^{1}and M. Ernzerhof

^{1,a)}

### Abstract

For molecular conductors, the source-sink potential (SSP) model provides a simple tool for the calculation of the electron transmission probability. Recently, the SSP method has been combined with graph theory, and criteria have been established under which two different molecular electronic devices yield identical transmission probabilities. Since these criteria have been arrived at within the Hückel approximation, we investigate the validity of these criteria by performing combined Kohn–Sham and Green’s function calculations for the transmission probability. We find that some systems, predicted to be equiconducting at the Hückel level, are approximately equiconducting at the nonempirical level while others are not. An explanation for the obtained discrepancies is proposed.

This work is supported by NSERC. We thank F. Goyer, X. Wang, and P. Rocheleau for helpful discussions. Furthermore, we also would like to express sincere thanks to F. Jiang for his contributions to the computer program for the conductance calculations.

I. INTRODUCTION

II. ISOSPECTRALITY WITHIN THE SSP-HÜCKEL METHOD

III. KOHN–SHAM THEORY COMBINED WITH THE GREEN’S FUNCTION APPROACH TO THE TRANSMISSION PROBABILITY

IV. EXAMINING EQUICONDUCTANCE IN SELECTED MOLECULES

V. TRANSMISSION PROBABILITIES CALCULATED WITH THE KOHN–SHAM GREEN’S FUNCTION METHOD

VI. THE ROLE OF THE MOLECULE-CONTACT INTERFACE

VII. CONCLUSION

### Key Topics

- Green's function methods
- 11.0
- Electrodes
- 6.0
- Gold
- 6.0
- Graph theory
- 6.0
- Electronic structure
- 5.0

## Figures

The molecules forming the central part of the MEDs considered. In all the systems, carbon atoms are hybridized to form a -electron system. As customary, hydrogen atoms are omitted. Molecules one (phenafulvene), two (ethylnaphthalene), and three (ethylphenanthrene) have equiconducting connections, i.e., they can be connected to the contacts in different ways while yielding the same (at the Hückel level). The pentalene derivatives (molecules four and five), if connected appropriately, also yield identical curves.

The molecules forming the central part of the MEDs considered. In all the systems, carbon atoms are hybridized to form a -electron system. As customary, hydrogen atoms are omitted. Molecules one (phenafulvene), two (ethylnaphthalene), and three (ethylphenanthrene) have equiconducting connections, i.e., they can be connected to the contacts in different ways while yielding the same (at the Hückel level). The pentalene derivatives (molecules four and five), if connected appropriately, also yield identical curves.

Phenafulvene connected through {4, 11} to gold electrodes. The electrodes are fcc(111) semi-infinite gold crystals of which only four layers are displayed. The sulfur atoms are placed above hollow sites of the contacts.

Phenafulvene connected through {4, 11} to gold electrodes. The electrodes are fcc(111) semi-infinite gold crystals of which only four layers are displayed. The sulfur atoms are placed above hollow sites of the contacts.

Transmission probabilities of MEDs derived from phenafulvene [ in Fig. 1]. In each plot, two connections are compared that are defined in the insert through points of matching color. The same color is used for the corresponding curve. The connections in the first plot are equiconducting at the Hückel level, whereas the others are not. In particular, close to the Fermi energy, the curves of the equiconductors are quite similar compared with the other pairs.

Transmission probabilities of MEDs derived from phenafulvene [ in Fig. 1]. In each plot, two connections are compared that are defined in the insert through points of matching color. The same color is used for the corresponding curve. The connections in the first plot are equiconducting at the Hückel level, whereas the others are not. In particular, close to the Fermi energy, the curves of the equiconductors are quite similar compared with the other pairs.

Current vs voltage curves of the MEDs derived from phenafulvene [ in Fig. 1]. The degree of similarity in of the different connections compared in Fig. 3 is reproduced in the curves. Connections {5,9} and {4,11} are equiconducting at the Hückel level.

Current vs voltage curves of the MEDs derived from phenafulvene [ in Fig. 1]. The degree of similarity in of the different connections compared in Fig. 3 is reproduced in the curves. Connections {5,9} and {4,11} are equiconducting at the Hückel level.

Transmission probabilities of the MEDs derived from ethylnaphthalene [ in Fig. 1]. In each plot, two connections are compared. The pairs of connections in the first and second plot are equiconducting at the Hückel level, whereas the others are not.

Transmission probabilities of the MEDs derived from ethylnaphthalene [ in Fig. 1]. In each plot, two connections are compared. The pairs of connections in the first and second plot are equiconducting at the Hückel level, whereas the others are not.

Transmission probabilities of the MEDs derived from ethylphenanthrene [ in Fig. 1]. In each plot, two connections are compared. The pair of connections in the first plot is equiconducting at the Hückel level, whereas the others are not.

Transmission probabilities of the MEDs derived from ethylphenanthrene [ in Fig. 1]. In each plot, two connections are compared. The pair of connections in the first plot is equiconducting at the Hückel level, whereas the others are not.

Transmission probabilities of the MEDs constructed from pentalene derivatives [ and in Fig. 1]. Even though at the Hückel level these two MEDs are equiconducting, the KS-GF approach yields somewhat dissimilar curves.

Transmission probabilities of the MEDs constructed from pentalene derivatives [ and in Fig. 1]. Even though at the Hückel level these two MEDs are equiconducting, the KS-GF approach yields somewhat dissimilar curves.

Transmission probabilities of the ethylphenanthrene and ethylnaphthalene based MEDs. The molecule-contact distance is reduced from 4.1 to 2.6 Å (2.1 Å is shown in Figs. 5 and 6). In the case of ethylphenanthrene the differential effect of the approaching contacts is dramatic and destroys the similarities in the curves.

Transmission probabilities of the ethylphenanthrene and ethylnaphthalene based MEDs. The molecule-contact distance is reduced from 4.1 to 2.6 Å (2.1 Å is shown in Figs. 5 and 6). In the case of ethylphenanthrene the differential effect of the approaching contacts is dramatic and destroys the similarities in the curves.

## Tables

Isospectral vertices and isospectral pairs in graphs , , and .

Isospectral vertices and isospectral pairs in graphs , , and .

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