Premium
Electron density and its derivatives at the nucleus for spherically confined hydrogen atom
Author(s) -
Montgomery H. E.,
Sen K. D.
Publication year - 2008
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21867
Subject(s) - hydrogen atom , radius , nucleus , atom (system on chip) , atomic physics , hydrogen , physics , derivative (finance) , bar (unit) , prime (order theory) , chemistry , crystallography , molecular physics , quantum mechanics , combinatorics , mathematics , computer security , meteorology , computer science , financial economics , economics , group (periodic table) , biology , embedded system , microbiology and biotechnology
It is shown that the energy of a hydrogen‐like atom confined inside a spherical cavity of radius, R , and potential barrier, V 0 , is quantitatively defined by the ratio $\left[{\eta_l^{\prime\prime} (0)\over\eta_l(0)}\right]$ . Here, the conventional spherical density $\overline\varrho$ ( r ) is scaled as η l ( r ) = ${\bar{\varrho} (r)\over r^{2l}}$ and the ratio of the second derivative η l ″ ( r ) to η l ( r ) is evaluated at the nucleus. Numerical results of the ratios are presented for 1 s , 2 s , 2 p , and 3 d states at several values of V 0 . For such states, the characteristic radii of confinement leading to the well‐defined values of energy are identified. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009