1. 1 Quantum Theory of DNA— An Approach to Electron Transfer in DNA H. Sugawara, 2005 Work being done with H. Ikemura 1.Introduction motivation ⇔ Ikemura Conjecture Ikemura Conjecture “Electron transfer in DNA is playing an important role in the information exchanges among the various sections of DNA.” Example

2. 2

3. 3 Standard technique in particle theory and in condensed matter theory but maybe not in quantum chemistry. Consider electrons interacting with the centers of potential (ions) located at R i : 2. Field Theory Technique electromagnetic interactions (gauge principle)

4. 4 ◎ electron-phonon interactions

5. 5 3. Hartree approximations Include in V(x) → Veff

6. 6

7. 7 Further approximations only nearest neighbors Then we have Special case of H → Su-Schrieffer-Heegger Hamiltonian ,  constant,  longitudinal →

8. 8 can also be defined in a similar way Then we replace

9. 9 Here was utilized

10. 10 RNA transcription DNA replication

11. 11 ◎ Consider classical and longitudinal oscillation ◎ general case with classical oscillation localized (tightly bound) wave function

12. 12 WKB solution

13. 13 ◎ The localization depends on the sign of and of ◎ Back to the descrete description applications (1)Luminescence quenching (2)Electric current (3)Absorption of light

14. 14 Luminescence quenching quenching occurs by a hole propagation inside DNA Note 1. Prokariote ・・・ closed string 2. Eukariote ・・・ open string end: telomere with certain protein mixed system Ru-ligand absorption luminescence Rh provides electrons ⇒ quenching

15. 15

16. 16 Probability of quenching DNA electrons transfer to (from) metals

17. 17 Density at Lh

18. 18 Electric current in DNA

19. 19

20. 20

21. 21 Coupling to backbone electrons This may be important in explaining the current? add

22. 22 There must be an overlap

23. 23 (1) E f is within the band (2) E f is outside of the band semiconductor-like

24. 24 Optical absorption (Sarukura’s proposal) em interaction excited band ground band

25. 25 absorption rate

26. 26 Conclusion (1)Comparison with experiments (2)Bound states with proteins (3)Quantized phonon (4)Improvement of approximations remaining problems (1)Three dimensional string action for DNA is derived (2)Approximate  -electron wave functions are derived (3)Applications to luminescence quenching, electric current through DNA and optical absorption are formulated