2.1 DFT Method
21
that functional. B3-LYP functional has two main weaknesses, including disregard
of dispersion interaction and the bad performance on charge transfer and Rydberg
excitations [40]. The first problem can be completed modified by DFT-D3 correction without additional computing time [41, 42]. The second one can be solved by
the variant CAM-B3-LYP functional [43]. These amendments continue to extend
the service life of B3-LYP functional. Although B3-LYP performs well in geometry optimizations, it is not suitable for energy calculations in Rh-catalyzed C–H
functionalization.
From many calculation results, M06, which is a Minnesota series functional
proposed by Truhlar in 2007, is one of the best alternative functionals of B3-LYP [12,
26]. The M06 is not only suitable for geometry optimizations but also well behaved
in energy calculations in Rh-catalyzed C–H functionalization [44, 45]. In this functional, dispersion effect is introduced in its fitting parameters, which reveals good
weak interactions [26]. The 54% HF exchange component leads to better performance
on the calculation of charge transfer and Rydberg excitation. The shortcoming is that
Minnesota series functionals require much higher accuracy of DFT integration grid
than B3-LYP [46]. It could be solved by the improvement of that, however, it will
obviously increase the time-consuming. Moreover, M06 functional is parameterized
for the main group elements, therefore, it might be unsuited for the calculation of
transition metal involved system. As an alternative, M06-L [12] and M11-L [47]
functional can be used in this case. It is worth noting that M06-L and M11-L are
designed to capture the main dependence of the exchange-correlation energy on local
spin density, spin density gradient, and spin kinetic energy density. Moreover, M06-L
and M11-L are parameterized to satisfy the uniform electron gas limit. Therefore,
M06-L and M11-L have good performance for energy calculations in Rh-catalyzed
C–H functionalization reaction [48].
The ωB97XD functional [49] is another alternative of B3LYP for geometry
optimizations of Rh-catalyzed C–H functionalization, which is proposed by HeadGordon group in 2008 [50]. This functional includes empirical dispersion at DFT-D2
level, which gives a good accuracy of weak interaction. Moreover, the introduction
of long-range correction into ωB97XD makes a good result in the calculation of
charge transfer and Rydberg excitation. The time consumption of ωB97XD is also
significantly higher than that of B3LYP [51, 52].
2.1.1 Basis Set
Generally, the time consuming of DFT calculations is mostly used in the calculation
of double-election integral, which is positively correlated with N
4 , in which N is the
total Gaussian type functions for a specific molecule [53]. Therefore, the computation
time consuming for a specific molecule depends on the selectivity of the basis set for
all atoms in this molecule. In fact, the selection of the basis set is also arbitrary, which
even could be based on experience and preferences [54]. Fortunately, the accuracy
of most DFT methods is always independent of the size of the selected basis set,
21
that functional. B3-LYP functional has two main weaknesses, including disregard
of dispersion interaction and the bad performance on charge transfer and Rydberg
excitations [40]. The first problem can be completed modified by DFT-D3 correction without additional computing time [41, 42]. The second one can be solved by
the variant CAM-B3-LYP functional [43]. These amendments continue to extend
the service life of B3-LYP functional. Although B3-LYP performs well in geometry optimizations, it is not suitable for energy calculations in Rh-catalyzed C–H
functionalization.
From many calculation results, M06, which is a Minnesota series functional
proposed by Truhlar in 2007, is one of the best alternative functionals of B3-LYP [12,
26]. The M06 is not only suitable for geometry optimizations but also well behaved
in energy calculations in Rh-catalyzed C–H functionalization [44, 45]. In this functional, dispersion effect is introduced in its fitting parameters, which reveals good
weak interactions [26]. The 54% HF exchange component leads to better performance
on the calculation of charge transfer and Rydberg excitation. The shortcoming is that
Minnesota series functionals require much higher accuracy of DFT integration grid
than B3-LYP [46]. It could be solved by the improvement of that, however, it will
obviously increase the time-consuming. Moreover, M06 functional is parameterized
for the main group elements, therefore, it might be unsuited for the calculation of
transition metal involved system. As an alternative, M06-L [12] and M11-L [47]
functional can be used in this case. It is worth noting that M06-L and M11-L are
designed to capture the main dependence of the exchange-correlation energy on local
spin density, spin density gradient, and spin kinetic energy density. Moreover, M06-L
and M11-L are parameterized to satisfy the uniform electron gas limit. Therefore,
M06-L and M11-L have good performance for energy calculations in Rh-catalyzed
C–H functionalization reaction [48].
The ωB97XD functional [49] is another alternative of B3LYP for geometry
optimizations of Rh-catalyzed C–H functionalization, which is proposed by HeadGordon group in 2008 [50]. This functional includes empirical dispersion at DFT-D2
level, which gives a good accuracy of weak interaction. Moreover, the introduction
of long-range correction into ωB97XD makes a good result in the calculation of
charge transfer and Rydberg excitation. The time consumption of ωB97XD is also
significantly higher than that of B3LYP [51, 52].
2.1.1 Basis Set
Generally, the time consuming of DFT calculations is mostly used in the calculation
of double-election integral, which is positively correlated with N
4 , in which N is the
total Gaussian type functions for a specific molecule [53]. Therefore, the computation
time consuming for a specific molecule depends on the selectivity of the basis set for
all atoms in this molecule. In fact, the selection of the basis set is also arbitrary, which
even could be based on experience and preferences [54]. Fortunately, the accuracy
of most DFT methods is always independent of the size of the selected basis set,