SEARCH · Search NASA
Results for “Real Analytic Functions”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
On the incorporation of the geometric phase in general single potential energy surface dynamics: A removable approximation to ab initio data
For two electronic states coupled by conical intersections, the line integral of the derivative coupling can be used to construct a complex-valued multiplicative phase factor that makes the real-valued adiabatic electronic wave function single-valued, provided that the curl of the derivative coupling is zero. Unfortunately for ab initio determined wave functions, the curl is never rigorously zero. However, when the wave functions are determined from a coupled two diabatic state Hamiltonian H d (fit to ab initio data), the resulting derivative couplings are by construction curl free, except at points of conical intersection. Here in this work we focus on a recently introduced diabatization scheme that produces the H d by fitting ab initio determined energies, energy gradients, and derivative couplings to the corresponding H d determined quantities in a least squares sense, producing a removable approximation to the ab initio determined derivative coupling. This approach and related numerical issues associated with the nonremovable ab initio derivative couplings are illustrated using a full 33-dimensional representation of phenol photodissociation. Finally, the use of this approach to provide a general framework for treating the molecular Aharonov Bohm effect is demonstrated.
Real single ion solvation free energies with quantum mechanical simulation
Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, this method partitions the energies into physically intuitive terms such as surface potential, cavity and charging energies which are amenable to descriptions with reduced models. Here, our research suggests that lithium's solvation free energy is dominated by the free energetics of a charged hard sphere, whereas fluoride exhibits significant quantum mechanical behavior that cannot be simply described with a reduced model.
Real-Time Time-Dependent Nuclear–Electronic Orbital Approach: Dynamics beyond the Born–Oppenheimer Approximation
The quantum mechanical treatment of both electrons and nuclei is crucial in nona- diabatic dynamical processes such as proton-coupled electron transfer. The nuclear electronic orbital (NEO) method provides an elegant framework for including nuclear quantum effects beyond the Born-Oppenheimer approximation. To enable the study of nonequilibrium properties, we derive and implement a real-time NEO (RT-NEO) approach based on time-dependent Hatree-Fock or density functional theory, in which both the electronic and nuclear degrees of freedom are propagated in a time-dependent variational framework. Nuclear and electronic spectral features can be resolved from the time-dependent dipole moment computed using the RT-NEO method. The test cases demonstrate the dynamical interplay between the quantum nuclei and the electrons through vibronic coupling. Moreover, vibrational excitation in the RT-NEO approach is demonstrated by applying a resonant driving eld, and electronic excitation is demonstrated by simulating excited state intramolecular proton transfer. This work shows that the RT-NEO approach is a promising tool to study nonadiabatic quantum dynamical processes within a time-dependent variational description for the coupled electronic and nuclear degrees of freedom.
Self-assembly and glass-formation in a lattice model of telechelic polymer melts: Influence of stiffness of the sticky bonds
Telechelic polymers are chain macromolecules that may self-assemble through the association of their two mono-functional end groups (called “stickers”). A deep understanding of the relation between microscopic molecular details and the macroscopic physical properties of telechelic polymers is important in guiding the rational design of telechelic polymer materials with desired properties. The lattice cluster theory (LCT) for strongly interacting, self-assembling telechelic polymers provides a theoretical tool that enables establishing the connections between important microscopic molecular details of self-assembling polymers and their bulk thermodynamics. The original LCT for self-assembly of telechelic polymers considers a model of fully flexible linear chains [J. Dudowicz and K. F. Freed, J. Chem. Phys. 136, 064902 (2012)], while our recent work introduces a significant improvement to the LCT by including a description of chain semiflexibility for the bonds within each individual telechelic chain [W.-S. Xu and K. F. Freed, J. Chem. Phys. 143, 024901 (2015)], but the physically associative (or called “sticky”) bonds between the ends of the telechelics are left as fully flexible. Motivated by the ubiquitous presence of steric constraints on the association of real telechelic polymers that impart an additional degree of bond stiffness (or rigidity), the present paper further extends the LCT to permit the sticky bonds to be semiflexible but to have a stiffness differing from that within each telechelic chain. An analytical expression for the Helmholtz free energy is provided for this model of linear telechelic polymer melts, and illustrative calculations demonstrate the significant influence of the stiffness of the sticky bonds on the self-assembly and thermodynamics of telechelic polymers. A brief discussion is also provided for the impact of self-assembly on glass-formation by combining the LCT description for this extended model of telechelic polymers with the Adam-Gibbs relation between the structural relaxation time and the configurational entropy.
Light-Matter Interaction in Ultrastable Tunneling Nanogaps
Light emission and detection through tunnel junctions have emerged as a promising platform for studying nanoscale light–matter interactions, including electroluminescence and photoassisted transport. However, controlling these interactions in the tunneling regime has been challenging due to complex underlying mechanisms that remain poorly understood. A major obstacle is the difficulty in forming stable junctions that can function reliably over extended periods. In this study, we fabricate ultrastable tunneling junctions consisting of epitaxial indium–tin-oxide, epitaxial lutetium oxide, and gold. With their stable and consistent tunneling currents, we investigate photon-assisted transport phenomena using simple direct-current detection. Our results demonstrate that optical rectification is the primary contributor to the laser-induced current, alongside thermal effects and hot-electron currents. Furthermore, owing to their epitaxial nature and high breakdown threshold, this ultrastable platform holds promise for future real-world applications, including nanoscale light sources and multifunctional photodetectors.
Exploring the exact limits of the real-time equation-of-motion coupled cluster cumulant Green’s functions
In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green’s function approach [Rehr et al., J. Chem. Phys. 152, 174113 (2020)]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz, ensuring the exactness in the expansion limit. In addition, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green’s function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green’s function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green’s function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green’s function approach and other Green’s function approaches in the numerical exact limit.
Performance of quantum Monte Carlo for calculating molecular bond lengths
This work investigates the accuracy of real-space quantum Monte Carlo (QMC) methods for calculating molecular geometries. We present the equilibrium bond lengths of a test set of 30 diatomic molecules calculated using variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods. The effect of different trial wavefunctions is investigated using single determinants constructed from Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals with LDA, PBE, and B3LYP functionals, as well as small multi-configurational self-consistent field (MCSCF) multi-determinant expansions. When compared to experimental geometries, all DMC methods exhibit smaller mean-absolute deviations (MADs) than those given by HF, DFT, and MCSCF. The most accurate MAD of 3 ± 2 × 10{sup −3} Å is achieved using DMC with a small multi-determinant expansion. However, the more computationally efficient multi-determinant VMC method has a similar MAD of only 4.0 ± 0.9 × 10{sup −3} Å, suggesting that QMC forces calculated from the relatively simple VMC algorithm may often be sufficient for accurate molecular geometries.
Melting Point Depression and Phase Identification of Sugar Alcohols Encapsulated in ZIF Nanopores
Sugar alcohols (SAs) have attractive characteristics as phase-change materials, but their relatively high melting temperature limits their application in the real world. Nanoconfinement can be a useful parameter to reduce the melting temperature to pragmatic ranges. Using molecular dynamics simulations, we investigate the phases and behaviors of encapsulated SA in ZIF-8 and ZIF-11, which cannot be experimentally observed. Based on reliable partial charges for the zeolitic imidazolate framework (ZIF) structures calculated by a density functional theory, structural analysis shows that the SA’s attractive interaction with the ZIF structure frustrates the SA crystallization and also elucidates the second-order phase transition between amorphous phases. A methodology is suggested to determine the phase transition temperature of confined materials and used to quantify the melting temperature depression of the ZIF-confined SAs. We also explored the thermal conductivity of SA-in-ZIF composites. Phonon frequency analysis verifies that the presence of SA molecules enhances the heat transfer by adding heat pathways between the nanoporous structure of ZIFs.
Automated generation and ensemble-learned matching of X-ray absorption spectra
X-ray absorption spectroscopy (XAS) is a widely used materials characterization technique to determine oxidation states, coordination environment, and other local atomic structure information. Analysis of XAS relies on comparison of measured spectra to reliable reference spectra. However, existing databases of XAS spectra are highly limited both in terms of the number of reference spectra available as well as the breadth of chemistry coverage. In this work, we report the development of XASdb, a large database of computed reference XAS, and an Ensemble-Learned Spectra IdEntification (ELSIE) algorithm for the matching of spectra. XASdb currently hosts more than 800,000 K-edge X-ray absorption near-edge spectra (XANES) for over 40,000 materials from the open-science Materials Project database. We discuss a high-throughput automation framework for FEFF calculations, built on robust, rigorously benchmarked parameters. FEFF is a computer program uses a real-space Green’s function approach to calculate X-ray absorption spectra. Here, we will demonstrate that the ELSIE algorithm, which combines 33 weak “learners” comprising a set of preprocessing steps and a similarity metric, can achieve up to 84.2% accuracy in identifying the correct oxidation state and coordination environment of a test set of 19 K-edge XANES spectra encompassing a diverse range of chemistries and crystal structures. The XASdb with the ELSIE algorithm has been integrated into a web application in the Materials Project, providing an important new public resource for the analysis of XAS to all materials researchers. Finally, the ELSIE algorithm itself has been made available as part of veidt, an open source machine-learning library for materials science.
Investigating the Role of Copper Oxide in Electrochemical CO 2 Reduction in Real Time
Copper oxides have been of considerable interest as electrocatalysts for CO 2 reduction (CO2R) in aqueous electrolytes. Yet, their role as an active catalyst in reducing the required overpotential and improving the selectivity of reaction compared with that of polycrystalline copper remains controversial. In this work, we present the use of selected-ion flow tube mass spectrometry, in concert with chronopotentiometry, in situ Raman spectroscopy, and computational modeling, to investigate CO2R on C u 2O nanoneedles, Cu 2 O nanocrystals, and Cu 2 O nanoparticles. We show experimentally that the selective formation of gaseous C2 products (i.e., ethylene) in CO 2 R is preceded by the reduction of the copper oxide (Cu 2 OR) surface to metallic copper. On the basis of density functional theory modeling, CO2R products are not formed as long as Cu 2 O is present at the surface because Cu 2 OR is kinetically and energetically more favorable than CO2R.
Revisiting the Growth Mechanism of Hierarchical Semiconductor Nanostructures: The Role of Secondary Nucleation in Branch Formation
Although advances in synthesizing hierarchical semiconductor materials, there have been few studies on the fundamental nucleation mechanisms to explain the origins of such complex structures. Resolving these nucleation and growth pathways is very difficult and time consuming, but is critical for developing predictive synthetic capabilities for the synthesis and applications of new materials. In this paper, we use state-of-the-art in-situ liquid phase scanning electron microscopy (SEM) and high-resolution transmission electron microscopy in combination of classical Density Functional Theory (cDFT) to study the nucleation of highly-branched wurtzite ZnO nanostructures via a facile, room temperature aqueous synthesis route. Using a range of precursor concentrations, we systematically vary their hierarchical organization. In situ liquid phase SEM demonstrates that all branches form through secondary nucleation and grow by classical processes. Neither random aggregation nor oriented attachment is observed. cDFT results imply the morphological evolution with increasing [Zn 2+ ] arises from an interplay between rising thermodynamic driving force, which promotes branch number and variability of orientation, and increasing barriers to interfacial transport due to ion correlation forces that alter the anisotropic kinetics of growth. Finally, these findings provide a quantitative picture of branching that sets to rest past controversies and advances efforts to decipher growth mechanisms of hierarchical structures in real solution environments.
A portable fiber optic sensor for the luminescent sensing of cobalt ions using carbon dots
Cobalt is critical to energy-relevant technologies, and demand for cobalt will increase significantly with growing global adoption of renewables. However, supply chain stability is threatened by economic and geopolitical factors, incentivizing domestic cobalt production from alternative resources such as coal, coal utilization byproducts (e.g., ash, acid mine drainage) and electronic waste. Rapid, inexpensive, and portable characterization techniques are needed to reduce production costs associated with cobalt prospecting and process monitoring. Here, in this research, we develop a compact, portable fiber optic luminescent probe for cobalt using phosphorus and nitrogen co-doped carbon dots as the sensing material. The carbon dot emission overlaps well with the cobalt absorption band at ~510 nm, leading to a selective decrease in emission as a function of cobalt concentration. The system responds nearly instantly to the presence of cobalt, with detection limits of 0.7 and 3.5 ppm in water and pH 1.68 buffer, respectively, providing comparable performance to a commercial spectrometer at a significantly lower cost. Moreover, the sensor is selective for cobalt in the presence of 13 of the most common metal ions encountered in coal utilization byproducts and is responsive to cobalt when spiked into an acid mine drainage leachate sample, highlighting the sensor's potential for real-world deployment in challenging matrices. In addition, integrating the carbon dots with a filter paper substrate produced ‘test strip’ sensors that exhibited a selective and sensitive visual response to cobalt using a handheld UV lamp. Taken together, the sensing system represents a significant step forward in the development of low-cost practical sensors for high-value metals in complex streams.
Stochastic Real-Time Second-Order Green’s Function Theory for Neutral Excitations in Molecules and Nanostructures
We present a real-time second-order Green’s function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(N e 3 ), where N e is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.
Quantum Simulation of Molecular Dynamics Processes─A Benchmark Study Using a Classical Simulator and Present-Day Quantum Hardware
Here, we explore how the fundamental problems in quantum molecular dynamics can be modeled using classical simulators (emulators) of quantum computers and the actual quantum hardware available to us today. The list of problems we tackle includes propagation of a free wave packet, vibration of a harmonic oscillator, and tunneling through a barrier. Each of these problems starts with the initial wave packet setup. Although Qiskit provides a general method for initializing wave functions, in most cases it generates deep quantum circuits. While these circuits perform well on noiseless simulators, they suffer from excessive noise on quantum hardware. To overcome this issue, we designed a shallower quantum circuit for preparing a Gaussian-like initial wave packet, which improves the performance of real hardware. Next, quantum circuits are implemented to apply the kinetic and potential energy operators for the evolution of a wave function over time. The results of our modeling on classical emulators of quantum hardware agree perfectly with the results obtained using the traditional (classical) methods. This serves as a benchmark and demonstrates that the quantum algorithms and Qiskit codes we developed are accurate. However, the results obtained on the actual quantum hardware available today, such as IBM’s superconducting qubits and IonQ’s trapped ions, indicate large discrepancies due to hardware limitations. This work highlights both the potential and challenges of using quantum computers to solve fundamental quantum molecular dynamics problems.
Understanding the Thermal Stability of Palladium–Platinum Core–Shell Nanocrystals by In Situ Transmission Electron Microscopy and Density Functional Theory
Core–shell nanocrystals offer many advantages for heterogeneous catalysis, including precise control over both the surface structure and composition, as well as reduction in loading for rare and costly metals. Although many catalytic processes are operated at elevated temperatures, the adverse impacts of heating on the shape and structure of core–shell nanocrystals are yet to be understood. In this work, we used ex situ heating experiments to demonstrate that Pd@Pt 4L core–shell nanoscale cubes and octahedra are promising for catalytic applications at temperatures up to 400 °C. We also used in situ transmission electron microscopy to monitor the thermal stability of the core–shell nanocrystals in real time. Our results demonstrate a facet dependence for the thermal stability in terms of shape and composition. Specifically, the cubes enclosed by {100} facets readily deform shape at a temperature 300 °C lower than that of the octahedral counterparts enclosed by {111} facets. A reversed trend is observed for composition, as alloying between the Pd core and the Pt shell of an octahedron occurs at a temperature 200 °C lower than that for the cubic counterpart. Density functional theory calculations provide atomic-level explanations for the experimentally observed behaviors, demonstrating that the barriers for edge reconstruction determine the relative ease of shape deformation for cubes compared to octahedra. Furthermore, the opposite trend for alloying of the core–shell structure can be attributed to a higher propensity for subsurface Pt vacancy formation in octahedra than in cubes.
Phase behaviors of supramolecular graft copolymers with reversible bonding
Phase behaviors of supramolecular graft copolymers with reversible bonding interactions were examined by the random-phase approximation and real-space implemented self-consistent field theory. The studied supramolecular graft copolymers consist of two different types of mutually incompatible yet reactive homopolymers, where one homopolymer (backbone) possesses multifunctional groups that allow second homopolymers (grafts) to be placed on. The calculations carried out show that the bonding strength exerts a pronounced effect on the phase behaviors of supramolecular graft copolymers. The length ratio of backbone to graft and the positions of functional groups along the backbone are also of importance to determine the phase behaviors. Phase diagrams were constructed at high bonding strength to illustrate this architectural dependence. It was found that the excess unbounded homopolymers swell the phase domains and shift the phase boundaries. The results were finally compared with the available experimental observations, and a well agreement is shown. The present work could, in principle, provide a general understanding of the phase behaviors of supramolecular graft copolymers with reversible bonding.
Real-time monitoring of ozone in air using substrate-integrated hollow waveguide mid-infrared sensors
Ozone is a strong oxidant that is globally used as disinfection agent for many purposes including indoor building air cleaning, during food preparation procedures, and for control and killing of bacteria such as E. coli and S. aureus. However, it has been shown that effective ozone concentrations for controlling e.g., microbial growth need to be higher than 5 ppm, thereby exceeding the recommended U.S. EPA threshold more than 10 times. Consequently, real-time monitoring of such ozone concentration levels is essential. Here, we describe the first online gas sensing system combining a compact Fourier transform infrared (FTIR) spectrometer with a new generation of gas cells, a so-called substrate-integrated hollow waveguide (iHWG). The sensor was calibrated using an UV lamp for the controlled generation of ozone in synthetic air. A calibration function was established in the concentration range of 0.3–5.4 mmol m23 enabling a calculated limit of detection (LOD) at 0.14 mmol m23 (3.5 ppm) of ozone. Given the adaptability of the developed IR sensing device toward a series of relevant air pollutants, and considering the potential for miniaturization e.g., in combination with tunable quantum cascade lasers in lieu of the FTIR spectrometer, a wide range of sensing and monitoring applications of beyond ozone analysis are anticipated.