Conduction and Transmittance in Molecular Devices A. Prociuk, Y. Chen, M. Shlomi, and B. D. Dunietz GF based Landauer Formalism 2,3 Computing lead GF 4,5 Conductance Switching Properties of Molecular Devices 6 Molecular conductance reduction upon excitation of the spin state of Fe(II)-Porphyrins. Further reduction due to doming effect. Au Citations 1 Q-Chem 2.0: A high-performance ab initio electronic structure program, J. Kong et. al., J. Comput. Chem. (2000) 21, S. Datta, Electronic Transport in Mesoscopic Systems. Cambridge Studies in Semiconductor Physics and Microelectronic Engineering: 3. Ed. H. Ahmed, M. Pepper, A. Broers. (New York: Cambridge University Press, 1995). 3 Y. Xue, S. Datta, M. A. Ratner, Chem. Phys. 281 (2002) S. Ke, H. U. Baranger, W. Yang, Phys. Rev. B 70 (2004) M. P. Lopez Sancho, J. M. Lopez Sancho, J. Rubio, J. Phys. F: Met. Phys. 14 (1984) Y. Chen, B. D. Dunietz, Porphyrin Ligating Fe(II) as a Molecular Electrical Switch based on different spin coupling states – An ab-initio study, (submitted for publication 2005) 7 N. D. Lang, P. H. Avouris, Phys. Rev. Lett. 84 (2000) N. D. Lang, Ph. Avouris, Phys. Rev. Lett. 81 (1998) Electrical Devices Composed of Single molecules Model Calculations: Molecular Wire 7,8 The structure is a device (C) sandwiched between two semi- infinite metallic gold leads (L,R). If a bias, V, is placed across the leads (and charge flows through the molecule), what will the current, I, be? I L RC V Inputs: one electron Hamiltonian (H) and overlap (S) matrices. Parse H and S, into device and lead regions (lead- lead Interactions are neglected). Landauer formalism describes the current passing through the device in terms of transmittance. GF methodology casts the transmittance in terms of a Green function / Self Energy picture: GOAL: Implement TDDFT / NEGF descriptions. Objectives Goal: Model transmittance and I-V properties of molecular systems Methodology (Landauer description 2,3 ): Implement TDDFT and non SC-NEGF 4 methods Modeling: Self-energy convergence and reliability Applications: – Iron-Porphyrin as molecular switch or spin-valve 6. – Customized tunnel junctions for highly efficient sensors. C Au Model structure calculations performed on a C 6 linear chain (shown left) connected at each end to an Au 24 linear chain to model the leads. The resulting chain was collinear. - Au-Au = 2.88 A (distance between two Au atoms in the (110) direction. - C-C = 1.3 A 7,8 - Au-C = A (calculated by unconstrained geometry optimization on a C6 chain with one Au attached to each end). How long must the modeled gold leads be before they approximate infinite leads? Does convergence depend on the method used to calculate the bulk GF? Does convergence depend on whether a given number of Au atoms are included in the device (C) ? NOTE: All geometry optimizations and single point calculations of the necessary Hamiltonian were performed with QChem using DFT with a B3LYP functional and correlation term and LANL2DZ basis set. L R C Two parameters were varied in the GF calculations: (1) The number, M, of Au atoms included on each side of the C 6 chain as part of the device (C) (2) The number, N, of Au atoms in each lead used to determine the bulk GF. M and N are the same for both leads in calculations performed thus far. Notation: The notation used for Transmittance curves is T-24(M)-N, with M and N defined above. Observations: One should include at least two Au atoms on each side of the C 6 chain as a part of the device to see convergent behavior. Peak height oscillation observed in constant DOS model results (figure 1) when (a) M even or (b) M odd. This oscillation vanishes for N=1,2 when using tight binding model (figure 2). Constant DOS model for the bulk GF:  DOS for bulk Au near the fermi level is approximately constant (dominated by s-band): Tight-binding calculation for actual cluster model used:  Model periodicity of the bulk Hamiltonian by dividing it into sub-blocks  coupled by nearest neighbor interactions  : This leads to recursion relations of the form: Such relations can be iterated until self consistency is reached. Figure 1: Constant DOS ModelFigure 2: Tight Binding Model (a) (b) Use heterogeneous tunnel junctions for sensors based on optimized resonance in conductance upon exposure to analyte molecule. Effect of analyte molecule on the observed resonance / anti-resonance tunneling Applications Employing Conductance ModelingMethodologyApplications Define Converged Self-Energy Model Molecular switch Porphyrin based or other system Molecular Sensors based on specialized Tunnel junction NEGF implementations: use TDDFT (freq- domain) electronic- structure information Implement an active-space TDDFT formalism