The Calculation of NMR Chemical Shifts in Periodic Systems Based on Gauge Including Atomic Orbitals and Density Functional Theory (original) (raw)

Abstract

We present here a method that can calculate NMR shielding tensors from first principles for systems with translational invariance. Our approach is based on Kohn-Sham density functional theory and gauge-including atomic orbitals. Our scheme determines the shielding tensor as the second derivative of the total electronic energy with respect to an external magnetic field and a nuclear magnetic moment. The induced current density due to a periodic perturbation from nuclear magnetic moments is obtained through numerical differentiation, whereas the influence of the responding perturbation in terms of the external magnetic field is evaluated analytically. The method is implemented into the periodic program BAND. It employs a Bloch basis set made up of Slater-type or numeric atomic orbitals and represents the Kohn-Sham potential fully without the use of effective core potentials. Results from calculations of NMR shielding constants based on the present approach are presented for isolated molecules as well as systems with one-, two-and three-dimensional periodicity. The reported values are compared to experiment and results from calculations on cluster models.

Loading...

Loading Preview

Sorry, preview is currently unavailable. You can download the paper by clicking the button above.

References (52)

  1. Zurek, E.; Autschbach, J. Int. J. Quantum Chem. 2009, 109, 3343-3367.
  2. Mauri, F.; Pfrommer, B. G.; Louie, S. G. Phys. ReV. Let. 1996, 77, 5300-5303.
  3. Pickard, C. J.; Mauri, F. Phys. ReV. B: Condens. Matter Mater. Phys. 2001, 63, 245101-245113.
  4. Thonhauser, T.; Ceresoli, D.; Mostofi, A. A.; Marzari, N.; Resta, R.; Vanderbilt, D. J. Chem. Phys. 2009, 131, 101101; arxiv.org:0709.4429v2.
  5. Thonhauser, T.; Ceresoli, D.; Marzari, N. Int. J. Quantum Chem. 2009, 109, 3336-3342.
  6. Sebastiani, D.; Parinello, M. J. Phys. Chem. A 2001, 105, 1951-1958.
  7. Keith, T. A.; Bader, R. F. W. Chem. Phys. Let. 1993, 210 (1-3), 223-231.
  8. te Velde, G.; Baerends, E. J. Phys. ReV. B: Condens. Matter Mater. Phys. 1991, 44, 7888-7903.
  9. Wiesenekker, G.; te Velde, G.; Baerends, E. J. J. Phys. C: Solid State Phys 1988, 21, 4263-4283.
  10. Wiesenekker, G.; Baerends, E. J. J. Phys.: Condens. Matter 1991, 3, 6721-6742.
  11. te Velde, G.; Baerends, E. J.; Philipsen, P. H. T.; Wiesenekker, G.; Groeneveld, J. A.; Berger, J. A.; de Boeij, P. L.; Klooster, R.; Kootstra, F.; Romaniello, P.; Snijders, J. G.; Kadantsev, E. S.; Ziegler, T. BAND, 2009.01, SCM: Theoretical Chem- istry, Vrije Universiteit: Amsterdam, The Netherlands; http:// www.scm.com/.
  12. Kadantsev, E. S.; Ziegler, T. J. Phys. Chem. A 2008, 112, 4521-4526.
  13. Kadantsev, E. S.; Ziegler, T. J. Phys. Chem. A 2009, 113, 1327-1334.
  14. Kohn, W.; Sham, L. J. Phys. ReV. 1965, 140, A1133-A1138.
  15. McWeeny, R. Methods of molecular quantum mechanics; Academic Press: San Diego, 1992.
  16. te Velde, G. PhD Thesis. Vrije Universiteit: Amsterdam, The Netherlands, 1990; (available on-line: http://www.scm.com/ Doc/BAND_thesis/BAND_Thesis.pdf).
  17. Ditchfield, R. Mol. Phys. 1974, 27 (4), 789-807.
  18. Gauss, J. Molecular properties. In Modern methods and algorithms of quantum chemistry, Proceedings; Grotendorst, J., Ed.; John von Neumann Institute for Computing, Ju ¨lich, NIC series, 2000, 3, 541-592.
  19. Jones, R. O. Introduction to density functional theory and exchange-correlation energy functionals. In Computational Nanoscience: Do It Yourself!; Grotendorst, J., Blu ¨gel, S., Marx, D., Eds.; John von Neumann Institute for Computing, Ju ¨lich, Germany, 2006, 31, 45-70.
  20. Pople, J. A.; Krishnan, R.; Schlegel, H. B.; Binkley, J. S. Int. J. Quantum Chem., Quantum Chem. Symp. 1971, 13, 225- 241.
  21. Kaxiras, E. Atomic and electronic structure of solids. Cambridge University Press: New York, NY, 2003.
  22. Fukui, H. Magn. Reson. ReV. 1987, 11, 205-274.
  23. Martin, R. M. Electronic structure. Basic theory and practical methods; Cambridge University Press: Cambridge, England, 2004.
  24. Amos, A. T.; Musher, J. I. Mol. Phys. 1967, 13, 509-515.
  25. Resta, R.; Ceresoli, D.; Thonhauser, T.; Vanderbilt, D. ChemPhysChem 2005, 6, 1815-1819. Thonhauser, T.; Cere- soli, D.; Vanderbilt, D.; Resta, R. Phys. ReV. Lett. 2005, 95, 137205-137214. Ceresoli, D.; Thonhauser, T.; Vanderbilt, D.; Resta, R. Phys. ReV. B: Condens. Matter Mater. Phys. 2006, 74, 024408-024413. Xiao, D.; Shi, J.; Niu, Q. Phys. ReV. Lett. 2005, 95, 137204-137214. Shi, J.; Vignale, G.; Xiao, D.; Niu, Q. Phys. ReV. Lett. 2007, 99, 197202-197206.
  26. Thonhauser, T.; Mostofi, A. A.; Marzari, N.; Resta, R.; Vanderbilt, D. arxiv.org:0709.4429v1.
  27. Mauri, F.; Louie, S. G. Phys. ReV. Lett. 1996, 76, 4246- 4249.
  28. Becke, A. D. Phys. ReV. A: At., Mol., Opt. Phys. 1988, 38, 3098-3100.
  29. Perdew, J. P. Phys. ReV. B: Condens. Matter Mater. Phys. 1986, 33, 8822-8824.
  30. Perdew, J. P. Phys. ReV. B: Condens. Matter Mater. Phys. 1986, 34, 7406.
  31. Baerends, E. J.; Autschbach, J.; Bashford, D.; Be ´rces, A.; Bickelhaupt, F. M.; Bo, C.; Boerrigter, P. M.; Cavallo, L.; Chong, D. P.; Deng, L.; Dickson, R. M.; Ellis, D. E.; van Faassen, M.; Fan, L.; Fischer, T. H.; Fonseca Guerra, C.; Ghysels, A.; Giammona, A.; van Gisbergen, S. J. A.; Go ¨tz, A. W.; Groeneveld, J. A.; Gritsenko, O. V.; Gru ¨ning, M.; Harris, F. E.; van den Hoek, P.; Jacob, C. R.; Jacobsen, H.; Jensen, L.; van Kessel, G.; Kootstra, F.; Krykunov, M. V.; van Lenthe, E.; McCormack, D. A.; Michalak, A.; Mitoraj, M.; Neugebauer, J.; Nicu, V. P.; Noodleman, L.; Osinga, V. P.; Patchkovskii, S.; Philipsen, P. H. T.; Post, D.; Pye, C. C.; Ravenek, W.; Rodrı ´guez, J. I.; Ros, P.; Schipper, P. R. T.; Schreckenbach, G.; Seth, M.; Snijders, J. G.; Sola `, M.; Swart, M.; Swerhone, D.; te Velde, G.; Vernooijs, P.; Versluis, L.; Visscher, L.; Visser, O.; Wang, F.; Wesolowski, T. A.; van Wezenbeek, E. M.; Wiesenekker, G.; Wolff, S. K.; Woo, T. K.; Yakovlev, A. L.; Ziegler, T. ADF , 2009.01; SCM: Theoretical Chemistry; Vrije Universiteit: Amsterdam, The Netherlands, 2009.
  32. te Velde, G.; Bickelhaupt, F. M.; van Gisbergen, S. J. A.; Fonseca Guerra, C.; Baerends, E. J.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931-967.
  33. Schreckenbach, G.; Ziegler, T. J. Phys. Chem. 1995, 99, 606- 611.
  34. Schreckenbach, G.; Ziegler, T. Int. J. Quantum Chem. 1996, 60, 753-766.
  35. Caminiti, R.; Pandolfi, L.; Ballirano, P. J. Macromol. Sci. 2000, B39 (4), 481-492.
  36. Yamanobe, T.; Sorita, T.; Comoto, T.; Ando, I. J. Mol. Struct. 1985, 131, 267-275.
  37. Yamanobe, T. Structure and dynamics of crystalline and noncrystalline phases in polymers. In Solid State NMR of Polymers; Ando, I., Ed.; Elsevier & Technology Books: Amsterdam, The Netherlands, 1998, pp 267-1306.
  38. Perego, G.; Luglia, G.; Pedretti, U.; Cesari, M. Makromol. Chem. 1988, 189, 2657-2669.
  39. Terao, T.; Maeda, S.; Yamabe, T.; Akagi, K.; Shirakawa, H. Chem. Phys. Let. 1984, 103 (5), 347-351.
  40. Tabor, B. J.; Magre, E. P.; Boon, J. Eur. Polym. J. 1971, 7, 1127-1133.
  41. Napolitano, R.; Pirozzi, B.; Salvione, A. Macromolecules 1999, 32, 7682-7687.
  42. Wade, B.; Abhiraman, A. S.; Wharry, S.; Sutherlin, D. J. Polym. Sci. 1990, B28, 1233-1249.
  43. Lowman, D. W.; Fagerburg, D. R. Bull. Magn. Reson. 1992, 14 (1-4), 148-152.
  44. Iwasaki, M. J. Polym. Sci., Part A: Polym. Chem. 2003, 1 (4), 1099-1104.
  45. Hasegawa, R.; Takanashi, Y.; Chatani, Y.; Tadokoro, H. Polym. J. (Tokyo) 1972, 3 (5), 600-610.
  46. Tonelli, A. E.; Schilling, F. C.; Cais, R. E. Macromolecules 1982, 15, 849-853.
  47. Gabuda, S. P.; Kozlova, S. G.; Paasonen, V. M.; Nazarov, A. S. J. Struct. Chem. 2000, 41 (1), 67-71.
  48. Sagunama, M.; Mizutami, U.; Kondow, T. Phys. ReV. B: Condens. Matter Mater. Phys. 1980, 22, 5079-5084.
  49. Marian, C. M.; Gastreich, M. Solid State Nucl. Magn. Reson. 2001, 19, 29-44.
  50. Merwin, L. H.; Johnson, C. E.; Weimer, W. A. J. Mater. Res. 1994, 9 (3), 631-635.
  51. Mauri, F.; Pfrommer, B. G.; Louie, S. G. Phys. ReV. Lett. 1997, 79 (12), 2340-2343.
  52. Alam, T. M. Mater. Chem. Phys. 2004, 85, 310-315. CT100046A