Ab initio study of mechanism of forming a spiro-Si-heterocyclic compound involving Ge from (CH₃)₂Ge=Si: and formaldehyde

Calculation methods

MP2/6-31G* [6] implemented in the Gaussian 98 package [7] was employed to locate all the stationary points along the reaction pathways. Full optimization and vibrational analysis were done for the stationary points on the reaction profile. Zero point energy, CCSD(T) single point energy corrections [CCSD(T)//MP2/6-31G*] and basis set superposition error (BSSE) corrections were included in the energy calculations. To explicitly establish the relevant species, the intrinsic reaction coordinate (IRC) [8, 9] was also calculated for all transition states appearing on the cycloaddition energy surface profile.

Reaction 1: the pathway to a three- membered ring product P1

Theoretical calculations show that the ground state of (CH₃)₂Ge=Si: is a singlet state. The geometrical parameters of the intermediate INT1, transition state TS1, and product P1 which appear in reaction 1 between (CH₃)₂Ge=Si: and formaldehyde are given in Figure 2. The energies are listed in Table 1, and the potential energy surface for the cycloaddition reaction is shown in Figure 3. According to Figure 3, reaction 1 consists of two steps: (i) the two reactants R1, R2 are transformed into an active intermediate INT1 in a barrier-free exothermic reaction of 28.7 kJ/mol; and (ii) intermediate INT1 isomerizes to a three-membered ring product P1 through transition state TS1 with an energy barrier of 56.0 kJ/mol.

Figure 2

Optimized MP2/6-31G* geometrical parameters and the atomic numbering for the species in cycloaddition reaction 1. Bond lengths (Å) and angles (°) are shown.

Figure 3

The potential energy surface for the cycloaddition reactions between (CH₃)₂Ge=Si: and formaldehyde calculated by using CCSD (T)//MP2/6-31G*.

Reaction 2: the pathways to a four-membered Ge-heterocyclic silylene P2, CH₃-transfer product P2.1 and H-transfer product P2.2

The geometrical parameters of transition states TS2, TS2.1, TS2.2 and products P2, P2.1, P2.2 which appear in reaction 2 between (CH₃)₂Ge=Si: and formaldehyde are given in Figure 4. The energies are listed in Table 1, and the potential energy surface for the cycloaddition reaction is shown in Figure 3. According to Figure 3, reaction 2 consists of four steps. In the first step, the two reactants R1, R2 form an intermediate INT2 in a barrier-free exothermic reaction of 22.7 kJ/mol. In the second step, the intermediate INT2 isomerizes to a four-membered Ge-heterocyclic ring silylene P2 via a transition state TS2 with an energy barrier of 2.4 kJ/mol. In the next two steps, product P2 undergoes a transfer of a CH₃ group and a H atom via transition states TS2.1 and TS2.2 with energy barriers of 128.6 and 154.3 kJ/mol, respectively, resulting in the formation of products P2.1 and P2.2. Because the energies of P2.1 and P2.2 are by 80.0 and 90.8 kJ/mol higher than that of P2, thus the transfer reactions of P2→P2.1 and P2→P2.2 are thermodynamically prohibited at normal temperature and pressure, and reaction 2 ends with product P2. Comparing reaction 2 with reaction 1, the energy barrier of TS2 is by 53.6 kJ/mol lower than that of TS1, therefore reaction 2 is the dominant reaction pathway.

Figure 4

Optimized MP2/6-31G* geometrical parameters of TS2, TS2.1, TS2.2, P2, P2.1, P2.2 and the atomic numbering for cycloaddition reaction 2. Bond lengths (Å) and angles (°) are shown.

Reaction 3: the pathway to a Ge-spiro-Si-heterocyclic ring compound P3

In reaction 3, the four-membered Ge-heterocyclic ring silylene P2 further reacts with formaldehyde (R2) to form a spiro-Si-heterocyclic compound involving Ge (P3). The geometrical parameters of the intermediate product INT3, transition state TS3, and product P3 which appear in reaction 3 are given in Figure 5. The energies are listed in Table 1, and the potential energy surface for the cycloaddition reaction is shown in Figure 3. According to Figure 3, reaction 3 involves the generation of a four-membered Ge-heterocyclic silylene P2 from the reactants R1, R2, which is followed by the reaction of P2 with formaldehyde to form an intermediate INT3 in a barrier-free exothermic reaction of 6.1 kJ/mol. Then intermediate INT3 isomerizes to a Ge-spiro-Si-heterocyclic compound P3 via a transition state TS3 with an energy barrier of 72.7 kJ/mol.

Figure 5

Optimized MP2/6-31G* geometrical parameters of INT3, TS3, P3 and the atomic numbering for cycloaddition reaction 3. Bond lengths (Å) and angles (°) are shown.

Reaction 4: the pathways to a four- membered Ge-heterocyclic silylene INT4, its isomer P4, a H-transfer product P4.1, and a CH₃-transfer product P4.2

The geometrical parameters of the four-membered Ge-heterocyclic silylene INT4, transition states TS4, TS4.1, TS4.2 and products P4, P4.1, P4.2 which appear in reaction 4 between (CH₃)₂Ge=Si: and formaldehyde are given in Figure 6. The energies are listed in Table 1, and the potential energy surface for the cycloaddition reaction is shown in Figure 3. According to Figure 3, reaction 4 consists of four steps: (i) the two reactants R1, R2 form a four-membered Ge-heterocyclic ring silylene INT4 in a barrier-free exothermic reaction of 74.4 kJ/mol; (ii) INT4 isomerizes to a distorted four-membered ring product P4 via the transition state TS4 with an energy barrier of 5.5 kJ/mol; (iii) INT4 undergoes hydrogen transfer via the transition state TS4.1 with an energy barrier of 21.1 kJ/mol, resulting in the formation of product P4.1; (iv) INT4 undergoes a transfer of a CH₃ group via the transition state TS4.2 with an energy barrier of 52.8 kJ/mol, resulting in the formation of product P4.2. Because the energy of P4.2 is by 3.0 kJ/mol higher than that of INT4, the transformation INT4→P4.2 is thermodynamically prohibited at normal temperature and pressure. The energy barrier of TS4 is by 15.6 kJ/mol lower than that of TS4.1, therefore, INT4→P4 is the dominant reaction pathway of reaction 4.

Figure 6

Optimized MP2/6-31G* geometrical parameters of INT4, TS4, TS4.1, TS4.2, P4, P4.1, P4.2 and the atomic numbering for the species in cycloaddition reaction 4. Bond lengths (Å) and angles (°) are shown.

According to Figures 3, 4, and 6 and thermodynamics formulas PT(i)=e-ΔGT(i)/RT∑ie-ΔGT(i)/RT and ΔG_T(i)=-RTlnK_i, it can be suggested that INT2 and INT4 are isomeric, R1+R2→INT2 and R1+R2→INT4 are two parallel reactions, and the equilibrium distributions of INT2 and INT4 are P_T(INT2)= K(INT2)/K(INT2)+K(INT4)≈0.0, P_T(INT4)=K(INT4)/K(INT2)+K(INT4)≈1.0, respectively. Accordingly, INT4 is the main intermediate product.

Reaction 5: the pathway to a Ge-spiro-Si-heterocyclic compound P5

In reaction 5, the four-membered Ge-heterocyclic silylene INT4 further reacts with formaldehyde (R2) to form a Ge-spiro-Si-heterocyclic compound P5. The geometrical parameters of intermediate INT5, transition state TS5, and product P5 which appear in reaction 5 are given in Figure 7. The energies are listed in Table 1, and the potential energy surface for the cycloaddition reaction is shown in Figure 3. According to Figure 3, reaction 5 involves the formation of a four-membered Ge-heterocyclic silylene INT4 from the two reactants R1, R2, followed by a barrier-free exothermic reaction of 2.1 kJ/mol with formaldehyde (R2) to form an intermediate INT5. Then the intermediate INT5 isomerizes to a Ge-spiro-Si-heterocyclic compound P5 via a transition state TS5 with an energy barrier of 18.8 kJ/mol. In a comparison of reaction 5 with reaction 4, it can be concluded that the two reactions compete mutually due to scrambling for INT4. The intermediate product INT4 can react with R2, which can reduce the system energy of 2.1 kJ/mol. In reaction 4, the energy barrier of INT4→P4 is 5.5 kJ/mol, therefore reaction 5 will be the dominant reaction pathway.

Figure 7

Optimized MP2/6-31G* geometrical parameters of INT5, TS5, P5 and the atomic numbering for cycloaddition reaction 5. Bond lengths (Å) and angles (°) are shown.

Theoretical analysis and explanation of the dominant reaction pathway

According to the analysis above, reaction 5, additionally explained in Figure 1 by reaction 5′, should be the dominant reaction channel of the cycloaddition reaction between singlet (CH₃)₂Ge=Si: (R1) and formaldehyde (R2). The frontier molecular orbitals for R2 and INT4 of this reaction are shown in Figure 8. These frontier molecular orbitals can be expressed by a schematic diagram shown in Figure 9. The mechanism of this reaction can be explained by analysis of Figures 2, 6, 7, and 9. According to Figures 2 and 6, the molecule of (CH₃)₂Ge=Si: initially interacts with formaldehyde by the [2+2] cycloaddition of the bonding π-orbitals resulting in the formation of a four-membered Ge-heterocyclic silylene INT4. Because INT4 is an active intermediate, it can further react with formaldehyde (R2) to form a spiro-Si-heterocyclic compound P5 that contains Ge. The mechanism of this reaction can be explained with Figures 7 and 9. When INT4 interacts with formaldehyde (R2), the 3p unoccupied orbital of the Si atom in INT4 will insert the π-orbital of formaldehyde from the oxygen side. Then the shift of π-electrons to the p-unoccupied orbital gives a π→p donor-acceptor bond, leading to the formation of intermediate INT5. As the reaction progresses, the angle for O(2)SiGe (INT5: 108.1°, TS5: 123.8°, P5: 219.8°) increases gradually, the angle for C(4)O(2)Si (INT5: 135.3°, TS5: 113.2°, P5: 69.5°) decreases gradually, and the length of the C(4)-O(2) bond (INT5: 1.374 Å, TS5: 1.395 Å, P5: 1.505 Å) elongates gradually. Finally, the Si atom in INT5 undergoes hybridization to the sp³ hybrid orbital after the transition state TS5, forming the more stable spiro-Si-heterocyclic compound (P5) containing Ge.

Figure 8

The frontier molecular orbitals of formaldehyde R2 and the intermediate product INT4.

Figure 9

A schematic interaction diagram for the frontier orbitals of INT4 and H₂C=O (R2).