hw8 - Or use the results of the previous problem to set up...

Chem 110A
1
Homework 8: Due MONDAY, December 7
This problem set to be turned in on the morning of the Final Exam
Chemistry 110A — 2009
Professor McCurdy
1. (Problem 9-4 in McQuarrie and Simon)
Determine the normalized wave function for
!
"
= c 1 s
A
" 1 s
B
( )
This problem is asking you to find the normalization constant, c, in terms of the overlap
integral !
*
1 s
A
"
( r ) !
1 s
B
( r ) d 3 r given in Eq. 9.11.
2. (Problem 9-8 in McQuarrie and Simon)
Show that H
AA
= H
BB
= ! 1/ 2 + J
and that H
AB
= ! S / 2 + K
in the simple molecular-orbital treatment of H
2
+
. The quantities J and K are given by
Eqs.(9.23) and (9.24). Atomic units are being used in these expressions in the text.
3. (Problem 9-10 in McQuarrie and Simon)
Show that for the antibonding orbital of H
2
+
the eigenvalue of the simple LCAO
treatment is E = E
1 s
+
J ! K
1 ! S
= !
1
2
+
J ! K
1 ! S
You can do this one of two ways: Either use the result of problem 1 above take the
expectation value of the Hamiltonian, making use of the results in problem 2.