5.1 Electronic Structure Methodology
The quality of the DFT calculated energy relies on the functional employed and the
basis set used. The computational efficiency, defined as the time required to complete a calculation, is very much dependent on the basis set size. For this reason,
medium-size basis set are commonly employed in the optimization of large systems.
A double-ζ basis set including polarization functions for all the atoms (metal and
non-metal) usually gives reliable optimized structures, but accurate energies demand
single-point calculations with an extended basis set.
Regarding the functional, “which functional should I choose?” is usually the first
question the modeler is asking him/herself before starting a computational project. It
is not the goal of this chapter to describe the enormous progress that has been made
in the last decades in the electronic structure methodology. An overview of the
performance of DFT methods for calculations of metal complexes can be found in
reference [66].
Focusing on the calculations of energy barriers in reactions with transition metal
containing organometallic systems, a major problem to assess the quality of the
functionals is the small number of experimentally determined Gibbs energies of
activation, necessary to benchmark calculations. Another issue is that usually the
reactions consist of several steps. The selected computational method should be able
to adequately describe all steps, but experimental quantitative energetic information
is not usually available for all steps. In the absence of experimental values, the very
accurate coupled-cluster method with single and double excitations and perturbative
triples, CCSD(T) with extrapolation to the complete basis set limit, is usually used
for benchmarking. The CCSD(T) method is widely considered to yield results close
to the full CI limit for many systems with straightforward electronic structures.
Unfortunately, the size of the organometallic systems to be computed prevents its
use in many cases. In the recent years local coupled-cluster methods, such as the
domain-based local pair natural orbital coupled cluster method with single, double,
and perturbative triple excitations (DLPNO–CCSD(T)) appear as efficient quantum
chemical methods which can be used for molecules with hundreds of atoms,
providing results of near-CCSD(T) quality at a fraction of the cost and with linear
scaling with respect to system size [67].
With the aim of evaluating how accurate is DFT for modeling organometallic
reactions, Hopmann has assessed the accuracy of a number of functional for
reproducing experimental Gibbs energies of activation of 11 iridium-mediated transformations which correspond to elementary steps usually found in iridium-catalyzed
chemistry [68]. Chen et al. have performed a similar study for iridium-catalyzed
hydrogenation of olefins [69] and Leitner et al. for ruthenium-catalyzed hydrogenation of olefins [70]. The general conclusion of these studies is that DFT is capable of
giving a meaningful description of the energy landscape of the reactions analyzed,
provided that dispersion corrections are included. Today it is currently recognized
that the inclusion of dispersion effects (as empirical correction, DFT-D, or by
dispersion corrected functionals) is mandatory for the computational study of
What Makes a Good (Computed) Energy Profile?
19
The quality of the DFT calculated energy relies on the functional employed and the
basis set used. The computational efficiency, defined as the time required to complete a calculation, is very much dependent on the basis set size. For this reason,
medium-size basis set are commonly employed in the optimization of large systems.
A double-ζ basis set including polarization functions for all the atoms (metal and
non-metal) usually gives reliable optimized structures, but accurate energies demand
single-point calculations with an extended basis set.
Regarding the functional, “which functional should I choose?” is usually the first
question the modeler is asking him/herself before starting a computational project. It
is not the goal of this chapter to describe the enormous progress that has been made
in the last decades in the electronic structure methodology. An overview of the
performance of DFT methods for calculations of metal complexes can be found in
reference [66].
Focusing on the calculations of energy barriers in reactions with transition metal
containing organometallic systems, a major problem to assess the quality of the
functionals is the small number of experimentally determined Gibbs energies of
activation, necessary to benchmark calculations. Another issue is that usually the
reactions consist of several steps. The selected computational method should be able
to adequately describe all steps, but experimental quantitative energetic information
is not usually available for all steps. In the absence of experimental values, the very
accurate coupled-cluster method with single and double excitations and perturbative
triples, CCSD(T) with extrapolation to the complete basis set limit, is usually used
for benchmarking. The CCSD(T) method is widely considered to yield results close
to the full CI limit for many systems with straightforward electronic structures.
Unfortunately, the size of the organometallic systems to be computed prevents its
use in many cases. In the recent years local coupled-cluster methods, such as the
domain-based local pair natural orbital coupled cluster method with single, double,
and perturbative triple excitations (DLPNO–CCSD(T)) appear as efficient quantum
chemical methods which can be used for molecules with hundreds of atoms,
providing results of near-CCSD(T) quality at a fraction of the cost and with linear
scaling with respect to system size [67].
With the aim of evaluating how accurate is DFT for modeling organometallic
reactions, Hopmann has assessed the accuracy of a number of functional for
reproducing experimental Gibbs energies of activation of 11 iridium-mediated transformations which correspond to elementary steps usually found in iridium-catalyzed
chemistry [68]. Chen et al. have performed a similar study for iridium-catalyzed
hydrogenation of olefins [69] and Leitner et al. for ruthenium-catalyzed hydrogenation of olefins [70]. The general conclusion of these studies is that DFT is capable of
giving a meaningful description of the energy landscape of the reactions analyzed,
provided that dispersion corrections are included. Today it is currently recognized
that the inclusion of dispersion effects (as empirical correction, DFT-D, or by
dispersion corrected functionals) is mandatory for the computational study of
What Makes a Good (Computed) Energy Profile?
19