different routes, by adding more and more terms in the functional form and/or
parameters to be fitted or by adding more ingredients. Differentiating HF exchange
into a short-term and long-term component in range-separated functionals [91] (such
as CAM-B3LYP [92], LC-ωPBE [93], or ωB97X-D [94] to name a few) was
followed by optimally tuned range separation [77], double hybrids [76, 95], and
other fancy features. Some of these made the computational cost go up manifold,
thereby losing one of the main advantages of using DFAs within density functional
theory (DFT), without an apparent systematic improvement for all different kinds of
interactions found in chemistry and physics.
3.1.2 The Effect of Dispersion, Solvation, Enthalpy, Entropy,
and Relativity
A number of (free) energy components (dispersion, solvation, relativity, enthalpy,
entropy) that are either included explicitly or added separately play an important role
in the determination of structures or their stability. Dispersion corrections such as
Grimme’s D 2 /D 3 [86, 87] are essential if weak interactions are present (typically
these are present in catalysis) and cannot be left out. Relativistic corrections [96] can
be included directly through, e.g., ZORA [97] or Douglas-Kroll-Hess [98, 99] or
alternatively in an approximated manner through effective core potentials (ECPs)
with corresponding basis sets (ECPBs); for first-row transition metals however, these
relativistic corrections only have a marginal effect on the structures or total energies
(they do of course influence nuclear properties). Kepp made a summary of systematic effects that these energy components have on low vs. high spin; for instance,
dispersion energy and solvation favor low-spin states, while entropy and zero-point
energies favor high-spin states [66].
Solvation should be separated into two terms: (1) an electrostatic term which can
be well described by dielectric continuum models such as COSMO [100, 101], PCM
[102], or SMD and (2) a covalent bonding term that can usually not be described
appropriately by dielectric continuum models and needs inclusion of explicit solvent
molecules in the QM system to be studied. Typical examples of this latter phenomenon are the binding of a solvent molecule (e.g., acetonitrile) to reach an octahedral
coordination environment around a metal and the strategic positioning of solvent
molecules (e.g., methanol) to stabilize vulnerable species such as superoxide through
H-bonding.
3.1.3 DFTB
Making DFT even faster can be achieved with the semi-empirical density functional
tight-binding (DFTB) approach, which needs system-dependent parameters that
were typically fitted to PBE reference data [103–106]. Until recently, no straightforward parameterization for transition metals was available, but a recent study for
nickel based on DFTB3 showed the feasibility of such an approach [107]. The
200
M. Swart
parameters to be fitted or by adding more ingredients. Differentiating HF exchange
into a short-term and long-term component in range-separated functionals [91] (such
as CAM-B3LYP [92], LC-ωPBE [93], or ωB97X-D [94] to name a few) was
followed by optimally tuned range separation [77], double hybrids [76, 95], and
other fancy features. Some of these made the computational cost go up manifold,
thereby losing one of the main advantages of using DFAs within density functional
theory (DFT), without an apparent systematic improvement for all different kinds of
interactions found in chemistry and physics.
3.1.2 The Effect of Dispersion, Solvation, Enthalpy, Entropy,
and Relativity
A number of (free) energy components (dispersion, solvation, relativity, enthalpy,
entropy) that are either included explicitly or added separately play an important role
in the determination of structures or their stability. Dispersion corrections such as
Grimme’s D 2 /D 3 [86, 87] are essential if weak interactions are present (typically
these are present in catalysis) and cannot be left out. Relativistic corrections [96] can
be included directly through, e.g., ZORA [97] or Douglas-Kroll-Hess [98, 99] or
alternatively in an approximated manner through effective core potentials (ECPs)
with corresponding basis sets (ECPBs); for first-row transition metals however, these
relativistic corrections only have a marginal effect on the structures or total energies
(they do of course influence nuclear properties). Kepp made a summary of systematic effects that these energy components have on low vs. high spin; for instance,
dispersion energy and solvation favor low-spin states, while entropy and zero-point
energies favor high-spin states [66].
Solvation should be separated into two terms: (1) an electrostatic term which can
be well described by dielectric continuum models such as COSMO [100, 101], PCM
[102], or SMD and (2) a covalent bonding term that can usually not be described
appropriately by dielectric continuum models and needs inclusion of explicit solvent
molecules in the QM system to be studied. Typical examples of this latter phenomenon are the binding of a solvent molecule (e.g., acetonitrile) to reach an octahedral
coordination environment around a metal and the strategic positioning of solvent
molecules (e.g., methanol) to stabilize vulnerable species such as superoxide through
H-bonding.
3.1.3 DFTB
Making DFT even faster can be achieved with the semi-empirical density functional
tight-binding (DFTB) approach, which needs system-dependent parameters that
were typically fitted to PBE reference data [103–106]. Until recently, no straightforward parameterization for transition metals was available, but a recent study for
nickel based on DFTB3 showed the feasibility of such an approach [107]. The
200
M. Swart