3.3.2 Verification of the Active Spaces
A practical way to perform the core hole calculations is to run a valence CASSCF
calculation first. One chooses the most important orbitals (e.g., localized or natural
orbitals around a breaking bond, 3d orbitals of an excited transition metal) which
have flexible occupations in the active space. The converged wavefunction serves
as the initial guess for the RASSCF calculation. The original active space is
included in the RAS2 space, and the excited core orbital is placed in the RAS1
space. Overall, one extra orbital (the core orbital) and two additional electrons (two
core electrons) are added to the active space for core hole calculations to achieve
more consistency in valence and core excited states calculations. Including additional virtual orbitals in the RAS3 space can help get a broader energy range for
easier comparison with experimental XANES spectra, especially when the ionic
potential is relatively high. For example, while studying the metal L 2,3 -edge spectra
from the np shell, the RAS2 space should be the 3d orbitals of the metal, and some
ligand orbitals can be included in the RAS3 space to represent the ligand-to-metal
or metal-to-ligand charge transfer effects [202].
Even though there are general guidelines for choosing the active space [189,
190], it is still necessary to verify by checking the convergence of energy and/or
spectra with the active space size. Figure 12 gives an example for the “UV
absorption” and “O1s XANES” spectra of a furan CoIn in the photo-induced
ring-opening reaction, obtained from a non-adiabatic molecular dynamics trajectory [208]. Such spectra may not be directly observed (because the system is in a
superposition of valence states instead of the ground electronic state), but serve as
good tests for the active space. They also give an estimate of the accuracy of the
calculated transition dipole moments (see next section) which are essential for
simulation of the time-domain nonlinear X-ray signals. In Fig. 12a, 10-stateaveraged CASSCF was used, and, as expected, a smaller active space expands a
broader energy range. Increase of the active space introduces more states with
smaller oscillator strengths, and 10 electrons in 10 orbitals (10, 10) is sufficient to
obtain essentially converged UV spectra. The optimized valence state wavefunction
serves as the initial guess for core hole calculations. In Fig. 12b, 50 states were
calculated using SA-RASSCF. Because core states have a higher density of states
than valence states, additional states are needed to get an energy range of several to
10 eV for spectral usage. The 10 valence orbitals (RAS2) plus 1 core orbital (RAS1)
[labeled as “(12, 1/10/0)”. Twelve electrons include the 10 valence electrons and
2 electrons originally in the O1s orbital; numbers separated by slashes refer to the
sizes of RAS1, RAS2, and RAS3] can give converged O1s XANES. Such active
space settings are enough to obtain accurate and consistent electronic structure for
both the valence and core-excited state manifolds. Note that here the convergence is
much faster than the valence level. A test that includes 20 more orbitals in the RAS3
space “(6, 1/4/20)” shows that it can generate more states in the higher-energy
region (534–540 eV) and modify the fine structure of spectra.
316
Y. Zhang et al.
A practical way to perform the core hole calculations is to run a valence CASSCF
calculation first. One chooses the most important orbitals (e.g., localized or natural
orbitals around a breaking bond, 3d orbitals of an excited transition metal) which
have flexible occupations in the active space. The converged wavefunction serves
as the initial guess for the RASSCF calculation. The original active space is
included in the RAS2 space, and the excited core orbital is placed in the RAS1
space. Overall, one extra orbital (the core orbital) and two additional electrons (two
core electrons) are added to the active space for core hole calculations to achieve
more consistency in valence and core excited states calculations. Including additional virtual orbitals in the RAS3 space can help get a broader energy range for
easier comparison with experimental XANES spectra, especially when the ionic
potential is relatively high. For example, while studying the metal L 2,3 -edge spectra
from the np shell, the RAS2 space should be the 3d orbitals of the metal, and some
ligand orbitals can be included in the RAS3 space to represent the ligand-to-metal
or metal-to-ligand charge transfer effects [202].
Even though there are general guidelines for choosing the active space [189,
190], it is still necessary to verify by checking the convergence of energy and/or
spectra with the active space size. Figure 12 gives an example for the “UV
absorption” and “O1s XANES” spectra of a furan CoIn in the photo-induced
ring-opening reaction, obtained from a non-adiabatic molecular dynamics trajectory [208]. Such spectra may not be directly observed (because the system is in a
superposition of valence states instead of the ground electronic state), but serve as
good tests for the active space. They also give an estimate of the accuracy of the
calculated transition dipole moments (see next section) which are essential for
simulation of the time-domain nonlinear X-ray signals. In Fig. 12a, 10-stateaveraged CASSCF was used, and, as expected, a smaller active space expands a
broader energy range. Increase of the active space introduces more states with
smaller oscillator strengths, and 10 electrons in 10 orbitals (10, 10) is sufficient to
obtain essentially converged UV spectra. The optimized valence state wavefunction
serves as the initial guess for core hole calculations. In Fig. 12b, 50 states were
calculated using SA-RASSCF. Because core states have a higher density of states
than valence states, additional states are needed to get an energy range of several to
10 eV for spectral usage. The 10 valence orbitals (RAS2) plus 1 core orbital (RAS1)
[labeled as “(12, 1/10/0)”. Twelve electrons include the 10 valence electrons and
2 electrons originally in the O1s orbital; numbers separated by slashes refer to the
sizes of RAS1, RAS2, and RAS3] can give converged O1s XANES. Such active
space settings are enough to obtain accurate and consistent electronic structure for
both the valence and core-excited state manifolds. Note that here the convergence is
much faster than the valence level. A test that includes 20 more orbitals in the RAS3
space “(6, 1/4/20)” shows that it can generate more states in the higher-energy
region (534–540 eV) and modify the fine structure of spectra.
316
Y. Zhang et al.