Essential state model

The above description of 2PA processes corresponds to a simplified essential state model which is widely used to analyze the structure-properties relationship of 2PA materials [8]. In practice, this theoretical approach is in a good agreement with experimental data for different types of organic compounds [54-56]. 

Essential-state Models for Two-photon Cross-section... 

Zojer et al.192 have discussed the limitations of the essential-state model in calculating the TPA of bis(dioxaborine-)-substituted chromophores. Lukes and Breza193 have made an AM1-ZINDO/SOS study of spirobifluorene type molecules. Jha et al.194 have employed their method of obtaining model exact solutions in the PPP approximation to calculate TPA cross-sections for trans-stilbene and 7,8-disubstituted stilbenes. Zhou et al 95 and Liu et al.196 have studied one and two photon absorption in octupolar compounds using DFT and ZINDO/SOS methods and the group has applied similar methods to trigonal dehydrobenzo[l8]annulenes.197... 

Nonlinear optical measurements provide the most direct probe of the electronic states. Conversely, the nonlinear susceptibilities can be calculated if there exists a theoretical imderstanding of the excited states. We describe the theory of linear and nonlinear optical processes, and recast the so-called essential states model in terms of the primary excitons. 

How macroscopic NLO properties of a material are determined from the response of its microscopic constituents was shown in the previous section. The origin of the NLO properties of these constituents is discussed here. A fundamental theoretical problem is to calculate the NLO response directly from the electronic configuration of the molecules. This section explores the molecular parameters that contribute to large h5 erpolarizabihties. Particular emphasis is on sum rule calculations and essential states models as guides to obtaining the optimal NLO response. 

Sum-Over-Essential States Models for Molecular Materials. 

The Two-Level Model for y and Its Limitations. Generally, essential-states-model calculations have been very successful in explaining and predicting the second-order response of noncentrosymmetric materials, but considerable work remains for understanding third-order materials. As a starting point, consider again the two-level model, which can be expressed for third-harmonic generation as(139)... 

Two-Photon Resonant Enhancement. The frequency dependence of the essential states models is also important as indicated by the potential for resonant enhancement in the denominators D of the sum-over-states (with appropriate damping effects not indicated in eq. 23). Generally, it is undesirable to operate near a resonance with either the fundamental input frequency > or the desired harmonic output. When 2co approaches com, however, an important intermediate two-photon resonance is evident from the second Dm term. In this case, resonant enhancement appears without imdesirable absorption effects. The (other types of frequency conversion and even the nonlinear retractive index. Intermediate resonant enhancement applies not only to the two-level model. Absorption and/or resonant enhancement... 

For Hubbard chains with V t> t, the ground state becomes a spin wave, with p = 0 for all n, and dipole processes are suppressed Eq. (42) then decreases as and the bond orders vanish when only virtual transfers are possible. Dipole-allowed transitions from B are still possible to A states with a C + C pair, however, in the manifold of states within t of ib U. Such excitations in Eq. (43) go as t /U in units of Eib. The only even-parity excited state, mAg, considered in the essential states model [146,147] for NLO is just above IB, which changes the sign of the left-hand side of Eq. (43) and implies [100] a strong two-photon resonance in the THG spectrum (Fig. 6.11) around 3o 3 eV. Vanishing 2A contributions in the essential states model also point to strong correlations, when 2A is a spin state based on two triplets. The intermediate nature of molecular correlations is again apparent correlations place 2A and nA far below the band limit, but the intense linear absorption is far from spin waves. 

Three excitation pathways dominate the expression of the static third-order susceptibility two positive contributions from the lA- IB— m3A IB—> lA and lA—> lB->m2A- IB—> lA channels and a negative contribution from the lA —> IB —V lA — IB lA channel. The 7 value mainly results from the incomplete cancellation between these terms. The 2A state is involved in two types of pathways lA—> IB—>2A IB —> lA and lA lB 2A nlB— lA. As these two contributions have opposite signs, the resulting role played by the 2A state in the description of the third-order nonlinearity is strongly reduced. We note, however, that the cancellation is only partial (in contrast to what is assumed in the essential-state model of Mazumdar and co-workers [137-139]) and that a quantitative estimate of the static 7 values requires to include in the SOS expression the following states lA, IB, 2A, m2A, m3 A, nlB, n2B, and n3B. These states form our model for the NLO response of thiophene oligomers. 

In the case of rt-conjugated molecules with qrradmpolar and octupolar symmetry for the description of the 2PA activity a tree- arrd foru-state models (generally called the essential state models) have been proposed. As this type of chromophore usually shows only a few (one-photon or two-photon) resonances and only the restricted nrrmber... 

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