Theoretical modeling of the electronic structure and exchange interactions in a Cu(II)Pc one-dimensional chain

Wei Wu, A. J. Fisher, and N. M. Harrison

Phys. Rev. B 84, 024427 – Published 18 July 2011

Abstract

We calculate the electronic structure and exchange interactions in a copper(II)phthalocyanine [Cu(II)Pc] crystal as a one-dimensional molecular chain using hybrid exchange density functional theory (DFT). In addition, the intermolecular exchange interactions are also calculated in a molecular dimer using Green’s function perturbation theory (GFPT) to illustrate the underlying physics. We find that the exchange interactions depend strongly on the stacking angle, but weakly on the sliding angle (defined in the text). The hybrid DFT calculations also provide an insight into the electronic structure of the Cu(II)Pc molecular chain and demonstrate that on-site electron correlations have a significant effect on the nature of the ground state, the band gap, and magnetic excitations. The exchange interactions predicted by our DFT calculations and GFPT calculations agree qualitatively with the recent experimental results on newly found $η$ -Cu(II)Pc and the previous results for the $α$ and $β$ phases. This work provides a reliable theoretical basis for the further application of Cu(II)Pc to molecular spintronics and organic-based quantum information processing.

Received 7 March 2011

DOI:https://doi.org/10.1103/PhysRevB.84.024427

Authors & Affiliations

Wei Wu^1,2,*, A. J. Fisher², and N. M. Harrison¹

¹Department of Chemistry and London Centre for Nanotechnology, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom
²UCL Department of Physics and Astronomy and London Centre for Nanotechnology, University College London, Gower Street, London, WC1E 6BT, United Kingdom

^*w.wu@imperial.ac.uk

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Issue

Vol. 84, Iss. 2 — 1 July 2011

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Images

Figure 1
Two neighboring Cu(II)Pc molecules from a side view and a top view to illustrate important geometrical parameters in the crystal structure. The atoms are color coded, i.e., copper in red, carbon in gray, nitrogen in blue, and hydrogen in white. The interplane distance is labeled as $d$ , the stacking angle $φ$ , and the sliding angle $ψ$ . The stacking axis is indicated by a black arrow connecting copper atoms. The vector $\vec{r}$ , and the $X$ and $Y$ axes are used to define the sliding angle, i.e., $\cos ψ = \hat{\vec{r}} \cdot \hat{\vec{X}}$ .Reuse & Permissions
Figure 2
The exchange interaction calculated using DFT as a function of the Cartesian coordinates $X$ and $Y$ . Notice that exchange interactions strongly depend on stacking angles (and hence on the distance from the center of the plot), but weakly on sliding angles, and peak at a stacking angle of $90^{\circ}$ with $4.78$ K.Reuse & Permissions
Figure 3
The band structure, DOS, and spin densities of AFM (left-hand column) and FM (right-hand column) configurations for $α$ -phase Cu(II)Pc are shown. In band structure the $d$ bands in spin up are highlighted in red, and spin down in blue. Notice that these bands are very narrow. In the DOS the spin up is displayed as positive and spin down as negative, and the PDOS is scaled by a factor of 5.0 to illustrate the singly occupied orbitals. The spin densities show the spin configurations in different calculations where spin up is in red and spin down in blue.Reuse & Permissions
Figure 4
The band structure, DOS, and spin densities of AFM (left-hand column) and FM (right-hand column) configurations for $β$ -phase Cu(II)Pc are shown. In band structure the $d$ bands in spin up are highlighted in red, and spin down in blue. Notice that these bands are very narrow. In the DOS the spin up is displayed as positive and spin down as negative, and the PDOS is scaled by a factor of 5.0 to illustrate the singly occupied orbitals. The spin densities show the spin configurations in different calculations where spin up is in red and spin down in blue.Reuse & Permissions
Figure 5
The band structure, DOS, and spin densities of AFM (left-hand column) and FM (right-hand column) configurations for $η$ -phase Cu(II)Pc are shown. In band structure the $d$ bands in spin up are highlighted in red, and spin down in blue. Notice that these bands are very narrow. In the DOS the spin up is displayed as positive and spin down as negative, and the PDOS is scaled by a factor of 5.0 to illustrate the singly occupied orbitals. The spin densities show the spin configurations in different calculations where spin up is in red and spin down in blue.Reuse & Permissions
Figure 6
Exchange interactions of Cu(II)Pc dimer calculated using perturbation theory as a function of the Cartesian coordinates $X$ and $Y$ . Notice that exchange interactions strongly depend on stacking angles, but weakly on sliding angles.Reuse & Permissions

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