Organic Radicals As Spin Filters Carmen Herrmann,* Gemma C. Solomon,* and Mark A. Ratner Department of Chemistry, Northwestern UniVersity, EVanston, Illinois 60208 Received December 11, 2009; E-mail: c-herrmann@northwestern.edu; g-solomon@northwestern.edu With the trend toward miniaturization, the notion of molecules as building blocks in electronic devices 1 has gained increasing popularity since its introduction in 1974. 2 Over the past decade, molecular electronics has been combined with spintronics, 3 often employing nonmagnetic molecular bridges with magnetism intro- duced to the system via ferromagnetic electrodes or via circularly polarized light. 4 Another experimental approach to molecular spintronics is a magnetic molecule between, in general, nonmagnetic probes. These magnetic bridges typically contain metal atoms, 5 but recently, organic radicals have been investigated in gold nanoarrays 6 as well as in in electron transfer experiments. 7 Here, we carry out first-principles transport calculations on stable organic radicals 8,9 to test them for their properties as spin filters, i.e., as devices favoring transport of electrons with either spin up or spin down. We predict that the transport properties of benzene- based model radicals may differ to a sufficient extent for electrons of different spins to make them suitable candidates for such filters and that they may be tuned systematically by introducing additional substituents. Furthermore, the qualitative predictions made for our model systems are transferable to certain larger stable radicals. As in previous work on electron tunneling through magnetic molecular systems, 10 we assume that correlations between tunneling electrons and the unpaired spins on the molecule play a minor role. There is both theoretical and experimental work on the importance of spin flips in tunneling processes. 6,11 Our analysis only holds for situations in which spin flips can be neglected, and it is not entirely clear yet to which molecules and conditions this applies. This theoretical analysis of molecular transport properties in gold- molecule-gold junctions uses the Landauer-Imry approach 12 in combination with nonequilibrium Green’s functions (NEGF) 13 and spin-unrestricted Kohn-Sham density functional theory (UKS- DFT). 14 This approach 15 relates the current I s (V) for electrons of spin s ∈ {R,} to the transmission function T s (E, V), integrated over an energy (E) interval which we take to be centered at the system’s Fermi energy E F , with a width determined by the symmetrically applied bias voltage V, e is the unit charge, and h Planck’s constant. This relationship holds in the coherent tunneling regime, i.e., for low temperatures and short molecular bridges with a large separation between the one-particle energy levels and the Fermi energies of the electrodes (“off-resonant” conditions). Furthermore, the number of electrons on the molecule is assumed to be constant in time. The zero-voltage differential conduc- tance may be estimated from the transmission at E F . In the NEGF approach, T s is calculated from a trace over matrices describing the coupling of a central region 16 to the left and right electrodes, Γ L/R,s , and the central system subblock of the retarded and advanced Green’s functions of the electrode-molecule-electrode system G C,s r/a , 17 the advanced Green’s function being the complex conjugate of the retarded. Γ X,s and G C,s r are calculated from the overlap and Fock matrices of a finite-cluster electrode-molecule-electrode system, The Fock and overlap matrices of the electrode-molecule-electrode system are divided into central, left-electrode, and right-electrode regions. S XC and H XC,s denote the coupling block of electrode X and molecule in the overlap and Fock matrix, respectively, while the molecule (or “central region”) subblocks of these matrices are indicated by the subscript C. The Green’s function matrices g X,s of the isolated, infinite electrodes are described in the wide-band-limit approximation (see Supporting Information (SI)) and are not taken to be spin polarized. To construct the finite-cluster system, the structures of the dithiol molecules were optimized, the thiol hydrogen atoms were removed, and the molecules were placed between two Au 9 clusters mimicking hollow site adsorption on Au(111) surfaces, with a sulfur-gold distance from a previous DFT Figure 1. R (majority spin) and  (minority spin) transmission calculated for meta- (left) and para-connected (right) model structures with various radical centers X in the doublet state. Closed-shell structures with an H atom added are given as a reference (bottom). B3LYP/LANL2DZ. I s (V) ) e h ∫ E F - eV 2 E F + eV 2 dET s (E, V) (1) T s (E, V) ) tr(Γ R,s G C,s r Γ L,s G C,s a ) (2) Γ X,s )-2Im[(ES XC - H XC,s ) † g X,s (ES XC - H XC,s )] (3) G C,s r ) ( ES C - H C,s + i 1 2 Γ R,s + i 1 2 Γ L,s) -1 (4) Published on Web 03/01/2010 10.1021/ja910483b  2010 American Chemical Society 3682 9 J. AM. CHEM. SOC. 2010, 132, 3682–3684