Chemistry Reference
In-Depth Information
so that the high-frequency term (paramagnetic contribution to the
diamagnetic susceptibility) is positive, of a sign opposite to that of the
Langevin term. So, we have for the diamagnetic susceptibility
d
L
hf
x
¼ x
þx
ð
10
:
84
Þ
a molecular property independent of T. For atoms in spherical
ground states,
hf
vanishes, since all transition integrals are zero
because of the orthogonality of the excited pseudostates
x
c
k
to the
ground state
c
0
:
hc
0
j
L
z
jc
k
i¼h
0
j
L
z
jki¼
m
h
0
jki¼
0 for
k 6¼
0
ð
10
:
85
Þ
(ii) Diatomic molecules in
S
singlet ground state
hf
For molecules,
x
6¼
0 and use is made of the average susceptibility:
3
X
a
3
X
a
1
1
d
L
aa
þ
hf
aa
¼ x
L
hf
x
¼
x
x
þ x
ð
10
:
86
Þ
where
e
2
6mc
2
h
r
2
L
x
¼
N
A
i
00
<
0
ð
10
:
87
Þ
2
hc
0
j
L
z
jc
k
i
2m
2
c
2
X
kð 6¼
0
Þ
h
2
e
2
hf
x
¼
N
A
>
0
ð
10
:
88
Þ
«
k
with
«
k
>
0 the excitation energy from the ground state
j
0
i
to the
pseudostate
jki
.
In Table 10.4 we give some values of diamagnetic susceptibilities for
ground-state H
2
calculated with different wavefunctions (Tillieu, 1957a,
1957b). We see (i) that the high-frequency contribution is sensibly smaller
than the low-fequency (Langevin) contribution, (ii) that the simple MO
wavefunction exhibits an exceptionally good performance, comparing
well with the accurate James-Coolidge wavefunction result of the last
row, (iii) that the HL (purely covalent) wavefunction shows a reasonable
behaviour, while (iv) the Weinbaum (HL plus ionic) wavefunction gives
results that are definitely too high either for
L
or
hf
.
x
x
