Dynamic treatment of vibrational energy relaxation in a heterogeneous and fluctuating environment

A computational approach to describe the energy relaxation of a high-frequency vibrational mode in a fluctuating heterogeneous environment is outlined. Extending previous work [H. Fujisaki, Y. Zhang, and J.E. Straub, J. Chem. Phys. {\bf 124}, 144910 (2006)], second-order time-dependent perturbation theory is employed which includes the fluctuations of the parameters in the Hamiltonian within the vibrational adiabatic approximation. This means that the time-dependent vibrational frequencies along an MD trajectory are obtained via a partial geometry optimization of the solute with fixed solvent and a subsequent normal mode calculation. Adopting the amide I mode of N-methylacetamide in heavy water as a test problem, it is shown that the inclusion of dynamic fluctuations may significantly change the vibrational energy relaxation. In particular, it is found that relaxation occurs in two phases, because for short times ($\lesssim$ 200 fs) the spectral density appears continuous due to the frequency-time uncertainty relation, while at longer times the discrete nature of the bath becomes apparent. Considering the excellent agreement between theory and experiment, it is speculated if this behavior can explain the experimentally obtained biphasic relaxation the amide I mode of N-methylacetamide.Comment: 24 pages, 7 figures, submitted to J. Chem. Phy

Current-induced nonequilibrium vibrations in single-molecule devices

Finite-bias electron transport through single molecules generally induces nonequilibrium molecular vibrations (phonons). By a mapping to a Fokker-Planck equation, we obtain analytical scaling forms for the nonequilibrium phonon distribution in the limit of weak electron-phonon coupling $\lambda$ within a minimal model. Remarkably, the width of the phonon distribution diverges as $\sim\lambda^{-\alpha}$ when the coupling decreases, with voltage-dependent, non-integer exponents $\alpha$. This implies a breakdown of perturbation theory in the electron-phonon coupling for fully developed nonequilibrium. We also discuss possible experimental implications of this result such as current-induced dissociation of molecules.Comment: 7 pages, 4 figures; revised and extended version published in Phys. Rev.

Molecular Wires Acting as Coherent Quantum Ratchets

The effect of laser fields on the electron transport through a molecular wire being weakly coupled to two leads is investigated. The molecular wire acts as a coherent quantum ratchet if the molecule is composed of periodically arranged, asymmetric chemical groups. This setup presents a quantum rectifier with a finite dc-response in the absence of a static bias. The nonlinear current is evaluated in closed form within the Floquet basis of the isolated, driven wire. The current response reveals multiple current reversals together with a nonlinear dependence (reflecting avoided quasi-energy crossings) on both, the amplitude and the frequency of the laser field. The current saturates for long wires at a nonzero value, while it may change sign upon decreasing its length.Comment: 4 pages, 4 figures, RevTeX

Model ab initio study of charge carrier solvation and large polaron formation on conjugated carbon chains

Using long C_{N}H_{2} conjugated carbon chains with the polyynic structure as prototypical examples of one-dimensional (1D) semiconductors, we discuss self-localization of excess charge carriers into 1D large polarons in the presence of the interaction with a surrounding polar solvent. The solvation mechanism of self-trapping is different from the polaron formation due to coupling with bond-length modulations of the underlying atomic lattice well-known in conjugated polymers. Model ab initio computations employing the hybrid B3LYP density functional in conjunction with the polarizable continuum model are carried out demonstrating the formation of both electron- and hole-polarons. Polarons can emerge entirely due to solvation but even larger degrees of charge localization occur when accompanied by atomic displacements

Monitoring and modeling infiltration–recharge dynamics of managed aquifer recharge with desalinated seawater

We study the relation between surface infiltration and groundwater recharge during managed aquifer recharge (MAR) with desalinated seawater in an infiltration pond, at the Menashe site that overlies the northern part of the Israeli Coastal Aquifer. We monitor infiltration dynamics at multiple scales (up to the scale of the entire pond) by measuring the ponding depth, sediment water content and groundwater levels, using pressure sensors, single-ring infiltrometers, soil sensors, and observation wells. During a month (January 2015) of continuous intensive MAR (2.45  ×  10⁶ m³ discharged to a 10.7 ha area), groundwater level has risen by 17 m attaining full connection with the pond, while average infiltration rates declined by almost 2 orders of magnitude (from  ∼  11 to  ∼  0.4 m d⁻¹). This reduction can be explained solely by the lithology of the unsaturated zone that includes relatively low-permeability sediments. Clogging processes at the pond-surface – abundant in many MAR operations – are negated by the high-quality desalinated seawater (turbidity  ∼  0.2 NTU, total dissolved solids  ∼  120 mg L⁻¹) or negligible compared to the low-permeability layers. Recharge during infiltration was estimated reasonably well by simple analytical models, whereas a numerical model was used for estimating groundwater recharge after the end of infiltration. It was found that a calibrated numerical model with a one-dimensional representative sediment profile is able to capture MAR dynamics, including temporal reduction of infiltration rates, drainage and groundwater recharge. Measured infiltration rates of an independent MAR event (January 2016) fitted well to those calculated by the calibrated numerical model, showing the model validity. The successful quantification methodologies of the temporal groundwater recharge are useful for MAR practitioners and can serve as an input for groundwater flow models

Traversal time for electron tunneling in water

The traversal time for tunneling is a measure of the time during which the transmitted particle can be affected by interactions localized in the barrier. The Buttiker-Landauer approach, which estimates this time by imposing an internal clock on the system, has been applied so far for relatively simple 1-dimensional models. Here we apply this approach to estimate the traversal time for electron tunneling through a realistic 3-dimensional model of a water layer. Observed structure in the energy dependence of times computed reflects the existence of transient tunneling resonances associated with instantaneous water structures.Comment: 9 pages, 3 figures. Submitted to the Journal of Chemical Physic

Current Profiles of Molecular Nanowires; DFT Green Function Representation

The Liouville-space Green function formalism is used to compute the current density profile across a single molecule attached to electrodes. Time ordering is maintained in real, physical, time, avoiding the use of artificial time loops and backward propagations. Closed expressions for molecular currents, which only require DFT calculations for the isolated molecule, are derived to fourth order in the molecule/electrode coupling.Comment: 21 page

Finite-size scaling from self-consistent theory of localization

Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the finite-size scaling procedure used for studies of the critical behavior in d-dimensional case and based on the use of auxiliary quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good agreement with numerical results: it signifies the absence of essential contradictions with the Vollhardt and Woelfle theory on the level of raw data. The results \nu=1.3-1.6, usually obtained at d=3 for the critical exponent of the correlation length, are explained by the fact that dependence L+L_0 with L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\nu} with \nu>1. For dimensions d\ge 4, the modified scaling relations are derived; it demonstrates incorrectness of the conventional treatment of data for d=4 and d=5, but establishes the constructive procedure for such a treatment. Consequences for other variants of finite-size scaling are discussed.Comment: Latex, 23 pages, figures included; additional Fig.8 is added with high precision data by Kramer et a

Electron transport through dipyrimidinyl-diphenyl diblock molecular wire: protonation effect

Recently, rectifying direction inversion has been observed in dipyrimidinyl-diphenyl (PMPH) diblock molecular wire [J. Am. Chem. Soc. (2005) 127, 10456], and a protonation mechanism was suggested to explain this interesting phenomena. In this paper, we study the protonation effect on transport properties of PMPH molecule by first principles calculations. No significant rectification is found for the pristine diblock molecular wire. Protonation leads to conductance enhancement and rectification. However, for all considered junctions with rectifying effect, the preferential current directions are samely from dipyrimidinyl side to diphenyl side. Effect of molecule-electrode anchoring geometry is studied, and it is not responsible for the discrepancy between experiment and theory.Comment: 17 pages, 8 figure

A self-consistent quantum master equation approach to molecular transport

We propose a self-consistent generalized quantum master equation (GQME) to describe electron transport through molecular junctions. In a previous study [M.Esposito and M.Galperin. Phys. Rev. B 79, 205303 (2009)], we derived a time-nonlocal GQME to cure the lack of broadening effects in Redfield theory. To do so, the free evolution used in the Born-Markov approximation to close the Redfield equation was replaced by a standard Redfield evolution. In the present paper, we propose a backward Redfield evolution leading to a time-local GQME which allows for a self-consistent procedure of the GQME generator. This approach is approximate but properly reproduces the nonequilibrium steady state density matrix and the currents of an exactly solvable model. The approach is less accurate for higher moments such as the noise.Comment: 9 pages, 4 figure