9.11 Accuracy of the Structural Parameters
259
Table 9.10 Experimental equilibrium structures of stibine (distances in pm and angle in degree)
(Cané et al. 2005 and 2006)
r e (SbH)
∠(HSbH)
121 SbH 3
170.0013(1)
91.5586(1)
123 SbH 3
170.0013(1)
91.55910(12)
121 SbD 3
170.0909(2)
91.6713(2)
123 SbD 3
170.0897(3)
91.67278(26)
Range
0.0889
0.1142
s(from mean)
0.051
0.065
s(from range)
0.040
0.057
s(from authors) a
0.06
0.06
a See text
s
2
=
1
n − 1
n
i=1
(r i − ¯
r )
2
(9.73)
where n is the number of different structures, and ¯
r =
r i /n is their mean. As the
number of data n is usually small, the standard deviation may also be estimated from
the range R of parameters. When the number n of independent determinations is at
least as large as three, the standard deviation may be estimated using the following
formula (Kyker 1983)
s =
R
1.40 n 1/3 with 3 ≤ n ≤ 12
(9.74)
The authors of the work also made an estimation of the uncertainty taking into
account the following sources of errors: (i) assumption of a linear dependence of the
rotational constants on vibrational quantum numbers (i.e., neglect of γ -terms, see
(6.1)), (ii) electronic correction depending on the molecular rotational g factors (see
Sect. 4.10), (iii) neglect of the anharmonic interaction between the stretching and
bending states. They found 0.06 pm for r e and 0.06° for θ e (HSbH), in good agreement with the results of (9.73–9.74), which are also given in Table 9.10. The main
discrepancy is between the H 3 and D 3 species with δr e = r(
121 SbD 3 ) − r(
121 SbH 3 )
≈ 0.0889(2) pm and δθ e = ∠(D
121 SbD) – ∠(H
121 SbH) ≈ 0.1127(2)°. It is easy to
eliminate the effect of the neglected anharmonic resonances because an accurate
anharmonic force field was calculated at the CCSD(T) level allowing us to derive a
semiexperimental structure which is not sensitive to anharmonic resonances. It gives
δr SE = 0.07 pm and δθ SE = 0.12° in satisfactory agreement with the experimental
values. It is also possible to take into account the effect of the g factors. They were
estimated at the B3LYP/VQZ level giving for
121 SbH 3 g bb = − 0.143 and g cc = −
0.183. Taking into account, this electronic correction slightly modifies the structure
(r e is decreased by 0.004 pm and the effect is negligible for θ e ) but does not affect
259
Table 9.10 Experimental equilibrium structures of stibine (distances in pm and angle in degree)
(Cané et al. 2005 and 2006)
r e (SbH)
∠(HSbH)
121 SbH 3
170.0013(1)
91.5586(1)
123 SbH 3
170.0013(1)
91.55910(12)
121 SbD 3
170.0909(2)
91.6713(2)
123 SbD 3
170.0897(3)
91.67278(26)
Range
0.0889
0.1142
s(from mean)
0.051
0.065
s(from range)
0.040
0.057
s(from authors) a
0.06
0.06
a See text
s
2
=
1
n − 1
n
i=1
(r i − ¯
r )
2
(9.73)
where n is the number of different structures, and ¯
r =
r i /n is their mean. As the
number of data n is usually small, the standard deviation may also be estimated from
the range R of parameters. When the number n of independent determinations is at
least as large as three, the standard deviation may be estimated using the following
formula (Kyker 1983)
s =
R
1.40 n 1/3 with 3 ≤ n ≤ 12
(9.74)
The authors of the work also made an estimation of the uncertainty taking into
account the following sources of errors: (i) assumption of a linear dependence of the
rotational constants on vibrational quantum numbers (i.e., neglect of γ -terms, see
(6.1)), (ii) electronic correction depending on the molecular rotational g factors (see
Sect. 4.10), (iii) neglect of the anharmonic interaction between the stretching and
bending states. They found 0.06 pm for r e and 0.06° for θ e (HSbH), in good agreement with the results of (9.73–9.74), which are also given in Table 9.10. The main
discrepancy is between the H 3 and D 3 species with δr e = r(
121 SbD 3 ) − r(
121 SbH 3 )
≈ 0.0889(2) pm and δθ e = ∠(D
121 SbD) – ∠(H
121 SbH) ≈ 0.1127(2)°. It is easy to
eliminate the effect of the neglected anharmonic resonances because an accurate
anharmonic force field was calculated at the CCSD(T) level allowing us to derive a
semiexperimental structure which is not sensitive to anharmonic resonances. It gives
δr SE = 0.07 pm and δθ SE = 0.12° in satisfactory agreement with the experimental
values. It is also possible to take into account the effect of the g factors. They were
estimated at the B3LYP/VQZ level giving for
121 SbH 3 g bb = − 0.143 and g cc = −
0.183. Taking into account, this electronic correction slightly modifies the structure
(r e is decreased by 0.004 pm and the effect is negligible for θ e ) but does not affect