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How does the ambiguity of the electronic stress tensor influence its ability to reveal the atomic shell structure

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Abstract

The electronic stress tensor is not uniquely defined. Therefore, shell indicators stemming from the quantum stress tensor may inherit this ambiguity. Based on a general formula of the stress tensor this ambiguity can be described by an external parameter λ. Two functions derived from the quantum stress tensor have been evaluated according to their ability to serve as shell indicators. The influence of λ is analyzed and the consequences for the representation of the atomic shell structure are discussed in detail. It is found that the trace of the stress tensor does not fully reveal the atomic shell structure. In contrast, the scaled trace (whereby the scaling function is proportional to the Thomas-Fermi kinetic energy density) produces fairly good representation of the atomic shell structure over a wide range of λ values.

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References

  1. Bartell LS, Brockway LO (1953) Phys Rev 90:833–838

    Article  CAS  Google Scholar 

  2. Waber JT, Cromer DT (1965) J Chem Phys 42:4116–4123

    Article  CAS  Google Scholar 

  3. Weinstein H, Politzer P, Srebrenik S (1975) Theor Chim Acta 38:159–163

    Article  CAS  Google Scholar 

  4. Boyd JR (1976) J Phys B 9:69–72

    Article  Google Scholar 

  5. Schmider H, Sagar R, Smith Jr VH (1994) Proc Indian Acad Sci 106:133–142

    CAS  Google Scholar 

  6. Sen KD, Slamet M, Sahni V (1993) Chem Phys Lett 205:313–316

    Article  CAS  Google Scholar 

  7. Sperber G (1971) Int J Quantum Chem 5:189–214

    Article  Google Scholar 

  8. Bader FWR (1990) Atoms in molecules—a quantum theory. Clarendon Press, Oxford

    Google Scholar 

  9. Shi Z, Boyd RJ (1987) J Chem Phys 88:4375–4377

    Article  Google Scholar 

  10. Sagar RP, Ku ACT, Smith Jr VH, Simas AM (1987) J Chem Phys 88:4367–4374

    Article  Google Scholar 

  11. Nagy A, March NH (1997) Mol Phys 90:271–276

    CAS  Google Scholar 

  12. Bohorquez HJ, Boyd RJ (2008) J Chem Phys 129:24110

    Article  Google Scholar 

  13. Kohout M, Savin A, Preuss H (1991) J Chem Phys 95:1928–1942

    Article  CAS  Google Scholar 

  14. Sagar RP, Ku ACT, Smith Jr VH, Simas AM (1988) Can J Chem 66:1005–1012

    Article  CAS  Google Scholar 

  15. Kohout M (2001) Int J Quantum Chem 83:324–331

    Article  CAS  Google Scholar 

  16. Wagner K, Kohout M (2011) Theor Chem Acc 128:39–46

    Article  CAS  Google Scholar 

  17. Finzel K, Kohout M, Grin Y (2012) Theor Chem Acc 131:1106

    Article  Google Scholar 

  18. Kohout M (2004) Int J Quantum Chem 97:651–658

    Article  CAS  Google Scholar 

  19. Kohout M, Pernal K, Wagner FR, Grin Y (2004) Theor Chem Acc 112:453–459

    Article  CAS  Google Scholar 

  20. Kohout M, Pernal K, Wagner FR, Grin Y (2005) Theor Chem Acc 113:287–293

    Article  CAS  Google Scholar 

  21. Kohout M, Wagner FR, Grin Y (2008) Theor Chem Acc 119:413–420

    Article  CAS  Google Scholar 

  22. Pendas AM, Kohout M, Blanco MA, Francisco E (2012) Beyond standard charge density topological analyses. In: Gatti C, Macchi P (eds) Modern charge density analyses. Springer, London

    Google Scholar 

  23. Silvi B (2003) J Phys Chem A 107:30813085

    Article  Google Scholar 

  24. Becke AD, Edgecombe KE (1990) J Chem Phys 92:5397–5403

    Article  CAS  Google Scholar 

  25. Savin A, Jepsen O, Flad J, Anderson OK, Preuss H, von Schnering HG (1992) Angew Chem Int Ed 31:187–188

    Article  Google Scholar 

  26. Schmider HL, Becke AD (2000) J Mol Struct Theochem 527:51–61

    Article  CAS  Google Scholar 

  27. Tao J, Vignale G, Tokatly I (2008) Phys Rev Lett 100:206405

    Article  Google Scholar 

  28. Tachibana A (2011) J Math Chem 49:1810–1821

    Article  Google Scholar 

  29. Szarek P, Sueda Y, Tachibana A (2008) J Chem Phys 129:094102

    Article  Google Scholar 

  30. Ichikawa K, Tachibana A (2009) Phys Rev A 80:062507

    Article  Google Scholar 

  31. Guervara-Gracía A, Echegaray E, Toro-Labbe A, Jenkins S, Kirk SR, Ayers PW (2011) J Chem Phys 134:234106

    Article  Google Scholar 

  32. Jenkins S, Kirk SR, Guervara-Gracía A, Echegaray E, Ayers PW, Toro-Labbe A (2011) Chem Phys Lett 510:18–20

    Article  CAS  Google Scholar 

  33. Anderson JSM, Ayers P, Hernandez JIR (2010) J Phys Chem A 114:8884–8895

    Article  CAS  Google Scholar 

  34. Schmider H, Sagar R, Smith Jr VH (1992) Can J Chem 70:506–512

    Article  CAS  Google Scholar 

  35. Bartolotti LJ, Parr RG (1980) J Chem Phys 72:1593–1596

    Article  CAS  Google Scholar 

  36. Bader RFW, Essen H (1984) J Chem Phys 80:1943–1960

    Article  CAS  Google Scholar 

  37. Epstein ST (1975) J Chem Phys 63:3573–3574

    Article  CAS  Google Scholar 

  38. Godfrey MJ (1988) Phys Rev B 37:10176–10183

    Article  Google Scholar 

  39. Rogers CL, Rappe AM (2002) Phys Rev B 65:224117

    Article  Google Scholar 

  40. Cohen L (1979) J Chem Phys 70:788–789

    Article  CAS  Google Scholar 

  41. Kohout M, Savin A (1997) J Comput Chem 18:1431–1439

    Article  CAS  Google Scholar 

  42. Clementi E, Roetti C (1974) At Data Nucl Data Tables 14:177–478

    Article  CAS  Google Scholar 

  43. Kohout M (2010) DGrid, version 4.6. Radebeul

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  1. Max-Planck-Institut für Chemische Physik fester Stoffe, Nöthnitzer Str. 40, 01187, Dresden, Germany

    K. Finzel & M. Kohout

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  1. K. Finzel
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  2. M. Kohout
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Finzel, K., Kohout, M. How does the ambiguity of the electronic stress tensor influence its ability to reveal the atomic shell structure. Theor Chem Acc 132, 1392 (2013). https://doi.org/10.1007/s00214-013-1392-2

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