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Chem 3502/5502
Physical Chemistry II (Quantum Mechanics)
3 Credits
Fall Semester 2009
Laura Gagliardi
Answers to Homework Set 8
From lecture 29: What is the value of
P
52
for water after the first SCF step (i.e., at cycle
2)? By what percentage did it change compared to the initial guess? By what percentage
did the total energy change for this same step?
We must evaluate
P
"#
=
2
a
"
i
a
#
i
i
occupied
$
for
λ
= 5 and
σ
= 2 using the occupied MO coefficients after the first SCF step which
were given in the lecture notes as
Occupied MO coefficients at cycle
2.
1
2
3
4
5
1
.994123
.233041
.000000
.103527
.000000
2
.026666
.834174
.000000
.541326
.000000
3
.000000
.000000
.000000
.000000
1.000000
4
.000000
.000000
.608401
.000000
.000000
5 .004400
.131110
.000000
.774771
.000000
6 .006039
.156851
.443140
.279656
.000000
7 .006039
.156851
.443140
.279656
.000000
As there are 5 occupied MOs, we will sum over all 5 the product of
a
5
i
with
a
2
i
. So, for
MO 1 we have –0.004400 times 0.026666. For MO 2, –0.131110 times 0.834174. For
MO 3, 0 times 0. For MO 4, 0.774771 times 0.541326. And, for MO 5, 0 times 0 again. If
we sum the three nonzero products and multiply by 2 (see equation above) we obtain
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This note was uploaded on 12/18/2010 for the course CHEM 3502 taught by Professor Staff during the Fall '08 term at Minnesota.
 Fall '08
 Staff
 Physical chemistry, pH

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