Quantum interference in polycyclic hydrocarbon molecular wires

Abstract

The construction of devices based on molecular components depends upon the development of molecular wires with adaptable current–voltage characteristics. Here, we report that quantum interference effects could lead to substantial differences in conductance in molecular wires which include some simple polycyclic aromatic hydrocarbons (PAHs). For molecular wires containing a single benzene, anthracene or tetracene molecule a large peak appears in the electron transmission probability spectrum at an energy just above the lowest unoccupied orbital (LUMO). For a molecular wire containing a single naphthalene molecule, however, this same peak essentially vanishes. Furthermore, the peak can be re-established by altering the attachment points of the molecular leads to the naphthalene molecule. A breakdown of the individual terms contributing the relevant peak confirms that these results are in fact due to quantum interference effects.

Introduction

A great deal of progress has recently been made towards realization of miniature electronic devices constructed from molecular components [1], [2]. The technological potential of these devices is obvious: such components could be orders of magnitude more powerful than their silicon counterparts [3]. Scientifically, the fundamental issues are of great interest, some are well understood [4], [5], while others – remain to be explored [6], [7], [8], [9], [10], [11], [12]. We know, that unlike macroscopic conventional wires, the conductance properties of the molecular counterparts are intricate functions of the underlying electronic structure [13]. Rather than the conductance being simply proportional to the applied voltage, it generally exhibits step-like features corresponding to resonances with the molecular eigenstates. As a consequence of this, organic molecules that are slightly dissimilar can exhibit substantial differences in conductance as the various resonances shift in position and change in size. These changes have been attributed to reductions in electronic delocalization [14], [15], [16], wire–electrode interactions [17], and quantum interference effects [14], [18].

There is a substantial body of experimental and theoretical work on the properties of polyacetylene molecular wires and their conduction behavior has been well understood for some time now [19], [20], [21], [22], [23]. More recently, experimental work on the conductance of molecular wires containing a single benzene molecule or benzene derivative has appeared [24], [25]. This was followed by sophisticated theoretical research on the conductance of benzene-based molecular wires [26], [27] that produced results in good agreement with the experiment. Researchers have since gone on to study both experimentally and theoretically the conductance of molecular wires based on even larger organic molecules. Work has appeared on the conductance of more complicated single organic molecules [28], [29]. Hush and co-workers [30] have done extensive theoretical research on the possibility of using linked porphyrin molecules as molecular wires. The possibility of exploiting quantum interference in molecular wires based on the C₆₀ molecule has also been noted [31]. Furthermore, the success in previous experimental studies on benzene-based molecular wires and the development of new synthetic techniques [32] strongly suggest that newly proposed systems will in fact be realizable.

One of the more striking differences between molecular and macroscopic wires is the possibility that quantum interference may be dominant. Such concepts were considered by Paddon-Row and Jordan [33] in discussing bridge-assisted electron transfer. In the context of transport, Joachim and co-workers [34], [35] studied theoretically a single benzene or benzene-based molecule embedded in a polyacetylene chain. The electron transmission probability was studied by Joachim and co-workers as a function of the attachment points of the polyacetylene chains to the ring structure. It was shown that the transmission changes quite significantly through such modifications and that interferences lead to dips in the transmission probability spectrum. Furthermore, a simple qualitative rule was given by Joachim and co-workers for determining whether or not two molecular eigenstates interfere with one another.

Recently, Baer and Neuhauser [36], [37] studied a series of molecular wires containing different polyacetylene loop structures. Unlike the previous work these loop structures contained branches having lengths greater than the de Broglie wavelength of the conducting electrons. Their study was carried out with the prime objective of fleshing out possible interference effects in molecular wires. The results showed a striking variation of the conductance depending on the contact points of the interference loop structure.

In this paper, we examine the issue of interference in a more elaborate setup. We consider molecular resonators shown in Fig. 1 consisting of single or multiple ring systems: benzene (one ring), naphthalene (two rings), anthracene (three ring) and tetracene (4 rings). For naphthalene and anthracene, two configurations of the polyacetylene chains are considered. A cis configuration in which the chains are attached at the same side of the resonator and a trans configuration in which the chains are attached at opposite ends of the resonator.

Utilizing a simple Hückel model, Baer and Neuhauser [36] showed that cis configurations are under “destructive interference” situation. In order to explain this, consider Fig. 2 where the 3–3^′ bond is ignored for simplicity. In the Hückel π-bond picture, all carbons are equivalent, all CC bonds are of the same length R_CC. The conduction electron mounts the molecular bridge at site 1 and leaves it at site 5. We show that the probability for this process is small. This conduction electron is within the Fermi level of the π system, having a de Broglie wavelength of λ_F=4R_CC (this is because of the half filled π band). There are two paths to consider: P₁={1,2,3,4,5} and P₂={1,1^′,2^′,3^′,4^′,5^′,5} with corresponding lengths of L[P₁]=4R_CC and L[P₂]=6R_CC. The phase difference of the two paths is then (2R_CC/λ_F)×2π=π. Thus two paths the interfere destructively, yielding the process highly unfavorable.

A similar reasoning, applied to the trans configuration, will involve the paths P₁={1,2,3,4,5,5^′} and P₂={1,1^′,2^′,3^′,4^′,5^′} both of the same length and therefore of the same phase. Thus, the conductance of trans molecules is expected to be high. This intuitive reasoning applies for all the systems and is borne out by exact Hückel calculations.

The arguments presented above contain many simplifying assumptions. For example, we have neglected the sigma system, assumed that all carbon atoms are identical, used unrelaxed nuclear configurations, did not account for realistic charge distributions and used an over simplified (one orbital per atom) basis set. In this paper, we endeavor to present more realistic computations that overcome some of these limitations employing a DFT-based approach. As we discuss in the next sections, there are still several effects we are not addressing here though and these will await further investigation. Within our model, we corroborate the previous conclusions that quantum interference can lead to significant differences in the conductance of these systems.