Chemistry Reference
In-Depth Information
is the nonexpanded dispersion energy due to the mutual polarization
(distortion) of A and B. The tilde on E
2
and its components means that we
are using a variational approximation to the second-order energies.
11.2 THE H-H EXPANDED INTERACTIONS
UP TO SECOND ORDER
We nowexpand the interatomic potential Vat long range
ð
R
r
1
;
r
2
Þ
in a
power series in R
n
up to R
3
:
1
r
B1
¼½
x
1
þ
y
1
þð
z
1
R
Þ
2
1
=
2
2z
1
R
þ
r
1
Þ
1
=
2
¼ð
R
2
!
1
=
2
r
1
R
2
1
R
1
2
z
1
¼
R
þ
2
3
ð
11
:
17
Þ
2
r
1
1
R
z
1
R
3
8
2
z
1
4
5
1
þ
2R
2
þ
þ
R
3z
1
r
1
2R
3
1
R
þ
z
1
R
2
þ
þ
O
ð
R
4
¼
Þ
where use was made of the Taylor expansion for x
¼
small:
1
2
x
þ
3
8
x
2
ð
1
þ
x
Þ
1
=
2
1
þ
ð
11
:
18
Þ
1
r
A2
¼½
x
2
þ
y
2
þð
z
2
þ
R
Þ
2
1
=
2
þ
2z
2
R
þ
r
2
Þ
1
=
2
¼ð
R
2
!
1
=
2
r
2
R
2
1
R
1
þ
2
z
2
¼
R
þ
2
3
2
ð
11
:
19
Þ
r
2
1
R
z
2
R
3
8
2
z
2
R
4
5
1
2R
2
þ
þ
3z
2
r
2
2R
3
1
R
z
2
R
2
þ
þ
O
ð
R
4
¼
Þ
