title: Towards the blackbox computation of magnetic exchange coupling parameters in polynuclear transition-metal complexes: theory, implementation, and application.
abstract: We present a method for calculating magnetic coupling parameters from a single spin-configuration via analytic derivatives of the electronic energy with respect to the local spin direction. This method does not introduce new approximations beyond those found in the Heisenberg-Dirac Hamiltonian and a standard Kohn-Sham Density Functional Theory calculation, and in the limit of an ideal Heisenberg system it reproduces the coupling as determined from spin-projected energy-differences. Our method employs a generalized perturbative approach to constrained density functional theory, where exact expressions for the energy to second order in the constraints are obtained by analytic derivatives from coupled-perturbed theory. When the relative angle between magnetization vectors of metal atoms enters as a constraint, this allows us to calculate all the magnetic exchange couplings of a system from derivatives with respect to local spin directions from the high-spin configuration. Because of the favorable computational scaling of our method with respect to the number of spin-centers, as compared to the broken-symmetry energy-differences approach, this opens the possibility for the blackbox exploration of magnetic properties in large polynuclear transition-metal complexes. In this work we outline the motivation, theory, and implementation of this method, and present results for several model systems and transition-metal complexes with a variety of density functional approximations and Hartree-Fock.
authors: Science of Advanced Materials, Central Michigan University, Mt. Pleasant, Michigan 48859, USA. phill3jj@cmich.edu
authors: Jordan J
authors: JJ
authors: Phillips
authors: Juan E
authors: JE
authors: Peralta
mesh_terms: D000465:Algorithms; D056831:Coordination Complexes / Q000737:chemistry*; D008280:Magnetics; D008958:Models, Molecular; D011789:Quantum Theory; D028561:Transition Elements / Q000737:chemistry*
chemical_list: D056831:Coordination Complexes; D028561:Transition Elements