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FIGURE 6.7
Schematic view of the potential energy surfaces showing the distortion
from the single-well cumulenic minimum (a), the wide minima of an averaged
cumulenic structure having a softened large-amplitude vibrational motion (b), to the
double-well acetylenic minima (c). ZPE: the level of summed zero point energy of
vibrational modes.
(10
29), the authors found a series of EAs that is distinctly lower than
the series for linear C
n
(n
n
9). They noticed also that there is a 4-fold
resemblance in the spectral details for n
10.
Handschuh et al. investigated the vibrational structures of carbon clus-
ters C
n
up to n
70 by UPS and discussed the structural transition from
linear, monocyclic, bicyclic, to fullerene-like cage structures as a function of
the cluster size [36]. Using dehydroannulene derivatives having carbon ring
size of n
¼
12, 16, 18, 20, and 24, Wakabayashi and Tobe measured photo-
electron spectra of C
n
liberated from the precursors by laser ablation under
vacuum [6]. In these experiments, the high-frequency vibrational progres-
sion (>2000 cm
1
) is observed for the clusters of 4m carbon atoms (m
¼
5, 6)
as in the spectrum in
Figure 6.8
[37].
For the assignment of the vibrational structure in the photoelectron
spectrum of C
20
in Figure 6.8, the electron distribution (square of the MO
wave function) is considered for the LUMO level from which the electron is
detached upon the UPS measurement. The LUMO of cyclic C
20
(see the
upper panels in
Figure 6.6
)
has higher electron density on the single bonds
that strengthens the single bonds to decrease the corresponding bond
lengths in the anionic state. Upon the electron detachment, the single bonds
are loosened to increase the bond lengths. This will induce the collective
motions of the carbon nuclei that enhance the acetylenic form. Accordingly,
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