Compound $\mathbf{D}$ was obtained through the following reaction sequence.

<MultiModal>![The diagram contains the following reaction: CC1C(=O)CCC1=O>BrCC#C.[O-][Na+].O>[A]，[A]>[O-][Na+].O>[*]，[*]>[H+]>[B]，[B]>[Hg++].[H+]>[C]，[C]>[O-][Na+].O>[*]，[*]>[H+]>[D]，where the intermediate $[*]$ is not shown in the original diagram](/media/uploads/6db13eb2-1705-4f64-aa25-b51feda22d0b.png)</MultiModal>

The chemical formula of $\mathbf{D}$ is $\mathrm{C_{9}H_{12}O_{3}}$, and the molecule contains two methyl groups.

If the reaction from $\mathbf{A}$ to $\mathbf{B}$ is skipped and the process is directly carried out as follows, in addition to the main product $\mathbf{D}$, a byproduct $\mathbf{D'}$ is also obtained.

<MultiModal>![[A]>[Hg++].[H+]>[X]，[X]>[O-][Na+].O>[*]，[*]>[H+]>[D].[D']，where the structure of $\mathbf{D'}$ is CC1CC(=O)C(=C1C)CC(=O)O](/media/uploads/50e22138-c6f6-466a-bf90-ad845f38950d.png)</MultiModal>

Determine how many times ring-opening and ring-closing reactions occur in total during the reaction mechanism from $\mathbf{X}$ to $\mathbf{D'}$.
人们通过以下反应得到了化合物$\mathbf{D}$。

<MultiModal>![图中包含如下反应：CC1C(=O)CCC1=O>BrCC#C.[O-][Na+].O>[A]，[A]>[O-][Na+].O>[*]，[*]>[H+]>[B]，[B]>[Hg++].[H+]>[C]，[C]>[O-][Na+].O>[*]，[*]>[H+]>[D]，中间体$[*]$原图未画出](/media/uploads/6db13eb2-1705-4f64-aa25-b51feda22d0b.png)</MultiModal>

$\mathbf{D}$的化学式为$\mathrm{C_{9}H_{12}O_{3}}$，分子中有两个甲基。

若不进行$\mathbf{A}$到$\mathbf{B}$的反应，而直接按如下过程反应，则除得到主产物$\mathbf{D}$外，还得到副产物$\mathbf{D'}$。

<MultiModal>![[A]>[Hg++].[H+]>[X]，[X]>[O-][Na+].O>[*]，[*]>[H+]>[D].[D']，其中\mathbf{D'}结构为CC1CC(=O)C(=C1C)CC(=O)O](/media/uploads/50e22138-c6f6-466a-bf90-ad845f38950d.png)</MultiModal>

求在从$\mathbf{X}$到$\mathbf{D'}$的反应机理中，开环和关环反应加起来总共发生了几次。
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The initial substrate is CC1C(=O)CCC1=O,
<MultiModal>![CC1C(=O)CCC1=O](/media/uploads/1bfa4909-7ac3-4122-8379-0f4bcfcf3113.png)</MultiModal>
in the presence of haloalkyne BrCC#C,
<MultiModal>![BrCC#C](/media/uploads/6ef1749c-bf2f-4d1b-a8aa-c6963441a4f9.png)</MultiModal>
and under basic aqueous solution conditions, alkylation occurs, and a propargyl group is attached to the common α-carbon of the two carbonyl groups, yielding $\mathbf{A}$, C#CCC1(C)C(=O)CCC1=O.

<MultiModal>![C#CCC1(C)C(=O)CCC1=O](/media/uploads/63e6602b-24d1-407a-996d-fdcb659439de.png)</MultiModal>

<Checkpoint>[A propargyl group is attached to the common α position of the two carbonyl groups of the substrate](1)</Checkpoint>

<Checkpoint>[$\mathbf{A}$ is C#CCC1(C)C(=O)CCC1=O](1)</Checkpoint>

In an aqueous $\mathrm{NaOH}$ solution, the carbonyl carbon of $\mathbf{A}$ is attacked by $\mathrm{OH^-}$, followed by ring-opening, breaking the bond between it and the common α-carbon of the diketone, and subsequent acidification yields the product $\mathbf{B}$ bearing a carboxyl group, C#CCC(C)C(=O)CCC(=O)O.

<MultiModal>![C#CCC(C)C(=O)CCC(=O)](/media/uploads/385e3611-3ec2-4de8-a1ac-a80f95b02fee.png)</MultiModal>

<Checkpoint>[The carbonyl carbon of $\mathbf{A}$ is attacked by hydroxide and the ring opens, and acidification yields $\mathbf{B}$ bearing a carboxyl group](1)</Checkpoint>

<Checkpoint>[$\mathbf{B}$ is C#CCC(C)C(=O)CCC(=O)O](1)</Checkpoint>

From $\mathbf{B}$ to $\mathbf{C}$, under acidic mercuric ion conditions, hydration of the terminal alkyne occurs, generating $\mathbf{C}$ with a methyl ketone structure, CC(CC(=O)C)C(=O)CCC(=O)O.

<MultiModal>![CC(CC(=O)C)C(=O)CCC(=O)O](/media/uploads/250210ef-204f-44d1-9f49-85d71be9258e.png)</MultiModal>

<Checkpoint>[Hydration of the terminal alkyne of $\mathbf{B}$ yields $\mathbf{C}$ with a methyl ketone structure](1)</Checkpoint>

<Checkpoint>[$\mathbf{C}$ is CC(CC(=O)C)C(=O)CCC(=O)O](1)</Checkpoint>

The ketone carbonyl group near the end of the $\mathbf{C}$ molecule undergoes condensation with the α position of the central ketone carbonyl group under basic conditions, eliminating one molecule of water, generating the five-membered ring product $\mathbf{D}$, CC1=C(CC(=O)O)C(=O)C(C)C1.

<MultiModal>![CC1=C(CC(=O)O)C(=O)C(C)C1](/media/uploads/d0da9483-e3ee-44ec-b37f-ccd3a01668f6.png)</MultiModal>

<Checkpoint>[$\mathbf{C}$ undergoes dehydration condensation to generate the five-membered ring product $\mathbf{D}$](1)</Checkpoint>

<Checkpoint>[$\mathbf{D}$ is CC1=C(CC(=O)O)C(=O)C(C)C1](1)</Checkpoint>

The molecular formula of $\mathbf{D}$ is $\mathrm{C_9H_{12}O_3}$. Compared with $\mathbf{A}$, it has more $\mathrm{C_3H_4O}$, which is equivalent to replacing one hydrogen atom with a propargyl group and adding one molecule of water, which is consistent with the above reasoning.

<Checkpoint>[Compared with $\mathbf{A}$, $\mathbf{D}$ is equivalent to replacing one hydrogen atom with a propargyl group and adding one molecule of water](1)</Checkpoint>

It can be seen that there are indeed two methyl groups in the $\mathbf{D}$ molecule.

Next, analyze the process of $\mathbf{A}\rightarrow\mathbf{X}\rightarrow\mathbf{D+D'}$.

From $\mathbf{A}$ to $\mathbf{X}$, again under acidic mercuric ion conditions, the terminal alkyne is oxidized to a methyl ketone, so the structure of $\mathbf{X}$ is CC(=O)CC1(C)C(=O)CCC1=O,

<MultiModal>![CC(=O)CC1(C)C(=O)CCC1=O](/media/uploads/e6044de7-8fc4-46d9-8f71-9f381182e853.png)</MultiModal>

<Checkpoint>[$\mathbf{X}$ is CC(=O)CC1(C)C(=O)CCC1=O](1)</Checkpoint>

Under basic aqueous solution conditions, $\mathbf{X}$ is attacked by the nucleophile $\mathrm{OH^-}$. Through a ring-opening - proton transfer - ring-closing process, $\mathbf{D}$ can also be obtained. The intermediates involved are
CC(=C(CCC(=O)[O-])[O-])CC(=O)C,

<MultiModal>![CC(=C(CCC(=O)[O-])[O-])CC(=O)C](/media/uploads/f5cad2db-65c0-47c0-865c-5c4ae68da09d.png)</MultiModal>
and
CC(CC(=O)C)C(=CCC(=O)[O-])[O-].

<MultiModal>![CC(CC(=O)C)C(=CCC(=O)[O-])[O-]](/media/uploads/d3485f01-76c3-4b72-a22b-e6ce171cc64a.png)</MultiModal>

If $\mathrm{OH^-}$ does not act as a nucleophile to attack, but deprotonation occurs, then the subsequent reaction is:

<Checkpoint>[$\mathrm{OH^-}$ acts as a base to remove the α-position proton of the exocyclic carbonyl group in $\mathbf{X}$](1)</Checkpoint>

<MultiModal>![图中涉及13个分子或离子，通过箭头连接成一串，按顺序分别为CC(=O)CC1(C)C(=O)CCC1=O，C/C(=C\C1(C)C(=O)CCC1=O)/[O]，CC(=O)C1C2(C)C(=O)CCC12[O]，CC1=C(CCC(=O)C1C(=O)C)[O]，CC12C(=O)CCC(=O)C1C2(C)[O]，CC(=O)C1(C)C=C(CCC1=O)[O]，CC(=O)C1(C)CC(=O)CCC1=O，CC(=O)C1(C)CC(=O)CCC1(O)[O]，CC(=O)[C-](C)CC(=O)CCC(=O)O，CC(CC(=O)[C-]CC(=O)O)C(=O)C，CC1CC(=O)C(CC(=O)O)C1(C)[O]，CC1CC(=O)[C-](CC(=O)O)C1(C)O，CC1CC(=O)C(=C1C)CC(=O)O](/media/uploads/90620c17-adfe-4d19-aa14-72fa64db882e.png)</MultiModal>

The specific process is that the α-position of the exocyclic carbonyl group of $\mathbf{X}$ is deprotonated to generate C/C(=C\C1(C)C(=O)CCC1=O)/[O]
<MultiModal>![C/C(=C\C1(C)C(=O)CCC1=O)/[O]](/media/uploads/82ab87c9-5ae0-4205-9e5b-59be8d6d5bd2.png)</MultiModal>
The enolate anion attacks the carbonyl carbon to obtain the [3.1.0] bridged ring CC(=O)C1C2(C)C(=O)CCC12[O]
<MultiModal>![CC(=O)C1C2(C)C(=O)CCC12[O]](/media/uploads/9d799e1d-5a96-4722-85bd-5369bf278692.png)</MultiModal>
The carbon-carbon bond breaks to obtain an enolate anion with a six-membered ring structure CC1=C(CCC(=O)C1C(=O)C)[O]
<MultiModal>![CC1=C(CCC(=O)C1C(=O)C)[O]](/media/uploads/f68409fb-81d8-4965-8b15-04f7a380b3c2.png)</MultiModal>
The enolate anion attacks the exocyclic carbonyl group to obtain the [4.1.0] bridged ring CC12C(=O)CCC(=O)C1C2(C)[O]
<MultiModal>![CC12C(=O)CCC(=O)C1C2(C)[O]](/media/uploads/e2c91667-90a9-4847-9c0e-ecb334333225.png)</MultiModal>
Ring opening yields another rearranged enolate anion CC(=O)C1(C)C=C(CCC1=O)[O]
<MultiModal>![CC(=O)C1(C)C=C(CCC1=O)[O]](/media/uploads/0cbd1038-6cc7-412e-8903-15ceffc284c2.png)</MultiModal>
Protonation yields CC(=O)C1(C)CC(=O)CCC1=O
<MultiModal>![CC(=O)C1(C)CC(=O)CCC1=O](/media/uploads/9f0ee9f8-7e0e-4863-91c5-7d23f7a8c752.png)</MultiModal>
The carbonyl group is attacked by an external hydroxyl group CC(=O)C1(C)CC(=O)CCC1(O)[O]
<MultiModal>![CC(=O)C1(C)CC(=O)CCC1(O)[O]](/media/uploads/ba3055de-0ee3-4af8-8f2e-e2d67d0c1158.png)</MultiModal>
Ring opening yields the carboxylic acid intermediate CC(=O)[C-](C)CC(=O)CCC(=O)O
<MultiModal>![CC(=O)[C-](C)CC(=O)CCC(=O)O](/media/uploads/5e2f7caa-618d-4545-8e00-f47e54a89f0d.png)</MultiModal>
Proton transfer generates CC(CC(=O)[C-]CC(=O)O)C(=O)C
<MultiModal>![CC(CC(=O)[C-]CC(=O)O)C(=O)C](/media/uploads/3be8666a-31db-4bac-8f77-d8b31bed3f07.png)</MultiModal>
Ring closure generates the five-membered ring CC1CC(=O)C(CC(=O)O)C1(C)[O]
<MultiModal>![CC1CC(=O)C(CC(=O)O)C1(C)[O]](/media/uploads/ca2c6927-1c19-47c5-9b66-f461b0f083b9.png)</MultiModal>
Proton transfer generates CC1CC(=O)[C-](CC(=O)O)C1(C)O
<MultiModal>![CC1CC(=O)[C-](CC(=O)O)C1(C)O](/media/uploads/b8028f53-2bb9-4089-9b66-9b5b9de2a8cc.png)</MultiModal>
Hydroxyl leaves to generate $\mathbf{D'}$ CC1CC(=O)C(=C1C)CC(=O)O.

<MultiModal>![CC1CC(=O)C(=C1C)CC(=O)O](/media/uploads/ba0c26b2-a0ec-4258-9c8f-ba451227911f.png)</MultiModal>


In the above process, a total of 3 ring closures and 3 ring openings occurred, so the total number of ring closures and ring openings involved is 6.

<Checkpoint>[3 ring closures, 3 ring openings](1)</Checkpoint>
一开始的底物CC1C(=O)CCC1=O，
<MultiModal>![CC1C(=O)CCC1=O](/media/uploads/1bfa4909-7ac3-4122-8379-0f4bcfcf3113.png)</MultiModal>
在卤代烃BrCC#C，
<MultiModal>![BrCC#C](/media/uploads/6ef1749c-bf2f-4d1b-a8aa-c6963441a4f9.png)</MultiModal>
以及碱性水溶液条件下，发生烷基化，在两个羰基的共同α-碳上连上了炔丙基，得到$\mathbf{A}$，C#CCC1(C)C(=O)CCC1=O。

<MultiModal>![C#CCC1(C)C(=O)CCC1=O](/media/uploads/63e6602b-24d1-407a-996d-fdcb659439de.png)</MultiModal>

<Checkpoint>[在底物两个羰基的共同α位连上炔丙基](1)</Checkpoint>

<Checkpoint>[$\mathbf{A}$为C#CCC1(C)C(=O)CCC1=O](1)</Checkpoint>

$\mathbf{A}$在$\mathrm{NaOH}$水溶液中，羰基碳被$\mathrm{OH^-}$进攻，随后开环，断开其与双羰基共同α-碳之间的键，之后酸化得到带有羧基的产物$\mathbf{B}$，C#CCC(C)C(=O)CCC(=O)O。

<MultiModal>![C#CCC(C)C(=O)CCC(=O)](/media/uploads/385e3611-3ec2-4de8-a1ac-a80f95b02fee.png)</MultiModal>

<Checkpoint>[$\mathbf{A}$的羰基碳被氢氧根进攻并开环，酸化得到带羧基的$\mathbf{B}$](1)</Checkpoint>

<Checkpoint>[$\mathbf{B}$为C#CCC(C)C(=O)CCC(=O)O](1)</Checkpoint>

从$\mathbf{B}$到$\mathbf{C}$，酸性汞离子条件，为端炔基的水合，生成具有甲基酮结构的$\mathbf{C}$，CC(CC(=O)C)C(=O)CCC(=O)O。

<MultiModal>![CC(CC(=O)C)C(=O)CCC(=O)O](/media/uploads/250210ef-204f-44d1-9f49-85d71be9258e.png)</MultiModal>

<Checkpoint>[$\mathbf{B}$的端炔基水合得到具有甲基酮结构的$\mathbf{C}$](1)</Checkpoint>

<Checkpoint>[$\mathbf{C}$为CC(CC(=O)C)C(=O)CCC(=O)O](1)</Checkpoint>

$\mathbf{C}$分子中靠近末端的酮羰基在碱性条件下与中部酮羰基的α位发生缩合，脱去1分子水，生成五元环产物$\mathbf{D}$，CC1=C(CC(=O)O)C(=O)C(C)C1。

<MultiModal>![CC1=C(CC(=O)O)C(=O)C(C)C1](/media/uploads/d0da9483-e3ee-44ec-b37f-ccd3a01668f6.png)</MultiModal>

<Checkpoint>[$\mathbf{C}$脱水缩合生成五元环产物$\mathbf{D}$](1)</Checkpoint>

<Checkpoint>[$\mathbf{D}$为CC1=C(CC(=O)O)C(=O)C(C)C1](1)</Checkpoint>

$\mathbf{D}$的分子式为$\mathrm{C_9H_{12}O_3}$，与$\mathbf{A}$相比，多了$\mathrm{C_3H_4O}$，相当于将一个氢原子替换成炔丙基并多了一分子水，这与上述推理相符。

<Checkpoint>[$\mathbf{D}$与$\mathbf{A}$相比，相当于将一个氢原子替换成炔丙基并多了一分子水](1)</Checkpoint>

可以看到$\mathbf{D}$的分子中确实存在两个甲基。

接下来分析$\mathbf{A}\rightarrow\mathbf{X}\rightarrow\mathbf{D+D'}$的过程。

$\mathbf{A}$到$\mathbf{X}$，同样是酸性汞离子条件，将端炔基氧化为甲基酮，故$\mathbf{X}$的结构为CC(=O)CC1(C)C(=O)CCC1=O，

<MultiModal>![CC(=O)CC1(C)C(=O)CCC1=O](/media/uploads/e6044de7-8fc4-46d9-8f71-9f381182e853.png)</MultiModal>

<Checkpoint>[$\mathbf{X}$为CC(=O)CC1(C)C(=O)CCC1=O](1)</Checkpoint>

$\mathbf{X}$在碱性水溶液条件下，受亲核试剂$\mathrm{OH^-}$进攻，经过开环-质子转移-关环过程同样可以得到$\mathbf{D}$，涉及的中间体为
CC(=C(CCC(=O)[O-])[O-])CC(=O)C，

<MultiModal>![CC(=C(CCC(=O)[O-])[O-])CC(=O)C](/media/uploads/f5cad2db-65c0-47c0-865c-5c4ae68da09d.png)</MultiModal>
和
CC(CC(=O)C)C(=CCC(=O)[O-])[O-]。

<MultiModal>![CC(CC(=O)C)C(=CCC(=O)[O-])[O-]](/media/uploads/d3485f01-76c3-4b72-a22b-e6ce171cc64a.png)</MultiModal>

若$\mathrm{OH^-}$并未作为亲核试剂进攻，而是发生了去质子化，则后续反应为：

<Checkpoint>[$\mathrm{OH^-}$作碱，将$\mathbf{X}$中环外羰基的α位质子拔除](1)</Checkpoint>

<MultiModal>![图中涉及13个分子或离子，通过箭头连接成一串，按顺序分别为CC(=O)CC1(C)C(=O)CCC1=O，C/C(=C\C1(C)C(=O)CCC1=O)/[O]，CC(=O)C1C2(C)C(=O)CCC12[O]，CC1=C(CCC(=O)C1C(=O)C)[O]，CC12C(=O)CCC(=O)C1C2(C)[O]，CC(=O)C1(C)C=C(CCC1=O)[O]，CC(=O)C1(C)CC(=O)CCC1=O，CC(=O)C1(C)CC(=O)CCC1(O)[O]，CC(=O)[C-](C)CC(=O)CCC(=O)O，CC(CC(=O)[C-]CC(=O)O)C(=O)C，CC1CC(=O)C(CC(=O)O)C1(C)[O]，CC1CC(=O)[C-](CC(=O)O)C1(C)O，CC1CC(=O)C(=C1C)CC(=O)O](/media/uploads/90620c17-adfe-4d19-aa14-72fa64db882e.png)</MultiModal>

具体过程为$\mathbf{X}$环外羰基的α位去质子，生成C/C(=C\C1(C)C(=O)CCC1=O)/[O]
<MultiModal>![C/C(=C\C1(C)C(=O)CCC1=O)/[O]](/media/uploads/82ab87c9-5ae0-4205-9e5b-59be8d6d5bd2.png)</MultiModal>
烯醇负离子进攻羰基碳得到[3.1.0]桥环CC(=O)C1C2(C)C(=O)CCC12[O]
<MultiModal>![CC(=O)C1C2(C)C(=O)CCC12[O]](/media/uploads/9d799e1d-5a96-4722-85bd-5369bf278692.png)</MultiModal>
碳碳键断开得到具有六元环结构的烯醇负离子CC1=C(CCC(=O)C1C(=O)C)[O]
<MultiModal>![CC1=C(CCC(=O)C1C(=O)C)[O]](/media/uploads/f68409fb-81d8-4965-8b15-04f7a380b3c2.png)</MultiModal>
烯醇负离子进攻环外羰基得到[4.1.0]桥环CC12C(=O)CCC(=O)C1C2(C)[O]
<MultiModal>![CC12C(=O)CCC(=O)C1C2(C)[O]](/media/uploads/e2c91667-90a9-4847-9c0e-ecb334333225.png)</MultiModal>
开环得到重排的另一种烯醇负离子CC(=O)C1(C)C=C(CCC1=O)[O]
<MultiModal>![CC(=O)C1(C)C=C(CCC1=O)[O]](/media/uploads/0cbd1038-6cc7-412e-8903-15ceffc284c2.png)</MultiModal>
质子化，得到CC(=O)C1(C)CC(=O)CCC1=O
<MultiModal>![CC(=O)C1(C)CC(=O)CCC1=O](/media/uploads/9f0ee9f8-7e0e-4863-91c5-7d23f7a8c752.png)</MultiModal>
羰基被外来羟基进攻CC(=O)C1(C)CC(=O)CCC1(O)[O]
<MultiModal>![CC(=O)C1(C)CC(=O)CCC1(O)[O]](/media/uploads/ba3055de-0ee3-4af8-8f2e-e2d67d0c1158.png)</MultiModal>
开环得到羧基中间体CC(=O)[C-](C)CC(=O)CCC(=O)O
<MultiModal>![CC(=O)[C-](C)CC(=O)CCC(=O)O](/media/uploads/5e2f7caa-618d-4545-8e00-f47e54a89f0d.png)</MultiModal>
质子转移，生成CC(CC(=O)[C-]CC(=O)O)C(=O)C
<MultiModal>![CC(CC(=O)[C-]CC(=O)O)C(=O)C](/media/uploads/3be8666a-31db-4bac-8f77-d8b31bed3f07.png)</MultiModal>
关环生成五元环CC1CC(=O)C(CC(=O)O)C1(C)[O]
<MultiModal>![CC1CC(=O)C(CC(=O)O)C1(C)[O]](/media/uploads/ca2c6927-1c19-47c5-9b66-f461b0f083b9.png)</MultiModal>
质子转移，生成CC1CC(=O)[C-](CC(=O)O)C1(C)O
<MultiModal>![CC1CC(=O)[C-](CC(=O)O)C1(C)O](/media/uploads/b8028f53-2bb9-4089-9b66-9b5b9de2a8cc.png)</MultiModal>
羟基离去生成$\mathbf{D'}$ CC1C=C(CC(=O)O)C(=O)C1。

<MultiModal>![CC1CC(=O)C(=C1C)CC(=O)O](/media/uploads/ba0c26b2-a0ec-4258-9c8f-ba451227911f.png)</MultiModal>


在上述过程中，总共发生了3次关环，3次开环，故涉及到的关环和开环次数总和为6。

<Checkpoint>[3次关环，3次开环](1)</Checkpoint>