Chemistry Reference
In-Depth Information
anisotropies
Dað
iu
Þ
of the two linear molecules:
¥
1
2
A
B
ð
iu
Þþ½ð
3cos
2
C
6
ðu
A
;u
B
;wÞ¼
du
fa
ð
iu
Þa
u
B
1
Þa
A
ð
iu
ÞDa
B
ð
iu
Þ
p
0
þð
3cos
2
u
A
1
ÞDa
A
ð
iu
Þa
B
ð
iu
Þ
þ½
4cos
2
A
cos
2
cos
2
cos
2
sin
2
A
sin
2
u
u
u
u
u
u
B
cos
w
B
A
B
þ
sin
2
A
sin
2
B
cos
2
u
u
wDa
ð
iu
ÞDa
ð
iu
Þg
ð
11
:
50
Þ
A
B
Averaging over angles, all coefficients involving polarizability aniso-
tropies are zero, giving the isotropic C
6
coefficient in the Casimir-Polder
form (11.32).
To get an illustrative numerical example, we can use the four-term
pseudospectrum of Table 11.3 for the dipole polarizabilities of the
1
g
S
ground state of the H
2
molecule at R
¼
1
:
4 a
0
, which gives for the dipole
polarizabilities of H
2
jj
?
ð
11
:
51
Þ
a
¼
6
:
378
; a
¼
4
:
559
results that are remarkably good for both polarizabilities, being 99.9%and
99.6% respectively of the accurate values (
jj
?
577)
obtained from the accurate 34-term pseudospectrum (Magnasco and
Ottonelli, 1996a).
We can then calculate the four-term approximation to the three
independent elementary dispersion constants (11.42) for the homodimer
H
2
-H
2
, obtaining the following numerical results:
a
¼
6
:
383 and
a
¼
4
:
A
¼
2
:
683
99
:
8
%
of the accurate value 2
:
689
B
¼
C
¼
2
:
018 99
:
3
%
of the accurate value 2
:
032
D
¼
1
:
524
98
:
8
%
of the accurate value 1
:
542
S
g
)atR
¼
1
Table 11.3 Four-termdipole pseudospectrum (atomic units) ofH
2
(
:
4a
0
jj
i
jj
i
a
i
«
i
i
a
«
1
4.567
0.473
2.852
0.494
2
1.481
0.645
1.350
0.699
3
0.319
0.973
0.335
1.157
4
0.011
1.701
0.022
2.207
