A hybrid memory kernel approach for condensed phase non-adiabatic dynamics.

The spin-boson model is a simplified Hamiltonian often used to study non-adiabatic dynamics in large condensed phase systems, even though it has not been solved in a fully analytic fashion. Herein, we present an exact analytic expression for the dynamics of the spin-boson model in the infinitely slow-bath limit and generalize it to approximate dynamics for faster baths. We achieve the latter by developing a hybrid approach that combines the exact slow-bath result with the popular non-interacting blip approximation (NIBA) method to generate a memory kernel that is formally exact to second-order in the diabatic coupling but also contains higher-order contributions approximated from the second-order term alone. This kernel has the same computational complexity as the NIBA, but is found to yield dramatically superior dynamics in regimes where the NIBA breaks down-such as systems with large diabatic coupling or energy bias. This indicates that this hybrid approach could be used to cheaply incorporate higher-order effects into second-order methods and could potentially be generalized to develop alternate kernel resummation schemes.

Reactions of Persistent Carbenes with Hydrogen-Terminated Silicon Surfaces.

Surface passivation has enabled the development of silicon-based solar cells and microelectronics. However, a number of emerging applications require a paradigm shift from passivation to functionalization, wherein surface functionality is installed proximal to the silicon surface. To address this need, we report here the use of persistent aminocarbenes to functionalize hydrogen-terminated silicon surfaces via Si-H insertion reactions. Through the use of model compounds (H-Si(TMS)3 and H-Si(OTMS)3), nanoparticles (H-SiNPs), and planar Si(111) wafers (H-Si(111)), we demonstrate that among different classes of persistent carbenes, the more electrophilic and nucleophilic ones, in particular, a cyclic (alkyl)(amino)carbene (CAAC) and an acyclic diaminocarbene (ADAC), are able to undergo insertion into Si-H bonds at the silicon surface, forming persistent C-Si linkages and simultaneously installing amine or aminal functionality in proximity to the surface. The CAAC (6) is particularly notable for its clean insertion reactivity under mild conditions that produces monolayers with 21 ± 3% coverage of Si(111) atop sites, commensurate with the expected maximum of ∼20%. Atomic force and transmission electron microscopy, nuclear magnetic resonance, X-ray photoelectron, and infrared spectroscopy, and time-of-flight secondary ion mass spectrometry provided evidence for the surface Si-H insertion process. Furthermore, computational studies shed light on the reaction energetics and indicated that CAAC 6 should be particularly effective at binding to silicon dihydride, trihydride, and coupled monohyride motifs, as well as oxidized surface sites. Our results pave the way for the further development of persistent carbenes as universal ligands for silicon and potentially other nonmetallic substrates.

Condensed phase electron transfer beyond the Condon approximation.

Condensed phase electron transfer problems are often simplified by making the Condon approximation: the approximation that the coupling connecting two charge-transfer diabatic states is a constant. Unfortunately, the Condon approximation does not predict the existence of conical intersections, which are ubiquitous in both gas-phase and condensed-phase photochemical dynamics. In this paper, we develop a formalism to treat condensed-phase dynamics beyond the Condon approximation. We show that even for an extremely simple test system, hexaaquairon(ii)/hexaaquairon(iii) self-exchange in water, the electronic coupling is expected to fluctuate rapidly and non-Condon effects must be considered to obtain quantitatively accurate ultrafast nonequilibrium dynamics. As diabatic couplings are expected to fluctuate substantially in many condensed-phase electron transfer systems, non-Condon effects may be essential to quantitatively capture accurate short-time dynamics.

Communication: CDFT-CI couplings can be unreliable when there is fractional charge transfer.

Constrained density functional theory with configuration interaction (CDFT-CI) is a useful, low-cost tool for the computational prediction of electronic couplings between pseudo-diabatic constrained electronic states. Such couplings are of paramount importance in electron transfer theory and transition state theory, among other areas of chemistry. Unfortunately, CDFT-CI occasionally fails significantly, predicting a coupling that does not decay exponentially with distance and/or overestimating the expected coupling by an order of magnitude or more. In this communication, we show that the eigenvalues of the difference density matrix between the two constrained states can be used as an a priori metric to determine when CDFT-CI are likely to be reliable: when the eigenvalues are near 0 or ±1, transfer of a whole electron is occurring, and CDFT-CI can be trusted. We demonstrate the utility of this metric with several illustrative examples.

Resummed memory kernels in generalized system-bath master equations.

Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between the two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the "Landau-Zener resummation" of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics.

What can density functional theory tell us about artificial catalytic water splitting?

Water splitting by artificial catalysts is a critical process in the production of hydrogen gas as an alternative fuel. In this paper, we examine the essential role of theoretical calculations, with particular focus on density functional theory (DFT), in understanding the water-splitting reaction on these catalysts. First, we present an overview of DFT thermochemical calculations on water-splitting catalysts, addressing how these calculations are adapted to condensed phases and room temperature. We show how DFT-derived chemical descriptors of reactivity can be surprisingly good estimators for reactive trends in water-splitting catalysts. Using this concept, we recover trends for bulk catalysts using simple model complexes for at least the first-row transition-metal oxides. Then, using the CoPi cobalt oxide catalyst as a case study, we examine the usefulness of simulation for predicting the kinetics of water splitting. We demonstrate that the appropriate treatment of solvent effects is critical for computing accurate redox potentials with DFT, which, in turn, determine the rate-limiting steps and electrochemical overpotentials. Finally, we examine the ability of DFT to predict mechanism, using ruthenium complexes as a focal point for discussion. Our discussion is intended to provide an overview of the current strengths and weaknesses of the state-of-the-art DFT methodologies for condensed-phase molecular simulation involving transition metals and also to guide future experiments and computations toward the understanding and development of novel water-splitting catalysts.

Addressable carbene anchors for gold surfaces.

New strategies to access functional monolayers could augment current surface modification methods. Here we present addressable N-heterocyclic carbene (ANHC) anchors for gold surfaces. A suite of experimental and theoretical methods was used to characterize ANHC monolayers. We demonstrate grafting of highly fluorinated polymers from surface-bound ANHCs. This work establishes ANHCs as viable anchors for gold surfaces.

Septipyridines as conformationally controlled substitutes for inaccessible bis(terpyridine)-derived oligopyridines in two-dimensional self-assembly.

The position of the peripheral nitrogen atoms in bis(terpyridine)-derived oligopyridines (BTPs) has a strong impact on their self-assembly behavior at the liquid/HOPG (highly oriented pyrolytic graphite) interface. The intermolecular hydrogen bonding interactions in these peripheral pyridine units show specific 2D structures for each BTP isomer. From nine possible constitutional isomers only four have been described in the literature. The synthesis and self-assembling behavior of an additional isomer is presented here, but the remaining four members of the series are synthetically inaccessible. The self-assembling properties of three of the missing four BTP isomers can be mimicked by making use of the energetically preferred N-C-C-N transoid conformation between 2,2'-bipyridine subunits in a new class of so-called septipyridines. The structures are investigated by scanning tunneling microscopy (STM) and a combination of force-field and first-principles electronic structure calculations.