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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.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Electrostatically controlled micromechanical gyroscope

An integrated electrostatically-controlled micromechanical gyroscope with a rotor encompassed within a rotor cavity and electrostatically spun within the cavity. The gyroscope includes a plurality of axial electrostatic rotor actuators above and below the rotor for controlling the axial and tilt position of the rotor within the cavity, and a plurality of radial electrostatic actuators spaced circumferentially around the rotor for controlling the radial and tilt position of the rotor within the cavity. The position of the rotor within the cavity is then resolved to determine the external forces acting on the rotor.

Hawkey, Timothy↗
NASA NTRS2008

Electrostatic Characterization of Lunar Dust

To ensure the safety and success of future lunar exploration missions, it is important to measure the toxicity of the lunar dust and its electrostatic properties. The electrostatic properties of lunar dust govern its behavior, from how the dust is deposited in an astronaut s lungs to how it contaminates equipment surfaces. NASA has identified the threat caused by lunar dust as one of the top two problems that need to be solved before returning to the Moon. To understand the electrostatic nature of lunar dust, NASA must answer the following questions: (1) how much charge can accumulate on the dust? (2) how long will the charge remain? and (3) can the dust be removed? These questions can be answered by measuring the electrostatic properties of the dust: its volume resistivity, charge decay, charge-to-mass ratio or chargeability, and dielectric properties.

Source record↗
NASA NTRS2010

Electrostatic Power Generation from Negatively Charged, Simulated Lunar Regolith

Research was conducted to develop an electrostatic power generator for future lunar missions that facilitate the utilization of lunar resources. The lunar surface is known to be negatively charged from the constant bombardment of electrons and protons from the solar wind. The resulting negative electrostatic charge on the dust particles, in the lunar vacuum, causes them to repel each other minimizing the potential. The result is a layer of suspended dust about one meter above the lunar surface. This phenomenon was observed by both Clementine and Surveyor spacecrafts. During the Apollo 17 lunar landing, the charged dust was a major hindrance, as it was attracted to the astronauts' spacesuits, equipment, and the lunar buggies. The dust accumulated on the spacesuits caused reduced visibility for the astronauts, and was unavoidably transported inside the spacecraft where it caused breathing irritation [1]. In the lunar vacuum, the maximum charge on the particles can be extremely high. An article in the journal "Nature", titled "Moon too static for astronauts?" (Feb 2, 2007) estimates that the lunar surface is charged with up to several thousand volts [2]. The electrostatic power generator was devised to alleviate the hazardous effects of negatively charged lunar soil by neutralizing the charged particles through capacitive coupling and thereby simultaneously harnessing power through electric charging [3]. The amount of power generated or collected is dependent on the areal coverage of the device and hovering speed over the lunar soil surface. A thin-film array of capacitors can be continuously charged and sequentially discharged using a time-differentiated trigger discharge process to produce a pulse train of discharge for DC mode output. By controlling the pulse interval, the DC mode power can be modulated for powering devices and equipment. In conjunction with a power storage system, the electrostatic power generator can be a power source for a lunar rover or other systems. The negatively charged lunar soil would also be neutralized mitigating some of the adverse effects resulting from lunar dust.

Choi, Sang H.↗
NASA NTRS2011

The Electrostatic Environments of Mars and the Moon

The electrical activity present in the environment near the surfaces of Mars and the moon has very different origins and presents a challenge to manned and robotic planetary exploration missions. Mars is covered with a layer of dust that has been redistributed throughout the entire planet by global dust storms. Dust, levitated by these storms as well as by the frequent dust devils, is expected to be electrostatically charged due to the multiple grain collisions in the dust-laden atmosphere. Dust covering the surface of the moon is expected to be electrostatically charged due to the solar wind, cosmic rays, and the solar radiation itself through the photoelectric effect. Electrostatically charged dust has a large tendency to adhere to surfaces. NASA's Mars exploration rovers have shown that atmospheric dust falling on solar panels can decrease their efficiency to the point of rendering the rover unusable. And as the Apollo missions to the moon showed, lunar dust adhesion can hinder manned and unmanned lunar exploration activities. Taking advantage of the electrical activity on both planetary system bodies, dust removal technologies are now being developed that use electrostatic and dielectrophoretic forces to produce controlled dust motion. This paper presents a short review of the theoretical and semiempirical models that have been developed for the lunar and Martian electrical environments.

Calle, Carlos I.↗
NASA NTRS2010

On Variable Geometric Factor Systems for Top-Hat Electrostatic Space Plasma Analyzers

Even in the relatively small region of space that is the Earth's magnetosphere, ion and electron fluxes can vary by several orders of magnitude. Top-hat electrostatic analyzers currently do not possess the dynamic range required to sample plasma under all conditions. The purpose of this study was to compare, through computer simulation, three new electrostatic methods that would allow the sensitivity of a sensor to be varied through control of its geometric factor (GF) (much like an aperture on a camera). The methods studied were inner filter plates, split hemispherical analyzer (SHA) and top-cap electrode. This is the first discussion of the filter plate concept and also the first study where all three systems are studied within a common analyzer design, so that their relative merits could be fairly compared. Filter plates were found to have the important advantage that they facilitate the reduction in instrument sensitivity whilst keeping all other instrument parameters constant. However, it was discovered that filter plates have numerous disadvantages that make such a system impracticable for a top-hat electrostatic analyzer. It was found that both the top-cap electrode and SHA are promising variable geometric factor system (VGFS) concepts for implementation into a top-hat electrostatic analyzer, each with distinct advantages over the other.

Kataria, Dhiren O.↗
NASA NTRS2011

Electrostatic Precipitation of Dust in the Martian Atmosphere: Implications for the Utilization of Resources During Future Manned Exploration Missions

Future human missions to Mars will require the utilization of local resources for oxygen, fuel. and water. The In Situ Resource Utilization (ISRU) project is an active research endeavor at NASA to develop technologies that can enable cost effective ways to live off the land. The extraction of oxygen from the Martian atmosphere. composed primarily of carbon dioxide, is one of the most important goals of the Mars ISRU project. The main obstacle is the relatively large amount of dust present in the Martian atmosphere. This dust must be efficiently removed from atmospheric gas intakes for ISRU processing chambers. A common technique to achieve this removal on earth is by electrostatic precipitation, where large electrostatic fields are established in a localized region to precipitate and collect previously charged dust particles. This technique is difficult to adapt to the Martian environment, with an atmospheric pressure of about one-hundredth of the terrestrial atmosphere. At these low pressures. the corona discharges required to implant an electrostatic charge to the particles to be collected is extremely difficult to sustain and the corona easily becomes biopolar. which is unsuitable for particle charging. In this paper, we report on our successful efforts to establish a stable corona under Martian simulated conditions. We also present results on dust collecting efficiencies with an electrostatic precipitator prototype that could be effectively used on a future mission to the red planet

Calle, Carlos I.↗
NASA NTRS2005

Ferrocene Containing Copolymers with Improved Electrostatic Dissipation Properties for Advanced Applications

Electrostatic dissipative polymers are used for a variety of functions. Typical methods utilized to transform electrically insulating polymers into either charge dissipative or conductive materials involve incorporating a conductive filler, conductive polymer, oxidizing the surface using plasma, or incorporating surfactants that act as surface wetting agents. Another approach is to synthesize a block copolymer that is expected to result in better electrical properties with minimal impacts to physical, fire, and thermal properties. One such block that can be added into the main chain of polymers is a diol terminated ferrocene oligomer, which is expected to impart electrostatic dissipative properties into the host polymer while concurrently improving the overall fire properties. Previous work with polyurethanes incorporating a ferrocene oligomer into the main chain resulted in much improved fire retardancy. In dealing with electrostatic dissipative materials the important questions are: how easily does the material charge and how quickly can the charge move to ground. One normally describes the materials conductivity, but conductivity only measures the fastest path for an electron not the slowest path. The slowest path is the one of interest, since it is left on the surface and thus can cause discharges. In order to assess ease of charging and decay times corona charge dissipation measurements can accurately assess these properties by introducing a charge on the surface of the material then measuring the surface voltage and the amount of charge deposited. The charge decay curve then will give an indication of a materials electrostatic dissipation properties. Normally, triboelectric testing can be performed, but results vary. Corona charge dissipation results are more repeatable.

Smith, T. M.↗
NASA NTRS2013

Characterizing the Performance of the Wheel Electrostatic Spectrometer

Insulators need to be discharged after each wheel revolution. Sensor responses repeatable within one standard deviation in the noise of the signal. Insulators may not need to be cleaned after each revolution. Parent Technology- Mars Environmental Compatibility Assessment/Electrometer Electrostatic sensors with dissimilar cover insulators Protruding insulators tribocharge against regolith simulant Developed for use on the scoop for the 2001 Mars Odyssey lander Wheel Electrostatic Spectrometer Embedded electrostatic sensors in prototype Martian rover wheel If successful, this technology will enable constant electrostatic testing on Mars Air ionizing fan used to neutralize the surface charge on cover insulators . WES rolled on JSClA lunar simulant Control experiment -Static elimination not conducted between trials -Capacitor discharged after each experiment Charge neutralization experiment -Static elimination conducted between trials -Capacitor discharged after each experiment. Air ionizing fan used on insulators after each wheel revolution Capacitor discharged after each trial Care was taken to roll WES with same speed/pressure Error bars represent one standard deviation in the noise of e ach sensor

Johansen, Michael R.↗
NASA NTRS2013

Separation and Purification of Mineral Salts from Spacecraft Wastewater Processing via Electrostatic Beneficiation

Electrostatic separation is a class of material processing technologies commonly used for the sorting of coarse mixtures by means of electrical forces acting on charged or polarized particles. Most if not all of the existing tribo-electrostatic separators had been initially developed for mineral ores beneficiation. It is a well-known process that has been successfully used to separate coal from minerals. Potash (potassium) enrichment where underground salt mines containing large amounts of sodium is another use of this techno logy. Through modification this technology can be used for spacecraft wastewater brine beneficiation. This will add in closing the gap be~een traveling around Earth's Gravity well and long-term space explorations. Food has been brought on all man missions, which is why plant growth for food crops continues to be of interest to NASA. For long-term mission considerations food productions is one of the top priorities. Nutrient recovery is essential for surviving in or past low earth orbit. In our advance bio-regenerative process instead of nitrogen gas produced; soluble nitrate salts that can be recovered for plant fertilizer would be produced instead. The only part missing is the beneficiation of brine to separate the potassium from the sodium. The use of electrostatic beneficiation in this experiment utilizes the electrical charge differences between aluminum and dried brine by surface contact. The helixes within the aluminum tribocharger allows for more surface contact when being agitated. When two materials are in contact, the material with the highest affinity for electrons becomes negatively charged, while the other becomes positively charged. This contact exchange of charge may cause the particles to agglomerate depending on their residence time within the tribocharger, compromising the efficiency of separation. The aim of this experiment is to further the development in electrostatic beneficiation by optimizing the separation of ersatz and possibly real wastewater brine residues. In doing so, ideally it will yield a high potassium enrichment for use in spacecraft plant systems.

Miles, John D., II↗
NASA NTRS2016

Meeting the Grand Challenge of Protecting Astronauts Health: Electrostatic Active Space Radiation Shielding for Deep Space Missions

This report describes the research completed during 2011 for the NASA Innovative Advanced Concepts (NIAC) project. The research is motivated by the desire to safely send humans in deep space missions and to keep radiation exposures within permitted limits. To this end current material shielding, developed for low earth orbit missions, is not a viable option due to payload and cost penalties. The active radiation shielding is the path forward for such missions. To achieve active space radiation shielding innovative large lightweight gossamer space structures are used. The goal is to deflect enough positive ions without attracting negatively charged plasma and to investigate if a charged Gossamer structure can perform charge deflections without significant structural instabilities occurring. In this study different innovative configurations are explored to design an optimum active shielding. In addition, to establish technological feasibility experiments are performed with up to 10kV of membrane charging, and an electron flux source with up to 5keV of energy and 5mA of current. While these charge flux energy levels are much less than those encountered in space, the fundamental coupled interaction of charged Gossamer structures with the ambient charge flux can be experimentally investigated. Of interest are, will the EIMS remain inflated during the charge deflections, and are there visible charge flux interactions. Aluminum coated Mylar membrane prototype structures are created to test their inflation capability using electrostatic charging. To simulate the charge flux, a 5keV electron emitter is utilized. The remaining charge flux at the end of the test chamber is measured with a Faraday cup mounted on a movable boom. A range of experiments with this electron emitter and detector were performed within a 30x60cm vacuum chamber with vacuum environment capability of 10-7 Torr. Experiments are performed with the charge flux aimed at the electrostatically inflated membrane structure (EIMS) in both charged and uncharged configurations. The amount of charge shielding behind and around the EIMS was studied for different combinations of membrane structure voltages and electron energies. Both passive and active shielding were observed, with active shielding capable of deflecting nearly all incoming electrons. The pattern of charge distribution around the structure was studied as well as the stability of the structures in the charge flow. The charge deflection experiments illustrate that the EIMS remain inflated during charge deflection, but will experience small amplitude oscillations. Investigations were performed to determine a potential cause of the vibrations. It is postulated these vibrations are due to the charge flux causing local membrane charge distribution changes. As the membrane structure inflation pressure is changed, the shape responds, and causes the observed sustained vibration. Having identified this phenomenon is important when considering electrostatically inflated membrane structures (EIMS) in a space environment. Additionally, this project included a study of membrane material impacts, specifically the impact of membrane thickness. Extremely thin materials presented new challenges with vacuum preparation techniques and rapid charging. The thinner and lighter membrane materials were successfully inflated using electrostatic forces in a vacuum chamber. However, care must be taken when varying the potentials of such lighter structures as the currents can cause local heating and melting of the very thin membranes. Lastly, a preliminary analysis is performed to study rough order of magnitude power requirements for using EIMS for radiation shielding. The EIMS power requirement becomes increasingly more challenging as the spacecraft voltage is increased. As a result, the emphasis is on the deflection of charges away from the spacecraft rather than totally stopping them. This significantly alleviates the initial power requirements. With modest technological development(s) active shielding is emerging to be a viable option.

Radiation↗
NASA NTRS2020

Implementation Concept of Operation for a Multi-Purpose Cassegrain Solar Concentrator, Micro-Spectrometers, and Electrostatic Neutralizers to Enable In Situ Construction Activities plus Lunar, Planetary, and Deep Space Science Exploration on the Moon

The ability to utilize regolith would support human missions to the Moon and Mars by both stabilizing the surface as well as the use of indigenous resources. Precision landing requirements include surface stabilization to prevent damage or contamination due to regolith projectiles as a result of plume interaction with regolith. The use of indigenous resources rather than hauling materials from Earth appears to be economically a palatable option by converting indigenous resources to usable products. However, such activities have new technical challenges to overcome the issues related to lunar environmental conditions, a wide range of temperature fluctuation, extremely high vacuum, and electrostatically charged fine regolith dusts. For both the regolith sintering and extraction of resources onsite, a Cassegrain solar concentrator was studied for not only sintering lunar regolith into a hardened stabilized surface, but also other multiple applications. This report illustrates a Cassegrain solar concentrator that has multi-functional capabilities for space missions. Proper design and implementation of high-performance lightweight composite materials for the primary mirror of the Cassegrain concentrator can offer multiple capabilities to be performed on the Moon. The multiple applications studied with Cassegrain concentrators are (1) Solar sintering for landing pad and habitats, (2) Harvest of volatiles: H2O, O2, H2, and He-3, (3) Space antenna for telemetry and telecommunication, and (4) Space telescope with 20-meter aperture that exceeds the space telescopes to date in terms of the State-of-Art (SOA) in resolution and aperture diameter. In this study, a key emphasis was placed on the NASA Langley-developed boron nitride nanotube (BNNT) nanocomposite technology which is ideal for the segmented primary mirror structure of the Cassegrain system because it promises a very low coefficient of thermal expansion (CTE) and negligible Poisson ratio. Also, BNNT nanocomposites offer several noticeable benefits, such as light weight, radiation shielding capability, and mechanical strength for structural applications. Additionally, the NASA Langley-developed bullet-like micro-spectrometer and electrostatic power generator were reviewed for mineral mapping applications and electrostatic power generation and dust mitigation from electrostatically charged regolith.

landing pad↗
DOE OSTI2019

Analysis and fringe field scaling of a legacy set of electrostatic deflector aberration formulas [Chapter Seven]

In this work we performed an analysis of the derivation of first and second order analytic aberration formulas by Wollnik (1965) for the case of electrostatic deflectors in the horizontal plane. We found that these aberration formulas are valid for the main field of the deflector; however, they do not account for any fringe field effects. To address this issue, we modified the aberration formulas from Wollnik (1965) for a hard edge fringe field by scaling the particle inclinations at the entrance and exit edges of the deflector. These modified aberration formulas fully agree with electrostatic aberration formulas derived by Valetov and Berz (2020), as well as with differential-algebraic (DA) calculations of electrostatic deflector aberrations using the code COSY INFINITY.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Protein C-GeM: A Coarse-Grained Electron Model for Fast and Accurate Protein Electrostatics Prediction

The electrostatic potential (ESP) is a powerful property for understanding and predicting electrostatic charge distributions that drive interactions between molecules. In this study, we compare various charge partitioning schemes including fitted charges, density-based quantum mechanical (QM) partitioning schemes, charge equilibration methods, and our recently introduced coarse-grained electron model, C-GeM, to describe the ESP for protein systems. Furthermore, when benchmarked against high quality density functional theory calculations of the ESP for tripeptides and the crambin protein, we find that the C-GeM model is of comparable accuracy to ab initio charge partitioning methods, but with orders of magnitude improvement in computational efficiency since it does not require either the electron density or the electrostatic potential as input.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Diabatization with Electrostatic Embedding for Studying Photophysics in Organic Molecular Crystals

Highly emissive organic molecular crystals find applications in several areas, such as organic electronics, solar cells, and sensors. Understanding the excited-state mechanisms underlying these applications is essential for optimizing and controlling them effectively. Exciton models coupled with nonadiabatic dynamics, particularly quantum dynamics, provide crucial insights into photochemical and photophysical processes in molecular crystals. Nevertheless, there remains a lack of general tools and automated workflows to facilitate such simulations. In this paper, we present a computational strategy to investigate the photoactivated dynamics of organic molecular crystals, bridging methodologies traditionally used for molecular systems and materials science, with a particular focus on the interplay between local excitations and charge transfer (CT) processes. We have implemented an interface between the fromage and Overdia programs, enabling the construction of vibronic Hamiltonians for molecular crystals within an excited-state ONIOM(QM:QM′) framework, incorporating long-range electrostatics through a RESP-based Ewald summation. Fragment-based diabatization provides a route to quantum dynamics simulations in weak-to-intermediate coupling regimes. The method was applied to the photophysics of dibenzo[g,p]chrysene (DBC) crystals using time-dependent DFT. The fromage/ Overdia interface was employed to compute the couplings of local excitations and CT states for 18 unique DBC dimers in the crystal and to quantify the influence of electrostatic embedding, which was found to be modest (10−20%). Simulations on π-stacked dimers reproduced the small red shift observed experimentally from solution to crystal, attributed to electronic interactions among fixed monomers rather than crystal electrostatics. Quantum dynamics simulations revealed ultrafast population transfer from bright local excitations to CT states. This approach establishes a robust framework linking molecular and solid-state excited-state dynamics, with potential applications for studying excitations, defects, and impurities in molecular crystals.

Crystals↗
DOE OSTI2022

Electrostatic Asymmetry of Wurtzite Nanocrystals and Resulting Photocatalytic Properties

Efficient light absorption and high energy of charge carriers of zinc cadmium sulfide (ZCS) make this semiconductor attractive for many photocatalytic reactions. Despite marked successes in shape-controlled synthesis of ZCS central to their photocatalytic performance, recombination of charge carriers as they migrate through the nanoscale particles results in losses of excitation energy, markedly reducing the photocatalytic activity of ZCS and other heterogeneous photocatalysts. Here, in this study, we show that the electrostatic asymmetry of nanostructures, previously discovered for nearly spherical nanoparticles, also manifests in wurtzite ZCS with planar geometry. The electrostatic asymmetry assists charge separation and substantially increases the yield of photocatalytic reactions in monocrystalline ZCS. The synthesized ZCS nanorods and nanoplates with identical chemical composition were found to have markedly different photocatalytic activity for evolution of hydrogen in water. Despite much smaller specific surface areas, the ~500 nm wide nanoplates displayed a hydrogen evolution rate 12 times higher than the ~35 nm long nanorods, also outperforming other ZCS photocatalysts. Experimental and computational data indicate that the homo- and heterojunction-free ZCS nanoplates with continuous wurtzite lattice behave essentially as nanoscale dipoles with intrinsic dipole moment as high as 48.39 D per unit cell. Electric-field-directed migration of charge carriers stimulates their localization on opposite parts of the nanoplates. Direct imaging of the intraparticle electrical field using off-axis electron holography confirmed their electrostatic asymmetry. Polarization-enhanced charge separation provides a new pathway to efficient and stable photocatalysts for sustainable energy technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Electrostatic Dissipation in 3D-Printable Silicone

Here, in this report, we describe the incorporation of single-walled carbon nanotubes (CNTs) into 3D printable siloxane elastomers for electrostatic dissipation. The composite was characterized, focusing on how rheological and mechanical properties of the siloxane are affected at various CNT loading levels. Electrical properties were also characterized to develop materials with effective electrostatic dissipation. We demonstrate that low loadings (<1 wt %) of CNTs can be sufficiently dispersed into silicone resins that can be 3D printed, and the resulting material shows a significant improvement in electrostatic dissipation through the reduction in electrical resistivity with minimal effect on its mechanical properties.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Accelerated steady-state electrostatic particle-in-cell simulation of Langmuir probes

First-principles particle-in-cell (PIC) simulation is a powerful tool for understanding plasma behavior, but this power often comes at great computational expense. Artificially reducing the ion/electron mass ratio is a time-honored practice to reduce simulation costs. Usually, this is a severe approximation. However, for steady-state collisionless, electrostatic (Vlasov–Poisson) systems, the solution with reduced mass ratio can be scaled to the solution for the real mass ratio, with no approximation. This “scaled mass” method, which works with already-existing PIC codes, can reduce the computation time for a large class of electrostatic PIC simulations by the square root of the mass ratio. The particle distributions of the resulting steady state must be trivially rescaled to yield the true distributions, but the self-consistent electrostatic field is independent of the mass ratio. This method is equivalent to “numerical timestepping,” an approach that evolves electron and ion populations with different time steps. Numerical timestepping can be viewed as a special case of the speed-limited PIC (SLPIC) method, which is not restricted to steady-state phenomena. Although the scaled-mass approach is simplest, numerical timestepping and SLPIC more easily generalize to include other effects, such as collisions. The equivalence of these new approaches is demonstrated by applying them to simulate a cylindrical Langmuir probe in electron–argon plasma, speeding up simulation by two orders of magnitude. Methods such as SLPIC can therefore play an invaluable role in interpreting probe measurements by including geometric effects, collisions, secondary emission, and non-Maxwellian distributions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A deep potential model with long-range electrostatic interactions

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make molecular simulations with the accuracy of quantum mechanical density functional theory possible at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation, we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei + core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the DP long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples: the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗