Polymer coupled-clusters

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). 

In the case of periodic polymers in the T2T2 approximation of the coupled cluster method we can write7... 

Ab initio equation of motion coupled cluster singles and doubles (EOM-CCSD) calculations of spin-spin couplings have been performed by Del Bene et for F-F and FI F couplings in cyclic FEI polymers (FEI)n, n = 2-6. The authors conclude that although both the Fermi contact term and VpF couplings increase and become positive when the cluster size increases, the FC term is not a good quantitative approximation to /ff-... 

The treatment of correlation, even in periodic polymers, presents a formidable and as yet only partially solved problem if the unit cell is large. This problem is examined by initially discussing localization techniques in larger molecules, and then presenting the first results of the application of localized orbitals for correlation calculations using many-body perturbation theory and the coupled-cluster approach. It is also shown how localization of the orbitals within a large unit cell can be applied for correlation calculations if this unit cell is repeated in a periodic way in the polymer. This chapter also deals with the correlation in polymers with smaller unit cells (like polyacetylene, polydiacetylene, and polyethylene) and includes a detailed discussion of the results obtained. Finally, some ideas about possibilities of treating correlation in disordered chains are noted. 

If one wishes to calculate the correlation energy of a polymer with the aid of equation (68), one has to substitute for (E)/,/ any size consistent expression to compute this quantity (MP2, MP2 + MP3, coupled cluster theory in certain approximations etc.). 

Coupled-cluster Theory DNA Bases and Base Pairs Ab Initio Calculations Green s Functions and Propagators for Chemistry M0ller-Plesset Perturbation Theory Polymers Semiempirical Calculations. 

For the calculation of the correlation energy per unit cell in the ground state of a polymer (either conductor or an insulator) one can use any size-consistent method (perturbation theory /18/, coupled cluster expansion /19/, electron pair theories /20/, etc.). In the case of insulators one can Fourier transform the delocalized Bloch orbitals into site semilocalized Wannier functions (WF-s) and perform the excitations between Wannier functions belonging to near lying sites /4/. (For the generation of optimally localized Wannier functions see /21/.) This procedure is, however,... 

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