Science of Diatomics

Electronic States in Hydrogen Atom:

We only have one electron, so we just need to describe its properties. An electron can be in any ONE orbital around the hydrogen nucleus; some orbitals are shown to the right. They have labels like 1s, 2s, 2p_x, 3d_xy etc.

Electronic States in Multi-electron Atoms:

We have many electrons, but an electronic state describes their positions and momentums of all electrons. The wavefunction is the collective group of orbitals including the single and paired electrons.

Shape of wavefunction (probability space of the electrons is the square of the wavefunction)

• s → S
• p → P
• d → D etc.

Number of unpaired electrons

• Singlet (¹) (0 unpaired electrons)
• Doublet (²) (1 unpaired electrons)
• Triplet (³) (2 unpaired electrons)
• Quartet (⁴) (3 unpaired electrons)
• Quintet (⁵) (4 unpaired electrons)
• And so on...

Electronic States in Diatomic Molecules:

In diatomic molecules, we describe the electronic state using things like shape of overall wavefunction

• s→ Sigma (Σ)
• p → Pi (Π)
• d→ Delta (Δ)
• f → Phi (ϕ)
• g → Gamma (Γ)

Electronic Energy:

The electronic energy of a molecule is the largest component of its overall energy. This, unlike vibrational and rotational can only be calculated experimentally.

T_e (Term Energy): energy of electronic state relative to the lowest electronic state of the molecule.

El. State (Electronic State): Quantum number associated with electronic component of quantum state. Electronic State is a more complex label, e.g.

A set of electronic states with transitions between these states.

Molecular systems have nuclei that can move. The nuclei rotate and vibrate.

Vibration:

As the energy levels increase the amount of nodes in the wave function increases meaning that probability of being within the wavefunction decreases.

ν : Vibrational Quantum Number (begins at 0 and increases in integer steps)

Using harmonic oscillator approximation:

Rotation:

Using rigid-rotor approximation: