3.2.3 Combined Efforts
Even though the double shell was needed for getting consistent results, in a number
of systems, it was found that 3s3p correlation was not satisfactorily described by
CASPT2 [141]. In order to remedy this, Pierloot and Harvey [133] therefore
followed the QM/QM Quild [142] approach whereby specific energies are
subtracted and added; in their case, they used CCSD(T) calculations for only the
3s3p correlation in order to correct the CASPT2 results. A separate approach was
performed by the Stuttgart team, where first the orbitals were prepared as best as
possible with stochastic CASSCF, which can then be followed by coupled cluster
using these orbitals [134].
3.3 Combining Wavefunctions and Density Functionals:
MC-PDFT and DMRG-PDFT
A recent new development is the combination of multiconfigurational methods with
pair-density functional theory (MC-PDFT), as done by Truhlar and Gagliardi and
co-workers [143]. The idea behind MC-PDFT is to use a multiconfigurational selfconsistent field (MC-SCF) wavefunction with correct spin and space symmetry to
compute the total electronic density, its gradient, the on-top pair density, and the
kinetic and Coulomb contributions to the total electronic energy. For the remaining
part of the total energy, this is combined with a functional which has the on-top pair
density as ingredient, in contrast to regular Kohn-Sham DFT. Because the on-top
pair density is an element of the two-particle density matrix, this goes beyond the
Hohenberg-Kohn theorem that refers only to the one-particle density. This was
followed very recently by including DMRG (DMRG-PDFT) [144].
3.4 Methods Put to the Test: Recent Benchmark Studies
Over the years, many studies [31, 65, 67, 68, 70, 85, 111, 112, 145–159] have been
reported on spin-state splittings for a wide variety of transition metals, in different
oxidation states, using a variety of DFAs and wavefunction methods. One of the
motivations for the ECOSTBio COST Action CM1305 [160] was indeed to gather
experts from different areas of chemical research and move forward in the search for
consensus on transition-metal chemistry and which computational and experimental
methods could be used for getting accurate descriptions of the geometry, electronic
structure, and spectroscopy of transition-metal complexes. In the past year, a number
of benchmark studies have appeared which focus mainly on the computational
aspect, which will be discussed below. Additionally, a recent review by Que and
co-workers focuses on the formation of Fe
V (O), or sometimes Fe
IV
(O), complexes
Dealing with Spin States in Computational Organometallic Catalysis
203
Even though the double shell was needed for getting consistent results, in a number
of systems, it was found that 3s3p correlation was not satisfactorily described by
CASPT2 [141]. In order to remedy this, Pierloot and Harvey [133] therefore
followed the QM/QM Quild [142] approach whereby specific energies are
subtracted and added; in their case, they used CCSD(T) calculations for only the
3s3p correlation in order to correct the CASPT2 results. A separate approach was
performed by the Stuttgart team, where first the orbitals were prepared as best as
possible with stochastic CASSCF, which can then be followed by coupled cluster
using these orbitals [134].
3.3 Combining Wavefunctions and Density Functionals:
MC-PDFT and DMRG-PDFT
A recent new development is the combination of multiconfigurational methods with
pair-density functional theory (MC-PDFT), as done by Truhlar and Gagliardi and
co-workers [143]. The idea behind MC-PDFT is to use a multiconfigurational selfconsistent field (MC-SCF) wavefunction with correct spin and space symmetry to
compute the total electronic density, its gradient, the on-top pair density, and the
kinetic and Coulomb contributions to the total electronic energy. For the remaining
part of the total energy, this is combined with a functional which has the on-top pair
density as ingredient, in contrast to regular Kohn-Sham DFT. Because the on-top
pair density is an element of the two-particle density matrix, this goes beyond the
Hohenberg-Kohn theorem that refers only to the one-particle density. This was
followed very recently by including DMRG (DMRG-PDFT) [144].
3.4 Methods Put to the Test: Recent Benchmark Studies
Over the years, many studies [31, 65, 67, 68, 70, 85, 111, 112, 145–159] have been
reported on spin-state splittings for a wide variety of transition metals, in different
oxidation states, using a variety of DFAs and wavefunction methods. One of the
motivations for the ECOSTBio COST Action CM1305 [160] was indeed to gather
experts from different areas of chemical research and move forward in the search for
consensus on transition-metal chemistry and which computational and experimental
methods could be used for getting accurate descriptions of the geometry, electronic
structure, and spectroscopy of transition-metal complexes. In the past year, a number
of benchmark studies have appeared which focus mainly on the computational
aspect, which will be discussed below. Additionally, a recent review by Que and
co-workers focuses on the formation of Fe
V (O), or sometimes Fe
IV
(O), complexes
Dealing with Spin States in Computational Organometallic Catalysis
203