GRMS, Or, Graphical Representation of Model Spaces: Basics

antisymmetric atomic B-type basis branching diagram calculation of matrix coefficients complicated corresponding coupled cycles cyclic permutation D-part density matrix Diophantine equations doubly excited doubly occupied orbital Duch and Karwowski Ecorr eigenfunctions electrons elementary loops example fagot graph formula four-segment loops four-slope graph full space Gelfand gives graph of Fig graph theory graphical representation group theory β Karwowski 1985 labeling M-diagram m₁ many-particle matrix elements model space non-fagot graphs non-zero elements number of particles number of paths obtained one-particle orbital configurations orbital orderings P₁ Paldus permutation point group symmetry positions k represented reversed lexical ordering Ŝ² segment values Shavitt shift operators shown in Fig simple singly occupied arcs slopes spin eigenfunctions spin functions spin orbitals spin path subgraph subspaces symmetric group symmetry Ŝz)-adapted Table three-slope graph transposition two-particle operator two-segment loops unitary group approach vertex vertices