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Optical activities of helical polymers: a crystal orbital theory based on Wannier functions

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Abstract

In this paper, a novel theory of optical activities for helical polymers has been formulated using crystal orbital methods under periodic boundary conditions. The selection rule of the optical transition was determined in the reciprocal space based on the helical angle of the unit cells. The optical rotatory strength was estimated using Wannier functions, which can be chosen to be real localized orbitals. Contrary to conventional exciton models, the structural parameters of helical polymers can be easily reflected in actual calculations of the optical rotatory strength within the crystal orbital framework. The theory was confirmed by evaluating the optical rotatory strength of a right-handed helical polyacetylene. This approach provides a promising method to evaluate the optical activities of helical polymers with itinerant electrons.

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The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

References

  1. Woody RW (1996) Theory of circular dichroism of proteins. In: Fasman GD (ed) Circular dichroism and conformational analysis of biomolecules. Plenum Press, New York, p 25

    Chapter  Google Scholar 

  2. Lightner DA (2000) The octant rule. In: Berova N, Nakanishi K, Woody RW (eds) Circular dichroism: principles and applications, 2nd edn. Wiley, New York

    Google Scholar 

  3. Moffitt W, Woodward RB, Moscowitz A, Klyne W, Djerassi C (1961) J Am Chem Soc 83:4013

    Article  CAS  Google Scholar 

  4. Moscowitz A (1962) Adv Chem Phys 4:67

    Google Scholar 

  5. Moffitt W (1956) J Chem Phys 25:467

    Article  CAS  Google Scholar 

  6. Moffitt W, Fitts DD, Kirkwood JG (1957) Proc Nat Acad Sci 43:723

    Article  CAS  Google Scholar 

  7. Tinoco I Jr (1962) Adv Chem Phys 4:113

    Google Scholar 

  8. Charney E (1965) Tetrahedron 21:3127

    Article  CAS  Google Scholar 

  9. Kemp CM, Mason SF (1966) Tetrahedron 22:629

    Article  CAS  Google Scholar 

  10. Gould RR, Hoffmann R (1970) J Am Chem Soc 92:1813

    Article  CAS  Google Scholar 

  11. Imamura A, Hirano T, Nagata C, Tsuruta T (1972) Bull Chem Soc Jpn 45:396

    Article  CAS  Google Scholar 

  12. Botek E, Champagne B (2007) J Chem Phys 127:204101

    Article  Google Scholar 

  13. Grimme S, Peyerimhoff SD, Bartram S, Vögtle F, Breest A, Hormes J (1993) Chem Phys Lett 213:32

    Article  CAS  Google Scholar 

  14. Hatanaka M (2013) Int J Quantum Chem 113:2447

    Article  CAS  Google Scholar 

  15. Stephens PJ, Devlin FJ, Cheeseman JR, Frisch MJ (2001) J Phys Chem A 105:5356

    Article  CAS  Google Scholar 

  16. Autschbach J, Ziegler T, van Gisbergen SJA, Baerends EJ (2002) J Chem Phys 116:6930

    Article  CAS  Google Scholar 

  17. Autschbach J, Patchkovskii S, Ziegler T, van Gisbergen SJA, Baerends EJ (2002) J Chem Phys 117:581

    Article  CAS  Google Scholar 

  18. Diedrich C, Grimme S (2003) J Phys Chem A 107:2524

    Article  CAS  Google Scholar 

  19. Ikai T, Okamoto Y (2009) Chem Rev 109:6077

    Article  CAS  Google Scholar 

  20. Shimomura K, Ikai T, Kanoh S, Yashima E, Maeda K (2014) Nat Chem 6:429

    Article  CAS  Google Scholar 

  21. Yashima E, Maeda K, Iida H, Furusho Y, Nagai K (2009) Chem Rev 109:6102

    Article  CAS  Google Scholar 

  22. Megens RP, Roelfes G (2011) Chem Eur J 17:8514

    Article  CAS  Google Scholar 

  23. Leigh T, Fernandez-Trillo P (2020) Nat Rev Chem 4:291

    Article  CAS  Google Scholar 

  24. Natta G, Pino P, Corradini P, Danusso F, Mantica E, Mazzanti G, Moraglio G (1955) J Am Chem Soc 77:1708

    Article  CAS  Google Scholar 

  25. Akagi K, Piao G, Kaneko S, Sakamaki K, Shirakawa H, Kyotani M (1998) Science 282:1683

    Article  CAS  Google Scholar 

  26. Akagi K, Mori T (2008) Chem Rec 8:395

    Article  CAS  Google Scholar 

  27. Green MM, Peterson NC, Sato T, Teramoto A, Cook R, Lifson S (1995) Science 268:1860

    Article  CAS  Google Scholar 

  28. Mayer S, Zentel R (2001) Prog Polym Sci 26:1973

    Article  CAS  Google Scholar 

  29. Tang H-Z, Lu Y, Tian G, Capracotta MD, Novak BM (2004) J Am Chem Soc 126:3722

    Article  CAS  Google Scholar 

  30. Tang H-Z, Novak BM, He J, Polavarapu PL (2005) Angew Chem 117:7464

    Article  Google Scholar 

  31. Schwartz E, Koepf M, Kitto HJ, Nolte RJM, Rowan AE (2011) Polym Chem 2:33

    Article  CAS  Google Scholar 

  32. Yashima E (2010) Polym J 42:3

    Article  CAS  Google Scholar 

  33. Nakano T, Okamoto Y (2001) Chem Rev 101:4013

    Article  CAS  Google Scholar 

  34. Hoffmann R (1963) J Chem Phys 39:1397

    Article  CAS  Google Scholar 

  35. Imamura A (1970) J Chem Phys 52:3168

    Article  CAS  Google Scholar 

  36. Pople JA, Walmsley SH (1962) Trans Faraday Soc 58:441

    Article  CAS  Google Scholar 

  37. Pugh D (1973) Mol Phys 26:1297

    Article  CAS  Google Scholar 

  38. Marzari N, Vanderbilt D (1997) Phys Rev B 56:12847

    Article  CAS  Google Scholar 

  39. Stewart JJP (2013) J Mol Model 19:1

    Article  CAS  Google Scholar 

  40. Stewart JJP, (2016) MOPAC2016, Stewart computational chemistry, Colorado Springs CO, Available at: http://OpenMOPAC.net

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number JP19K05392.

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  1. Division of Materials Science and Engineering, Graduate School of Engineering, Tokyo Denki University, 5 Senju-Asahi-cho, Adachi-ku, 120-8551, Tokyo, Japan

    M. Hatanaka

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  1. M. Hatanaka
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Correspondence to M. Hatanaka.

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Hatanaka, M. Optical activities of helical polymers: a crystal orbital theory based on Wannier functions. Theor Chem Acc 140, 153 (2021). https://doi.org/10.1007/s00214-021-02843-9

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