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2. Calculations for the electronic transport in molecular nanostructures Gotthard Seifert Institut für Physikalische Chemie und Elektrochemie Technische Universität Dresden

3. Greens-Function Method Calculation of Transport Properties in molecular Systems Aldo di Carlo! Model: Molecule (M) and two contacts (α, β) Green‘s FunctionG(E) S,H – Overlap- and Hamilton Matrices Calculation of H and S matrices

4. LCAO Ansatz Atomic Orbitals - AO Slater Type Orbitals - STO

5. Hamilton matrix Overlap matrix Density-Functional based „tight binding“ DF-TB

6. Total Energy in DFT - EDFT - electron density - magnetization density Density fluctuations:

7. Expansion of EDFT around n=n0, μ=0

8. Approximations: Minimal(valence) basis in LCAO ansatz Neglect of pseudopotential terms in h0μν2-center approximation -Mulliken gross population at j 2nd order approximation in energy

9. Cancellation of „double counting terms“ U(Rjk) EB/eV R/aB Li2 - dimer EB - U(Rjk) Short range repulsive energy U(Rjk)

10. Approximation for magnetization density

11. Energy:

12. Hamiltonian:: Self Consistent Charge method SCC-DFTB

13. Transmission coefficient T(E) with Γα- Spectral functions of the Selfenergy-operators

14. Electronic Current – I Keldysh formalism Contact scattering functions Scattering function Inelastic processes (e-e, e-p intereaction) Non-equilibrium Green‘s functions

15. External bias – V Modification of the Hamiltonian matrix elements Calculation of I-V curves

16. Application ∞ Examples

17. Nanotubes of Carbon • S. Iijima Nature354 (1991) 56 ~1nm ~ μm Single-wall Nanotubes – SWNT‘s

18. (10,0) zig-zag tube 10-10 arm chair tube

19. Electronic Structure of Nanotubes Band-structure graphene monolayer k  Rolling „Zone folding“

20. zig-zag tube (n,0) mod(n,3)=0 mod(n,3)≠0

21. arm chair tube (n,n)

22. Functionalizationof Carbon Nanotubes? Graphite > Lamellar intercalation: Li, Na, K, Rb; Cl, Br, I > Lamellar covalent: O, F, S Fluorination

23. Fluorination 2Cgraphite + F2 2CF F sp2-Cgraphite sp3-C F

24. Carbon Nanotubes fluorination 2C + F2 2CF 2C+1/2F2 C2F

26. Decoration pattern – no „frustration“!

27. C2F – fluorine decoration pattern F Ethylen - like n,0

28. C2F – fluorine decoration pattern Ethylen - like

29. Density-of-States EF 10,0 CNT 10,0 C2F NT Large gap

30. C2F – fluorine decoration pattern n,0 F C trans-polyacetylen – like helical C ∞

31. C2F – fluorine decoration pattern Trans-polyacetylen – like helical C C ∞

32. Density-of-States 10,0 C2F NT Density-of-States small gap energy/eV

33. projected Density-of-States

34. C2F – fluorine decoration pattern cis-polyacetylen – like chain C C ∞

35. Density-of-States 10,0 C2F NT Density-of-States no gap

37. Transmission cis-polyacetylen – like chain ethylen - like 10,0 C2F NanoTubes

38. Transmission as function of coverage C2F (10,0) Nanotube cis-polyacetylen – like chain

39. trans-Polyacetylene

40. C2F (10,10) Nanotube chain (10,10) Nanotube

42. (9,0) Nanotube

43. 9,0 C2F NT ring HOMO –LUMO „aromatic“ π-states

45. Carbon Fluorine

47. Outlook/Problems • ->Contacts – Molecule interaction • -> electron-phonon interaction • -> electron-electron interaction? • -> non-adiabatic description • ->Applications • . • . • .

48. Thanks Aldo di Carlo (Rome) Thomas Niehaus (Paderborn) Nitesh Ranjan (Dresden)