Response function eigenvalue problem

Specific for ISC and other predissociative curve-crossings is that the response function approach can be afflicted by instabilities which has to be treated with some care. The instabilities encountered for the MCLR eigenvalue equation near curve crossings is a structural problem of the method itself. Partitioning the MCSCF Hessian to orbital and configuration parts on one hand, and excitation and deexcitations on the other, gives the structure... 

This eigenvalue problem has a dimension double with respect to the corresponding problem for an isolated molecule [11], However, by neglecting the out-of-diagonal block responsible of the coupling between the and response equations [12], the linear response functions (4.5) reduces to... 

An alternative approach is based on the time-dependent density functional theory [40]. From the linear response theory, it can be shown that proper treatment of the excited states can be obtained from the solutions of a non-Hermitian eigenvalue problem [41],... 

To avoid numerical problems in gaussian basis set due to the unbalance description of the basis set and the vanishing small eigenvalue of the density response matrix, the approximated KLI and LHF (or CEDA or ELP) effective exact-exchange methods can be used. These methods are still computationally much more elaborated than conventional local, semilocal or hybrid functionals, because the calculation of the Slater potential as well as the (self-consistent) correction term is required. A straightforward construction of the Slater potential... 

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