Smallest Electrical Wire Based on Extended Metal-Atom Chains Te-Wei Tsai, Qian-Rui Huang, Shie-Ming Peng, and Bih-Yaw Jin* Department of Chemistry and Center for Theoretical Sciences, National Taiwan UniVersity, Taipei, Taiwan, Republic of China ReceiVed: August 14, 2009; ReVised Manuscript ReceiVed: January 3, 2010 An ideal electrical wire needs not only good conductivity for its central conductor but also a surrounding insulating layer to protect its current from leaking. We show that the extended metal-atom chain is a promising candidate to be the smallest molecular electrical wire for future practical applications. The electron can move through core metals, while the internal current is insulated from outside by the surrounding π-conjugated functional group. Moreover, we also show the existence of unavoidable hidden pathways at each site to the electrodes in a nanoscaled quantum circuit. Nevertheless, the Kirchhoff’s junction rule still holds when the current inflow and outflow arising from the additional terms of the self-energies of contacts are included. It is an important issue to find potential single molecular wires that can be functional units of nanotransistors for electronic apparatus application. 1 The current understanding of the electron transfer through a single molecular wire is mainly built on organic molecules with and without π-electron conjugated systems. 2-4 People have realized that in order to reach high conductivity the delocalized electrons in the bridge are needed to play the role of charge transfer. Pure organic molecules such as oligo(phenylene ethynylene) (OPE) 5 and oligo(phenylene vinylene) (OPV) 6 are often discussed for their long π-conjugated chains. However, in the fabrication of nanodevices, it is unavoidable to have multiple molecular wires packed in proximity. The wave function of one conductor can mix with the other through the overlap of electron clouds, which may result in the unwanted transversal hopping of charge carriers. In view of this, one-dimensional metal string complexes 7 can be a promising candidate without the above problem. Extended metal-atom chain (EMAC) complexes consist of a central metal-containing backbone and four specifically designed polydentate ligands. The use of the poly(pyridylamine) ligand with a flexible 1D metal chain developed individually by Cotton and Peng has led to the isolation of metal chains with 3-9 metal atoms. 7 Structurally, the EMAC is possibly the smallest version of an ordinary electrical wire that one can synthesize. In this article, we focus on the conductive properties of the trinuclear compound of the type, [M 3 (μ 3 -dpa) 4 (NCS) 2 ] (M ) Cr, Co, Ni; dpa ) syn-syn-bis(R-pyridyl)amido) (see Figure 1). Experimen- tally, these mixed-valence stacks of organic as well as inorganic molecules exhibit unusual electrical properties. 8-10 Bond orders for the symmetric and neutral complexes of nickel, cobalt, and chromium are 0, 0.5, and 1.5, which indicate the degree of the electron delocalization and thus the efficiency of the electron transfer through metal centers. 8,11 To calculate the electron-transfer properties, we use the code Hu ¨ ckel IV 3.0, 12 which is based on the nonequilibrium Green’s function (NEGF) formalism. The influence of the outside effect (contact) is incorporated into the main body of the device through self-energy matrices. 13,14 The Hamiltonian of the system is constructed in the extended Hu ¨ ckel theory and obtained from the YAeHMOP, 15 in which the orbital asymmetry parameter is used to take care of the counterintuitive orbital mixing. 16 We assume that the molecule is connected to the surface (111) of gold atoms with the separation 1.905 Å. 17 The whole system has been reduced to an “extended molecule” including the molecule itself and three connected gold atoms on each metal surface, to account for the molecular adsorption. We adopt the Landauer-Bu ¨ttiker formalism 13,14 which includes the effect of the phase-breaking arising from the interaction of electrons with the surrounding bath. The CNDO (complete neglect of dif- ferential overlap) 18,19 method is used for the calculation of the self-consistent potential 12 at nonzero bias. While most of studies focus on the total differential conduc- tance and I-V characteristics of single molecules, we investigate the internal loop currents 20,21 with an emphasis on the role of multiple pathways in EMACs. The internal current per unit energy between neighboring sites i and j is given by 13,14 where ψ i is the wave function at the site i, F is the Fock matrix, the correlation function G n is G n ) G(Γ 1 f 1 + Γ 2 f 2 )G † , and G is the retarded Green’s function, G ) (ES - F - Σ 1 - Σ 2 ) -1 . Γ 1(2) ) i(Σ 1(2) - Σ 1(2) † ) represents the broadening of energy levels for the introduction of electrodes, in which the self-energy of the left (right) electrode Σ 1(2) is numerically calculated in a recursive way. 22 f 1(2) (E) ) [1 + exp((E - μ 1(2) )/k B T)] -1 is the Fermi distribution function of the left (right) electrode. The chemical potential is μ 1(2) ) E f - 1/2eV at the applied bias, V, * To whom correspondence should be addressed. E-mail: byjin@ ntu.edu.tw. Figure 1. Model for the EMAC bridge connecting with Au electrodes. Central metals can be Cr, Co, and Ni. The organic functional group, dpa ) syn-syn-bis(R-pyridyl)amido), protects core metals from the outside. The internal current on the marked M-N bond (*) flows through ligands rather than the central bridge and will be discussed later. i ij (E) ) 4e p Im[ψ i *F ij ψ j ] ) 4e h Im[F ij G ij n (E)] (1) J. Phys. Chem. C 2010, 114, 3641–3644 3641 10.1021/jp907893q  2010 American Chemical Society Published on Web 02/04/2010