0
1
0
-1/2
1/2
-1/2
1/2
0
0
For an alternated chain with hopping integrals t 2n+1,2n = t for strong bonds and
t 2n−1,2n = t′ for weak bonds. The application of Eq. (14.9) leads to c 4 /c 2 = −t′/t = c 4 /
c 6 = c 2n+2 /c 2n . The spin density wave is exponentially damped, as illustrated below
for the case τ/t = 1/2 = t′/t.
1
0
-1/2
1/4
-1/8
1/16
0
0
0
The comparison between these two cases suggests that the spin density wave
introduced by an external magnetic site on a conjugated hydrocarbon has a long
range spatial extent when the bonds of the conjugated system are weakly contrasted. This is the case in fused polycyclic hydrocarbons.
Let us consider series of examples which will be studied by mean of DFT
calculations in Sect. 14.5. They are represented in Fig. 14.1 with specific labels
combining the number of 6-membered rings and a letter which refer to the various
series a, b and c. One should note that some molecules belong to several series and
Fig. 14.1 Atom labelling for the 3 series of free radicals
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