State average CASSCF

We first define a suitable electronic basis. In what follows, Qo represents the geometry of a conical intersection between So and Si chosen as a reference point. The two degenerate electronic wave functions, I o) and are the result of an electronic structure calculation at the state-averaged CASSCF level at the reference point. For any geometry Q, the first two singlet adiabatic states will be noted Q)... 

Convergence of state-averaged CASSCF calculations for the X and A states of NHj°. 

Figure 2.2 depicts the spectrum of the ground and the first 10 excited states of E+ symmetry as computed at the level of a state-averaged CASSCF (4, 26)/aug-cc-pVDZ. The PECs of the excited states exhibit clearly the presence of deep minima, of barriers and of avoided crossings. 

Figure 2.2 The first 11 potential energy curves of Be2 from a state-averaged CASSCF (4, 26)/aug-cc-pVDZ calculation. Considerable state mixing takes place in the region where the weak Be2 bond of the ground state is formed. See text.

Figure 2.3 The first seven E+ states of Be2 at the state-averaged CASSCF (4e/26o)- -l - - 2 (=MRCISD) level of theory, with the aug-cc-pVQZ basis set. The energy minima of all states are below the ionization threshold at about 7.4 eV. state of BeJ). At this computational level, with the 1s electrons kept frozen, De = 791 cm at = 2.489 A.

Multiconfigurational quasi-degenerate perturbation theory (MC-QDPT) [5,6] We have also proposed a multistate multireference perturbation theory, the QDPT with MCSCF reference functions (MC-QDPT). In this PT, state-averaged CASSCF is first performed to set reference functions, and then an elfective Hamiltonian is constructed, which is finally diagonalized to obtain the energies of interest. 

In electronic spectroscopy one is often interested in obtaining wave functions and energies for a set of electronic states of the same symmetry. It might be difficult or even impossible to make a separate calculation for each state. A compromise, which is often used with success, is to use the same orbitals for aU states of that symmetry. The optimization is then carried out for the average energy (state average CASSCF). 

Minima and transition states (TSs) were optimized using the state specific complete active-space self-consistent field (SS-CASSCF) method. MECIs were optimized using state-averaged CASSCF (SA-CASSCF) [71] with equal weighting given to the two states forming the Cl. 

The general strategy for CASSCF/CASPT2 calculations of electronic spectra is to first perform a state-averaged CASSCF calculation, where all the excited states of a given symmetry are included in the averaging. This model is also followed here. Some calculations were performed in symmetry, others in Cl- In the former case, a state average was performed separately in the two symmetries A and A", in the latter case over all excited states. 

For the CASPT2 calculations of the spectra, the active space was extended with the second Scys 3p orbital. No symmetry was used in the calculations, and all states were included in one state-averaged CASSCF calculation. With 13 electrons in 12 orbitals, seven states, consisting of all ligand-field states as well as the two Scys -> Cu charge-transfer states, could be included in the calculations. 

Conical intersection optimization using state-averaged CASSCF. 

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