Competition between charge migration and charge transfer induced by nuclear motion following core ionization: Model systems and application to Li2.

Attosecond and femtosecond spectroscopies present opportunities for the control of chemical reaction dynamics and products, as well as for quantum information processing; we address the somewhat unique situation of core-ionization spectroscopy which, for dimeric chromophores, leads to strong valence charge localization and hence tightly paired potential-energy surfaces of very similar shape. Application is made to the quantum dynamics of core-ionized Li2 +. This system is chosen as Li2 is the simplest stable molecule facilitating both core ionization and valence ionization. First, the quantum dynamics of some model surfaces are considered, with the surprising result that subtle differences in shape between core-ionization paired surfaces can lead to dramatic differences in the interplay between electronic charge migration and charge transfer induced by nuclear motion. Then, equation-of-motion coupled-cluster calculations are applied to determine potential-energy surfaces for 8 core-excited state pairs, calculations believed to be the first of their type for other than the lowest-energy core-ionized molecular pair. While known results for the lowest-energy pair suggest that Li2 + is unsuitable for studying charge migration, higher-energy pairs are predicted to yield results showing competition between charge migration and charge transfer. Central is a focus on the application of Hush's 1975 theory for core-ionized X-ray photoelectron spectroscopy to understand the shapes of the potential-energy surfaces and hence predict key features of charge migration.

Gold surfaces and nanoparticles are protected by Au(0)-thiyl species and are destroyed when Au(I)-thiolates form.

The synthetic chemistry and spectroscopy of sulfur-protected gold surfaces and nanoparticles is analyzed, indicating that the electronic structure of the interface is Au(0)-thiyl, with Au(I)-thiolates identified as high-energy excited surface states. Density-functional theory indicates that it is the noble character of gold and nanoparticle surfaces that destabilizes Au(I)-thiolates. Bonding results from large van der Waals forces, influenced by covalent bonding induced through s-d hybridization and charge polarization effects that perturbatively mix in some Au(I)-thiolate character. A simple method for quantifying these contributions is presented, revealing that a driving force for nanoparticle growth is nobleization, minimizing Au(I)-thiolate involvement. Predictions that Brust-Schiffrin reactions involve thiolate anion intermediates are verified spectroscopically, establishing a key feature needed to understand nanoparticle growth. Mixing of preprepared Au(I) and thiolate reactants always produces Au(I)-thiolate thin films or compounds rather than monolayers. Smooth links to O, Se, Te, C, and N linker chemistry are established.

A priori calculations of the free energy of formation from solution of polymorphic self-assembled monolayers.

Modern quantum chemical electronic structure methods typically applied to localized chemical bonding are developed to predict atomic structures and free energies for meso-tetraalkylporphyrin self-assembled monolayer (SAM) polymorph formation from organic solution on highly ordered pyrolytic graphite surfaces. Large polymorph-dependent dispersion-induced substrate-molecule interactions (e.g., -100 kcal mol(-1) to -150 kcal mol(-1) for tetratrisdecylporphyrin) are found to drive SAM formation, opposed nearly completely by large polymorph-dependent dispersion-induced solvent interactions (70-110 kcal mol(-1)) and entropy effects (25-40 kcal mol(-1) at 298 K) favoring dissolution. Dielectric continuum models of the solvent are used, facilitating consideration of many possible SAM polymorphs, along with quantum mechanical/molecular mechanical and dispersion-corrected density functional theory calculations. These predict and interpret newly measured and existing high-resolution scanning tunnelling microscopy images of SAM structure, rationalizing polymorph formation conditions. A wide range of molecular condensed matter properties at room temperature now appear suitable for prediction and analysis using electronic structure calculations.

Intermixed adatom and surface-bound adsorbates in regular self-assembled monolayers of racemic 2-butanethiol on Au(111).

In situ scanning tunneling microscopy combined with density functional theory molecular dynamics simulations reveal a complex structure for the self-assembled monolayer (SAM) of racemic 2-butanethiol on Au(111) in aqueous solution. Six adsorbate molecules occupy a (10×√3)R30° cell organized as two RSAuSR adatom-bound motifs plus two RS species bound directly to face-centered-cubic and hexagonally close-packed sites. This is the first time that these competing head-group arrangements have been observed in the same ordered SAM. Such unusual packing is favored as it facilitates SAMs with anomalously high coverage (30%), much larger than that for enantiomerically resolved 2-butanethiol or secondary-branched butanethiol (25%) and near that for linear-chain 1-butanethiol (33%).

Non-adiabatic effects in thermochemistry, spectroscopy and kinetics: the general importance of all three Born-Oppenheimer breakdown corrections.

Using a simple model Hamiltonian, the three correction terms for Born-Oppenheimer (BO) breakdown, the adiabatic diagonal correction (DC), the first-derivative momentum non-adiabatic correction (FD), and the second-derivative kinetic-energy non-adiabatic correction (SD), are shown to all contribute to thermodynamic and spectroscopic properties as well as to thermal non-diabatic chemical reaction rates. While DC often accounts for >80% of thermodynamic and spectroscopic property changes, the commonly used practice of including only the FD correction in kinetics calculations is rarely found to be adequate. For electron-transfer reactions not in the inverted region, the common physical picture that diabatic processes occur because of surface hopping at the transition state is proven inadequate as the DC acts first to block access, increasing the transition state energy by (ℏω)(2)λ/16J(2) (where λ is the reorganization energy, J the electronic coupling and ω the vibration frequency). However, the rate constant in the weakly-coupled Golden-Rule limit is identified as being only inversely proportional to this change rather than exponentially damped, owing to the effects of tunneling and surface hopping. Such weakly-coupled long-range electron-transfer processes should therefore not be described as "non-adiabatic" processes as they are easily described by Born-Huang ground-state adiabatic surfaces made by adding the DC to the BO surfaces; instead, they should be called just "non-Born-Oppenheimer" processes. The model system studied consists of two diabatic harmonic potential-energy surfaces coupled linearly through a single vibration, the "two-site Holstein model". Analytical expressions are derived for the BO breakdown terms, and the model is solved over a large parameter space focusing on both the lowest-energy spectroscopic transitions and the quantum dynamics of coherent-state wavepackets. BO breakdown is investigated pertinent to: ammonia inversion, aromaticity in benzene, the Creutz-Taube ion, the bacterial photosynthetic reaction centre, BNB, the molecular conductor Alq3, and inverted-region charge recombination in a ferrocene-porphyrin-fullerene triad photosynthetic model compound. Throughout, the fundamental nature of BO breakdown is linked to the properties of the cusp catastrophe: the cusp diameter is shown to determine the magnitudes of all couplings, numerical basis-set and trajectory-integration requirements, and to determine the transmission coefficient κ used to understand deviations from transition-state theory.

Electron-vibration entanglement in the Born-Oppenheimer description of chemical reactions and spectroscopy.

Entanglement is sometimes regarded as the quintessential measure of the quantum nature of a system and its significance for the understanding of coupled electronic and vibrational motions in molecules has been conjectured. Previously, we considered the entanglement developed in a spatially localized diabatic basis representation of the electronic states, considering design rules for qubits in a low-temperature chemical quantum computer. We extend this to consider the entanglement developed during high-energy processes. We also consider the entanglement developed using adiabatic electronic basis, providing a novel way for interpreting effects of the breakdown of the Born-Oppenheimer (BO) approximation. We consider: (i) BO entanglement in the ground-state wavefunction relevant to equilibrium thermodynamics, (ii) BO entanglement associated with low-energy wavefunctions relevant to infrared and tunneling spectroscopies, (iii) BO entanglement in high-energy eigenfunctions relevant to chemical reaction processes, and (iv) BO entanglement developed during reactive wavepacket dynamics. A two-state single-mode diabatic model descriptive of a wide range of chemical phenomena is used for this purpose. The entanglement developed by BO breakdown correlates simply with the diameter of the cusp introduced by the BO approximation, and a hierarchy appears between the various BO-breakdown correction terms, with the first-derivative correction being more important than the second-derivative correction which is more important than the diagonal correction. This simplicity is in contrast to the complexity of BO-breakdown effects on thermodynamic, spectroscopic, and kinetic properties. Further, processes poorly treated at the BO level that appear adequately treated using the Born-Huang adiabatic approximation are found to have properties that can only be described using a non-adiabatic description. For the entanglement developed between diabatic electronic states and the nuclear motion, qualitatively differently behavior is found compared to traditional properties of the density matrix and hence entanglement provides new information about system properties. For chemical reactions, this type of entanglement simply builds up as the transition-state region is crossed. It is robust to small changes in parameter values and is therefore more attractive for making quantum qubits than is the related fragile ground-state entanglement, provided that coherent motion at the transition state can be sustained.

A unified diabatic description for electron transfer reactions, isomerization reactions, proton transfer reactions, and aromaticity.

While diabatic approaches are ubiquitous for the understanding of electron-transfer reactions and have been mooted as being of general relevance, alternate applications have not been able to unify the same wide range of observed spectroscopic and kinetic properties. The cause of this is identified as the fundamentally different orbital configurations involved: charge-transfer phenomena involve typically either 1 or 3 electrons in two orbitals whereas most reactions are typically closed shell. As a result, two vibrationally coupled electronic states depict charge-transfer scenarios whereas three coupled states arise for closed-shell reactions of non-degenerate molecules and seven states for the reactions implicated in the aromaticity of benzene. Previous diabatic treatments of closed-shell processes have considered only two arbitrarily chosen states as being critical, mapping these states to those for electron transfer. We show that such effective two-state diabatic models are feasible but involve renormalized electronic coupling and vibrational coupling parameters, with this renormalization being property dependent. With this caveat, diabatic models are shown to provide excellent descriptions of the spectroscopy and kinetics of the ammonia inversion reaction, proton transfer in N2H7(+), and aromaticity in benzene. This allows for the development of a single simple theory that can semi-quantitatively describe all of these chemical phenomena, as well as of course electron-transfer reactions. It forms a basis for understanding many technologically relevant aspects of chemical reactions, condensed-matter physics, chemical quantum entanglement, nanotechnology, and natural or artificial solar energy capture and conversion.

Bond angle variations in XH3 [X = N, P, As, Sb, Bi]: the critical role of Rydberg orbitals exposed using a diabatic state model.

Ammonia adopts sp(3) hybridization (HNH bond angle 108°) whereas the other members of the XH3 series PH3, AsH3, SbH3, and BiH3 instead prefer octahedral bond angles of 90-93°. We use a recently developed general diabatic description for closed-shell chemical reactions, expanded to include Rydberg states, to understand the geometry, spectroscopy and inversion reaction profile of these molecules, fitting its parameters to results from Equation of Motion Coupled-Cluster Singles and Doubles (EOM-CCSD) calculations using large basis sets. Bands observed in the one-photon absorption spectrum of NH3 at 18.3 eV, 30 eV, and 33 eV are reassigned from Rydberg (formally forbidden) double excitations to valence single-excitation resonances. Critical to the analysis is the inclusion of all three electronic states in which two electrons are placed in the lone-pair orbital n and/or the symmetric valence σ* antibonding orbital. An illustrative effective two-state diabatic model is also developed containing just three parameters: the resonance energy driving the high-symmetry planar structure, the reorganization energy opposing it, and HXH bond angle in the absence of resonance. The diabatic orbitals are identified as sp hybrids on X; for the radical cations XH3(+) for which only 2 electronic states and one conical intersection are involved, the principle of orbital following dictates that the bond angle in the absence of resonance is acos(-1/5) = 101.5°. The multiple states and associated multiple conical intersection seams controlling the ground-state structure of XH3 renormalize this to acos[3 sin(2)(2(1/2)atan(1/2))/2 - 1/2] = 86.7°. Depending on the ratio of the resonance energy to the reorganization energy, equilibrium angles can vary from these limiting values up to 120°, and the anomalously large bond angle in NH3 arises because the resonance energy is unexpectedly large. This occurs as the ordering of the lowest Rydberg orbital and the σ* orbital swap, allowing Rydbergization to compresses σ* to significantly increase the resonance energy. Failure of both the traditional and revised versions of the valence-shell electron-pair repulsion (VSEPR) theory to explain the ground-state structures in simple terms is attributed to exclusion of this key physical interaction.

Controlling the stereochemistry and regularity of butanethiol self-assembled monolayers on au(111).

The rich stereochemistry of the self-assembled monolayers (SAMs) of four butanethiols on Au(111) is described, the SAMs containing up to 12 individual C, S, or Au chiral centers per surface unit cell. This is facilitated by synthesis of enantiomerically pure 2-butanethiol (the smallest unsubstituted chiral alkanethiol), followed by in situ scanning tunneling microscopy (STM) imaging combined with density functional theory molecular dynamics STM image simulations. Even though butanethiol SAMs manifest strong headgroup interactions, steric interactions are shown to dominate SAM structure and chirality. Indeed, steric interactions are shown to dictate the nature of the headgroup itself, whether it takes on the adatom-bound motif RS(•)Au(0)S(•)R or involves direct binding of RS(•) to face-centered-cubic or hexagonal-close-packed sites. Binding as RS(•) produces large, organizationally chiral domains even when R is achiral, while adatom binding leads to rectangular plane groups that suppress long-range expression of chirality. Binding as RS(•) also inhibits the pitting intrinsically associated with adatom binding, desirably producing more regularly structured SAMs.

A multiscale simulation technique for molecular electronics: design of a directed self-assembled molecular n-bit shift register memory device.

A general method useful in molecular electronics design is developed that integrates modelling on the nano-scale (using quantum-chemical software) and on the micro-scale (using finite-element methods). It is applied to the design of an n-bit shift register memory that could conceivably be built using accessible technologies. To achieve this, the entire complex structure of the device would be built to atomic precision using feedback-controlled lithography to provide atomic-level control of silicon devices, controlled wet-chemical synthesis of molecular insulating pillars above the silicon, and controlled wet-chemical self-assembly of modular molecular devices to these pillars that connect to external metal electrodes (leads). The shift register consists of n connected cells that read data from an input electrode, pass it sequentially between the cells under the control of two external clock electrodes, and deliver it finally to an output device. The proposed cells are trimeric oligoporphyrin units whose internal states are manipulated to provide functionality, covalently connected to other cells via dipeptide linkages. Signals from the clock electrodes are conveyed by oligoporphyrin molecular wires, and µ-oxo porphyrin insulating columns are used as the supporting pillars. The developed multiscale modelling technique is applied to determine the characteristics of this molecular device, with in particular utilization of the inverted region for molecular electron-transfer processes shown to facilitate latching and control using exceptionally low energy costs per logic operation compared to standard CMOS shift register technology.

Weak, strong, and coherent regimes of Fröhlich condensation and their applications to terahertz medicine and quantum consciousness.

In 1968, Fröhlich showed that a driven set of oscillators can condense with nearly all of the supplied energy activating the vibrational mode of lowest frequency. This is a remarkable property usually compared with Bose-Einstein condensation, superconductivity, lasing, and other unique phenomena involving macroscopic quantum coherence. However, despite intense research, no unambiguous example has been documented. We determine the most likely experimental signatures of Fröhlich condensation and show that they are significant features remote from the extraordinary properties normally envisaged. Fröhlich condensates are classified into 3 types: weak condensates in which profound effects on chemical kinetics are possible, strong condensates in which an extremely large amount of energy is channeled into 1 vibrational mode, and coherent condensates in which this energy is placed in a single quantum state. Coherent condensates are shown to involve extremely large energies, to not be produced by the Wu-Austin dynamical Hamiltonian that provides the simplest depiction of Fröhlich condensates formed using mechanically supplied energy, and to be extremely fragile. They are inaccessible in a biological environment. Hence the Penrose-Hameroff orchestrated objective-reduction model and related theories for cognitive function that embody coherent Fröhlich condensation as an essential element are untenable. Weak condensates, however, may have profound effects on chemical and enzyme kinetics, and may be produced from biochemical energy or from radio frequency, microwave, or terahertz radiation. Pokorný's observed 8.085-MHz microtubulin resonance is identified as a possible candidate, with microwave reactors (green chemistry) and terahertz medicine appearing as other feasible sources.

Chain-branching control of the atomic structure of alkanethiol-based gold-sulfur interfaces.

Density functional theory structure calculations at 0 K and simulations at 300 K of observed high-resolution in situ scanning tunneling microscopy (STM) images reveal three different atomic-interface structures for the self-assembled monolayers (SAMs) of three isomeric butanethiols on Au(111): direct binding to the Au(111) surface without pitting, binding to adatoms above a regular surface with extensive pitting, and binding to adatoms with local surface vacancies and some pitting. Thermal motions are shown to produce some observed STM features, with a very tight energy balance controlling the observed structures. Variation of the degree of substitution on the α carbon is found to significantly change the relative energies for interaction of the different types of adatom structures with the surface, while the nature of the surface cell, controlled primarily by inter-adsorbate steric interactions, controls substrate reorganization energies and adsorbate distortion energies. Most significantly, by manipulating these features, chemical control of the adsorbate can produce stable interfaces with surface pitting eliminated, providing new perspectives for technological applications of SAMs.

Quantum entanglement between electronic and vibrational degrees of freedom in molecules.

We consider the quantum entanglement of the electronic and vibrational degrees of freedom in molecules with tendencies towards double welled potentials. In these bipartite systems, the von Neumann entropy of the reduced density matrix is used to quantify the electron-vibration entanglement for the lowest two vibronic wavefunctions obtained from a model Hamiltonian based on coupled harmonic diabatic potential-energy surfaces. Significant entanglement is found only in the region in which the ground vibronic state contains a density profile that is bimodal (i.e., contains two separate local maxima). However, in this region two distinct types of density and entanglement profiles are found: one type arises purely from the degeneracy of energy levels in the two potential wells and is destroyed by slight asymmetry, while the other arises through strong interactions between the diabatic levels of each well and is relatively insensitive to asymmetry. These two distinct types are termed fragile degeneracy-induced entanglement and persistent entanglement, respectively. Six classic molecular systems describable by two diabatic states are considered: ammonia, benzene, BNB, pyridine excited triplet states, the Creutz-Taube ion, and the radical cation of the "special pair" of chlorophylls involved in photosynthesis. These chemically diverse systems are all treated using the same general formalism and the nature of the entanglement that they embody is elucidated.

Penrose-Hameroff orchestrated objective-reduction proposal for human consciousness is not biologically feasible.

Penrose and Hameroff have argued that the conventional models of a brain function based on neural networks alone cannot account for human consciousness, claiming that quantum-computation elements are also required. Specifically, in their Orchestrated Objective Reduction (Orch OR) model [R. Penrose and S. R. Hameroff, J. Conscious. Stud. 2, 99 (1995)], it is postulated that microtubules act as quantum processing units, with individual tubulin dimers forming the computational elements. This model requires that the tubulin is able to switch between alternative conformational states in a coherent manner, and that this process be rapid on the physiological time scale. Here, the biological feasibility of the Orch OR proposal is examined in light of recent experimental studies on microtubule assembly and dynamics. It is shown that the tubulins do not possess essential properties required for the Orch OR proposal, as originally proposed, to hold. Further, we consider also recent progress in the understanding of the long-lived coherent motions in biological systems, a feature critical to Orch OR, and show that no reformation of the proposal based on known physical paradigms could lead to quantum computing within microtubules. Hence, the Orch OR model is not a feasible explanation of the origin of consciousness.

Formation of gold-methanethiyl self-assembled monolayers.

The energetics of formation of thiyl-gold self-assembled monolayers is investigated using density-functional theory simulations. It is found that the chemisorption of dimethyl disulfide on the reconstructed Au(111) (22 x radical3) surface is most favored at the fcc reconstruction stripe, with initial physisorption leading to disulfide dissociation, adatom/vacancy-pair formation, and then, at a coverage of 7.8% sulfur atoms per gold atom, surface reconstruction lifting. At higher coverages, monolayer formation proceeds similarly on the unreconstructed surface, leading to surface pitting. Formation of the analogous adatom/vacancy-pair bound dissociated adsorbate complex on exposure of the clean unreconstructed surface to methanethiol is shown to be endothermic, however.

Assignment of the Qy absorption spectrum of photosystem-I from Thermosynechococcus elongatus based on CAM-B3LYP calculations at the PW91-optimized protein structure.

The Qy absorption spectrum of Photosystem-I from Thermosynecochoccus elongatus (formerly Synecochoccus elongatus) is calculated using the CAM-B3LYP density functional and INDO schemes based on a quantum-mechanically refined structure for the entire photosystem obtained using the PW91 density functional. These methods present a priori predictions of the absorption and linear dichroism spectra and include protein electrostatic effects, short range inductive effects, long-range and short-range exciton couplings, and superexchange effects involving aromatic residues and carotenes. CAM-B3LYP is used as it is the only known density functional that correctly describes the Q bands of chlorophylls, all other methods contaminating them with erroneous charge-transfer excitations. A critical feature is found to be the use of fully optimized heavy-atom coordinates, with those obtained from just X-ray crystallography providing a poor description of the electronic properties of the chromophores. The result is a realistic first-principles prediction of the observed absorption band that identifies the nature of the red-shifted chlorophylls as well as the energies of the reaction-center chlorophylls and the exciton couplings acting between them. The "special pair" appears more like a dimer of dimers than a self-contained functional unit, with the exciton couplings between its members and the accessory chlorophylls exceeding the internal coupling.

Charge delocalization in the special-pair radical cation of mutant reaction centers of Rhodobacter sphaeroides from Stark spectra and nonadiabatic spectral simulations.

Stark and absorption spectra for the hole-transfer band of the bacteriochlorophyll special pair in the wild-type and L131LH, M160LH, and L131LH/M160LH mutants of the bacterial reaction center of Rhodobacter sphaeroides are presented, along with extensive analyses based on nonadiabatic spectral simulations. Dramatic changes in the Stark spectra are induced by the mutations, changes that are readily interpreted in terms of the redox-energy asymmetry and degree of charge localization in the special-pair radical cation. The effect of mutagenesis on key properties such as the electronic coupling within the special pair and the reorganization energy associated with intervalence hole transfer are determined for the first time. Results for the L131LH and M160LH/L131LH mutants indicate that these species can be considered as influencing the special pair primarily through modulation of the redox asymmetry, as is usually conceptualized, but M160LH is shown to develop a wide range of effects that can be interpreted in terms of significant mutation-induced structural changes in and around the special pair. The nonadiabatic spectra simulations are performed using both a simple two-state 1-mode and an extensive four-state 70-mode model, which includes the descriptions of additional electronic states and explicitly treats the major vibrational modes involved. Excellent agreement between the two simulation approaches is obtained. The simple model is shown to reproduce key features of the Stark effect of the main intervalence transition, while the extensive model quantitatively reproduces most features of the observed spectra for both the electronic and the phase-phonon regions, thus giving a more comprehensive description of the effect of the mutations on the properties of the special-pair radical cation. These results for a series of closely related mixed-valence complexes show that the Stark spectra provide a sensitive indicator for the properties of the mixed-valence complexes and should serve as an instructive example on the application of nonadiabatic simulations to the study of mixed-valence complexes in general as well as other chemical systems akin to the photosynthetic special pair.

Coexistence of multiple conformations in cysteamine monolayers on Au(111).

The structural organization, catalytic function, and electronic properties of cysteamine monolayers on Au(111) have been addressed comprehensively by voltammetry, in situ scanning tunneling microscopy (STM) in anaerobic environment, and a priori molecular dynamics (MD) simulation and STM image simulation. Two sets of voltammetric signals are observed. One peak at -(0.65-0.70) V (SCE) is caused by reductive desorption of cysteamine. The other signal, at -(0.25-0.40) V consists of a peak doublet. The pH dependence of the latter suggests that the origin is catalytic dihydrogen evolution. The doublet feature is indicative of two distinct cysteamine configurations. Cysteamine monolayer formation from initial nucleation to a highly ordered phase has been successfully observed in real time using oxygen-free in situ STM. Random cellular patterns, disordered adlayer formation accompanied by high step edge mobility, and ultimately a highly ordered (square root 3 x 4) R30 degrees lattice are observed sequentially. Pits are formed due to enclosure of the mobile edges during the adsorption process. In the highly ordered cysteamine layer, each unit has two spots with apparent 0.6 A height difference in STM images. The coverage 5.7 +/- 0.1 x 10(-10) mol cm(-2) determined by voltammetry supports that the spots represent two individual cysteamine molecules. A priori MD and density functional simulations hold other clues to the image interpretation and indicate that the NH(3)(+) groups dominate the tunneling contrast. A wide range of interface structures, showing variations in the sulfur binding site and orientation, gauche and trans conformers, and especially hydrogen-bonding interactions, are examined, from which it is concluded that the adsorbate structure is controlled by interactions with the solvent rather than with the substrate.

An overview of the first half-century of molecular electronics.

The seminal ideas from which molecular electronics has developed were the theories of molecular conduction advanced in the late 1940s by Robert S. Mulliken and Albert Szent-Gyorgi. These were, respectively, the concept of donor-acceptor charge transfer complexes and the possibility that proteins might in fact not be insulators The next two decades saw a burgeoning of experimental and theoretical work on electron transfer systems, together with a lone effort by D.D. Eley on conduction in proteins. The call by Feynman in his famous 1959 lecture There's Plenty of Room at the Bottom for chemists, engineers and physicists to combine to build up structures from the molecular level was influential in turning attention to the possibility of engineering single molecules to function as elements in information-processing systems. This was made tangible by the proposal of Aviram and Ratner in 1974 to use a Mulliken-like electron donor-acceptor molecule as a molecular diode, generalizing molecular conduction into molecular electronics. In the early 1970s the remarkably visionary work of Forrest L. Carter of the U.S. Naval Research Laboratories began to appear: designs for molecular wires, switches, complex molecular logic elements, and a host of related ideas were advanced. Shortly after that, conferences on molecular electronics began to be held, and the interdisciplinary programs that Feynman envisaged. There was a surge in both experimental and theoretical work in molecular electronics, and the establishment of many research centres. The past five years or so have seen extraordinarily rapid progress in fabrication and theoretical understanding. The history of how separate lines of research emanating from fundamental insights of about 50 years ago have coalesced into a thriving international research program in what might be called the ultimate nanotechnology is the subject of this review; it concentrates on the lesser-appreciated early developments in the field.

An atomistic approach to conduction between nanoelectrodes through a single molecule.

Capacitance and other properties of nanoelectrodes, finite-size metal clusters envisaged for use in complex molecular-electronic devices, are discussed. The applicability of classical electrostatics (Coulomb's and Gauss' law, Poisson's equation, etc.) to atomistic systems is investigated and the self-energy necessary to store a finite charge on an atom is found to be of central importance. In particular, the neglect of electron exchange is found to introduce severe limitations, with quantum calculations predicting fundamentally different electronic structures. Also, the well-known poor representation of the atomic self-energy inherent to modern DFT is discussed, along with its implications for molecular electronics calculations. An INDO/S method is introduced with new parameters for gold. This is the simplest approximate computational scheme that correctly includes quantum electrostatic, resonance, and spin effects, and is capable of describing arbitrary excited electronic states. Encouraging results are obtained for some trial problems. In particular, voltage differential between the electrodes in electrode-molecule-electrode conduction is obtained, not through an a priori prescription but rather by moving whole electrons between the electrodes and analyzing the response. The voltage drops across the molecule-electrode junctions and the central molecular region are then deduced. This alternative to the current Landauer-based 1-particle transmission equations for electrode-molecule-electrode conduction is discussed in terms of the use of the electronic states of the system. It provides a proper description not only of conduction via electrode-to-molecule charge or hole transfer but also of conduction via simultaneous charge and hole transfer via low-lying excited molecular electronic states, including the ability to account for electroluminescence and other chemical effects. In addition, various aspects of our research on the quantitative prediction of the I(V) curves for electrode-molecule-electrode conduction are reviewed, including demonstration of the equivalence of the formalisms generated by the Datta and the Mujica-Ratner groups, and the development of analytically solvable paradigms, including the conduction through a linear-chain Hückel wire.