Electronic Transitions

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### Electronic Transitions Overview Electronic transitions occur when an electron in an atom or molecule moves from one energy level to another. This typically involves the absorption or emission of electromagnetic radiation (photons). The energy difference between the levels ($\Delta E$) must match the photon's energy ($h\nu$). $$\Delta E = E_{final} - E_{initial} = h\nu$$ Where: - $h$ is Planck's constant - $\nu$ is the frequency of the photon ### Molecular Orbitals (MOs) Understanding electronic transitions requires knowledge of molecular orbitals. - **Bonding ($\sigma, \pi$):** Lower energy, formed by constructive overlap. - $\sigma$ (sigma): Strongest, head-on overlap, free rotation. - $\pi$ (pi): Weaker, sideways overlap, restricted rotation. - **Non-bonding ($n$):** Intermediate energy, lone pair electrons, not involved in bonding. - **Antibonding ($\sigma^*, \pi^*$):** Higher energy, formed by destructive overlap. - $\sigma^*$ (sigma antibonding): Higher energy counterpart to $\sigma$. - $\pi^*$ (pi antibonding): Higher energy counterpart to $\pi$. #### Energy Ordering of MOs (General) $\sigma ### Types of Electronic Transitions Transitions are categorized by the initial and final molecular orbitals involved. The energy required for each transition type follows a general trend. #### 1. $\sigma \rightarrow \sigma^*$ Transitions - **Description:** Excitation of an electron from a bonding sigma ($\sigma$) orbital to an antibonding sigma ($\sigma^*$) orbital. - **Energy:** Highest energy requirement. - **Wavelength:** Occur in the vacuum ultraviolet (VUV) region ( ### Charge Transfer (CT) Transitions - **Description:** Electron moves from an orbital localized primarily on one atom/ligand to an orbital localized primarily on another atom/ligand. - **Energy:** Varies widely, can be very intense. - **Wavelength:** Often in the visible region, leading to strong colors. - **Types:** - **Ligand-to-Metal Charge Transfer (LMCT):** Electron moves from ligand orbital to metal orbital (e.g., $\text{MnO}_4^-$). - **Metal-to-Ligand Charge Transfer (MLCT):** Electron moves from metal orbital to ligand orbital (e.g., $\text{Ru(bpy)}_3^{2+}$). - **Intermolecular CT:** Electron transfer between separate molecules in a complex. - **Compounds:** Transition metal complexes, donor-acceptor systems. ### d-d and f-f Transitions - **Description:** Transitions between d-orbitals in transition metals or f-orbitals in lanthanides/actinides. - **Energy:** Typically in the visible region for d-d transitions (giving color to many transition metal complexes). - **Wavelength:** d-d: Visible; f-f: Sharp, often weak, in visible/NIR. - **Intensity:** Usually weak due to Laporte selection rule (forbidden for centrosymmetric complexes). - **Compounds:** Transition metal complexes (d-d), Lanthanide and Actinide compounds (f-f). ### Selection Rules These rules dictate whether a transition is "allowed" or "forbidden," affecting its intensity. - **Spin Selection Rule:** $\Delta S = 0$ (spin multiplicity must not change). - Transitions involving a change in spin (e.g., singlet to triplet) are spin-forbidden and weak. - **Laporte Selection Rule:** $\Delta l = \pm 1$ (change in angular momentum quantum number). - For d-d or f-f transitions, this rule means they are formally forbidden if the molecule has a center of symmetry. Vibrational coupling can relax this rule, leading to weak bands. - $\sigma \rightarrow \sigma^*$, $\pi \rightarrow \pi^*$, $n \rightarrow \sigma^*$, $n \rightarrow \pi^*$ transitions are typically allowed or partially allowed.