Theory of the self-consistent field for states with open shells

Equations for determination of vector coupling coefficients in systems with two open shells. Ions of transition metals with pMdN configuration

“…2G (10) , 2F (12) , 2D (13); 2P (9). 2S (4), wher~ the ,numbers in theparenthese$' denote the number of tepns with the given symmetry. The saI!leas in ,the simpler ease ofatom~ with d N ,configuration, a:.fprmallyeorrect caleulation of multiple terms (fromthe standpointof the variational principle) requires going be-' yondthe framework of theHartt'ee -Fock method ( 1 5 ) .…”

“…In the unified coupling operator (UCO) method [4][5][6][7][8]16], the energy of an atom electronic configuration pNpdNd in astate described by quantum numbers Land S has…”

“…In the Hartree-Fock (HF) method, the atomic states are calcu1ated by the use of a specia1ly written atomic program [2,3], since in the general Hartree-Fock theory of open shells -the unified coup1ing operator (UCO) method [4][5][6][7][8] -the problem of calculating ionized atoms is not completely solved. In particular, difficulty is recognized in using the ueo method to calculate ions in states with two degenerate open shells [9,10].…”

Coupling coefficients for systems with two open electronic shells: Transition metal ions with pM dN configuration

“…Within the framework of the general eoupling operator (Gco) method [4][5][6][7][8]16], the energy of atom with pNpd Nd eleetronie eonfiguration being in the 2S+1L state is as folIows: …”

“…Within the framework of the restricted Hartree-Fock method (RHF), the atoms are calculated by the specialized atomic program [2,3], as the problem on ionized atom calculation is not completely resolved within the framework of general open-shell SCF theory (i.e., in the general eoupling operator (Gco) method [4][5][6][7][8]). In partieular, there are some difficulties in ealculating ionized atoms with two open electronic shells by the GCO method [9,10].…”