3.3 MCSCF Method
The multiconfigurational self-consistent-field (MCSCF) method, particularly of the
complete active space SCF (CASSCF) type, has become a practical tool for
studying systems with near-degenerate states, e.g., molecules with open-shell
character, conical intersections (CoIns), transition metal complexes, and bond
breaking molecules (see [173] for a recent review). It describes static correlation
in medium-sized molecules well with affordable computational cost, and serves as
the basis for more accurate methods which consider the dynamical correlation
better, such as MRPT, MRCI, or multireference coupled cluster (MRCC) methods.
CASSCF [174–176], which allows full CI expansion in the pre-selected active
orbital space, is the most common and successful MCSCF implementation. The
concept was introduced in the 1970–1980s by Ruedenberg et al. [177–179] under
the name full optimization reaction space (FORS) and it is now known as complete
active space, as coined by Roos, Tayler, and Siegbahn [174]. The essential step is
the choice of active orbitals. Starting orbitals include localized orbitals [180–183],
natural orbitals [184, 185], or pair natural orbitals [186–188], and the corresponding
guidance has been reviewed [189, 190]. As a variation to CASSCF, the restricted
active space (RASSCF) method [191, 192] decomposes the active space into three
subspaces (RAS1, RAS2, RAS3), which allows one to consider more orbitals. Full
CI is only allowed in RAS2 while a maximum number of holes and electrons are
enforced in RAS1 and RAS3, respectively. Many excellent reviews of the MCSCF
method exist (see [173] and references therein), but these mainly focus on the
ground and valence excited states. Below we discuss the calculation of core excited
states.
3.3.1 Manipulation of the Core Hole
MCSCF core state calculations were first performed in the 1980s by Ågren
et al. [193–196], who studied the state-specific low-lying single and double core
hole (DCH) states of a series of small molecules, systematically investigated the
influence of correlation and relaxation effects on energies, and computed the
effective transition dipole moments (TDMs) between separately optimized
MCSCF states. The method was rediscovered about 20 years later [197]. In recent
years it was employed for work on DCH states and spectra of various small
molecules by Tashiro et al. [198–201]. Odelius et al. [202] first employed the
state-averaged RASSCF (SA-RASSCF) method [192] in conjunction with the
state-interaction treatment of SO effects [203] for L-edge XANES and RIXS
spectra of transition-metal-based complexes, and soon calculations were performed
for various other similar systems [204–207]. Hua et al. applied it to study the O
K-edge ASRS signals of furan conical intersections in the photo-induced ringopening reaction [208].
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Y. Zhang et al.
The multiconfigurational self-consistent-field (MCSCF) method, particularly of the
complete active space SCF (CASSCF) type, has become a practical tool for
studying systems with near-degenerate states, e.g., molecules with open-shell
character, conical intersections (CoIns), transition metal complexes, and bond
breaking molecules (see [173] for a recent review). It describes static correlation
in medium-sized molecules well with affordable computational cost, and serves as
the basis for more accurate methods which consider the dynamical correlation
better, such as MRPT, MRCI, or multireference coupled cluster (MRCC) methods.
CASSCF [174–176], which allows full CI expansion in the pre-selected active
orbital space, is the most common and successful MCSCF implementation. The
concept was introduced in the 1970–1980s by Ruedenberg et al. [177–179] under
the name full optimization reaction space (FORS) and it is now known as complete
active space, as coined by Roos, Tayler, and Siegbahn [174]. The essential step is
the choice of active orbitals. Starting orbitals include localized orbitals [180–183],
natural orbitals [184, 185], or pair natural orbitals [186–188], and the corresponding
guidance has been reviewed [189, 190]. As a variation to CASSCF, the restricted
active space (RASSCF) method [191, 192] decomposes the active space into three
subspaces (RAS1, RAS2, RAS3), which allows one to consider more orbitals. Full
CI is only allowed in RAS2 while a maximum number of holes and electrons are
enforced in RAS1 and RAS3, respectively. Many excellent reviews of the MCSCF
method exist (see [173] and references therein), but these mainly focus on the
ground and valence excited states. Below we discuss the calculation of core excited
states.
3.3.1 Manipulation of the Core Hole
MCSCF core state calculations were first performed in the 1980s by Ågren
et al. [193–196], who studied the state-specific low-lying single and double core
hole (DCH) states of a series of small molecules, systematically investigated the
influence of correlation and relaxation effects on energies, and computed the
effective transition dipole moments (TDMs) between separately optimized
MCSCF states. The method was rediscovered about 20 years later [197]. In recent
years it was employed for work on DCH states and spectra of various small
molecules by Tashiro et al. [198–201]. Odelius et al. [202] first employed the
state-averaged RASSCF (SA-RASSCF) method [192] in conjunction with the
state-interaction treatment of SO effects [203] for L-edge XANES and RIXS
spectra of transition-metal-based complexes, and soon calculations were performed
for various other similar systems [204–207]. Hua et al. applied it to study the O
K-edge ASRS signals of furan conical intersections in the photo-induced ringopening reaction [208].
314
Y. Zhang et al.