Chemistry Reference
In-Depth Information
Table 10.3 Calculated diamagnetic susceptibilities for simple atoms
2
2
0
L
10
6
cgs
Atom
Method
h
r
i
00
=
a
x
=
=
emu
H
Exact
3
2.376
He
Hydrogenic
0.75
1.188 0
1-term SCF
a
1.053 5
1.668 7
2-term SCF
a
1.183 2
1.874 3
5-term SCF
a
1.184 7
1.876 5
Accurate
b
1.193 5
1.890 5
HF
c
Li
15.2
HF
c
Be
14.1
HF
c
Ne
7.4
HF
c
Ar
20.9
HF
c
Kr
33.0
a
Clementi and Roetti, 1974.
b
Pekeris, 1959.
c
Strand and Bonham, 1964.
8905
10
6
cgs
only 68%of the accurate value
ð
1
emu
Þ
obtained
by Pekeris (1959). The single-term SCF (optimization of the orbital
exponent c
0
of a minimum STO basis) improves the result to 88%,
while a five-term SCF (practically HF) gives over 99% of the Pekeris
result. Pretty good results are also obtained from the HF calculations
(Strand and Bonham, 1964) on the heavier rare gases (7.4 instead of
accurate 6.7 for Ne, 20.9 instead of 19.0 for Ar, 33.0 instead of 28.0
for Kr), showing a limited effect of electronic correlation on diamag-
netic susceptibility.
For the high-frequency part, expanding the second-order energy in
pseudostates
fc
k
g
, we have
:
=
eh
eh
2mc
L
H
jc
k
ihc
k
j
2mc
L
H
jc
0
i
hc
0
j
E
h
2
¼hc
0
j
H
1
jc
1
i¼
X
kð 6¼
0
Þ
E
k
E
0
4m
2
c
2
H
2
X
kð 6¼
0
Þ
jhc
0
j
L
z
jc
k
ij
h
2
2
e
2
¼
«
k
ð
10
:
82
Þ
whence, referring to a mole:
2
0
¼
N
A
hc
0
j
L
z
jc
k
i
2m
2
c
2
X
kð 6¼
0
Þ
h
2
¼
@
2
e
2
E
@
H
2
hf
x
>
0
ð
10
:
83
Þ
«
k
