Spin-density calculation via the graphical unitary group approach

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