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

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)10.1063/1.2145878]. 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.