Spin-density calculation via the graphical unitary group approach

In this work we discuss the calculation of the spin-density matrix from fundamental spin principles as implemented in the COLUMBUS Program System employing the graphical unitary group approach (GUGA). First, a general equation for the spin-density matrix is derived in terms of the one-and two-particle reduced density matrices, quantities that are spin-independent and readily available within the GUGA formalism. Next, the evaluation of this equation using the Shavitt loop values is discussed. Finally, the spatially resolved counterpart of the spin-density matrix, the spin distribution, is calculated for the phenalenyl radical and structures produced by heteroatoms with mono- and di-substitutions. The physical meaning of the spin-density along with its computational description using various methods is discussed putting special emphasis on negative contributions to the spin-density and their quantification via a spin-promotion index.