Semiempirical local spin: Theory and implementation of the ZILSH method for predicting Heisenberg exchange constants of polynuclear transition metal complexes

Abstract

ABSTRACT:The local spin formalism (Clark, A. E.; Davidson, E. R. J Chem Phys 2001, 115, 7382-7392) for computing expectation values ͗S A ⅐ S B ͘ that appear in the Heisenberg spin model has been extended to semiempirical single determinant wave functions. An alternative derivation of expectation values in restricted and unrestricted cases is given that takes advantage of the zero differential overlap (ZDO) approximation. A formal connection between single determinant wave functions (which are not in general spin eigenfunctions) and the Heisenberg spin model was established by demonstrating that energies of single determinants that are eigenfunctions of the local spin operators with eigenvalues corresponding to high-spin radical centers are given by the same Heisenberg coupling constants { J AB } that describe the true spin states of the system. Unrestricted single determinant wave functions for transition metal complexes are good approximations of local spin eigenfunctions when the metal d orbitals are local in character and all unpaired electrons on each metal have the same spin (although spins on different metals might be reversed). Good approximations of the coupling constants can then be extracted from local spin expectation values ͗S A ⅐ S B ͘ energies of the single determinant wave functions. Once the coupling constants are obtained, diagonalization of the Heisenberg spin Hamiltonian provides predictions of the energies and compositions of the spin states. A computational method is presented for obtaining coupling constants and spin-state energies in this way for polynuclear ϩ , a priori predictions of the coupling constants yield a ground-state spin of zero, in agreement with variable-temperature magnetization data, and corroborate spin alignments proposed earlier on the basis of structural considerations. This demonstrates the potential of the ZILSH method to aid in understanding magnetic interactions in polynuclear transition metal complexes.

Electron tunneling in respiratory complex I

“…The Heisenberg spin Hamiltonian and the resulting spin states of polynuclear transition metal complexes computed with ZINDO agree well with the experimental data (24). ZINDO also reproduces the electronic absorption spectra of mononuclear and binuclear Fe/S clusters (25).…”

DFT Computational Rationalization of an Unusual Spin Ground State in an Mn12 Single‐Molecule Magnet with a Low‐Symmetry Loop Structure

“…The exchange constants were found by fitting calculated energies and spin couplings to the Heisenberg Hamiltonian. [19,20] Figure 1 (top). The dashed line separates the two S = 7/2 fragments that are coupled by the interactions between Mn1-Mn6' and Mn1'-Mn6; if these interactions are antiferromagnetic (negative J values), the resultant spin of the complete molecule is S = 7.…”

Spin polarization and annihilation for radicals and diradicals

“…(9) for the energy levels. If the Noodleman-Yamaguchi approach is applied to a UHF calculation on a molecule containing two spin centers, it might lead to the same result as spin projection [14,15]. For this to be true, it is sufficient that (i) the molecular orbitals (MOs) in the high and low M calculations differ only by spin flips, and (ii) there is no spin polarization so R is S A ϩ S B for both high and low M. With these assumptions, the average energy of the projected wave function will be given correctly by the Heisenberg Hamiltonian.…”