The ground-state atomic carbon can react with alkenes. When <i>cis</i>-2-butene is used, the reaction produces two different pairs of racemates, $\mathbf{A}$ and $\mathbf{B}$, with a product ratio $\mathbf{A:B}$ close to $1:1$. If <i>trans</i>-2-butene is used, two pairs of racemates, $\mathbf{B}$ and $\mathbf{D}$, and one achiral product, $\mathbf{C}$, are formed. The ratio of $\mathbf{B:C}$ is approximately $1:1$, while the yield of $\mathbf{D}$ is relatively low. Indicate the symmetry of each product $\mathbf{A,B,C,D}$.
基态原子态碳可与烯烃发生反应。若使用顺-2-丁烯，反应生成两对不同的外消旋体$\mathbf{A,B}$，且产物比例$\mathbf{A:B}$接近$1:1$，若使用反-2-丁烯，生成两对外消旋体$\mathbf{B,D}$和一种非手性产物$\mathbf{C}$，产物中$\mathbf{B,C}$的比例接近$1:1$，而产物$\mathbf{D}$则较少。指出产物$\mathbf{A,B,C,D}$各自的对称性。
$\mathbf{A}:C_2,\mathbf{B}:C_1,\mathbf{C}:S_4,\mathbf{D}:D_2.$
$\mathbf{A}:C_1,\mathbf{B}:D_2,\mathbf{C}:C_{2\mathrm{h}},\mathbf{D}:C_2.$
$\mathbf{A}:C_2,\mathbf{B}:C_1,\mathbf{C}:S_4,\mathbf{D}:D_2.$
$\mathbf{A}: C_2, \mathbf{B}: D_2, \mathbf{C}: C_{2\mathrm{v}}, \mathbf{D}: C_1.$
$\mathbf{A}:D_2,\mathbf{B}:C_1,\mathbf{C}:C_{2\mathrm{v}},\mathbf{D}:C_2.$
$\mathbf{A}:D_2,\mathbf{B}:C_2,\mathbf{C}:C_{2\mathrm{h}},\mathbf{D}:C_1.$
$\mathbf{A}:C_1,\mathbf{B}:C_2,\mathbf{C}:S_4,\mathbf{D}:D_2.$
$\mathbf{A}:C_1,\mathbf{B}:D_2,\mathbf{C}:C_{2\mathrm{h}},\mathbf{D}:C_2.$
$\mathbf{A}:C_2,\mathbf{B}:C_1,\mathbf{C}:S_4,\mathbf{D}:D_2.$
$\mathbf{A}:C_2,\mathbf{B}:D_2,\mathbf{C}:C_{2\mathrm{v}},\mathbf{D}:C_1.$
$\mathbf{A}:D_2,\mathbf{B}:C_1,\mathbf{C}:C_{2\mathrm{v}},\mathbf{D}:C_2.$
$\mathbf{A}:D_2,\mathbf{B}:C_2,\mathbf{C}:C_{2\mathrm{h}},\mathbf{D}:C_1.$
The reaction of ground-state carbon atoms with alkenes yields products featuring a spiro[2.2]pentane skeleton.

<Checkpoint>[Product has spiro[2.2]pentane skeleton](1)</Checkpoint>

For *cis*-2-butene or *trans*-2-butene, the resulting product should incorporate four methyl groups on the non-spiro atoms of the spiro[2.2]pentane molecule.

<Checkpoint>[Product has four methyl groups](1)</Checkpoint>

Thus, ignoring stereoisomers, the product is:
<MultiModal>![CC1C(C)C12C(C)C2C](/media/uploads/06bf9050-f8c0-4c5a-ba34-6e349e135dc3.png)</MultiModal>

The spectroscopic term for the ground-state carbon atom is $^3\mathrm{P}$, and its reactivity resembles that of a triplet carbene.

<Checkpoint>[Ground-state carbon atom resembles triplet carbene](1)</Checkpoint>

Consequently, its reaction mechanism with the first molecule of *cis*-2-butene or *trans*-2-butene involves radical addition, forming a diradical intermediate, followed by spin inversion and cyclization to yield a cyclopropane carbene intermediate.

<Checkpoint>[First step is radical addition](1)</Checkpoint>

<MultiModal>![CC1[C..]C1C](/media/uploads/e6aff786-f01f-422b-8657-5a38ba1ae89e.png)</MultiModal>

The generated cyclopropane intermediate exists in both *cis* and *trans* configurations, with their abundance ratio close to $1:1$.

The *cis* intermediate is:
<MultiModal>![C[C@H]1[C..][C@@H]1C](/media/uploads/08ea0ef6-a237-4dc6-bbc7-c3665720859b.png)</MultiModal>

The *trans* intermediate is:
<MultiModal>![C[C@H]1[C..][C@H]1C](/media/uploads/b38e0afd-f433-43c0-8ef1-4baf64a15866.png)</MultiModal>
and its enantiomer.

<Checkpoint>[Intermediate exists in both *cis* and *trans* forms](1)</Checkpoint>

The carbene intermediate, influenced by the high ring strain of the cyclopropane, adopts a singlet state, with the HOMO orbital lying within the plane of the cyclopropane ring and the LUMO orbital perpendicular to it.

<Checkpoint>[Cyclopropane intermediate is a singlet](1)</Checkpoint>

This singlet intermediate further undergoes a $\left[1+2\right]$ cycloaddition reaction with the second molecule of *cis*-2-butene or *trans*-2-butene, yielding stereospecific products.

<Checkpoint>[$\left[1+2\right]$ cycloaddition occurs](1)</Checkpoint>

If *cis*-2-butene reacts with the *cis* intermediate, the product is:
<MultiModal>![C[C@@H]1[C@H](C)[C@]12[C@@H](C)[C@H]2C](/media/uploads/37e68432-c5aa-464c-bd38-4074aeaee86c.png)</MultiModal>

This product contains one $R$ and one $S$ chiral carbon in each cyclopropane ring, along with a chiral axis ($R$ or $S$). It can only be formed from the reaction of ground-state carbon atoms with *cis*-2-butene, designated as $\mathbf{A}$, with a point group of $C_2$.

<Checkpoint>[$\mathbf{A}$ has point group $C_2$](1)</Checkpoint>

If *cis*-2-butene reacts with the *trans* intermediate or *trans*-2-butene reacts with the *cis* intermediate, the product is:
<MultiModal>![C[C@@H]1[C@H](C)C12[C@@H](C)[C@@H]2C](/media/uploads/a3dbe647-9e19-4263-9aba-c29de7bedd4d.png)</MultiModal>

This product lacks axial chirality but exhibits asymmetric chiral center distribution: one cyclopropane ring has one $R$ and one $S$ chiral carbon, while the other has two $R$ or two $S$ chiral carbons. This molecule can be formed from either *cis*-2-butene or *trans*-2-butene, designated as $\mathbf{B}$, with a point group of $C_1$.

<Checkpoint>[$\mathbf{B}$ has point group $C_1$](1)</Checkpoint>

If *trans*-2-butene reacts with the *trans* intermediate, two outcomes are possible. Under lower steric hindrance, the product is:
<MultiModal>![C[C@H]1[C@H](C)C12[C@@H](C)[C@@H]2C](/media/uploads/85c3f877-0039-4767-a794-530f909a8839.png)</MultiModal>
Here, one cyclopropane ring has two $R$ chiral carbons, and the other has two $S$ chiral carbons, resulting in an achiral molecule with an $S_4$ point group, designated as $\mathbf{C}$.

<Checkpoint>[$\mathbf{C}$ has point group $S_4$](1)</Checkpoint>

Under higher steric hindrance, the product is:
<MultiModal>![C[C@@H]1[C@@H](C)C12[C@@H](C)[C@@H]2C](/media/uploads/0ab8e6ce-37f0-4ec1-ad8b-b78f1117f3aa.png)</MultiModal>
Here, all four tertiary carbons are either $R$ or $S$, and the molecule lacks axial chirality, with a point group of $D_2$, designated as $\mathbf{D}$.

<Checkpoint>[$\mathbf{D}$ has point group $D_2$](1)</Checkpoint>

<Checkpoint>[Yield difference between $\mathbf{C}$ and $\mathbf{D}$ arises from steric hindrance](1)</Checkpoint>
基态碳原子与烯烃反应，得到的产物具有螺戊烷形式的骨架。

<Checkpoint>[产物有螺戊烷骨架](1)</Checkpoint>

对于顺-2-丁烯或反-2-丁烯，得到的产物应当在螺戊烷分子中除螺原子之外的原子上加入4个甲基。

<Checkpoint>[产物有4个甲基](1)</Checkpoint>

因此，若忽略立体异构，产物为
<MultiModal>![CC1C(C)C12C(C)C2C](/media/uploads/06bf9050-f8c0-4c5a-ba34-6e349e135dc3.png)</MultiModal>

基态碳原子对应的光谱项为$^3\mathrm{P}$，其反应性与三线态卡宾相近。

<Checkpoint>[基态碳原子类似三线态卡宾](1)</Checkpoint>

故其与第一分子的顺-2-丁烯或反-2-丁烯的反应机理为自由基加成，生成双自由基中间体，再经过自旋翻转和关环得到三元环卡宾中间体。

<Checkpoint>[第一步反应为自由基加成](1)</Checkpoint>

<MultiModal>![CC1[C..]C1C](/media/uploads/e6aff786-f01f-422b-8657-5a38ba1ae89e.png)</MultiModal>

生成的三元环中间体同时具有顺式和反式结构，两类中间体含量比接近$1:1$。

其中，顺式中间体为：
<MultiModal>![C[C@H]1[C..][C@@H]1C](/media/uploads/08ea0ef6-a237-4dc6-bbc7-c3665720859b.png)</MultiModal>

反式中间体为：
<MultiModal>![C[C@H]1[C..][C@H]1C](/media/uploads/b38e0afd-f433-43c0-8ef1-4baf64a15866.png)</MultiModal>
及其对映体。

<Checkpoint>[中间体即有顺式也有反式](1)</Checkpoint>

生成的卡宾中间体受三元环的高张力影响，为单线态卡宾，HOMO轨道位于三元环平面内，LUMO轨道与该平面垂直。

<Checkpoint>[三元环中间体为单线态](1)</Checkpoint>

这一单线态中间体继续与第二分子的顺-2-丁烯或反-2-丁烯发生$\left[1+2\right]$环加成反应，产物具有立体专一性。

<Checkpoint>[发生$\left[1+2\right]$环加成](1)</Checkpoint>

若顺-2-丁烯与顺式中间体发生环加成，得到的产物为

<MultiModal>![C[C@@H]1[C@H](C)[C@]12[C@@H](C)[C@H]2C](/media/uploads/37e68432-c5aa-464c-bd38-4074aeaee86c.png)</MultiModal>

该产物的两个三元环中各有一个$R$和一个$S$手性碳，且存在手性轴（$R$或$S$），该产物只能由基态碳原子与顺-2-丁烯生成，故为$\mathbf{A}$，其点群为$C_2$。

<Checkpoint>[$\mathbf{A}$的点群为$C_2$](1)</Checkpoint>

若顺-2-丁烯与反式中间体环加成，或反-2-丁烯与顺式中间体环加成，得到的产物为

<MultiModal>![C[C@@H]1[C@H](C)C12[C@@H](C)[C@@H]2C](/media/uploads/a3dbe647-9e19-4263-9aba-c29de7bedd4d.png)</MultiModal>

其没有轴手性，但手性中心分布不对称，其中一个三元环上有一个$R$和一个$S$手性碳，另一个三元环上有两个$R$或两个$S$手性碳。该分子既可由基态碳原子与顺-2-丁烯也由基态碳原子与反-2-丁烯生成，故为$\mathbf{B}$，其点群为$C_1$。

<Checkpoint>[$\mathbf{B}$的点群为$C_1$](1)</Checkpoint>

若反-2-丁烯与反式中间体发生环加成反应，则有两种可能，对于位阻较小的情形，产物为
<MultiModal>![C[C@H]1[C@H](C)C12[C@@H](C)[C@@H]2C](/media/uploads/85c3f877-0039-4767-a794-530f909a8839.png)</MultiModal>
分子中一个三元环上有两个$R$手性碳，另一个三元环上有两个$S$手性碳，整体无手性，为$S_4$点群，故为$\mathbf{C}$。

<Checkpoint>[$\mathbf{C}$的点群为$S_4$](1)</Checkpoint>

对于位阻较大的情形，产物为

<MultiModal>![C[C@@H]1[C@@H](C)C12[C@@H](C)[C@@H]2C](/media/uploads/0ab8e6ce-37f0-4ec1-ad8b-b78f1117f3aa.png)</MultiModal>
其中，4个三级碳的手性要么都是$R$，要么都是$S$，分子不含轴手性，分子点群为$D_2$。为$\mathbf{D}$。

<Checkpoint>[$\mathbf{D}$的点群为$D_2$](1)</Checkpoint>

<Checkpoint>[$\mathbf{C}$与$\mathbf{D}$的产率差异来自位阻](1)</Checkpoint>