CHEM 550 Homework Final Homework
Due Fri. Dec 6 at noon in Prof. Ginger’s mailbox. Page 1/1
CIRCLE YOUR ANSWERS AND KEY INTERMEDIATE RESULTS
STAPLE YOUR PAPERS TOGETHER
INCLUDE ALL COMPUTER PRINTOUTS
Levine Problems: (Levine 6
th
Ed)
13.14 – atomic units
13.24 – review MO diagrams and relative stability
Levine Problems: (Levine 5
th
Ed)
13.14 – atomic units
13.28 – review MO diagrams and relative stability
Additional Problems:
1) Atomic emission spectroscopy can be used to detect the presence of certain metals at
very low concentration. The basic concept is simple enough, and you may have even
done this in some form or another in a chemistry lab: heat the sample until it is hot
enough to emit light and see what color the flame is glowing. Sodium makes the flame
glow yellow because of an electronic transition from the (3p)
2
P
3/2
to the (3s)
2
S
1/2
level.
Calculate the percentage of atoms in the relative populations of these levels in thermal
equilibrium in flames at temperatures of 1500, 2500 and 3500K.
2) Choose a MO wave-function for the H
2+
ground state using 1s-like orbitals with the
exponent (nuclear charge) as the variational parameter (Levine 5
th
edition eqns 13.43 and
13.44). Set up the coordinate system as suggested in lecture so that you won’t need to
learn confocal elliptical coordinates.
2A) Evaluate the overlap integral (S) for the H
2+
MO wave function.
2B) Evaluate the Coulomb (H
aa
) and Exchange (H
ab
) integrals for H
2+
MO wave function.
2C) Using your results from 2 and 3, plot minimized E (as a function of the variational
parameter, k) as a function of R for the H
2+
ion for the bonding and antibonding
molecular orbitals. Optional: Plot E vs R for the orbitals with k=1.
2D) Use your calculation to find the equilibrium bond length, and the dissociation
energy, of the H
2+
molecule. Use your calculation to find the energy required to excite
the molecule from the n=0 to n=1 vibrational level.
Tips: Make sure you use the ‘assume’ command to tell the computer everything you
know about parameters such as a
0
, R
AB
(are they positive, real, etc.) or you won’t get a
correct answer.
