Perimeter free electron model

The physical reasons for this unusual nonmonotonic behavior, which differs from what one would expect for an atom or for the free-electron model of the perimeter, are related to the only n-fold symmetry which is present in the polygon of n perimeter atoms, instead of full cylindrical symmetry (Michl and West, 1980). The fact that the magnetic moment can either increase or decrease for a transition from A to A + 1 is of fundamental importance for an understanding of MCD spectra. (Cf. Section 3.3.)... 

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... 

The PFEO model is a restatement of the free electron model presented above, but assumes that the bounding container is the perimeter of the molecule. The first four levels expected from the wave function are shown in Fig. 2.7. 

Both singlet and triplet states are generated by the orbital promotion of an electron, n- -it transitions are totally allowed. These energy values can also be calculated from HQckel molecular orbital (HMO) method. For benzene, the free electron perimeter model has been found to be useful. The energy levels and nodal properties of benzene molecule are given in Figure 2.19. 

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... 

In other physical chemical analyses, the perimeter model [73] has been employed to analyze the spectral intensities and MCD signals for a series of porphyrinoid macrocycles derived from the C20H20 perimeter, including the parent, benz-free analogue of texaphyrin 158 [74], These calculations were then compared with the MCD spectra of a number of substituted cadmium texaphyrins (e.g. 116,143, and 148-152, c.f. Scheme 16) [75]. The results confirmed that the perimeter model accounts in a simple way for the signs of the MCD B terms associated with the low-lying electronic transitions of these metallotexaphyrins. 

Fock matrix (1.5.1) reaction field (2.7.2) matrix element of the Fock operator between AOs and (I-5.1) electron repulsion operator (1.2.3) ground state of the 3 x 3 model (4.4.1) and of 4)V-electron perimeter (2.2.7) free energy (1.4.3) one-electron operator of kinetic and potential energy (1.2.3)... 

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