Biomedical Engineering Reference
In-Depth Information
is 4.430
4.616 eV. The Morse potential for
1
H
35
Cl is shown in Figure 3.7,
compared to the simple harmonic model. The full curve is the simple harmonic potential,
the dashed curve the Morse potential.
+
0.186 eV
=
7
·
10
-18
6
·
10
-18
5
·
10
-18
4
·
10
-18
3
·
10
-18
2
·
10
-18
1
·
10
-18
0
5
·
10
-11
1
·
10
-10
1.5
·
10
-10
Interatomic distance R/m
2
·
10
-10
Figure 3.7
Simple harmonic and Morse curves for HCl
3.6 More Advanced Potentials
More often than not, the following spectroscopic constants are available for a diatomic
molecule:
R
e
the equilibrium internuclear separation;
D
e
the dissociation energy;
k
s
the force constant;
ω
e
x
e
the anharmonicity constant (sometimes written
x
e
only);
α
e
the vibration-rotation coupling constant.
Usually these five constants can be found to good experimental accuracy.
There are a number of three- to five-parameter potential functions in the literature, of
which the Morse potential is the most popular. A typical five-parameter potential is the
Linnett function (Linnett 1940, 1942)
K
x
m
−
U
(
x
)
=
b
exp(
−
tx
)
[
1
+
g
1
(
x
−
1)
+
g
2
(
x
−
1)
2
]
