English

• 1. INTRODUCTION

  The unsaturated olefins of main group IV elements (C, Si, Ge, Sn) are all active intermediates^[1-6], and their cycloaddition reaction has been studied^[7-12]. With the progress of these studies, researches on unsaturated stannylene have been mentioned on the agenda. At present, Bundhun et al. have conducted very good research on unsaturated stannylene^[13], but there is no report about cycloaddition reactions of X₂Ge=Sn: (X = H, Me, F, Cl, Br, Ph, Ar···) till now. The X₂Ge=Sn: (X = H, Me, F, Cl, Br, Ph, Ar···) are new chemical species and new study field of stannylene chemistry. In particular, the study on the mechanism of their cycloaddition reaction is rare. To explore the rules of cycloaddition reaction between X₂Ge=Sn: and the symmetric π-bonded compounds, Me₂Ge=Sn: and ethylene were selected as model molecules in this paper, and the cycloaddition reaction mechanism was investigated and analyzed theoretically. The research result indicates the laws of cycloaddition reaction between X₂Ge=Sn: and the symmetric π-bonded compounds, which are significant for the synthesis of small-ring with Ge and Sn as well as the Ge-heterocyclic spiro-Sn-heterocyclic ring compound. The study extends the research area and enriches the research content of stannylene chemistry.

  2. CALCULATION METHODS

  We used the method of second-order perturbation theory (MP2)^[14] and Gaussian 09 package to optimize the structure of Me₂Ge=Sn: and its cycloaddition reaction with ethylene. Its transition state forms at the MP2/GENECP(C, H, Ge in 6-311++G**; Sn in LanL2dz) theory level. In order to further confirm the correctness of the relevant species and get the thermodynamic function for the species, vibration analysis is included. Finally, the intrinsic reaction coordinate (IRC)^{[15, 16]} is also calculated for all the transition states to determine the reaction paths and directions.

  3. RESULTS AND DISCUSSION

  Theoretical calculation shows that the ground state of Me₂Ge=Sn: (R1) is a singlet state, and its cycloaddition reaction with ethylene (R2) has the following two possible ways:

  (1)

  (2)

  The geometrical parameters of the intermediates (INT1, INT2), transition states (TS1, TS2) and products (P1, P2) which appear in the above two reactions are given in Fig. 1. The energies are listed in Table 1, and the entropy, enthalpy and Gibbs free energy are given in Table 2. The potential energy profiles of these two reactions are shown in Fig. 2.

  Figure 1

  

  Figure 1.  Optimized MP2/GENECP(C, H, Ge in 6-311++G**; Sn in LanL2dz) geometrical parameters and the atomic numbering for the species in cycloaddition reaction between Me₂Ge=Sn: and ethylene. Bond lengths in angstroms and bond angles in degree

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  Table 1

  

  Table 1.  Electronic Structure Energies (E_ese, in a.u) and Relative Energies (E_R, in kJ/mol)for the Species from MP2/GENECP (C, H, Ge in 6-311++G**; Sn in LanL2dz) Method at 298 K and 101325 Pa

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  Reaction		Species		MP2/GENECP
  				Eese	ER
  a Reaction (1)		R1 + R2		–2236.73989	0.0
  		INT1		–2236.77185	–83.9
  		TS1 (INT1-P1)		–2236.77116	–82.1
  		P1		–2236.79498	–144.6
  b Reaction (2)		P1 + R2		–2315.14151	0.0
  		INT2		–2315.16208	–54.0
  		TS2(INT2-P2)		–2315.14646	–13.0
  		P2		–2315.14871	–18.9
  aER = Eese－Eese, (R1 + R2), bER = Eese－Eese (P1+R2)

  Table 2

  

  Table 2.  Entropy (S, in a.u), Enthalpy (H, in a.u) and Gibbs Free Energy (G, in a.u) for the Species from MP2/GENECP(C, H, Ge in 6-311++G**; Sn in LanL2dz) Methods at 298 K and 101325 Pa

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  Reaction		Species		H/a.u		S/a.u		G/a.u
  Reaction (1)		R1 + R2		–2236.60272		2.29531 × 10–4		–2236.60272
  		INT1		–2236.63303		1.70226 × 10–4		–2236.68380
  		TS1 (INT1-P1)		–2236.63348		1.58468 × 10–4		–2236.68074
  		P1		–2236.65622		1.61005 × 10–4		–2236.70425
  Reaction (2)		P1 + R2		–2314.94790		2.44631 × 10–4		–2315.02087
  		INT2		–2314.96585		1.84860 × 10–4		–2315.02099
  		TS2(INT2-P2)		–2314.95167		1.77660 × 10–4		–2315.00456
  		P2		–2314.95294		1.84240 × 10–4		–2315.00790

  Figure 2

  

  Figure 2.  Potential energy surface for the cycloaddition reactions between Me₂Ge=Sn: and ethylene with MP2/GENECP(C, H, Ge in 6-311++G**; Sn in LanL2dz)

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  The unique imaginary frequency of transition states TS1 and TS2 through vibrational analysis is 61.5 and 66.2 i·cm^-1, so they can be affirmed as the real ones. IRC (with the step-length of 0.1 amu^–1/2⋅bohr) analysis confirms that TS1 connects with INT1 and P1, while TS2 connects with INT2 and P2.

  According to Fig. 2, reaction (1) consists of two steps. The first one is that two reactants (R1, R2) form an intermediate (INT1). According to Fig. 2 and Table 2, this is a barrier-free exothermic reaction, and the molar constant volume heat of reaction (Δ_rU_m) and molar heat of reaction (Δ_rH_m) at normal temperature and pressure are –83.9 and –79.6 kJ/mol, and the molar Gibbs free energy of reaction (Δ_rG_m) is –212.9 kJ/mol. The second is that the INT1 isomerizes into a four-membered Ge-heterocyclic ring stannylene (P1) via a transition state TS1 with an energy barrier of 1.8 kJ/mol. According to Fig. 2 and Table 2, it is an exothermic reaction, and the Δ_rU_m and Δ_rH_m at normal temperature and pressure are –60.7 and –60.9 kJ/mol, and Δ_rG_m = –53.7 kJ/mol. So, R1 + R2 → P1 will be a thermodynamically spontaneous reaction at normal temperature and pressure.

  In reaction (2), the four-membered Ge-heterocyclic ring stannylene (P1) further reacts with ethylene (R2) to form a Ge-heterocyclic spiro-Sn-heterocyclic ring compound (P2). According to Fig. 2, the process of reaction (2) is as follows: on the basis of P1 formed in reaction (1), it further reacts with ethylene (R2) to form an intermediate (INT2). According to Fig. 2 and Table 2, this is a barrier-free exothermic reaction: Δ_rU_m = –54.0 and Δ_rH_m = –47.1 kJ/mol at normal temperature and pressure, and Δ_rG_m = –0.3 kJ/mol. Then the intermediate (INT2) isomerizes to a Ge-heterocyclic spiro-Sn-heterocyclic ring compound (P2) via a transition state (TS2) with an energy barrier of 41.0 kJ/mol. According to Fig. 2 and Table 2, the reaction is endothermic, and Δ_rU_m = 35.1 and Δ_rH_m = 33.9 kJ/mol at normal temperature and pressure, and Δ_rG_m = 34.4 kJ/mol. Considering the Δ_rG_m of INT2 → P2 is 34.4 kJ/mol and the Δ_rG_m of P1 + R2 → P2 is 34.1 kJ/mol, P1 + R2 → INT2 → P2 is a continuous reaction. According to the following thermodynamic formula :

  $ \Delta G({p_2}) - \Delta G({p_1}) = \int_{{p_1}}^{{p_2}} {\Delta Vdp} $

  Under liquid phase conditions at 298 K, the reaction P1 + R2 → P2 must be carried out, and the pressure of the reaction system must be higher than 135725 Pa (1.4 atm).

  According to all analyses, reaction (2) should be the dominant reaction channel of the cycloaddition reaction between singlet Me₂Ge=Sn: and ethylene namely:

  $ {\text{R1}} + {\text{R2}} \to {\text{INT1}}\xrightarrow{{{\text{TS1}}}}{\text{P1}}\xrightarrow{{ + {\text{R2}}}}{\text{INT2}}\xrightarrow{{{\text{TS2}}}}{\text{P2}} $

  In this reaction, the frontier molecular orbitals of R1, R2, and P1 are shown in Fig. 3, according to which the mechanism of reaction (2) could be explained with the frontier molecular orbital diagrams (Figs. 4 and 5). Figs. 1 and 4 show when Me₂Ge=Sn: (R1) initially interacts with ethylene (R2), the 5p unoccupied orbital of the Sn atom in Me₂Ge=Sn: (R1) inserts the π orbital of ethylene to form a π → p donor-acceptor bond, leading to an intermediate (INT1). As the reaction goes on, the Sn–C(3) bond (INT1 2.484, TS1 2.362, P1 2.227 Å) and ∠GeSnC(3)C(4) (INT1 87.2°, TS1 65.7°, P1 29.5°) gradually decreases, and the Ge–Sn and C(3)–C(4) bonds (INT1: 2.531, 1.409; TS1: 2.539, 1.428; P1: 2.709, 1.547 Å) gradually lengthen. Before the transition state (TS1), Sn and C(3) form a covalent bond. After the transition state (TS1), Ge and C(4) generate a covalent bond. Thus, INT1 isomerizes to a four-membered Ge-heterocyclic ring stannylene (P1) via transition state (TS1). Because P1 is still an active molecule, it may further react with ethylene to form a Ge-heterocyclic spiro-Sn-heterocyclic ring compound (P2), and the mechanism can be explained with Figs. 5 and 1. According to the rule of molecular orbital symmetry adaptation, when P1 interacts with ethylene (R2), the 5p unoccupied orbital of the Sn atom in P1 inserts the π orbital of ethylene to afford a π → p donor-acceptor bond, thus forming an intermediate (INT2). As the reaction goes on, the Sn–C(5) and Sn–C(6) bonds (INT2: 2.543, 2.358; TS2: 2.218, 2.168; P2: 2.145, 2.144 Å) gradually decrease, the ∠GeSnC(5) (INT2: 66.8°, TS2: 120.2°, P2: 147.7°) gradually increases, and the C(5)–C(6) bond (INT2: 1.410, TS2: 1.495, P2: 1.534 Å) gradually lengthens. Before the transition state (TS2), the covalent bond is formed between Sn, C(5) and Sn, C(6). AfterTS2, the Sn atom hybridizes into a sp³ hybrid orbital. Thus, the INT2 isomerizes to a Ge-heterocyclic spiro-Sn-heterocyclic ring compound (P2) via transition state (TS2).

  Figure 3

  

  Figure 3.  Frontier molecular orbitals of R1, R2 and P1

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  Figure 4

  

  Figure 4.  A schematic interaction diagram for the frontier orbitals of Me₂Ge=Sn: (R1) and C₂H₄ (R2)

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  Figure 5

  

  Figure 5.  Schematic diagram for the frontier orbitals of P1 and C₂H₄ (R2)

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  4. CONCLUSION

  According to the potential energy profile, the cycloaddition reaction between singlet Me₂Ge=Sn: and ethylene obtained at the MP2 level of theory together with the 6-311++G**basis set for C, H and Ge atoms and the LanL2dz basis set for Sn atoms can be predicted. This reaction has one dominant channel. It consists of four steps: (1) The two reactants first form an intermediate (INT1) through a barrier-free exothermic reaction of 83.9 kJ/mol; (2) The intermediate (INT1) isomerizes to a four-membered Ge-heterocyclic ring stannylene (P1) via transition state (TS1) with an energy barrier of 1.8 kJ/mol; (3) The four-membered Ge-heterocyclic ring stannylene (P1) further reacts with ethylene (R2) to form another intermediate (INT2) through a barrier-free exothermic reaction of 54.0 kJ/mol; and (4) Intermediate (INT2) isomerizes to a Ge-heterocyclic spiro-Sn-heterocyclic ring compound (P2) via a transition state (TS2) with an energy barrier of 41.0 kJ/mol. At 298 K under liquid phase conditions, the reaction is carried out, and the pressure of the reaction system needs to be greater than 135725Pa (1.4 atm).

  The 5p unoccupied orbital of Sn: in X₂Ge=Sn: is the object in cycloaddition reaction of X₂Ge=Sn: and the symmetric π-bonded compounds. The 5p unoccupied orbital of Sn: in X₂Ge=Sn: and the π orbital of symmetric π-bonded compounds forming a π → p donor-acceptor bond, resulting in the formation of an intermediate. Instability of the intermediate makes it isomerize into a four-membered Ge-heterocyclic ring stannylene. Because the 5p unoccupied orbital of Sn atom in the four-membered Ge-heterocyclic ring stannylene and the π orbital of symmetric π-bonded compounds form a π → p donor-acceptor bond, the four-membered Ge-heterocyclic ring stannylene further combines with symmetric π-bonded compounds to form another intermediate. Because the Sn atom in the intermediate adopts sp³ hybridization, the intermediate isomerizes to a Ge-heterocyclic spiro-Sn-heterocyclic ring compound.

  
  
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• 

  Figure 1  Optimized MP2/GENECP(C, H, Ge in 6-311++G**; Sn in LanL2dz) geometrical parameters and the atomic numbering for the species in cycloaddition reaction between Me₂Ge=Sn: and ethylene. Bond lengths in angstroms and bond angles in degree

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  Figure 2  Potential energy surface for the cycloaddition reactions between Me₂Ge=Sn: and ethylene with MP2/GENECP(C, H, Ge in 6-311++G**; Sn in LanL2dz)

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  Figure 3  Frontier molecular orbitals of R1, R2 and P1

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  Figure 4  A schematic interaction diagram for the frontier orbitals of Me₂Ge=Sn: (R1) and C₂H₄ (R2)

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  Figure 5  Schematic diagram for the frontier orbitals of P1 and C₂H₄ (R2)

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  Table 1.  Electronic Structure Energies (E_ese, in a.u) and Relative Energies (E_R, in kJ/mol)for the Species from MP2/GENECP (C, H, Ge in 6-311++G**; Sn in LanL2dz) Method at 298 K and 101325 Pa

  Reaction		Species		MP2/GENECP
  				Eese	ER
  a Reaction (1)		R1 + R2		–2236.73989	0.0
  		INT1		–2236.77185	–83.9
  		TS1 (INT1-P1)		–2236.77116	–82.1
  		P1		–2236.79498	–144.6
  b Reaction (2)		P1 + R2		–2315.14151	0.0
  		INT2		–2315.16208	–54.0
  		TS2(INT2-P2)		–2315.14646	–13.0
  		P2		–2315.14871	–18.9
  aER = Eese－Eese, (R1 + R2), bER = Eese－Eese (P1+R2)

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  Table 2.  Entropy (S, in a.u), Enthalpy (H, in a.u) and Gibbs Free Energy (G, in a.u) for the Species from MP2/GENECP(C, H, Ge in 6-311++G**; Sn in LanL2dz) Methods at 298 K and 101325 Pa

  Reaction		Species		H/a.u		S/a.u		G/a.u
  Reaction (1)		R1 + R2		–2236.60272		2.29531 × 10–4		–2236.60272
  		INT1		–2236.63303		1.70226 × 10–4		–2236.68380
  		TS1 (INT1-P1)		–2236.63348		1.58468 × 10–4		–2236.68074
  		P1		–2236.65622		1.61005 × 10–4		–2236.70425
  Reaction (2)		P1 + R2		–2314.94790		2.44631 × 10–4		–2315.02087
  		INT2		–2314.96585		1.84860 × 10–4		–2315.02099
  		TS2(INT2-P2)		–2314.95167		1.77660 × 10–4		–2315.00456
  		P2		–2314.95294		1.84240 × 10–4		–2315.00790

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•