### Abstract

In order to investigate the magnetic properties of transition metal salts, we have developed the open shell single determinant Hartree - Fock SCF molecular orbital method for transition metal ion complexes. This cluster approach removes many of the shortcomings of earlier treatments^{1} and, in principle, provides a framework for obtaining fairly accurate and meaningful results within the single determinant approximation. These wave functions thus provide a realistic basis set for configuration interaction calculations of superexchange and other properties. By choosing a special one-center basis set for the cluster, we are able to compute all matrix elements of the molecular Hamiltonian accurately including the effects of the crystal field external to the cluster. Furthermore, the computation is sufficiently fast so that we may include all electrons of the molecular cluster while allowing considerable variational freedom in all representations. Detailed self-consistent field calculations have been made using, as example, KNiF_{3}, the antiferromagnetic Perovskite treated extensively by previous workers. ^{1} By considering a NiF_{6}^{4-} cluster in its crystalline environment, the crystal field splitting parameter 10 Dq is found to be in fairly good agreement with experiment, but sensitive to a number of factors. The resulting molecular orbitals are compared with those obtained by earlier LCAO calculations. While the radial distributions are quite reasonable, the limitations imposed on these first calculations with this one-center method are apparent; the restriction to low angular momentum in the basis sets used leads to a poor description of ligand core orbitals. Spin densities throughout the cluster have been computed; neutron magnetic form factors have been calculated for comparison with experiment. In agreement with earlier work ^{2} based on a single parameter LCAO scheme, we find that the cluster spin density gives a large peak in the form factor near zero scattering angles compared with the Ni^{2+} free ion result. This peak is seen to arise from the e_{g} spin density on the ligand sites; the spin density from all the remaining molecular orbitals, unpaired by exchange polarization, is found to be small (≈2%). The limitations imposed by the restricted basis set used have led us to consider a triatomic system, Ni_{2}F, as the cluster for the calculation of F^{19} hyperfine interactions. While the calculated isotropic hyperfine term was found to be too large relative to experiment, the computed anisotropic hyperfine interaction agreed (surprisingly) well. A full report will be submitted to the Physical Review.

Original language | English |
---|---|

Pages (from-to) | 1051 |

Number of pages | 1 |

Journal | Journal of Applied Physics |

Volume | 38 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1967 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

_{3}.

*Journal of Applied Physics*,

*38*(3), 1051. https://doi.org/10.1063/1.1709481

**Open-shell Hartree - Fock molecular orbital theory of transition metal ion complexes : KNiF _{3}.** / Ellis, D. E.; Freeman, Arthur J; Ros, P.

Research output: Contribution to journal › Article

_{3}',

*Journal of Applied Physics*, vol. 38, no. 3, pp. 1051. https://doi.org/10.1063/1.1709481

}

TY - JOUR

T1 - Open-shell Hartree - Fock molecular orbital theory of transition metal ion complexes

T2 - KNiF3

AU - Ellis, D. E.

AU - Freeman, Arthur J

AU - Ros, P.

PY - 1967

Y1 - 1967

N2 - In order to investigate the magnetic properties of transition metal salts, we have developed the open shell single determinant Hartree - Fock SCF molecular orbital method for transition metal ion complexes. This cluster approach removes many of the shortcomings of earlier treatments1 and, in principle, provides a framework for obtaining fairly accurate and meaningful results within the single determinant approximation. These wave functions thus provide a realistic basis set for configuration interaction calculations of superexchange and other properties. By choosing a special one-center basis set for the cluster, we are able to compute all matrix elements of the molecular Hamiltonian accurately including the effects of the crystal field external to the cluster. Furthermore, the computation is sufficiently fast so that we may include all electrons of the molecular cluster while allowing considerable variational freedom in all representations. Detailed self-consistent field calculations have been made using, as example, KNiF3, the antiferromagnetic Perovskite treated extensively by previous workers. 1 By considering a NiF64- cluster in its crystalline environment, the crystal field splitting parameter 10 Dq is found to be in fairly good agreement with experiment, but sensitive to a number of factors. The resulting molecular orbitals are compared with those obtained by earlier LCAO calculations. While the radial distributions are quite reasonable, the limitations imposed on these first calculations with this one-center method are apparent; the restriction to low angular momentum in the basis sets used leads to a poor description of ligand core orbitals. Spin densities throughout the cluster have been computed; neutron magnetic form factors have been calculated for comparison with experiment. In agreement with earlier work 2 based on a single parameter LCAO scheme, we find that the cluster spin density gives a large peak in the form factor near zero scattering angles compared with the Ni2+ free ion result. This peak is seen to arise from the eg spin density on the ligand sites; the spin density from all the remaining molecular orbitals, unpaired by exchange polarization, is found to be small (≈2%). The limitations imposed by the restricted basis set used have led us to consider a triatomic system, Ni2F, as the cluster for the calculation of F19 hyperfine interactions. While the calculated isotropic hyperfine term was found to be too large relative to experiment, the computed anisotropic hyperfine interaction agreed (surprisingly) well. A full report will be submitted to the Physical Review.

AB - In order to investigate the magnetic properties of transition metal salts, we have developed the open shell single determinant Hartree - Fock SCF molecular orbital method for transition metal ion complexes. This cluster approach removes many of the shortcomings of earlier treatments1 and, in principle, provides a framework for obtaining fairly accurate and meaningful results within the single determinant approximation. These wave functions thus provide a realistic basis set for configuration interaction calculations of superexchange and other properties. By choosing a special one-center basis set for the cluster, we are able to compute all matrix elements of the molecular Hamiltonian accurately including the effects of the crystal field external to the cluster. Furthermore, the computation is sufficiently fast so that we may include all electrons of the molecular cluster while allowing considerable variational freedom in all representations. Detailed self-consistent field calculations have been made using, as example, KNiF3, the antiferromagnetic Perovskite treated extensively by previous workers. 1 By considering a NiF64- cluster in its crystalline environment, the crystal field splitting parameter 10 Dq is found to be in fairly good agreement with experiment, but sensitive to a number of factors. The resulting molecular orbitals are compared with those obtained by earlier LCAO calculations. While the radial distributions are quite reasonable, the limitations imposed on these first calculations with this one-center method are apparent; the restriction to low angular momentum in the basis sets used leads to a poor description of ligand core orbitals. Spin densities throughout the cluster have been computed; neutron magnetic form factors have been calculated for comparison with experiment. In agreement with earlier work 2 based on a single parameter LCAO scheme, we find that the cluster spin density gives a large peak in the form factor near zero scattering angles compared with the Ni2+ free ion result. This peak is seen to arise from the eg spin density on the ligand sites; the spin density from all the remaining molecular orbitals, unpaired by exchange polarization, is found to be small (≈2%). The limitations imposed by the restricted basis set used have led us to consider a triatomic system, Ni2F, as the cluster for the calculation of F19 hyperfine interactions. While the calculated isotropic hyperfine term was found to be too large relative to experiment, the computed anisotropic hyperfine interaction agreed (surprisingly) well. A full report will be submitted to the Physical Review.

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U2 - 10.1063/1.1709481

DO - 10.1063/1.1709481

M3 - Article

VL - 38

SP - 1051

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 3

ER -