Virtual excited state

In (34), the effective Hamiltonian H2) is still a matrix in the orbital space of electron wave functions. Similar to (17), it describes intersite orbital exchange coupling. In (34) and (35), the factor J(i - ) is the parameter of orbital exchange coupling, same as in (3.7). This time it is supported by the assumption of weak JT coupling. The matrix elements (0 Qy (i) n) are determined with zero-coupling oscillator wave functions. They take a nonzero value for = 1 only. In other words, in the effective Hamiltonian H2), the virtual excited states are one-phonon states. Therefore, the effective Hamiltonian (34) describes phonon-mediated orbital exchange. 

Morley. J.O.. Pavlides. P.. Pugh, D. On the calculation of the hyperpolarizabilities of organic molecules by the sum over virtual excited states method. Int. J. Quant. Chem. 43. 7-26 (1992)... 

Stleltles Orbitals. Conventional molecular orbitals, such as bound Hartree-Fock orbitals or the virtual excited-state orbitals obtained In the presence of static potential fields, have discrete negative energies and are unity normalized (11,12). By contrast, the positive energy scattering functions associated with ejected electrons have oscillatory spatial tails, and so are normalized differently. 

Gersten et treat this model using an Anderson model. They note a threshold behavior, as mentioned above. A dependence on the electric potential is also predicted. When the virtual excited state resides on the molecule (metal-molecule CT), then more positive potentials will require higher excitation frequencies. For molecule-to-metal CT, more positive potentials should be associated with lower frequencies for SERS. The CT model also rationalizes the continuum background as real transitions which occurred and had suffered some decay in the metal. 

The term third harmonic generation, THG, refers to the generation of a light beam that consists of photons having three times the energy of the photons of the input beam. THG can be easily detected and is, therefore, widely employed in the third-order nonlinear characterization of newly developed materials [28]. THG is a four-photon process, in which three incident photons with angular frequency co create a photon with frequency 3[Pg.83]

Fig. 3.4 Energy level diagram illustrating third harmonic generation. Arrows denote photon energies, horizontal solid lines represent energy states of the medium, and dashed lines represent virtual excited states.

V = 1 state, is first promoted to a virtual excited state, then successively returns to the ground vibrational state, v = 0. The energy of the scattered photon is vo + vi and the spectral fine is shifted to a lower wavelength and a higher frequency than the incident radiation. However, since the majority of the molecules are in the groimd vibrational state at room temperature, the Stokes lines is stronger compared to the anti-Stokes lines. 

A third approach, the one most important for the current discussions, is to treat the electric-field as a source of perturbation of the total molecular energy using real and virtual excited state transitions. This approach uses electronic wave functions either for all of the electrons of the molecule (ab initio calculations) or for only the valence electrons (so-called semiempirical theories). Semiempirical Hamiltonians may ignore electron interactions completely (Huckel theory). They may assume one jt-orbital per carbon and assume no overlap between adjacent electron orbitals (Pariser-Parr-Pople or PPP). Or, they may include both the a and... 

Anti-Stokes scattering Scattering interactions that start from a virtual excited state a type of inelastic scattering. 

Due to the fact that the first hyperpolarizability involves multiple virtual excited states (O Eq. 11.68), the property has proven to be more sensitive to electron correlation effects than the polarizability (Christiansen et al. 2006). Molecules with push-pull conjugated structures are often characterized by large first hyperpolarizabilities. Due to the problems facing many... 

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