Bonding in Coordination Compounds — Revision Notes

⚡ 30-Second Revision

VBT — Hybridization ($sp^3$, $dsp^2$, $d^2sp^3$, $sp^3d^2$) $\rightarrow$ Geometry (Tetrahedral, Square Planar, Octahedral).
Magnetic Moment — Count unpaired electrons (n). $\\mu = \\sqrt{n(n+2)}\text{ BM}$.
CFT — Electrostatic interaction $\rightarrow$ d-orbital splitting (\\Delta).
Octahedral Splitting — $t_{2g}$ (lower, $-0.4\\Delta_o$) and $e_g$ (higher, $+0.6\\Delta_o$).
Tetrahedral Splitting — $e$ (lower, $-0.6\\Delta_t$) and $t_2$ (higher, $+0.4\\Delta_t$). $\\Delta_t \approx \\frac{4}{9}\\Delta_o$.
Spectrochemical Series — $I^- < Br^- < Cl^- < F^- < H_2O < NH_3 < en < CN^- < CO$.
High Spin — Weak field ligands, small \\Delta, maximize unpaired electrons (P > \\Delta).
Low Spin — Strong field ligands, large \\Delta, minimize unpaired electrons (\\Delta > P).
Color — d-d transitions, absorbed energy = \\Delta, observed color is complementary.

2-Minute Revision

Bonding in coordination compounds is explained by Valence Bond Theory (VBT) and Crystal Field Theory (CFT). VBT focuses on the formation of coordinate covalent bonds through hybridization of metal orbitals ($sp^3$, $dsp^2$, $d^2sp^3$, $sp^3d^2$), which dictates the geometry (tetrahedral, square planar, octahedral) and magnetic properties (paramagnetic if unpaired electrons, diamagnetic if all paired).

Strong field ligands can force electron pairing, leading to inner orbital complexes, while weak field ligands result in outer orbital complexes.

CFT, a more quantitative approach, treats metal-ligand interactions as purely electrostatic. This causes the splitting of degenerate d-orbitals into different energy levels. For octahedral complexes, d-orbitals split into lower energy $t_{2g}$ and higher energy $e_g$ sets, with an energy difference of $\\Delta_o$.

The magnitude of \\Delta depends on the ligand (spectrochemical series), metal oxidation state, and metal series. If \\Delta is large (strong field ligand), electrons pair up (low spin); if \\Delta is small (weak field ligand), electrons occupy higher energy orbitals unpaired (high spin).

CFT explains the color of complexes via d-d transitions and allows for calculation of magnetic moments using the spin-only formula $\\mu = \\sqrt{n(n+2)}\text{ BM}$.

5-Minute Revision

A comprehensive understanding of bonding in coordination compounds requires mastering both Valence Bond Theory (VBT) and Crystal Field Theory (CFT). VBT, a qualitative approach, explains the formation of coordinate covalent bonds by the overlap of vacant metal hybrid orbitals with filled ligand orbitals.

The hybridization type ($sp^3$, $dsp^2$, $d^2sp^3$, $sp^3d^2$) determines the complex's geometry (tetrahedral, square planar, octahedral). The presence of unpaired electrons in the metal's d-orbitals dictates its magnetic nature (paramagnetic or diamagnetic).

Strong field ligands tend to cause electron pairing, leading to inner orbital complexes (e.g., $d^2sp^3$), while weak field ligands result in outer orbital complexes (e.g., $sp^3d^2$).

Example (VBT): For $[Co(NH_3)_6]^{3+}$: $Co^{3+}$ is $3d^6$. $NH_3$ is a strong field ligand, forcing pairing. This makes two $3d$ orbitals available. Hybridization: $d^2sp^3$. Geometry: Octahedral. Magnetic nature: Diamagnetic (0 unpaired electrons).

CFT provides a more quantitative explanation by treating metal-ligand interactions as purely electrostatic. Ligands create an electric field that lifts the degeneracy of the metal's d-orbitals, splitting them into different energy levels.

For octahedral complexes, the $d_{xy}, d_{yz}, d_{zx}$ (t$_{2g}$) orbitals are lowered in energy by $0.4\\Delta_o$, and the $d_{x^2-y^2}, d_{z^2}$ (e$_g$) orbitals are raised by $0.6\\Delta_o$. The Crystal Field Splitting Energy (CFSE), $\\Delta_o$, is crucial.

Its magnitude depends on the ligand (spectrochemical series), metal oxidation state, and the metal's position in the periodic table. Strong field ligands cause large \\Delta, leading to low spin complexes (electrons pair up if $\\Delta > P$, pairing energy).

Weak field ligands cause small \\Delta, leading to high spin complexes (electrons occupy higher energy orbitals unpaired if $P > \\Delta$).

Example (CFT): For $[Fe(CN)_6]^{4-}$: $Fe^{2+}$ is $3d^6$. $CN^-$ is a strong field ligand, causing large $\\Delta_o$. Thus, it's a low spin complex. Electrons fill $t_{2g}$ first, then pair up: $t_{2g}^6 e_g^0$. Number of unpaired electrons = 0. Magnetic moment = 0 BM (diamagnetic). CFSE = $(-0.4 \times 6 + 0.6 \times 0)\\Delta_o + 3P = -2.4\\Delta_o + 3P$.

CFT also explains the color of complexes: d-d transitions occur when electrons absorb light energy equal to \\Delta, promoting them to higher d-orbitals. The observed color is the complementary color of the absorbed light. For NEET, remember the spectrochemical series and practice calculating magnetic moments using $\\mu = \\sqrt{n(n+2)}\text{ BM}$ and CFSE for various d-electron configurations in octahedral and tetrahedral fields.

Prelims Revision Notes

Bonding in Coordination Compounds: NEET Quick Recall

I. Valence Bond Theory (VBT)

Core Idea — Coordinate covalent bond formation via orbital overlap.
Hybridization & Geometry — Central metal provides vacant orbitals for hybridization.

* CN=2: $sp$ (Linear) * CN=4: $sp^3$ (Tetrahedral) or $dsp^2$ (Square Planar) * CN=5: $sp^3d$ (Trigonal Bipyramidal) * CN=6: $d^2sp^3$ (Inner Orbital, Octahedral) or $sp^3d^2$ (Outer Orbital, Octahedral)

Magnetic Properties — Determined by unpaired electrons.

* Paramagnetic: Unpaired electrons present. * Diamagnetic: All electrons paired.

Ligand Influence — Strong field ligands (e.g., $CN^-$, $CO$, $NH_3$) force electron pairing, leading to inner orbital/low spin complexes. Weak field ligands (e.g., $Cl^-$, $H_2O$) do not force pairing, leading to outer orbital/high spin complexes.
Limitations — Doesn't explain color, quantitative magnetic properties, or thermodynamic stability.

II. Crystal Field Theory (CFT)

Core Idea — Purely electrostatic interaction between metal ion and ligands (point charges/dipoles).
d-orbital Splitting — Ligand field lifts degeneracy of d-orbitals.

* Octahedral (O_h): $t_{2g}$ (lower, $d_{xy}, d_{yz}, d_{zx}$) and $e_g$ (higher, $d_{x^2-y^2}, d_{z^2}$). Energy difference = $\\Delta_o$. * $E_{t_{2g}} = -0.4\\Delta_o$ * $E_{e_g} = +0.6\\Delta_o$ * Tetrahedral (T_d): $e$ (lower, $d_{x^2-y^2}, d_{z^2}$) and $t_2$ (higher, $d_{xy}, d_{yz}, d_{zx}$). Energy difference = $\\Delta_t$. * $E_e = -0.6\\Delta_t$ * $E_{t_2} = +0.4\\Delta_t$ * $\\Delta_t \approx \\frac{4}{9}\\Delta_o$

Crystal Field Stabilization Energy (CFSE)

* $CFSE = (-0.4 n_{t_{2g}} + 0.6 n_{e_g})\\Delta_o$ (for octahedral) * Add pairing energy (P) if electrons are forced to pair due to strong field.

Spectrochemical Series (Increasing \\Delta)

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

High Spin vs. Low Spin (for $d^4-d^7$ octahedral)

* High Spin (Weak Field): Small \\Delta. Electrons fill orbitals to maximize unpaired electrons (P > \\Delta). * Low Spin (Strong Field): Large \\Delta. Electrons pair up in lower energy orbitals (\\Delta > P).

Magnetic Moment — Calculated from number of unpaired electrons (n).

* $\\mu = \\sqrt{n(n+2)}\text{ BM}$ (Spin-only formula)

Color — Explained by d-d transitions. Absorbed energy ($E = h\\nu = \\Delta$) corresponds to electron promotion. Observed color is complementary.
Factors Affecting \\Delta — Ligand nature, metal oxidation state, metal series (3d < 4d < 5d), geometry.
Limitations — Purely ionic model, doesn't account for covalent character or \\pi-bonding effectively.

Vyyuha Quick Recall

To remember the spectrochemical series (common ligands, increasing field strength):

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I$^{-}$ (Iodide)
Br$^{-}$ (Bromide)
S$^{2-}$ (Sulfide)
SCN$^{-}$ (Thiocyanate - S-bonded)
Cl$^{-}$ (Chloride)
NO$_3^{-}$ (Nitrate)
F$^{-}$ (Fluoride)
OH$^{-}$ (Hydroxide)
W — (H$_2$O - Water)
NCS$^{-}$ (Isothiocyanate - N-bonded)
EDTA$^{4-}$ (Ethylenediaminetetraacetate)
NH$_3$ (Ammonia)
en — (Ethylenediamine)
NO$_2^{-}$ (Nitrite)
CN$^{-}$ (Cyanide)
CO — (Carbonyl)

(Note: The mnemonic covers common ligands and provides a good approximation of the series for NEET purposes. Some minor variations exist in comprehensive series.)