In the ion $\mathrm{[Fe_{5}O(CH_{3}COO)_{12}]^{+}}$, iron exhibits two coordination numbers and two chemical environments, with a ratio of $2:3$. The acetate groups act as bridging or monodentate ligands.  

Among the following statements about the structure of this compound, identify the correct one.
在离子$\mathrm{[Fe_{5}O(CH_{3}COO)_{12}]^{+}}$中，铁有两种配位数和两种化学环境，其数目比是$2:3$，醋酸根为桥联或单齿配体。

对该化合物的结构的以下说法中，指出其中正确的一项。
In this complex, the $\mathrm{O}$ monoatomic ligand is connected to four $\mathrm{Fe}$ atoms.
In this complex, there is a 5-coordinated $\mathrm{Fe}$.
In this complex, a five-membered ring structure is present.
In this complex, the bridging acetate ligand has only one chemical environment.
There are no atoms at the geometric center of this complex ion.
In this complex, there exists a Y-shaped structure formed with the participation of $\mathrm{Fe}$ atoms, which is coplanar or nearly coplanar.
In this complex, if all freely rotatable parts connected by single bonds are considered spherical and minor deviations are neglected, the order of the point group to which the complex belongs is 3.
In this complex, the monodentate acetate ligand and the monatomic $\mathrm{O}$ ligand can occupy adjacent positions in the coordination polyhedron of the $\mathrm{Fe}$ atom.
None of the above options is correct
该配合物中，$\mathrm{O}$单原子配体与4个$\mathrm{Fe}$相连。
该配合物中，存在5配位的$\mathrm{Fe}$。
该配合物中，存在五元环结构。
该配合物中，桥联的醋酸根配体只有1种化学环境。
该配合物离子的几何中心处没有原子。
该配合物中，存在有$\mathrm{Fe}$原子参与构成的共平面或接近共平面的Y形结构。
在该配合物中，若将所有以单键相连的可自由转动部分视为球形，并忽略微小偏离，则配合物所属的点群阶数为3。
该配合物中，单齿的醋酸根配体与单原子$\mathrm{O}$配体可处于同一个$\mathrm{Fe}$原子配位多面体的邻位。
以上选项均不正确
Examining the composition of $\mathrm{[Fe_{5}O(CH_{3}COO)_{12}]^{+}}$, there is one single-atom $\mathrm{O}$ ligand, which is preferentially placed at the center. The five $\mathrm{Fe}$ atoms are divided into two chemical environments in a 2:3 ratio, likely forming a $\mathrm{Fe_{5}O}$ trigonal bipyramidal structure around $\mathrm{O}$, where two $\mathrm{Fe}$ atoms occupy axial positions and three $\mathrm{Fe}$ atoms occupy equatorial positions.

<Checkpoint>[$\mathrm{Fe_{5}O}$ trigonal bipyramid exists](1)</Checkpoint>

Among the 12 acetate ligands, there are two coordination modes: monodentate and bridging. Due to the core $\mathrm{Fe-O-Fe}$ structure, the acetate ligands can form stable six-membered rings when bridging. Therefore, when arranging the acetate ligands, bridging should be prioritized.

<Checkpoint>[Bridging acetates can participate in forming six-membered rings](1)</Checkpoint>

Within the trigonal bipyramid, excluding the axial pair of $\mathrm{Fe}$ atoms, the five $\mathrm{Fe}$ atoms can form nine adjacent $\mathrm{FeFe}$ pairs: three in the equatorial plane and six along the meridional direction. If each $\mathrm{FeFe}$ pair is bridged by one acetate, nine acetates are consumed, leaving three terminal acetates, which can be placed on the equatorial $\mathrm{Fe}$ atoms.

The resulting structure of the $\mathrm{[Fe_{5}O(CH_{3}COO)_{12}]^{+}}$ ion is as follows:

<MultiModal>![$\mathrm{O}$ is at the center, with five $\mathrm{Fe}$ atoms forming a trigonal bipyramid around it. The two axial $\mathrm{Fe}$ atoms are tetrahedrally 4-coordinated, while the three equatorial $\mathrm{Fe}$ atoms are octahedrally 6-coordinated. On the coordination polyhedra of the equatorial $\mathrm{Fe}$ atoms, the position opposite to the central $\mathrm{O}$ is occupied by terminal $\mathrm{OOCCH_{3}}$ groups—three in total. There are nine bridging $\mathrm{O \frown O}$ groups, each connecting two different $\mathrm{Fe}$ atoms: three in the equatorial plane, linking the equatorial $\mathrm{Fe}$ atoms pairwise, and six along the meridional direction, connecting axial and equatorial $\mathrm{Fe}$ atoms.](/media/uploads/8fa01980-1770-4c47-ba44-afa15a083309.png)</MultiModal>

In the figure, $\mathrm{O\frown O}$ represents bridging acetate groups. It can be seen that the five $\mathrm{Fe}$ atoms form a trigonal bipyramid around the central $\mathrm{O}$, with two chemical environments: three 6-coordinated $\mathrm{Fe}$ atoms and two 4-coordinated $\mathrm{Fe}$ atoms, along with three terminal acetates and nine bridging acetates, satisfying the given conditions.

<Checkpoint>[There are three 6-coordinated $\mathrm{Fe}$ atoms, two 4-coordinated $\mathrm{Fe}$ atoms, three terminal acetates, and nine bridging acetates](1)</Checkpoint>

In this complex structure, a $\mathrm{Fe_{5}O}$ trigonal bipyramid exists, with the oxygen atom being 5-coordinated, so $\mathbf{A}$ is incorrect.

This complex has three 6-coordinated $\mathrm{Fe}$ atoms and two 4-coordinated $\mathrm{Fe}$ atoms, with no 5-coordinated $\mathrm{Fe}$ atoms, so $\mathbf{B}$ is incorrect.

In this complex, the smallest ring is $\mathrm{O_{central}-Fe-O_{acetic}-C-O_{acetic}-Fe}$, a six-membered ring, so $\mathbf{C}$ is incorrect.

<Checkpoint>[The smallest ring is a six-membered ring](1)</Checkpoint>

In this complex, the nine bridging acetates are divided into two types: three in the equatorial plane and six along the meridional direction, with different chemical environments, so $\mathbf{D}$ is incorrect.

<Checkpoint>[Bridging acetates are divided into three in the equatorial plane and six along the meridional direction](1)</Checkpoint>

From the complex structure, it can be seen that the geometric center is the 5-coordinated $\mathrm{O}$ atom, so $\mathbf{E}$ is incorrect.

<Checkpoint>[The geometric center is the 5-coordinated $\mathrm{O}$ atom](1)</Checkpoint>

Extracting the equatorial $\mathrm{Fe_{3}O}$ from the $\mathrm{Fe_{5}O}$ trigonal bipyramid reveals an approximately coplanar Y-shaped structure. Thus, $\mathbf{F}$ is correct.

<Checkpoint>[In the $\mathrm{Fe_{5}O}$ trigonal bipyramid, the equatorial direction forms an approximately coplanar Y-shaped $\mathrm{Fe_{3}O}$](1)</Checkpoint>

From the complex structure, the core framework is a $\mathrm{Fe_{5}O}$ trigonal bipyramid, and all acetate ligands are symmetrically distributed (ignoring minor rotational orientations and atomic deviations). Thus, the overall point group is $D_\mathrm{3h}$ with an order of 12, so $\mathbf{G}$ is incorrect.

<Checkpoint>[The point group is $D_\mathrm{3h}$](1)</Checkpoint>

In this complex structure, the monodentate acetates are located at the positions opposite to the single-atom $\mathrm{O}$ ligand on the octahedrally 6-coordinated $\mathrm{Fe}$ atoms, so $\mathbf{H}$ is incorrect.

<Checkpoint>[The monodentate acetates are located at the positions opposite to the single-atom $\mathrm{O}$ ligand on the octahedrally 6-coordinated $\mathrm{Fe}$ atoms](1)</Checkpoint>

In conclusion, the correct option is $\mathbf{F}$.
观察$\mathrm{[Fe_{5}O(CH_{3}COO)_{12}]^{+}}$的组成，有1个单原子的$\mathrm{O}$配体，优先考虑将其放在中心。5个$\mathrm{Fe}$按$2:3$的数目比分为两种化学环境，可能是在$\mathrm{O}$周围形成了$\mathrm{Fe_{5}O}$三角双锥结构，其中2个$\mathrm{Fe}$位于轴向，3个$\mathrm{Fe}$位于赤道面。

<Checkpoint>[存在$\mathrm{Fe_{5}O}$三角双锥](1)</Checkpoint>

12个醋酸根配体中，存在单齿和桥联两种配位方式，由于核心$\mathrm{Fe-O-Fe}$，醋酸根在桥联时可以形成稳定的六元环结构，故在安排醋酸根配体时，可以尽量桥联。

<Checkpoint>[桥联醋酸根可参与形成六元环](1)</Checkpoint>

三角双锥中的5个$\mathrm{Fe}$之间，除了轴向的一对$\mathrm{Fe}$原子外，可组合成9组邻位$\mathrm{FeFe}$对，其中赤道面方向为3组，经线方向有6组。若每一组$\mathrm{FeFe}$对上都有一个桥联的醋酸根，则用掉9个醋酸根，剩下3个醋酸根为端基，可放在赤道面的$\mathrm{Fe}$原子上。

这样得到的$\mathrm{[Fe_{5}O(CH_{3}COO)_{12}]^{+}}$离子结构如下：

<MultiModal>![O位于中心，5个Fe在O周围构成三角双锥结构，轴向的2个Fe为四面体4配位，赤道面上的3个Fe为八面体6配位，在赤道面上的3个Fe的配位多面体上，中心O的对位为端基OOCCH3，这样的端基有3个，有9个桥联的O \frown O，其两端均连接不同的Fe，3个位于赤道面上，将赤道面上的3个Fe两两连接，6个位于经线方向，连接轴向Fe和赤道面上的Fe。](/media/uploads/8fa01980-1770-4c47-ba44-afa15a083309.png)</MultiModal>

图中，$\mathrm{O\frown O}$表示桥联的醋酸根，可以看出，5个$\mathrm{Fe}$在中心$\mathrm{O}$的周围形成三角双锥，由两种化学环境，有3个6配位$\mathrm{Fe}$和2个4配位$\mathrm{Fe}$，3个端基醋酸根和9个桥联醋酸根，满足题述条件。

<Checkpoint>[有3个6配位$\mathrm{Fe}$和2个4配位$\mathrm{Fe}$，3个端基醋酸根和9个桥联醋酸根](1)</Checkpoint>

该配合物结构中，存在$\mathrm{Fe_{5}O}$三角双锥，氧原子为5配位，$\mathbf{A}$错误。

该配合物中有3个6配位$\mathrm{Fe}$和2个4配位$\mathrm{Fe}$，不存在5配位$\mathrm{Fe}$，$\mathbf{B}$错误。

该配合物中，最小的环是$\mathrm{O_{central}-Fe-O_{acetic}-C-O_{acetic}-Fe}$，为六元环，$\mathbf{C}$错误。

<Checkpoint>[最小的环是六元环](1)</Checkpoint>

该配合物中，9个桥联醋酸根分为赤道面方向（3个）和经线方向（6个）两类，化学环境不同，$\mathbf{D}$错误。

<Checkpoint>[桥联醋酸根分为赤道面方向的3个和经线方向的6个](1)</Checkpoint>

从配合物结构中可以看出，该配合物几何中心为5配位的$\mathrm{O}$，$\mathbf{E}$错误。

<Checkpoint>[几何中心为5配位的$\mathrm{O}$](1)</Checkpoint>

从$\mathrm{Fe_{5}O}$三角双锥中，截取赤道面方向的$\mathrm{Fe_{3}O}$，为近似共平面的Y形结构。$\mathbf{F}$正确。

<Checkpoint>[$\mathrm{Fe_{5}O}$三角双锥中，赤道面方向为近似共平面Y形的$\mathrm{Fe_{3}O}$](1)</Checkpoint>

由配合物结构可以看出，该配合物的核心骨架为$\mathrm{Fe_{5}O}$三角双锥，且所有醋酸根配体在忽略可转动部分取向和原子间微小偏移的情况下，分布对称，故整体点群为$D_\mathrm{3h}$，阶数为12，$\mathbf{G}$错误。

<Checkpoint>[点群为$D_\mathrm{3h}$](1)</Checkpoint>

该配合物结构中，单齿醋酸根位于6配位八面体$\mathrm{Fe}$上与单原子$\mathrm{O}$配体的对位，$\mathbf{H}$错误。

<Checkpoint>[单齿醋酸根位于6配位八面体$\mathrm{Fe}$上与单原子$\mathrm{O}$配体的对位](1)</Checkpoint>

综上，正确选项为$\mathbf{F}$。