6 Group 13–15 Needle-Shaped Oligomers and Nanorods: Structures. . .
247
(Fig. 6.24g, h) obviously have the same origin as the orbitals of open hydrogensubstituted oligomers (Fig. 6.24c, d). The only difference is observed for the
HOMO, where in methyl-substituted oligomers p orbitals of C atoms make a significant contribution. However, HOMO and LUMO of the closed methyl-substituted
oligomers (Fig. 6.24e, f) are different from those of closed hydrogen-substituted
analogs (Fig. 6.24a, b). While LUMO is semilocalized near the N-capped edge of
the oligomer, the HOMO is delocalized along the oligomer. Thus, it is supposed
that for the long but finite methyl-substituted oligomers [CH 3 GaNH] 3n+1 , HOMO
energy will coincide with the top of the valence band of the [CH 3 GaNH] 3∞
polymer, and LUMO will be located only slightly below the bottom of the
conduction band.
Taking into account that methyl-substituted oligomers exhibit the constant red
shift in the energy spectrum compared to hydrogen-substituted analogs, one can
estimate that open methyl-substituted oligomers with the length of about 10 nm
will have the energy gap less than 1.4 eV. Although numerical values of the energy
levels obtained with DFT approach are not totally reliable, the qualitative behavior
is expected to be valid. Values of band gap change drastically upon the change of
terminal groups; they are also strongly dependent on the length of the oligomer.
6.3.4.3 Thermodynamic Characteristics of the Oligomer Elongation
It is of interest to compare relative energetic favorability of open and closed
oligomers. It was found [53] that formal capping process, that is, termination of
the H 3 [HGaNH] 3n H 3 oligomer by reaction with NH 3 and GaH 3 with formation
of [HGaNH] 3n+1 and release of five molecules of H 2 is exothermic, and the
exothermicity increases with the increase of the oligomerization degree. One can
compare an energy associated with the attachment of each additional ring of open
and closed oligomers by considering energetic characteristics of formal reactions
leading to the oligomer of a particular length (processes 6.6 and 6.7).
3nGaR 3 + 3nNH 3 = R 3 [RGaNH] 3n H 3 + (6n − 3) RH
(6.6)
(3n + 1) GaR 3 + (3n + 1) NH 3 = [RGaNH] 3n+1 + (6n + 2) RH
(6.7)
Both standard enthalpies and standard Gibbs energies of the reactions (6.6) and
(6.7), with R=H or CH 3 , are linear functions of the number of trimeric [HGaNH] 3
rings n. These reactions are exothermic and exergonic, and favorability of cluster
formation increases with increase of n. Entropy change in these reactions is
unfavorable, but it remains approximately constant upon elongation of the rod.
Let us compare H ◦ and G ◦ of reactions of open (6.6) and closed (6.7)
oligomer formation with n ≤ 10. The differences between processes (6.7) and (6.6)
are the reaction (6.8) of formal capping of the open oligomers:
GaR 3 + NH 3 + R 3 [RGaNH] 3n H 3 = [RGaNH] 3n+1 + 5 RH
(6.8)
247
(Fig. 6.24g, h) obviously have the same origin as the orbitals of open hydrogensubstituted oligomers (Fig. 6.24c, d). The only difference is observed for the
HOMO, where in methyl-substituted oligomers p orbitals of C atoms make a significant contribution. However, HOMO and LUMO of the closed methyl-substituted
oligomers (Fig. 6.24e, f) are different from those of closed hydrogen-substituted
analogs (Fig. 6.24a, b). While LUMO is semilocalized near the N-capped edge of
the oligomer, the HOMO is delocalized along the oligomer. Thus, it is supposed
that for the long but finite methyl-substituted oligomers [CH 3 GaNH] 3n+1 , HOMO
energy will coincide with the top of the valence band of the [CH 3 GaNH] 3∞
polymer, and LUMO will be located only slightly below the bottom of the
conduction band.
Taking into account that methyl-substituted oligomers exhibit the constant red
shift in the energy spectrum compared to hydrogen-substituted analogs, one can
estimate that open methyl-substituted oligomers with the length of about 10 nm
will have the energy gap less than 1.4 eV. Although numerical values of the energy
levels obtained with DFT approach are not totally reliable, the qualitative behavior
is expected to be valid. Values of band gap change drastically upon the change of
terminal groups; they are also strongly dependent on the length of the oligomer.
6.3.4.3 Thermodynamic Characteristics of the Oligomer Elongation
It is of interest to compare relative energetic favorability of open and closed
oligomers. It was found [53] that formal capping process, that is, termination of
the H 3 [HGaNH] 3n H 3 oligomer by reaction with NH 3 and GaH 3 with formation
of [HGaNH] 3n+1 and release of five molecules of H 2 is exothermic, and the
exothermicity increases with the increase of the oligomerization degree. One can
compare an energy associated with the attachment of each additional ring of open
and closed oligomers by considering energetic characteristics of formal reactions
leading to the oligomer of a particular length (processes 6.6 and 6.7).
3nGaR 3 + 3nNH 3 = R 3 [RGaNH] 3n H 3 + (6n − 3) RH
(6.6)
(3n + 1) GaR 3 + (3n + 1) NH 3 = [RGaNH] 3n+1 + (6n + 2) RH
(6.7)
Both standard enthalpies and standard Gibbs energies of the reactions (6.6) and
(6.7), with R=H or CH 3 , are linear functions of the number of trimeric [HGaNH] 3
rings n. These reactions are exothermic and exergonic, and favorability of cluster
formation increases with increase of n. Entropy change in these reactions is
unfavorable, but it remains approximately constant upon elongation of the rod.
Let us compare H ◦ and G ◦ of reactions of open (6.6) and closed (6.7)
oligomer formation with n ≤ 10. The differences between processes (6.7) and (6.6)
are the reaction (6.8) of formal capping of the open oligomers:
GaR 3 + NH 3 + R 3 [RGaNH] 3n H 3 = [RGaNH] 3n+1 + 5 RH
(6.8)