Spin-density calculation via the graphical unitary group approach

Abstract

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.

GRAPHICAL ABSTRACT

Keywords:

• Graphical unitary group approach
• spin-density
• phenalenyl
• spin-promotion index

Acknowledgements

We are grateful for supply of computer time at the HPCC facilities of Texas Tech University. The authors also thank Lab-CCAM from ITA for computational resources.

Disclosure statement

The authors declare no conflict of interest.

Additional information

Funding

R.F.K.S. acknowleges support by Fundação de Amparo à Pesquisado Estado de Sào Paulo (FAPESP) [grant number 2019/07671-4], Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [grant numbers 407760/2018-0 and 307846/2021-0]. M.P.F. was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) [grant number 88887.581913/2020-00]. R.S. was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, Gas Phase Chemical Physics program through Argonne National Laboratory [contract DE-AC02-06CH11357]. H.L. wants to acknowledge support by the National Science Foundation [grant number 2107923], Division of Chemistry.