Core Formulas

1. Steric Number (SN): $\text{SN} = n_\sigma + n_{lp}$ where $n_\sigma$ = number of sigma bonds, $n_{lp}$ = number of lone pairs on central atom.

2. Dipole Moment: $\mu = q \times d \quad [\text{C·m}; \quad 1\text{ D} = 3.336 \times 10^{-30} \text{ C·m}]$

3. MOT Bond Order: $\text{Bond Order (BO)} = \frac{N_b - N_a}{2}$ where $N_b$ = electrons in bonding MOs, $N_a$ = electrons in antibonding MOs.

4. Born-Haber Cycle (Hess's Law): $\Delta H_f^\circ = \Delta H_{sub} + \frac{1}{2}\Delta H_{diss} + IE + EA + U$ $\therefore \quad U = \Delta H_f^\circ - \Delta H_{sub} - \frac{1}{2}\Delta H_{diss} - IE - EA$

5. Lattice Energy (Coulombic approximation): $U \propto \frac{z^+ \times z^-}{r^+ + r^-}$

6. Born-Landé Equation (exact): $U = -\frac{N_A M z^+ z^- e^2}{4\pi\varepsilon_0 r_0}\left(1 - \frac{1}{n}\right)$ where $M$ = Madelung constant, $n$ = Born exponent, $r_0$ = interionic distance.

7. Vector Addition of Two Dipoles: $\mu_{net} = \sqrt{\mu_1^2 + \mu_2^2 + 2\mu_1\mu_2\cos\theta}$ Special cases: $\theta=180°$: $\mu_{net}=|\mu_1-\mu_2|$; $\theta=0°$: $\mu_{net}=\mu_1+\mu_2$.

8. Formal Charge: $FC = V - N - \frac{1}{2}B$ where $V$ = valence electrons, $N$ = non-bonding electrons, $B$ = bonding electrons.

MO Filling Orders

For $Z \leq 7$ (mixing): $\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \pi_{2p} < \sigma_{2p} < \pi^*_{2p} < \sigma^*_{2p}$

For $Z > 7$ (no mixing): $\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \sigma_{2p} < \pi_{2p} < \pi^*_{2p} < \sigma^*_{2p}$