Transverse interaction

Nevertheless, certain collective excitations can occur in the condensed phase. These may be brought about by longitudinal coulombic interaction (plasmons in thin films) or by transverse interaction, as in the 7-eV excitation in condensed benzene, which is believed to be an exciton [12]. Special conditions must be satisfied by the real and imaginary parts of the dielectric function of the condensed phase for collective excitations to occur. After analyzing these factors, it has been concluded that in most ordinary liquids such as water, collective excitations would not result by interaction of fast charged particles [13,14]. 

A selfconsistent treatment of the transverse interaction in conventional ab initio methods is often based on the Gaunt approximation [48], There are, however, no density functionals available within this approximation. 

Transverse Interaction. This phase covers most of the nontechnical factors such as political (legislation, zoning, etc.), public... 

The importance of a self-consistent treatment of the transverse interaction is examined in Table 4.2. 

Table 4.2 also demonstrates the accuracy of the KLI approximation in the relativistic situation. In fact, for heavy elements the differences between the KLI and the full OPM energies are smaller than those resulting from a perturbative treatment of the transverse interaction. 

In principle, not only low-order perturbative Ec can be obtained in this way, but also resummed forms like the RPA (Engel and Facco Bonetti 2000). In practice, however, the resulting functionals are computationally much more demanding than the exact Ex, so that until now only the lowest-order contribution has been applied. Within the no-pair approximation and neglecting the transverse interaction, this second-order term reads... 

Moreover, using the decomposition of the photon propagator into the Coulomb and the transverse interaction, ex nQ) can be split accordingly [29,190],... 

Departure from 1-D electronic structure The transverse interactions... 

The main problem is the competition between these different instabilities. A departure from ideal 1-D situation, by increasing the transverse interactions, will suppress the Peierls state, as described by a mean-field approach [29]. Nevertheless, this description does not strictly apply to these low-dimensional systems, where large fluctuative regimes are present, as observed by diffuse X ray techniques [13,30]. 

For the tetraselenatetracene and phthalocyanine salts it appears that the electronic correlations are weak. In these molecules, larger than the TTF type, it turns out that U < 41, and the delicate balance between the kinetic and the correlation energies seems to be destroy (i.e. U 2V 41 ). Besides, one must repeat that the transverse interactions have to be included, to account for the transition temperatures (see above), even if it is often delicate to estimate these parameters. As a conclusion, we can say that this approach may give clues as to why, among so many series of molecular conductors, only a few exhibit an AF or SC ground state. 

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