Abstract
When any two electrons are considered simultaneously, the radial density function D(r) in many-electron atoms is shown to be rigorously separated into inner D <(r) and outer D >(r) radial densities. Accordingly, radial properties such as the electron–nucleus attraction energy V en and the diamagnetic susceptibility χ d are the sum of the inner and outer contributions. The electron–electron repulsion energy V ee has an approximate relation with the minus first moment of the outer density D >(r). For the 102 atoms He through Lr in their ground states, different characteristics of local maxima in the radial densities D <(r), D >(r), and D(r) are reported based on the numerical Hartree-Fock wave functions. Relative contributions of the inner and outer components to V en and are also discussed for these atoms.
Similar content being viewed by others
References
Levine IN (2000) Quantum chemistry, 5th edn. Prentice Hall, Upper Saddle River, pp 146, 310
Bartell LS, Brockway LO (1953) Phys Rev 90:833
Boyd RJ (1976) J Phys B 9:L69
Politzer P, Parr RG (1976) J Chem Phys 64:4634
Simas AM, Sagar RP, Ku ACT, Smith VH Jr (1988) Can J Chem 66:1923
Sen KD, Slamet M, Sahni V (1993) Chem Phys Lett 205:313
Banyard KE, Baker CC (1969) J Chem Phys 51:2680
Spanier J, Oldham KB (1987) An atlas of functions. Springer, Berlin Heidelberg New York, p 63
Kato T (1957) Commun Pure Appl Math 10:151
Steiner E (1963) J Chem Phys 39:2365
Hoffmann-Ostenhof M, Hoffmann-Ostenhof T (1977) Phys Rev A 16:1782
Tal Y (1978) Phys Rev A 18:1781
Handy NC, Marron MT, Silverstone HJ (1969) Phys Rev 180:45
Handler GS, Smith DW, Silverstone HJ (1980) J Chem Phys 73:3936
Davis CL, Jensen HJA, Monkhorst HJ (1984) J Chem Phys 80:840
Ishida T, Ohno K (1992) Theor Chim Acta 81:355
Koga T (2004) J Chem Phys 121:3939
Koga T, Matsuyama H (2004) J Chem Phys 121:7708
Koga T, Matsuyama H (2005) J Chem Phys 122:024113
Messiah A (1999) Quantum mechanics. Dover, Mineola, p 497
Warner JW, Bartell LS, Blinder SM (1980) Int J Quantum Chem 18:921
Froese Fischer C (1972) Comput Phys Commun 4:107
Avery J (2003) In: Wilson S (ed) Handbook of molecular physics and quantum chemistry, vol 1. Wiley, Chichester, pp 236–249
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Koga, T., Matsuyama, H. Inner and outer radial density functions in many-electron atoms. Theor Chem Acc 115, 59–64 (2006). https://doi.org/10.1007/s00214-005-0676-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00214-005-0676-6