236
A. V. Pomogaeva and A. Y. Timoshkin
LUMO belongs to totally symmetric irreducible representation. Note that in case of
open oligomers, HOMO and LUMO are strongly localized on the different ends
of the rod. The orbitals are more delocalized in case of closed oligomers. We
should note also that besides HOMO/HOMO−1 (for open rods) and LUMO (for
all rods), HOMO−2, HOMO−3, HOMO−4, LUMO+1, and LUMO+2 are also
end localized in open oligomers, while HOMO−2, HOMO−3, and LUMO+3 are
localized at the end of the rod for closed oligomers.
Figure 6.18 presents electronic states and PDOS analysis for the energy states
in vicinity of HOMO-LUMO gaps. The highest occupied states of the oligomers
are predominantly p orbitals, and the lowest unoccupied states are predominantly s
orbitals. For highest occupied states of the closed oligomers, the largest contribution
comes from the p states of nitrogen atoms, and it increases with increasing of atomic
radius of metal element. In contrast, HOMOs of the open oligomers have larger
contribution from p states of metal atoms, and major contribution comes from p
states of carbon atoms of terminal methyl groups. There is some contribution from
metal d states to the highest occupied states. Unlike closed oligomers, in the open
ones, HOMO is localized and easily distinguished in PDOS. Note a difference in the
nature of the lowest unoccupied state. For both open and closed oligomers, LUMO
consists of s states of metal atoms and N-bonded hydrogens with the portion of metal
contribution increasing in order Al < Ga < In. However, in case of open oligomers,
the hydrogen atoms at the ends of the rod play the major role in electronic structure
of LUMO. s states of LUMO of closed oligomers are delocalized over the whole
molecule. In case of indium compounds, s orbitals of In have the major contribution
to LUMO.
It is worth to mention that research on three-dimensional Ga-N nanodots and GaN nanowires [183] suggests valence band to be predominantly of nitrogen p orbitals
and the lowest unoccupied states are of Ga p (nanowires) and Ga s and p orbitals
(nanodots).
From the observations above, it is understandable that substitution of gallium
atoms at the end where the LUMO is localized should have a more profound effect
on the electronic structure than substitution at the opposite, (CH 3 ) 3 capped side. It is
more important in case of replacement of Ga with In atoms because of predominant
role of indium s orbitals on the LUMO.
From the results obtained for the small rod-shaped clusters (n = 3), it is expected
that change in the nature of the terminal groups on the ends of the oligomer will
significantly influence the electronic structure of open oligomer.
6.3.3.3 Excitation Spectra
Absorption spectra of closed and open oligomers with n = 3 generated from
vertical excitation energies with transition dipole moment are presented in Fig. 6.19.
Test computations indicate that PBE0 hybrid DFT functional is better suited for
excitation spectra treatment than B3LYP (see Table 6.2). Thus, in further discussion
we will refer to the results of PBE0/TZVP TDDFT computations. However, please
A. V. Pomogaeva and A. Y. Timoshkin
LUMO belongs to totally symmetric irreducible representation. Note that in case of
open oligomers, HOMO and LUMO are strongly localized on the different ends
of the rod. The orbitals are more delocalized in case of closed oligomers. We
should note also that besides HOMO/HOMO−1 (for open rods) and LUMO (for
all rods), HOMO−2, HOMO−3, HOMO−4, LUMO+1, and LUMO+2 are also
end localized in open oligomers, while HOMO−2, HOMO−3, and LUMO+3 are
localized at the end of the rod for closed oligomers.
Figure 6.18 presents electronic states and PDOS analysis for the energy states
in vicinity of HOMO-LUMO gaps. The highest occupied states of the oligomers
are predominantly p orbitals, and the lowest unoccupied states are predominantly s
orbitals. For highest occupied states of the closed oligomers, the largest contribution
comes from the p states of nitrogen atoms, and it increases with increasing of atomic
radius of metal element. In contrast, HOMOs of the open oligomers have larger
contribution from p states of metal atoms, and major contribution comes from p
states of carbon atoms of terminal methyl groups. There is some contribution from
metal d states to the highest occupied states. Unlike closed oligomers, in the open
ones, HOMO is localized and easily distinguished in PDOS. Note a difference in the
nature of the lowest unoccupied state. For both open and closed oligomers, LUMO
consists of s states of metal atoms and N-bonded hydrogens with the portion of metal
contribution increasing in order Al < Ga < In. However, in case of open oligomers,
the hydrogen atoms at the ends of the rod play the major role in electronic structure
of LUMO. s states of LUMO of closed oligomers are delocalized over the whole
molecule. In case of indium compounds, s orbitals of In have the major contribution
to LUMO.
It is worth to mention that research on three-dimensional Ga-N nanodots and GaN nanowires [183] suggests valence band to be predominantly of nitrogen p orbitals
and the lowest unoccupied states are of Ga p (nanowires) and Ga s and p orbitals
(nanodots).
From the observations above, it is understandable that substitution of gallium
atoms at the end where the LUMO is localized should have a more profound effect
on the electronic structure than substitution at the opposite, (CH 3 ) 3 capped side. It is
more important in case of replacement of Ga with In atoms because of predominant
role of indium s orbitals on the LUMO.
From the results obtained for the small rod-shaped clusters (n = 3), it is expected
that change in the nature of the terminal groups on the ends of the oligomer will
significantly influence the electronic structure of open oligomer.
6.3.3.3 Excitation Spectra
Absorption spectra of closed and open oligomers with n = 3 generated from
vertical excitation energies with transition dipole moment are presented in Fig. 6.19.
Test computations indicate that PBE0 hybrid DFT functional is better suited for
excitation spectra treatment than B3LYP (see Table 6.2). Thus, in further discussion
we will refer to the results of PBE0/TZVP TDDFT computations. However, please