in molecular problems. Suppose that we wanted to approximate the ground-state wavefunction of a hydrogen atom by the above Gaussian function. What would the percent error in the energy be? [10 marks]
Maple hints: The exponential function 
is exp(u)
in Maple and 
is Pi.
Maple will need to know that c>0. Use subs() to
substitute your best value of c into your variational energy,
then use simplify() to get an initial simplification.
You will need to complete the simplification process by hand.
electronic transition of
1,3-butadiene 
occurs at 217nm.
Calculate the value of the resonance integral 
from
this information. Note that is negative.
where R is the internuclear distance and D, and
are parameters specific to a particular molecule.
.
Maple hint: If you use Maple for this problem, Maple
will need to know that 
.
is the equilibrium bond length. .
Maple hints: Use subs() to substitute the equilibrium bond length into the expression and simplify() to clean up the answer.
is the displacement of the bond length from its equilibrium.
Suppose that for a certain molecule, the electronic ground state is such
that 
and 
while for an excited electronic
state, 
and 
.
Are electronic transitions in which the molecule is in the
ground vibrational state both before and after the transition
likely to occur?
Maple hint: is Pi in Maple.
Hückel matrix: Element (i,j) is -1 if atoms i and j
participate in the electron network and are bonded to each other,
0 otherwise.
The orbital energies are scaled as follows:
.
, 
,
Ground-state wavefunction:
where
and 
.
Reduced mass:
Volume element: 
Angular ranges: 
, 
1s wavefunction:
