Electronic Spectra and Magnetic Properties — Revision Notes

⚡ 30-Second Revision

d-d Transitions: — Electron jumps between split d-orbitals, causes color.
Color: — Complementary to absorbed light. $E_{absorbed} = \Delta_o$ or $\Delta_t$.
Spectrochemical Series: — $I^- < Br^- < Cl^- < F^- < H_2O < NH_3 < en < CN^- < CO$ (increasing $\Delta$).
Factors affecting $\Delta$: — Ligand strength, metal oxidation state, metal identity (3d < 4d < 5d), geometry ($\Delta_o > \Delta_t$).
Paramagnetism: — Unpaired electrons ($n>0$), attracted to magnetic field.
Diamagnetism: — All electrons paired ($n=0$), weakly repelled.
Spin-Only Magnetic Moment: — $\mu_s = \sqrt{n(n+2)}\,\text{BM}$.
High Spin: — Weak field ligands, $\Delta_o < P$, max unpaired electrons ($d^4-d^7$ octahedral).
Low Spin: — Strong field ligands, $\Delta_o > P$, min unpaired electrons ($d^4-d^7$ octahedral).
Tetrahedral: — Always high spin, $\Delta_t \approx \frac{4}{9}\Delta_o$.

2-Minute Revision

Coordination compounds exhibit vibrant colors and distinct magnetic properties due to the interaction between the central metal ion's d-orbitals and the surrounding ligands. This interaction, explained by Crystal Field Theory (CFT), causes the d-orbitals to split into different energy levels (e.g., $t_{2g}$ and $e_g$ in octahedral complexes). The energy difference, $\Delta$, is the crystal field splitting energy.

Electronic Spectra & Color: When a complex absorbs visible light, an electron undergoes a d-d transition from a lower to a higher energy d-orbital. The energy of the absorbed light corresponds to $\Delta$.

The color observed is the complementary color of the absorbed light. The magnitude of $\Delta$ depends on the ligand (spectrochemical series: strong field ligands like $CN^-$ cause large $\Delta$, weak field ligands like $H_2O$ cause small $\Delta$), the metal's oxidation state (higher charge, larger $\Delta$), and the complex's geometry ($\Delta_o > \Delta_t$).

Magnetic Properties: These depend on the number of unpaired electrons ($n$). Paramagnetic complexes have unpaired electrons and are attracted to a magnetic field, quantified by the spin-only magnetic moment $\mu_s = \sqrt{n(n+2)}\,\text{BM}$.

Diamagnetic complexes have all paired electrons ($n=0$) and are weakly repelled. For $d^4$ to $d^7$ octahedral complexes, the spin state (high spin or low spin) is crucial. If $\Delta_o < P$ (pairing energy), it's high spin (max $n$).

If $\Delta_o > P$, it's low spin (min $n$). Tetrahedral complexes are always high spin.

5-Minute Revision

Electronic spectra and magnetic properties are fundamental to coordination chemistry, providing insights into electronic structure and bonding. The core concept is Crystal Field Theory (CFT), which describes the electrostatic interaction between metal d-orbitals and ligands, leading to d-orbital splitting.

For octahedral complexes, d-orbitals split into lower energy $t_{2g}$ and higher energy $e_g$ sets, with an energy difference of $\Delta_o$. For tetrahedral complexes, the splitting is inverted and smaller, $\Delta_t \approx \frac{4}{9}\Delta_o$.

Electronic Spectra and Color: The vibrant colors of many transition metal complexes arise from d-d transitions. An electron absorbs a photon of visible light, gaining energy equal to $\Delta$, and jumps from a $t_{2g}$ to an $e_g$ orbital.

The color observed is the complementary color of the light absorbed. For instance, if a complex absorbs blue light, it appears yellow. The magnitude of $\Delta$ dictates the energy (and thus wavelength) of absorbed light.

Strong field ligands (e.g., $CN^-, CO$) cause large $\Delta$, absorbing high-energy (short-wavelength) light, while weak field ligands (e.g., $F^-, H_2O$) cause small $\Delta$, absorbing low-energy (long-wavelength) light.

This is summarized by the spectrochemical series. Other factors influencing $\Delta$ include the metal's oxidation state (higher charge $\rightarrow$ larger $\Delta$) and the metal's position in the periodic table (4d/5d metals have larger $\Delta$ than 3d metals).

Magnetic Properties: These are determined by the presence of unpaired electrons. Substances with unpaired electrons are paramagnetic (attracted to a magnetic field), while those with all paired electrons are diamagnetic (weakly repelled).

The **spin-only magnetic moment ($\mu_s$)** quantifies paramagnetism: $\mu_s = \sqrt{n(n+2)}\,\text{BM}$, where $n$ is the number of unpaired electrons. For $d^4, d^5, d^6, d^7$ octahedral complexes, the electron distribution depends on the relative values of $\Delta_o$ and the pairing energy (P) (energy required to pair electrons in an orbital).

High Spin Complexes: — Formed with weak field ligands (e.g., $H_2O, F^-$) where $\Delta_o < P$. Electrons occupy orbitals singly as much as possible, maximizing $n$.
Low Spin Complexes: — Formed with strong field ligands (e.g., $CN^-, en$) where $\Delta_o > P$. Electrons pair up in lower energy orbitals first, minimizing $n$.

Example: For $Fe^{2+}$ ($d^6$):

In $[Fe(H_2O)_6]^{2+}$ ($H_2O$ is weak field): High spin, $t_{2g}^4 e_g^2$, $n=4$, $\mu_s \approx 4.90\,\text{BM}$.
In $[Fe(CN)_6]^{4-}$ ($CN^-$ is strong field): Low spin, $t_{2g}^6 e_g^0$, $n=0$, diamagnetic.

Tetrahedral complexes always exhibit high spin behavior because $\Delta_t$ is typically much smaller than P. Mastering these concepts allows for predicting and explaining the observed properties of coordination compounds.

Prelims Revision Notes

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Oxidation State & d-Configuration: — Always start by finding the oxidation state of the central metal and its d-electron configuration (e.g., $Fe^{3+}$ is $d^5$). Remember that for transition metals, $s$-electrons are removed before $d$-electrons during ionization.
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Spectrochemical Series (Key Ligands): — Memorize the order of common ligands: $I^- < Br^- < Cl^- < F^- < OH^- < H_2O < NCS^- < NH_3 < en < CN^- < CO$. Weak field ligands are on the left (small $\Delta$), strong field on the right (large $\Delta$).
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d-Orbital Splitting:

* Octahedral: $t_{2g}$ (lower energy, 3 orbitals) and $e_g$ (higher energy, 2 orbitals). $\Delta_o = E_{e_g} - E_{t_{2g}}$. * Tetrahedral: $e$ (lower energy, 2 orbitals) and $t_2$ (higher energy, 3 orbitals). $\Delta_t = E_{t_2} - E_e$. Note: $\Delta_t \approx \frac{4}{9}\Delta_o$.

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**High Spin vs. Low Spin (Octahedral $d^4-d^7$):**

* High Spin: Weak field ligands, $\Delta_o < P$. Electrons fill $t_{2g}$ and $e_g$ singly before pairing. Maximizes unpaired electrons. * Low Spin: Strong field ligands, $\Delta_o > P$. Electrons pair up in $t_{2g}$ before filling $e_g$. Minimizes unpaired electrons. * For $d^1, d^2, d^3, d^8, d^9, d^{10}$ octahedral, spin state is fixed regardless of ligand strength.

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Magnetic Moment:

* Paramagnetic: $n > 0$ (unpaired electrons). Attracted to magnetic field. Calculate $\mu_s = \sqrt{n(n+2)}\,\text{BM}$. * Diamagnetic: $n = 0$ (all paired electrons). Weakly repelled by magnetic field. * Orbital contribution is usually quenched, so spin-only formula is applicable.

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Color:

* Caused by d-d transitions (absorption of visible light). $E_{absorbed} = \Delta$. * Observed color is complementary to absorbed color (e.g., absorbs blue, appears yellow). * Higher $\Delta$ means higher energy absorption, shorter wavelength, higher frequency. * Tetrahedral complexes generally have more intense colors than octahedral due to lack of centrosymmetry (less Laporte forbidden).

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**Factors Affecting $\Delta$:**

* Ligand: Stronger ligand $\rightarrow$ larger $\Delta$. * Metal Oxidation State: Higher charge $\rightarrow$ larger $\Delta$. * Metal Identity: $3d < 4d < 5d$ (for same group, $\Delta$ increases down the group). * Geometry: $\Delta_o > \Delta_t$.

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Common $d^8$ Case: — Square planar complexes (e.g., $Ni^{2+}$ with strong field ligands like $CN^-$) are often diamagnetic ($n=0$).

Vyyuha Quick Recall

To remember the spectrochemical series for common ligands (increasing $\Delta$):

I Brought Some Cold Clam Noodles For Our Hungry Chef, Who Never Eats Any Pasta Except New Chicken Curry.

$I^- < Br^- < S^{2-} < SCN^- < Cl^- < NO_3^- < F^- < OH^- < C_2O_4^{2-} < H_2O < NCS^- < EDTA^{4-} < NH_3 < py < en < NO_2^- < CN^- < CO$