Dimerized half-filled systems

In another paper [1] in this volume we have discussed some basic notions of the spectroscopy of charge transfer (CT) crystals and molecular conductors, mainly based on ver> simple dimeric models. The practical applicability of these models is limit to dimerized systems with localized electron states. This situation most often occurs for half-filled systems with intermediate to strong electron correlations. 

The argument, just briefly outlined, show that, in a quarter-filled system, the presence of strong on-site correlations leads to deviations of the optical properties fi om the Drude behavior [3] expected for independent electrons. Such deviations are not as large, as those predicted for a half-filled system, and, in particular, do not relate directly to U itself, but, rather, to dimeric lattice distortions and, possibly, to the nearest-neighbor repulsion V. 

When the effective on-site Coulomb repulsive energy (Geff) of the solid composed of Tt-radical molecules is smaller than the bandwidth (W), then the solid becomes a half-filled metal provided that the molecules stack uniformly without dimerization and can be described by a band picture. So far, no such radical molecules have been prepared. In order to decrease Ues and stabilize radical molecules chemically, a push-pull effect and an extension of the re-system have been implemented, though a large U ff and high reactivity (polymerization) are stiU crucial for the metallic transport. Table 2 summarizes selected organic conductors of neutral 7t-radical molecules. 

M(dmit)2 molecule is 1/2-, frequently observed value, the conduction band is the half-filled (anti-bonding) HOMO band. This two-dimensional HOMO band has narrow width as a result of the strong dimerization (the effective band width is correlated to the interdimer transfer integrals). Therefore, the system tends to become a Mott insulator. 

Infinite linear polyenes show a bond alternation between successive long and short C-C bonds [1], a consequence of the Peierls theorem on the nonexistence of one-dimensional metals [2], This Peierls distortion (or instability) is very important both from a theoretical and a practical point of view, being a typical example of a metal-insulator transition [3]. Consider an infinite chain of equally spaced sites -(CH)-, each of them bearing one electron in a single valence orbital. In this case we have a half-filled band and the system has metallic character. If we distort the chain into an alternating sequence of short and long bonds -(CH=CH)-, the half-filled band splits into a lower one completely filled and an upper empty band, separated by a gap. This dimerized polyacetylene is an insulator. 

We can summarize this brief discussion of the electronic spectroscopy of dimers by noting that,in the dimer with two electrons, which is the simplest molecular cluster analog of an half-filled band system, the effect of the effective on-site correlation U is twofold (i) it shifts the charge transfer band to higher energies (ii) it reduces the oscillator strength of the CT transition. This behavior is shown in Fig. 2 for dimensionless quantities. 

The infrared spectra of RbTCNQF4 shown in Fig. 5 provide an illustrative example of the dramatic spectral changes displayed by half-filled ion radical stack systems when they undergo a structural transition from regular to dimerized. 

Another instance where spin state is important and has a direct bearing on structure is in one-dimensional systems. Just as in Section 13.2 where we showed how a half-filled band usually results in a pairing distortion, so similar reasoning suggests that a quarter-filled band should result in a tetramerization 13.72. However, if the distorted arrangement is magnetic then dimerization is the process that is favored 13.73. Again prediction of the mode of distortion is not at all easy. 

---