Optimal diabatic bases via thermodynamic bounds.

Describing kinetic processes within a perturbation theory approach such as Fermi's golden rule requires an understanding of the initial and final states of the system. A number of different methods have been proposed for obtaining these diabatic-like states, but a robust criterion for evaluating their accuracy has not been established. Here, we approach the problem of determining the most appropriate set of diabatic states for use in incoherent rate expressions. We develop a method that rotates an initial set of diabats into an optimized set beginning with a zeroth-order diabatic Hamiltonian and choosing the rotation that minimizes the effect of non-diabatic terms on the thermodynamic free energy. The Gibbs-Bogoliubov (GB) bound on the Helmholtz free energy is thus used as the diabatic criterion. We first derive the GB free energy for a two site system and then find an expression general for any electronic system Hamiltonian. Efficient numerical methods are used to perform the minimization subject to orthogonality constraints, and we examine the resulting diabats for system Hamiltonians in various parameter regimes. The transition from localized to delocalized states is clearly seen in these calculations, and some interesting features are discussed.

Polarizabilities of adsorbed and assembled molecules: measuring the conductance through buried contacts.

We have measured the polarizabilities of four families of molecules adsorbed to Au{111} surfaces, with structures ranging from fully saturated to fully conjugated, including single-molecule switches. Measured polarizabilities increase with increasing length and conjugation in the adsorbed molecules and are consistent with theoretical calculations. For single-molecule switches, the polarizability reflects the difference in substrate-molecule electronic coupling in the ON and OFF conductance states. Calculations suggest that the switch between the two conductance states is correlated with an oxidation state change in a nitro functional group in the switch molecules.

Electronic properties of disordered organic semiconductors via QM/MM simulations.

Organic semiconductors (OSCs) have recently received significant attention for their potential use in photovoltaic, light emitting diode, and field effect transistor devices. Part of the appeal of OSCs is the disordered, amorphous nature of these materials, which makes them more flexible and easier to process than their inorganic counterparts. In addition to their technological applications, OSCs provide an attractive laboratory for examining the chemistry of heterogeneous systems. Because OSCs are both electrically and optically active, researchers have access to a wealth of electrical and spectroscopic probes that are sensitive to a variety of localized electronic states in these materials. In this Account, we review the basic concepts in first-principles modeling of the electronic properties of disordered OSCs. There are three theoretical ingredients in the computational recipe. First, Marcus theory of nonadiabatic electron transfer (ET) provides a direct link between energy and kinetics. Second, constrained density functional theory (CDFT) forms the basis for an ab initio model of the diabatic charge states required in ET. Finally, quantum mechanical/molecular mechanical (QM/MM) techniques allow us to incorporate the influence of the heterogeneous environment on the diabatic states. As an illustration, we apply these ideas to the small molecule OSC tris(8- hydroxyquinolinato)aluminum (Alq(3)). In films, Alq(3) can possess a large degree of short-range order, placing it in the middle of the order-disorder spectrum (in this spectrum, pure crystals represent one extreme and totally amorphous structures the opposite extreme). We show that the QM/MM recipe reproduces the transport gap, charge carrier hopping integrals, optical spectra, and reorganization energies of Alq(3) in quantitative agreement with available experiments. However, one cannot specify any of these quantities accurately with a single number. Instead, one must characterize each property by a distribution that reflects the influence of the heterogeneous environment on the electronic states involved. For example, the hopping integral between a given pair of Alq(3) molecules can vary by as much as a factor of 5 on the nanosecond timescale, but the integrals for two different pairs can easily differ by a factor of 100. To accurately predict mesoscopic properties such as carrier mobilities based on these calculations, researchers must account for the dynamic range of the microscopic inputs, rather than just their average values. Thus, we find that many of the computational tools required to characterize these materials are now available. As we continue to improve this computational toolbox, we envision a future scenario in which researchers can use basic information about OSC deposition to simulate device operation on the atomic scale. This type of simulation could allow researchers to obtain data that not only aids in the interpretation of experimental results but also guides the design of more efficient devices.

Chemical fabrication of heterometallic nanogaps for molecular transport junctions.

We report a simple and reproducible method for fabricating heterometallic nanogaps, which are made of two different metal nanorods separated by a nanometer-sized gap. The method is based upon on-wire lithography, which is a chemically enabled technique used to synthesize a wide variety of nanowire-based structures (e.g., nanogaps and disk arrays). This method can be used to fabricate pairs of metallic electrodes, which exhibit distinct work functions and are separated by gaps as small as 2 nm. Furthermore, we demonstrate that a symmetric thiol-terminated molecule can be assembled into such heterometallic nanogaps to form molecular transport junctions (MTJs) that exhibit molecular diode behavior. Theoretical calculations demonstrate that the coupling strength between gold and sulfur (Au-S) is 2.5 times stronger than that of Pt-S. In addition, the structures form Raman hot spots in the gap, allowing the spectroscopic characterization of the molecules that make up the MTJs.

Chiral electron transport: scattering through helical potentials.

We present a model for the transmission of spin-polarized electrons through oriented chiral molecules, where the chiral structure is represented by a helix. The scattering potential contains a confining term and a spin-orbit contribution that is responsible for the spin-dependent scattering of electrons by the molecular target. The differential scattering cross section is calculated for right- and left-handed helices and for arbitrary electron spin polarizations. We apply our model to explain chiral effects in the intensity of photoemitted polarized electrons transmitted through thin organic layers. These are molecular interfaces that exhibit spin-selective scattering with surprisingly large asymmetry factors as well as a number of remarkable magnetic properties. In our model, differences in intensity are generated by the preferential transmission of electron beams whose polarization is oriented in the same direction as the sense of advance of the helix. This model can be easily extended to the Landauer regime of conductance where conductance is due to elastic scattering, so that we can consider the conductance of chiral molecular junctions.

Transport in state space: voltage-dependent conductance calculations of benzene-1,4-dithiol.

We implement a method to study transport in a basis of many-body molecular states using the nonequilibrium Hubbard Green's function technique. A well-studied system, a junction consisting of benzene-dithiol on gold, is the focus of our consideration. Electronic structure calculations are carried out at the Hartree-Fock (HF), density functional theory (DFT), and coupled-cluster singles and doubles (CCSD) levels, and multiple molecular states are included in the transport calculation. The conductance calculation yields new information about the transport mechanism in BDT junctions.

Spectroscopic tracking of molecular transport junctions generated by using click chemistry.

Click to fill the gap: The in situ modular fabrication of molecular transport junctions in nanogaps generated by on-wire lithography is achieved by using click chemistry (see picture). The formation of molecular junctions proceeds in high yields and can be used to test different molecules; the triazole group also maintains conjugation in the molecular wires. Raman spectroscopy is used to characterize the molecular assembly processes.

Ultrafast intersystem crossing and spin dynamics of photoexcited perylene-3,4:9,10-bis(dicarboximide) covalently linked to a nitroxide radical at fixed distances.

Time-resolved transient optical absorption and EPR (TREPR) spectroscopies are used to probe the interaction of the lowest excited singlet state of perylene-3,4:9,10-bis(dicarboximide) ((1*)PDI) with a stable tert-butylphenylnitroxide radical ((2)BPNO(*)) at specific distances and orientations. The (2)BPNO(*) radical is connected to the PDI with the nitroxide and imide nitrogen atoms either para (1) or meta (3) to one another, as well as through a second intervening p-phenylene spacer (2). Transient absorption experiments on 1-3 reveal that (1*)PDI undergoes ultrafast enhanced intersystem crossing and internal conversion with tau approximately = 2 ps to give structurally dependent 8-31% yields of (3*)PDI. Energy- and electron-transfer quenching of (1*)PDI by (2)BPNO(*) are excluded on energetic and spectroscopic grounds. TREPR experiments at high magnetic fields (3.4 T, 94 GHz) show that the photogenerated three-spin system consists of the strongly coupled unpaired electrons confined to (3*)PDI, which are each weakly coupled to the unpaired electron on (2)BPNO(*) to form excited doublet (D(1)) and quartet (Q) states, which are both spectrally resolved from the (2)BPNO(*) (D(0)) ground state. The initial spin polarizations of D(1) and Q are emissive for 1 and 2 and absorptive for 3, which evolve over time to the opposite spin polarization. The subsequent decays of D(1) and Q to ground-state spin polarize D(0). The rates of polarization transfer depend on the molecular connectivity between PDI and (2)BPNO(*) and can be rationalized in terms of the dependence on molecular structure of the through-bond electronic coupling between these species.

Enhanced intersystem crossing in three-spin systems: a perturbation theory treatment.

We present a simple model for analyzing the spin dynamics of a three-spin system representing a photoexcited chromophore coupled to a stable radical species. Perturbation theory yields a Fermi's Golden Rule-type rate expression that describes the formation of a local triplet on the chromophore through spin exchange with the radical. The error introduced by perturbation theory is evaluated for a number of parameters. Finally, we explore the effect of different energetic and coupling parameters on the rate of triplet formation and suggest how this model can be used to tune the enhanced intersystem crossing in three-spin systems.

Constructing diabatic states from adiabatic states: extending generalized Mulliken-Hush to multiple charge centers with boys localization.

This article shows that, although Boys localization is usually applied to single-electron orbitals, the Boys method itself can be applied to many electron molecular states. For the two-state charge-transfer problem, we show analytically that Boys localization yields the same charge-localized diabatic states as those found by generalized Mulliken-Hush theory. We suggest that for future work in electron transfer, where systems have more than two charge centers, one may benefit by using a variant of Boys localization to construct diabatic potential energy surfaces and extract electronic coupling matrix elements. We discuss two chemical examples of Boys localization and propose a generalization of the Boys algorithm for creating diabatic states with localized spin density that should be useful for Dexter triplet-triplet energy transfer.

Switching in molecular transport junctions: polarization response.

We discuss several proposed explanations for the switching and negative differential resistance (NDR) behavior seen in some molecular junctions. Several theoretical models are discussed, and we present results of electronic structure calculations on a series of substituted oligo(phenylene ethynylene) molecules. It is shown that a previously proposed polaron model is successful in predicting NDR behavior, and the model is elaborated with image charge effects and parameters from electronic structure calculations. This model now incorporates substituent effects and includes the effects of conformational change, charging, and image charge stabilization.

Dynamics of charge transfer: rate processes formulated with nonequilibrium Green's functions.

The authors examine the connection between electron transport under bias in a junction and nonadiabatic intramolecular electron transfer (ET). It is shown that under certain assumptions it is possible to define a stationary current that allows the computation of the intramolecular transfer rate using the same formalism that is employed in the description of transport. They show that the nonequilibrium Green's function formalism of quantum transport can be used to calculate the ET rate. The formal connection between electron transport and electron transfer is made, and they work out the simple case of an electronic level coupled to a vibrational mode representing a thermal bath and show that the result is the same as expected from a Fermi golden rule treatment, and in the high-temperature limit yields the Marcus electron transfer theory. The usefulness of this alternative formulation of rates is discussed.

Effects of anharmonicity on nonadiabatic electron transfer: a model.

The effect of anharmonicity in the intramolecular modes of a model system for exothermic intramolecular nonadiabatic electron transfer is probed by examining the dependence of the transition probability on the exoergicity. The Franck-Condon factor for the Morse potential is written in terms of the Gauss hypergeometric function both for a ground initial state and for the general case, and comparisons are made between the first-order perturbation theory results for transition probability for harmonic and Morse oscillators. These results are verified with quantum dynamical simulations using wave-packet propagations on a numerical grid. The transition-probability expression incorporating a high-frequency quantum mode and low-frequency medium mode is compared for Morse and harmonic oscillators in different temperature ranges and with various coarse-graining treatments of the delta function from the Fermi golden rule expression. We find that significant deviations from the harmonic approximation are expected for even moderately anharmonic quantum modes at large values of exoergicity. The addition of a second quantum mode of opposite displacement negates the anharmonic effect at small energy change, but in the inverted regime a significantly flatter dependence on exoergicity is predicted for anharmonic modes.