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*Ab initio* calculation of anisotropic magnetic properties of complexes. I. Unique definition of pseudospin Hamiltonians and their derivation

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10.1063/1.4739763

### Abstract

A methodology for the rigorous nonperturbative derivation of magnetic pseudospin Hamiltonians of mononuclear complexes and fragments based on *ab initio* calculations of their electronic structure is described. It is supposed that the spin-orbit coupling and other relativistic effects are already taken fully into account at the stage of quantum chemistry calculations of complexes. The methodology is based on the establishment of the correspondence between the *ab initio*wave functions of the chosen manifold of multielectronic states and the pseudospin eigenfunctions, which allows to define the pseudospin Hamiltonians in the unique way. Working expressions are derived for the pseudospin Zeeman and zero-field splitting Hamiltonian corresponding to arbitrary pseudospins. The proposed calculation methodology, already implemented in the SINGLE_ANISO module of the MOLCAS-7.6 quantum chemistry package, is applied for a first-principles evaluation of pseudospin Hamiltonians of several complexes exhibiting weak, moderate, and very strong spin-orbit couplingeffects.

© 2012 American Institute of Physics

Received 10 April 2012
Accepted 10 July 2012
Published online 13 August 2012

Acknowledgments: Liviu Ungur is post-doc of the Flemish Science Foundation (FWO) and gratefully acknowledges financial support from the Institute of Nanoscale Physics and Chemistry (INPAC) and Methusalem program of the KU Leuven. The authors thank Maarten Thewissen for his help with *ab initio* calculations of the cobalt complex.

Article outline:

I. INTRODUCTION

II. PSEUDOSPIN HAMILTONIANS OF MONONUCLEAR COMPLEXES FROM *AB INITIO* CALCULATIONS

A. Unique definition of pseudospin Hamiltonians

B. Explicitly correlated *ab initio* calculations of mononuclear complexes

III. THE PSEUDOSPIN

A. Zeeman pseudospin Hamiltonian

B. The sign of the main values of the *g*tensor

C. Example: *g*tensors of Dy(III) complexes

D. Example: *g*tensor of Yb(III) complex

IV. THE PSEUDOSPIN = 1

A. Zeeman pseudospin Hamiltonian

B. ZFS pseudospin Hamiltonian

C. Example: *g* and *D*tensors of a Ni(II) complex

D. Example: The ZFS and *g*tensors of U(IV) fragments in UO_{2}

V. HIGHER PSEUDOSPINS: IRREDUCIBLE TENSOR DESCRIPTION OF PSEUDOSPIN HAMILTONIANS

A. ITO decomposition of Zeeman and ZFS pseudospin Hamiltonians

1. Zeeman**g**tensors for arbitrary pseudospins

2. ZFS **D**tensors for arbitrary pseudospins

3. Symmetry aspects

B. Approximate definition of pseudospin for

C. Example: *D*, *g* and higher rank Zeemantensors for a high-spin Co(II) complex

VI. CONCLUSIONS

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2012-08-13

2014-04-23

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