6 Group 13–15 Needle-Shaped Oligomers and Nanorods: Structures. . .
257
The HOMO energies of long oligomers (Fig. 6.32c, d) increase in the order
X = F < CF 3 < H < CH 3 . The effect of terminal substituents on the HOMO
energies is less pronounced than on the LUMO energies. The largest difference in
the energies between long open oligomers (n = 10 or 38) with X = F and X = CH 3
of is ~0.65 eV (Fig. 6.32c). For long needle-shaped oligomers (Fig. 6.32d), the
difference does not exceed 0.16 eV. It correlates with the observation that terminal
groups in the Ga-terminated end of long closed oligomers do not contribute to the
HOMO (see Fig. 6.31b). The elongation of open oligomers has a drastic effect on
the HOMO and LUMO energies (see Fig. 6.32). The average downshift of LUMO
energies of open rods is ~0.58 eV (Fig. 6.32a) with elongation from n = 10–38. The
respective upshift for the HOMO energies is ~0.62 eV (Fig. 6.31a).
As expected, X substituents do not influence the energy of LUMO, and Y
substituents do not influence the HOMO energies for oligomers with n = 10 or
38. However, the substituents play a significant role in molecules with n = 3 where
the opposite ends of the molecule are close enough to interact with each other. For
any particular substituents at the nitrogen atom, LUMO energies decrease in the
order of substituents at the gallium atom (X) as CH 3 > H > CF 3 > F for closed and
as CH 3 > H > F > CF 3 for open oligomers with n = 3. On the other hand, for any
particular substituent at the gallium atom, HOMO energies of oligomers with n = 3
increase with changing Y substituents in order CF 3 < F < H < CH 3 for open and
as CF 3 < H < F < CH 3 for closed oligomers. On the whole, for short oligomers the
substituents Y at the nitrogen-terminated end have a larger effect on the energies
of HOMO and LUMO and, consequently, the HOMO-LUMO gap values, than the
substituents X at the gallium-terminated end.
Electronic energies and partial density of states in the vicinity of HOMO-LUMO
gaps of F 3 [HGaNH] 114 F 3 and (CH 3 ) 3 [HGaNH] 114 (CH 3 ) 3 oligomers are given in
Fig. 6.33. At such a length (circa 10 nm), the terminal substituents do not affect the
opposite ends of the rod. Thus, the PDOS in the vicinity of the HOMO and LUMO
of the oligomers with the smallest (X=CH 3 and Y=F) and the largest (X=F and
Y=CH 3 ) energy gaps are expected to be the same as the respective local PDOS
shown in Fig. 6.33a, b.
The estimated band gap of the [HGaNH] ∞ polymer, extrapolated from the
oligomer computations, is circa 7.0 eV. Finite open oligomers have a number of
localized states within the band gap of the parent polymer. These states are clearly
seen in the energy spectra shown in Fig. 6.33 as spatially separated levels in the
vicinity of the HOMO-LUMO gap in contrast to nearly continuous spectra in
valence and conductivity bands. Most of the HOMOs exhibit density distribution
over the N atoms near the Ga-terminated end, while lower unoccupied states
have the main contribution from the Ga atoms near the N-terminated end. The
contribution of terminal groups is noticeable not only in HOMO and LUMO states
but also deeper in the spectrum. F substituents produce a relatively sparse spectrum
of lower unoccupied localized states which results in the maximal downshift of the
LUMO energy (Fig. 6.33a). By withdrawing electrons from N atoms, F substituents
induce vacant orbitals of the lowest energy which result in lower LUMO energies.
257
The HOMO energies of long oligomers (Fig. 6.32c, d) increase in the order
X = F < CF 3 < H < CH 3 . The effect of terminal substituents on the HOMO
energies is less pronounced than on the LUMO energies. The largest difference in
the energies between long open oligomers (n = 10 or 38) with X = F and X = CH 3
of is ~0.65 eV (Fig. 6.32c). For long needle-shaped oligomers (Fig. 6.32d), the
difference does not exceed 0.16 eV. It correlates with the observation that terminal
groups in the Ga-terminated end of long closed oligomers do not contribute to the
HOMO (see Fig. 6.31b). The elongation of open oligomers has a drastic effect on
the HOMO and LUMO energies (see Fig. 6.32). The average downshift of LUMO
energies of open rods is ~0.58 eV (Fig. 6.32a) with elongation from n = 10–38. The
respective upshift for the HOMO energies is ~0.62 eV (Fig. 6.31a).
As expected, X substituents do not influence the energy of LUMO, and Y
substituents do not influence the HOMO energies for oligomers with n = 10 or
38. However, the substituents play a significant role in molecules with n = 3 where
the opposite ends of the molecule are close enough to interact with each other. For
any particular substituents at the nitrogen atom, LUMO energies decrease in the
order of substituents at the gallium atom (X) as CH 3 > H > CF 3 > F for closed and
as CH 3 > H > F > CF 3 for open oligomers with n = 3. On the other hand, for any
particular substituent at the gallium atom, HOMO energies of oligomers with n = 3
increase with changing Y substituents in order CF 3 < F < H < CH 3 for open and
as CF 3 < H < F < CH 3 for closed oligomers. On the whole, for short oligomers the
substituents Y at the nitrogen-terminated end have a larger effect on the energies
of HOMO and LUMO and, consequently, the HOMO-LUMO gap values, than the
substituents X at the gallium-terminated end.
Electronic energies and partial density of states in the vicinity of HOMO-LUMO
gaps of F 3 [HGaNH] 114 F 3 and (CH 3 ) 3 [HGaNH] 114 (CH 3 ) 3 oligomers are given in
Fig. 6.33. At such a length (circa 10 nm), the terminal substituents do not affect the
opposite ends of the rod. Thus, the PDOS in the vicinity of the HOMO and LUMO
of the oligomers with the smallest (X=CH 3 and Y=F) and the largest (X=F and
Y=CH 3 ) energy gaps are expected to be the same as the respective local PDOS
shown in Fig. 6.33a, b.
The estimated band gap of the [HGaNH] ∞ polymer, extrapolated from the
oligomer computations, is circa 7.0 eV. Finite open oligomers have a number of
localized states within the band gap of the parent polymer. These states are clearly
seen in the energy spectra shown in Fig. 6.33 as spatially separated levels in the
vicinity of the HOMO-LUMO gap in contrast to nearly continuous spectra in
valence and conductivity bands. Most of the HOMOs exhibit density distribution
over the N atoms near the Ga-terminated end, while lower unoccupied states
have the main contribution from the Ga atoms near the N-terminated end. The
contribution of terminal groups is noticeable not only in HOMO and LUMO states
but also deeper in the spectrum. F substituents produce a relatively sparse spectrum
of lower unoccupied localized states which results in the maximal downshift of the
LUMO energy (Fig. 6.33a). By withdrawing electrons from N atoms, F substituents
induce vacant orbitals of the lowest energy which result in lower LUMO energies.