230
A. V. Pomogaeva and A. Y. Timoshkin
In the following discussion, we will distinguish between the HOMO-LUMO gap
and the bandgap, which is obtained by extrapolation to the edges of BZ of bands,
obtained by mapping of MOs on reciprocal space. We should note that in case of
long periodic oligomer in which HOMO and LUMO are well delocalized, HOMOLUMO gap and bandgap could be close numerically but are not the same.
6.3.3 Small Open (CH 3 ) 3 [CH 3 MNH] 9 H 3 and Closed
[CH 3 MNH] 10 Mixed Metal Oligomers (M = Al, Ga, In)
It is natural to start the consideration from clusters of relatively small size. On
the one hand, cluster of three trimeric [RMNH] 3 rings is a minimal unit for
which the term “nanorod” is appropriate; on the other hand, these oligomers are
small enough to be studied comprehensively in detail with R=CH 3 and different metal atom. Methyl substituents are interesting because the alkyl-substituted
derivatives of the needle-shaped Ga-N clusters are experimentally known [119].
In this section we provide a direct comparison of electronic properties of open
(CH 3 ) 3 [CH 3 MNH] 3n H 3 and closed [CH 3 MNH] 3n+1 mixed metal oligomers with
n = 3 (M = Al, Ga, In) [56, 57].
6.3.3.1 Structures of Mixed Metal Oligomers
Table 6.3 provides selected structural parameters for [CH 3 MNH] 10 and
(CH 3 ) 3 [CH 3 MNH] 9 H 3 (M = Al, Ga, In) oligomers. The specified bond lengths
and angles are indicated in Fig. 6.15.
Binary closed oligomers possess C 3v point group, while open ones are C 3
symmetric. Three terminal methyl groups in open oligomers are almost free rotors;
thus, the global minimum is shallow with respect to the mutual orientation of
the hydrogen atoms of the methyl groups. Terminal CH 3 groups are rotated by
8.8 ◦ , 17.6 ◦ , and 23.6 ◦ for M = Al, Ga, and In, respectively. For the mixed metal
oligomers, it was found that the rotation angle θ Me of the terminal methyl groups
depends only on the type of the closest metal atom.
M-N bond lengths vary significantly over the oligomer core for both closed and
open oligomers. M-N distances in the middle of M 3 N 3 rings are by 0.01–0.02 Å
shorter than those in the outmost rings. Considering the middle M 3 N 3 rings, one
can notice that M-N bond lengths are slightly shorter and both M-N-M and N-MN angles are slightly larger for closed oligomers than for open ones. M-N bond
lengths between M 3 N 3 rings are generally shorter than ones within rings. M-N
bonds connecting the end’s MCH 3 group with the first ring are among the longest.
Al-N bond lengths are about 3% shorter, and In-N bond lengths are about 10%
longer than respective Ga-N distances. Similar trends in bond lengths are observed
for bulk wurtzitic Al/Ga/In nitride structures [181]. Our computations indicate that
A. V. Pomogaeva and A. Y. Timoshkin
In the following discussion, we will distinguish between the HOMO-LUMO gap
and the bandgap, which is obtained by extrapolation to the edges of BZ of bands,
obtained by mapping of MOs on reciprocal space. We should note that in case of
long periodic oligomer in which HOMO and LUMO are well delocalized, HOMOLUMO gap and bandgap could be close numerically but are not the same.
6.3.3 Small Open (CH 3 ) 3 [CH 3 MNH] 9 H 3 and Closed
[CH 3 MNH] 10 Mixed Metal Oligomers (M = Al, Ga, In)
It is natural to start the consideration from clusters of relatively small size. On
the one hand, cluster of three trimeric [RMNH] 3 rings is a minimal unit for
which the term “nanorod” is appropriate; on the other hand, these oligomers are
small enough to be studied comprehensively in detail with R=CH 3 and different metal atom. Methyl substituents are interesting because the alkyl-substituted
derivatives of the needle-shaped Ga-N clusters are experimentally known [119].
In this section we provide a direct comparison of electronic properties of open
(CH 3 ) 3 [CH 3 MNH] 3n H 3 and closed [CH 3 MNH] 3n+1 mixed metal oligomers with
n = 3 (M = Al, Ga, In) [56, 57].
6.3.3.1 Structures of Mixed Metal Oligomers
Table 6.3 provides selected structural parameters for [CH 3 MNH] 10 and
(CH 3 ) 3 [CH 3 MNH] 9 H 3 (M = Al, Ga, In) oligomers. The specified bond lengths
and angles are indicated in Fig. 6.15.
Binary closed oligomers possess C 3v point group, while open ones are C 3
symmetric. Three terminal methyl groups in open oligomers are almost free rotors;
thus, the global minimum is shallow with respect to the mutual orientation of
the hydrogen atoms of the methyl groups. Terminal CH 3 groups are rotated by
8.8 ◦ , 17.6 ◦ , and 23.6 ◦ for M = Al, Ga, and In, respectively. For the mixed metal
oligomers, it was found that the rotation angle θ Me of the terminal methyl groups
depends only on the type of the closest metal atom.
M-N bond lengths vary significantly over the oligomer core for both closed and
open oligomers. M-N distances in the middle of M 3 N 3 rings are by 0.01–0.02 Å
shorter than those in the outmost rings. Considering the middle M 3 N 3 rings, one
can notice that M-N bond lengths are slightly shorter and both M-N-M and N-MN angles are slightly larger for closed oligomers than for open ones. M-N bond
lengths between M 3 N 3 rings are generally shorter than ones within rings. M-N
bonds connecting the end’s MCH 3 group with the first ring are among the longest.
Al-N bond lengths are about 3% shorter, and In-N bond lengths are about 10%
longer than respective Ga-N distances. Similar trends in bond lengths are observed
for bulk wurtzitic Al/Ga/In nitride structures [181]. Our computations indicate that