1) Determine the radial part of the wavefunction for a H2 molecule, using the LCAO approach.
Plot the following on a single axis, using Excel:
a) The individual 1s atomic orbitals
b) The bonding molecular orbital (sum)
c) The antibonding molecular orbital (difference)
2) Plot the sum of the probability distributions (ψ2
) for the individual 1s orbitals and the
probability distributions for b) and c) on a single axis. Use Excel.
3) Using numerical integration:
a) Normalize the probability distributions of the bonding and antibonding orbitals. HINT:
start by calculating the area under the unnormalized probability distributions.
b) Plot the normalized bonding and antibonding orbitals on a single axis, using Excel.
c) Evaluate the probability of finding an electron in the internuclear region for the bonding
and antibonding orbitals using the normalized probability distributions.*
4) Comment on the significance of the result from 3) part c).
Problem 2
For the molecule shown on the right:
1) If X is a second-row element, use group theory to
determine the atomic orbitals that comprise the hybrid
orbitals of the molecule.
2) If X is a third-row element, list all the possible atomic
orbital combinations with n = 3 that could produce a
suitable hybrid orbital.
3) Discuss how the choice of axis system affects your answer above.