.

Because variational transition states are more difficult to obtain a geometry optimization of the variational transition state was only carried out in one calculational method. The energies chosen for the discussion that follows are based on the G3B3 calculations. This choice is based on the various results observed in the propene

hydroboration study. In that case the G3B3 energy transition leading to the products Markovnikov and anti-Markovnikov were found to match quite closely with other high- level calculations, including CCSD(T) calculations employing very large basis sets. In the propene hydroboration case a more extensive computational work was straightforwardly done, including CCSD(T) with an extrapolated to infinite basis set. This was feasible due the reality that unlike in this system the computational power required was reasonable.

We were able to follow the free-energy alongside the reaction progress starting with separate starting materials. The starting materials lead to the variational transition states 4e-23‡ and 4e-24‡, and these lead 4e-3 and 4e-4. From π-complex 4e-3 the two transition structures 4e-7‡ and 4e-8‡ lead to the regioisomeric products 4e-18 and 4e-15 respectively. The ΔΔG‡ for 4e-7‡ and 4e-8‡ was predicted to be 0.0 kcal/mol, of that no selectivity would be predicted between the two products. The barrier associated with these structures form the π-complex 4e-3 is 3.6 kcal/mol. Both structures are of course higher in potential energy than 4e-3. In the case of 4e-24‡ to form π-complex 4e-4 the two transition structures 4e-9‡ _{and 4e-10}‡ _{lead to the regioisomeric products 4e-16 and}

4e-17, respectively.

The ΔΔG‡ for 4e-9‡ versus 4e-10‡ was predicted to be 0.0 kcal/mol. The barrier associated with these structures form the π-complex 4e-4 is 2.7 kcal/mol. No selectivity is predicted between the regiio isomeric product 4e-16 and 4e-17. The reaction coordinate diagram for these reactions involving they hydroboration of the equatorial methylcyclohexene as shown in Figure 4.6.

We also predicted the energies of the cis and trans attack of the BH3 to the 3-

methylcyclohexene with the methyl on the axial position, structure 4e-2. The reaction coordinate diagram for these pathways are illustrated in Figure 4.7. Because the difficulty of calculating variational transition structures were located for the axial 3- methylcyclohexene reactions. The equatorial variational transition structures 4e-23‡ and 4e-24‡ are more likely to be the ones reacting in solution. The expected variational transition state energies for these reactions are positioned qualitatively in the reaction coordinate diagrams. Based on the energies for 4e-23‡ and 4e-24‡ this is likely an underestimate of the free energy of the variational transition states from BH3 associated

to 4e-2. Graph (a) in Figure 4.5 shows the pathway of the π-complex 4e-5 leads to the two transition structures 4e-11‡ and 4e-12‡. These transition structures lead to the regioisomeric products 4e-22 and 4e-19, respectively. The ΔΔG‡ for 4e-11‡ versus 4e- 12‡ _{was predicted to be 0.5 kcal/mol. The barriers associated with these structures from}

4e-5 were 3.8 and 4.3 kcal/mol, repectively. Graph (b) illustrates the reaction coordinate diagram when the borane attacks the axial methylcyclohexene from the opposite face. This forms π-complex 4e-6. Complex 4e-6 leads to two transition structures 4e-13‡ and 4e-14‡_{. These transition structures lead to the regioisomeric products 4e-20 and 4e-21,}

respectively. The ΔΔG‡ for 4e-13‡ and 4e-14‡ was predicted to be 0.2 kcal/mol, the barrier associated with these structures from 4e-3 is between 1.4 and 1.6 kcal/mol, repectively. These approximations predict an experimental ratio representing no selectivity between C-1 and C-2 in any case. This is not in agreement with experimental

results. Importantly, no anharmonic correction has been considered for any or these predictions.

Figure 4.6. Reaction coordinate diagram for the hydroboration of equatorial 3- methylcyclohexene based on the predicted G3B3 enthalpies and free energies. (A) trans attack of the borane and (B) cis attack of the borane.

Figure 4.7. Reaction coordinate diagram for the hydroboration of axial 3- methylcyclohexene based on the predicted G3B3 enthalpies and free energies. (A) trans attack of the borane and (B) cis attack of the borane.

We hypothesize that the anharmonic correction of the energies found could give a more accurate approximation, which is expected to lead a truthful comparison of the

experimental and ratio calculated. We expect a significant impact from these corrections as we have already considered potential miscalculations in other hydroboration systems and we find second-order perturbative anharmonic contributions to the vibrational energies and entropy to impact the results due to the fact that we are predicting such small ΔΔG‡

. Also, other potential errors in the prediction of ΔΔG‡

in the hydroboration of propene with BH3 were considering, such as tunneling. Yet, in this case since the barrier associated between transition structures 4e-7‡

and 4e-8‡

was negligible, tunneling should contribute little to the rate of the anti-Markovnikov process. Any simple error of in the relative energies of the transition structures cannot be directly excluded.

We have calculated the contributions from the second-order perturbative anharmonic corrections to the vibrational energies and entropy to fix the predicted ΔG for all the barriers from π-complexes to all transition structures leading to any possible Markovnikov or anti-Markovnikov product relative to the corrected separate starting materials. The newly corrected prediction, expressed in kcal/mol, for starting material 4e-2 are listed on Table 4.8, π-complexes 4e-3 to 4e-6 are reported on Table 4.15, predictions for the transition structures 4e-7‡ to 4e-10‡ corresponding to the reaction of BH3/3-methylcyclohexene with the methyl in the equatorial position and the transition

structures 4e-11‡ _{to 4e-14}‡_{, corresponding to the reaction of BH}

3/3-methylcyclohexene

Table 4.15. Predicted free energy after anharmonic adjustment for all structures located for the complexes formed form combining BH3 with 3-methylcyclohexene with the

methyl in the axial position according to a variety of methods/basis set calculations, the energetics are relative to the starting material and expressed in kcal/mol.

Table 4.16. Calculated free energy after anharmonic adjustment for the transition state structures located for the reaction of BH3 with 3-methylcyclohexene with the methyl in

Table 4.17. Calculated free energy after anharmonic adjustment for the transition state structures located for the reaction of BH3 with 3-methylcyclohexene with the methyl in

Figure 4.8. Reaction coordinate diagram for the hydroboration of equitorial 3- methylcyclohexene based on the predicted G3B3 enthalpies and free energies after anharmonic corrections. (A) trans attack of the borane and (B) cis attack of the borane.

Figure 4.9. Reaction coordinate diagram for the hydroboration of axial 3- methylcyclohexene based on the predicted G3B3 enthalpies and free energies after anharmonic corrections. (A) trans attack of the borane and (B) cis attack of the borane.

Having properly allowed for the anharmonic adjustment we were able to establish theoretical energy differences for contrast against experimental. Restructuring, all over again, the free-energy alongside the reaction progress starting with separate starting material but now with the rationalized energies after the tuning are represented in Figures 4.8 and 4.9. Figure 4.8-a illustrates the reaction of BH3 approaching the 3-

methylcyclohexene trans to the methyl in the equatorial position. The initial barriers 4e- 23‡ _{and 4e-24}‡ _{to form 4e-3 and 4e-4 have not been changed. Now from π-complex 4e-3}

the two transition structures 4e-7‡ and 4e-8‡ lead to the regioisomeric products 4e-18 and 4e-15 respectively the barrier is calculated to be 3.8 and 4.2 kcal/mol correspondingly. The ΔΔG‡ for 4e-7‡ and 4e-8‡ was corrected to be 0.4 kcal/mol, this will theoretically represent a selectivity of 34:66 of 4e-8‡ and 4e-7‡. Both structures are of course still higher in potential energy than 4e-3. In the case of Figure 4.8-b, the reaction of BH3

approaching the 3-methylcyclohexene cis to the methyl in the equatorial, the position 4e- 24‡ to form π-complex 4e-4 was not changed. For the two transition structures 4e-9‡ and 4e-10‡ leading to the regioisomeric products 4e-16 and 4e-17 the barriers were 2.4 and 0.9 kcal/mol from π-complex 4e-4. The ΔΔG‡ _{for 4e-9}‡ _{and 4e-10}‡ _{was corrected to be}

1.4 kcal/mol, the ratio expected experimentally, according to this difference in energy will be in theory 9:91 of 4e-10‡ and 4e-9‡.

As shown in Figure 4.9, we also predicted the energies of the cis and trans attack of the BH3 to the 3-methylcyclohexene with the methyl on the axial position, structure

4e-2 after corrections. However, as in the other cases, only the variational transition structures that were more likely be the ones reacting in solution, the variational transition

structures 4e-23‡ and 4e-24‡, corresponding to the cis and trans association of BH3 and 3-

methylcyclohexene with the methyl on the equatorial position (4e-1), were located due to the time consuming process in locating these structures. Nonetheless we decided to position the more stable corresponding variational transition structures to help visualize a complete reaction coordinate for these cases, as this is an underestimate of the free energy of the variational transition states from BH3 associated to 4e-2. Figure 4.9

represents π-complex 4e-5 the two transition structures 4e-11‡ _{and 4e-12}‡ _{lead to the}

regioisomeric products 4e-22 and 4e-19 respectively after the anharmonic adjustments. The ΔΔG‡ for 4e-11‡ and 4e-12‡ was predicted, after adjustments, to be 0.6 kcal/mol, for such a small difference in energy the experimental selectivity expected for 4e-12‡ and 4e- 11‡ will be close to 27:73. The barriers associated with these structures form 4e-5 are now 5.2 and 5.8 kcal/mol. In the case of graph b in Figure 4.9, form π-complex 4e-6 the two transition structures 4e-13‡ and 4e-14‡ lead to the regioisomeric products 4e-20 and 4e-21, the ΔΔG‡ for 4e-13‡ and 4e-14‡ was calculated to be 0.1 kcal/mol, in other words the ratio calculated for 4e-14‡ and 4e-13‡ approximates a mixture of 45.5:54.5. The barriers associated with these structures form 4e-3 are approximately 2.2 and 2.3 kcal/mol.

We make out that in each and every one of the approximations for ΔΔGs‡ show the barrier for the formation of the C-2 product as lower in energy, experimentally this would predicts a ratio representing a preference in selectivity for C-2 over C-1 in every case, which is not always true for the experimental results obtained. Experimentally, C-2 was determined to be the preferred product but only in the case of the trans attack of the

BH3, which leads to the transition structure 4e-7‡. On the other hand, every experiment

performed by Brown as well as our results point at product 4e-16, formed from transition state 4e-9‡, was the least selective. This implicated that transition state theory is not adequate to predict the regioselectivity between C1 and C2 in the hydroboration of 3- methylcyclohexene with BH3.

When compared the stability of products does not match the experimental mixture of products. Products 4e-15 and 4e-17 were obtained approximately equally experimentally. Computationally, 4e-18 was found lowest in energy and very close in energy to 4e-16, 4e-18 were 4e-16 is the least favored experimentally. Yet, the lowest energy transition state was 4e-10‡, which leads to product 4e-17. The comparison of products afforded by the reactions performed and the stability of the free energy of the products were not in agreement. As a result, the experimental regioselectivity observed was not a consequence of the stability of the products.

We proposed the hydroboration of 3-methylcyclohexene with BH3 to be a case of

dynamics. Where the association barriers, the variational transition structures 4e-23‡ and 4e-24‡, may cause the formation of π-complexes to provide considerable excess energy. Thus excess energy is available for π -complex to pass to product faster that thermal equilibration with solvent. From this idea we decided to perform dynamic trajectories from the variational transition structures 4e-23‡ and 4e-24‡. Trajectories started from 4e- 23‡, did not afforded many products after 5000 fs. From 45 trajectories, 14 bounced back to starting material, 29 stayed equilibrating close to the π -complex 4e-3 and 2 formed product. The product formed corresponded to the product from the C-2 attack, product

4e-18 from transition state 4e-7‡. We explore a series of classical trajectory form variational transition structure 4e-24‡ and they were slightly more successful after 5000 fs than trajectories form variational transition structure 4e-23‡. From 93 trajectories, 24 bounced back to starting material, 55 stayed equilibrating nearby the π-complex 4e-4 and 10 trajectories formed product. The products formed corresponded to a ratio of products of 10:4 from the C-2 attack and the C-1 attack respectively, which are products 4e-16 and 4e-17. At this point an initial tendency was observed a preference for the formation of product from the C-2 attack of the BH3 in agreement with the energetics calculated.

Although the fact that initial tendencies are in agreement is not indicative that the inclination will be the same if more trajectories were consider.

More dynamic trajectories required to determine if concrete prediction of the regioselectivity in this case and to conclude it these will be in agreement with the experimental ratio of products. An influential amount of trajectories were reached due to the fact that the barriers for the formation of product are large translating in a more time consuming task. This is due the reality that unlike in other previously discussed systems the computational power required was unreasonable.

Despite this, we conclude that in this case transition state theory is not able to account for the ratio of products afforded experimentally. We strongly believe this is a case of dynamics.

Overall, for the hydroboration of internal disubstituted and trisubstituted alkenes we found an entropic association barrier for the formation of π-complex in all cases. It was determine for the internal disubstituted and trisubstituted alkenes that the formation

of such π-complex is enthalpically barrierless. Dynamics cases were establish, when the enthalpic association barrier found was the rate-limiting step and the barrier for the formation of products form π -complex were small. Various isotope effects were determined. These isotope effects were too small for the conventional mechanism to be the predominate pathway.

CHAPTER V