6.6 Experimental Equilibrium Structure
143
Table 6.7 Comparison of an accurate equilibrium structure, r e , (in pm) and the structure, r e (α),
determined using the experimental α constants and neglecting anharmonic interactions
Molecule
Parameter
r e
r e (α)
r e − r e (α)
OCS a
r(C=O)
115.62(1)
115.45(2)
0.17(2)
r(C=S)
156.14(1)
156.30
−0.16
HCO +b
r(C –H)
109.19(9)
109.725(4)
−0.53(9)
r(C=O)
110.55(3)
110.474(2)
0.08(3)
HCP c
r(C –H)
107.02(10)
106.60(1)
0.42(10)
r(C≡P)
153.99(2)
154.045(2)
−0.06(2)
FCP d
r(C –F)
127.61(7)
128.4
−0.8
r(C≡P)
154.45(6)
153.8
0.6
a Lahaye et al. (1987)
b Woods (1988) and Puzzarini et al. (1996)
c Puzzarini et al. (1996b)
d Dréan et al. (1996)
As a typical example, details of the corrections used to calculate the experimental
rotational constants of
32 S
16 O 2 are given in Table 6.8. The first conclusion is that at
least one order of magnitude in precision is lost when going from the ground-state
constants to the equilibrium ones. However, the final standard deviations are too optimistic because they are calculated using the law of propagation of errors that does
not take into account the systematic errors. As expected, the main correction comes
from the α-constants; see (6.1). The contribution of the γ -constants is not negligible,
although it is difficult to evaluate accurately. Flaud and Lafferty (1993) give
γ /4
= 2.70 MHz, whereas Morino and Tanimoto (1994) estimate it at 1.9 MHz. It is
easy to understand why: whereas it is relatively easy to obtain accurate rotational
constants for the fundamental vibrational states, it is much more difficult to achieve
the same goal for the combination and overtone bands because most of them are
perturbed thereby significantly affecting the γ -constants. This accuracy problem is
Table 6.8 Experimental equilibrium rotational constants of 32 S 16 O 2 (all values in MHz) a
X
A
B
C
X 0
60778.5526(39)
10318.07332(60)
8799.70375(54)
α/2
−273.5665
41.1766
45.2091
γ /4
2.7025
0.0161
−0.1918
γ 222 /8
0.0713
0.0000
0.0000
X rovib
−276.1977
41.1604
45.4009
X elec
19.9137
0.6564
0.4271
X cd
−0.1014
−0.2081
0.2570
X e
60522.17(52)
10359.682(74)
8845.7887(77)
a Source of experimental data: Flaud and Lafferty (1993)
143
Table 6.7 Comparison of an accurate equilibrium structure, r e , (in pm) and the structure, r e (α),
determined using the experimental α constants and neglecting anharmonic interactions
Molecule
Parameter
r e
r e (α)
r e − r e (α)
OCS a
r(C=O)
115.62(1)
115.45(2)
0.17(2)
r(C=S)
156.14(1)
156.30
−0.16
HCO +b
r(C –H)
109.19(9)
109.725(4)
−0.53(9)
r(C=O)
110.55(3)
110.474(2)
0.08(3)
HCP c
r(C –H)
107.02(10)
106.60(1)
0.42(10)
r(C≡P)
153.99(2)
154.045(2)
−0.06(2)
FCP d
r(C –F)
127.61(7)
128.4
−0.8
r(C≡P)
154.45(6)
153.8
0.6
a Lahaye et al. (1987)
b Woods (1988) and Puzzarini et al. (1996)
c Puzzarini et al. (1996b)
d Dréan et al. (1996)
As a typical example, details of the corrections used to calculate the experimental
rotational constants of
32 S
16 O 2 are given in Table 6.8. The first conclusion is that at
least one order of magnitude in precision is lost when going from the ground-state
constants to the equilibrium ones. However, the final standard deviations are too optimistic because they are calculated using the law of propagation of errors that does
not take into account the systematic errors. As expected, the main correction comes
from the α-constants; see (6.1). The contribution of the γ -constants is not negligible,
although it is difficult to evaluate accurately. Flaud and Lafferty (1993) give
γ /4
= 2.70 MHz, whereas Morino and Tanimoto (1994) estimate it at 1.9 MHz. It is
easy to understand why: whereas it is relatively easy to obtain accurate rotational
constants for the fundamental vibrational states, it is much more difficult to achieve
the same goal for the combination and overtone bands because most of them are
perturbed thereby significantly affecting the γ -constants. This accuracy problem is
Table 6.8 Experimental equilibrium rotational constants of 32 S 16 O 2 (all values in MHz) a
X
A
B
C
X 0
60778.5526(39)
10318.07332(60)
8799.70375(54)
α/2
−273.5665
41.1766
45.2091
γ /4
2.7025
0.0161
−0.1918
γ 222 /8
0.0713
0.0000
0.0000
X rovib
−276.1977
41.1604
45.4009
X elec
19.9137
0.6564
0.4271
X cd
−0.1014
−0.2081
0.2570
X e
60522.17(52)
10359.682(74)
8845.7887(77)
a Source of experimental data: Flaud and Lafferty (1993)