resulting DFTB structures for a number of nickel complexes compare favorably to
available X-ray structures, and an encouraging agreement with the B3LYP/aug-ccpVTZ reference data was observed.
Grimme and co-workers used a different approach using an extended tightbinding semi-empirical approach, which is robust and provides geometries, frequencies, and non-covalent interactions (GFN-xtb, GFN2-xtb) rapidly [108, 109]. The
main focus in designing the method and obtaining the parameters was put on
organic, organometallic, and biochemical systems on the order of a few thousand
atoms. Most importantly, the methods are parameterized for all elements up to radon
(Z ¼ 86), making it directly applicable to transition-metal complexes, and can serve
as a screening tool for conformational effects, weak interactions, etc., followed by a
more precise DFA treatment.
3.2 Wavefunction Theory
Improving the wavefunction is the main goal in ab initio post-Hartree-Fock methods;
the shortcomings of HF are well described in textbooks and in the literature
[78, 110–113]. Within a certain basis set, and within the Born-Oppenheimer approximation of separating the electronic degrees of freedom from those of the nuclei, the
best wavefunction that can be obtained is full CI [27, 28, 58]. However, this method
scales very unfavorably, and only a small number of electrons in a limited number of
orbitals can be treated fully, to cover fully the correlation energy (defined as E Full-CI –
E HF ). Several improvements to the wavefunction can be made to cover the static
correlation (with multiconfigurational approaches) or the dynamic correlation. A
detailed description of the methods is outside the scope of this chapter and can be
found in reference works [114, 115].
3.2.1 Multiconfigurational Approaches
Hartree-Fock (also known as self-consistent field [27, 28]) uses a single Slater
determinant, which in many cases is sufficient but not always. An improved description of the total wavefunction can be obtained by including different configurations
(determinants) in a multiconfigurational SCF (MC-SCF), each with its own weight;
both the orbitals used in the determinants and the weights are optimized to reach the
best description of the total wavefunction. Different approaches can be taken such as
complete active space self-consistent field (CASSCF), in which the orbital space is
divided into different regions: a frozen region where all orbitals are (almost) doubly
occupied, a frozen region where all orbitals are negligibly occupied, and an active
space inbetween that contains all orbitals that are important for understanding the
system under study; within this active space then a full-CI treatment is performed
with single, double, triple, etc. excitations. This active space can be restricted
(RASSCF) into different spaces (RAS1, RAS2, RAS3), with different rules for
Dealing with Spin States in Computational Organometallic Catalysis
201
available X-ray structures, and an encouraging agreement with the B3LYP/aug-ccpVTZ reference data was observed.
Grimme and co-workers used a different approach using an extended tightbinding semi-empirical approach, which is robust and provides geometries, frequencies, and non-covalent interactions (GFN-xtb, GFN2-xtb) rapidly [108, 109]. The
main focus in designing the method and obtaining the parameters was put on
organic, organometallic, and biochemical systems on the order of a few thousand
atoms. Most importantly, the methods are parameterized for all elements up to radon
(Z ¼ 86), making it directly applicable to transition-metal complexes, and can serve
as a screening tool for conformational effects, weak interactions, etc., followed by a
more precise DFA treatment.
3.2 Wavefunction Theory
Improving the wavefunction is the main goal in ab initio post-Hartree-Fock methods;
the shortcomings of HF are well described in textbooks and in the literature
[78, 110–113]. Within a certain basis set, and within the Born-Oppenheimer approximation of separating the electronic degrees of freedom from those of the nuclei, the
best wavefunction that can be obtained is full CI [27, 28, 58]. However, this method
scales very unfavorably, and only a small number of electrons in a limited number of
orbitals can be treated fully, to cover fully the correlation energy (defined as E Full-CI –
E HF ). Several improvements to the wavefunction can be made to cover the static
correlation (with multiconfigurational approaches) or the dynamic correlation. A
detailed description of the methods is outside the scope of this chapter and can be
found in reference works [114, 115].
3.2.1 Multiconfigurational Approaches
Hartree-Fock (also known as self-consistent field [27, 28]) uses a single Slater
determinant, which in many cases is sufficient but not always. An improved description of the total wavefunction can be obtained by including different configurations
(determinants) in a multiconfigurational SCF (MC-SCF), each with its own weight;
both the orbitals used in the determinants and the weights are optimized to reach the
best description of the total wavefunction. Different approaches can be taken such as
complete active space self-consistent field (CASSCF), in which the orbital space is
divided into different regions: a frozen region where all orbitals are (almost) doubly
occupied, a frozen region where all orbitals are negligibly occupied, and an active
space inbetween that contains all orbitals that are important for understanding the
system under study; within this active space then a full-CI treatment is performed
with single, double, triple, etc. excitations. This active space can be restricted
(RASSCF) into different spaces (RAS1, RAS2, RAS3), with different rules for
Dealing with Spin States in Computational Organometallic Catalysis
201