Session D35: Focus Session: DFT II: Molecular Conductance; Charge Transfer

On the derivative discontinuity in molecular junctions

Both the wave and particle aspects of the electron play essential roles in transport through single-molecule junctions. The wave character is implicit both in the Landauer formula used to understand nanoscale transport and in the very chemical bonds holding the junction together, while the particle aspect is manifested in phenomena such as Coulomb blockade and shot noise. The dominant computational paradigm for transport in single-molecule junctions involves local or semilocal approximations to density functional theory combined with nonequilibrium Green's functions. This approach does exceptionally well at describing the wave aspect of the electron, but fails to describe the particle aspect---due to the omission of the derivative discontinuity in the exchange-correlation potential that arises in the limit of vanishing lead-molecule coupling. To understand the role of the derivative discontinuity in molecular junctions, we investigated the transport and occupancy of a simple Anderson model of a molecular junction. We showed\footnote{Justin P. Bergfield, Zhenfei Liu, Kieron Burke, Charles A. Stafford, arXiv:1106.3104v2} that the exact single-particle Kohn-Sham potential of density functional theory reproduces the linear-response transport of the Anderson model exactly, despite the lack of a Kondo peak in its spectral function. Using Bethe ansatz techniques, we calculated this potential exactly for all coupling strengths, including the cross-over from mean-field behavior to charge quantization caused by the derivative discontinuity. The implications of our results for more complex molecular junctions will be discussed.   

A density functional that works for transport through Anderson junction

Transport through an Anderson junction can be exactly described by density functional theory, at zero temperature and in the linear response regime. Using Bethe ansatz, we calculate the exact Kohn-Sham potential delivering the exact transmission. We propose a simple parametrization for the Kohn-Sham potential, using a known exact condition. Our parametrization faithfully reproduces numerical results, including the gradual development of the derivative discontinuity that is essential in describing Coulomb blockade correctly.   

Non-steady state in quantum transport

The standard approach to quantum transport combines the Landauer-Buettiker (LB) formalism with ground-state density functional theory (DFT). The basic assumption of this approach is that a steady state is achieved after turning on a DC bias. Here we show that this assumption is ``not'' valid in general and and give examples for which no steady state develop within several adiabatic (time-local) approximations as well as in non-interacting systems. In these cases a time-dependent description of transport is essential. For the non-interacting case, the presence of bound states in a biased system is shown analytically and numerically to lead to persistent, localized current oscillations which can be much larger than the steady part of the current (PCCP. 11, 4535(2009)). For the interacting case, the discontinuity of the exchange-correlation potential of DFT in the context of electron transport for an interacting nanojunction attached to biased leads, gives rise to a dynamical state characterized by correlation-induced current oscillations in the Coulomb-blockade regime (PRL. 104, 236801(2010)). In addition, for multistable systems, the time-dependent approach describes if and how a solution can be reached through time evolution.   

DFT methods for conjugated materials: From benchmarks to functionals

From a theoretical standpoint, many of the problems of interest in the study of pi-conjugated materials for organic electronics applications pose a particular challenge for many modern density functional theory methods. Systematic errors have been observed, for instance, in the description of charge-transfer excitations at donor/acceptor interfaces, in linear and non-linear polarizabilites, as well as in the geometric and electronic properties of conjugated polymers [1,2]. We will discuss recent results in our lab aimed at: (i) understanding the sources of error for some of these problems; (ii) addressing these errors using tuned long-range corrected functionals; and (iii) using these results to guide the development of state-of-the-art methodologies in a new open-source DFT code. \\[4pt] [1] J. S. Sears, T. Korzdorfer, C. R. Zhang, and J. L. Bredas, J. Chem. Phys. 135 151103 (2011)\\[0pt] [2] T. Korzdorfer, J. S. Sears, C. Sutton, and J. L. Bredas, J. Chem. Phys., accepted.   

Fundamental and excitation gaps in molecules of relevance for organic photovoltaics from an optimally tuned range-separated hybrid functional

The fundamental and optical gaps of relevant molecular systems are of primary importance for organic-based photovoltaics. Unfortunately, whereas optical gaps are accessible with time-dependent density functional theory (DFT), the highest -occupied - lowest-unoccupied eigenvalue gaps resulting from DFT calculations with semi-local or hybrid functionals routinely and severely underestimate the fundamental gaps of gas-phase organic molecules. Here, we show that a range-separated hybrid functional, optimally tuned so as to obey Koopmans' theorem, provides fundamental gaps that are very close to benchmark results obtained from many-body perturbation theory in the GW approximation. We then show that using this functional does not compromise the possibility of obtaining reliable optical gaps from time-dependent DFT. We therefore suggest optimally-tuned range-separated hybrid functionals as a practical and accurate tool for DFT-based predictions of photovoltaically relevant and other molecular systems. For more details, see S. Refaely-Abramson, R. Baer, L. Kronik, Phys. Rev. B 84, 075144 (2011).   

(1) Modeling emissive charge-transfer states in solution phase functionalized silsesquioxanes. (2) On symmetry hidden charge transfer states: Lessons for the design of functionals

Range separate hybrid functionals are used to study the charge transfer processes in chromophores attached to silsesquioxanes molecular species. We investigate the experimentally observed red shifting of the emission spectra in comparison to the spectral shift for the individual ligand. Solvent effects are accounted for via a combination of constrained density functional theory and the polarizable continuum (PCM) model. We quantitatively reproduce the experimental red shift and identify the emissive state as a ligand-to-ligand, rather than a ligand-to-silsesquioxane, charge-transfer state. We also find that the enhanced red-shift cannot be explained without accounting for solvation effects and demonstrate the importance of using a range-separated hybrid functional, as opposed to more traditional functionals such as B3LYP, to obtain reliable predictions regarding the emissive state. If time allows we will also discuss the limitations and successes of RSH functionals in treating the case of charge transfer processes that are hidden by system symmetry. We use related models to draw insight for designing improved functionals.   

Density Functional Methods and Electronic Processes in Organic Materials

When modeling the fundamental processes in organic electronic materials, ab initio calculations play an important role because they provide an independent source of information. It is thus critical to use accurate and reliable ab initio methods. In this talk, we will share our experience in using density functional methods to study charge generation and transport in some organic systems. These include prototypical polythiophene and polyfluorene, as well as some newly synthesized conjugated molecules. They all have strong dispersion forces and strong electron-vibration coupling; both are well-known difficult effects for density functional methods to capture accurately. We will describe our effort in exploring ways to do meaningful calculations. Close collaborations with experimental work will also be emphasized.   

Modelling Charge Transfer Reactions and Excitations with Subsystem DFT

The subsystem formulation of DFT known as Frozen Density Embedding (FDE) offers an excellent platform for studying charge transfer reactions in solvated systems, such as biosystems. We present the necessary theory developments for the calculation of the electronic couplings as well as the charge transfer excitations from FDE derived densities. We present preliminary calculations on DNA oligomers radical cations that include donor-bridge, donor-bridge-acceptor, and fully solvated systems.   

Ab initio molecular dynamics study of the electric double-layer capacitance at solution-electrode interfaces

Electric double-layer (EDL) is known as an important stage for electrochemical reactions at electrode-liquid interfaces. It has also attracted growing interest for its applications to electronic devices, called EDL capacitors (supercapacitors) and EDL transistors. In efficient development of each device, predicting the EDL capacitance in light of the material features is required. However, Helmholtz capacitance, the part of the EDL capacitance depending on the microscopic structure, has still not been estimated theoretically. Therefore, to evaluate that, we calculated the structure of solution-electrode interfaces by using ab initio molecular dynamics with effective screening medium method. As a result, we made it possible to estimate the Helmholtz capacitance taking the effect of the molecular orientation of the water and the electronic polarization in the water molecules due to the electric field into account. Apparent dielectric constant of the water near the interface can also be calculated. Interestingly, the results reveal that the existence of a first layer of the water molecules near the electrode determines the distance of closest approach of hydrated ions. Moreover, the estimated dielectric constant of the first layer differs from that predicted by the classical theory.   

Assessing the fitness of various exchange-correlation functionals for TD-DFT studies of charge-transfer excitations in organic dyes

Dye Sensitized Solar Cells (DSSCs) are a possible alternative to the more expensive silicon-based cells. Theoretical research in this field has highlighted some of the issues with time-dependent density functional theory (TD-DFT) that is widely used to study electronic excitations of matter. The situation is complicated by the fact that several classes of approximations to the exchange correlation functional can be employed, however, not one of these strictly outperforms the others in its description of charge-transfer excitations. In this work, UV-Vis spectra are calculated using TD-DFT for several organic dyes -- alizarin, squaraine, 4-(N, N-dimethylamino) benzonitrile, polyene-linker dyes and triphenylamine-donor dyes. We studied the dyes within three approximations (PBE, B3LYP and CAM-B3LYP) to the exchange-correlation functional. In the dyes considered here, a correlation exists between the functional performance and the spatial overlap of the states involved in the excitations. This overlap can be quantified to provide a good guideline for choosing the right functional when studying intramolecular charge transfer in dyes. It will be an invaluable tool when studying these molecules within more challenging systems, such as dye-titania complexes in DSSCs.   

Electronic density functional theory in the grand canonical ensemble, electrochemistry, and the underpotential deposition of Cu/Pt(111)

The study of electrochemical systems within electronic density functional theory requires the handling of non-neutral electronic systems in the plane-wave basis in order to accurately describe charged metallic surfaces; this can be accomplished in joint density functional theory by adding an electrolyte with Debye screening \footnote{K. L. Weaver and T. A. Arias (under preparation)}. This capability opens up the opportunity to work in the grand canonical ensemble at fixed chemical potential $\mu$ for the electrons, which corresponds directly to the experimental setting in electrochemistry. We present efficient techniques for electronic density functional calculations at fixed $\mu$, and demonstrate the improvement in predictive power over conventional neutral calculations using the underpotential deposition of Cu/Pt(111) as an example: for the first time, we calculate absolute voltages for electrochemical processes in excellent agreement with experiment, instead of voltage shifts alone.   

First-Principles Studies of Structure and Energy Level Alignment of Thiophene Assemblies on Methyl-Terminated Si(111)

Adsorption of organic molecules on semiconductor photocatalysts has attracted significant attention for energy conversion applications. In this work, we use density functional theory and many-body perturbation theory within the GW approximation to study the geometry, binding energetics, and energy level alignment of a model ligand, thiophene (C4H4S), chemisorbed via a C-Si bond on methyl-terminated silicon(111) substrates. We quantify the impact of coverage, interface dipoles, hybridization, and polarization effects on level alignment. For sufficiently weakly-coupled frontier orbitals, we explore the extent to which the self-energy change upon adsorption relative to the gas phase is dominated by nonlocal electrostatic polarization effects [1]. The implications of our results for other thiophene-related ligands, and future spectroscopic experiments, will be thoroughly discussed. We acknowledge DOE for support through JCAP, and NERSC for computational resources.\\[4pt] [1] J. B. Neaton, M. S. Hybertsen and S. G. Louie, Phys. Rev. Lett. 97, 216405 (2006).   

Electronic level alignment at a metal-molecule interface from a short-range hybrid functional

Hybrid functionals often exhibit a marked improvement over semi-local functionals in the description of the electronic structure of organic materials. Because short-range hybrid functionals, notably the Heyd-Scuseria-Ernzerhof (HSE) functional, can also describe the electronic structure of metals reasonably well, it is interesting to examine to which extent they can correctly describe the electronic structure at metal-organic interfaces. Here, we address this question by comparing HSE calculations with many-body perturbation theory calculations in the GW approximation, or with experimental photoemission data, for two prototypical systems: benzene on graphite and benzene diamine on gold. For both cases, we find that while HSE yields results that are somewhat closer to experiment than those of semi-local functionals, the HSE prediction is still lacking quantitatively by $\sim$1 eV. We show that this quantitative failure arises because HSE does not correctly capture the fundamental gap of the organic, or its renormalization by the metal. These discrepancies are traced back to missing long-range exchange and correlation components, an explanation which applies to any conventional or short-range hybrid functional.