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Origin of the magnetic and orbital ordering in α-Sr 2 CrO 4

Motivated by recent experimental progress in transition metal oxides with the K 2 NiF 4 structure, in this study we investigate the magnetic and orbital ordering in α-Sr 2 CrO 4 . Using first principles calculations, first we derive a three-orbital Hubbard model, which reproduces the ab initio band structure near the Fermi level. The unique reverse splitting of t 2g orbitals in α-Sr 2 CrO 4 , with the 3d 2 electronic configuration for the Cr 4+ oxidation state, opens up the possibility of orbital ordering in this material. Using real-space Hartree-Fock for multi-orbital systems, we constructed the ground state phase diagram for the two dimensional compound α-Sr 2 CrO 4 . We found stable ferromagnetic, antiferromagnetic, antiferro-orbital, and staggered orbital stripe ordering in robust regions of the phase diagram. Furthermore, using the density matrix renormalization group method for two-leg ladders with the realistic hopping parameters of α-Sr 2 CrO 4 , we explore magnetic and orbital ordering for experimentally relevant interaction parameters. Again, we find a clear signature of antiferromagnetic spin ordering along with antiferro-orbital ordering at moderate to large Hubbard interaction strength. We also explore the orbital-resolved density of states with Lanczos, predicting insulating behavior for the compound α-Sr 2 CrO 4 , in agreement with experiments. Finally, an intuitive understanding of the results is provided based on a hierarchy between orbitals, with d xy driving the spin order, while electronic repulsion and the effective one dimensionality of the movement within the d xz and d yz orbitals driving the orbital order.

36 MATERIALS SCIENCE↗

Features of solar wind acceleration according to radio occultation data

In addressing one of the fundamental problems in solar physics establishing the mechanism(s) responsible for the solar wind acceleration and the corona heating - it is essential to have a reliable knowledge of the heliocentric radial dependence of the solar wind properties. Adequate data are available for small solar distances R less than 4 R(solar mass) from coronal white light and EUV observations and at distances R greater than 60 R(solar mass) from in situ measurements. One of the few methods available to fill in the gap between these boundaries is the radio scintillation technique. Taking the example of the solar wind velocity, the most reliable such measurements are obtained when phase fluctuation observations of scattered radio waves, which are not susceptible to saturation effects, are recorded at two or more widely-spaced ground stations. Two extensive observation campaigns of this type were carried out with the Venus-orbiting satellites Venera 10 in 1976 and Venera 15/16 in 1984. The observations were performed over the course of three months near superior conjunction at solar offset distances R approximately 6-80 R(solar mass). The main results from the subsequent analysis of these data are: (1) velocities vary between 250 and 380 km s(exp -1) for R greater than 20 R(solar mass), agreeing with similar measurements using natural sources (IPS); (2) velocities derived from two-station phase fluctuation observations varv between 70 and 120 km s(exp -1) for R less than 12 R(solar mass), i.e. values substantially lower than those derived from conventional IPS data; and (3) it is suggested that the different velocity profiles derived from the two data sets at small R may be due to the effects of magnetosonic and Alfvenic waves on radio wave scattering. Further analysis of additional radio sounding data should help resolve the apparent discrepancy.

Efimov, A. I.↗

Mechanical Amplifier for a Piezoelectric Transducer

A mechanical amplifier has been devised to multiply the stroke of a piezoelectric transducer (PZT) intended for use at liquid helium temperatures. Interferometry holds the key to high angular resolution imaging and astrometry in space. Future space missions that will detect planets around other solar systems and perform detailed studies of the evolution of stars and galaxies will use new interferometers that observe at mid- and far-infrared wavelengths. Phase-measurement interferometry is key to many aspects of astronomical interferometry, and PZTs are ideal modulators for most methods of phase measurement, but primarily at visible wavelengths. At far infrared wavelengths of 150 to 300 m, background noise is a severe problem and all optics must be cooled to about 4 K. Under these conditions, piezos are ill-suited as modulators, because their throw is reduced by as much as a factor of 2, and even a wavelength or two of modulation is beyond their capability. The largest commercially available piezo stacks are about 5 in. (12.7 cm) long and have a throw of about 180 m at room temperature and only 90 m at 4 K. It would seem difficult or impossible to use PZTs for phase measurements in the far infrared were it not for the new mechanical amplifier that was designed and built.

Moore, James↗

Evidence from Galactic Cosmic Rays That the Sun Has Likely Entered A Secular Minimum in Solar Activity

Since the beginning of the space age, the Sun has been in a multi-cycle period of elevated activity (secular maximum). This secular maximum is the longest in the last 9300 years. Since the end of solar cycle 21 (SC21), however, the Sun has shown a decline in over-all activity, which has remarkably increased the fluxes of galactic cosmic rays (GCRs). Here, we investigate the correlation between the modulation of GCRs, the heliospheric magnetic field, and solar wind speed for the last 24 solar cycles to find trends that can potentially be used to predict future solar activity. Specifically, we develop a tool for predicting future magnetic field intensity, based on the hysteresis in the GCR variation, during the last phases of the current cycle. This method estimates that SC25 will be as weak as or weaker than SC24. This would mean that the Sun has likely entered a secular minimum, which, according to historical records, should last for another two cycles (SC2527and SC26).

Solar cycles↗

The ZBOT-NC Experiment - Effects of Non-Condensable Gases on Propellant Tank Pressurization and Pressure Control

Introduction Integral to all phases of NASA’s projected planetary expeditions is affordable and reliable cryogenic fluid storage for use in propellant or life support systems. It is greatly advantageous to develop innovative vent-less pressure control designs based on cooling/mixing of the bulk tank fluid to allow storage of the cryogenic fluid with zero or reduced boil-off. The presence of noncondensable gases, can interfere with the condensation at the interface impacting tank pressure control during subcooled jet mixing especially in microgravity. The Zero-Boil-Off Tank (ZBOT) Experiments are a series of small-scale experiments aboard the International Space Station (ISS) that use a transparent volatile simulant fluid in a transparent sealed tank to delineate various fundamental fluid flow, heat and mass transport, and phase change phenomena associated with storage tank pressurization and pressure control in microgravity. The ZBOT-1 experiment was performed on the ISS 2017-2018 timeframe and collected data to validate a state-of-the-art CFD model for tank pressurization and pressure control for a pure system. The ZBOT-NC Experiment is the second experiment in the series to be performed on the International Space Station (ISS) in 2025. Its goal is to investigate the effects of noncondensable gases on interfacial evaporation and condensation during self -pressurization and jet-mixing pressure control in microgravity for a two-component system. Materials & Methods In this work, we will describe the detailed features of the ZBOT-NC experimental hardware and Diagnostics that includes nonintrusive Quantum Dot Thermometry (QDT) for whole field temperature measurement. All microgravity pressurization and pressure control tests will be performed for both the pure and the two-components systems with Xenon and Neon as the two noncondensable gases spanning small and large molecular weights and sizes. The two-phase CFD model that is developed as part of the project will be also presented and discussed. Results Ground-based pressurization and jet mixing experiments and CFD simulation results are compared to each other to validate both the fidelity of the CFD model predictions and the accuracy of the QDT measurement. Model simulations for noncondensable gas effects will also be compared against large Cryogenic LH2-GHe experiments to indicate the noncondensable gas effects on tank pressure control during jet mixing in 1G. Finally, CFD results will be presented to predict the effects of the noncondensable gas during subcooled jet mixing during the ZBOT-NC in advance of the microgravity experiment in 2015.

Evaporation Condensation↗

The Zero-Boil-Off Tank Experiment: the Effects of Non-Condensable Gases on Pressurization and Pressure Control of Propellant Tanks in Microgravity

Introduction Integral to all phases of NASA’s projected planetary expeditions is affordable and reliable cryogenic fluid storage for use in propellant or life support systems. It is greatly advantageous to develop innovative vent-less pressure control designs based on cooling/mixing of the bulk tank fluid to allow storage of the cryogenic fluid with zero or reduced boil-off. The presence of noncondensable gases, can interfere with the condensation at the interface impacting tank pressure control during subcooled jet mixing especially in microgravity. The Zero-Boil-Off Tank (ZBOT) Experiments are a series of small-scale experiments aboard the International Space Station (ISS) that use a transparent volatile simulant fluid in a transparent sealed tank to delineate various fundamental fluid flow, heat and mass transport, and phase change phenomena associated with storage tank pressurization and pressure control in microgravity. The ZBOT-1 experiment was performed on the ISS 2017-2018 timeframe and collected data to validate a state-of-the-art CFD model for tank pressurization and pressure control for a pure system. The ZBOT-NC Experiment is the second experiment in the series to be performed on the International Space Station (ISS) in 2025. Its goal is to investigate the effects of noncondensable gases on interfacial evaporation and condensation during self -pressurization and jet-mixing pressure control in microgravity for a two-component system. Materials & Methods In this work, we will describe the detailed features of the ZBOT-NC experimental hardware and Diagnostics that includes nonintrusive Quantum Dot Thermometry (QDT) for whole field temperature measurement. All microgravity pressurization and pressure control tests will be performed for both the pure and the two-components systems with Xenon and Neon as the two noncondensable gases spanning small and large molecular weights and sizes. The two-phase CFD model that is developed as part of the project will be also presented and discussed. Results Ground-based pressurization and jet mixing experiments and CFD simulation results are compared to each other to validate both the fidelity of the CFD model predictions and the accuracy of the QDT measurement. Model simulations for noncondensable gas effects will also be compared against large Cryogenic LH2-GHe experiments to indicate the noncondensable gas effects on tank pressure control during jet mixing in 1G. Finally, CFD results will be presented to predict the effects of the noncondensable gas during subcooled jet mixing during the ZBOT-NC in advance of the microgravity experiment in 2015.

Evaporation Condensation↗

Experimenting Galileo on Board the International Space Station

The SCaN Testbed is an advanced integrated communications system and laboratory facility installed on the International Space Station (ISS) in 2012. The testbed incorporates a set of new generation of Software Defined Radio (SDR) technologies intended to allow researchers to develop, test, and demonstrate new communications, networking, and navigation capabilities in the actual environment of space. Qascom, in cooperation with ESA and NASA, is designing a Software Defined Radio GalileoGPS Receiver capable to provide accurate positioning and timing to be installed on the ISS SCaN Testbed. The GalileoGPS waveform will be operated in the JPL SDR that is constituted by several hardware components that can be used for experimentations in L-Band and S-Band. The JPL SDR includes an L-Band Dorne Margolin antenna mounted onto a choke ring. The antenna is connected to a radio front end capable to provide one bit samples for the three GNSS frequencies (L1, L2 and L5) at 38 MHz, exploiting the subharmonic sampling. The baseband processing is then performed by an ATMEL AT697 processor (100 MIPS) and two Virtex 2 FPGAs. The JPL SDR supports the STRS (Space Telecommunications Radio System) that provides common waveform software interfaces, methods of instantiation, operation, and testing among different compliant hardware and software products. The standard foresees the development of applications that are modular, portable, reconfigurable, and reusable. The developed waveform uses the STRS infrastructure-provided application program interfaces (APIs) and services to load, verify, execute, change parameters, terminate, or unload an application. The project is divided in three main phases. 1)Design and Development of the GalileoGPS waveform for the SCaN Testbed starting from Qascom existing GNSS SDR receiver. The baseline design is limited to the implementation of the single frequency Galileo and GPS L1E1 receiver even if as part of the activity it will be to assess the feasibility of a dual frequency implementation (L1E1+L5E5a) in the same SDR platform.2)Qualification and test the GalileoGPS waveform using ground systems available at the NASA Glenn Research Center. Experimenters can have access to two SCaN Testbed ground based systems for development and verification: the Experimenter Development System (EDS) that is intended to provide initial opportunity for software testing and basic functional validation and the Ground Integration Unit (GIU) that is a high fidelity version of the SCaN Testbed flight system and is therefore used for more controlled final development testing and verification testing.3)Perform in-orbit validation and experimentation: The experimentation phase will consists on the collection of raw measurements (pseudorange, Carrier phase, CN0) in space, assessment on the quality of the measurements and the receiver performances in terms of signal acquisition, tracking, etc. Finally computation of positioning in space (Position, Velocity and time) and assessment of its performance.(Complete abstract in attached document).

GPS↗

Experimenting Galileo on Board the International Space Station

The SCaN Testbed is an advanced integrated communications system and laboratory facility installed on the International Space Station (ISS) in 2012. The testbed incorporates a set of new generation of Software Defined Radio (SDR) technologies intended to allow researchers to develop, test, and demonstrate new communications, networking, and navigation capabilities in the actual environment of space. Qascom, in cooperation with ESA and NASA, is designing a Software Defined Radio GalileoGPS Receiver capable to provide accurate positioning and timing to be installed on the ISS SCaN Testbed. The GalileoGPS waveform will be operated in the JPL SDR that is constituted by several hardware components that can be used for experimentations in L-Band and S-Band. The JPL SDR includes an L-Band Dorne Margolin antenna mounted onto a choke ring. The antenna is connected to a radio front end capable to provide one bit samples for the three GNSS frequencies (L1, L2 and L5) at 38 MHz, exploiting the subharmonic sampling. The baseband processing is then performed by an ATMEL AT697 processor (100 MIPS) and two Virtex 2 FPGAs. The JPL SDR supports the STRS (Space Telecommunications Radio System) that provides common waveform software interfaces, methods of instantiation, operation, and testing among different compliant hardware and software products. The standard foresees the development of applications that are modular, portable, reconfigurable, and reusable. The developed waveform uses the STRS infrastructure-provided application program interfaces (APIs) and services to load, verify, execute, change parameters, terminate, or unload an application. The project is divided in three main phases. 1)Design and Development of the GalileoGPS waveform for the SCaN Testbed starting from Qascom existing GNSS SDR receiver. The baseline design is limited to the implementation of the single frequency Galileo and GPS L1E1 receiver even if as part of the activity it will be to assess the feasibility of a dual frequency implementation (L1E1+L5E5a) in the same SDR platform.2)Qualification and test the GalileoGPS waveform using ground systems available at the NASA Glenn Research Center. Experimenters can have access to two SCaN Testbed ground based systems for development and verification: the Experimenter Development System (EDS) that is intended to provide initial opportunity for software testing and basic functional validation and the Ground Integration Unit (GIU) that is a high fidelity version of the SCaN Testbed flight system and is therefore used for more controlled final development testing and verification testing.3)Perform in-orbit validation and experimentation: The experimentation phase will consists on the collection of raw measurements (pseudorange, Carrier phase, CN0) in space, assessment on the quality of the measurements and the receiver performances in terms of signal acquisition, tracking, etc. Finally computation of positioning in space (Position, Velocity and time) and assessment of its performance.(Complete abstract in attached document).

Galileo↗

Volume and Mass Estimation of Three-Phase High Power Transformers for Space Applications

Spacecraft historically have had sub-1kW(sub e), electrical requirements for GN&C, science, and communications: Galileo at 600W(sub e), and Cassini at 900W(sub e), for example. Because most missions have had the same order of magnitude power requirements, the Power Distribution Systems (PDS) use existing, space-qualified technology and are DC. As science payload and mission duration requirements increase, however, the required electrical power increases. Subsequently, this requires a change from a passive energy conversion (solar arrays and batteries) to dynamic (alternator, solar dynamic, etc.), because dynamic conversion has higher thermal and conversion efficiencies, has higher power densities, and scales more readily to higher power levels. Furthermore, increased power requirements and physical distribution lengths are best served with high-voltage, multi-phase AC to maintain distribution efficiency and minimize voltage drops. The generated AC-voltage must be stepped-up (or down) to interface with various subsystems or electrical hardware. Part of the trade-space design for AC distribution systems is volume and mass estimation of high-power transformers. The volume and mass are functions of the power rating, operating frequency, the ambient and allowable temperature rise, the types and amount of heat transfer available, the core material and shape, the required flux density in a core, the maximum current density, etc. McLyman has tabulated the performance of a number of transformers cores and derived a "cookbook" methodology to determine the volume of transformers, whereas Schawrze had derived an empirical method to estimate the mass of single-phase transformers. Based on the work of McLyman and Schwarze, it is the intent herein to derive an empirical solution to the volume and mass estimation of three-phase, laminated EI-core power transformers, having radiated and conducted heat transfer mechanisms available. Estimation of the mounting hardware, connectors, etc. is not included.

Kimnach, Greg L.↗

Better, Cheaper, Faster Molecular Dynamics

Recent, revolutionary progress in genomics and structural, molecular and cellular biology has created new opportunities for molecular-level computer simulations of biological systems by providing vast amounts of data that require interpretation. These opportunities are further enhanced by the increasing availability of massively parallel computers. For many problems, the method of choice is classical molecular dynamics (iterative solving of Newton's equations of motion). It focuses on two main objectives. One is to calculate the relative stability of different states of the system. A typical problem that has' such an objective is computer-aided drug design. Another common objective is to describe evolution of the system towards a low energy (possibly the global minimum energy), "native" state. Perhaps the best example of such a problem is protein folding. Both types of problems share the same difficulty. Often, different states of the system are separated by high energy barriers, which implies that transitions between these states are rare events. This, in turn, can greatly impede exploration of phase space. In some instances this can lead to "quasi non-ergodicity", whereby a part of phase space is inaccessible on time scales of the simulation. To overcome this difficulty and to extend molecular dynamics to "biological" time scales (millisecond or longer) new physical formulations and new algorithmic developments are required. To be efficient they should account for natural limitations of multi-processor computer architecture. I will present work along these lines done in my group. In particular, I will focus on a new approach to calculating the free energies (stability) of different states and to overcoming "the curse of rare events". I will also discuss algorithmic improvements to multiple time step methods and to the treatment of slowly decaying, log-ranged, electrostatic effects.

Pohorille, Andrew↗

Phases of 2D massless QCD with qubit regularization

We investigate the possibility of reproducing the continuum physics of 2D S U ( N ) gauge theory coupled to a single flavor of massless Dirac fermion using qubit regularization. The continuum theory is described by N free fermions in the ultraviolet (UV) and a coset Wess-Zumino-Witten (WZW) model in the infrared (IR). In this work, we first explore how well these features can be reproduced using the Kogut-Susskind (KS) Hamiltonian with a finite-dimensional link Hilbert space and a generalized Hubbard coupling. We do this by analyzing the renormalization group (RG) flow diagram of the continuum theory and identifying important phases of the theory. Using strong coupling expansions, we show that our lattice model exhibits a gapped dimer phase and a spin-chain phase. Furthermore, for N = 2 , using tensor network methods, we show that there is a second-order phase transition between these two phases, which we identify as the critical surface of the continuum theory that connects the IR and UV fixed points. In the IR, we identify the critical theory at the transition as the expected S U ( 2 ) 1 WZW model. Lastly, we argue that modifications of our model may allow the study of the UV physics of free fermions. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Combined loading criterial influence on structural performance

An investigation was conducted to determine the influence of combined loading criteria on the space shuttle structural performance. The study consisted of four primary phases: Phase (1) The determination of the sensitivity of structural weight to various loading parameters associated with the space shuttle. Phase (2) The determination of the sensitivity of structural weight to various levels of loading parameter variability and probability. Phase (3) The determination of shuttle mission loading parameters variability and probability as a function of design evolution and the identification of those loading parameters where inadequate data exists. Phase (4) The determination of rational methods of combining both deterministic time varying and probabilistic loading parameters to provide realistic design criteria. The study results are presented.

Kuchta, B. J.↗

He-3 cooling systems for space

The development of a space-compatible He(3) refrigerator would provide a significant improvement in several areas of research in the 0.3 to 1 K temperature range. There are several methods of achieving these temperatures on Earth: He(3) refrigeration, dilution refrigeration, and adiabatic demagnetization refrigeration. The progress of adapting He(3) refrigeration for use in space is described. Various cycles and possible embodiments of He(3) refrigerators are described. Also included is an analysis of the liquid confinement and liquid-vapor phase-separation system. A possible configuration is then analyzed. Finally, the results of ground-based experiments will be discussed.

Kittel, P.↗

Phase partitioning experiment (8-IML-1)

Phase partitioning is a method of separating biological cells and macromolecules via their differential distribution in two phase aqueous polymer solutions. The ultimate goal of the experiment is to test the hypothesis that the efficiency of separation of closely related cell types, by partitioning in immiscible aqueous phases, will be enhanced in the non-convective environment provided by space. Before a cell separation experiment can be performed, the demixing of immiscible aqueous polymer solutions must be understood and controlled in order to optimize the experimental conditions for a cell separation experiment in the future. The present Phase Partitioning Experiment (PPE) is the third in a series, the first two flew on STS 51-D in Apr. 1985 and STS 26 in Oct. 1988. In those experiments the immiscible aqueous phases demixed spontaneously at different rates, the final disposition being one in which the phase which wetted the container wall surrounded the second phase which formed an 'egg yolk' in the center of the chamber.

Brooks, Donald E.↗

Flight Dynamics Mission Support and Quality Assurance Process

This paper summarizes the method of the Computer Sciences Corporation Flight Dynamics Operation (FDO) quality assurance approach to support the National Aeronautics and Space Administration Goddard Space Flight Center Flight Dynamics Support Branch. Historically, a strong need has existed for developing systematic quality assurance using methods that account for the unique nature and environment of satellite Flight Dynamics mission support. Over the past few years FDO has developed and implemented proactive quality assurance processes applied to each of the six phases of the Flight Dynamics mission support life cycle: systems and operations concept, system requirements and specifications, software development support, operations planing and training, launch support, and on-orbit mission operations. Rather than performing quality assurance as a final step after work is completed, quality assurance has been built in as work progresses in the form of process assurance. Process assurance activities occur throughout the Flight Dynamics mission support life cycle. The FDO Product Assurance Office developed process checklists for prephase process reviews, mission team orientations, in-progress reviews, and end-of-phase audits. This paper will outline the evolving history of FDO quality assurance approaches, discuss the tailoring of Computer Science Corporations's process assurance cycle procedures, describe some of the quality assurance approaches that have been or are being developed, and present some of the successful results.

Oh, InHwan↗

Aeroacoustic Flow Phenomena Accurately Captured by New Computational Fluid Dynamics Method

One of the challenges in the computational fluid dynamics area is the accurate calculation of aeroacoustic phenomena, especially in the presence of shock waves. One such phenomenon is "transonic resonance," where an unsteady shock wave at the throat of a convergent-divergent nozzle results in the emission of acoustic tones. The space-time Conservation-Element and Solution-Element (CE/SE) method developed at the NASA Glenn Research Center can faithfully capture the shock waves, their unsteady motion, and the generated acoustic tones. The CE/SE method is a revolutionary new approach to the numerical modeling of physical phenomena where features with steep gradients (e.g., shock waves, phase transition, etc.) must coexist with those having weaker variations. The CE/SE method does not require the complex interpolation procedures (that allow for the possibility of a shock between grid cells) used by many other methods to transfer information between grid cells. These interpolation procedures can add too much numerical dissipation to the solution process. Thus, while shocks are resolved, weaker waves, such as acoustic waves, are washed out.

Blech, Richard A.↗

Redox Defect Thermochemistry of FeAl 2 O 4 Hercynite in Water Splitting from First-Principles Methods

Solar thermochemical hydrogen (STCH) production is a promising route to produce fuels from sunlight via high-temperature water splitting. However, efficient and technologically viable implementations of this process only allow a narrow window of thermodynamic boundary conditions that can be used to cycle the system, thus limiting the design space for suitable metal oxide redox mediators. An oxygen defect redox mechanism can contribute a favorable reduction entropy to expand this window, and computational evaluation of materials with high oxygen defect entropies could play a pivotal role in guiding the discovery and design of suitable oxides. This study employs first-principles calculations to investigate the redox mediating defect mechanism of the STCH candidate material, hercynite (FeAl 2 O 4 ). We compare the results of total energy calculations from density functional theory (DFT) with beyond-DFT approaches, including hybrid functionals and the random phase approximation, which are among the most advanced methods currently feasible for supercell defect calculations. Using the predicted formation energies, we perform thermodynamic modeling of FeAl2O4 reduction and oxidation via free energy minimization that incorporates ideal gas, configurational, and vibrational entropy contributions evaluated within the quasi-harmonic approximation. Special attention is devoted to understanding interactions among co-existing defects, such as the association of pairs and complexes of O vacancies and cation antisite defects, and the effect of mutually compensating defect charges. Our results corroborate the notion that the details of defect interactions can be decisive for the viability of hydrogen production within the desirable STCH process window.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Assessing entropy for catalytic processes at complex reactive interfaces

When chemical reactions are accelerated by a catalyst, entropy differences between reactants and their transient intermediates can be the driving force behind the promotion or inhibition of desired and parasitic chemical pathways. Understanding and controlling catalytic processes therefore requires both a fundamental and practicable understanding of entropy in addition to enthalpy. In unstructured media such as the vapor phase equilibrated with sparsely covered surfaces, entropy can be adequately accounted for by well-established approaches based on translational, rotational, and harmonic vibrational partition functions. However, these approximations become inadequate in more complex condensed phase environments, e.g., solid liquid interfaces of confined reaction spaces. In this chapter, we provide an overview of the state-of-art in the computational quantification of entropy and its known ramifications on catalysis. The fundamental roles of thermodynamics and kinetics in catalysis are covered in enough detail to appreciate and contextualize the computational methods employed to compute chemically accurate estimates of entropy. These methods are discussed in appropriate detail and range from the ubiquitous harmonic oscillator approximation where entropy unrelated to high frequency oscillations is typically underestimated, to enhanced free energy sampling with molecular dynamics where the desired accuracy must be weighed against the associated computational cost of obtaining it. The rising importance of machine learning and artificial intelligence in accelerating methodological progress in this field is touched upon, as well. Finally, applications, successes, and pitfalls of using these methods are provided to showcase past and present accomplishments while clarifying where improvements in both understanding and methodology are still needed.

Kollias, Loukas↗