Introduction

Since unsaturated carbene [XYC=C: (X, Y=H, F, Cl, Me, Ph, ……)] was recognized as an active intermediate in the 1960s, it has not only attracted much attention from theoretic chemists but also been practically applied to the organic chemistry [1, 2]. For example, it has been proved that unsaturated carbene can provide a simple and direct way for synthesizing the small-ring, highly strained compounds as well as those that can hardly be synthesized through conventional ways [2]. So far, in depth exploration has been done on the rearrangement reaction of alkylidene carbene [3, 4], and the insertion reaction of alkylidene carbene has also been studied [5, 6]. Apeloig et al. [7] and Fox et al. [8] have made experimental and theoretic studies on the 3-dimensional selectivity of substituting groups from the products of the vinylidene-olefins addition reaction of alkylidene carbene. Meanwhile, we have done some relatively systematic theoretic investigations on the cycloaddition reaction of alkylidene carbene [9–13]. However, there has been no published reports about analog XYGe=Ge: (X, Y=H, F, Cl, Me, Ph, ……) of unsaturated carbene, and they are new study field of unsaturated germylenes chemistry. It is quite difficult to investigate the mechanisms of the cycloaddition reaction by experimental methods directly due to the high activity of unsaturated germylenes; therefore, the theoretic study is more practical. To explore the rules of the cycloaddition reactions between unsaturated germylene [XYGe=Ge: (X,Y=H, F, Cl, Me, Ph, ……)] and the symmetric π-bonded compounds, H2Ge=Ge: and ethene were selected as model molecules, the cycloaddition reaction mechanism (considering the H transfer simultaneously) was investigated and analyzed theoretically. The results show that the cycloaddition reaction consists of two possible pathways, as follows:

(1)
(2)

The research result indicates the laws of cycloaddition reaction between H2Ge=Ge: and its derivatives and the symmetric π-bonded compounds, which is significant for the synthesis of small-ring and spiro-Ge-heterocyclic compounds. The study extends research area and enriches research content of germylene chemistry; it opened up a new research field for germylene chemistry.

Calculation methods

B3LYP/6-311 ++G** [14] implemented in the Gaussian 09 package [15] is employed to locate all the stationary points along the reaction pathways. Full optimization and vibrational analysis are done for the stationary points on the reaction profile. In order to explicitly establish the relevant species, the intrinsic reaction coordinate (IRC) [16, 17] is also calculated for all the transition states appearing on the cycloaddition energy surface profile.

Results and discussion

Reaction (1): channels of forming the four-membered Ge-heterocyclic ring germylene (INT1), H transfer products (P1.1, P1.2 and P1.3)

Theoretic researches show that the ground state of H2Ge=Ge: is a singlet state. The geometrical parameters of the intermediate (INT1), transition state (TS1.1, TS1.2, TS1.3), and product (P1.1, P1.2, P1.3) which appear in reaction (1) between H2Ge=Ge: and ethene are given in Fig. 1, the energies and Gibbs free energy are listed in Table 1, and the potential energy profile for the cycloaddition reaction is shown in Fig. 2. According to Fig. 2, it can be seen that the reaction (1) consists of four steps: the first one is that the two reactants (R1, R2) form a four-membered Ge-heterocyclic ring germylene (INT1), which is a barrier-free exothermic reaction of 104.8 kJ/mol; the second, third, and fourth steps are that the INT1 undergoes H transfer via transition states TS1.1, TS1.2, and TS1.3 with energy barriers of 63.6, 89.9, and 160.1 kJ/mol, respectively, resulting in the formation of products P1.1, P1.2, and P1.3. According to Table 1, the ΔG of R1 + R2 → INT1 is −38.9 kJ/mol, so R1 + R2 → INT is thermodynamics of spontaneous reaction at 298 K and 101.325 kPa because of the ΔG of INT1 → P1.1, INT1 → P1.2, and INT1 → P1.3 are 37.6, 1.65, and 65.3 kJ/mol, respectively; INT1 → P1.1, INT1 → P1.2, and INT1 → P1.3 are prohibited in thermodynamics at 298 K and 101.325 kPa, and reaction (1) will end in product INT1.

Fig. 1
figure 1

Optimized B3LYP/6-311 ++G** geometrical parameters of INT1, TS1.1, TS1.2, TS1.3. P1.1, P1.2, P1.3, and the atomic numbering for these species in cycloaddition reaction (1). Bond lengths and angles are in Å and (°)

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Table 1 The electronic structure energy (E ese, a.u), relative energies (E R, kJ/mol) and Gibbs free energy (G, a.u) for the species from B3LYP/6-311 ++G** method at the 298 K and 101,325 Pa
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Fig. 2
figure 2

The potential energy profile for the cycloaddition reactions between H2Ge=Ge: and H2C=CH2 with B3LYP/6-311 ++G**

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Reaction (2): channel of forming a spiro-Ge-heterocyclic ring compound (P2)

In reaction (2), the four-membered Ge-heterocyclic ring germylene (INT1) further reacts with ethene (R2) to form a spiro-Ge-heterocyclic ring compound (P2). The geometrical parameters of intermediate (INT2), transition state (TS2), and product (P2), which appear in reaction (2) are given in Fig. 3. The energy and Gibbs free energy are listed in Table 1, and the potential profile for the cycloaddition reaction is shown in Fig. 2. According to Fig. 2, it can be seen that the process of reaction (2) as follows: on the basis of INT1 formed from the reaction (1) between R1 and R2, the INT1 further reacts with ethene to form an intermediate (INT2), which is a barrier-free exothermic reaction of 54.4 kJ/mol; next, the intermediate (INT2) isomerizes to a spiro-Ge-heterocyclic ring compound (P2) via a transition state (TS2) with an energy barrier of 8.2 kJ/mol. According to Table 1, the ΔG of INT1 + R2 → INT2, INT1 → P2, and INT1 + R2 → P2 are 8.5, −0.8, and 7.6 kJ/mol, respectively, so the reactions INT1 + R2 → INT2 and INT1 + R2 → P2 at 298 K and 101, 325 Pa are prohibited in thermodynamics and the spontaneous tendency of INT1 → P2 is very small. Considering INT1 + R2 → INT2 and INT1 + R2 → P2 are volume reduced reaction to make the reaction goes on increasing the pressure of the system can make INT1 + R2 → P2 complete. According to the formula:

Fig. 3
figure 3

Optimized B3LYP/6-311 ++G** geometrical parameters of INT2, TS2, P2 and the atomic numbering for cycloaddition reaction (2). Bond lengths and angles are in Å and (°)

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$$ \left( {\frac{\partial (\Updelta G)}{\partial P}} \right)_{T} = \Updelta V,\,\Updelta G(p_{2} ) - \Updelta G(p_{1} ) = \int\limits_{{p_{1}^{{}} }}^{{p_{2}^{{}} }} {\Updelta Vdp} $$

We can know that when the pressure of the system is 149.825 kPa at 298 K, the ΔG of INT1 + R2 → INT2, INT1 + R2 → P2, and R1 + R2 → INT1 are −40.0, −40.9, and −87.4 kJ/mol, respectively; so \( {\text{R}1} + {\text{R}2} \to {\text{INT}1}\mathop{\longrightarrow}\limits^{+R2} {\text{INT2}}\mathop{\longrightarrow}\limits^{TS2}{\text{P2}} \) will be the dominant reaction pathway of cycloaddition reaction between singlet H2Ge=Ge: and ethane.

Theoretic analysis and explanation of the dominant reaction channel

According to the above analysis, the dominant reaction channel of the cycloaddition reaction between singlet H2Ge=Ge: and ethane at 298 K and 149.825 kPa is as follows:

$$ {\text{R}}1 + {\text{R}}2 \to {\text{INT}}1\mathop{\longrightarrow}\limits^{+\text{R}2}\;{\text{INT}}2\mathop{\longrightarrow}^{\text{TS}2}\;{\text{P}}2$$
(Reaction (2))

In the reaction, the frontier molecular orbitals of R2 and INT1 are shown in Fig. 4. According Fig. 4, the frontier molecular orbitals of R2 and INT1 can be expressed in schematic diagram 5. The mechanism of the reaction could be explained with the molecular orbital diagram (Fig. 5) and Figs. 1 and 3. According to Fig. 1, as H2Ge=Ge: initially interacts with ethene, the [2 + 2] cycloaddition of two bonding π-orbitals firstly results in a four-membered Ge-heterocyclic ring germylene (INT1). Because the INT1 is an active intermediate, it could further reacts with ethene (R2) to form a spiro-Ge-heterocyclic ring compound (P2). The mechanism of the reaction could be explained with Figs. 1, 3, and 5, according to orbital symmetry matching condition, when INT1 interacts with ethene (R2), the 4p unoccupied orbital of the Ge(2) atom in INT1 will insert the orbital of ethene, the 4p unoccupied orbital of the Ge(2) atom in INT1 will insert the π orbital of ethane, then the shift of π-electrons to the p unoccupied orbital gives a π → p donor–acceptor bond, leading to the formation of intermediate (INT2). As the reaction goes on, because of C(3)–Ge(2) bond (INT2: 2.435 Å, TS2: 2.117 Å, P2: 1.972 Å) gradually shorten, ∠C(2)Ge(2)C(1) (INT2: 90.2°, TS2:103.3°, P2: 127.80°) increase gradually, ∠C(4)C(3)Ge2Ge1(INT2: 167.0°, TS2: 150.4°, P2: 126.9°) decrease gradually, and the C(4)C(3) bond (INT2: 1.393 Å, TS2: 1.466Å, P2: 1.534Å) elongate gradually, the Ge(2) in INT2 happens sp3 hybridization after the transition state (TS2), forming a spiro-Ge-heterocyclic ring compound (P2).

Fig. 4
figure 4

The frontier molecular orbitals of R2, INT1

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Fig. 5
figure 5

A schematic diagram for the frontier orbitals of INT1 and H2C=CH2 (R2)

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Conclusion

On the basis of the potential energy profile and Gibbs free energy (G) obtained with the B3LYP/6-311 ++G** method for the cycloaddition reaction between singlet H2Ge=Ge: and ethene, it can be predicted that the reaction (2) is one dominant reaction pathway of cycloaddition reaction between singlet H2Ge=Ge: and ethene at 298 K and 149.825 kPa. The process of reaction (2) consists of three steps: the first step is that the two reactants (R1, R2) form a four-membered Ge-heterocyclic ring germylene (INT1), which is a barrier-free exothermic reaction of 104.8 kJ/mol; the second step is that intermediate (INT1) further reacts with ethene (R2) to form an intermediate (INT2), which is also a barrier-free exothermic reaction of 54.4 kJ/mol; and the third step is that intermediate (INT2) isomerizes to a spiro-Ge-heterocyclic ring compound (P2) via a transition state (TS2) with an energy barrier of 8.2 kJ/mol.