6 Group 13–15 Needle-Shaped Oligomers and Nanorods: Structures. . .
225
Table 6.1 Distances (Å) and
angles (degrees) of
[RGaNH] 4 cubane clusters
optimized at different levels
of theory
Method Basis set [HGaNH] 4
[CH 3 GaNH] 4
Ga-N N-Ga-N Ga-N N-Ga-N
CCSD
TZVP
1.989 87.49
1.994 87.50
QZVP
1.997 87.76
–
–
B3LYP SVP
2.001 87.64
2.005 87.60
TZV
2.003 87.46
2.008 87.46
TZVP
2.004 87.52
2.009 87.52
QZVP
2.003 87.61
2.008 87.59
VWN5 SVP
1.969 88.10
1.972 88.09
TZV
1.972 87.81
1.977 87.85
TZVP
1.973 87.94
1.976 87.88
QZVP
1.971 88.00
1.975 87.95
PBE0
SVP
1.986 87.97
1.989 87.94
TZV
1.987 87.76
1.992 87.81
TZVP
1.988 87.88
1.992 87.82
QZVP
1.987 87.98
1.991 87.92
HSSE
SVP
1.987 87.91
1.990 87.88
TZV
1.989 87.73
1.993 87.76
TZVP
1.989 87.83
1.993 87.77
QZVP
1.988 87.92
1.992 87.88
overestimated with respect to 1.997 Å at CCSD/QZVP level than Ga-N distances
obtained with other DFT functionals. Similarly, N-Ga-N angles at B3LYP/SVP level
differ from CCSD/QZVP by only about 0.12 ◦ that is slightly smaller compared to
other DFT methods. Overall, the computations show that bond lengths and bond
angles optimized at the B3LYP/SVP level of theory have smaller deviation from the
benchmark CCSD/QZVP results than other considered functionals (probably due
to fortunes cancelation of errors between incompleteness of the basis set and the
electron correlation treatment).
Additionally, computations for selected long oligomers were performed at
PBE0/SVP, B3LYP/SVP, and B3LYP/TZVP levels of theory in order to ensure
that the reliability of the chosen B3LYP/SVP computational approach remains valid
with the elongation of the oligomer. It was found that PBE0 functional reproduces
elongation effects qualitatively similar to B3LYP method. For example, in case of
geometry optimization of H 3 [HGaNH] 30 H 3 , Ga-N bond lengths at PBE0 level are
shorter than at B3LYP level by about 0.015−0.019 Å. The values of the band gap
energy computed at PBE0 level are by circa 0.6 eV larger than computed at B3LYP
level for a wide range of the oligomers of different lengths.
The average difference in Ga-N bond lengths computed using TZVP and SVP
basis sets (circa 0.002 Å) is the same for H 3 [HGaNH] 9 H 3 and H 3 [HGaNH] 30 H 3
compounds. Thus, we conclude that the error does not increase notably with the
elongation of the oligomer. A difference in the reaction energies of formation of
H 3 [HGaNH] 3n H 3 from GaH 3 and NH 3 calculated using TZVP and SVP basis sets
is about 1% of the value obtained using the TZVP basis set, irrespective of the
225
Table 6.1 Distances (Å) and
angles (degrees) of
[RGaNH] 4 cubane clusters
optimized at different levels
of theory
Method Basis set [HGaNH] 4
[CH 3 GaNH] 4
Ga-N N-Ga-N Ga-N N-Ga-N
CCSD
TZVP
1.989 87.49
1.994 87.50
QZVP
1.997 87.76
–
–
B3LYP SVP
2.001 87.64
2.005 87.60
TZV
2.003 87.46
2.008 87.46
TZVP
2.004 87.52
2.009 87.52
QZVP
2.003 87.61
2.008 87.59
VWN5 SVP
1.969 88.10
1.972 88.09
TZV
1.972 87.81
1.977 87.85
TZVP
1.973 87.94
1.976 87.88
QZVP
1.971 88.00
1.975 87.95
PBE0
SVP
1.986 87.97
1.989 87.94
TZV
1.987 87.76
1.992 87.81
TZVP
1.988 87.88
1.992 87.82
QZVP
1.987 87.98
1.991 87.92
HSSE
SVP
1.987 87.91
1.990 87.88
TZV
1.989 87.73
1.993 87.76
TZVP
1.989 87.83
1.993 87.77
QZVP
1.988 87.92
1.992 87.88
overestimated with respect to 1.997 Å at CCSD/QZVP level than Ga-N distances
obtained with other DFT functionals. Similarly, N-Ga-N angles at B3LYP/SVP level
differ from CCSD/QZVP by only about 0.12 ◦ that is slightly smaller compared to
other DFT methods. Overall, the computations show that bond lengths and bond
angles optimized at the B3LYP/SVP level of theory have smaller deviation from the
benchmark CCSD/QZVP results than other considered functionals (probably due
to fortunes cancelation of errors between incompleteness of the basis set and the
electron correlation treatment).
Additionally, computations for selected long oligomers were performed at
PBE0/SVP, B3LYP/SVP, and B3LYP/TZVP levels of theory in order to ensure
that the reliability of the chosen B3LYP/SVP computational approach remains valid
with the elongation of the oligomer. It was found that PBE0 functional reproduces
elongation effects qualitatively similar to B3LYP method. For example, in case of
geometry optimization of H 3 [HGaNH] 30 H 3 , Ga-N bond lengths at PBE0 level are
shorter than at B3LYP level by about 0.015−0.019 Å. The values of the band gap
energy computed at PBE0 level are by circa 0.6 eV larger than computed at B3LYP
level for a wide range of the oligomers of different lengths.
The average difference in Ga-N bond lengths computed using TZVP and SVP
basis sets (circa 0.002 Å) is the same for H 3 [HGaNH] 9 H 3 and H 3 [HGaNH] 30 H 3
compounds. Thus, we conclude that the error does not increase notably with the
elongation of the oligomer. A difference in the reaction energies of formation of
H 3 [HGaNH] 3n H 3 from GaH 3 and NH 3 calculated using TZVP and SVP basis sets
is about 1% of the value obtained using the TZVP basis set, irrespective of the