Yuta Tsuji

Dependence of Single-Molecule Conductance on Molecule Junction Symmetry

The symmetry of a molecule junction has been shown to play a significant role in determining the conductance of the molecule, but the details of how conductance changes with symmetry have heretofore been unknown. Herein, we investigate a naphthalenedithiol single-molecule system in which sulfur atoms from the molecule are anchored to two facing gold electrodes. In the studied system, the highest single-molecule conductance, for a molecule junction of 1,4-symmetry, is 110 times larger than the lowest single-molecule conductance, for a molecule junction of 2,7-symmetry. We demonstrate clearly that the measured dependence of molecule junction symmetry for single-molecule junctions agrees with theoretical predictions.

Orbital Views of Molecular Conductance Perturbed by Anchor Units

Site-specific electron transport phenomena through benzene and benzenedithiol derivatives are discussed on the basis of a qualitative Hückel molecular orbital analysis for better understanding of the effect of anchoring sulfur atoms. A recent work for the orbital control of electron transport through aromatic hydrocarbons provided an important concept for the design of high-conductance connections of a molecule with anchoring atoms. In this work the origin of the frontier orbitals of benzenedithiol derivatives, the effect of the sulfur atoms on the orbitals and on the electron transport properties, and the applicability of the theoretical concept on aromatic hydrocarbons with the anchoring units are studied. The results demonstrate that the orbital view predictions are applicable to molecules perturbed by the anchoring units. The electron transport properties of benzene are found to be qualitatively consistent with those of benzenedithiol with respect to the site dependence. To verify the result of the Hückel molecular orbital calculations, fragment molecular orbital analyses with the extended Hückel molecular orbital theory and electron transport calculations with density functional theory are performed. Calculated results are in good agreement with the orbital interaction analysis. The phase, amplitude, and spatial distribution of the frontier orbitals play an essential role in the design of the electron transport properties through aromatic hydrocarbons.

Close relation between quantum interference in molecular conductance and diradical existence

Significance It might seem that the existence of a dramatic diminution in molecular conductance across a hydrocarbon (quantum interference, QI) would be unrelated to the existence of an important class of organic molecules with two electrons in two orbitals, diradicals. However, if you add two carbons to a planar π-electron hydrocarbon, you get a diradical if and only if there is a QI feature in conductance when two electrodes are attached to the molecule at the same sites. When you remove the two carbons where the electrodes are attached, you also generate a diradical. The connection, first empirically observed, is proven. Two kinds of diradicals, with different ground state spin consequences, are also easily distinguished by the relationship. An empirical observation of a relationship between a striking feature of electronic transmission through a π-system, destructive quantum interference (QI), on one hand, and the stability of diradicals on the other, leads to the proof of a general theorem that relates the two. Subject to a number of simplifying assumptions, in a π-electron system, QI occurs when electrodes are attached to those positions of an N-carbon atom N-electron closed-shell hydrocarbon where the matrix elements of the Green’s function vanish. These zeros come in two types, which are called easy and hard. Suppose an N+2 atom, N+2 electron hydrocarbon is formed by substituting 2 CH2 groups at two atoms, where the electrodes were. Then, if a QI feature is associated with electrode attachment to the two atoms of the original N atom system, the resulting augmented N+2 molecule will be a diradical. If there is no QI feature, i.e., transmission of current is normal if electrodes are attached to the two atoms, the resulting hydrocarbon will not be a diradical but will have a classical closed-shell electronic structure. Moreover, where a diradical exists, the easy zero is associated with a nondisjoint diradical, and the hard zero is associated with a disjoint one. A related theorem is proven for deletion of two sites from a hydrocarbon.

Quantum interference in polyenes.

The explicit form of the zeroth Greens function in the Hückel model, approximated by the negative of the inverse of the Hückel matrix, has direct quantum interference consequences for molecular conductance. We derive a set of rules for transmission between two electrodes attached to a polyene, when the molecule is extended by an even number of carbons at either end (transmission unchanged) or by an odd number of carbons at both ends (transmission turned on or annihilated). These prescriptions for the occurrence of quantum interference lead to an unexpected consequence for switches which realize such extension through electrocyclic reactions: for some specific attachment modes the chemically closed ring will be the ON position of the switch. Normally the signs of the entries of the Greens function matrix are assumed to have no physical significance; however, we show that the signs may have observable consequences. In particular, in the case of multiple probe attachments - if coherence in probe connections can be arranged - in some cases new destructive interference results, while in others one may have constructive interference. One such case may already exist in the literature.

Enhancing the conductivity of molecular electronic devices

We show in this work that conjugated π-electron molecular chains can, in quite specific and understood circumstances, become more conductive the longer they get, in contradiction to what would be expected intuitively. The analysis, done in the framework of the source and sink potential method, and supported by detailed transmission calculations, begins by defining “relative transmission,” an inherent measure of molecular conduction. This, in turn, for conjugated hydrocarbons, is related to a simple molecular orbital expression—the ratio of secular determinants of a molecule and one where the electrode contacts are deleted—and a valence bond idea, since these secular determinants can alternatively be expressed in terms of Kekule structures. A plausible argument is given for relating the relative transmission to the weight of the diradical resonance structures in the resonance hybrid for a molecule. Chemical intuition can then be used to tune the conductivity of molecules by “pushing” them towards more or l...

The Green’s function for the Hückel (tight binding) model

Applications of the Huckel (tight binding) model are ubiquitous in quantum chemistry and solid state physics. The matrix representation of this model is isomorphic to an unoriented vertex adjacency matrix of a bipartite graph, which is also the Laplacian matrix plus twice the identity. In this paper, we analytically calculate the determinant and, when it exists, the inverse of this matrix in connection with the Green’s function, G, of the N×N Huckel matrix. A corollary is a closed form expression for a Harmonic sum (Eq. (12)). We then extend the results to d− dimensional lattices, whose linear size is N. The existence of the inverse becomes a question of number theory. We prove a new theorem in number theory pertaining to vanishing sums of cosines and use it to prove that the inverse exists if and only if N + 1 and d are odd and d is smaller than the smallest divisor of N + 1. We corroborate our results by demonstrating the entry patterns of the Green’s function and discuss applications related to transpo...

Structural Diversity and Electron Confinement in Li4N: Potential for 0-D, 2-D, and 3-D Electrides

In pursuit of new lithium-rich phases and potential electrides within the Li-N phase diagram, we explore theoretically the ground-state structures and electronic properties of Li4N at P = 1 atm. Crystal structure exploration methods based on particle swarm optimization and evolutionary algorithms led to 25 distinct structures, including 23 dynamically stable structures, all quite close to each other in energy, but not in detailed structure. Several additional phases were obtained by following the imaginary phonon modes found in low-energy structures, as well as structures constructed to simulate segregation into Li and Li3N. The candidate Li4N structures all contain NLin polyhedra, with n = 6-9. They may be classified into three types, depending on their structural dimensionality: NLin extended polyhedral slabs joined by an elemental Li layer (type a), similar structures, but without the Li layer (type b), and three-dimensionally interconnected NLin polyhedra without any layering (type c). We investigate the electride nature of these structures using the electron localization function and partial charge density around the Fermi level. All of the structures can be characterized as electrides, but they differ in electronic dimensionality. Type-a and type-b structures may be classified as two-dimensional (2-D) electrides, while type-c structures emerge quite varied, as 0-D, 2-D, or 3-D. The calculated structural variety (as well as detailed models for amorphous and liquid Li4N) points to potential amorphous character and likely ionic conductivity in the material.

Helical Oligoenes: Conformations, Bond Alternation, and Competing Through-Bond and Through-Space Transmission.

There is a consensus that long-range electron transfer/transport occurs by a through-bond rather than through-space mechanism. In helical all-Z, all-s-cis oligoenes, one can set up an interesting competition in the medium-separation regime between a closer (in distance) through-space path and a more distant through-bond one. Although such oligoene conformations/isomers are unstable (by around 4 kcal mol(-1) per double bond relative to all-E, all-s-trans isomers), recent synthetic efforts on truncated helicenes and oligothiophenes have provided related molecules. On the way to transmission calculations with electrodes attached to the termini of helical oligoenes, we uncover an interesting conformational ambiguity in all-Z, all-s-cis oligoenes, the existence of a broad conformational minimum for helical compression, with hints of end-to-end frontier-orbital-caused stabilization. There is relationship between helical oligoene structures and the corresponding substructure of a helicene, but there are also significant differences in the number of olefin subunits per helix turn. In Hückel transport calculations, the role of TB or TS mechanisms is obscured to an extent by variations in bond alternation and dihedral angle along the oligomer chain. However, the operation of a dominant through bond mechanism emerges clearly in local transmission plots. In moving the electrodes to carbon position related by quantum interference, it is possible to uncover a through space mechanism.

A Bipodal Dicyano Anchor Unit for Single‐Molecule Spintronic Devices

The conductance through single 7,7,8,8-tetracyanoquinodimethane (TCNQ) connected to gold electrodes is studied with the nonequilibrium Greens function method combined with density functional theory. The aim of the study is to derive the effect of a dicyano anchor group, =C(CN)2, on energy level alignment between the electrode Fermi level and a molecular energy level. The strong electron-withdrawing nature of the dicyano anchor group lowers the LUMO level of TCNQ, resulting in an extremely small energy barrier for electron injection. At zero bias, electron transfer from electrodes easily occurs and, as a consequence, the anion radical state of TCNQ with a magnetic moment is formed. The unpaired electron in the TCNQ anion radical causes an exchange splitting between the spin-α and spin-β transmission spectra, allowing the single TCNQ junction to act as a spin-filtering device.

Quantum Interference, Graphs, Walks, and Polynomials

In this paper, we explore quantum interference (QI) in molecular conductance from the point of view of graph theory and walks on lattices. By virtue of the Cayley-Hamilton theorem for characteristic polynomials and the Coulson-Rushbrooke pairing theorem for alternant hydrocarbons, it is possible to derive a finite series expansion of the Greens function for electron transmission in terms of the odd powers of the vertex adjacency matrix or Hückel matrix. This means that only odd-length walks on a molecular graph contribute to the conductivity through a molecule. Thus, if there are only even-length walks between two atoms, quantum interference is expected to occur in the electron transport between them. However, even if there are only odd-length walks between two atoms, a situation may come about where the contributions to the QI of some odd-length walks are canceled by others, leading to another class of quantum interference. For nonalternant hydrocarbons, the finite Greens function expansion may include both even and odd powers. Nevertheless, QI can in some circumstances come about for nonalternants from cancellation of odd- and even-length walk terms. We report some progress, but not a complete resolution, of the problem of understanding the coefficients in the expansion of the Greens function in a power series of the adjacency matrix, these coefficients being behind the cancellations that we have mentioned. Furthermore, we introduce a perturbation theory for transmission as well as some potentially useful infinite power series expansions of the Greens function.