Electronic polaron model

Besides the mentioned aperiodicity problem the treatment of correlation in the ground state of a polymer presents the most formidable problem. If one has a polymer with completely filled valence and conduction bands, one can Fourier transform the delocalized Bloch orbitals into localized Wannier functions and use these (instead of the MO-s of the polymer units) for a quantum chemical treatment of the short range correlation in a subunit taking only excitations in the subunit or between the reference unit and a few neighbouring units. With the aid of the Wannier functions then one can perform a Moeller-Plesset perturbation theory (PX), or for instance, a coupled electron pair approximation (CEPA) (1 ), or a coupled cluster expansion (19) calculation. The long range correlation then can be approximated with the help of the already mentioned electronic polaron model (11). 

Sec. 5.3 Electronic Polaron Model and Quasi-Particle Band Structure... 

ELECTRONIC POLARON MODEL AND THE QUASI-PARTICLE BAND STRUCTURE OF POLYMERS... 

In the actual calculation the complicated side chains R were substituted by an H atom. For the first step (calculation of the HF band structures) a 6-3IG basis set (double C + polarization function on both the carbon and hydrogen atoms) was applied. The valence and conduction bands obtained in this way were then corrected using the generalized electronic polaron model [quasi-particle (QP) band structures see Section 5.3]. The lowest sin et-exciton enei es (at K = 0) were then calculated using the QP one-electron levels and performing the three steps described in the previous section after equation (8.22). Table 8.1 shows the results obtained in this way for both PTS and TCDU. ... 

One can define a generalized Koopmans theorem if, by calculating quantity (8.27), one takes into account correlation effects and determines a quasi-particle (QP) band structure based on the generalized electronic polaron model (see Section 5.3). One can then write for a polymer... 

Neutron paramagnetic form factor 99 3.4. The electronic polaron model 127... 

The electronic polaron model is based on the assumption that the band calculation using the local-density functional approximation gives the correct ground state of the system. The agreement between the calculated Fermi surface geometry and the... 

Fig. 36. Schematic diagrams showing the distinction between the mechanisms for energy band formation of (a) the spin fluctuation resonance model, and (b) the electronic polaron model.

Fig. 38. Schematic representation of the band structure obtained Irom the electronic polaron model (Liu 1987, 1988).

Fig. 42. The magnetic susceptibility per lanthanide or actinide atom as a function of temperature, as predicted by the electronic polaron model. The susceptibility is in units of /iln/ri, where the effecitve moment includes the orbital contribution, as discussed in Liu (1988).

Fig. 43, The electrical resistivity versus temperature as predicted by the electronic polaron model (Liu 1988).

In Section 4 the MK theory will be applied to correct the band structure of polymers. For this the ab initio form of the electronic polaron model will be developed. This method gives the correlation corrected one-electron energies (the so-called QP energies) within a band as the difference of the pair correlation energies (the MP2 total energy can be expressed with their help, see below) of an IV -F 1 and N electron system (in the case of unfilled bands) or of an (V and N — 1 electron system (in case of the filled bands) (N is the number of electrons in the ground state). 

CORRELATION CORRECTED (QUASI PARTICLE) BAND STRUCTURE BASED ON THE ELECTRONIC POLARON MODEL... 

Figure 4 Energy-band gap of trans-PA vs. the HF energy per C2H2 unit obtained with the five different basis sets (a-e) defined in Table 4. O denotes HF calculation with fixed bond alternation. -I- HF calculation with optimized bond alternation, HF-l-MP/2 calculation with optimized bond alternation but using Aeg = ficond min(HF) - fivai max(HF), and X the electronic polaron model ASg — cond min(QF) — val max(QF)...

Besides the total energy one can correct in the band structure at least the physically interesting conduction and valence bands of a polymer by taking into account correlation effects. Namely, one can define following Takeuti s /5/ and Kunz and coworkers /29/ electronic polaron model (see also /22/) quasiparticle (QP) energy levels in the conduction and valence band, respectively,... 

---