Is it possible to determine rigorous magnetic Hamiltonians in spin s=1 systems from density functional theory calculations?

Abstract

The variational energies of broken-symmetry single determinants are frequently used (especially in the Kohn-Sham density functional theory) to determine the magnetic coupling between open-shell metal ions in molecular complexes or periodic lattices. Most applications extract the information from the solutions of m(s)(max) and m(s)(min) eigenvalues of S(z) magnetic spin momentum, assuming that a mapping of these energies on the energies of an Ising Hamiltonian is grounded. This approach is unable to predict the possible importance of deviations from the simplest form of the Heisenberg Hamiltonians. For systems involving s=1 magnetic centers, it cannot provide an estimate of neither the biquadratic exchange integral nor the three-body operator interaction that has recently been proven to be of the same order of magnitude [Phys. Rev. B 70, 132412 (2007)]. The present work shows that one may use other broken-symmetry solutions of intermediate values of m(s) to evaluate the amplitude of these additional terms. The here-derived equations rely on the assumption that an extended Hubbard-type Hamiltonian rules the interactions between the magnetic electrons. Numerical illustrations on a model problem of two O(2) molecules and a fragment of the La(2)NiO(4) lattice are reported. The results obtained using a variable percentage of Fock exchange in the BLYP functional are compared to those provided by elaborate wave function calculations. The relevant percentage of Fock exchange is system dependent but a mean value of 30% leads to acceptable amplitudes of the effective exchange interaction.

Spin-Pure Stochastic-CASSCF via GUGA-FCIQMC Applied to Iron–Sulfur Clusters

“…To quantify this discrepancy and analyze how well a biquadratic model suits the ab initio results, we show the relative average error per state ω (in percent) of the corresponding bilinear and biquadratic Heisenberg fits to the CASCI (blue solid and striped) and CASSCF (orange solid and striped) results in Figure 8 b. Following ref ( 90 ), ω is defined as where E S C is the computed ab initio spin gap of spin state S relative to the singlet ground state and E S M is the energy obtained by fitting the bilinear and biquadratic model ( eqs 16 and 18 ). N is the number of considered states (with N = 5 in the FeS dimer case, as we only consider the spin gap relative to the singlet ground state), and Δ E max C is the ab initio energy difference between the S = 5 and singlet states.…”

“…Both contributions can be related to additional biquadratic terms in the Heisenberg Hamiltonian. 90 − 92 , 153 …”

A Bis‐Binuclear NiII Complex with Easy and Hard Axes of Magnetization: Complementary Experimental and Theoretical Insights

“…The main advantage of this approach over WF‐based methods is its application to larger systems. It is also particularly suited to geometry optimizations, and the determination of subtle interactions such as double exchange and bi‐quadratic exchange in systems with spin S = 1 . The same procedure was used to calculate the intra‐ and interdimer exchange couplings: Two broken‐symmetry solutions were computed, namely M S = m s 1 + m s 2 = 0, which has the local m s 1 = 1 and m s 2 = –1 components on each Ni II , and M S = 2 ( m s 1 = 1 and m s 2 = 1).…”

Rationalization of the behavior of M2(CH3CS2)4I (M = Ni, Pt) chains at room temperature from periodic density functional theory and ab initio cluster calculations

“…This interval includes the typical percentages that have been used in the literature to obtain accurate electronic structure parameters (such as J and t ) in other transition‐metal materials. [92–96]…”