Page 317 - Academic Press Encyclopedia of Physical Science and Technology 3rd Analytical Chemistry

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Encyclopedia of Physical Science and Technology EN009N-447 July 19, 2001 23:3

834 Microwave Molecular Spectroscopy

molecules. Since the vibrational contributions are slightly TABLE XVIII Equilibrium Structure and Various
different for different isotopic species, the structural pa- Ground-State Structures of SO a 2
rameters obtained from different combinations of isotopic Structure r ( ˚ A) θ
species are slightly different. The spread in these effective
◦
parameters is much larger than expected from the experi- Equilibrium (r e ) 1.4308 119 19
◦
mental uncertainty in the moments of inertia. On the other Average ( r ) 1.4349 119 21
◦
hand, equilibrium parameters obtained from different sets Effective (r 0 ) 1.4336 119 25
◦
of moments of inertia are consistent with the experimen- Substitution (r s ) 1.4312 119 30
tal uncertainties in the moments of inertia. Because of this Mass dependence (r m ) 1.4307 119 20
◦
general problem, different procedures have been devel- Scaled (r ρ ) 1.4308 119 19
◦
oped to minimize these troublesome vibrational effects.
This has led to different definitions of structural parame-
ters depending on their method of calculation. An under- librium bond distance for a diatomic molecule X—Yis
standing of these differentstructural measures is important evaluated from
if comparisons are to be made of structural parameters. " # 1/2
m X + m Y e
The different structural parameters are defined as follows: r e = I b , (87)
m X m Y
1. Equilibrium structure r e : the bond length or angle where
for the vibrationless state, evaluated by correction for the h/8π 2
e
effects of vibration I = (88)
b
B e
2. Average structure r or r z : the bond length or angle
and the conversion factor is given by
association with the average configuration of the atoms in
the ground vibrational state, evaluated by partial correc- h/8π = 505,376 amu A MHz. (89)
2
˚ 2
tion for the effects of vibration
3. Effective structure r 0 : the bond length or angle ob- With more complicated molecules, additional isotopic
tained from effective ground-state moments of inertia data are needed. For a linear molecule such as XYZ, the
4. Substitution structure r s : the bond length or angle moments of inertia for two molecular species and the ex-
derived from isotopic data using differences in ground- pression from Table II give two equations to be solved
state moments of inertia for the two bond lengths. Alternately, the coordinates of,
5. Mass-dependence structure r m : the bond length or for example, the X-atom z X , that is, the distance from the
angle derived from a large number of isotopic species by center of mass, can be evaluated from Kraitchman’s equa-
∗
a first-order treatment of isotopic effects tion (see Section VIII.D) using isotopic data from X YZ.
6. Scaled structure r ρ : The bond length or angle de- Subsequently, this coordinate can be used in the moment-
rived from scaled effective moments of inertia employing of-inertia and first-moment equations for the XYZ species,
a scaling factor obtained from a set of isotopic species. 2
I X = m i z , m i z i = 0, (90)
i
The r 0 and r s structures are defined operationally and
do not provide well-defined physical parameters. At this
time the r ρ structures provide the best near-equilibrium TABLE XIX Comparison of Various Bond
Lengths ( ˚ A) for Some Diatomic Molecules
structures. A comparison of these different structures for
SO 2 is given in Table XVIII. The evaluation of these dif- Molecule r e r 0 r
ferent structures is reviewed briefly using diatomic and
HF 0.9170 0.9257 0.9326
linear molecules as the principal examples. The values of
DF 0.9171 0.9234 0.9284
r e , r , and r 0 are compared for some diatomic molecules
TF 0.9177 0.9230 0.9272
in Table XIX.
35
H Cl 1.2745 1.2837 1.2904
Some of the unique structural information which can
37
H Cl 1.2746 1.2837 1.2904
be obtained from microwave spectroscopy has been dis-
35
D Cl 1.2744 1.2813 1.2858
cussed in Section IV.E.
37
D Cl 1.2744 1.2813 1.2858
35
T Cl 1.2746 1.2800 1.2853
A. Equilibrium Structure T Cl 1.2746 1.2800 1.2853
37
127 35 2.3209 2.3236 2.3246
I Cl
By correcting B 0 for the effects of vibration, as discussed
127 37 2.3209 2.3235 2.3245
I Cl
previously, one can obtain B e . From Table II the equi-