Unrestricted compact model potentials for ab initio embedded cluster calculations: Magnetic interactions in KNiF3

The superexchange mechanism in crystalline compounds. The case of KMF3(M = Mn, Fe, Co, Ni) perovskites

The ferromagnetic and antiferromagnetic wavefunctions of four KMF₃(M = Mn, Fe, Co and Ni) perovskites have been obtained quantum-mechanically with the CRYSTAL code, by using the Hartree-Fock (HF) Hamiltonian and three flavours of DFT (PBE, B3LYP and PBE0) and anall-electronGaussian type basis set. In the Fe and Co cases, with d⁶and d⁷occupation, the Jahn-Teller distortion of the cubic cell is as large as 0.12 Å. Various features of the superexchange interaction energies (SIE), namely additivity, dependence on the M-M distance, on theMFM̂angle, and on the adopted functional, are explored. The contribution to SIE by the Coulomb, exchange and kinetic energy terms is analyzed. It is shown that, when using density functionals, SIE clearly correlates with the amount of exact (Hartree-Fock) exchange in the functional. The effect of SIE on the equilibrium geometry and volume of the unit cell is discussed, and it is shown that the key quantity is the spin polarization of the (closed shell) F ions along the M-F-M path. The effect of thismagneticpressureis evaluated quantitatively for the first time. The superexchange coupling constantJ, evaluated at the HF level and through the Ising model, underestimates the experimental values by about 60%-70%. The more sophisticated Yamaguchi model (that takes into account the contamination of the FM and AFM spin states) does not reduce the discrepancy. The B3LYP hybrid functional overestimates the experiments. These last are bracketed by HF and PBE0. For PBE, the overestimation is huge. Finally, Mulliken population data, charge and spin density maps and density of states are used to illustrate the electronic structure.

Simple minimum principle to derive a quantum-mechanical/ molecular-mechanical method

We propose a minimum principle to derive a QM/MM (quantum-mechanical/molecular-mechanical) method from the first principle. We approximate the Hamiltonian of a spectator substituent as the structure-dependent effective Hamiltonian in a least-squares sense. This effective Hamiltonian is expanded with the orthogonal operator set called the normal-ordered product. We determine the structure-dependent energy that corresponds to the classical MM energy and the extra one-electron potential that takes account of the interface effects. This QM/MM method is free from the double-counting problem and the artificial truncation of the localized molecular orbitals. As a numerical example we determine the one-electron effective Hamiltonian of the methyl group. This effective Hamiltonian is applied to the ethane and CH(3)CH(2)X molecules (X=CH(3), NH(2), OH, F, COOH, NH(3) (+), OH(2) (+), and COO(-)). It reproduced the relative energies, potential energy curves, and the Mulliken populations of the all-electron calculations fairly well.