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Towards the blackbox computation of magnetic exchange coupling parameters in polynuclear transition-metal complexes: Theory, implementation, and application
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10.1063/1.4802776
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Affiliations:
1 Science of Advanced Materials, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
2 Department of Physics, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
a) Author to whom correspondence should be addressed. Electronic mail: phill3jj@cmich.edu
J. Chem. Phys. 138, 174115 (2013)
/content/aip/journal/jcp/138/17/10.1063/1.4802776
http://aip.metastore.ingenta.com/content/aip/journal/jcp/138/17/10.1063/1.4802776

## Figures

FIG. 1.

(Left) Molecular scheme of [FeOCl], where Cl, O, and Fe atoms are colored green, red, and metallic gray, respectively. (Right) Löwdin spin populations for the zeroth-order z-component , first-order x-component , and the first-order rotation defined as . These results were obtained using LDA.

FIG. 2.

Schematic representation of blackbox approach to calculating couplings in polynuclear TM complexes, for the hypothetical case of a pentanuclear system. Here (a) indicates that the off-diagonal elements of the constraint Hessian grant directly the “off-terms” of the couplings, while (b) indicates that the remaining − 1 couplings are obtained by summing the respective columns of derivatives,

FIG. 3.

(a) Molecular scheme for the H–He “snowflake” model system, with H–He distance of 1.5 Å. By symmetry there are two unique magnetic coupling, and . (b) Zeroth-order spin-density. (c) First-order spin-density from a torque perturbation between H-1 and H-2. (d) First-order spin-density from a torque perturbation between H-1 and H-3. All spin-densities visualized here were obtained with LDA.

FIG. 4.

(Left) Molecular structure of the biomimetic trinuclear Mn complex. (Right-Top) perturbation Hessian, in units of Hartrees. (Right-Bottom) Constraint Hessian, in units of cm. These results were obtained using LDA+15%HFX.

FIG. 5.

(Left) Molecular structure of the ferromagnetic trinuclear Mn complex. (Right-Top) Perturbation Hessian, in units of Hartrees. (Right-Bottom) Constraint Hessian, in units of cm. These results were obtained using LDA+15%HFX.

FIG. 6.

(Left) Molecular structure of the tetranuclear Fe “ferric-star” complex. (Right-Top) Perturbation Hessian, in units of Hartrees. (Right-Bottom) Constraint Hessian, in units of cm. These results were obtained using LDA+15%HFX.

## Tables

Table I.

Comparison of magnetic coupling parameters calculated by spin-projected energy-differences ( ), and as calculated by our noncollinear coupled-perturbed method utilizing derivatives with respect to spin rotations ( and ). All couplings are in cm.

Table II.

Comparison of magnetic coupling parameters calculated by energy differences ( ), and as calculated by our noncollinear coupled-perturbed method utilizing derivatives with respect to spin rotations ( ), for the Hydrogen-Helium “snowflake” system (shown in Figure ). All couplings are in cm.

Table III.

Comparison of magnetic coupling parameters calculated by energy differences ( ), and as calculated by our noncollinear coupled-perturbed method utilizing derivatives with respect to spin rotations ( ), for the biomimetic trinuclear Mn complex (shown in Figure ). All couplings are in cm.

Table IV.

Comparison of magnetic coupling parameters calculated by energy differences ( ), and as calculated by our noncollinear coupled-perturbed method utilizing derivatives with respect to spin rotations ( ), for the ferromagnetic trinuclear Mn complex (shown in Figure ). All couplings are in cm.

Table V.

Comparison of magnetic coupling parameters calculated by energy differences ( ), and as calculated by our noncollinear coupled-perturbed method utilizing derivatives with respect to spin rotations ( ), for the tetranuclear Fe “ferric-star” complex (shown in Figure ). All couplings are in cm.

/content/aip/journal/jcp/138/17/10.1063/1.4802776
2013-05-07
2014-04-19

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