Abstract
The Hamiltonian
H
, leading to the vibrational energy levels of a gaseous diatomic molecule, is normally written in the form (see Buckingham 1958)
H
=
H
0
+
H
a
(1·1) = -
hcB
c
d
2
/dξ
2
+
hcω
c
2
/4
B
c
{ξ
2
+
A
/
ω
c
ξ
3
+
B
/
ω
c
ξ
4
+ ...}, (1·2) where
H
0
= -
hcB
c
d
2
/dξ
2
+
hcω
c
2
/4
B
c
ξ
2
is the harmonic oscillator Hamiltonian, and
hcω
c
2
/2
B
c
r
c
2
is the force-constant; ξ = (
r
—
r
e
)/
r
e
is a dimensionless parameter proportional to the displacement from the equilibrium inter-nuclear distance
r
e
;
A
/
ω
e
,
B/ω
e
,..., are anharmonic coefficients. The constants
r
e
,
ω
e
,
B
e
,
A
,
B
, ..., can be obtained from the vibration-rotation spectrum of the gas by comparing the observed energies with those obtained by treating the anharmonic Hamiltonian
H
a
as a small perturbation to
H
0
(see Herzberg 1950).
Cited by
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