Noel S. Hush

Distance Dependence of Electron Transfer Rates

Abstract Electron exchange processes between complex ions or aromatic radical ions in solution are typically close to electronically adiabatic. This will generally not be the case for electron transfers over large distances, particularly those in biological (e.g. photosynthetic) systems. The factors governing variation of rate constant with distance are discussed. An important result is that, in favourable cases, ‘through-σ-bond’ interaction can result in decrease of the electron coupling integral J according to a relatively low inverse power law, rather than the exponential fall-off with distance expected for ‘through-space’ interaction.1,2

Formalism, analytical model, and a priori Green’s-function-based calculations of the current–voltage characteristics of molecular wires

Various Green’s-function-based formalisms which express the current I as a function of applied voltage V for an electrode–molecule–electrode assembly are compared and contrasted. The analytical solution for conduction through a Huckel (tight binding) chain molecule is examined and only one of these formalisms is shown to predict the known conductivity of a one-dimensional metallic wire. Also, from this solution we extract the counter-intuitive result that the imaginary component of the self-energy produces a shift in the voltage at which molecular resonances occur, and complete analytical descriptions are provided of the conductivity through one-atom and two-atom bridges. A method is presented by which a priori calculations could be performed, and this is examined using extended-Huckel calculations for two gold electrodes spanned by the dithioquinone dianion. A key feature of this is the use of known bulk-electrode properties to model the electrode surface rather than the variety of more approximate schemes which are in current use. These other schemes are shown to be qualitatively realistic but not sufficiently reliable for use in quantitative calculations. We show that in such calculations it is very important to obtain accurate estimates of both the molecule–electrode coupling strength and the location of the electrode’s Fermi energies with respect to the molecular state energies.Various Green’s-function-based formalisms which express the current I as a function of applied voltage V for an electrode–molecule–electrode assembly are compared and contrasted. The analytical solution for conduction through a Huckel (tight binding) chain molecule is examined and only one of these formalisms is shown to predict the known conductivity of a one-dimensional metallic wire. Also, from this solution we extract the counter-intuitive result that the imaginary component of the self-energy produces a shift in the voltage at which molecular resonances occur, and complete analytical descriptions are provided of the conductivity through one-atom and two-atom bridges. A method is presented by which a priori calculations could be performed, and this is examined using extended-Huckel calculations for two gold electrodes spanned by the dithioquinone dianion. A key feature of this is the use of known bulk-electrode properties to model the electrode surface rather than the variety of more approximate schem...

The structure, energetics, and nature of the chemical bonding of phenylthiol adsorbed on the Au(111) surface: implications for density-functional calculations of molecular-electronic conduction.

The adsorption of phenylthiol on the Au(111) surface is modeled using Perdew and Wang density-functional calculations. Both direct molecular physisorption and dissociative chemisorption via S-H bond cleavage are considered as well as dimerization to form disulfides. For the major observed product, the chemisorbed thiol, an extensive potential-energy surface is produced as a function of both the azimuthal orientation of the adsorbate and the linear translation of the adsorbate through the key fcc, hcp, bridge, and top binding sites. Key structures are characterized, the lowest-energy one being a broad minimum of tilted orientation ranging from the bridge structure halfway towards the fcc one. The vertically oriented threefold binding sites, often assumed to dominate molecular electronics measurements, are identified as transition states at low coverage but become favored in dense monolayers. A similar surface is also produced for chemisorption of phenylthiol on Ag(111); this displays significant qualitative differences, consistent with the qualitatively different observed structures for thiol chemisorption on Ag and Au. Full contours of the minimum potential energy as a function of sulfur translation over the crystal face are described, from which the barrier to diffusion is deduced to be 5.8 kcal mol(-1), indicating that the potential-energy surface has low corrugation. The calculated bond lengths, adsorbate charge and spin density, and the density of electronic states all indicate that, at all sulfur locations, the adsorbate can be regarded as a thiyl species that forms a net single covalent bond to the surface of strength 31 kcal mol(-1). No detectable thiolate character is predicted, however, contrary to experimental results for alkyl thiols that indicate up to 20%-30% thiolate involvement. This effect is attributed to the asymptotic-potential error of all modern density functionals that becomes manifest through a 3-4 eV error in the lineup of the adsorbate and substrate bands. Significant implications are described for density-functional calculations of through-molecule electron transport in molecular electronics.

Adsorption of Benzene on Copper, Silver, and Gold Surfaces.

The adsorption of benzene on the Cu(111), Ag(111), Au(111), and Cu(110) surfaces at low coverage is modeled using density-functional theory (DFT) using periodic-slab models of the surfaces as well as using both DFT and complete-active-space self-consistent field theory with second-order Møller-Plesset perturbation corrections (CASPT2) for the interaction of benzene with a Cu13 cluster model for the Cu(110) surface. For the binding to the (111) surfaces, key qualitative features of the results such as weak physisorption, the relative orientation of the adsorbate on the surface, and surface potential changes are in good agreement with experimental findings. Also, the binding to Cu(110) is predicted to be much stronger than that to Cu(111) and much weaker than that seen in previous calculations for Ni(110), as observed. However, a range of physisorptive-like and chemisorptive-like structures are found for benzene on Cu(110) that are roughly consistent with observed spectroscopic data, with these structures differing dramatically in geometry but trivially in energy. For all systems, the bonding is found to be purely dispersive in nature with minimal covalent character. As dispersive energies are reproduced very poorly by DFT, the calculated binding energies are found to dramatically underestimate the observed ones, while CASPT2 calculations indicate that there is no binding at the Hartree-Fock level and demonstrate that the expected intermolecular correlation (dispersive) energy is of the correct order to explain the experimental binding-energy data. DFT calculations performed for benzene on Cu(110) and for benzene on the model cluster indicate that this cluster is actually too reactive and provides a poor chemical model for the system.

Mixed valence: origins and developments

Mixed-valence compounds were recognized by chemists more than a century ago for their unusual colours and stoichiometries, but it was just 40 years ago that two seminal articles brought together the then available evidence. These articles laid the foundations for understanding the physical properties of such compounds and how the latter correlate with molecular and crystal structures. This introduction to a discussion meeting briefly surveys the history of mixed valence and sets in context contributions to the discussion describing current work in the field.

An Overview of the First Half‐Century of Molecular Electronics

Abstract: 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 Theres 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.

Long-range exchange contribution to singlet-singlet energy transfer in a series of rigid bichromophoric molecules

Abstract Intramolecular singlet-singlet energy transfer is reported in a series of compounds containing a 1,4-dimethoxy-naphthalene chromophore as the energy donor and a cyclic ketone as the energy acceptor connected by rigid, elongated, saturated hydrocarbon bridges with an effective length of 4, 6, and 8 CC σ bonds. The rate of energy transfer is found to be proportional to the spectral overlap - as varied by solvent variation - and to show an exponential distance dependence while its magnitude significantly exceeds that predicted for a dipole-dipole coupling mechanism. From this it is concluded that energy transfer occurs predominantly via an exchange mechanism. Exchange integrals of 60, 10, and 2.5 cm −1 across 4, 6, and 8 σ bonds are calculated. The magnitude of these is proposed to signify through-bond exchange interaction between symmetry-matched donor (ππ*) and acceptor (nπ*) states.

The validity of electrostatic predictions of the shapes of van der Waals dimers

Abstract The interaction energies of the van der Waals dimers H 2 O-H 2 O, Cl 2 -HF, ClF-HF and N 2 O-HF have been calculated for a range of geometries using ab initio SCF techniques. The SCF binding energies have been decomposed into electrostatic, exchange, polarisation and charge-transfer contributions and the intermolecular angles optimised with respect to various combinations of the above components. The effects of exchange, polarisation and charge transfer on the shape of a given dimer are found approximately to cancel, so that in each case a purely electrostatic model is capable of predicting intermolecular angles that agree well with those of a full SCF treatment, as well as with experiment. These findings are consistent with the proposals and earlier calculations of Buckingham and Fowler.

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. Pokornýs 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.

Electron transfer in retrospect and prospect 1: Adiabatic electrode processes

The development of the theory of adiabatic electrode processes leading to its current state is briefly reviewed.