190
M. Lundberg and M. G. Delcey
Both CI coefficients and orbital shapes are optimized. Correlation outside of the
active space can be treated with a low-level method, typically second-order perturbation theory (PT2). Basic equations for the active-space methods can be found in
Chap. 5 of this book. Although multiconfigurational methods are essentially ab initio,
their accuracy and computational cost can be tuned through the choice of a number
of simulation parameters, with the most critical choice being the choice of orbitals
in the active space. This flexibility, together with the relatively high-computational
cost, necessitates an understanding of the effect of model choices on the cost and
accuracy of the calculation. To demonstrate the methodology and the impact of
the different parameters, we will in this section extensively use examples from
L-edge XAS modeling of ferric (3d
5 ) reference systems with well-known electronic
structures, namely high-spin [FeCl 6 ]
3− (ferric chloride) and low-spin [Fe(CN) 6 ]
3−
(ferricyanide) [23, 71, 73].
3.1 System Selection
Before starting the modeling, as with any theoretical chemistry calculation, the first
step is the choice of the system. This choice is constrained by the cost of the calculation. The cost of multiconfigurational methods depends on both the total system size
and the size of the active space. The active space will be discussed in more details in
the next paragraph, but the severe scaling with respect to the number of active orbitals
typically restricts calculations to a single transition metal center, as opposed to DFT
where large clusters [60], and even extended systems can be described [13]. On the
other hand, the scaling with system size is less drastic, especially if PT2 calculations
can be avoided. For example, X-ray calculations of the heme iron systems with more
than forty heavy atoms have been performed using RAS [34, 74]. Additionally, due
to the locality of X-ray spectroscopy, the convergence of the spectrum with the system size is expected to be rapid, allowing more crude models than would otherwise
be recommended. Because of the prohibitive cost of geometry optimization with
correlated multiconfigurational methods, starting geometries are often taken from
experiments or from another level of theory, typically DFT. It is worth noting that in
some cases, especially for very covalent metal–ligand bonds with strong multiconfigurational effects, the starting geometry can be of insufficient quality for accurate
spectrum calculations. In such cases, reoptimization of a few geometrical parameters can be performed with multiconfigurational perturbation theory [85]. Finally,
environment effects can be included in the same way as for calculations of valence
states, such as the polarizable continuum model to describe solvent effects [18, 50].
M. Lundberg and M. G. Delcey
Both CI coefficients and orbital shapes are optimized. Correlation outside of the
active space can be treated with a low-level method, typically second-order perturbation theory (PT2). Basic equations for the active-space methods can be found in
Chap. 5 of this book. Although multiconfigurational methods are essentially ab initio,
their accuracy and computational cost can be tuned through the choice of a number
of simulation parameters, with the most critical choice being the choice of orbitals
in the active space. This flexibility, together with the relatively high-computational
cost, necessitates an understanding of the effect of model choices on the cost and
accuracy of the calculation. To demonstrate the methodology and the impact of
the different parameters, we will in this section extensively use examples from
L-edge XAS modeling of ferric (3d
5 ) reference systems with well-known electronic
structures, namely high-spin [FeCl 6 ]
3− (ferric chloride) and low-spin [Fe(CN) 6 ]
3−
(ferricyanide) [23, 71, 73].
3.1 System Selection
Before starting the modeling, as with any theoretical chemistry calculation, the first
step is the choice of the system. This choice is constrained by the cost of the calculation. The cost of multiconfigurational methods depends on both the total system size
and the size of the active space. The active space will be discussed in more details in
the next paragraph, but the severe scaling with respect to the number of active orbitals
typically restricts calculations to a single transition metal center, as opposed to DFT
where large clusters [60], and even extended systems can be described [13]. On the
other hand, the scaling with system size is less drastic, especially if PT2 calculations
can be avoided. For example, X-ray calculations of the heme iron systems with more
than forty heavy atoms have been performed using RAS [34, 74]. Additionally, due
to the locality of X-ray spectroscopy, the convergence of the spectrum with the system size is expected to be rapid, allowing more crude models than would otherwise
be recommended. Because of the prohibitive cost of geometry optimization with
correlated multiconfigurational methods, starting geometries are often taken from
experiments or from another level of theory, typically DFT. It is worth noting that in
some cases, especially for very covalent metal–ligand bonds with strong multiconfigurational effects, the starting geometry can be of insufficient quality for accurate
spectrum calculations. In such cases, reoptimization of a few geometrical parameters can be performed with multiconfigurational perturbation theory [85]. Finally,
environment effects can be included in the same way as for calculations of valence
states, such as the polarizable continuum model to describe solvent effects [18, 50].