6 Group 13–15 Needle-Shaped Oligomers and Nanorods: Structures. . .
227
Table 6.2 Excitation energies (in eV) to low-lying excited (singlet) states of [HGaNH] 4 at
different levels of theory
Electronic state
Method
Basis set 1
2
3
4
5
6
7
8
EOM-CCSD TZVPD
6.318 6.318 6.318 6.368 6.368 6.506 6.506 6.506
PBE0
TZVP
6.314 6.314 6.316 6.316 6.316 6.447 6.447 6.447
QZVP
6.193 6.193 6.199 6.199 6.199 6.301 6.301 6.301
TZVPD
6.120 6.120 6.128 6.128 6.128 6.227 6.227 6.227
QZVPD 6.095 6.095 6.103 6.103 6.103 6.197 6.197 6.197
HSSE
TZVP
6.258 6.258 6.259 6.259 6.259 6.383 6.383 6.383
QZVP
6.143 6.143 6.147 6.147 6.147 6.245 6.245 6.245
TZVPD
6.075 6.075 6.082 6.082 6.082 6.176 6.176 6.176
QZVPD 6.052 6.052 6.058 6.058 6.058 6.148 6.148 6.148
M06
TZVP
6.177 6.177 6.179 6.179 6.179 6.301 6.301 6.301
QZVP
5.779 5.779 5.809 5.809 5.809 5.855 5.855 5.855
TZVPD
5.618 5.618 5.625 5.625 5.625 5.678 5.678 5.678
QZVPD 5.554 5.554 5.563 5.563 5.563 5.614 5.614 5.614
B3LYP
TZVP
6.101 6.101 6.112 6.112 6.112 6.218 6.218 6.218
QZVP
5.976 5.976 5.989 5.989 5.989 6.070 6.070 6.070
TZVPD
5.903 5.903 5.919 5.919 5.919 5.997 5.997 5.997
QZVPD 5.874 5.874 5.889 5.889 5.889 5.963 5.963 5.963
All computations discussed in this chapter were performed using Gaussian
09 program package [164]. PDOS for a chosen fragment was computed using
GaussSum code [165].
6.3.2.2 Band Structure Computation Method
Periodicity is an essential property of bulk semiconductors, and band structure is an
important characteristic of their electronic properties. Being intermediates between
molecules and bulk crystals, semiconducting nanoparticles also exhibit periodic
properties in structural as well as in electronic features. It is a common approach
treating nanorods within PBC [166–169]. PBC approximation allows to study the
effect of surface dangling bonds [167, 170]. It was found that the band gaps of
Ga-N [167] or GaAs [171] nanorods are ruled by surface states and do not change
with the diameter of the nanorods according to the trend dictated by the quantum
confinement effect. However, the PBC approach is difficult to be used for studying
structures with local defects and substituents, and it is not applicable for studying
the effect of dangling bonds at the terminal edges of nanorods.
On the other hand, the edge effects for rather short nanorods can be studied using
ab initio methods. Investigation of finite size carbon nanotubes shows that terminal
effects have strong impacts on the vibrational frequencies [172], and the study of
finite graphene nanoribbons shows that the gap defined by the end-localized states
227
Table 6.2 Excitation energies (in eV) to low-lying excited (singlet) states of [HGaNH] 4 at
different levels of theory
Electronic state
Method
Basis set 1
2
3
4
5
6
7
8
EOM-CCSD TZVPD
6.318 6.318 6.318 6.368 6.368 6.506 6.506 6.506
PBE0
TZVP
6.314 6.314 6.316 6.316 6.316 6.447 6.447 6.447
QZVP
6.193 6.193 6.199 6.199 6.199 6.301 6.301 6.301
TZVPD
6.120 6.120 6.128 6.128 6.128 6.227 6.227 6.227
QZVPD 6.095 6.095 6.103 6.103 6.103 6.197 6.197 6.197
HSSE
TZVP
6.258 6.258 6.259 6.259 6.259 6.383 6.383 6.383
QZVP
6.143 6.143 6.147 6.147 6.147 6.245 6.245 6.245
TZVPD
6.075 6.075 6.082 6.082 6.082 6.176 6.176 6.176
QZVPD 6.052 6.052 6.058 6.058 6.058 6.148 6.148 6.148
M06
TZVP
6.177 6.177 6.179 6.179 6.179 6.301 6.301 6.301
QZVP
5.779 5.779 5.809 5.809 5.809 5.855 5.855 5.855
TZVPD
5.618 5.618 5.625 5.625 5.625 5.678 5.678 5.678
QZVPD 5.554 5.554 5.563 5.563 5.563 5.614 5.614 5.614
B3LYP
TZVP
6.101 6.101 6.112 6.112 6.112 6.218 6.218 6.218
QZVP
5.976 5.976 5.989 5.989 5.989 6.070 6.070 6.070
TZVPD
5.903 5.903 5.919 5.919 5.919 5.997 5.997 5.997
QZVPD 5.874 5.874 5.889 5.889 5.889 5.963 5.963 5.963
All computations discussed in this chapter were performed using Gaussian
09 program package [164]. PDOS for a chosen fragment was computed using
GaussSum code [165].
6.3.2.2 Band Structure Computation Method
Periodicity is an essential property of bulk semiconductors, and band structure is an
important characteristic of their electronic properties. Being intermediates between
molecules and bulk crystals, semiconducting nanoparticles also exhibit periodic
properties in structural as well as in electronic features. It is a common approach
treating nanorods within PBC [166–169]. PBC approximation allows to study the
effect of surface dangling bonds [167, 170]. It was found that the band gaps of
Ga-N [167] or GaAs [171] nanorods are ruled by surface states and do not change
with the diameter of the nanorods according to the trend dictated by the quantum
confinement effect. However, the PBC approach is difficult to be used for studying
structures with local defects and substituents, and it is not applicable for studying
the effect of dangling bonds at the terminal edges of nanorods.
On the other hand, the edge effects for rather short nanorods can be studied using
ab initio methods. Investigation of finite size carbon nanotubes shows that terminal
effects have strong impacts on the vibrational frequencies [172], and the study of
finite graphene nanoribbons shows that the gap defined by the end-localized states