Journal of the Korean Chemical Society (대한화학회지)

Korean Chemical Society (대한화학회)
권호 표지

Calculation of the Cubic Crystal Field Splitting 10 Dq in KNiF$_3$. An Integral Hellmann-Feynman Approach

Integral Hellmann-Feynman Approach에 의한 KNiF$_3$의 Cubic Crystal Field Splitting 10 Dq의 계산

  • Hojing Kim (Department of Chemistry, College of Liberal Arts and Sciences, Seoul National University) ;
  • Hie-Joon Kim (Department of Chemistry, College of Liberal Arts and Sciences, Seoul National University)
  • 김호징 (서울대학교 문리과대학 화학과) ;
  • 김희준 (서울대학교 문리과대학 화학과)
  • Published : 1973.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

By use of an Integral Hellmann-Feynman formula, the cubic crystal field splitting 1O Dq in $KNiF_3$ is calculated from first principles. Numerical values of covalency parameters and necessary integrals are quoted from Sugano and Shulman. The result, 7100$cm^{-1}$, is in excellent agreement with the observed value, 7250$cm^{-1}$. It is found that higher order perturbation energy correction is of the same order of magnitude as 10 Dq itself and is, therefore, essential tin calculating 10 Dq from first principles. It is also found that the point charge potential is the dominant part of the crystal field potential.

Integral Hellmann-Feynman formula를 사용하여 $KNiF_3$의 cubic crystal splitting 10Dq를 first principle로부터 계산하였다. Covalency parameter들과 필요한 적분치들은 Sugano와 Shulman의 계산치를 사용하였다. 계산치 7100$cm^{-1}$는 실험치 7250$cm^{-1}$와 대단히 잘 일치하였다. 고차섭동에너지 보정치는 10 Dq 자체와 같은 order of magnitude를 가지며 따라서 first principle로부터 10 Dq를 계산하는데 있어서 반드시 고려되어야 할 몫이라는 것을 발견하였다. 또한 point charge potential이 crystal field potential의 압도적인 부분을 차지하는 것을 발견하였다.

Keywords

References

  1. Ann. Physik v.3 H. Bethe
  2. Phys. Rev. v.41 J.H. Van Vleck
  3. J. Chem. Phys. v.7 J.H. Van Vleck
  4. Physica v.9 D. Polder
  5. J. Chem. Phys. v.20 W.H. Kleiner
  6. J. Phys. Soc. Japan v.11 Y. Tanabe;S. Sugano
  7. Phys. Chem. Solids v.11 J.C. Phillips
  8. Phys. Rev. v.120 A.J. Freeman;R.E. Watson
  9. Phys. Rev. v.130 R.G. Shulman;S. Sugano
  10. Phys. Rev. v.134 K. Knox;R.G. Shulman;S. Sugano
  11. Phys. Rev. v.130 S. Sugano;R.G. Shulman
  12. Phys. Rev. v.134 R.E. Watson;A.J. Freeman
  13. Phys. Status Solidi v.4 E. Simanek;Z. Sroubek
  14. J. Phys. Soc. Japan v.20 S. Sugano;Y. Tanabe
  15. J. Chem. Phys. v.47 P.O. Offenhartz
  16. Phys. Rev. v.180 H.M. Gladney;A. Veillard
  17. Proc. Phys. Soc. (London) v.88 J. Hubbard;D.E. Rimmer;F.R.A. Hopgood
  18. J. Korean Chem. Soc. v.17 H. Kim;H.J. Kim;U.R. Kim
  19. Phys. Rev. v.118 R.E. Watson
  20. The Theory of Atomic Spectra E.U. Condon;G.H. Shortley
  21. Proc. Cambridge Phil. Soc. v.53 C. Froese