Magnetic exchange couplings from constrained density functional theory: An efficient approach utilizing analytic derivatives

Abstract

We introduce a method for evaluating magnetic exchange couplings based on the constrained density functional theory (C-DFT) approach of Rudra, Wu, and Van Voorhis [J. Chem. Phys. 124, 024103 (2006)]. Our method shares the same physical principles as C-DFT but makes use of the fact that the electronic energy changes quadratically and bilinearly with respect to the constraints in the range of interest. This allows us to use coupled perturbed Kohn-Sham spin density functional theory to determine approximately the corrections to the energy of the different spin configurations and construct a priori the relevant energy-landscapes obtained by constrained spin density functional theory. We assess this methodology in a set of binuclear transition-metal complexes and show that it reproduces very closely the results of C-DFT. This demonstrates a proof-of-concept for this method as a potential tool for studying a number of other molecular phenomena. Additionally, routes to improving upon the limitations of this method are discussed.

Spin Adapted versus Broken Symmetry Approaches in the Description of Magnetic Coupling in Heterodinuclear Complexes

“…It is worth pointing out that some alternative methods have been proposed to calculate exchange couplings, such as the variation of constrained DFT 51 based on the use of coupled-perturbed Kohn−Sham equations as proposed by Phillips and Peralta. 52 However, to our knowledge, this method has not been used in heteronuclear systems. It would be interesting to see if it can reproduce the exchange couplings in this case, where spin flip TDDFT fails to give physical results.…”

Magnetization Dynamics from Time-Dependent Noncollinear Spin Density Functional Theory Calculations

“…To this end, we choose an initial state where the local spins are in a noncollinear configuration (see, e.g., Figure ). This is implemented by applying constraints introduced via Lagrange multipliers in the same way some of us have done previously , for the static calculation of magnetic exchange couplings. Using local projectors , , we write the local magnetization at atom A as where P μν is the spin-density matrix vector whose Cartesian components are and In eq , is defined from the Löwdin partitioning as where S is the AO overlap matrix.…”

Implementation of non-collinear spin-constrained DFT calculations in SIESTA with a fully relativistic Hamiltonian

“…The constrained-spin DFT was first developed by Dederichset al [12]. Over the past two and a half decades a number of interesting problems have been studied successfully using CDFT, such as the effect of Cerium impurities [12], long-range electron transfer [13], spin-dynamics [14], and magnetic exchange couplings [15][16][17] (see [11] for a review). As we will see in the following, these theoretical developments allow calculations of both s and MAEs.…”

“…One is the so-called frozen magnon approximation [18], in which the spin configuration is constrained to a spin wave with periodicity determined by a wave vector q and the energy of this spin wave is calculated through the generalized Bloch theorem for a spin-spiral configuration [19]. In the other approach, the coupling constants are calculated directly from the change of the total energy associated with constrained rotations of the spin-polarization at the sites involved [16,17,20]. The later will be the approach followed in this work.…”