State-averaged MCSCF

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. 

As a eonelusion, the ealculation will be performed using a state-averaged MCSCF treatment in a well-designed active space. 

Scaling of different methods with basis set, 145 State averaged MCSCF, 147 ... 

NACMEs based on state-averaged MCSCF wave functions and analytic derivative methods. This should provide NACME s of similar overall accuracy to that obtained for the adiabatic potentials. 

Coupled Perturbed State-Averaged MCSCF Ekjuations Orbital Derivatives... 

MCSCF) or a state-averaged-MCSCF (SA-MCSCF) procedure and are denoted M/MRCI where M = SCF, MCSCF or SA-MCSCF. In this chapter the most general option, the SA-MCSCF/MRCI wave functions, will be used. 

The only aspect of the computational approach not explicitly given above is the determination of the U (R). The U (R) are obtained by differentiating the (state averaged) MCSCF equations. The resulting equations are referred to as the coupled perturbed (state averaged) MCSCF equations. The numerical effort required for the evaluation of equation (66b) can be further reduced by avoiding the explicit determination of U (R), Discussion of these aspects of the evaluation can again be found in Refs, 11 and 10,... 

So far in our discussion of Cl and MCSCF theory, we have found it convenient to employ a redundant parametrization of the configuration space - see Section 11.4.1 for the (3 wave function and Section 12.2.1 for the MCSCF wave function. This parametrization has the advantage of simplicity, which for many purposes such as the optimization of the wave function offsets the disadvantages arising from the presence of the redundancy. Nevertheless, in some situations, it is best to remove this redundancy and to use a parametrization where the electronic states are described by a set of independent, nonredundant variables. One such situation arises in the state-averaged MCSCF scheme discussed in Section 12.7, where several MCSCF states are generated simultaneously in the same orbital basis. 

The parametrization of the state-averaged MCSCF energy (12.7.4) adopted in the present subsection differs hum the single-state parametrization introduced in Section 12.2.1 Since we require the states to be orthogonal (12.7.2), it is no longer convenient to employ, as our primary variational parameters, the individual Cl coefficients of the expansions (12.7.1). Instead, we base our description on the exponential parametrization of the configuration space of Section 12.6 and write the MCSCF wave functions in the form... 

State averaged MCSCF, 147 State correlation diagram, 356 St4te selected CI/MCSCF, 123 Static electron correlation, 118 Static properties, 235 Statistical error, 375... 

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