For this catalytic synthesis reaction, experimental studies have proved that Au(PPh3)Cl is the most effective gold catalyst. According to the experimental conditions, theoretical calculations are based on Au(PPh3)+ as the catalyst model, which interacts with the allene reactant a in Scheme 1 and the terminal unsaturated bond is activated to obtain the initial reaction complex 1a-int. The frontier molecular orbital and the electrostatic potential diagram of the reaction complex 1a-int are shown in Fig. 1. It can be seen from the LUMO molecular orbital that the π electrons on the terminal C = C double bond of the allene group in the molecule 1a-int are filled on the d orbital of Au+, the π bond is activated and the electrons on the orbital have a large overlap degree. In addition, on the two molecular orbitals of HOMO and HOMO-1, the non-terminal carbon-carbon double bond in the allene group and the vinyl group in the molecule have strong π electrons, especially the vinyl group is easy to interact with activated carbon-carbon bond of the allene group undergoes an intramolecular cycloaddition reaction to complete the ring closure. The energy gap between the HOMO and LUMO orbitals of the molecule is 0.16 hartree, and the smaller energy difference helps the electron transition to complete the cyclization process. The electrostatic potential diagram clearly shows that most of the atoms in the molecule are electropositive, only three oxygen atoms and the π system show weak electronegativity. In the calculation study of this reaction process, 1a-int was used as the initial reaction complex to explore the specific reaction mechanism.
3.1 Reaction Mechanism
The free energy profiles of gold(I)-catalyzed intramolecular cycloaddition and rearrangement reactions starting from reactant 1a-int is given in Fig. 2. The key geometric geometries giving the main structural parameters are shown in Fig. 3. In 1a-int, the two new gold-carbon bonds Au-C1 and Au-C2 formed by the gold(I) ion and allene group are 2.403 and 2.276 Å respectively. The C1-C2 bond is also further activated by Au(PPh3)+, elongating to 1.360 Å. From Fig. 2 along the initial complex 1a-int, the allene group and the terminal carbon atom of the vinyl group undergo an intramolecular cycloaddition reaction through the transition state 12a-ts to form the intermediate 2a-int. At the same time, the gold atom also transferred to the middle carbon atom of the allene group. The only imaginary frequency of 12a-ts is 255.04 i cm− 1 and the energy barrier of this step is 12.42 kcal/mol relative to 1a-int, and the energy of 2a-int is 2.42 kcal/mol. In 12a-ts, the distance of the interacting C1-C3 bond is 2.075 Å, the Au atom is also completely transferred to the C2 atom and the Au-C2 bond is shortened to 2.128 Å, while the C1-C2 bond is stretched to 1.449 Å. From 1a-int to 2a-int, the unsaturated group completes the ring closure to form a cyclohexene six-membered ring structure 2a-int, and the C1 and C3 atoms are also transformed from sp2 to sp3 hybridization. The C1-C2 and C1-C3 bonds both exhibit the characteristics of a single bond, and the bond lengths in 2a-int are 1.517 and 1.563 Å respectively. However, the four-membered ring skeleton in the 2a-int structure still has certain instability. He can easily construct the four-membered ring into a more stable five-membered ring through the semipinacol rearrangement process of the transition state 23a-ts (imaginary frequency is 194.93 i cm− 1) to obtain a more stable intermediate 3a-int. The activation free energy of this step is 9.59 kcal/mol relative to the intermediate 2a-int. For 23a-ts, the C5-C6 bond tends to dissociate and stretch to 1.758 Å, and C4-C6 has a tendency to form bonds, with a bond length of 2.239 Å. The formation of 3a-int structure indicates that the rearrangement process has been completed, and its energy is reduced by 26.23kcal/mol compared to 2a-int, which is a step of strong exothermic process. The spirocyclo[4.5]decane skeleton has been initially formed in the 3a-int structure. The C4 atom transitions to the sp3 hybrid mode and the newly formed C4-C6 bond is 1.554 Å. The six-membered ring and the five-membered ring form two planes that are approximately perpendicular to each other. Then, the H+ in the water in the reaction system attacks the intermediate 3a-int through the transition state 34a-ts to obtain the intermediate 4a-int and release the catalyst Au(PPh3)+. The activation energy of this step is relatively low with 4.44 kcal/mol, The energy of the step of generating 4a-int is almost unchanged and only reduced by 1.62 kcal/mol. The only virtual frequency in 34a-ts is 768.64 i cm− 1, and its vibration mode is mainly shown in the H between Au and C2 atoms, where the Au-H and H-C2 bond lengths are 1.834 and 1.826 Å, respectively. Finally, the excess OH− in the water interacts with the intermediate 4a-int to remove the TESOH molecule to obtain the final product a-p, whose energy continues to decrease by 3.44kcal/mol.
Throughout the entire catalytic reaction process, the first step of the intramolecular cycloaddition process is the rate-determining step of the entire reaction, and its energy is relatively low at 12.42 kcal/mol. This is consistent with the experimental results that the synthesis reaction can be carried out under the reaction conditions at room temperature, and the product with a high yield of 95% can be obtained. The activation free energy of the second key step of semipinacol rearrangement is lower than that of the first step, and the reaction process of the second step is easier to complete. Moreover, the entire reaction is also an exothermic process with an exothermic amount of 28.87 kcal/mol. This provides a good explanation for the detailed reaction mechanism reported by Zheng et al.
3.2 The influence of the substituents on the reactant allenyl group
According to experimental reports, in order to further investigate the influence of substituents on the reactivity, the MOMO(CH2)2 group in the reaction substrate a was replaced by a phenyl group as a new reactant b (Scheme 1), and the reaction mechanism was studied by the same theoretical calculation method. The specific reaction process and mechanism similar to the reaction substrate a is shown in Fig. 4. The geometric structure containing the main parameters is shown in Fig. 5. In the reaction complex 1b-int, the newly formed Au-C1 bond is 0.018 Å longer than that of 1a-int, while the Au-C2 bond is shorter than the corresponding one by 0.025 Å. It can be clearly seen from Fig. 4 that starting from the complex 1b-int and going through the transition states 12b-ts, 23b-ts and 34b-ts along the reaction path, it also goes through three steps, namely intramolecular cycloaddition, semipinacol rearrangement and the elimination process of releasing the catalyst, etc. The activation free energy of the three steps is 16.79, 12.49 and 5.13kcal/mol respectively, which are 4.37, 2.90 and 0.69kcal/mol higher than the activation free energy of the 1a-int reaction channel respectively. The reaction system shows that the cycloaddition process (the first step) is still the rate-determining step of the entire catalytic reaction process, and its reaction barrier is also slightly higher than 1a-int. This reaction channel is also a strong exothermic process, and its exothermic heat is almost the same as that of the 1a-int reaction channel, its value is -29.59 kcal/mol, which is only 0.72kcal/mol higher. From the structural point of view, the basic skeleton of the intermediate and transition state structure is basically similar to that of the 1a-int reaction channel, except that the phenyl group replaces the MOMO(CH2)2- group to cause systematic changes in some parameters. The IRC calculation results confirm that 12b-ts, 23b-ts, and 34b-ts are connected to the corresponding intermediates 1b-int, 2b-int, 3b-int and 4b-int, respectively.
The Au(I)-catalyzed reaction of allene-containing allylic silyl ether to synthesize spirocyclo[4.5]decane skeleton has lower activation free energy (channels a and b are 12.42 and 16.79 kcal/mol, respectively). Moreover, the reaction barrier of intramolecular cycloaddition is higher than that of semipinacol rearrangement. However, comparing the reactivity of gold-catalyzed substrates with two different substituents, it is obvious that the activation barrier of MOMO(CH2)2- is 4.37 kcal/mol lower than that of phenyl, and it has higher reactivity. The calculated results can well support the experimental report results. The experiment shows that the yields of the two products a-p and b-p are 95% and 65%, respectively. This experimental phenomenon is also consistent with the calculation result that the product a-p has a lower activation energy, and the product b-p has a higher energy barrier.