Skip to main content
SpringerLink
Log in

The Fourier space restricted Hartree-Fock method for the electronic structure calculation of linear poly(tetrafluoroethylene)

  • Articles
  • Special Issue Quantum Chemistry for Extended Systems—In honor of Prof. J.M. André for his 70th birthday
  • Published:
Science China Chemistry Aims and scope Submit manuscript

Abstract

Building on the pioneering work of Jean-Marie André and working in the laboratory he founded, the authors have developed a code called FT-1D to make Hartree-Fock electronic structure computations for stereoregular polymers using Ewald-type convergence acceleration methods. That code also takes full advantage of all line-group symmetries to calculate only the minimal set of two-electron integrals and to optimize the computation of the Fock matrix. The present communication reports a benchmark study of the FT-1D code using polytetrafluoroethylene (PTFE) as a test case. Our results not only confirm the algorithmic correctness of the code through agreement with other studies where they are applicable, but also show that the use of convergence acceleration enables accurate results to be obtained in situations where other widely-used codes (e.g., PLH and Crystal) fail. It is also found that full attention to the line-group symmetry of the PTFE polymer leads to an increase of between one and two orders of magnitude in the speed of computation. The new code can therefore be viewed as extending the range of electronic-structure computations for stereoregular polymers beyond the present scope of the successful and valuable code Crystal.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. André JM, Moseley DH, Champagne B, Delhalle J, Fripiat JG, Brédas JL, Vanderveken DJ, Vercauteren DP. LCAO Ab initio band structure calculations for polymers. In: Clementi E, Ed. Methods and Techniques in Computational Chemistry: METECC-94. Cagliari (Italy): STEF, 1993, Vol. B: 423–480

    Google Scholar 

  2. Ewald PP. Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann Phys-Leipzig, 1921, 64: 253–287

    Article  Google Scholar 

  3. Flamant I. Fourier space restricted Hartree-Fock method for the electronic structure calculation of stereoregular polymers. Dissertation for the doctoral degree. Namur (Belgium): University of Namur, 1998

    Google Scholar 

  4. Flamant I, Fripiat JG, Delhalle J, Harris FE. Efficient electronic structure calculations for systems of one-dimensional periodicity with the restricted Hartree-Fock-linear combination of atomic orbitals method implemented in Fourier space. Theor Chem Acc, 2000, 104: 350–357

    Article  CAS  Google Scholar 

  5. Fripiat JG, Delhalle J, Flamant I, Harris FE. Ewald-type formulas for Gaussianbasis bloch states in one-dimensionally periodic systems. J Chem Phys, 2010, 132: 044108

    Article  Google Scholar 

  6. Fripiat JG, Harris FE. Ewald-type formulas for Gaussian-basis in one-dimensionally periodic systems. Theor Chem Acc, 2012, 131: 1257

    Article  Google Scholar 

  7. Ambrosiano J, Greengard L, Rokhlin V. The fast multipole method for gridless particle simulation. Comput Phys Commun, 1988, 48: 117–125

    Article  CAS  Google Scholar 

  8. Lambert CG, Darden TA, Board JA Jr. Multipole-based algorithm for efficient calculation of forces and potentials in macroscopic periodic assemblies of particles. J Comput Phys, 1996, 126: 274–285

    Article  CAS  Google Scholar 

  9. Strain MC, Scuseria GE, Frisch MJ. Achieving linear scaling for the electronic quantum coulomb problem. Science, 1996, 271: 51–53

    Article  CAS  Google Scholar 

  10. Ismaylov AF, Scuseria GE, Frisch MJ. Efficient evaluation of short-range Hartree-Fock exchange in large molecules and periodic systems. J Chem Phys, 2006, 125: 104103

    Article  Google Scholar 

  11. Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ. Gaussian 09, Revision A.2. Wallingford (CT): Gaussian, Inc., 2009

    Google Scholar 

  12. Pisani C, Dovesi R, Roetti C, Causà M, Orlando R, Casassa S., Saunders VR. CRYSTAL and EMBED, two computational tools for the ab initio study of electronic properties of crystals. Int J Quantum Chem, 2000, 77: 1032–1048

    Article  CAS  Google Scholar 

  13. Saunders VR, Freyria-Fava C, Dovesi R, Roetti C. On the electrostatic potential in linear periodic polymers. Comput Phys Commun, 1994, 84: 156–172

    Article  CAS  Google Scholar 

  14. Champagne B. Ab initio polymer quantum theory. In: Galiatsatos V, Ed. Molecular simulation method for predicting polymer properties. New York: John Wiley & Sons, 2005. 1–46

    Google Scholar 

  15. Hirata S. Quantum chemistry of macromolecules and solids. Phys Chem Chem Phys, 2009, 11: 8397–8412

    Article  CAS  Google Scholar 

  16. Terras R. A miller algorithm for an incomplete bessel function. J Comput Phys, 1981, 39: 233–240

    Article  Google Scholar 

  17. Chaudhry MA, Zubair SM. Generalized incomplete gamma functions with applications. J Comput Appl Math, 1994, 55: 99–123

    Article  Google Scholar 

  18. Chaudhry MA, Temme NM, Veling EJM. Asymptotics and closed form of a generalized incomplete gamma function. J Comput Appl Math, 1996, 67: 371–379

    Article  Google Scholar 

  19. Harris FE. New approach to calculation of the leaky aquifer function. Int J Quantum Chem, 1997, 63: 913–916

    Article  CAS  Google Scholar 

  20. Harris FE. More about the leaky aquifer function. Int J Quantum Chem, 1998, 70: 623–626

    Article  CAS  Google Scholar 

  21. Alford JA. Calculation of the generalized leaky aquifer integral. Comput Phys Commun, 2005, 173: 1–8

    Article  CAS  Google Scholar 

  22. Harris FE. Incomplete Bessel, generalized incomplete gamma, or leaky aquifer functions. J Comput Appl Math, 2008, 215: 260–269

    Article  Google Scholar 

  23. Harris FE, Fripiat JG. Methods for incomplete Bessel function evaluation. Int J Quantum Chem, 2009, 109: 1728–1740

    Article  CAS  Google Scholar 

  24. Dupuis M, King HF. Molecular symmetry and closed-shell SCF calculations. Int J Quantum Chem, 1977, 11: 613–625

    Article  CAS  Google Scholar 

  25. Vujičić M, Božović IB, Herbut F. Construction of the symmetry groups of polymer molecules. J Phys A, 1977, 10: 1271–1280

    Article  Google Scholar 

  26. Fripiat JG, Flamant I, Harris FE, Delhalle J. Computational aspects of polymer band structure calculations by the Fourier space restricted Hartree-Fock method. Int J Quantum Chem, 2000, 80: 856–862

    Article  CAS  Google Scholar 

  27. Fripiat JG, Delhalle J. Efficient calculation of the exchange in the Fourier representation of HF-LCAO-SCF equations for 1D periodic systems. Int J Quantum Chem, 2009, 109: 2960–2967

    Article  CAS  Google Scholar 

  28. Hehre WJ, Stewart RF, Pople JA. Self consistent molecular orbital methods. I. Use of gaussian expansions of slater type atomic orbitals. J Chem Phys, 1969, 51: 2657–2664

    Article  CAS  Google Scholar 

  29. Dennington R, Keith T, Millam J. GaussView Version 5. Shawnee Mission (KS): Semichem Inc., 2009

    Google Scholar 

  30. Suhai S, Bagus PS, Ladik J. An error analysis for Hartree-Fock crystal orbital calculations. Chem Phys, 1982, 68: 467–471

    Article  CAS  Google Scholar 

  31. Delhalle J, Piela L, Brédas JL, André JM. Multipole expansion in tight-binding Hartree-Fock calculations for infinite model polymers. Phys Rev B, 1980, 22: 6254–6267

    Article  CAS  Google Scholar 

  32. Saunders VR, Dovesi R, Roetti C, Causà M, Harrison NM, Orlando R, Zicovich-Wilson CM. Crystal 98 User’s Manual. Turin(Italy): University of Turin, Theoretical Chemistry Group, and Daresbury, Warrington (UK): Computational Materials Science Group, CLRC Daresbury Laboratory. 1999

    Google Scholar 

  33. McCubbin WL. Effects of symmetry on the band structure of polymers. In: André JM, Ladik J, Eds. Electronic structure of polymers and molecular crystals. NATO Advanced Study Institute Series: Series B, Physics, 1974, 9: 171–198

    Google Scholar 

  34. Otto P, Ladik J, Förner W. The energy band structure of polyfluoroethylene: influence of chemical substitution and conformation. Chem Phys, 1985, 95: 365–372

    Article  CAS  Google Scholar 

  35. Seki K, Tanaka H, Ohta T, Aoki Y, Imamura A, Fujimoto H, Yamamoto H, Inokuchi H. Electronic structure of poly(tetrafluoroethylene) studied by UPS, VUV absorption, and band calculations. Phys Scripta, 1990, 41: 167–171

    Article  CAS  Google Scholar 

  36. Falk JE, Fleming RJ. Study of the electronic band structure of polyacetylene and the polyuoroethylenes. J Phys, 1975, C8: 627–646

    Google Scholar 

  37. Hehre WJ, Ditchfield R, Pople JA. Self consistent molecular orbital methods. XII. Further extensions of gaussian type basis sets for use in molecular orbital studies of organic molecules. J Chem Phys, 1972, 56: 2257–2261

    Article  CAS  Google Scholar 

  38. Hariharan PC, Pople JA. The influence of polarization functions on molecular orbital hydrogenation energies. Theor Chim Acta, 1973, 28: 213–222

    Article  CAS  Google Scholar 

  39. Delhalle J, Delhalle S. Computation of the electronic density of states distributions of stereoregular polymers. Int J Quantum Chem, 1977, 11: 349–358

    Article  CAS  Google Scholar 

  40. Delhalle J, Delhalle S, André JM, Pireaux JJ, Riga J, Caudano R, Verbist JJ. Electronic structure of linear fluoropolymers: theory and ESCA measurements revisited. J Electron Spectrosc, 1977, 12: 293–303

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Chimie Théorique, Unité de chimie physique théorique et structurale, University of Namur, Rue de Bruxelles, 61, B-5000, Namur, Belgium

    Joseph G. Fripiat

  2. Department of Physics, University of Utah, Salt Lake City, UT, 84112, USA

    Frank E. Harris

  3. Quantum Theory Project, University of Florida, Gainesville, FL, 32611, USA

    Frank E. Harris

Authors
  1. Joseph G. Fripiat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Frank E. Harris
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joseph G. Fripiat.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fripiat, J.G., Harris, F.E. The Fourier space restricted Hartree-Fock method for the electronic structure calculation of linear poly(tetrafluoroethylene). Sci. China Chem. 57, 1355–1362 (2014). https://doi.org/10.1007/s11426-014-5104-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11426-014-5104-0

Keywords

Search

Navigation