1a. (25 pts) on its own separate framework, draw each one of the four vb orbitals belonging to one of the three-center four-electron bonds, in the single resonance form shown below.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "explain_then_answer", "tutor" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Valence Bond Theory", "Three-Center Four-Electron Bond", "Hypervalent Molecules" ], "current_concepts": [ "Valence Bond Theory", "Three-Center Four-Electron Bond", "Hypervalent Molecules" ] } ## Identify the 3c-4e bond The molecule shown is $\text{XeOF}_4$. The central xenon atom has a $3+$ formal charge, an apical oxygen atom with a single bond and a negative charge ($\text{O}^-$), and four equatorial fluorine atoms (two covalently bound, and two as isolated fluoride anions $\text{F}^-$ in this specific resonance structure). The three-center four-electron (3c-4e) bonding system in this resonance form is formed along the linear $\text{F}-\text{Xe}-\text{F}$ axes. Specifically, each linear $\text{F}-\text{Xe}-\text{F}$ unit consists of: 1. A central xenon atom ($\text{Xe}^{3+}$). 2. Two equatorial fluorine atoms on opposite sides. In this resonance structure, one is covalently bound (sharing a pair of electrons with Xe) and the other is an isolated fluoride ion ($\text{F}^-$) with a full octet. Thus, there are two perpendicular linear 3c-4e systems in the equatorial plane: - One along the $\text{F}-\text{Xe}\cdots\text{F}^-$ axis (left-to-right). - One along the other $\text{F}-\text{Xe}\cdots\text{F}^-$ axis (front-to-back). Let us focus on one of these linear $\text{F}-\text{Xe}\cdots\text{F}^-$ 3c-4e bonds to describe its four Valence Bond (VB) orbitals. ## Determine the VB orbitals In Valence Bond theory, a three-center four-electron (3c-4e) bond is described by localized atomic orbitals on each of the three participating atoms. For a linear $\text{F}_a-\text{Xe}-\text{F}_b$ system: - The central $\text{Xe}$ uses a $p$-orbital aligned along the bond axis (let's call it the $p_x$ orbital). - The two terminal fluorine atoms ($\text{F}_a$ and $\text{F}_b$) each use a $p$-orbital directed along the bond axis (their respective $p_x$ orbitals). The four valence electrons in this 3c-4e system occupy two localized VB orbitals (each containing a pair of electrons): 1. **Covalent Bond Orbital**: A localized bonding orbital between $\text{Xe}$ and the covalently bound fluorine ($\text{F}_a$). This is formed by the overlap of the $\text{Xe}$ $p_x$ orbital and the $\text{F}_a$ $p_x$ orbital. 2. **Fluoride Lone Pair Orbital**: A localized non-bonding lone pair orbital residing entirely on the isolated fluoride ion ($\text{F}_b^-$). This is a fully occupied $p_x$ orbital on $\text{F}_b^-$. To fully represent the VB description of this resonance structure, we draw the active atomic orbitals that participate in this bonding scheme across the four frameworks: - **Orbital 1**: The $p$-orbital on the covalently bound fluorine atom ($\text{F}$) pointing toward $\text{Xe}$. - **Orbital 2**: The $p$-orbital on the central $\text{Xe}$ atom pointing toward the covalently bound fluorine. - **Orbital 3**: The $p$-orbital on the central $\text{Xe}$ atom pointing toward the isolated fluoride ion ($\text{F}^-$). - **Orbital 4**: The $p$-orbital on the isolated fluoride ion ($\text{F}^-$) pointing toward $\text{Xe}$. *(Note: Orbitals 2 and 3 represent the two lobes of the single $p$-orbital on the central $\text{Xe}$ atom aligned along this axis).* ## Describe the drawings for each framework To represent these four VB orbitals on the four separate molecular frameworks provided: - **Framework 1 (F $p$-orbital)**: Draw a $p$-orbital (two lobes, shaded/unshaded or $+/-$ signs) on the covalently bound equatorial $\text{F}$ atom, with its lobes oriented along the $\text{F}-\text{Xe}$ axis. - **Framework 2 (Xe $p$-orbital lobe 1)**: Draw the lobe of the $\text{Xe}$ $p$-orbital that points directly toward the covalently bound equatorial $\text{F}$ atom. - **Framework 3 (Xe $p$-orbital lobe 2)**: Draw the opposite lobe of the $\text{Xe}$ $p$-orbital that points directly toward the isolated equatorial $\text{F}^-$ ion. - **Framework 4 (F$^-$ $p$-orbital)**: Draw a $p$-orbital on the isolated equatorial $\text{F}^-$ ion, with its lobes oriented along the $\text{Xe}\cdots\text{F}^-$ axis. To represent the four Valence Bond (VB) orbitals belonging to one of the three-center four-electron (3c-4e) bonds along a linear $\text{F}-\text{Xe}\cdots\text{F}^-$ axis, draw the following atomic orbital components on each of the four frameworks from left to right: 1. **First Framework (Terminal Covalent Fluorine Orbital):** Draw a $p$-orbital on the covalently bound equatorial $\text{F}$ atom, with its lobes aligned along the $\text{F}-\text{Xe}$ bonding axis pointing toward the central $\text{Xe}$ atom. 2. **Second Framework (Central Xenon Orbital - Lobe A):** Draw one lobe of the central $\text{Xe}$ $p$-orbital pointing directly along the axis toward the covalently bound equatorial $\text{F}$ atom. 3. **Third Framework (Central Xenon Orbital - Lobe B):** Draw the second, oppositely phased lobe of the central $\text{Xe}$ $p$-orbital pointing along the axis toward the isolated equatorial $\text{F}^-$ ion. 4. **Fourth Framework (Terminal Fluoride Ion Orbital):** Draw a fully occupied $p$-orbital on the isolated equatorial $\text{F}^-$ ion, with its lobes aligned along the $\text{Xe}\cdots\text{F}^-$ axis pointing toward the central $\text{Xe}$ atom. { "subject": "Natural Science", "question_type": "Free Response", "knowledge_point": [ "Natural Science", "Chemistry", "Inorganic Chemistry" ] }

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Identify the 3c-4e bond

Determine the VB orbitals

Describe the drawings for each framework

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