DFT study on the gold(I)-catalyzed cycloaddition and rearrangement reactions of allene-containing allylic silyl ether

The DFT calculation at the B3LYP/B3LYP-D3(BJ) level was carried out to explore the reaction mechanism of the synthesis of spirocyclo[4,5]decane skeleton by gold-catalyzed allenyl compounds. The more accurate energy under the CH3CN solvent in the experiment is calculated by the single-point energy of the SMD model. Computational studies have shown that the reaction consists of three main steps: intramolecular cycloaddition of the end group carbon atoms of allenyl and vinyl groups, the semipinacol rearrangement process in which the four-membered ring is reconstructed into the five-membered ring, the elimination reaction releases the catalyst and obtains the product. The calculation results show that Zheng et al. reported that the gold-catalyzed synthesis reaction can easily occur under the experimental conditions due to its low activation free energy (12.07–15.49 kcal/mol). Furthermore, it was found that the MOMO(CH2)2 substituent has higher reactivity than the corresponding reactant of the phenyl substituent.


Introduction
Molecules with a spirocyclo [4,5]decane skeleton have good biological properties due to the important moiety of the quaternary carbon center, which is widely present in various pharmaceutical molecules and natural bioactive products, such as spirojatamol, erythrodiene, and cedrene [1][2][3][4][5][6]. However, the key part of the structure of the scaffold containing quaternary carbon is difficult to construct directly in the synthesis due to the large steric repulsion [7][8][9][10][11]. The development of an effective synthesis method is also one of the synthesis problems that need to be overcome, and it has also attracted a large number of chemists to carry out related research work [12][13][14][15]. Over the years, some synthetic methods have been developed and molecular functionalization studies have been carried out. Especially intramolecular cycloaddition or intermolecular cycloaddition reaction is the most common, such as intramolecular dearomatization cyclization of phenols [16], photo-induced intramolecular [2 + 2] cyclization [17], intermolecular [4 + 2] or [3 + 2] cycloaddition [18,19]. In addition, in order to further improve the reaction efficiency and enhance the diversity of product structures, transition metal catalysis and rearrangement reactions are also widely used in the synthesis of such products. The semipinacol rearrangement is also considered to be a very effective method to build a quaternary carbon skeleton through migration or recombination. Studies have reported that both vinylogous α-ketol and α-hydroxy epoxide alcohol have been used to construct spirocyclo [4.5] decane skeletons through semipinacol rearrangement [20][21][22].
In order to further explore new rearrangement modes for introducing the required functional groups more effectively, recent studies by Zheng et al. found that Au(I)-catalyzed allyl alcohol compounds (a or b) can easily undergo intramolecular cyclization/semipinacol rearrangement reaction, and high yields (95% and 65%) of spirocyclic [4.5]-decane skeleton (Scheme 1) can be generated by Au(PPh 3 )Cl catalyst in CH 3 CN solution at room temperature [23]. Based on the experimental research results of Zheng's research team, a key intermediate was given to predict the possible reaction process. In order to further explore the detailed catalytic reaction mechanism, a feasible channel was given to synthesize spirocyclo [4.5]decane skeleton of quaternary carbon center from allene-containing allylic silyl ether (Scheme 2). First, the allylic alcohols reactant (a) is activated by Au(I) + catalyst to obtain intermediate I. Then, the allene group and the terminal carbon of the vinyl group undergo intramolecular cyclization to form intermediate II. Next, a rearrangement reaction occurred on the four-membered ring in intermediate II and the corresponding five-membered ring intermediate III was formed, which is also the possible intermediate structure mentioned in the experimental report. Finally, water molecules are added to the intermediate III to obtain the final product a-p and release the gold(I) catalyst and (CH 3 CH 2 ) 3 SiOH (referred to as TESOH) molecules.
As far as we know, there is no relevant theoretical research report to explain the new gold-catalyzed synthesis of quaternary carbon-containing framework from allenes reported by Zheng and co-workers. In this article, based on the experimental phenomenon of Zheng et al., we carried out a calculation study of the density functional theory on the mechanism of the cyclization and rearrangement of allene-containing allylic silyl ether catalyzed by gold(I) catalyst. We hope to clarify the specific reaction mechanism and learn more about the factors that control the activity of this reaction through theoretical research.

Computational details
The DFT calculations [24] of all research systems are performed using Gaussian 09 software [25]. Both geometric optimization and frequency calculation are done using the B3LYP calculation method [26] of density functional theory. The def2-TZVPPD (the balanced triple-ζ valence basis set with double polarization and diffuse functions basis set) [27] is selected for the Au, while other atoms applied 6-31 + + G (d, p) basis set [28]. We also determined and verified the TS structure to correctly connect the two corresponding stable structures through IRC calculations [29]. In order to obtain the precise energy corresponding to the experimental reaction solvent system, we used B3LYP-D3(BJ) calculation method [30] and a larger basis set to recalculate the single-point energy of all optimized geometries in the corresponding experimental solvents. This is also a widely used method to obtain accurate energy in catalytic reactions [31][32][33][34]. The larger basis set of 6-311 + + G (d, p) for all atoms except for Au and the def2-TZVPPD (the balanced triple-ζ valence basis set with double polarization and diffuse functions basis set) for Au in the SMD implicit solvent environment [35] with acetonitrile (solvent = CH 3 CN, ε = 35.688) is used. The zeroth-order regular approximation (ZORA) [36] has been employed to consider the scalar relativistic effect. Unless otherwise specified, all energy values discussed in the context are relative Gibbs energy (kcal/mol) corrected by the single-point energy of solvation. The threedimensional (3D) structures were obtained directly from the calculated output using CYLview software [37].

Results and discussion
For this catalytic synthesis reaction, experimental studies have proved that Au(PPh 3 )Cl is the most effective gold catalyst. According to the experimental conditions, theoretical calculations are based on Au(PPh 3 ) + as the catalyst model, which interacts with the allene reactant a in Scheme 1 and the terminal unsaturated bond is activated to obtain the possible initial reaction complex conformation 1a-int, 1a'-int, 1a''-int, and 1a'''-int. The specific structure and energy of each conformation of reactant a are given in Fig. 1. The calculation results show that 1a-int is the lowest energy (− 2548.696908 hartree) in all conformations, and it is also the most stable skeleton in the reactant molecule a. Affected by steric hindrance and cycloaddition factors, the gold catalyst tends to attack the propadienyl group from the outer side in the same direction as MOMO(CH 2 ) 2 -to form a more stable reaction complex a-int. The frontier molecular orbital and the electrostatic potential diagram of the reaction complex 1a-int are shown in Fig. 2. 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 1aint 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 an isodensity surface, and the range from red to blue is − 0.110 to 0.110 a.u. The basic blue color in the molecule clearly shows that most of the atoms in the molecule are electropositive, only three oxygen atoms, and the π system shows weak electronegativity. In the calculation study of Fig. 1 The possible conformation of the reactant molecule a (R = MOMOCH 2 CH 2 -in Scheme 1). The energies are given in hartree this reaction process, 1a-int was used as the initial reaction complex to explore the specific reaction mechanism.

Reaction mechanism
The free energy profiles of gold(I)-catalyzed intramolecular cycloaddition and rearrangement reactions starting from reactant 1a-int are given in Fig. 3. The key geometries giving the main structural parameters are shown in Fig. 4. 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(PPh 3 ) + , elongating to 1.360 Å. From Fig. 3 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 12ats is 255.04 i cm −1 and the energy barrier of this step is 12.07 kcal/mol relative to 1a-int, and the energy of 2a-int is 2.18 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 sp 2 to sp 3 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. It 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 9.17 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 24.96 kcal/ 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 sp 3 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 hydrogen in the water molecule 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(PPh 3 ) + . The activation energy of this step is relatively low with 4.16 kcal/mol; the energy of the step of generating 4a-int is almost unchanged and only reduced by 1.93 kcal/mol. This step of the reaction is the process of combining two molecules to form a single one. The contribution of entropy to the activity should be fully considered. A more accurate energy can be obtained at 298 K by adding the correction term RT ln V m 0 = 1.89 kcal/ mol [38]. This step is almost a barrier-free process, and the activation free energy is reduced to 2.27 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 2.97 kcal/mol. Fig. 4 The optimized structures with the key bond lengths in Å for pathway a are shown in Fig. 3 Throughout the entire catalytic reaction process, the first step of the intramolecular cycloaddition process is the ratedetermining step of the entire reaction, and its energy is relatively low at 12.07 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 27.68 kcal/mol. This provides a good explanation for the detailed reaction mechanism reported by Zheng et al.

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(CH 2 ) 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 are shown in Fig. 5. The geometric structure containing the main parameters is shown in Fig. 6. In the reaction complex 1b-int, the newly formed Au-C1 bond is 0.018 Å longer than that of 1aint, while the Au-C2 bond is shorter than the corresponding one by 0.025 Å. It can be clearly seen from Fig. 5 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. The activation free energy of the three steps is 15.49, 11.52, and 4.73 kcal/ mol, respectively, which is 3.42, 2.35, and 0.57 kcal/mol higher than the activation free energy of the 1a-int reaction channel, respectively. In the last step, considering the contribution of entropy, the activation free energy is reduced to 2.84 kcal/mol, which is a barrier-free process. 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 − 28.91 kcal/mol, which is only 1.23 kcal/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(CH 2 ) 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 12.07 and 15.49 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(CH 2 ) 2 -is 3.42 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.
In order to further explore the influence of different substituents on the reactivity and construct the regularity of the structure-activity relationship. Subsequently, we selected CH 3 O-, CH 3 CO-, (CH 3 ) 2 N-, and NO 2 -groups respectively to replace the R in the reactant, which is called the reactant 1(c-f)-int. Computational studies have found that the first step of the cycloaddition reaction is the rate-determining step of the entire reaction process. A series of studies have been conducted on the reactivity of this step for reactants with different substituents. The free energies of activation are shown in Fig. 7. The barrier heights for the cycloaddition reactions increase in the order 12f-ts (7.96 kcal/mol) < 12cts (8.82 kcal/mol) < 12d-ts (9.75 kcal/mol) < 12a-ts (12.07 kcal/mol) < 12b-ts (15.49 kcal/mol) < 12e-ts (19.42 kcal/mol). The energy of the reaction is from − 4.21 to 3.44 for 2(a-f)-int. It can be seen that the first step reaction has almost no thermal effect. More importantly, our calculations show that (CH 3 ) 2 N-has a great influence on the cycloaddition barrier. In other words, NO 2 -substituted reactant 1f-int is prone to cycloaddition reactions. Studies have found that strong electron-withdrawing groups are beneficial to this type of gold-catalyzed cycloaddition reaction, while strong electron-donating groups are prone to produce higher reaction barriers, which are unfavorable for the reaction.

Conclusions
In this work, we provide detailed calculation studies and theoretical analysis of B3LYP-D3(BJ) level for the synthesis of spirocyclo [4.5]decane skeleton catalyzed by gold complexes. Detailed calculations and precise parameters of the geometry and energy of the intermediates and transition states on the reaction channel are given. Based on the experimental report of Zheng et al., the optimal reaction path of the catalytic reaction was given, including three main steps: intramolecular cycloaddition, semipinacol rearrangement, and elimination of the release catalyst. The first step of the reaction, the cycloaddition process is the rate-determining step of the entire catalytic cycle. Studies have found that this type of reaction has relatively low activation-free energy, and the reaction barrier for the product a-p is 12.07 kcal/mol. For gold catalyst substrates with two different substituents, MOMO(CH 2 ) 2 -is more reactive than phenyl. The study of reaction complexes with different substituents found that strong electron-withdrawing groups are more beneficial to this type of cycloaddition reaction. The detailed theoretical calculation results are completely consistent with the experimental phenomenon, which provides a good explanation and supplement for the experimental research.