A generalized electron-pair density function for atoms

Toshikatsu Koga
2001 Journal of Chemical Physics  
For many-electron atoms, we discuss a generalized electron-pair density function g(q;a,b) that represents the probability density function for the magnitude ͉ar i ϩbr j ͉ of the two-electron vector ar i ϩbr j to be q, where a and b are real-valued parameters. It is pointed out that the function g(q;a,b) connects smoothly the single-electron density (r), the electron-pair intracule ͑relative motion͒ density h(r 12 ), and the electron-pair extracule ͑center-of-mass motion͒ density d(R). Moreover,
more » ... ity d(R). Moreover, (r) is found to be a local extremum function of g(q;1,b) with respect to the parameter b. Analogously, the single-electron moments ͗r n ͘ are local extrema of the moments ͗q n ͘ (a,b) associated with g(q;a,b). An illustrative example is given for the helium atom within the Kellner approximation.
doi:10.1063/1.1328750 fatcat:jjfhquqevffizeziqsr6fu2xz4