Simple calculation of Löwdin’s alpha function. II. Easier procedure for evaluating b K k(L M‖l ), and vanishing of h n,2n−i(L M‖l ) for special values of i and n

Publisher Website
Google Scholar
Abstract
This paper subsequent to the one [J. Math. Phys. 2 5, 1133 (1984)] (referred to as Part I) presents the following new results: It is found out that for M=L and L−1 the coefficients bK k(L M‖l) in Löwdin’s α‐function have properties other than manifested in Part I. The expression for bK k(L M‖l) is shown to be equivalent to the one into which Sharma’s expression, obtained in a different manner from that in Part I, is simplified by Rashid. The use of Rashid’s expression leads to the recurrence formula for bK k(L M‖l) with respect to M only. This formula and the expression for the bK k(L M‖l) with M=L provide an easier procedure for successively evaluating bK k(L M‖l) than in Part I. Furthermore, it is proved that the coefficients hn,2n−i(L M‖l) in the asymptotic form of the α‐function vanish for i<l+M and for n<l.