Platt perimeter model

Modified Notation.—The Platt notation is applied mainly to aromatic molecules and based on the conceptually simple perimeter model description of electronic excitations (7). Ground states are labeled A, the excited states involved in certain very high intensity transitions are labeled B and the excited states produced in partially forbidden transitions (i.e., those in which selection rules are violated) are labeled L and C. The notation is derived from selection rules appropriate for imaginary monocyclic aromatic systems. States to which transitions are forbidden because of a large change in angular momentum are L states. Transitions to C states are parity forbidden that is, they violate the g g, u u selection rule. In common aromatics other than benzene these selection rules break down and transitions to L and C states occur but at lower intensities relative to B states. 

Several qualitative models, e.g. Platt s ring perimeter model [88], Clar s model [89] and Randic s conjugated circuits model [90-92] have either been or are frequently used for the rationalisation of their properties. All these qualitative models rationalise the properties of aromatic and anti-aromatic hydrocarbons in terms of the Hiickel [4n+2] and [4n] rules. The extra stability of a PAH, due to 7t-electron delocalisation, can also be determined, computationally or experimentally, by either considering homodesmotic relationships [36] or by the reaction enthalpy of the reaction of the PAH towards suitable chosen reference compounds [93],... 

Jhe perimeter model introduced by Platt (1949), reformulated in the LCAO Mo form by Moffitt (1954a), and extended by Gouterman (1%1), Heilbron-ner and Murrell (1%3), and Michl (1978), has been very useful in understanding trends in the electronic spectra of cyclic Jt systems. It applies equally to singlet and triplet states and has provided the commonly used nomenclature for both. The following discussion is limited to the singlet states, which are more important in ordinary spectroscopy. 

Platt s original perimeter model was a free-electron (FEMO) model based on a one-dimensional circular potential along which the jt electrons can move freely. The orbitals of an electron confined to such a circular ring are given by... 

AHOMO and ALUMO may be derived from a perturbational treatment of the union of the [I l]annulenyl cation and C or of the [I3]annulenide anion and C , respectively. This also shows that these molecules have further excited states in addition to those derived from a (4N + 2)-electron perimeter. This is true for the longest-wavelength transitions of both molecules, which therefore cannot be labeled within the framework of Platt s nomenclature. Hence, a prediction of their MCD sign on the basis of the perimeter model is also impossible. However, the next two bands correspond to the L, and Lj states of a (4Af + 2)-electron perimeter and show the expected behavior in the MCD spectra. In acenaphthylene the order of the B terms is -, + and in pleiadiene -f-, -. These signs are not changed by perturbing substituents since the difference between AHOMO and ALUMO is too large. Both molecules represent hard chromophores. 

Biphenylene and trisdehydro[12]annulene are representatives of conjugated hydrocarbons with a 4 -membered ring. The pattern of their absorption spectra is completely different from that of benzenoid aromatics. Their HOMO and LUMO are derived from the two NBMOs of an ideal perimeter and both the lowest excited singlet and triplet state can be described by the configuration A ho lu- The transition is symmetry forbidden in molecules of D2h symmetry or higher. Nonradiative decay usually dominates their photophysical properties. Quantum yields of fluorescence and intersystem crossing are low.307 The LCAO version of Platt s perimeter model has been extended to treat conjugated systems with AN jt-electrons derived from [ ]annulenes.308,309... 

Logically, though not historically,1 the next step was taken by Moffitt.39 Moffitt pointed out that Platt s perimeter model could be reformulated within the framework of the Hiickel theory if it... 

These data indicate more clearly the problems theoretical methods (TDDFT in this case) have in accovmting for the change of electronic structure upon excitation. For the ionic La states of the aromatic compounds (using Platts nomenclature derived from the perimeter model, see. Ref. 9 e.g.) and the 1B state of the polyene, a systematic underestimation of the excitation energies is observed while the opposite is true for the other more covalent states that exhibit stronger multiconfigurational character (for a more detailed discussion of these problems see Refs. 35 and 36). 

As a first example, let us consider the vibronic structure of the first absorption band in the UV spectrum of anthracene. In agreement with experiment, the TDDFT calculation gives an Si state with B2 symmetry and a vertical excitation energy of 3.23 eV [AE° °(exp.) = 3.43 eV]. This band can be described by a HOMO LUMO excitation and in the Platt nomenclature (perimeter model) it is denoted as the La state. Both states were optimized at the (TD)DFT-B3LYP/TZV(d,p) level in D21, symmetry. 

Estimate the HOMO LUMO tt tt wavelength for anthracene (C14H10) using the Platt Perimeter extension of the POR model. 

Compare (calculate) the HOMO LUMO tt tt wavelength for azulene (CioHg) using the Platt Perimeter extension of the POR model compare your result for the example calculation for naphthalene in the text. What does this say about the Perimeter model Evaluate the energy of the = land n = 2 levels of an electron-in-a-box for L= 10 A in... 

The state symbols 1Fb, xLa, lBb and xBa shown in Figure 4.27 were introduced in 1949 by Platt.297,298 He assumed a free-electron model, similar to the electron-in-a-box, in which the 7t-electrons of a cyclic system are confined to a one-dimensional loop of constant potential (a circular wire). The eigenvalues of a single electron in a perimeter of length / are given by Equation 4.37. 

The three electronic absorption bands of benzene are listed in Table 3.1, identified by two common systems of notation. Platt developed the perimeter or free-electron model of the absorption bands of polycyclic aromatic hydrocarbons... 

In the partide-in-a-ring model for benzene proposed by J. R. Platt, the jt electrons are considered to move around the perimeter of a cirde of constant potential bounded by infinite walls of the circle. 

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