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Double machine learning is a statistical method for leveraging complex black-box models to construct approximately unbiased treatment effect estimates given observational data with high-dimensional covariates, under the assumption of a partially linear model. The idea is to first fit on a subset of the samples two non-linear predictive models, one for the continuous outcome of interest and one for the observed treatment, and then to estimate a linear coefficient for the treatment using the remaining samples through a simple orthogonalized regression. While this methodology is flexible and can accommodate arbitrary predictive models, typically trained independently of one another, this paper argues that a carefully coordinated learning algorithm for deep neural networks may reduce the estimation bias. The improved empirical performance of the proposed method is demonstrated through numerical experiments on both simulated and real data., Comment: 9 pages, 6 figures

It is shown that the residual entropy (entropy minus that of the ideal gas at the same temperature and density) is mostly synonymous with the independent variable of density scaling, identifying a direct link between these two approaches. The two-body residual entropy is demonstrated to not be a suitable surrogate for the total residual entropy in the gas phase. The residual entropy and the effective hardness of interaction (itself a derivative at constant residual entropy) are studied for the Lennard-Jones monomer and dimer as well as a range of rigid molecular models for carbon dioxide. It is observed that the density scaling exponent is related to the two-body interactions.

The solvated electron represents an elementary quantum system in a liquid environment. Electrons solvated in water have raised strong interest because of their prototypical properties, their role in radiation chemistry, and their relevance for charge separation and transport. Nonequilibrium dynamics of photogenerated electrons in water occur on ultrafast time scales and include charge transfer, localization, and energy dissipation processes. We present new insight in the role of fluctuating electric fields of the liquid for generating electrons in presence of an external terahertz field and address polaronic many-body properties of solvated electrons. The article combines a review of recent results from experiment and theory with a discussion of basic electric interactions of electrons in water., Comment: 44 pages, 9 figures

The distinct structures of contact ion pairs in water are identified. Nonlinear infrared (IR) spectroscopy and theoretical calculations allow for the separation and assignment of spectral features and interactions.

We discern hydration geometries around the sugar-phosphate-backbone of an RNA double helix at the molecular level. RNA disordering upon melting is connected with a transition from ordered water structures towards local phosphate group hydration shells.

Quantum mechanics describes the unitary time evolution of isolated systems. In reality, every quantum system interacts with its environment, leading to an irreversible loss of the phase relation. Path integral based methods provide a rigorous description of the process of decoherence. We provide an overview over recent numerical methods suited to describe the non-perturbative regime of system bath interaction. -- Quantenmechanik beschreibt die unit\"are Zeitentwicklung isolierter Systeme. In der Realit\"at interagiert jedes Quantensystem mit seiner Umwelt, was zu einem irreversiblen Verlust von Phasenbeziehungen f\"uhrt. Pfadintegralbasierte Methoden erlauben eine rigorose Beschreibung dieser Dekoh\"arenzprozesse., Comment: 2 figures, in German

The terahertz (THz) response of solvated electrons in liquid water is studied in nonlinear ultrafast pump-probe experiments. Free electrons with concentrations from c_e = 4 to 140 \times 10-6 moles/liter are generated by high-field THz or near-infrared multiphoton excitation. The time-resolved change of the dielectric function as mapped by broadband THz pulses exhibits pronounced oscillations persisting up to 30 ps. Their frequency increases with electron concentration from 0.2 to 1.5 THz. The oscillatory response is assigned to impulsively excited coherent polarons involving coupled electron and water shell motions with a frequency set by the local electric field., Comment: 5 pages, 2 figures

Electric interactions have a strong impact on the structure and dynamics of biomolecules in their native water environment. Given the variety of water arrangements in hydration shells and the femto- to subnanosecond time range of structural fluctuations, there is a strong quest for sensitive noninvasive probes of local electric fields. The stretching vibrations of phosphate groups, in particular the asymmetric (PO2)- stretching vibration {\nu}AS(PO2)-, allow for a quantitative mapping of dynamic electric fields in aqueous environments via a field-induced redshift of their transition frequencies and concomitant changes of vibrational line shapes. We present a systematic study of {\nu}AS(PO2)- excitations in molecular systems of increasing complexity, including dimethyl phosphate (DMP), short DNA and RNA duplex structures, and transfer RNA (tRNA) in water. A combination of linear infrared absorption, two-dimensional infrared (2D-IR) spectroscopy, and molecular dynamics (MD) simulations gives quantitative insight in electric-field tuning rates of vibrational frequencies, electric field and fluctuation amplitudes, and molecular interaction geometries. Beyond neat water environments, the formation of contact ion pairs of phosphate groups with Mg2+ ions is demonstrated via frequency upshifts of the {\nu}AS(PO2)- vibration, resulting in a distinct vibrational band. The frequency positions of contact geometries are determined by an interplay of attractive electric and repulsive exchange interactions., Comment: 9 pages, 6 figures

Infrared (IR) absorption in the 1000-3700 cm-1 range and 1H NMR spectroscopy reveal the existence of an asymmetric protonated water trimer, H7+O3, in acetonitrile. The core H7+O3 motif persists in larger protonated water clusters in acetonitrile up to at least 8 water molecules. Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations reveal irreversible proton transport promoted by propagating the asymmetric H7+O3 structure in solution. The QM/MM calculations allow for the successful simulation of the measured IR absorption spectra of H7+O3 in the OH stretch region, which reaffirms the assignment of the H7+O3 spectra to a hybrid-complex structure: a protonated water dimer strongly hydrogen-bonded to a third water molecule with the proton exchanging between the two possible shared-proton Zundel-like centers. The H7+O3 structure lends itself to promoting irreversible proton transport in presence of even one additional water molecule. We demonstrate how continuously evolving H7+O3 structures may support proton transport within larger water solvates., Comment: 10 Tages, 11 figures

Ions interacting with hydrated RNA play a central role in defining its secondary and tertiary structure. While spatial arrangements of ions, water molecules, and phosphate groups have been inferred from X-ray studies, the role of electrostatic and other noncovalent interactions in stabilizing compact folded RNA structures is not fully understood at the molecular level. Here, we demonstrate that contact ion pairs of magnesium (Mg2+) and phosphate groups embedded in local water shells stabilize the tertiary equilibrium structure of transfer RNA (tRNA). Employing dialyzed tRNAPhe from yeast and tRNA from Escherichia coli, we follow the population of Mg2+ sites close to phosphate groups of the ribose-phosphodiester backbone step by step, combining linear and nonlinear infrared spectroscopy of phosphate vibrations with molecular dynamics simulations and ab initio vibrational frequency calculations. The formation of up to six Mg2+/phosphate contact pairs per tRNA and local field-induced reorientations of water molecules balance the phosphate-phosphate repulsion in nonhelical parts of tRNA, thus stabilizing the folded structure electrostatically. Such geometries display limited sub-picosecond fluctuations in the arrangement of water molecules and ion residence times longer than 1 {\mu}s. At higher Mg2+ excess, the number of contact ion pairs per tRNA saturates around 6 and weakly interacting ions prevail. Our results suggest a predominance of contact ion pairs over long-range coupling of the ion atmosphere and the biomolecule in defining and stabilizing the tertiary structure of tRNA., Comment: 7 pages, 4 figures

Bridge-mediated electron transfer (ET) between a donor and an acceptor is prototypical for the description of numerous most important ET scenarios. While multi-step ET and the interplay of sequential and direct superexchange transfer pathways in the donor-bridge-acceptor (D-B-A) model is increasingly understood, the influence off-diagonal system-bath interactions on the transfer dynamics is less explored. Off-diagonal interactions account for the dependence of the ET coupling elements on nuclear coordinates (non-Condon effects) and are typically neglected. Here we numerically investigate with quasi-adiabatic propagator path integral (QUAPI) simulations the impact of off-diagonal system-environment interactions on the transfer dynamics for a wide range of scenarios in the D-B-A model. We demonstrate that off-diagonal system-environment interactions can have profound impact on the bridge-mediated ET dynamics. In the considered scenarios the dynamics itself does not allow for a rigorous assignment of the underlying transfer mechanism. Further, we demonstrate how off-diagonal system-environment interaction mediates anomalous localization by preventing long-time depopulation of the bridge B and how coherent transfer dynamics between donor D and acceptor A can be facilitated. The arising non-exponential short-time dynamics and coherent oscillations are interpreted within an equivalent Hamiltonian representation of a primary reaction coordinate model that reveals how the complex vibronic interplay of vibrational and electronic degrees of freedom underlying the non-Condon effects can impose donor-to-acceptor coherence transfer on short timescales., Comment: 29 pages, 10 figures

Quantum mechanics describes the unitary time evolution of closed systems. In practice, every quantum system interacts with the environment leading to an irreversible loss of coherence. The Spin-Boson model (SBM) is central to the understanding of the fundamental process of decoherence of a two-state quantum system interacting with a bosonic heat bath but the nature of transient dynamics in the presence of hybrid diagonal and off-diagonal system-bath interactions remains largely unexplored. Here, we investigate how the hybrid system-bath interactions of an Ohmic environment induce localization in the bias-free SBM. For strong coupling to the environment, localization is strongly affected by a dynamically generated bias via the renormalization of the tunneling amplitude. We find that counteractive effects of Hamiltonian parameters on non-exponential short-time dynamics and long-time population equilibration can lead to a separation of timescales and non-equilibrium quantum coherent dynamics that can persist even for ultra-strong system-bath interaction. The findings offer novel opportunities to exploit coherence as a resource in quantum devices operating in the ultra-strong coupling regime.

Up to now, the methods available for measuring the rate constants of reactions taking place on heterogeneous catalysts require that the catalyst be stable over long measurement times. But catalyst are often non-stationary, they may become activated under reaction conditions or become poisoned through use. It is therefore desirable to develop methods with high data acquisition rates for kinetics, so that transient rates can be measured on non-stationary catalysts. In this work, we present velocity resolved kinetics using high repetition rate pulsed laser ionization and high-speed ion imaging detection. The reaction is initiated by molecular beam pulses incident at the surface and the product formation rate is observed by a sequence of laser pulses at a high repetition rate. Ion imaging provides the desorbing product flux (reaction rate) as a function of reaction time for each laser pulse. We demonstrate the method using a 10 Hz pulsed CO molecular beam pulse train to initiate CO desorption from Pd(332) - desorbing CO is detected every millisecond by non-resonant multiphoton ionization using a 1-kHz Ti:Sapphire laser. This approach overcomes the time-consuming scanning of the delay between CO and laser pulses needed in past experiments and delivers a data acquisition rate that is 10-1000 times higher. We also apply this method to CO oxidation on Pd(332) - we record kinetic traces of CO$_2$ formation while a CO beam titrates oxygen atoms from an O-saturated surface. This provides the reaction rate as a function of O-coverage in a single experiment. We exploit this to produce controlled yet inhomogeneously mixed reactant samples for measurements of reaction rates under diffusion-controlled conditions., Comment: submitted to ACS-Cataslysis

Liquid water at ambient temperature displays ultrafast molecular motions and concomitant fluctuations of very strong electric fields originating from the dipolar H2O molecules. We show that such random intermolecular fields induce tunnel ionization of water molecules, which becomes irreversible if an external terahertz (THz) pulse imposes an additional directed electric field on the liquid. Time-resolved nonlinear THz spectroscopy maps charge separation, transport and localization of the released electrons on a few-picosecond time scale. The highly polarizable localized electrons modify the THz absorption spectrum and refractive index of water, a manifestation of a highly nonlinear response. Our results demonstrate how the interplay of local electric field fluctuations and external electric fields allows for steering charge dynamics and dielectric properties in aqueous systems.

Real-time three dimensional (3D) ultrasound provides complete visualization of inner body organs and blood vasculature, which is crucial for diagnosis and treatment of diverse diseases. However, 3D systems require massive hardware due to the huge number of transducer elements and consequent data size. This increases cost significantly and limits both frame rate and image quality, thus preventing 3D ultrasound from being common practice in clinics worldwide. A recent study proposed a technique, called convolutional beamforming algorithm (COBA), which obtains improved image quality while allowing notable element reduction. COBA was developed and tested for 2D focused imaging using full and sparse arrays. The later was referred to as sparse COBA (SCOBA). In this paper, we build upon previous work and introduce a nonlinear beamformer for 3D imaging, called COBA-3D, consisting of 2D spatial convolution of the in-phase and quadrature received signals. The proposed technique considers diverging-wave transmission, thus, achieves improved image resolution and contrast compared with standard delay-and-sum beamforming, while enabling high frame rate. Incorporating 2D sparse arrays into our method creates SCOBA-3D: a sparse beamformer which offers significant element reduction and thus allows to perform 3D imaging with the resources typically available for 2D setups. To create 2D thinned arrays, we present a scalable and systematic way to design 2D fractal sparse arrays. The proposed framework paves the way for affordable ultrafast ultrasound devices that perform high-quality 3D imaging, as demonstrated using phantom and ex-vivo data.

The extent of contact and solvent shared ion pairs of phosphate groups with Na$^+$, Ca$^{2+}$ and Mg$^{2+}$ ions in aqueous environment and their relevance for the stability of polyanionic DNA and RNA structures is highly debated. Employing the asymmetric phosphate stretching vibration of dimethyl phosphate (DMP), a model system of the sugar-phosphate backbone of DNA and RNA, we present linear infrared, femtosecond infrared pump-probe and absorptive 2D-IR spectra that report on contact ion pair formation via the presence of blue shifted spectral signatures. Compared to the linear infrared spectra, the nonlinear spectra reveal contact ion pairs with increased sensitivity because the spectra accentuate differences in peak frequency, transition dipole moment strength, and excited state lifetime. The experimental results are corroborated by long time scale MD simulations, benchmarked by density functional simulations on phosphate-ion-water clusters. The microscopic interpretation reveals subtle structural differences of ion pairs formed by the phosphate group and the ions Na$^+$, Ca$^{2+}$ and Mg$^{2+}$. Intricate properties of the solvation shell around the phosphate group and the ion are essential to explain the experimental observations. The present work addresses a challenging to probe topic with the help of a model system and establishes new experimental data of contact ion pair formation, thereby underlining the potential of nonlinear 2D-IR spectroscopy as an analytical probe of phosphate-ion interactions in complex biological systems.

The water hydration shell has decisive impact on the structural and functional properties of RNA. Changes of RNA structure upon melting and in biochemical processes are accompanied by a change of hydration patterns, a process which is barely characterized. To discern hydration geometries around the backbone phosphate groups of an RNA double helix at the molecular level, we combine two-dimensional infrared spectroscopy of phosphate vibrations with theoretical simulations. There are three distinct coexisting hydration motifs of the RNA A-helix, an ordered chain-like arrangement of water molecules with links between neighboring phosphate groups, separate local hydration shells of up to six water molecules, and hydrated phosphate/counterion contact pairs. RNA disordering upon melting is connected with a transition from predominant ordered water structures to local hydration shells around phosphate units. Structural fluctuations are dominated by librational water motions occurring on a 300 fs time scale, without exchange between hydration motifs.

The interaction of phosphate groups with ions in an aqueous environment has a strong impact on the structure and folding processes of DNA and RNA. The dynamic variety of ionic arrangements, including both contact pairs and water separated ions, and the molecular coupling mechanisms are far from being understood. In a combined experimental and theoretical approach, we address the properties of contact ion pairs of the prototypical system dimethyl-phosphate with Na$^+$, Ca$^{2+}$, and Mg$^{2+}$ ions in water. Linear and femtosecond two-dimensional infrared (2D-IR) spectroscopy of the asymmetric (PO$_2$)$^-$ stretching vibration separates and characterizes the different species via their blue-shifted vibrational signatures and 2D-IR lineshapes. Phosphate-magnesium contact pairs stand out as the most compact geometry while the contact pairs with Ca$^{2+}$ and Na$^+$ display a wider structural variation. Microscopic density functional theory simulations rationalize the observed frequency shifts and reveal distinct differences between the contact geometries.

Biomolecules couple to their aqueous environment through a variety of noncovalent interactions. Local structures at the surface of DNA and RNA are frequently determined by hydrogen bonds with water molecules, complemented by non-specific electrostatic and many-body interactions. Structural fluctuations of the water shell result in fluctuating Coulomb forces on polar and/or ionic groups of the biomolecular structure and in a breaking and reformation of hydrogen bonds. Two-dimensional infrared (2D-IR) spectroscopy of vibrational modes of DNA and RNA gives insight into local hydration geometries, elementary molecular dynamics, and the mechanisms behind them. In this chapter, recent results from 2D-IR spectroscopy of native and artificial DNA and RNA are presented, together with theoretical calculations of molecular couplings and molecular dynamics simulations. Backbone vibrations of DNA and RNA are established as sensitive noninvasive probes of the complex behavior of hydrated helices. The results reveal the femtosecond fluctuation dynamics of the water shell, the short-range character of Coulomb interactions, and the strength and fluctuation amplitudes of interfacial electric fields., Comment: To appear as Chapter 8 of Springer Series in Optical Sciences: Coherent Multidimensional Spectroscopy -- Editors: Cho, Minhaeng (Ed.), 2019

The solvation structure of protons in aqueous media is highly relevant to electric properties and to proton transport in liquids and membranes. At ambient temperature, polar liquids display structural fluctuations on femto- to picosecond time scales with a direct impact on proton solvation. We apply two-dimensional infrared (2D-IR) spectroscopy for following proton dynamics in acetonitrile/water mixtures with the Zundel cation H$_5$O$_2^+$ prepared in neat acetonitrile as a benchmark. The 2D-IR spectra of the proton transfer mode of H$_5$O$_2^+$ demonstrate stochastic large-amplitude motions in the double-minimum proton potential, driven by fluctuating electric fields. In all cases the excess proton is embedded in a water dimer, forming an H$_5$O$_2^+$ complex as major solvation species. This observation is rationalized by quantum mechanics/molecular mechanics molecular dynamics simulations including up to 4 water molecules embedded in acetonitrile. The Zundel motif interacts with its closest water neighbor in an H$_7$O$_3^+$ unit without persistent proton localization.