Molecular electronics (sometimes called moletronics) is an interdisciplinary theme that spans physics, chemistry, and materials science. The unifying feature of this area is the use of molecular building blocks for the fabrication of electronic components, both passive (e.g. resistive wires) and active (e.g transistors). The concept of molecular electronics has aroused much excitement both in science fiction and among scientists due to the prospect of size reduction in electronics offered by molecular-level control of properties. Molecular electronics provides a means to extend Moore's Law beyond the foreseen limits of small-scale conventional silicon integrated circuits.
Concept genesis and theory
Study of charge transfer in molecules was advanced in the 1940s by Robert Mulliken and Albert Szent-Gyorgi in discussion of so-called "donor-acceptor" systems and developed the study of charge transfer and energy transfer in molecules. Likewise, a 1974 paper from Mark Ratner and Ari Aviram 1 illustrated a theoretical molecular rectifier. Later, in 1988, Aviram described in detail a theoretical single-molecule field-effect transistor . Further concepts were proposed by Forrest Carter of the Naval Research Laboratory, including single-molecule logic gates.
Unfortunately, the direct measurement of the electronic characteristics of individual molecules awaited the development of methods for making molecular-scale electrical contacts. This was no easy task. Thus, the first experiment measuring the conductance of a single molecule was only reported in 1997 by Mark Reed and co-workers. Since then, this branch of the field has progressed rapidly. Likewise, as it has become possible to measure such properties directly, the theoretical predictions of the early workers have been mostly confirmed.
However, while mostly operating in the quantum realm of less than 100 nanometers, "molecular" electronic processes often collectively manifest on a macro scale. Examples include quantum tunneling, negative resistance, phonon-assisted hopping, polarons, and the like. Thus, macro-scale active devices were described decades before molecular-scale ones. E.g., in 1974, John McGinness and his coworkers described  the putative "first experimental demonstration of an operating molecular electronic device". This was a voltage-controlled switch. As its active element, this device used DOPA melanin, an oxidized mixed polymer of polyacetylene, polypyrrole, and polyaniline. The "ON" state of this switch exhibited almost metallic conductivity.
Since the 1970's, scientists have developed an entire panoply of new materials and devices. These findings have opened the door to plastic electronics and optoelectronics, which are beginning to find commercial application.
Charge transfer complexes
The first highly-conductive organic compounds were the Charge transfer complexes. In 1954, researchers at Bell Labs and elsewhere reported Charge transfer complexes with resistivities as low as 8 ohms-cm  . In the early 1970's, salts of tetrathiafulvalene were shown to exhibit almost metallic conductivity, while superconductivity was demonstrated in 1980. Broad research on charge transfer salts continues today.
The linear-backbone "polymer blacks" (polyacetylene, polypyrrole, and polyaniline) and their copolymers are the main class of conductive polymers. Historically, these are known as Melanins. In 1963 Australians DE Weiss and coworkers reported  iodine-doped oxidized polypyrrole blacks with resistivities as low as 1 ohm/cm. Subsequent papers  reported resistances as low as 0.03 Ohm/cm. With the notable exception of Charge transfer complexes (some of which are even superconductors), organic molecules had previously been considered insulators or at best weakly conducting semiconductors.
Over a decade later in 1977, Shirakawa, Heeger, and MacDiarmid reported equivalent high conductivity in rather similarly oxidized and iodine-doped polyacetylene. They later received the 2000 Nobel prize in chemistry for " The discovery and development of conductive polymers " . The Nobel citation made no reference to Weiss et al's similar earlier work. Also see Nobel Prize controversies.
C60 and carbon nanotubes
From graphite to C60
In polymers, classical organic molecules are composed of both carbon and hydrogen (and sometimes additional compounds such as nitrogen, chlorine or sulfur). They are obtained from petrol and can often be synthethized in large amounts. Most of these molecules are insulating when their length exceeds a few nanometers. However, naturally occurring carbon is conducting. In particular, graphite (recovered from coal or encountered naturally) is conducting. From a theoretical point of view, graphite is a semi-metal, a category in between metals and semi-conductors. It has a layered structure, each sheet being one atom thick. Between each sheet, the interactions are weak enough to allow an easy manual cleavage.
Tailoring the graphite sheet to obtain well defined nanometer-sized objects remains a challenge. However, by the close of the twentieth century, chemists were exploring methods to fabricate extremely small graphitic objects that could be considered single molecules. After studying the interstellar conditions under which carbon is known to form clusters, Richard Smalley 's group (Rice university, Texas) set up an experiment in which graphite was vaporized using laser irradiation. Mass spectrometry revealed that clusters containing specific "magic numbers" of atoms were stable, in particular those clusters of 60 atoms. Harry Kroto, an English chemist who assisted in the experiment, suggested a possible geometry for these clusters - atoms covalently bound with the exact symmetry of a soccer ball. Coined buckminsterfullerenes, buckyballs or C60, the clusters retained some properties of graphite, such as conductivity. These objects were rapidly envisioned as possible building blocks for molecular electronics.
Theory of Molecular Electronics
The theory of single molecule devices is particularly interesting since the system under consideration is an open quantum system in nonequilibrium (driven by voltage). In the low bias voltage regime, the nonequilibrium nature of the molecular junction can be ignored, and the current-voltage characteristics of the device can be calculated using the equilibrium electronic structure of the system. However, in stronger bias regimes a more sophisticated treatment is required, as there is no longer a variational principle. In the elastic tunneling case (where the passing electron does not exchange energy with the system), the formalism of Rolf Landauer can be used to calculate the transmission through the system as a function of bias voltage, and hence the current. In inelastic tunneling, an elegant formalism based on the non-equilibrium Green's functions of Leo Kadanoff and Gordon Baym, and independently by Leonid Keldysh was put forth by Ned Wingreen and Yigal Meir. This Meir-Wingreen formulation has been used to great success in the molecular electronics community to examine the more difficult and interesting cases where the transient electron exchanges energy with the molecular system (for example through electron-phonon coupling or electronic excitations).
Recent progress in nanotechnology and nanoscience has facilitated both experimental and theoretical study of molecular electronics. In particular, the development of the scanning tunneling microscope (STM) and later the atomic force microscope (AFM) have facilitated manipulation of single-molecule electronics.
Work is also being done on the use of single-wall carbon nanotubes as field-effect transistors. Most of this work is being done by IBM.
The Aviram-Ratner model for a molecular rectifier, which until recently was entirely theoretical, has been confirmed experimentally and unambiguously in a number of experiments by a group led by Geoffrey J. Ashwell at Cranfield University, UK. Many rectifying molecules have so far been identified, and the number and efficiency of these systems is expanding rapidly.
An important issue in molecular electronics is the determination of the resistance of a single molecule (both theoretical and experimental). For example, Bumm, et al used STM to analyze a single molecular switch in a self-assembled monolayer to determine how conductive such a molecule can be. Another problem faced by this field is the difficulty to perform direct characterization since imaging at the molecular scale is often difficult in many experimental devices.
- For the history of the field, see the following references:
- Cassoux, P. “Molecular Metals: Staying Neutral for a Change” Science Sciencce 2001 volume 291, pages 263-264. [DOI: 10.1126/science.291.5502.263.
- "An Overview of the First Half-Century of Molecular Electronics" by Noel S. Hush, Ann. N.Y. Acad. Sci. 1006: 1–20 (2003) and
- Bendikov, M; Wudl, F; Perepichka, D. F. “Tetrathiafulvalenes, Oligoacenenes, and Their Buckminsterfullerene Derivatives: The Brick and Mortar of Organic Electronics” Chemical Reviews 2004, volume 104, 4891-4945.
- Y. Okamoto and W. Brenner Organic Semiconductors, Rheinhold (1964)
- H. Akamatsu, H.Inokuchi, and Y.Matsunaga, “Electrical Conductivity of the Perylene–Bromine Complex” Nature volume, 173 (1954) 168
- Aviram, A. & Ratner, M.A. Molecular Rectifiers. Chem. Phys. Lett. 29, 277 (1974).
- BA Bolto, R McNeill and DE Weiss, Electronic Conduction in Polymers. III. Electronic Properties of Polypyrrole, Australian Journal of Chemistry 16(6) 1090 - 1103 (1963) 
- John McGinness, Corry, P, Proctor, P.H. Amorphous Semiconductor Switching in Melanins,Science, vol 183, 853-855 (1974) 
- S. J. Tans, M. H. Devoret, H. Dai, A. Thess, R. E. Smalley, L. J. Geerligs, & C. Dekker, Nature, vol 386, 474 (1997).
- H. W. Kroto, J. R. Heath, S. C. O'Brien, R. F. Curl & R. E. Smalley, Nature, vol 318, 162 (1985)
- H. W. Kroto, Nature, vol 329, 529 (1987)
- T. Oberlin, M. Endo, & T. Koyama, Journ. of Crystal Growth, 32, 335 (1976).
- Geoffrey J. Ashwell and Daniel S. Gandolfo, J. Mater. Chem. 12
- M.A. Reed, C. Zhou, C.J. Muller, T.P. Burgin, and J.M. Tour, “Conductance of a molecular junction”, Science 278, 252 (1997).