a$)$ A common unit when describing the energy of bonding and antibonding

MOs is the electronvolt, eV$.$ What is the value of

j$0$

a$0$

$=$ mee$4$

$4\backslash$epsi $2$

$0$h$2$

in units of eV $(1$ eV $=1\mathrm{.}60221019$ J$)?$

$($b$)$ Assume that the distance between the two nuclei is R $=2\mathrm{.}5$a$0.$ What

are the energies of the bonding and antibonding MOs in eV$?$

Hint: EH$1$s $=13\mathrm{.}5983$ eV$,$ and it is easier to evaluate the energy ex$-$

pression by writing it out in terms of j$0/$a$0.$

c$)$ Using the results from part $($b$)$ sketch a molecular orbital energy level

diagram. What are the energies of the bonding and antibonding MOs

relative to the hydrogen$-$like $1$s orbital?

$($d$)$ Assume that the MO diagram in part $($c$)$ is the same for H$+$

$2,$ H$2$ and H$$

$2.$

Arrange the molecules in terms of strongest bond, and also in terms of

bond length.

$($e$)$ Consider the He$2$ dimer. Would the energy of the dimer be higher or

lower than the energy of the unbound pair He$+$He$?$

For the O$2$ molecule some of the bonding and antibonding molecular orbitals

$($MOs$)$ can be approximated by considering linear combinations of hydrogen$-$

like $2$s and $2$p atomic orbitals $($AOs$).$ Due to difference in energy the $2$s and

$2$p atomic orbitals do not mix.

$($a$)$ Which set of orbitals form $\backslash$sigma and $\backslash$sigma $$ type orbitals? Express the MOs as

linear combinations of AOs.

$($b$)$ Which set of orbtials form $\backslash$pi and $\backslash$pi $$ type orbitals? Express the MOs as

linear combinations of AOs.

$($c$)$ Sketch the resulting $\backslash$sigma and $\backslash$pi bonding orbitals.

$($d$)$ Consider now the inversion symmetry of the bonding MOs and

denote whether they have even $($g$)$ or odd $($u$)$ symmetry

Consider the molecules O$+$

$2,$ O$2$ and O$2$

$2.$

$($a$)$ Sketch the molecular orbital energy level diagrams for each molecule.

$($b$)$ Are the molecules paramagnetic or diamagnetic?

$($c$)$ Write out the electronic configuration of the molecules.

$($d$)$ Calculate the bond order of each species.