CHEM 550 Homework
Due Dec. 2 at 5pm 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:
13.14 – atomic units
13.28 – review MO diagrams
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) 2P3/2 to the (3s) 2S1/2 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 H2+ ground state using 1s-like orbitals with the
exponent (nuclear charge) as the variational parameter (Levine 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 H2+ MO wave function.
2B) Evaluate the Coulomb (Haa) and Exchange (Hab) integrals for H2+ MO wave function.
2C) Using your results from 2 and 3, plot minimized E (as a function of the variational
parameters, k) as a function of R for the H2+ 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 H2+ 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 a0 , RAB (are they positive, real, etc.) or you won’t get a
correct answer.