Zero-order approximation excited state

Fig. 11. Reaction coordinate diagram for ECL system involving rubrene (A) and 9,10-diphenylan-thracene (B). Potential energy curves are presented in the zero-order approximation, without removing the degeneracy at the crossing points of the potential energy curves. Broken lines represent the vibronically excited triplet state.

If 4>no and (A = 1,2) are localized ground- and excited-state wave functions of the chromophores k, the ground state of the two-chromophore system may be described by Pq = 4>,o4>2o. whereas the excited states 4 = N (4>i,4>2o 4> 4>2f) are degenerate in zero-order approximation. The exci-ton-chirality model only takes into account the interaction between the transition dipole moments A/, and localized in the chromophores. Thus, the interaction gives rise to a Davydov splitting by 2Vj2 of the energies of combinations and of locally excited states. From the dipole-dipole approximation one obtains... 

An approximate ground-state DFT calculation is done, finding a self-consistent KS potential. Transitions from occupied to unoccupied KS orbitals provide zero-order approximations to the optical excitations. 

CASPT2 is most useful for calculations on excited states and diradicals, where multireference wavefunctions are required. However, there are methods available for including electron correlation for radicals and radical ions for which single-determinantal wavefunctions represent good zero-order approximations, without resorting to multideterminantal (i.e., CASSCF) reference wavefunctions. Two of these methods are discussed in the following sections, and we recommend them over CASPT2 for most calculations on molecules with just one unpaired electron. 

The zero-order states are the Hartree-Fock determinant and the determinants excited with respect to this state. The resulting theory is known as M0ller-Plessetperturbation theory (MPPT) [5], For systems with small static correlation contributions, the Hartree-Fock wave function provides an adequate zero-order approximation to the FCI wave function. In such situations, the Mpller-PIesset partitioning of the Hamiltonian is both appealing and well motivated the averaged electron-electron interactions are incorporated in the zero-order operator and the perturbation operator (the fluctuation potential) represents the difference between the averaged and instantaneous interactions. 

They include the vibronic state tjjj = jtjjj vac), the zero-order approximation of the electronically excited state, which carries oscillator strength to the ground state and the vibronic manifold tit = vac). The vibronic manifold corresponds to a lower electronic state that are quasi-degenerate with tjjj and does not carry oscillator... 

The other source of congestion is due to the molecular core. It is most readily discussed using the inverse Bom-Oppenheimer point of view to define the zero-order quantum numbers. Here each state of the ionic core has its very own series of high Rydberg states. The physical reality of this approximation is the observation [36,43] of the long-time stable ZEKE states not just below the lowest ionization threshold but also just below the threshold of ionization processes that leave an excited ionic core. Indeed, it is for this very reason that ZEKE spectroscopy is useful for the spectroscopy of ions (or for such neutrals that are produced by ionization of negative ions... 

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