Semiempirical Calculations of Excitation Energies

Pariser and Parr (1953) and Pople (1953) developed the PPP method independently by introducing the ZDO approximation and empirical values of electron-repulsion integrals into the MO method for jr-electron systems. This methc has proven very useful for calculating the properties of transitions for both unsaturated and aromatic molecules. 

The LCAO-MO coefficients are given as components of the eigenvector c, of the Fock matrix F with elements 

The excited-state wave functions are written as linear combinations of spin-adapted configurational functions 

It has been shown that two principal factors are responsible for the ordering of the low-lying excited states  

First-order Cl, which for alternant hydrocarbons gives rise to the distinction between plus and minus states (cf. Section 1.2.4). 

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Indazoles have been subjected to certain theoretical calculations. Kamiya (70BCJ3344) has used the semiempirical Pariser-Parr-Pople method with configuration interaction for calculation of the electronic spectrum, ionization energy, tt-electron distribution and total 7T-energy of indazole (36) and isoindazole (37). The tt-densities and bond orders are collected in Figure 5 the molecular diagrams for the lowest (77,77 ) singlet and (77,77 ) triplet states have also been calculated they show that the isomerization (36) -> (37) is easier in the excited state. 

The results described above represent the first example of the FR mechanism (Scheme 1). Semiempirical calculations on this molecule showed that the intersystem crossing to the excited triplet state is favored The reaction cannot be sensitized by xanthone because the triplet state of 3,4-diphenyl-1,2,5-oxadiazole is lower than that of xanthone. The cleavage of the triplet state to the biradical is favored, considering the relative energy of this intermediate (Fig. 23) (OOOUPl). 

The electron densities, bond orders, first six excitation energies, oscillator strengths, and weighting factors of pyrido[l,2-f)]pyridazinium cation were calculated by the PPP semiempirical version of the SCFMO-CI method, which indicated that protonation is expected to take place at the nonbridgehead nitrogen, and nucleophilic substitution is predicted to occur at position 3 (68TCA417i... 

Semiempirical calculations indicate that there is a local energy minimum for the endoperoxide 37 with a barrier height of 6 kcalmoE corresponding to a lifetime of ca 10 s, in agreement with experimental results However, the most important result, which corroborates the hypothesis of 37 as the HEI in luminol chemiluminescence, is the state correlation between the ground state of 37 and the excited state of 3-AP. ... 

The MO-type calculation has been employed by Bramanti et al. (4) to explain the absorption spectrum of Tl+ in KC1. The calculated positions of the TT energy levels in KC1 explained changes in the spectrum on going from free ions to the solid state. Similarly, in the case of hydrogen impurity in LiF, Hayns (5) has shown that the excitation energy predicted by calculation is in accord with experimental results. These results have inspired confidence in the semiempirical method as a means for providing qualitative explanations for several electronic phenomena. 

Early semiempirical calculations laid the foundations for subsequent ab initio methods which can now not only describe the electronic structure of optically accessible excited states, but also model the wavepacket propagation on the resulting potential energy surfaces. These models are supported by ultrafast studies using femptosecond (fs) pulsed lasers with a variety of detection systems. Many systems use indirect detection of excited-state processes because many excited states are unbound and not amenable to spectroscopic techniques. 

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