Single excited state approach

The single excited state approach leads to the quasi-equilibrium constant of the nonequilibrium process (3-28) ... 

There are other noteworthy single excited-state theories. Gorling developed a stationary principle for excited states in density functional theory [41]. A formalism based on the integral and differential virial theorems of quantum mechanics was proposed by Sahni and coworkers for excited state densities [42], The local scaling approach of Ludena and Kryachko has also been generalized to excited states [43]. 

Murrell described and illustrated the theory of weakly interacting chromo-phores. His approach may be used in a straightforward way for analysis of the electronic spectra of vdW systems. Unless the states of one subsystem are mixed by the field of the other subsystems (i.e. in the absence of the field effect), the decisive matrix elements of the total Hamiltonian between the ground state, the singly excited states and the doubly excited state are then (the symbols used by Murrell are employed) ... 

Recently, a new approach of treating a single excited state has been presented It is based on Kato s theorem and is valid for Coulomb external potential (i.e. free atoms, molecules and solids). It has the advantage that one can treat a single excited state. In this paper this theory is reviewed and the differential virial theorem is derived. Excitation energies are presented for the Li, Na and K atoms and inner-shell transition energies are shown for the Be atom. 

In Tables 2 and 3, triplet doubly excited energies of 2s ns (n = 3,4,. .10) states and 3s ns (n = 4, 5,11) states of He, computed at the CSCF level, are presented. Calculations of Ref. [46] were restricted to only singly excited states. Therefore, we compare our CSCF calculations with accurate theoretical calculations based on a configuration interaction approach with the explicitly correlated HyUeraas basis set functions [48]. One can see that the accuracy of the CSCF calculations is improved when n increases. This observation is in agreement with Ref. [46]. whose authors pointed out that In those states where n 1, the electrons are spatially well separated and one might anticipate intuitively that they will be weakly correlated and that the Hartree-Fock method, which neglects such effects, may be an excellent approximation. ... 

We mention that there are other noteworthy single excited-state theories the stationary-principle theory of Gorling [33], the formalism of Sahni [34] or the local scaling approach of Ludena and Kryachko [35]. Beyond the time-independent theories mentioned above the time-dependent density functional theory [36] provides... 

For separable initial states the single excitation terms can be set to zero at all times at this level of approximation. Eqs. (32),(33),(34) together with the CSP equations and with the ansatz (31) for the total wavefunction are the working equations for the approach. This form, without further extension, is valid only for short time-domains (typically, a few picoseconds at most). For large times, higher correlations, i.e. interactions between different singly and doubly excited states must be included. 

A different approach for calculating excited states is based on indirect methods that allow one to calculate excitation energies based on a single reference wavefunction. Single reference methods for the calcualtion of excited states of large molecules have... 

---