For the reaction occurring with the following substances, it can yield a polymeric product:

<MultiModal>![The SMILES of the reaction can be expressed as: C12=C(C#CC3=C(C#C2)C=CC=C3)C=CC=C1.O=C(OCCCCCCOC(C1=CC(C(C)C)=C(C(C(C)C)=C1)N=[N+]=[N-])=O)C2=CC(C(C)C)=C(C(C(C)C)=C2)N=[N+]=[N-]
>>，where the first reactant is denoted as $\bf A$, and the second reactant is denoted as $\bf B$](/media/uploads/89d0c1d4-b738-4c5f-a17c-0e82b1551481.png)</MultiModal>

In the resulting polymeric product, there are two possible basic repeating unit structures:

- Repeating unit 1:

<MultiModal>![The SMILES of repeating unit 1: CC(C1=CC(C(OCOC(C2=CC(C(C)C)=C(N3C4=C(N=N3)C5=C(C6=C(N=NN6[*])C7=C4C=CC=C7)C=CC=C5)C(C(C)C)=C2)=O)=O)=CC(C(C)C)=C1[*])C, where [*] indicates connection to other repeating units in the polymer](/media/uploads/1b90bb5e-073c-40cf-9b90-cfa47da6cf5d.png)</MultiModal>

- Repeating unit 2:

<MultiModal>![The SMILES of repeating unit 2: CC(C1=CC(C(OCOC(C2=CC(C(C)C)=C(N3N=NC4=C3C5=C(C6=C(C7=C4C=CC=C7)N=NN6[*])C=CC=C5)C(C(C)C)=C2)=O)=O)=CC(C(C)C)=C1[*])C, where [*] indicates connection to other repeating units in the polymer](/media/uploads/b08172c1-3672-4343-8d32-4f366b63bfad.png)</MultiModal>

Regarding the above reaction and the polymer formed, the following propositions are made:

1.  This reaction requires the addition of a transition metal catalyst to proceed.
2.  This reaction cannot proceed at room temperature and requires heating conditions.
3.  In the polymer, the content of repeating unit 2 is greater than that of repeating unit 1.
4.  Let $k_1$ be the reaction rate when one molecule of reactant $\bf B$ is added to one molecule of reactant $\bf A$, and $k_2$ be the reaction rate when the intermediate product at this time receives another molecule of reactant $\bf B$, then $k_1>k_2$.
5.  Let $S=\dfrac{[\mathbf{A}]}{[\mathbf{B}]}$, then for the four cases of $S_{1,2,3,4}=0.83,0.91,1.10,1.20$ the order of the number-average molecular weight of the polymers formed is $S_3>S_4>S_2>S_1$.

Calculate the value of $z=\dfrac{\text{sum of squares of correct proposition numbers}}{\text{sum of incorrect proposition numbers}+1}$, and select the correct option.
对于以下物质发生的反应，其可以得到高分子产物：

<MultiModal>![反应的SMILES可以表示为：C12=C(C#CC3=C(C#C2)C=CC=C3)C=CC=C1.O=C(OCCCCCCOC(C1=CC(C(C)C)=C(C(C(C)C)=C1)N=[N+]=[N-])=O)C2=CC(C(C)C)=C(C(C(C)C)=C2)N=[N+]=[N-]
>>，其中，第一个反应物记号为 $\bf A$，第二个反应物记号为 $\bf B$](/media/uploads/89d0c1d4-b738-4c5f-a17c-0e82b1551481.png)</MultiModal>

其生成的高分子产物中，有两种可能的基本重复单元结构：

- 重复单元 1：

<MultiModal>![重复单元 1 的SMILES：CC(C1=CC(C(OCOC(C2=CC(C(C)C)=C(N3C4=C(N=N3)C5=C(C6=C(N=NN6[*])C7=C4C=CC=C7)C=CC=C5)C(C(C)C)=C2)=O)=O)=CC(C(C)C)=C1[*])C，其中 [*] 表示与高分子中其他重复单元相连](/media/uploads/1b90bb5e-073c-40cf-9b90-cfa47da6cf5d.png)</MultiModal>

- 重复单元 2：

<MultiModal>![重复单元 2 的SMILES: CC(C1=CC(C(OCOC(C2=CC(C(C)C)=C(N3N=NC4=C3C5=C(C6=C(C7=C4C=CC=C7)N=NN6[*])C=CC=C5)C(C(C)C)=C2)=O)=O)=CC(C(C)C)=C1[*])C，其中 [*] 表示与高分子中其他重复单元相连](/media/uploads/b08172c1-3672-4343-8d32-4f366b63bfad.png)</MultiModal>

对于以上反应及其所形成的高分子，有以下命题：

1. 该反应需要加入过渡金属催化才能够进行。
2. 该反应在室温下无法进行，需要加热的条件。
3. 在高分子中，重复单元 2 的含量大于重复单元 1。
4. 记当一分子反应物 $\bf B$ 加成于一分子反应物 $\bf A$ 的时的反应速率为 $k_1$，此时的中间产物再收到另一分子反应物 $\bf B$ 加成的反应速率为 $k_2$，则 $k_1>k_2$。
5. 记 $S=\dfrac{[\mathbf{A}]}{[\mathbf{B}]}$，则 $S_{1,2,3,4}=0.83,0.91,1.10,1.20$ 四种情况下生成的聚合物，其数均分子量的大小顺序为 $S_3>S_4>S_2>S_1$。

计算 $z=\dfrac{\text{正确命题序号}^2\text{的和}}{\text{错误命题序号和}+1}$ 的值，选出正确的选项。
All other options are incorrect
0.067
0.286
0.385
0.692
0.833
1.333
1.545
2.273
2.600
3.222
5.857
其他选项均不正确
0.067
0.286
0.385
0.692
0.833
1.333
1.545
2.273
2.600
3.222
5.857
The reaction is a dual strain-promoted azide-alkyne cycloaddition (DSPAAC) reaction with an active intermediate as a polymerization reaction. After one molecule of reactant $\bf B$ is added to one molecule of reactant $\bf A$, in the resulting intermediate, one alkyne in the original eight-membered ring dialkyne of reactant $\bf A$ becomes an alkene. This conversion process leads to a large repulsive force between the phenyl group connected to the azide and the benzene ring on the eight-membered ring in the intermediate, making the eight-membered ring non-planar and more distorted, which increases the tension of the remaining alkyne bond in the eight-membered ring. Therefore, it will quickly undergo a DSPAAC reaction with another molecule of alkyne.

<Checkpoint>[The eight-membered ring of the addition intermediate is more distorted, and the reactivity of the internal alkyne is higher than that of reactant $\bf A$](1)</Checkpoint>

Based on the above inference, analyze each proposition:

1.  This reaction requires the addition of a transition metal catalyst to proceed.

This is a dual strain-promoted azide-alkyne cycloaddition (DSPAAC) reaction with an intermediate, rather than a traditional alkyne and azide CuAAC reaction catalyzed by Cu. Based on the 3+2 Click reaction of the alkyne in the eight-membered ring with azide, driven by ring strain, it is not necessary to add Cu or other transition metals as catalysts.

<Checkpoint>[This reaction proceeds under the driving force of ring strain and does not require a transition metal catalyst](1)</Checkpoint>

2.  This reaction cannot proceed at room temperature and requires heating conditions.

The conditions for the Click reaction are mild. Combined with the previous discussion, it does not require heating and can proceed at room temperature.

<Checkpoint>[This reaction can proceed at room temperature and does not require heating](1)</Checkpoint>

3.  In the polymer, the content of repeating unit 2 is greater than that of repeating unit 1.

In repeating unit 2, the orientations of the two azide $\bf B$ after addition to alkyne $\bf A$ are the same, while in repeating unit 1, the orientations of the azide substituents are different. Considering the intermediate after one molecule of $\bf B$ is added to one molecule of $\bf A$, if the orientation of the azide substituent is the same as the orientation of the substituent of the first molecule added when another molecule of $\bf B$ is added, the reaction energy barrier will increase due to steric hindrance, which is not conducive to the formation of repeating unit 2. Therefore, in the polymer, the content of repeating unit 2 is less than that of repeating unit 1.

<Checkpoint>[The content of repeating unit 2 is less than that of repeating unit 1](1)</Checkpoint>

4.  Let $k_1$ be the reaction rate when one molecule of reactant $\bf B$ is added to one molecule of reactant $\bf A$, and $k_2$ be the reaction rate when the intermediate at this time receives another molecule of reactant $\bf B$ for addition, then $k_1>k_2$.

Based on the previous discussion about the DSPAAC reaction, considering the intermediate after one molecule of $\bf B$ is added to one molecule of $\bf A$, the phenyl group connected to the azide forms a large repulsive force with the benzene ring on the eight-membered ring, which increases the ring strain of the eight-membered ring and increases the reactivity of the intermediate. Therefore, $k_2>k_1$.

<Checkpoint>[The reactivity of the intermediate is higher than that of the reactant, $k_2>k_1$](1)</Checkpoint>

5.  Let $S=\dfrac{[\mathbf{A}]}{[\mathbf{B}]}$, then for the polymers generated under the four conditions of $S_{1,2,3,4}=0.83,0.91,1.10,1.20$, the order of their number-average molecular weight is $S_3>S_4>S_2>S_1$.

Considering that the reactivity of the reaction intermediate is higher than that of reactant $\bf A$, and the two alkynes in $\bf A$ have a mutually promoting effect, therefore, when reactant $\bf A$ is in excess, it will not significantly affect the number-average degree of polymerization of the polymer, but will only cause a slight decrease in the number-average degree of polymerization, while when reactant $\bf B$ is in excess, since the two azides in $\bf B$ have no promoting effect, it will cause a relatively large decrease in the number-average degree of polymerization.

<Checkpoint>[The two alkynes in $\bf A$ have a promoting effect, while the two azides in $\bf B$ have no promoting effect](0.5)</Checkpoint>

Therefore, for the polymers generated under the four conditions of $S_{1,2,3,4}=0.83,0.91,1.10,1.20$, the order of their number-average molecular weight is $S_3>S_4>S_2>S_1$.

<Checkpoint>[For the polymers generated under the four conditions of $S_{1,2,3,4}=0.83,0.91,1.10,1.20$, the order of their number-average molecular weight is $S_3>S_4>S_2>S_1$](1)</Checkpoint>

Finally, calculate the value of $z$:

$$ z=\dfrac{\text{Sum of the squares of the correct proposition numbers}}{\text{Sum of the incorrect proposition numbers}+1} = \dfrac{5^2}{11} \approx 2.273 $$

<Checkpoint>[$z=2.273$](1)</Checkpoint>

Therefore, select option **I**.
该反应是一个具有活性中间体的双应变促进叠氮化物-炔烃点击反应 (DSPAAC) 作为聚合反应。当一分子反应物 $\bf B$ 加成于一分子反应物 $\bf A$ 的后，此时的中间产物中，反应物 $\bf A$ 原本的八元环内双炔烃中，一个炔烃变成了烯烃，该转换过程会导致中间产物中与叠氮相连苯基与八元环上的苯环形成较大斥力，使得八元环无法共平面、更加扭曲，导致八元环中仅剩的炔键的张力变大，因此会很快地与另一分子的炔烃发生 DSPAAC 反应。

<Checkpoint>[加成的中间产物八元环更扭曲，环内炔烃反应性高于反应物 $\bf A$](1)</Checkpoint>

基于以上推断，分析各个命题：

1. 该反应需要加入过渡金属催化才能够进行。

这是一个中间体的双应变促进叠氮化物-炔烃点击反应 (DSPAAC)，而非传统的炔烃与叠氮在 Cu 催化下进行的 CuAAC 反应，基于八元环内炔烃在环张力驱动下发生的与叠氮的 3+2 Click 反应时，不需要加入 Cu 或其他过渡金属作为催化剂的。

<Checkpoint>[该反应在环张力的驱动下进行，不需要过渡金属催化剂](1)</Checkpoint>

2. 该反应在室温下无法进行，需要加热的条件。

Click 反应的条件温和，结合之间的论述，其不需要加热，在室温条件下即可进行。

<Checkpoint>[该反应在室温下即可进行，不需要加热](1)</Checkpoint>

3. 在高分子中，重复单元 2 的含量大于重复单元 1。

重复单元 2 中两个叠氮 $\bf B$ 加成炔烃 $\bf A$ 后，叠氮取代基的取向相同，而重复单元 1 中叠氮取代基的取向不同。考虑一分子 $\bf B$ 加成于一分子 $\bf A$ 的后的中间产物，若另一分子 $\bf B$ 加成时，叠氮的取代基方向与第一分子加成的取代基方向一致，则会由于空间位阻效应导致反应能垒升高，不利于重复单元 2 的形成，因此在高分子中，重复单元 2 的含量小于重复单元 1。

<Checkpoint>[重复单元 2 的含量小于重复单元 1](1)</Checkpoint>

4. 记当一分子反应物 $\bf B$ 加成于一分子反应物 $\bf A$ 的时的反应速率为 $k_1$，此时的中间产物再收到另一分子反应物 $\bf B$ 加成的反应速率为 $k_2$，则 $k_1>k_2$。

基于先前关于 DSPAAC 反应的论述，考虑一分子 $\bf B$ 加成于一分子 $\bf A$ 的后的中间产物，与叠氮相连苯基与八元环上的苯环形成较大斥力，使得八元环张力增大，提升了中间产物的反应活性，因此 $k_2>k_1$。

<Checkpoint>[中间产物的反应活性高于反应物，$k_2>k_1$](1)</Checkpoint>

5. 记 $S=\dfrac{[\mathbf{A}]}{[\mathbf{B}]}$，则 $S_{1,2,3,4}=0.83,0.91,1.10,1.20$ 四种情况下生成的聚合物，其数均分子量的大小顺序为 $S_3>S_4>S_2>S_1$。

考虑反应的中间产物反应活性高于反应物 $\bf A$，$\bf A$ 中两个炔烃存在彼此促进的效应，因此，当反应物 $\bf A$ 过量时，并不会显著影响聚合物的数均聚合度，只会导致数均聚合度略微降低，而当反应物 $\bf B$ 过量时，由于 $\bf B$ 中两个叠氮并无促进作用，会导致数均聚合度产生较大幅的下降。

<Checkpoint>[$\bf A$ 中两个炔烃存在促进作用，而$\bf B$ 中两个叠氮并无促进作用](0.5)</Checkpoint>

因此，$S_{1,2,3,4}=0.83,0.91,1.10,1.20$ 四种情况下生成的聚合物，其数均分子量的大小顺序为 $S_3>S_4>S_2>S_1$。

<Checkpoint>[$S_{1,2,3,4}=0.83,0.91,1.10,1.20$ 四种情况下生成的聚合物，其数均分子量的大小顺序为 $S_3>S_4>S_2>S_1$](1)</Checkpoint>

最终，计算 $z$ 的值：

$$ z=\dfrac{\text{正确命题序号}^2\text{的和}}{\text{错误命题序号和}+1} = \dfrac{5^2}{11} \approx 2.273 $$

<Checkpoint>[$z=2.273$](1)</Checkpoint>

因此，选择选项 **I**。