224
A. V. Pomogaeva and A. Y. Timoshkin
6.3.2 Analysis of Computational Approaches
6.3.2.1 ´hoice of the Level of the Theory of the Computational Method
Nowadays, DFT is a common approach for theoretical studies of molecular
systems. Many exchange-correlation functionals are available, and the choice of
the functional for the particular application must be justified. Computations [47] on
cubane cluster [HAlNH] 4 that could be considered as the smallest closed oligomer
[HAlNH] 3n+1 with n = 1 showed the reliability of B3LYP/TZVP approach compared to the results obtained at CCSD(T)/cc-PVTZ level of theory. However, results
of a systematic study [149] of several exchange-correlation functionals indicate
that for extended metal-containing systems, including 13–15 semiconductor materials, B3LYP [150, 151] optimized lattice constants for Ga-containing compounds
are overestimated by 0.6–2.2% with respect to experimental values, while those
obtained with nonempirical hybrid PBE0 [152] or HSSE [153] functionals provide
the lattice constants within 0.9% from the experimental values. Test computations
have been performed to compare the performance of different DFT methods against
the CCSD [154] method for geometry optimization on the example of [RGaNH] 4
cubanes with R=H, CH 3 . The LDA correlation functional VWN5 [155] and hybrid
GGA, B3LYP, PBE0, and HSSE methods, were considered.
A series of def-2 basis sets developed for all elements by Weigend and Ahlrichs
[156], equally efficient for DFT, HF, and post-HF computational levels, were
chosen. In the following, we will omit def-2 when indicating the used basis set.
Split-valence basis plus set of polarization functions (SVP), triple-zeta (TZV),
corresponding basis with additional polarization functions (TZVP), and quadruple
zeta (QZVP) valence quality basis sets (for the [HGaNH] 4 compound only) were
tested.
Selected structural parameters obtained using these various methods are shown
in Table 6.1. The influence of basis set on Ga-N distances is rather small, Ga-N
bond lengths agree with each other within 0.004 Å for each DFT method and within
0.008 Å for CCSD method. N-Ga-N angle varies within maximum 0.29 ◦ in all cases.
Moreover, the cancelation of errors results in good agreement between the results
obtained with relatively small SVP basis set and nearly complete QZVP basis set
for all DFT methods.
The difference in performance of different DFT methods is more profound.
While PBE0 and HSSE optimized geometries are very similar, optimized distances
at VWN5 level of theory are shorter by about 0.015 Å, and distances at B3LYP level
are longer by about 0.016 Å, compared to values obtained using PBE0 and HSSE
methods. Optimized valence angles at VWN5, PBE0, and HSSE levels of theory are
similar and smaller by more than 0.3 ◦ compared to B3LYP values. Substitution of
H atoms by CH 3 groups on Ga atoms increases Ga-N distances by about 0.005 Å
and only slightly affects N-Ga-N angles. CCSD geometry optimization yields
results somewhat intermediate between those obtained with B3LYP and PBE0
methods. B3LYP/SVP Ga-N bond length in [HGaNH] 4 is 2.001Å, and it is less
A. V. Pomogaeva and A. Y. Timoshkin
6.3.2 Analysis of Computational Approaches
6.3.2.1 ´hoice of the Level of the Theory of the Computational Method
Nowadays, DFT is a common approach for theoretical studies of molecular
systems. Many exchange-correlation functionals are available, and the choice of
the functional for the particular application must be justified. Computations [47] on
cubane cluster [HAlNH] 4 that could be considered as the smallest closed oligomer
[HAlNH] 3n+1 with n = 1 showed the reliability of B3LYP/TZVP approach compared to the results obtained at CCSD(T)/cc-PVTZ level of theory. However, results
of a systematic study [149] of several exchange-correlation functionals indicate
that for extended metal-containing systems, including 13–15 semiconductor materials, B3LYP [150, 151] optimized lattice constants for Ga-containing compounds
are overestimated by 0.6–2.2% with respect to experimental values, while those
obtained with nonempirical hybrid PBE0 [152] or HSSE [153] functionals provide
the lattice constants within 0.9% from the experimental values. Test computations
have been performed to compare the performance of different DFT methods against
the CCSD [154] method for geometry optimization on the example of [RGaNH] 4
cubanes with R=H, CH 3 . The LDA correlation functional VWN5 [155] and hybrid
GGA, B3LYP, PBE0, and HSSE methods, were considered.
A series of def-2 basis sets developed for all elements by Weigend and Ahlrichs
[156], equally efficient for DFT, HF, and post-HF computational levels, were
chosen. In the following, we will omit def-2 when indicating the used basis set.
Split-valence basis plus set of polarization functions (SVP), triple-zeta (TZV),
corresponding basis with additional polarization functions (TZVP), and quadruple
zeta (QZVP) valence quality basis sets (for the [HGaNH] 4 compound only) were
tested.
Selected structural parameters obtained using these various methods are shown
in Table 6.1. The influence of basis set on Ga-N distances is rather small, Ga-N
bond lengths agree with each other within 0.004 Å for each DFT method and within
0.008 Å for CCSD method. N-Ga-N angle varies within maximum 0.29 ◦ in all cases.
Moreover, the cancelation of errors results in good agreement between the results
obtained with relatively small SVP basis set and nearly complete QZVP basis set
for all DFT methods.
The difference in performance of different DFT methods is more profound.
While PBE0 and HSSE optimized geometries are very similar, optimized distances
at VWN5 level of theory are shorter by about 0.015 Å, and distances at B3LYP level
are longer by about 0.016 Å, compared to values obtained using PBE0 and HSSE
methods. Optimized valence angles at VWN5, PBE0, and HSSE levels of theory are
similar and smaller by more than 0.3 ◦ compared to B3LYP values. Substitution of
H atoms by CH 3 groups on Ga atoms increases Ga-N distances by about 0.005 Å
and only slightly affects N-Ga-N angles. CCSD geometry optimization yields
results somewhat intermediate between those obtained with B3LYP and PBE0
methods. B3LYP/SVP Ga-N bond length in [HGaNH] 4 is 2.001Å, and it is less