242
A. V. Pomogaeva and A. Y. Timoshkin
For both closed and open oligomers, there is a contraction of interring Ga-N
bond lengths (Fig. 6.21b) as well as expansion of the intra-ring Ga-N bond lengths
(Fig. 6.21a) toward the edges of the rod. For closed oligomers of all lengths,
the contraction near the Ga-capped edge of the rod is 0.007 Å (~0.3%) from
the interring Ga-N bond lengths of 1.993 Å at the center of the oligomer. The
contraction near the N-capped edge of the oligomer is 0.02 Å (~1.0%). In open
oligomers, the contraction of the interring Ga-N bond lengths is somewhat larger
(up to 0.04 Å, 2%) and depends on the length of the oligomer. These structural
changes are quantitatively similar to those predicted for the contraction of surface
Ga-N bond lengths in hydrogen-substituted Ga-N nanorods with diameters up to
3.5 nm studied at PBC level [183]. The expansion of intra-ring Ga-N bond lengths in
closed nanorods near the Ga-capped edge is 0.011 Å ~ 0.6%, and near the N-capped
edge is 0.019 Å (~1.0% relative the bond lengths at the center of the rod). For open
oligomers, the expansion is also length-dependent and amounts up to 0.04 Å (2%
relative to the bond lengths at the center of the oligomer).
Methyl-substituted oligomers within considered lengths with n ≤ 9 demonstrate
the same tendencies as hydrogen-substituted analogs. All structural parameters of
the methyl-substituted oligomers are very similar, with Ga-N bond lengths being
slightly longer (within 0.005 Å) and N-Ga-N angles being slightly smaller (within
1 ◦ ) than related parameters in the hydrogen-substituted oligomers of the same length
and the same type of termination.
Overall, the impact of the terminal groups is found to be surprisingly large.
Quite large oligomers, with 19 equivalent structural units (38 [HGaNH] 3 rings) and
differences only in the terminal groups, coincide in their geometrical parameters
only in a small section (about 10 [HGaNH] 3 rings) in the central part of the rod.
Moreover, the needle-shaped (closed) oligomers exhibit comparative regularity in
the geometric parameters of the [HGaNH] 3 units, with the exception of those closest
to the edges. The tube-like (open) oligomers are monotonically compressed from the
center to the edges. Such significant difference in structural characteristics of open
and closed oligomers results in pronounced differences in their electronic properties.
6.3.4.2 Band Structure of [RGaNH] n Polymer and Electronic Structure
of Finite Size Oligomers
It was stressed above (Sect. 6.3.4.1) that oligomers with a closed type of termination
maintain periodicity, that is, all structural parameters of neighboring [HGaNH] 3
repeating units are almost equivalent. The exception is the outmost GaH and NH
units whose influence on the electronic structure is supposed to be rather local. The
[HGaNH] 115 oligomer has 19 repeating units [HGaNH] 6 and capping GaH and NH
groups. More than 15 equivalent unit cells of an oligomer are generally enough to
extract band structure of the related polymer from the finite oligomer calculation
[174]. Indeed, except for a limited number of localized states, MOs of the closed
oligomer with n = 38 are found to be properly delocalized along the chain. In Fig.
6.23a circles show positions of these delocalized MOs in the first BZ of [HGaNH] 3∞
A. V. Pomogaeva and A. Y. Timoshkin
For both closed and open oligomers, there is a contraction of interring Ga-N
bond lengths (Fig. 6.21b) as well as expansion of the intra-ring Ga-N bond lengths
(Fig. 6.21a) toward the edges of the rod. For closed oligomers of all lengths,
the contraction near the Ga-capped edge of the rod is 0.007 Å (~0.3%) from
the interring Ga-N bond lengths of 1.993 Å at the center of the oligomer. The
contraction near the N-capped edge of the oligomer is 0.02 Å (~1.0%). In open
oligomers, the contraction of the interring Ga-N bond lengths is somewhat larger
(up to 0.04 Å, 2%) and depends on the length of the oligomer. These structural
changes are quantitatively similar to those predicted for the contraction of surface
Ga-N bond lengths in hydrogen-substituted Ga-N nanorods with diameters up to
3.5 nm studied at PBC level [183]. The expansion of intra-ring Ga-N bond lengths in
closed nanorods near the Ga-capped edge is 0.011 Å ~ 0.6%, and near the N-capped
edge is 0.019 Å (~1.0% relative the bond lengths at the center of the rod). For open
oligomers, the expansion is also length-dependent and amounts up to 0.04 Å (2%
relative to the bond lengths at the center of the oligomer).
Methyl-substituted oligomers within considered lengths with n ≤ 9 demonstrate
the same tendencies as hydrogen-substituted analogs. All structural parameters of
the methyl-substituted oligomers are very similar, with Ga-N bond lengths being
slightly longer (within 0.005 Å) and N-Ga-N angles being slightly smaller (within
1 ◦ ) than related parameters in the hydrogen-substituted oligomers of the same length
and the same type of termination.
Overall, the impact of the terminal groups is found to be surprisingly large.
Quite large oligomers, with 19 equivalent structural units (38 [HGaNH] 3 rings) and
differences only in the terminal groups, coincide in their geometrical parameters
only in a small section (about 10 [HGaNH] 3 rings) in the central part of the rod.
Moreover, the needle-shaped (closed) oligomers exhibit comparative regularity in
the geometric parameters of the [HGaNH] 3 units, with the exception of those closest
to the edges. The tube-like (open) oligomers are monotonically compressed from the
center to the edges. Such significant difference in structural characteristics of open
and closed oligomers results in pronounced differences in their electronic properties.
6.3.4.2 Band Structure of [RGaNH] n Polymer and Electronic Structure
of Finite Size Oligomers
It was stressed above (Sect. 6.3.4.1) that oligomers with a closed type of termination
maintain periodicity, that is, all structural parameters of neighboring [HGaNH] 3
repeating units are almost equivalent. The exception is the outmost GaH and NH
units whose influence on the electronic structure is supposed to be rather local. The
[HGaNH] 115 oligomer has 19 repeating units [HGaNH] 6 and capping GaH and NH
groups. More than 15 equivalent unit cells of an oligomer are generally enough to
extract band structure of the related polymer from the finite oligomer calculation
[174]. Indeed, except for a limited number of localized states, MOs of the closed
oligomer with n = 38 are found to be properly delocalized along the chain. In Fig.
6.23a circles show positions of these delocalized MOs in the first BZ of [HGaNH] 3∞