Answer the following questions:
$(i)$ Give the molecular orbitals and their types formed by $LCAO$ from $2s, 2p_{x}, 2p_{y}$ and $2p_{z}$ atomic orbitals.
$(ii)$ Provide the energy order of molecular orbitals for $Li_{2}, Be_{2}, C_{2}, N_{2}, O_{2}$ and $F_{2}$.

Molecular orbitals formed by $LCAO$:

$AO$	Combination of atomic orbitals $(LCAO)$	Molecular orbital $(MO)$
$2s$	$\psi(2s) + \psi(2s)$,$\psi(2s) - \psi(2s)$	$BMO: \sigma(2s)$,$ABMO: \sigma^{*}(2s)$
$2p_{z}$	$\psi(2p_{z}) + \psi(2p_{z})$,$\psi(2p_{z}) - \psi(2p_{z})$	$BMO: \sigma(2p_{z})$,$ABMO: \sigma^{*}(2p_{z})$
$2p_{x}$	$\psi(2p_{x}) + \psi(2p_{x})$,$\psi(2p_{x}) - \psi(2p_{x})$	$BMO: \pi(2p_{x})$,$ABMO: \pi^{*}(2p_{x})$
$2p_{y}$	$\psi(2p_{y}) + \psi(2p_{y})$,$\psi(2p_{y}) - \psi(2p_{y})$	$BMO: \pi(2p_{y})$,$ABMO: \pi^{*}(2p_{y})$

Energy order of orbitals:
The increasing order of energy of $MO$ for $Li_{2}, Be_{2}, B_{2}, C_{2}, N_{2}$ is:
$\sigma 1s < \sigma^{*} 1s < \sigma 2s < \sigma^{*} 2s < (\pi 2p_{x} = \pi 2p_{y}) < \sigma 2p_{z} < (\pi^{*} 2p_{x} = \pi^{*} 2p_{y}) < \sigma^{*} 2p_{z}$
The increasing order of energy of $MO$ for $O_{2}$ and $F_{2}$ is:
$\sigma 1s < \sigma^{*} 1s < \sigma 2s < \sigma^{*} 2s < \sigma 2p_{z} < (\pi 2p_{x} = \pi 2p_{y}) < (\pi^{*} 2p_{x} = \pi^{*} 2p_{y}) < \sigma^{*} 2p_{z}$