Bond length alternation model

Harmonic oscillator model of aromaticity (HOMA) — This is a geometry-based index of aromaticity that takes into account two effects. These are the increase in bond-length alternation (GEO term) and the increase in mean bond length in the system (EN term) such that HOMA= 1-EN-GEO <2004PCP249>. For examples see Sections 2.2.42.3, 2.3.42.3, and 244.2.3. 

Whereas strained ring systems are usually reactive and often unstable, molecules which satisfy the criteria for aromaticity exhibit enhanced stability. As is evident from the structural formula of 1, the cycloproparenes set these features in juxtaposition as they are strained molecules in which a single carbon atom is fused across adjacent centres of an aromatic system. The interest of the experimentalist in strained molecules has been matched by the theoretician in the search for suitable models for developing the concepts of chemical bonding and aromaticity. The cycloproparenes have been particularly important in this regard as they meet the criterion for partial aromatic bond localization and consequent bond length alternation in the aromatic ring as proposed by Mills and Nixon in 1930, viz. la vs lb. The cation 5, anion 6 and radical 7 derived from 1, and also the ketone 8 and exocyclic methylene derivative 9, are of interest in this respect. 

The alternation of the single and double bonds in the polyene chain is inverted in the VB and CT forms, see Fig. 3.21, so that the model molecule can also be described in terms of the bond length alternation (BLA). The BLA is defined as ... 

The degree of bond length alternation is closely related to the magnitude of the forbidden energy gap, E, which in turn affeqts electrical, optical and other physical properties of the system. Within the one-electron picture (Huckel-model) one can show, that E = 2 I lo where 0 and are... 

Luo et al. have investigated the influence of the solvent polarity on the NLO properties of a simple donor-acceptor polyene molecule (Scheme 4) at the ab initio level of theory applying the continuum model of solvent [107]. It has been shown that the evolution of the TPA cross section with respect to the bond length alternation (BLA) closely follows that of the static first-order hyperpolarizability, p. The TPA cross section is strongly dependent on the geometrical changes. Moreover, these authors have noticed that the solvent effect on the TPA cross section (for the CT excited state) in tlie typical donor-acceptor polyene molecule exhibiting the positive solvatochromism is smaller than the influence of the solvent on the values of p. 

Some examples of intuition-based or modeling-based advances in nonlinear properties, specifically the first hyperpolarizability response p, have been developed in the past three decades. These include the bond-length alternation motif, the idea of octopolar molecular structures, the stronger responses of excited states and the use of purposely twisted -ir-electron molecules to modify the admixture of quinoid and aromatic structures. 

Besides these qualitative differences, there also exist quantitative discrepancies between the Hiickel model for polyenes and the experimental observations. The Hiickel theory predicts an order of magnitude larger oscillator strength in the absorption to the lowest dipole allowed state [4]. The bond length alternation required to fit the optical gap in polyenes within a Hiickel model is twice the experimentally observed bond alternation. Thus, the Hiickel model is mainly of pedagogical interest and one needs to go beyond it for dealing accurately with realistic conjugated systems. 

In order to assess the accuracy of the dynamic SDMRG technique, we have performed a series of model calculations we computed the dynamic linear polarizabilities (0(0 )) and third-order polarizabilities (7(0 , 01,0 )) corresponding to the third harmonic generation (THG), for the Hubbard and J7—V polyene-like chains of up to 20 sites with and without dimerizations (note that the dimerization parameter S reflects the degree of carbon-carbon bond-length alternation along the polyene chain nonzero S leads to alternating t and V values while zero 5 means uniform t and V). 

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