3.10 Direct Potential Fit (DPF)
75
data are directly fitted to the parameters defining an analytic potential energy function.
It allows us to use more sophisticated potential energy functions, which extrapolate
realistically at both large and small distances. The difficulty is that the fit is non-linear.
This method has been recently reviewed by Le Roy (2011), and a typical example
is the analysis of the rovibrational spectra of hydrogen halides by Coxon and
Hajigeorgiou (2015).
3.11 Conclusion
Spectroscopy allows us to determine the Born–Oppenheimer equilibrium structure
of diatomic molecules as light as LiH and as heavy as PbTe with an accuracy better
than 10
−3 pm using (3.78) (or (3.83) when a heavy atom is present); see Tables 3.6
and 3.8. This is much better than can be achieved by ab initio methods. However, a
word of caution is needed: The given uncertainties correspond to statistical errors.
Among others, they do not take into account the systematic errors. For this reason,
the true uncertainty is generally one order of magnitude larger; see, for instance,
Table 3.8 Born–Oppenheimer bond lengths (in pm) for some diatomic molecules
Molecule
r corr
e
a
r b
e
References
ArD +
128.0375(7)
128.0349
Laughlin et al. (1987)
LiH
159.490811(16)
159.5595
Bellini et al. (1995)
LiCl
202.0700(8)
202.6914
Watson (1973)
BF
126.2672(7)
126.2762
Cazzoli et al. (1989)
CO
112.82427(6)
112.8336
Watson (1973)
112.82428(6)
Le Floch (1991)
112.8230(1)
Authier et al. (1993)
CS
153.48192(12)
153.4943
Bogey et al. (1982)
HF
91.683897(4)
91.68942
Coxon and Hajigeorgiou (2015)
HCl
127.46149(9)
127.4572
Watson (1973)
127.460400(108)
Ogilvie (1994)
127.460651(2)
Odashima (2006)
127.454677(6)
Coxon and Hajigeorgiou (2015)
HBr
141.4426(5)
141.4465
Coxon and Hajigeorgiou (1991)
141.44843(2)
Odashima (2006)
141.44292(1)
Coxon and Hajigeorgiou (2015)
PtS
203.8553(4)
203.9822
Cooke and Gerry (2004)
PbTe
259.4975987(11)
259.4977
Giuliano et al. (2008)
a Calculated from U 01 , (3.78), or ¯
U 01 , (3.83)
b Calculated from Y 01 , (3.56; 3.76)
75
data are directly fitted to the parameters defining an analytic potential energy function.
It allows us to use more sophisticated potential energy functions, which extrapolate
realistically at both large and small distances. The difficulty is that the fit is non-linear.
This method has been recently reviewed by Le Roy (2011), and a typical example
is the analysis of the rovibrational spectra of hydrogen halides by Coxon and
Hajigeorgiou (2015).
3.11 Conclusion
Spectroscopy allows us to determine the Born–Oppenheimer equilibrium structure
of diatomic molecules as light as LiH and as heavy as PbTe with an accuracy better
than 10
−3 pm using (3.78) (or (3.83) when a heavy atom is present); see Tables 3.6
and 3.8. This is much better than can be achieved by ab initio methods. However, a
word of caution is needed: The given uncertainties correspond to statistical errors.
Among others, they do not take into account the systematic errors. For this reason,
the true uncertainty is generally one order of magnitude larger; see, for instance,
Table 3.8 Born–Oppenheimer bond lengths (in pm) for some diatomic molecules
Molecule
r corr
e
a
r b
e
References
ArD +
128.0375(7)
128.0349
Laughlin et al. (1987)
LiH
159.490811(16)
159.5595
Bellini et al. (1995)
LiCl
202.0700(8)
202.6914
Watson (1973)
BF
126.2672(7)
126.2762
Cazzoli et al. (1989)
CO
112.82427(6)
112.8336
Watson (1973)
112.82428(6)
Le Floch (1991)
112.8230(1)
Authier et al. (1993)
CS
153.48192(12)
153.4943
Bogey et al. (1982)
HF
91.683897(4)
91.68942
Coxon and Hajigeorgiou (2015)
HCl
127.46149(9)
127.4572
Watson (1973)
127.460400(108)
Ogilvie (1994)
127.460651(2)
Odashima (2006)
127.454677(6)
Coxon and Hajigeorgiou (2015)
HBr
141.4426(5)
141.4465
Coxon and Hajigeorgiou (1991)
141.44843(2)
Odashima (2006)
141.44292(1)
Coxon and Hajigeorgiou (2015)
PtS
203.8553(4)
203.9822
Cooke and Gerry (2004)
PbTe
259.4975987(11)
259.4977
Giuliano et al. (2008)
a Calculated from U 01 , (3.78), or ¯
U 01 , (3.83)
b Calculated from Y 01 , (3.56; 3.76)