Bond order alternation model

Furthermore, Lee et al. used a four-state model to describe the NLO properties of an octopolar molecule such as crystal violet [98]. In addition, they showed that one can use the concept of bond order alternation (BOA) to analyze the NLO structure-property relationship in octopolar molecules. 

Quantum mechanical analysis based on a simple two-level model [22] and bond-order alternation (BOA) principle exploiting aromaticity [23] have worked surprisingly well in providing useful structure/property relationships for the design of chromophores with ever improving molecular hyperpolarizability. Table 1 provides some representative examples with improved molecular optical nonlinearity developed over the past decade. It has been shown that very large nonlinearities... 

Figure 2 Dependence of the first and second hyperpolarizabilities on bond-order alternation (BOA) calculated for a donor-acceptor polyene under the influence of an external electric field. The left-hand side of each plot corresponds to a structure dominated by the neutral resonance structure, whereas the right-hand side corresponds to a zwitterionic structure. In a two-state model BOA = 0 corresponds to an equal mixture of the two resonance forms.

Run benzene using HMO. Write out the full bond order matr ix, enter ing zero for any element off the tridiagonal. What is the bond order of benzene Is there any Kekule-type alternation in this model ... 

Thus there are five bonding electrons giving a bond order of 2.5, consistent with the bond length of 115 pm, versus 121 pm for the four-electron bond in O2 and 110 pm for the six-electron bond in N2. For these and other related molecules, the double-quartet model is a convenient and useful alternative to the conventional molecular orbital model. Moreover, it shows that for a singly bonded terminal atom such as F or Cl there is a ring of six nonbonding electrons rather than three separate lone pairs. As we will see in Chapters 7 and 8, this conclusion is confirmed by the analysis of electron density distributions. 

Based on a Huckel model for the anthracene fragments of BA (which is an even alternant hydrocarbon) one can show that the delocalized LE state and the CT states should all have the same 7t bond order. This in turn implies that the vibrational modes and frequencies should be similar for LE, CT, and CT. Thus the vibrations of bianthryl can be ignored in the energy dependence on z (even for highly polar solvents). 

Perusal of CC bond distances and the accompanying 7r-bond orders presented in Table 7 reveals that an appreciable MN effect occurs in systems 20-22. This is evidenced by alternation of their IBDs values and differences (benzene) relative to free benzene gauge value. Bond fixation is reflected in the corresponding bond localization indices L(d). They read 0.064(0.068), 0.099(0.167), 0.155(0.242) and 0.153(0.238) for 12, 20, 21, and 22, respectively, where the first number refers to the MP2 results whereas the Hartree-Fock model calculations are given within parentheses. It follows that oxa-heteroanalog 21 exhibits the largest MN effect. It is also apparent that the HF model exaggerates the bond fixation in the aromatic moiety, but its qualitative predictions are correct in most cases. 

The first model implies the rupture of the coordination bonds. This is inconsistent with the inertness of the macrobicyclic complex because its decomposition causes the rupture not only of M-N bonds, but also of C-C and C-H bonds. Therefore, this model predicts a relatively long lifetime of the state for the [Cr(sep)]3+ cation. In fact, the E states for [Cr(en)s] and [Cr(sep)] + cations have very similar lifetimes (of the order of 10 ps) in DMF at 0°C and similar spectral characteristics (both of them show an intense band at 15 151 cm-i and possess a quantitatively similar low-intensity vibronic structure). The macrobicyclic ligand ensures that ligand dissociation will have a large activation barrier, even in metal-centred electronic exited states. Neither the first model nor the second one adequately accounts for the photolytic similarities of [Cr(sep)]3+, [Cr(en)3] + and [Cr(NH3)e] cations. The third model seems the most realistic alternative [159]. 

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. 

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