Electronic Configuration of Molecules — Revision Notes

⚡ 30-Second Revision

MO Energy Order ($le 14$ e$^-$) — $sigma_{1s} < sigma^*_{1s} < sigma_{2s} < sigma^*_{2s} < pi_{2p_x} = pi_{2p_y} < sigma_{2p_z} < pi^*_{2p_x} = pi^*_{2p_y} < sigma^*_{2p_z}$
MO Energy Order ($> 14$ e$^-$) — $sigma_{1s} < sigma^*_{1s} < sigma_{2s} < sigma^*_{2s} < sigma_{2p_z} < pi_{2p_x} = pi_{2p_y} < pi^*_{2p_x} = pi^*_{2p_y} < sigma^*_{2p_z}$
Bond Order (BO) — $BO = \frac{1}{2}(N_b - N_a)$
Stability — Higher BO $implies$ Higher Stability
Bond Length — Higher BO $implies$ Shorter Bond Length
Paramagnetic — Unpaired electrons (attracted to magnetic field)
Diamagnetic — All electrons paired (repelled by magnetic field)
Rules — Aufbau, Pauli, Hund's (fill degenerate orbitals singly first)

2-Minute Revision

Molecular Orbital Theory (MOT) explains how electrons are arranged in molecules, forming molecular orbitals (MOs) from atomic orbitals (AOs). These MOs are either bonding (lower energy, stabilizing) or antibonding (higher energy, destabilizing).

Electrons fill these MOs following the Aufbau principle, Pauli's exclusion principle, and Hund's rule. Crucially, the energy order of MOs differs for diatomic molecules with $le 14$ electrons (e.g., N$_2$) versus those with $> 14$ electrons (e.

g., O$_2$) due to s-p mixing. For $le 14$ electrons, $pi_{2p}$ orbitals are lower than $sigma_{2p_z}$; for $> 14$ electrons, $sigma_{2p_z}$ is lower. From the electronic configuration, we calculate Bond Order (BO) using $BO = \frac{1}{2}(N_b - N_a)$, where $N_b$ are bonding and $N_a$ are antibonding electrons.

A higher BO means greater stability and shorter bond length. The presence of unpaired electrons makes a molecule paramagnetic (attracted to a magnet), while all paired electrons make it diamagnetic (repelled).

Mastering these concepts allows prediction of molecular properties.

5-Minute Revision

Molecular Orbital Theory (MOT) provides a powerful framework for understanding the electronic configuration of molecules, which dictates their fundamental properties. When atoms combine, their atomic orbitals (AOs) linearly combine to form an equal number of molecular orbitals (MOs).

These MOs are broadly categorized into bonding molecular orbitals (BMOs), which are lower in energy and stabilize the molecule, and antibonding molecular orbitals (ABMOs), which are higher in energy and destabilize it.

Sigma ($sigma$) MOs result from head-on overlap, while pi ($pi$) MOs result from sideways overlap.

Electrons are filled into these MOs following three key rules:

1
Aufbau Principle — Fill from lowest energy MO to highest.
2
Pauli Exclusion Principle — Max two electrons per MO, with opposite spins.
3
Hund's Rule — For degenerate MOs (same energy), fill one electron in each with parallel spins before pairing any.

The energy order of MOs is critical and depends on the total number of electrons in the diatomic molecule:

For $le 14$ electrons (e.g., N$_2$, C$_2$, B$_2$) — $sigma_{1s} < sigma^*_{1s} < sigma_{2s} < sigma^*_{2s} < pi_{2p_x} = pi_{2p_y} < sigma_{2p_z} < pi^*_{2p_x} = pi^*_{2p_y} < sigma^*_{2p_z}$. (Note $pi_{2p}$ is below $sigma_{2p_z}$ due to s-p mixing).
For $> 14$ electrons (e.g., O$_2$, F$_2$) — $sigma_{1s} < sigma^*_{1s} < sigma_{2s} < sigma^*_{2s} < sigma_{2p_z} < pi_{2p_x} = pi_{2p_y} < pi^*_{2p_x} = pi^*_{2p_y} < sigma^*_{2p_z}$. (Note $sigma_{2p_z}$ is below $pi_{2p}$ as s-p mixing is negligible).

Once the configuration is written, we can determine:

1
Bond Order (BO) — $BO = \frac{1}{2}(N_b - N_a)$, where $N_b$ is the number of electrons in bonding MOs and $N_a$ in antibonding MOs. A higher positive BO indicates greater molecular stability and a shorter bond length. A BO of 0 means the molecule is unstable and does not exist (e.g., He$_2$).
2
Magnetic Properties — If there are any unpaired electrons in the MOs, the molecule is paramagnetic (attracted to a magnetic field, e.g., O$_2$, B$_2$). If all electrons are paired, it is diamagnetic (repelled by a magnetic field, e.g., N$_2$, F$_2$).

Example: O$_2$ (16 electrons)

Configuration: $(sigma_{1s})^2 (sigma^*_{1s})^2 (sigma_{2s})^2 (sigma^*_{2s})^2 (sigma_{2p_z})^2 (pi_{2p_x})^2 (pi_{2p_y})^2 (pi^*_{2p_x})^1 (pi^*_{2p_y})^1$ $N_b = 10$, $N_a = 6$. $BO = \frac{1}{2}(10-6) = 2$. Two unpaired electrons $implies$ paramagnetic. This explains O$_2$'s double bond and paramagnetism.

Mastering these steps and the two energy orders is key to solving NEET problems related to molecular electronic configuration.

Prelims Revision Notes

Electronic Configuration of Molecules (MOT) - NEET Revision Notes

1. Molecular Orbitals (MOs):

Formed by Linear Combination of Atomic Orbitals (LCAO).
Number of MOs formed = Number of AOs combined.
Bonding MOs (BMOs) — Lower energy, increased electron density between nuclei, stabilize molecule ($sigma, pi$).
Antibonding MOs (ABMOs) — Higher energy, nodal plane between nuclei, decreased electron density, destabilize molecule ($sigma^*, pi^*$).

2. Rules for Filling MOs:

Aufbau Principle — Fill lowest energy MOs first.
Pauli Exclusion Principle — Max 2 electrons per MO, with opposite spins.
Hund's Rule — For degenerate MOs, fill singly with parallel spins before pairing.

3. MO Energy Level Order (Crucial for Diatomics):

**For total electrons $le 14$ (e.g., H$_2$, Li$_2$, B$_2$, C$_2$, N$_2$) - *with s-p mixing***:

$sigma_{1s} < sigma^*_{1s} < sigma_{2s} < sigma^*_{2s} < pi_{2p_x} = pi_{2p_y} < sigma_{2p_z} < pi^*_{2p_x} = pi^*_{2p_y} < sigma^*_{2p_z}$

**For total electrons $> 14$ (e.g., O$_2$, F$_2$, Ne$_2$) - *without s-p mixing***:

$sigma_{1s} < sigma^*_{1s} < sigma_{2s} < sigma^*_{2s} < sigma_{2p_z} < pi_{2p_x} = pi_{2p_y} < pi^*_{2p_x} = pi^*_{2p_y} < sigma^*_{2p_z}$

4. Key Properties Derived from Configuration:

Bond Order (BO) — $BO = \frac{1}{2}(N_b - N_a)$

* $N_b$: Electrons in bonding MOs. * $N_a$: Electrons in antibonding MOs. * $BO > 0 implies$ Stable molecule. * $BO = 0 implies$ Unstable, does not exist (e.g., He$_2$).

Molecular Stability — Directly proportional to BO (Higher BO = More stable).
Bond Length — Inversely proportional to BO (Higher BO = Shorter bond length).
Magnetic Properties

* Paramagnetic: Contains one or more unpaired electrons (attracted to magnetic field, e.g., O$_2$, B$_2$). * Diamagnetic: All electrons are paired (repelled by magnetic field, e.g., N$_2$, F$_2$).

5. Common NEET Traps:

Misapplying the MO energy order (s-p mixing vs. no s-p mixing).
Incorrectly counting total electrons, especially for ions.
Forgetting Hund's rule for degenerate orbitals, leading to wrong magnetic property prediction.
Confusing bond order with number of sigma/pi bonds (e.g., C$_2$ has BO=2 from two $pi$ bonds, no $sigma_{2p}$ bond).

Practice: Be able to quickly write configurations, calculate BO, and predict magnetic nature for H$_2$, He$_2$, Li$_2$, B$_2$, C$_2$, N$_2$, O$_2$, F$_2$ and their common ions (e.g., N$_2^+$, O$_2^-$, O$_2^+$). Also, practice heteronuclear diatomics like CO, NO, CN$^-$ by analogy or general rules.

Vyyuha Quick Recall

To remember the MO energy order for $le 14$ electrons (with s-p mixing), think: 'Sigma Star Sigma Star Pi Pi Sigma Pi Star Pi Star Sigma Star'

For $> 14$ electrons (without s-p mixing), think: 'Sigma Star Sigma Star Sigma Pi Pi Pi Star Pi Star Sigma Star'

(Remember to add '1s' and '2s' for the first four, and '2p' for the rest, and that Pi orbitals are degenerate, so they appear twice in the mnemonic for filling.)