State-averaged orbitals

State average orbitals are not optimized for a specific electronic state. Normally, this is not a problem and a subsequent CASPT2 calculation will correct for most of it because the first order wave function contains CFs that are singly excited with respect to the CASSCF reference function. However, if the MOs in the different excited states are very different it may be needed to extend the active space such that it can describe the differences. A typical example is the double shell effect that appears for the late first row transition metals as described above. 

The idea is quite simple Assume that N CASPT2 calculations have been performed starting from a set of CASSCF reference functions, first order (CASPT2) wave functions are denoted xh i =, N. Let the N function % = dy + Xt form the basis for a pseudo-variational calculation, where all third order terms appearing in the Hamiltonian... 

Figure 2.1 Reaction coordinate (linear interpolation) for electron transfer in BMA, CASSCF(3,4)/3-21G. Upper curve (squares), state-averaged orbitals lower curve (diamonds), without state-averaging. (From Blancafort, L., Jolibois, F., Olivucci, M., and Robb, M.A., J. Am. Chem. Soc., 123, 722-732, 2001. With permission.)...

In the present work, at each step, a CASSCF calculation is done with state-averaged orbitals over two states. The Hessian used in the integration of Newton s equation of motion is calculated for the highest of the two roots of the SA calculation. 

State averaging gives a wave function that describes the first few electronic states equally well. This is done by computing several states at once with the same orbitals. It also keeps the wave functions strictly orthogonal. This is necessary to accurately compute the transition dipole moments. 

Perform a series of state-averaged 4,4 CAS calculations on the ground state, using the active space you have selected. Normally, a CAS calculation optimizes the orbitals and hence the wavefimction for the state of interest (as specified by the NRoot option). However, in a state-averaged CAS, orbitals are optimi. ed to provide the best description of the specified group of states as a whole that is possible with a single set of orbitals... 

A more balanced description requires MCSCF based methods where the orbitals are optimized for each particular state, or optimized for a suitable average of the desired states (state averaged MCSCF). It should be noted that such excited state MCSCF solutions correspond to saddle points in the parameter space for the wave function, and second-order optimization techniques are therefore almost mandatory. In order to obtain accurate excitation energies it is normally necessarily to also include dynamical Correlation, for example by using the CASPT2 method. 

The extensive calculations of Serrano-Andres et al [31] have shown a spurious valence-Rydberg mixing in the CASSCF wave functions when valence (7t,7r )and Rydberg orbitals are optimized all together in a state average calculation it was shown that these orbitals loose their diffuse character and instead tend to provide an extra correlation to valence orbitals. To avoid such interaction, the orbitals used for the Cl treatment of the electronic spectrum were obtained by a two step procedure ... 

---