excitations from one to the other. Finally, recently the density matrix renormalization
group (DMRG) has been reintroduced as a very efficient method for treating the
multiconfigurational wavefunction [116, 117]. CASSCF is typically limited to, e.g.,
16 electrons in 14 orbitals, which can be easily extended to ca. 30–50 active orbitals
in DMRG [117]. An alternative way of including more active orbitals is obtained in
stochastic CASSCF, as shown by LiManni and co-workers [118]. Gagliardi reported
the generalized active space SCF (GASSCF) [119] and localized active space SCF
(LASSCF) [120], while Lindh and co-workers reported the driven similarity
renormalization group (DSRG) in different forms [121].
Most of the methods mentioned above provide static correlation and not yet
dynamic correlation [122]. The most common way of including it was the
CASPT2 approach, but because of issues with paramagnetic molecules, an IPEA
shift [123] (of 0.25 a.u.) was introduced. In recent years, several researchers have
played with this value [124–128], claiming that it should be adapted for getting
correct results; however, this is not recommendable because it will lead to arbitrariness. It is better to keep with the value of 0.25 [129], and accept any issues with
CASPT2 results as failings of the method which is after all based on perturbation
theory, or not use an IPEA shift at all [130]. Alternative methods are available such
as n-electron valence second-order perturbation theory (NEVPT2) [131] or cumulant
approximated second-order perturbation theory based on DMRG [132, 133].
A very important aspect with these MC-SCF calculations is the choice of orbitals
to be included in the active space, in particular if the total number of orbitals that can
be included is limited in size. LiManni and co-workers [118, 134], for instance,
could include >30 orbitals in stochastic CASSCF, including all Goutermann orbitals
[135, 136]. Especially for the d-shell, it was essential to include a double shell of
orbitals [137].
3.2.2 Coupled Cluster
The coupled cluster approach is an alternative and efficient method to reach full CI,
and unlike truncated CI, it is size consistent. Often it is assumed that CCSD(T) is the
golden standard, although it is in many cases not yet fully accurate. This is in
particular true for paramagnetic transition-metal complexes, where many choices
have to be made regarding the choice of orbitals and how to solve the CC equations
(vide infra). Approximations can be made, such as Neese’s domain-based local
pair natural orbitals (DLPNO) [138, 139] or local CC, which will be described in
more detail in Sect. 3.4, or Kats/Manby’s distinguishable cluster approximation
[140] which with a computational cost similar to CCSD often provides results of
CCSD(T) quality, and hence can be a very attractive method for the future.
202
M. Swart
group (DMRG) has been reintroduced as a very efficient method for treating the
multiconfigurational wavefunction [116, 117]. CASSCF is typically limited to, e.g.,
16 electrons in 14 orbitals, which can be easily extended to ca. 30–50 active orbitals
in DMRG [117]. An alternative way of including more active orbitals is obtained in
stochastic CASSCF, as shown by LiManni and co-workers [118]. Gagliardi reported
the generalized active space SCF (GASSCF) [119] and localized active space SCF
(LASSCF) [120], while Lindh and co-workers reported the driven similarity
renormalization group (DSRG) in different forms [121].
Most of the methods mentioned above provide static correlation and not yet
dynamic correlation [122]. The most common way of including it was the
CASPT2 approach, but because of issues with paramagnetic molecules, an IPEA
shift [123] (of 0.25 a.u.) was introduced. In recent years, several researchers have
played with this value [124–128], claiming that it should be adapted for getting
correct results; however, this is not recommendable because it will lead to arbitrariness. It is better to keep with the value of 0.25 [129], and accept any issues with
CASPT2 results as failings of the method which is after all based on perturbation
theory, or not use an IPEA shift at all [130]. Alternative methods are available such
as n-electron valence second-order perturbation theory (NEVPT2) [131] or cumulant
approximated second-order perturbation theory based on DMRG [132, 133].
A very important aspect with these MC-SCF calculations is the choice of orbitals
to be included in the active space, in particular if the total number of orbitals that can
be included is limited in size. LiManni and co-workers [118, 134], for instance,
could include >30 orbitals in stochastic CASSCF, including all Goutermann orbitals
[135, 136]. Especially for the d-shell, it was essential to include a double shell of
orbitals [137].
3.2.2 Coupled Cluster
The coupled cluster approach is an alternative and efficient method to reach full CI,
and unlike truncated CI, it is size consistent. Often it is assumed that CCSD(T) is the
golden standard, although it is in many cases not yet fully accurate. This is in
particular true for paramagnetic transition-metal complexes, where many choices
have to be made regarding the choice of orbitals and how to solve the CC equations
(vide infra). Approximations can be made, such as Neese’s domain-based local
pair natural orbitals (DLPNO) [138, 139] or local CC, which will be described in
more detail in Sect. 3.4, or Kats/Manby’s distinguishable cluster approximation
[140] which with a computational cost similar to CCSD often provides results of
CCSD(T) quality, and hence can be a very attractive method for the future.
202
M. Swart