Internal Control of Electron Transfer through a Single Iron Atom by

Article pubs.acs.org/JPCC

Internal Control of Electron Transfer through a Single Iron Atom by Chelating Porphyrin Nikolai Lebedev,*,† Igor Griva,‡ and Anders Blom§ †

Center for Bio-Molecular Science and Engineering, Naval Research Laboratory, Washington, DC 20375, United States Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030, United States § QuantumWise A/S, Lersø Parkallé 107, DK-2100 Copenhagen, Denmark ‡

S Supporting Information *

ABSTRACT: Construction of efficient and highly integrated electronic devices is the main challenge and goal of nanoelectronics. The main problem in the construction of such devices is the fusion between conducting and controlling parts of the device, substantially reducing the efficiency of regulation. To approach the problem we study the electron transfer through a carbon nanotube (CNT)-histidine-hemehistidine-CNT conjugate with an orthogonal porphyrin orientation relative to the CNT electrodes. Using density functional theory and nonequilibrium Green’s function calculations we show that at low bias the CNT molecular orbitals are electronically coupled only to the Fe atom but uncoupled from the tetrapyrrole ring of the porphyrin. We found that at low bias the electrons pass exclusively through the central Fe atom of the porphyrin, but at higher bias they are partially scattered by the tetrapyrrole ring, leading to a reduction of the total current through the molecule (negative differential resistance). This allows for keeping the electron flow through the device at a specific level and for controlling the current through the device by the redox state of the tetrapyrrole ring. In the orthogonal orientation, neither of the porphyrin side groups directly participates in the electron transfer through the heme and can thus be used for porphyrin binding and orientation to proteins or electrodes. These results open the possibility for the construction of a highly integrated electronic field effect transistor in a single molecule with controllable electron transfer through individual iron atoms. tetrapyrrole ring in the plane of the molecule.5b,7 Meanwhile, in biological systems the orientation of the porphyrin ring is often normal or nearly perpendicular to the main pathway of the electron transfer.4a,8 The effect of this orientation is unknown. Single atomic nanowires, consisting particularly of Fe atoms, have received increasing attention as possible components of molecular memory and particularly in spintronic devices.9 But without an external magnet the spin transfer through them is difficult to control. Attachment of a tetrapyrrole ring to the Fe atom as in heme-porphyrins could open a possibility for using the internal spin−orbital coupling to control the metal spin state by the tetrapyrrole ring. To evaluate the possibility of the construction of highly integrated single molecular electronic devices with well separated electron transfer and controlling functions, we consider a device composed of an iron-containing porphyrin placed between two carbon nanotube (CNT) electrodes and calculate the electron transfer properties of the CNT− porphyrin conjugate with an orthogonal porphyrin orientation

1. INTRODUCTION Most of the molecular electronic devices developed up to now use for switching their conductivity an external gate electrode (structurally separated from the nanowire) connected to the device through air or a conductive electrolyte.1 Though several exciting results have been demonstrated for these devices, the general perturbation of the nanowire through air or the electrolyte is nonlocal, nonspecific, and slow. In addition, the control of the source-drain electron transfer (ET) by the redoxactive chemical groups located in the main ET path inside the nanowire leads to a substantial source-gate current leakage,1,2 reducing the total device efficiency. For more efficient operation, integrated multifunctional single molecular electronic devices are instead needed.2,3 Porphyrins are the main ET components developed by nature for all living organisms, where they serve as effective redox mediators and ET regulators.4 Porphyrins composed of tetrapyrrole rings have a highly delocalized electronic structure and a metal atom (particularly, Fe) in the center. The strong electron delocalization within the tetrapyrrole ring reduces the band gap and allows for easy and reversible charging.5 Though porphyrins are widely studied as potential components of nanoelectronic devices,6 they have been considered mainly for their ability of channeling electron transfer through the © 2013 American Chemical Society

Received: November 27, 2012 Revised: March 11, 2013 Published: April 1, 2013 6933

dx.doi.org/10.1021/jp311686c | J. Phys. Chem. C 2013, 117, 6933−6939

The Journal of Physical Chemistry C

Article

relative to the direction of the electron flow. In these calculations we use an approach that combines density functional theory (DFT) with nonequilibrium Green’s function (NEGF). Our calculations show that at low bias the CNT molecular orbitals (MOs) are efficiently electronically coupled to the Fe atom, but spatially and energetically uncoupled from the tetrapyrrole ring of the porphyrin. That allows for the controlling of electron transfer through the CNT-His-Fe-HisCNT path by the redox state of the tetrapyrrole ring, which operates as an internal gate without gate current leakage. This approach opens up possibilities for the construction of new highly integrated molecular electronic devices with various functionalities. The peripheral side groups of the porphyrin do not participate in the electron transfer and can be used for the device direct chemical attachment to another electrode or a protein.

in the central scattering region, which includes the His-HemeHis conjugate and six layers of carbon atoms near each electrode. ΓL and ΓR are broadening matrices, which describe the strength of the coupling of the electrodes to the conducting scattering region. They are calculated as the imaginary parts of the self-energy matrices of the left and right electrodes. The Fermi level in case of a finite bias voltage is the average of the electrochemical potentials of two electrodes. We use the total transmission spectrum and the density of states to interpret the conductance properties of our systems. The effective potential was calculated by using the Kohn−Sham approach. The calculations were performed in vacuum at a temperature of 300 K with periodic boundary conditions in a box measuring 24 × 24 Ǻ in the plane perpendicular to the nanotubes.

3. RESULTS AND DISCUSSION Electronic Structure of Histidine-Fe-Porphyrin-Histidine Conjugate. The optimized molecular structure and frontier molecular orbitals (MOs) of the His-Heme-His conjugate are shown in Figure 1. The conjugate has a planar porphyrin configuration with an Fe atom in the center and two His facing the iron atom on both sides. Direct X-ray structural analyses of several crystallized cytochromes reveal similar structures in which both His are oriented perpendicular to the porphyrin ring.13 The calculated

2. METHODS Molecular and electronic structure optimizations of the hemeHis conjugate (with six coordinated Fe) were performed with Gaussian0910 using a DFT approach with a nonlocal exchangecorrelation functional comprised of Becke’s three-parameter exchange functional and the Lee−Yang−Parr correlation functional (B3LYP) with a 6-31G(d) basis set.11 The structure of the conductive (3,3) CNT was taken from Quantum Wise’s12 molecular library, cleaved and capped at the scattering region. Then the tubes were separated by the distance corresponding to the size of the Heme-(His)2 conjugate that was inserted between them. The structure of the total complex was then optimized in Z direction (along the tubes) until the forces on all atoms were lower than 0.03 eV/Ǻ , and the calculations of density of states (DOS), energy spectrum, electron transmission spectrum, eigenstates, and transmission pathways were performed. The eigenstates and pathways were also calculated for an iron-containing CNT-HisFe-His-CNT complex, obtained by removing the tetrapyrrole part from the optimized CNT-His-Heme-His-CNT structure. For the calculation of ET properties we use the NEGF approach implemented in Atomistix ToolKit.12 This code uses a linear combination of atomic orbitals (LCAO) of the SIESTA type as basis set. In our calculations we use a double-ζ basis set with polarization orbitals and the generalized gradient approximation (GGA) as parametrized by Perdew−Burke− Ernzerhof (PBE) for the exchange correlation functional. For the electronic transport calculations, the system is initially divided into three regions, namely, the right and left electrodes and a central scattering region. The electrodes for the system are taken as semi-infinite repetitions of the carbon nanotube. The current was calculated for a range of applied bias voltages using the Landauer−Büttiker formula, I (V ) =

∫ T(E , V )[nf (E − μL ) − nf (E − μR )] dE

where nf is the temperature-dependent Fermi function and μL and μR are the electrochemical potentials of the left and right electrodes, respectively. The total transmission at each energy is given by T (E , V ) = Tr[ΓLG ΓR G+]

where we note that the transmission probability is a function of both energy and the applied bias for each converged DOS of the entire system. G and G+ are the retarded and advanced Green’s functions, which describe the dynamics of the electrons

Figure 1. Optimized structure (A) and frontier orbitals (B and C) of His-Heme-His conjugate viewed at different orientations of the porphyrin ring. 6934



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Figure 2. Central panel: ET spectrum for CNT-His-Heme-His-CNT (red) and CNT-His-Fe-His-CNT (green). Left and right panels show spatial distribution of the eigenfunctions of the main transmission bands. The structure of the device is shown below the graph. The numbers at the images and in the graph indicate energies (in eV, relative to Fermi). Source-drain voltage = 0 V.

It is interesting to note that, in the heme, neither the frontier MOs nor other orbitals close to them in energy spread outside of the central part of the molecule, and neither of them have components localized on the porphyrin peripheral groups. This opens the possibility for various modification, substitution, and even elimination of the porphyrin side groups without affecting the heme frontier electronic structure and the corresponding ET properties. One of the practical consequences of this is the possibility of using them for heme binding to peptides, proteins, or electrodes. Electron Transmission Spectrum and Local Density of States of CNT-Histidine-Heme-Histidine-CNT Complex. The electron transmission spectrum of the CNT-His-HemeHis-CNT complex at zero source-drain bias potential is shown in Figure 2. It has three strong bands close to the Fermi level and several other bands below them. The eigenstates of the three transmission bands around the Fermi level are totally delocalized between the two carbon tubes and the iron, while for the other bands the eigenstates are localized on the porphyrin ring (Figure 2). To identify the role of iron in the formation of the described transmission bands we also calculate the ET spectrum for a CNT-His-Fe-His-CNT complex. This complex is similar to the

highest occupied molecular orbital (HOMO) of the conjugate is localized exclusively on the porphyrin ring and does not include electrons from iron or the histidines (Figure 1). On the other hand, the lowest unoccupied molecular orbital (LUMO) is delocalized between the two His and iron in the tetrapyrrole ring and only weakly interacts with tetrapyrrole. Since MO delocalization is the main parameter determining the efficiency of ET through the molecule,14 the LUMO delocalization between His and Fe indicates the possibility for efficient ET through this MO in the direction perpendicular to the porphyrin ring. The atomic charge distribution in the conjugate can be seen from a Mulliken population analysis. It shows that the positive charge is mainly localized on the Fe atom, and the negative charges are more or less homogeneously distributed over the tetrapyrrole nitrogens (see Supporting Information, Table S1). The heme oxidation increases the conjugate dipole moment, indicating substantial asymmetry of the charge distribution. Also, the optimized structure shows a slight squeezing of the histidines and pyrroles toward the iron, resulting in a slight reduction of the Fe-His(N) and Fe-POR(N) bond lengths in the oxidized state. 6935



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Figure 3. (A) DOS projected to Fe atom (red curve) and to the conjugated tetrapyrrole ring (blue cureve). (B and C) Atoms used for the projected DOS computation (shown in green). Source-drain voltage = −0.9 V.

previous one, but is lacking the porphyrin ring. This structure only has bands around the Fermi level, and their positions and relative intensities are very similar to those obtained for CNTHis-POR-His-CNT (Figure 2). The absence of the porphyrin ring in CNT-His-Fe-His-CNT leads only to some narrowing of the main iron bands. No other significant bands below them are present without the porphyrin ring. Further confirmation of the spatial localization of the bands in the CNT-His-POR-His-CNT ET spectrum comes from the analysis of the projected density of states (DOS). At sourcedrain bias voltage 0.9 V the DOS projected to Fe has three wellresolved bands around the Fermi level while the bands below have lower intensity (Figure 3). On the other hand, the DOS bands projected onto the atoms participating in the formation of the tetrapyrrole ring are very weak at the Fermi level but much stronger below it. Thus, in a good agreement with the prediction made from the analysis of the MO spatial distribution in the His-Heme-His conjugate, the CNT-His-POR-His-CNT complex has two main functional parts responsible for ET; one, corresponding to the LUMO in the isolated conjugate, spreads throughout the CNT, His, and Fe, while the other, corresponding to the HOMO, localizes on the tetrapyrrole part of the heme. Since neither of the eigenstates in the studied energy range goes outside of the tetrapyrrole ring, neither of the porphyrin side groups seems to be involved in the ET. Electron Transmission Pathways and I−V Curve. Calculation of the spatial distribution of the electrostatic difference potential shows that the identified two parts of the complex, corresponding to CNT-His-Fe-His-CNT and the porphyrin ring, respectively, are energetically isolated (Figure 4). The barrier between them can reach 1.5 eV. Thus at least at

Figure 4. Profile of the spatial distribution of electrostatic difference potential in CNT-His-Heme-His-CNT complex. Source-drain voltage = −0.9 V.

bias voltages below 1.5 V the ET through the complex should go mainly through CNT-His-Fe-His-CNT without interfering with the tetrapyrrole ring. Direct calculation of ET pathways for the main transmission bands confirms this (Figure 5). Indeed, for the three transmission bands around the Fermi level, the main pathway goes through His and Fe, while the pathway for the bands at lower energies involves scattering to the tetrapyrrole ring. One 6936



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Figure 5. ET paths for eigenstates at +0.37, +0.05, −0.38, and −1.28 eV (the arrow thickness indicates ET efficiency, color shows direction (blue arrow = from left to right; red arrow = opposite). Source-drain voltage = −0.9 V.

of the interesting results of the ET pathway calculation is in the possibility of some circulation of electrons in the porphyrin ring, well seen for the transmission band at −0.38 eV (Figure 5). This circulation is totally perpendicular to the direction of the electron transfer between the CNTs and thus cannot contribute to the charge transfer. One of the possible origins of this circulation might be current-induced generation of a magnetic field around it. The calculation of the current through CNT-His-Heme-HisCNT at various source-drain bias voltages reveals an enhanced conductance at 0, 0.45, and 1.6 V bias (Figure 6), consistent with the positions of the bands in the ET spectrum (Figure 7). The current−voltage curve also has the expected shape (Figure 6). In addition, the analysis of the I−V curve reveals a decrease in the current through the device (negative differential resistance, NDR,15 at about 1 V. The onset of this decrease coincides with the beginning of electron scattering to the tetrapyrrole ring, indicating that the charging of the tetrapyrrole ring might be the origin of the NDR. It seems that the

Figure 6. Conductance (dashed curve) and current−voltage dependence (solid curve) for the CNT-His-Heme-His-CNT device.

tetrapyrrole part of the porphyrin is not passive, but instead it acts as an active component of the molecule that restricts (focuses) the electron current into the iron atom. This opens the possibility for controlling the current through the device by 6937



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ASSOCIATED CONTENT

S Supporting Information *

Atomic charges in His-Heme-His conjugate. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

* E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the support of this work by the Air Force Office of Scientific Research and the Office of Naval Research through the Naval Research Laboratory base program.

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REFERENCES

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Figure 7. ETS of CNT-His-Heme-His-CNT complex. The numbers at the bands and in the panels indicate their energies (in eV, relative to Fermi). Source-drain voltage = −0.9 V.

the redox state of the tetrapyrrole ring. In this respect it is interesting that our (see above) and other authors’ Mulliken population analyses show that in both the reduced and the oxidized states of the heme, the extra electrons are localized mainly at the tetrapyrrole ring (see Supporting Information, Table S1). In addition, the restriction of the electron transfer path to the iron atom allows for spin-selective control of the electron transfer through the device. Since no porphyrin side groups are directly involved in the electron transfer, they can be used to obtain a correct heme binding and orientation relative to the direction of electron flow in proteins (and other) scaffolds. It is important to note that in our consideration presented here we do not take into account the effect of solvent. Though very important if the direct electron transfer is impossible,14b the conductivity through surrounding solvent has minute contribution compared to the direct electron transfer through the delocalized MO of conjugated systems, like CNT or polypyrroles.16

4. CONCLUSION In conclusion, our results indicate that in the orthogonal heme orientation, electrons flow through the molecule mainly at the Fe atom. The heme can control the rate of electron transfer through the iron by charging the tetrapyrrole ring. Neither of the porphyrin side groups directly participates in the electron transfer and thus can be used for specific heme binding and orientation inside the protein or to the electrodes. These results open the possibility for the construction of a highly integrated electronic field effect transistor in a single molecule with controllable electron transfer through individual iron atoms. 6938



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Internal Control of Electron Transfer through a Single Iron Atom by

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