Chemistry Reference
In-Depth Information
Table 10.1 Pseudostate approximations to
a
for the ground state of the H atom
3
0
w
c
m=
ea
0
«=
E
h
a=
a
2p
z
0.5
0.7449
0.375
2.96
2p
z
0.7970
0.9684
0.4191
4.48
2p
z
1-term
1
1
0.5
4.0
0
:
4082
1
0
0
:
3333
2p
z
þ
3p
z
2-term
1
0
:
9129
:
4
4
:
1667
<
:
<
:
<
:
:
:
:
0
8153
0
:
5572
0
0
3811
0
:
6166
1
3
4887
1
:
0070
0
2p
z
þ
3p
z
þ
4p
z
3-term
1
:
0605
:
7023
:
0043
10.5.1 Single Pseudostate
Choose as a convenient variational function satisfying all symmetry
prescriptions the normalized 2p STO:
1
=
2
c
5
p
x ¼
exp
ð
cr
Þ
z
;
z
¼
r cos
u
ð
10
:
48
Þ
We have
c
1
¼ w ¼
CF
x;
ð
10
:
49
Þ
hc
0
jxi¼
0
the order being carried by the linear parameter C, and omitted for brevity,
while c is a nonlinear parameter.
Then, optimization against the single linear variation parameter (single-
term approximation) gives
2
E
2
ð
best
Þ¼
F
2
m
ð
10
:
50
Þ
«
where
5
2
c
p
m ¼hxj
z
jc
0
i¼ðc
0
xj
z
Þ¼
ð
10
:
51
Þ
c
þ
1
1
2
ð
c
2
« ¼hxj
H
0
E
0
jxi¼
c
þ
1
Þ
ð
10
:
52
Þ
