8.5 Empirical Correlations (Legon and Demaison 2011)
223
correlation between the C–H and C≡C bond lengths in HC≡CX molecules. In
symmetrically para-disubstituted benzenes, the ipso angle and the non-bonded
distance C1…C4 are linearly correlated. More interestingly, Hargittai (1985) found
a correlation between S=O bond lengths and ∠(OSO) bond angles in sulfones,
and McKean (1976) observed a similar correlation between CH bond lengths and
∠(HCH) bond angles in methyl groups. These correlations can be easily explained
using the LCP model, Sect. 8.4. If we consider of molecule ZXY 2 where X and Y are
atoms and Z is either an atom or a group of atom and if d is the interatomic distance
between the two geminal ligands Y, it follows that
∠(YXY) = 2 arcsin
d(Y . . . Y)
2r (XY)
(8.16)
As the interligand distance d is almost constant, it gives a nice correlation between
the bond angle ∠(YXY) and the bond length r(XY).
8.5.3.3 Correlation Between the Lengths of Similar Bonds in Different
Molecules
If we consider the same bond in two series of molecules, there is usually a nice correlation. A typical example is between the C–X bond in XC≡N and CH 3 X molecules
(Demaison et al. 2003). It can even be extended to different bonds. For instance, it
is known that the halides (with the exception of fluorides) have similar properties.
Therefore, a relationship between r(C–Br) and r(C–Cl) is expected, and it is indeed
found with a correlation coefficient of 0.993 for 24 different molecules (Demaison
et al. 2003).
8.5.3.4 Correlation Between the C–C Bond Length and the Bond
Multiplicity
It is established that the CC bond distances in organic molecules decrease with the
bond multiplicity, see Fig. 8.5. It can be explained using the LCP model, Sect. 8.4.
Stoicheff (1962) showed that this effect can be represented by a linear function of the
number n of bonds adjacent to the C–C bond in question. Later, Kuchitsu (1972) using
r g bond lengths (average internuclear distances, see Chap. 7) proposed a quadratic
equation that is more accurate. The original equation (in pm) is
r g (n) = 128.5 + 5.33n − 0.20n
2
(8.17)
Using more recent equilibrium values, it gives
r e (n) = 126.8(21) + 5.8(11)n − 0.27(14)n
2
(8.18)
223
correlation between the C–H and C≡C bond lengths in HC≡CX molecules. In
symmetrically para-disubstituted benzenes, the ipso angle and the non-bonded
distance C1…C4 are linearly correlated. More interestingly, Hargittai (1985) found
a correlation between S=O bond lengths and ∠(OSO) bond angles in sulfones,
and McKean (1976) observed a similar correlation between CH bond lengths and
∠(HCH) bond angles in methyl groups. These correlations can be easily explained
using the LCP model, Sect. 8.4. If we consider of molecule ZXY 2 where X and Y are
atoms and Z is either an atom or a group of atom and if d is the interatomic distance
between the two geminal ligands Y, it follows that
∠(YXY) = 2 arcsin
d(Y . . . Y)
2r (XY)
(8.16)
As the interligand distance d is almost constant, it gives a nice correlation between
the bond angle ∠(YXY) and the bond length r(XY).
8.5.3.3 Correlation Between the Lengths of Similar Bonds in Different
Molecules
If we consider the same bond in two series of molecules, there is usually a nice correlation. A typical example is between the C–X bond in XC≡N and CH 3 X molecules
(Demaison et al. 2003). It can even be extended to different bonds. For instance, it
is known that the halides (with the exception of fluorides) have similar properties.
Therefore, a relationship between r(C–Br) and r(C–Cl) is expected, and it is indeed
found with a correlation coefficient of 0.993 for 24 different molecules (Demaison
et al. 2003).
8.5.3.4 Correlation Between the C–C Bond Length and the Bond
Multiplicity
It is established that the CC bond distances in organic molecules decrease with the
bond multiplicity, see Fig. 8.5. It can be explained using the LCP model, Sect. 8.4.
Stoicheff (1962) showed that this effect can be represented by a linear function of the
number n of bonds adjacent to the C–C bond in question. Later, Kuchitsu (1972) using
r g bond lengths (average internuclear distances, see Chap. 7) proposed a quadratic
equation that is more accurate. The original equation (in pm) is
r g (n) = 128.5 + 5.33n − 0.20n
2
(8.17)
Using more recent equilibrium values, it gives
r e (n) = 126.8(21) + 5.8(11)n − 0.27(14)n
2
(8.18)