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Multidimensional wave function: a superposition of Gaussian coherent states guided by Ehrenfest trajectories suited to clone and swap their electronic amplitudes.
Nonlinear multidimensional spectroscopy is ubiquitous in the optical and radio frequency regions as a powerful tool to access structure and dynamics. The extension of this technique into the extreme ultraviolet (XUV) region with attosecond pulses holds promise for probing electronic dynamics and correlations with unprecedented time and spatial resolution. In this work, we use noncollinear four-wave mixing of a weak XUV attosecond pulse train (11–17 eV) and few-femtosecond NIR pulses (800 nm) to spectroscopically and dynamically probe the dipole-forbidden double-well potential of the a" 1 Σ + g electronic state of nitrogen. The results demonstrate optical coupling of the inner and outer limits of the initial XUV-prepared vibrational wave packet in the valence character b' 1 Σ + u state to the inner and outer wells, respectively, of the a" 1 Σ + g double well state by 800 nm light. Two four-wave mixing schemes with different pulse timing sequences and noncollinear beam geometries are used (one NIR pulse collinear and one NIR pulse noncollinear versus both NIR pulses noncollinear to the XUV beam) to measure the a" dark state energetic structure and to control the dynamical preparation and motion of a dark state wave packet by selective population of either the inner Rydberg or outer valence-character potential well. Finally, experimental measurements of the a" 1 Σ + g outer well vibrational spacing and anharmonicity closely match the values theoretically predicted for this previously unobserved state.
Thermal rate coefficients and kinetic isotope effects have been calculated for an important atmospheric reaction H/D + O 3 → OH/OD + O2 based on an accurate permutation invariant polynomial-neural network potential energy surface, using ring polymer molecular dynamics (RPMD), quasi-classical trajectory (QCT) and variational transition-state theory (VTST) with multidimensional tunneling. The RPMD approach yielded results that are generally in better agreement with experimental rate coefficients than the VTST and QCT ones, especially at low temperatures, attributable to its capacity to capture quantum effects such as tunneling and zero-point energy. Additionally, the theoretical results support one group of existing experiments over the other. In addition, rate coefficients for the D + O 3 → OD + O 2 reaction are also reported using the same methods, which will allow a stringent assessment of future experimental measurements, thus helping to reduce the uncertainty in the recommended rate coefficients of this reaction.
Controlling the electrochemical interfacial processes that govern the durability of electrochromic devices represents a key challenge in developing sustainable and cost-effective smart windows. Here, we revisit the classical tungsten trioxide (WO 3 ) materials as a platform to uncover the previously unknown interrelationship between phase transformation, morphological evolution, and nanoscale color heterogeneity in these materials. Through synchrotron/electron spectroscopic and imaging analyses, we report that the WO 3 –electrolyte interface is influenced by the tungsten dissolution and redeposition during the electrochemical cycling. The tungsten redeposition provokes the in situ crystal growth, which ultimately leads to the phase transformation from the semicrystalline WO 3 to a nanoflake-shaped, proton-trapped tungsten trioxide dihydrate (H x WO 3 · 2 H 2 O). The multidimensional quantification of the electronic structure reveals that the tungsten reduction caused by the proton trapping is heterogeneous at the nanometric scale and is responsible for the nanoscale color heterogeneity. The interplay between phase transformation, morphological evolution, and nanoscale color heterogeneity results in degraded optical modulation, switching kinetics, coulombic efficiency, and bleached-state transparency. Our results highlight that the high interfacial reactivity near the electrode surface may be the underlying mechanism for undesired bulk structural changes of electrochromic materials, and calls for fundamental studies in probing and controlling the electrode–electrolyte interfacial processes in electrochromic devices.
Both computational and experimental material discovery bring forth the challenge of exploring multidimensional and multimodal parameter spaces, such as phase diagrams of Hamiltonians with multiple interactions, composition spaces of combinatorial libraries, material structure image spaces, and molecular embedding spaces. Often these systems are black-boxes and time-consuming to evaluate, which resulted in strong interest towards active learning methods such as Bayesian optimization (BO). However, these systems are often noisy which make the black box function severely multi-modal and non-differentiable, where a vanilla BO can get overly focused near a single or faux optimum, deviating from the broader goal of scientific discovery. To address these limitations, here we developed Strategic Autonomous Non-Smooth Exploration (SANE) to facilitate an intelligent Bayesian optimized navigation with a proposed cost-driven probabilistic acquisition function to find multiple global and local optimal regions, avoiding the tendency to becoming trapped in a single optimum. To distinguish between a true and false optimal region due to noisy experimental measurements, a human (domain) knowledge driven dynamic surrogate gate is integrated with SANE. We implemented the gate-SANE into pre-acquired piezoresponse spectroscopy data of a ferroelectric combinatorial library with high noise levels in specific regions, and piezoresponse force microscopy (PFM) hyperspectral data. SANE demonstrated better performance than classical BO to facilitate the exploration of multiple optimal regions and thereby prioritized learning with higher coverage of scientific values in autonomous experiments. Our work showcases the potential application of this method to real-world experiments, where such combined strategic and human intervening approaches can be critical to unlocking new discoveries in autonomous research.
Lanthanide ion solvation chemistry in nonaqueous phases is key to understanding and developing effective separation processes for these critical materials. Due to the complexity and inherent disorder of the solution phase, a comprehensive picture of the solvated metal ion is often difficult to generate solely from conventional spectroscopic approaches and electronic structure calculations, particularly in the extractant phase. In this work, we use classical molecular dynamics (MD) simulation with an advanced sampling technique, metadynamics, supplemented by experimental spectroscopy and speciation analysis, to measure lanthanide solvation free energy landscapes. We define coordination-based collective variables to probe the entire range of solvation configurations in the organic phase of lanthanum (La), europium (Eu), and lutetium (Lu) nitrate salts bound with a commonly used extractant, N,N′-dimethyl, N,N′-dioctylhexylethoxymalonamide (DMDOHEMA). The known lanthanide extraction trend of La ≈ Eu > Lu is readily explained by the measured free energy surfaces, which show consistent DMDOHEMA coordination from La to Eu, followed by loss of DMDOHEMA coordination from Eu to Lu. These simulations suggest how ligand crowding at the metal center can control selectivity, in this case resulting in the opposite extraction trend as observed with other conventional extractants, where the enthalpic contribution from increasing lanthanide charge density across the series dominates the extraction energetics. We also find that the presence of inner-sphere water, verified by time-resolved fluorescence, diversifies the accessible solvation structures. As a result, understanding solvation requires consideration of an entire thermodynamic ensemble, rather than the single dominant lowest-energy structure, as is often considered out of necessity in interpretation of spectroscopic data or in electronic structure-based ligand design approaches. In general, we demonstrate how metadynamics uniquely enables investigation of complex, multidimensional solvation energetic landscapes, and how it can explain selectivity trends where extraction is controlled by more complex mechanisms than simple charge density-based selectivity.
The electrochemical carbon dioxide reduction reaction (CO 2 RR) using renewable energy sources is a promising solution for mitigating CO 2 emissions. In particular, CO 2 RR to formate represents a commercially profitable target. However, a comprehensive understanding of the catalytic mechanisms of Sn-based catalysts under reaction conditions, including the real-time structural evolution of catalysts and the role of all key reaction intermediates in influencing the CO 2 RR selectivity, is still lacking. The current study reports a framework to study the selectivity preference of Sn-based bimetallic catalysts using a combination of electrochemical measurements, in situ characterization, and density functional theory (DFT) calculations. The addition of a second metal (Co, Ni, Ag, Zn, Ga, Bi) was found to play a vital role in affecting the CO 2 RR performance. In situ X-ray absorption near edge structure (XANES) measurements revealed a dynamic evolution in the Sn valence state induced by different secondary metals. A multidimensional descriptor involving all the key reaction intermediates was developed to assess formate selectivity using a 2-dimensional volcano plot. Finally, this research offers an effective framework for understanding CO 2 RR catalytic selectivity by considering both the real-time structural evolution of catalysts and all the key intermediates involved.
It was recently reported that boron monoxide (BO) is formed through the cross-linking of B 4 O 2 structural building units. Multiple theoretical phases agree with this description. Using pycnometry, multidimensional 17 O NMR spectroscopy, and plane-wave DFT calculations we determined the likely polymorph to be a one-dimensional polymer initially proposed in 1955.
Context: Recent, nonlinear simulations of wave generation and propagation in full-star models have been carried out in the anelastic approximation using spectral methods. Although it makes long time steps possible, this approach excludes the physics of sound waves completely and requires rather high artificial viscosity and thermal diffusivity for numerical stability. A direct comparison with observations is thus limited. Aims: In this study, we explore the capabilities of our compressible multidimensional Seven-League Hydro (SLH) code to simulate stellar oscillations. Methods: We compare some fundamental properties of internal gravity and pressure waves in 2D SLH simulations to linear wave theory using two test cases: (1) an interval gravity wave packet in the Boussinesq limit and (2) a realistic 3 M ⊙ stellar model with a convective core and a radiative envelope. Oscillation properties of the stellar model are also discussed in the context of observations. Results: Our tests show that specialized low-Mach techniques are necessary when simulating oscillations in stellar interiors. Basic properties of internal gravity and pressure waves in our simulations are in good agreement with linear wave theory. As compared to anelastic simulations of the same stellar model, we can follow internal gravity waves of much lower frequencies. The temporal frequency spectra of velocity and temperature are flat and compatible with the observed spectra of massive stars. Conclusion: The low-Mach compressible approach to hydrodynamical simulations of stellar oscillations is promising. Our simulations are less dissipative and require less luminosity boosting than comparable spectral simulations. The fully-compressible approach allows for the coupling of gravity and pressure waves in the outer convective envelopes of evolved stars to be studied in the future.
A fundamental assumption adopted in nearly every extragalactic study that analyzes optical emission lines is that the attenuation of different emission lines can be described by a single attenuation curve, scaled by a single reddening parameter, usually E(B - V). Here we show this assumption fails in many cases with important implications for derived results. We developed a new method to measure the differential nebular attenuation among three kinds of transitions: the Balmer lines of hydrogen; high-ionization transitions (> 13.6 eV) including [Ne III], [O III], and [S III]; and low-ionization transitions (≲13.6 eV) including [O II], [N II], and [S II]. This method bins the observed data in a multidimensional space spanned by attenuation-insensitive line ratios. Within each small bin, the variations in nebular parameters such as the metallicity and ionization parameter are negligible compared to the variation in the nebular attenuation. This allowed us to measure the nebular attenuation using both forbidden lines and Balmer lines. We applied this method to a sample of 2.4 million star-forming (SF) spaxels from the Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey. We found that the attenuation of high ionization lines and Balmer lines can be well described by a single Fitzpatrick (1999, PASP, 111, 63) extinction curve with R V = 3.1. However, no single attenuation curve can simultaneously account for these transitions and the derived attenuation of low-ionization lines. This strongly suggests that different lines have different effective attenuations, likely because spectroscopy at hundreds of parsecs to kiloparsecs of resolution mixes multiple physical regions that exhibit different intrinsic line ratios and different levels of attenuation. As a result, the assumption that different lines follow the same attenuation curve breaks down. Using a single attenuation curve determined by Balmer lines to correct attenuation-sensitive forbidden line ratios could bias the nebular parameters derived by 0.06–0.25 dex at A V = 1, depending on the details of the dust attenuation model. Observations of a statistically large sample of H II regions with high spatial resolutions and large spectral coverage are vital for improved modeling and deriving accurate corrections for this effect.
Convection is one of the most important mixing processes in stellar interiors. Hydrodynamic mass entrainment can bring fresh fuel from neighboring stable layers into a convection zone, modifying the structure and evolution of the star. Because flows in stellar convection zones are highly turbulent, multidimensional hydrodynamic simulations are fundamental to accurately capture the physics of mixing processes. Under some conditions, strong magnetic fields can be sustained by the action of a turbulent dynamo, adding another layer of complexity and possibly altering the dynamics in the convection zone and at its boundaries. In this study, we used our fully compressible S EVEN -L EAGUE H YDRO code to run detailed and highly resolved three-dimensional magnetohydrodynamic simulations of turbulent convection, dynamo amplification, and convective boundary mixing in a simplified setup whose stratification is similar to that of an oxygen-burning shell in a star with an initial mass of 25 M ⊙ . We find that the random stretching of magnetic field lines by fluid motions in the inertial range of the turbulent spectrum (i.e., a small-scale dynamo) naturally amplifies the seed field by several orders of magnitude in a few convective turnover timescales. During the subsequent saturated regime, the magnetic-to-kinetic energy ratio inside the convective shell reaches values as high as 0.33, and the average magnetic field strength is ∼10 10 G. Such strong fields efficiently suppress shear instabilities, which feed the turbulent cascade of kinetic energy, on a wide range of spatial scales. The resulting convective flows are characterized by thread-like structures that extend over a large fraction of the convective shell. The reduced flow speeds and the presence of magnetic fields with strengths up to 60% of the equipartition value at the upper convective boundary diminish the rate of mass entrainment from the stable layer by ≈20% as compared to the purely hydrodynamic case.
Context. Because Cepheid variable stars have long been used as a cosmic benchmark for scaling distances in our Galaxy and beyond, the accuracy of stellar evolution models for Cepheids have wide-reaching effects. However, our understanding of the dynamics in the interiors of these physically complex stars is limited. Aims. Our goal is to provide a detailed multi-dimensional picture of hydrodynamic convection and convective boundary mixing in the interior of Cepheids. Methods. Using the Modules for Experiments in Stellar Astrophysics (MESA), we studied the structure of intermediate-mass stars that cross the instability strip. Then, we performed two-dimensional hydrodynamic simulations of six stars with the fully compressible Multidimensional Stellar Implicit Code (MUSIC). Our simulations did not model the radial pulsations but focused on the interior structure of this family of stars. We developed and applied a new statistical analysis to examine convection and convective boundary mixing in the interior of these stellar simulations. Results. Based on a grid of MESA models, we demonstrated that a common structure for intermediate mass Cepheids includes an interior convective shell as well as a thin outer convective envelope. Using the extreme value theory approach to analyze our MUSIC simulation data, we found that overshooting above the convective shell fills the space between these convectively unstable layers. We developed a new statistical analysis that provides a clearer picture of how overshooting fills this layer; it also allowed us to formulate a detailed comparison between overshooting above and below the convective shell. Our analysis effectively decomposes the overshooting layer into two layers: a weak overshooting layer and a strong overshooting layer. Statistically, this is accomplished by decomposing the strongly non-Gaussian probability density function into a mixture of gamma distributions. Using our mixture model, we showed that the ratio of overshooting lengths above and below the convective shell depends directly on the radial extent of the convective shell as well as its depth in the star. We proposed a new form for the diffusion coefficient that addresses the need for overlapping overshooting layers between convective shells. We introduced the idea of a “super-mixing layer” where overshooting from both the convective shell and the convective envelope results in efficient mixing and could be viewed as merging the two adjacent convective zones.
Since the earliest measurements in the '70, hadronic physics deals with a number of surprising phenomena that cannot be explained in the framework of perturbative QCD. Examples are the small fraction of the proton spin carried by the valence quark spins, the persistence at high energies of single spin asymmetries and azimuthal asymmetries in unpolarized processes. It is now believed that the answer to these questions may come from the transverse motion of partons inside the nucleon, which is encoded in the Transverse Momentum Dependent (TMD) Parton Distribution Functions. Among the large variety of processes that can be described in terms of TMDs, a major role is played by Semi-Inclusive Deep Inelastic Scattering (SIDIS) reactions, in which, together with the scattered electron, one or more hadrons are detected in the final state. Single and Double Spin Asymmetries are the experimental observables sensitive to TMDs. The identification of the final hadrons allows the tagging of the quark involved in the reaction at the parton level, and then the flavor separation of the relevant TMDs. SIDIS reactions are studied at Jefferson Laboratories since many years and are one of the main items in the physics program after the upgrade of the CEBAF accelerator. The large amount of new data that will be available in few years calls for the implementation of new tools, such as multidimensional analyses and refined techniques of TMDs extraction from the experimental asymmetries. In this talk, the more recent results obtained at 6 GeV will be shown and the future measurements will be discussed.
In this study, we present some of the main features of the multidimensional COMPASS multiplicities, via our analysis using the simple Gaussian model. We briefly discuss these results in connection with azimuthal asymmetries.
Jefferson Laboratory is finishing a major upgrade and has already started operations with the 12 GeV continuous electron beam. The main research direction is the study of the structure of hadrons, including a search for gluon excitations in the spectra of light mesons and baryons, and studies of multidimensional images of the nucleon. Studied of certain properties of atomic nuclei are also ongoing. Furthermore there is also an active program of searching for effects beyond the Standard Model in parity-violating electron scattering, as well as a search for new particles.
In this paper, we investigate the saturation mechanisms of backward stimulated Raman scattering (BSRS) induced by nonlinear kinetic effects. In particular, we stress the importance of accounting for both the nonlinear frequency shift of the electron plasma wave and the growth of sidebands, in order to understand what stops the coherent growth of Raman scattering. Using a Bernstein-Greene-Kruskal approach, we provide an estimate for the maximum amplitude reached by a BSRS-driven plasma wave after the phase of monotonic growth. This estimate is in very good agreement with the results from kinetic simulations of stimulated Raman scattering using both a Vlasov and a Particle in Cell code. Our analysis, which may be generalized to a multidimensional geometry, should provide a means to estimate the limits of backward Raman amplification or the effectiveness of strategies that aim at strongly reducing Raman reflectivity in a fusion plasma.
The thermodynamics and kinetics of protein folding and protein conformational changes are governed by the underlying free energy landscape. However, the multidimensional nature of the free energy landscape makes it difficult to describe. We propose to use a weighted-graph approach to depict the free energy landscape with the nodes on the graph representing the conformational states and the edge weights reflecting the free energy barriers between the states. Our graph is constructed from a molecular dynamics trajectory and does not involve projecting the multi-dimensional free energy landscape onto a low-dimensional space defined by a few order parameters. The calculation of free energy barriers was based on transition-path theory using the MSMBuilder2 package. We compare our graph with the widely used transition disconnectivity graph (TRDG) which is constructed from the same trajectory and show that our approach gives more accurate description of the free energy landscape than the TRDG approach even though the latter can be organized into a simple tree representation. The weighted-graph is a general approach and can be used on any complex system.
Given a quantum many-body system, the Self-Consistent Phonons (SCP) method provides an optimal harmonic approximation by minimizing the free energy. In particular, the SCP estimate for the vibrational ground state (zero temperature) appears to be surprisingly accurate. We explore the possibility of going beyond the SCP approximation by considering the system Hamiltonian evaluated in the harmonic eigenbasis of the SCP Hamiltonian. It appears that the SCP ground state is already uncoupled to all singly- and doubly-excited basis functions. So, in order to improve the SCP result at least triply-excited states must be included, which then reduces the error in the ground state estimate substantially. For a multidimensional system two numerical challenges arise, namely, evaluation of the potential energy matrix elements in the harmonic basis, and handling and diagonalizing the resulting Hamiltonian matrix, whose size grows rapidly with the dimensionality of the system. Using the example of water hexamer we demonstrate that such calculation is feasible, i.e., constructing and diagonalizing the Hamiltonian matrix in a triply-excited SCP basis, without any additional assumptions or approximations. Our results indicate particularly that the ground state energy differences between different isomers (e.g., cage and prism) of water hexamer are already quite accurate within the SCP approximation.