Spin in density‐functional theory

Abstract

The accurate description of open-shell molecules, in particular of transition metal complexes and clusters, is still an important challenge for quantum chemistry. Although density-functional theory (DFT) is widely applied in this area, the sometimes severe limitations of its currently available approximate realizations often preclude its application as a predictive theory. Here, we review the foundations of DFT applied to open-shell systems, both within the nonrelativistic and the relativistic framework. In particular, we provide an in-depth discussion of the exact theory, with a focus on the role of the spin density and possibilities for targeting specific spin states. It turns out that different options exist for setting up Kohn-Sham DFT schemes for open-shell systems, which imply different definitions of the exchangecorrelation energy functional and lead to different exact conditions on this functional. Finally, we suggest possible directions for future developments.

Spin contamination analogy, Kramers pairs symmetry and spin density representations at the 2-component unrestricted Hartree–Fock level of theory

“…Actually, the rigor definition of DFT at the general 4c level should account for (spin and electron) density current instead of electron and spin density [30,31,32,33]. Nevertheless, spin magnetization (which is directly represented by the NCOL approach) is nowadays used as an approximation in the 2c/4c spin-DFT and spin time dependent DFT (spin TD-DFT) calculations [28,29,34,35,36,37,38,32,33]. Besides DFT/TD-DFT, spin and spin density have an important role in the polarized neutron (PN) scattering theory, both from the theoretical and from the experimental point of view [39,40].…”

“…First of all, the collinear and noncollinear approaches which introduce the analog of the spin density at the 2c / 4c level of theory have to be briefly outlined [28,29,34,35,36,37,38,33]. The collinear approach uses the z component of the spin operatorŜ z , which leads to the following form of spin density [29] …”

Density matrix renormalization group with efficient dynamical electron correlation through range separation

“…Apart from an extension of our implementation to a spin-unrestricted framework in the srDFT part, also spin-state-specific short-range functionals will further be crucial for molecules with an open-shell electronic structure 93 . Alternative approaches for a simultaneous treatment of static and dynamic correlation in a hybrid DMRG approach that avoid a range-separation ansatz exist.…”

Interactive Chemical Reactivity Exploration

“…[42] were employed in com- bination with a STO-2G basis [43] for the calculation of the overlap matrix. We note that studying bond breaking processes with standard DFT methods require the breaking of the spin symmetry [44].…”