Problem Set 5: Quantum Mechanics: Atoms and Molecules II
1. Based upon the ground-state electronic configurations of B2 and C2, predict which
molecule should have the larger bond dissociation energy.
2. Which of the molecules CN, N2, NO, and O2 would you expect to be stabilized by
(i) the addition of an electron to form the anion AB-, and (ii) the removal of an
electron to form the cation AB+ ?
3. Very generally, the length of a bond decreases and the strength of a bond
increases with increasing bond order. Given this information, arrange the
following species: O2+, O2, O2-, and O2-2, in order of increasing bond lengths.
4. Longer and More Difficult, a “Mini-Project”:
Consider a pair of H atoms, with the nuclei separated by a distance of 1 x 10-10 m.
The overlap integral (denoted S) between 1s orbitals centered upon H atom nuclei
separated by a distance R is given by:
2


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S  1  R    R   e  R / a0
a
a
  0  3 0  
where a0 is the Bohr radius (a0 = 0.529 x 10-10 m).
(i)
(ii)
(iii)
(iv)
Calculate expressions for the amplitudes of the normalized bonding and
antibonding LCAO-MO molecular orbital wavefunctions that can be
formed as linear combinations using this pair of 1s orbitals for this
molecule.
Use your result from Part (i), together with the function that represents the
1s orbital/wavefunction for an H atom, to calculate the electron density
midway between the nuclei for both the normalized bonding and
antibonding MOs.
Recall that for the H2 molecule, the bonding molecular orbital is doubly
occupied, while the antibonding molecular orbital is vacant. Use this fact,
together with your result from Part (ii), to estimate the electron density in
an H2 molecule at the point that is midway between the nuclei.
Compare your results for the electron density from Part (iii) with: the
anticipated electron density midway between a pair of non-interacting H
atoms separated by 1 x 10-10 m, where each electron occupies a 1s orbital
on each atom, and there is no formation of molecular orbitals, the atoms
are assumed to behave as though they do not see each other.
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