Quantum Mechanics, Transition Metals, and Crystal Field Theory Study Notes

Schrodinger's Equation

The core equation of quantum mechanics expressed as: $\hat{H}\Psi = E\Psi$.

Principal Quantum Number (n)

Defines the distance of electrons from the nucleus with values as discrete integers: $n = 1, 2, 3, 4…$.

Angular Momentum Quantum Number (l)

Determines the shape of the orbital with a range of $l = 0, \dots n-1$.

Magnetic Quantum Number (m_l)

Determines the orientation of the orbital in space; range: $m_l = -l, \dots +l$.

D Orbitals

Condition: $n = 3$, $l = 2$; characterized by five orientations with magnetic quantum numbers: $m_l = -2, -1, 0, 1, 2$.

Crystal Field Splitting

Separation of d orbitals into different energy levels due to the influence of ligands.

Ligands

Molecules that form coordinate bonds with metals; they act as Lewis bases.

High-Spin State

Caused by weak ligands; electrons fill all d orbitals singly before pairing.

Low-Spin State

Caused by strong ligands; electrons pair up in lower-energy orbitals before occupying higher-energy ones.

Crystal Field Splitting Energy (Δo)

The difference in energy between split d orbitals caused by crystal field interactions.