Robust Bayes-Like Estimation: Rho-Bayes estimation

We consider the problem of estimating the joint distribution $P$ of $n$ independent random variables within the Bayes paradigm from a non-asymptotic point of view. Assuming that $P$ admits some density $s$ with respect to a given reference measure, we consider a density model $\overline S$ for $s$ that we endow with a prior distribution $\pi$ (with support $\overline S$) and we build a robust alternative to the classical Bayes posterior distribution which possesses similar concentration properties around $s$ whenever it belongs to the model $\overline S$. Furthermore, in density estimation, the Hellinger distance between the classical and the robust posterior distributions tends to 0, as the number of observations tends to infinity, under suitable assumptions on the model and the prior, provided that the model $\overline S$ contains the true density $s$. However, unlike what happens with the classical Bayes posterior distribution, we show that the concentration properties of this new posterior distribution are still preserved in the case of a misspecification of the model, that is when $s$ does not belong to $\overline S$ but is close enough to it with respect to the Hellinger distance.Comment: 68 page

Experimental Access to Mode-Specific Coupling between Quantum Molecular Vibrations and Classical Bath Modes

The interaction of quantum-mechanical systems with a fluctuating thermal environment (bath) is fundamental to molecular mechanics and energy transport/dissipation. Its complete picture requires mode-specific measurements of this interaction and an understanding of its nature. Here, we present a combined experimental and theoretical study providing detailed insights into the coupling between a high-frequency vibrational two-level system and thermally excited terahertz modes. Experimentally, two-dimensional terahertz-infrared-visible spectroscopy reports directly on the coupling between quantum oscillators represented by CH3 streching vibrations in liquid dimethyl sulfoxide and distinct low-frequency modes. Theoretically, we present a mixed quantum-classical formalism of the sample response to enable the simultaneous quantum description of high-frequency oscillators and a classical description of the bath. We derive the strength and nature of interaction and find different coupling between CH3 stretch and low-frequency modes. This general approach enables quantitative and mode-specific analysis of coupled quantum and classical dynamics in complex chemical systems

Experimental Access to Mode-Specific Coupling between Quantum Molecular Vibrations and Classical Bath Modes

The interaction of quantum-mechanical systems with a fluctuating thermal environment (bath) is fundamental to molecular mechanics and energy transport/dissipation. Its complete picture requires mode-specific measurements of this interaction and an understanding of its nature. Here, we present a combined experimental and theoretical study providing detailed insights into the coupling between a high-frequency vibrational two-level system and thermally excited terahertz modes. Experimentally, two-dimensional terahertz-infrared-visible spectroscopy reports directly on the coupling between quantum oscillators represented by CH3 streching vibrations in liquid dimethyl sulfoxide and distinct low-frequency modes. Theoretically, we present a mixed quantum-classical formalism of the sample response to enable the simultaneous quantum description of high-frequency oscillators and a classical description of the bath. We derive the strength and nature of interaction and find different coupling between CH3 stretch and low-frequency modes. This general approach enables quantitative and mode-specific analysis of coupled quantum and classical dynamics in complex chemical systems

Boosting Biexciton Collection Efficiency at Quantum Dot–Oxide Interfaces by Hole Localization at the Quantum Dot Shell

Harvesting multiexcitons from semiconductor quantum dots (QDs) has been proposed as a path toward photovoltaic efficiencies beyond the Shockley–Queisser limit. Although multiexciton generation efficiencies have been quantified extensively in QD structures, the challenge of actually collecting multiple excitons at electrodesa prerequisite for high-efficiency solar cell deviceshas received less attention. Here, we demonstrate that multiexciton collection (MEC) at the PbS QD/mesoporous SnO₂ interface can be boosted 5-fold from ∼15 to reach ∼80% quantum yield, by partial localization of holes in a QD molecular capping shell. The resulting weakened Coulombic interactions give rise to reduced Auger recombination rates within the molecularly capped QDs, so that biexciton Auger relaxation, competing with MEC, is strongly suppressed. These results not only highlight the importance of surface chemistry and energetics at QD/ligand interfaces for multiexciton extraction but also provide clear design principles for realizing the benefits of MEG in sensitized systems exploited in solar cells and fuel geometries

Background-Free Fourth-Order Sum Frequency Generation Spectroscopy

The recently developed 2D sum frequency generation spectroscopy offers new possibilities to analyze the structure and structural dynamics of interfaces in a surface-specific manner. Its implementation, however, has so far remained limited to the pump–probe geometry, with its inherent restrictions. Here we present 2D SFG experiments utilizing a novel noncollinear geometry of four incident laser pulses generating a 2D SFG response, analogous to the triangle geometry applied in bulk-sensitive 2D infrared spectroscopy. This approach allows for background-free measurements of fourth-order nonlinear signals, which is demonstrated by measuring the fourth-order material response from a GaAs (110) surface. The implementation of phase-sensitive detection and broadband excitation pulses allows for both highest possible time resolution and high spectral resolution of the pump axis of a measured 2D SFG spectrum. To reduce the noise in our spectra, we employ a referencing procedure, for which we use noncollinear pathways and individual focusing for the signal and local oscillator beams. The 2D spectra recorded from the GaAs (110) surface show nonzero responses for the real and imaginary component, pointing to contributions from resonant electronic pathways to the χ⁽⁴⁾ response

Quantifying Surfactant Alkyl Chain Orientation and Conformational Order from Sum Frequency Generation Spectra of CH Modes at the Surfactant–Water Interface

We combine second-order nonlinear vibrational spectroscopy and quantum-chemical calculations to quantify the molecular tilt angle and the structural variation of a decanoic acid surfactant monolayer on water. We demonstrate that there is a remarkable degree of delocalization of the vibrational modes along the backbone of the amphiphilic molecule. A simulation-based on modeled sum frequency generation (SFG) spectra offers quantitative insights into the disorder of surfactant monolayers at the water–air interface. It is shown that an average of one gauche defect in the alkyl chain suffices to give rise to the methylene stretch intensity similar in magnitude to the methyl stretch

Trap-Free Hot Carrier Relaxation in Lead–Halide Perovskite Films

Photovoltaic devices that employ lead–halide perovskites as photoactive materials exhibit power conversion efficiencies of 22%. One of the potential routes to go beyond the current efficiencies is to extract charge carriers that carry excess energy, that is, nonrelaxed or “hot” carriers, before relaxation to the band minima is completed. Lead–halide perovskites have been demonstrated to exhibit hot-carrier relaxation times exceeding 100 ps for both single- and polycrystalline samples. Here, we demonstrate, using a combined time-resolved photoluminescence and transient absorption study supported by basic modeling of the dynamics, that the decay of the high-energy part of the photoluminescence occurs on a time scale (∼100 ps) very similar to the repopulation of the band minima when excited with a photon energy larger than 2.6 eV. The similarity between the two time scales indicates that the depopulation of hot states occurs without transient trapping of electrons or holes

Efficient Hot Electron Transfer in Quantum Dot-Sensitized Mesoporous Oxides at Room Temperature

Hot carrier cooling processes represent one of the major efficiency losses in solar energy conversion. Losses associated with cooling can in principle be circumvented if hot carrier extraction toward selective contacts is faster than hot carrier cooling in the absorber (in so-called hot carrier solar cells). Previous work has demonstrated the possibility of hot electron extraction in quantum dot (QD)-sensitized systems, in particular, at low temperatures. Here we demonstrate a room-temperature hot electron transfer (HET) with up to unity quantum efficiency in strongly coupled PbS quantum dot-sensitized mesoporous SnO₂. We show that the HET efficiency is determined by a kinetic competition between HET rate (<i>K</i>_HET) and the thermalization rate (<i>K</i>_TH) in the dots. <i>K</i>_HET can be modulated by changing the excitation photon energy; <i>K</i>_TH can be modified through the lattice temperature. DFT calculations demonstrate that the HET rate and efficiency are primarily determined by the density of the state (DoS) of QD and oxide. Our results provide not only a new way to achieve efficient hot electron transfer at room temperature but also new insights on the mechanism of HET and the means to control it

Tuning Electron Transfer Rates through Molecular Bridges in Quantum Dot Sensitized Oxides

Photoinduced electron transfer processes from semiconductor quantum dots (QDs) molecularly bridged to a mesoporous oxide phase are quantitatively surveyed using optical pump–terahertz probe spectroscopy. We control electron transfer rates in donor–bridge–acceptor systems by tuning the electronic coupling strength through the use of <i>n</i>-methylene (SH–[CH₂]_<i>n</i>–COOH) and <i>n</i>-phenylene (SH–[C₆H₄]_<i>n</i>–COOH) molecular bridges. Our results show that electron transfer occurs as a nonresonant quantum tunneling process with characteristic decay rates of β_<i>n</i> = 0.94 ± 0.08 and β_<i>n</i> = 1.25 per methylene and phenylene group, respectively, in quantitative agreement with reported conductance measurements through single molecules and self-assembled monolayers. For a given QD donor–oxide acceptor separation distance, the aromatic <i>n</i>-phenylene based bridges allow faster electron transfer processes when compared with <i>n</i>-methylene based ones. Implications of these results for QD sensitized solar cell design are discussed

Unveiling the Amphiphilic Nature of TMAO by Vibrational Sum Frequency Generation Spectroscopy

By combining heterodyne-detected sum-frequency generation (SFG) spectroscopy, <i>ab initio</i> molecular dynamics (AIMD) simulation, and a post-vibrational self-consistent field (VSCF) approach, we reveal the orientation and surface activity of the amphiphile trimethylamine-<i>N</i>-oxide (TMAO) at the water/air interface. Both measured and simulated C–H stretch SFG spectra show a strong negative and a weak positive peak. We attribute these peaks to the symmetric stretch mode/Fermi resonance and antisymmetric in-plane mode of the methyl group, respectively, based on the post-VSCF calculation. These positive and negative features evidence that the methyl groups of TMAO are oriented preferentially toward the air phase. Furthermore, we explore the effects of TMAO on the interfacial water structure. The O–H stretch SFG spectra manifest that the hydrogen bond network of the aqueous TMAO-solution/air interface is similar to that of the amine-<i>N</i>-oxide (AO) surfactant/water interface. This demonstrates that, irrespective of the alkyl chain length, the AO groups have a similar impact on the hydrogen bond network of the interfacial water. In contrast, we find that adding TMAO to water makes the orientation of the free O−H groups of the interfacial water molecules more parallel to the surface normal. Invariance of the free O–H peak amplitude despite the enhanced orientation of the topmost water layer illustrates that TMAO is embedded in the topmost water layer, manifesting the clear contrast of the hydrophobic methyl group and the hydrophilic AO group of TMAO