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DOE OSTI2024

Frequency Nadir Constrained Unit Commitment for High Renewable Penetration Island Power Systems

The process of energy decarbonization in island power systems is accelerated due to the swift integration of inverter-based renewable energy resources (IBRs). The unique features of such systems, including rapid frequency changes resulting from potential generation outages or imbalances due to the unpredictability of renewable power, pose a significant challenge in maintaining the frequency nadir without external support. This paper presents a unit commitment (UC) model with data-driven frequency nadir constraints, including either frequency nadir or minimum inertia requirements, helping to limit frequency deviations after significant generator outages. The constraints are formulated using a linear regression model that takes advantage of real-world, year-long generation scheduling and dynamic simulation data. The efficacy of the proposed UC model is verified through a year-long simulation in an actual island power system using historical weather data. The alternative minimum inertia constraint, derived from actual system operation assumptions, is also evaluated. Findings demonstrate that the proposed frequency nadir constraint notably improves the system's frequency nadir under high photovoltaic (PV) penetration levels, albeit with a slight increase in generation costs, when compared to the alternative minimum inertia constraint.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Frequency Response Improvement in a Standalone Small Hydropower Plant Using Battery Storage

This paper proposes a control architecture for frequency, current, and voltage control that facilitates using battery storage to improve the response of standalone small hydropower plants. The frequency controller uses rate-of-change of frequency and frequency-Watt-based generations to produce active power commands. The distinctive feature of the controller design is that it nicely integrates response to frequency change with constraints on frequency and state of battery to enable power injections. The current and voltage control scheme allows incorporating the frequency controller. The distinctive feature of this controller is that it incorporates a bounded integral control strategy that guarantees stability. Results on the stability of the hydropower plant with proposed scheme are presented and robust ways to choose the controller gains are investigated via root locus analysis. In conclusion, simulations performed show that: the hydropower plant response is significantly improved with battery storage using the proposed scheme; the load carrying capability of the hydropower plant is significantly improved with battery storage; the proposed scheme has the capability to recharge the battery; and the proposed control scheme gives improved performance.

13 HYDRO ENERGY↗

DOE OSTI2018

Analytic Analysis for Dynamic System Frequency in Power Systems Under Uncertain Variability

In this paper, a new systematic method is proposed to analyze the system frequency in power systems under uncertain variability (UV). UV gradually increases in power systems, which originates from the renewable energy generation, random loads, frequency measurement, and communication channels, exerting noteworthy impacts on dynamic system frequency. The UV is modeled as a stochastic process in this paper. Then, the stochastic differential equations are used to describe the dynamic system frequency response (SFR) of a power system under UV, which is based on the SFR model. To assess system frequency dynamics under UV, an index of intra-range probability is put forward. Based on stochastic analysis theory, an analytic method is proposed to analyze the system frequency under UV, by which the intra-range probability can be analytically solved. Compared with Monte Carlo simulation in a typical SFR case and the Iceland electricity transmission network, the proposed method shows almost the same results using much less computation resource. Finally, insights for improving the SFR under UV are provided. The proposed method can be used to quickly verify whether the system frequency could withstand the UV and stay in the security range.

42 ENGINEERING↗

DOE OSTI2026

Analytical Models of Frequency and Voltage in Large-Scale All-Inverter Power Systems

Low-order frequency response models for power systems have a decades-long history in optimization and control problems such as unit commitment, economic dispatch, and wide-area control. With a few exceptions, these models are built upon the Newtonian mechanics of synchronous generators, assuming that the frequency dynamics across a system are approximately homogeneous, and assume the dynamics of nodal voltages for most operating conditions are negligible, and thus are not directly computed at all buses. As a result, the use of system frequency models results in the systematic underestimation of frequency minimum nadir and maximum RoCoF, and provides no insight into the reactive power-voltage dynamics. This paper proposes a low-order model of both frequency and voltage response in grid-forming inverter-dominated power systems. The proposed model accounts for spatial-temporal variations in frequency and voltage behavior across a system and as a result, demonstrates the heterogeneity of frequency response in future renewable power systems. Electromagnetic transient (EMT) simulations are used to validate the utility, accuracy, and computational efficiency of these models, setting the basis for them to serve as fast, scalable alternatives to EMT simulation, especially when dealing with very large-scale systems, for both planning and operational studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Frequency-Nadir-Constrained Unit Commitment for Low-Inertia, High-IBR Island Power Systems [Slides]

14 SOLAR ENERGY↗

DOE OSTI2016

FREQUENCY-DEPENDENT DISPERSION MEASURES AND IMPLICATIONS FOR PULSAR TIMING

The dispersion measure (DM), the column density of free electrons to a pulsar, is shown to be frequency dependent because of multipath scattering from small-scale electron-density fluctuations. DMs vary between propagation paths whose transverse extent varies strongly with frequency, yielding arrival times that deviate from the high-frequency scaling expected for a cold, uniform, unmagnetized plasma (1/frequency{sup 2}). Scaling laws for thin phase screens are verified with simulations; extended media are also analyzed. The rms DM difference across an octave band near 1.5 GHz is ∼ 4 × 10{sup −5} pc cm{sup −3} for pulsars at ∼1 kpc distance. The corresponding arrival-time variations are a few to hundreds of nanoseconds for DM ≲ 30 pc cm{sup −3} but increase rapidly to microseconds or more for larger DMs and wider frequency ranges. Chromatic DMs introduce correlated noise into timing residuals with a power spectrum of “low pass” form. The correlation time is roughly the geometric mean of the refraction times for the highest and lowest radio frequencies used, ranging from days to years, depending on the pulsar. We discuss implications for methodologies that use large frequency separations or wide bandwidth receivers for timing measurements. Chromatic DMs are partially mitigable by including an additional chromatic term in arrival time models. Without mitigation, an additional term in the noise model for pulsar timing is implied. In combination with measurement errors from radiometer noise, an arbitrarily large increase in total frequency range (or bandwidth) will yield diminishing benefits and may be detrimental to overall timing precision.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

The Frequency-dependent Damping of Slow Magnetoacoustic Waves in a Sunspot Umbral Atmosphere

High spatial and temporal resolution images of a sunspot, obtained simultaneously in multiple optical and UV wavelengths, are employed to study the propagation and damping characteristics of slow magnetoacoustic waves up to transition region heights. Power spectra are generated from intensity oscillations in sunspot umbra, across multiple atmospheric heights, for frequencies up to a few hundred mHz. It is observed that the power spectra display a power-law dependence over the entire frequency range, with a significant enhancement around 5.5 mHz found for the chromospheric channels. The phase difference spectra reveal a cutoff frequency near 3 mHz, up to which the oscillations are evanescent, while those with higher frequencies propagate upward. The power-law index appears to increase with atmospheric height. Also, shorter damping lengths are observed for oscillations with higher frequencies suggesting frequency-dependent damping. Using the relative amplitudes of the 5.5 mHz (3 minute) oscillations, we estimate the energy flux at different heights, which seems to decay gradually from the photosphere, in agreement with recent numerical simulations. Furthermore, a comparison of power spectra across the umbral radius highlights an enhancement of high-frequency waves near the umbral center, which does not seem to be related to magnetic field inclination angle effects.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2015

An Initial Assessment of the Surface Reference Technique Applied to Data from the Dual-Frequency Precipitation Radar (DPR) on the GPM Satellite

It has long been recognized that path-integrated attenuation (PIA) can be used to improve precipitation estimates from high-frequency weather radar data. One approach that provides an estimate of this quantity from airborne or spaceborne radar data is the surface reference technique (SRT), which uses measurements of the surface cross section in the presence and absence of precipitation. Measurements from the dual-frequency precipitation radar (DPR) on the Global Precipitation Measurement (GPM) satellite afford the first opportunity to test the method for spaceborne radar data at Ka band as well as for the Ku-band-Ka-band combination. The study begins by reviewing the basis of the single- and dual-frequency SRT. As the performance of the method is closely tied to the behavior of the normalized radar cross section (NRCS or sigma(0)) of the surface, the statistics of sigma(0) derived from DPR measurements are given as a function of incidence angle and frequency for ocean and land backgrounds over a 1-month period. Several independent estimates of the PIA, formed by means of different surface reference datasets, can be used to test the consistency of the method since, in the absence of error, the estimates should be identical. Along with theoretical considerations, the comparisons provide an initial assessment of the performance of the single- and dual-frequency SRT for the DPR. The study finds that the dual-frequency SRT can provide improvement in the accuracy of path attenuation estimates relative to the single-frequency method, particularly at Ku band.

space-borne weather radars↗

DOE OSTI2024

Frequency‐Locked Wireless Multifunctional Surface Acoustic Wave Sensors

Abstract Surface acoustic waves (SAWs) have shown great potential for developing sensors for structural health monitoring (SHM) and lab‐on‐a‐chip (LOC) applications. Existing SAW sensors mainly rely on measuring the frequency shifts of high‐frequency (e.g., >0.1 GHz) resonance peaks. This study presents frequency‐locked wireless multifunctional SAW sensors that enable multiple wireless sensing functions, including strain sensing, temperature measurement, water presence detection, and vibration sensing. These sensors leverage SAW resonators on piezoelectric chips, inductive coupling‐based wireless power transmission, and, particularly, a frequency‐locked wireless sensing mechanism that works at low frequencies (e.g., <0.1 GHz). This mechanism locks the input frequency on the slope of a sensor's reflection spectrum and monitors the reflection signal's amplitude change induced by the changes of sensing parameters. The proof‐of‐concept experiments show that these wireless sensors can operate in a low‐power active mode for on‐demand wireless strain measurement, temperature sensing, and water presence detection. Moreover, these sensors can operate in a power‐free passive mode for vibration sensing, with results that agree well with laser vibrometer measurements. It is anticipated that the designs and mechanisms of the frequency‐locked wireless SAW sensors will inspire researchers to develop future wireless multifunctional sensors for SHM and LOC applications.

Bo, Luyu↗

DOE OSTI2025

Injection Locking of Gigahertz‐Frequency Surface Acoustic Wave Phononic Crystal Oscillator

Low-noise gigahertz (GHz) frequency sources are essential for applications in signal processing, sensing, and telecommunications. Surface acoustic wave (SAW) resonator-based oscillators offer compact form factors and low-phase noise due to their short mechanical wavelengths and high-quality (Q) factors. However, their small footprint makes them vulnerable to environmental variation, resulting in their poor long-term frequency stability. Injection locking is widely used to suppress frequency drift of lasers and oscillators by synchronizing to an ultra-stable reference. Here, injection locking of a 1-GHz SAW phononic-crystal oscillator is demonstrated, achieving 40-dB phase noise reduction at low offset frequencies and unperturbed low noise at large offset frequencies. Compared to a free-running SAW oscillator, which typically exhibits frequency drifts of several hundred hertz over minutes, the injection-locked oscillator reduces the frequency deviation to below 0.35 Hz. The locking range and oscillator dynamics is also investigated in the injection pulling region. The demonstrated injection-locked SAW oscillator could find applications in high-performance portable telecommunications and sensing systems.

injection locking↗

DOE OSTI2019

Simultaneous photonic generation of multiple chirp and unchirp microwave waveform with frequency multiplying capability for optical beam forming system

A photonic technique based on the Mach–Zehnder Modulator and the dual parallel Mach–Zehnder modulator is proposed for the simultaneous generation of multiple chirp and unchirp microwave waveform with frequency multiplying capability for efficient beam steering applications. There is provision to obtain a single chirp signal of a particular center frequency and chirp rate from a multiple chirp signal without any alternation in the experimental setup. In the proposed methodology, the PIN photodetector is used for the detection of 12 GHz unchirp microwave waveform showing the frequency doubling characteristics and the balance photodetector is used for the detection of multiple chirp signal with frequency components 6, 12, and 18 GHz. The same experimental setup is used to generate dual linear chirp microwave signal of 12 GHz center frequency. This can be achieved by adjusting the bias voltage of the phase modulator. Time bandwidth product and bandwidth of the signal are 18.33 and 410 MHz, respectively. This technique is tunable in frequency, but the generation of higher frequency microwave signals is limited by the speed and bandwidth of the Mach–Zehnder Modulator and photodetector. The novelty of our proposed scheme is that we are going to drive MZM by chirp RF signal to multiply the chirp rate in manifold. To the best of our knowledge the effect of chirp microwave signal on photonic highly steerable beam forming system has not yet been studied experimentally in past, which we are targeting under this paper. It is expected that the range of beam steering performance should be improved substantially as compared to previously reported results.

42 ENGINEERING↗

DOE OSTI2018

The Effect of Loading Frequency on Fatigue Life of Green onyx under Fully Reversed Loading

Rock structures, in reality, may be subjected to reversed tension-compression loading conditions due to blasting, earthquake, and traffic or injection-recovery process. In this case, loading frequency may have a great influence on fatigue life and behavior of rocks. The effect of loading frequency on fatigue life of a crystalline rock sample under fully reversed loading condition was examined. A new apparatus, based on the R. R. Moore fatigue test machine, was used to assess the fully reversed loading condition. The experimental tests were conducted with five sets of loading frequency and five levels of stress based on the ultimate tensile strength of samples. The test results showed that the variation of ultimate fatigue stress versus loading cycle number (S-N curve) of crystalline rock samples were in accordance with the observed results in other materials such as metals and ceramics. The results showed that fatigue life of a component is positively correlated with the frequency level. The fatigue life improves with increasing the loading frequency, but the improvement was more tangible at lower stress levels than at higher stress levels. The effect of loading frequency in an ordinary S-N equation was also formulated. The results also showed that the loading frequency does not influence the fatigue limit.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Joint scheduling of energy, fast and primary frequency response reserves in integrated transmission–distribution networks

Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.

Noh, Seung-Gil↗

DOE OSTI2017

The role of frequency on fretting corrosion of Alloy 690TT against 304 stainless steel in high temperature high pressure water

Highlights: • Delamination, material transfer and oxidation dominated fretting corrosion behavior in HTHP water. • Delamination was pure mechanical wear to produce fresh surface exposed to HTHP water for oxidation. • Increased frequency enhanced the maximum thickness of oxide film in worn surface. • Increased frequency accelerated the formation of tribologically transformed structure (TTS). • Increased frequency accelerated the escape of wear debris, which originated from the TTS and crushed oxide particles. - Abstract: In high temperature high pressure (HTHP) water, the role of frequency in fretting corrosion behavior and mechanism of Alloy 690TT against Type 304 stainless steel were investigated. Results indicated that wear mechanisms of delamination, material transfer and oxidation collectively dominated the fretting corrosion behavior. The delamination was related to pure mechanical wear to produce fresh surface exposed to HTHP water for oxidation, resulting in the increase of wear depth and volume. The increasing frequency played little role in oxide type of worn surfaces, which consisted of (Ni,Fe)(Fe,Cr){sub 2}O{sub 4} and Cr{sub 2}O{sub 3}. However, it enhanced the maximum thickness of oxide film in the worn surface. The increasing frequency resulted in the acceleration of the formation of nanostructured tribologically transformed structure (TTS) layer because it could aggravate the plastic deformation and increase the contact temperature for dynamic recrystallization. The increasing frequency accelerated the escape of the ultra-fine grained wear debris, which originated from not only the damage of TTS layer but also the crushed oxide particles generated in the contact gap.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Future Intensity‐Duration‐Frequency Curves of Extreme Precipitation in the Midwest United States From Convection‐Permitting Modeling

Abstract During the last four decades, global warming has statistically significant intensified extreme precipitation events in the Midwestern United States (defined here as the region covering Illinois, Indiana, Ohio, and Kentucky), leading to increased risks to human life, property, and infrastructure. To enable climate change adaptation and resilience across various economic and social sectors in this region, updated information about future climate changes, specifically at finer spatial scales, is essential. Leveraging a new 150‐year dynamical downscaling data set at convection‐permitting resolution, this study introduces a framework to construct the projected future intensity‐duration‐frequency (IDF) curves of heavy precipitation, which are prominent tools for infrastructure design and water resources management. This framework generates IDF curves at both sub‐daily and multi‐day duration utilizing hourly in situ observations as well as quantile‐based statistical techniques in bias‐correction and return levels selection. The assumption of non‐stationarity in the distribution parameter fitting process is also implemented in this workflow. Compared to historical IDF curves for 1980–2022, future projected IDF curves for 2058–2100 under Representative Concentration Pathway (RCP) 4.5 and RCP 8.5 scenarios indicate an average intensity increase of approximately 15% and 25%, respectively, across 74 stations, considering both annual and seasonal timescales. Future projections suggest that extreme precipitation events may become more severe across six investigated return periods, with longer return periods showing a greater increase. The frequency of future extreme precipitation events in the Midwest region is also projected to double. Furthermore, current results reveal spatial heterogeneity of future trends across stations owing to the high‐resolution input data set. Plain Language Summary This study investigates the evolving nature of extreme precipitation events in the Midwestern United States under a changing climate. By leveraging a high‐resolution dynamical downscaling data set, we construct projected intensity‐duration‐frequency (IDF) curves for future extreme rainfall events. These curves serve as vital tools for infrastructure planning and water resource management. Our analysis reveals a significant increase in both the intensity and frequency of extreme precipitation events in the region. Future projected IDF curves for the late century indicate an average intensity increase of approximately 15%–25% compared to historical values. Moreover, the frequency of such events is expected to double. Spatial heterogeneity in future trends is observed across different stations within the Midwest, highlighting the importance of high‐resolution modeling in capturing localized climate variability. These findings underscore the urgent need for climate adaptation strategies to mitigate the increasing risks associated with extreme precipitation events in the region. Key Points This study introduces a workflow to construct future intensity‐duration‐frequency (IDF) curves over the Midwest United States using a new convection‐permitting modeling data set The current IDF construction workflow reproduces well the historical observed IDF 30 curves in summer months with median relative errors of 2.4% among 74 stations and 6 investigated durations The projected IDF curves show diverse future trends of extreme precipitation across stations, with intensity increases of approximately 15% and 25% under RCP4.5 and RCP8.5 climate scenarios, respectively, and a doubling of frequency on average

Nguyen, Trung↗

DOE OSTI2024

Decoupling excitons from high-frequency vibrations in organic molecules

The coupling of excitons in π-conjugated molecules to high-frequency vibrational modes, particularly carbon–carbon stretch modes (1,000–1,600 cm -1 ) has been thought to be unavoidable. These high-frequency modes accelerate non-radiative losses and limit the performance of light-emitting diodes, fluorescent biomarkers and photovoltaic devices. Here, by combining broadband impulsive vibrational spectroscopy, first-principles modelling and synthetic chemistry, we explore exciton–vibration coupling in a range of π-conjugated molecules. We uncover two design rules that decouple excitons from high-frequency vibrations. First, when the exciton wavefunction has a substantial charge-transfer character with spatially disjoint electron and hole densities, we find that high-frequency modes can be localized to either the donor or acceptor moiety, so that they do not significantly perturb the exciton energy or its spatial distribution. Second, it is possible to select materials such that the participating molecular orbitals have a symmetry-imposed non-bonding character and are, thus, decoupled from the high-frequency vibrational modes that modulate the π-bond order. We exemplify both these design rules by creating a series of spin radical systems that have very efficient near-infrared emission (680–800 nm) from charge-transfer excitons. We show that these systems have substantial coupling to vibrational modes only below 250 cm -1 , frequencies that are too low to allow fast non-radiative decay. This enables non-radiative decay rates to be suppressed by nearly two orders of magnitude in comparison to π-conjugated molecules with similar bandgaps. Our results show that losses due to coupling to high-frequency modes need not be a fundamental property of these systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2013

Optimal geometries and harmonic vibrational frequencies of the global minima of water clusters (H2O)n, n = 2–6, and several hexamer local minima at the CCSD(T) level of theory

We report the first optimum geometries and harmonic vibrational frequencies for the ring pentamer and several water hexamer (prism, cage, cyclic and two book) at the CCSD(T)/aug-cc-pVDZ level of theory. All five hexamer isomer minima previously reported by MP2 are also minima on the CCSD(T) potential energy surface (PES). In addition, all CCSD(T) minimum energy structures for the n=2-6 cluster isomers are quite close to the ones previously obtained by MP2 on the respective PESs, as confirmed by a modified Procrustes analysis that quantifies the difference between any two cluster geometries. The CCSD(T) results confirm the cooperative effect of the homodromic ring networks (systematic contraction of the nearest-neighbor (nn) intermolecular separations with cluster size) previously reported by MP2, albeit with O-O distances shorter by ~0.02 Å, indicating that MP2 overcorrects this effect. The harmonic frequencies at the minimum geometries were obtained by the double differentiation of the CCSD(T) energy using an efficient scheme based on internal coordinates that reduces the number of required single point energy evaluations by ~15% when compared to the corresponding double differentiation using Cartesian coordinates. Negligible differences between MP2 and CCSD(T) are found for the librational modes, while uniform increases of ~15 and ~25 cm -1 are observed for the bending and “free” OH harmonic frequencies. The largest differences between MP2 and CCSD(T) are observed for the harmonic hydrogen bonded frequencies. The CCSD(T) red shifts from the monomer frequencies (Δω) are smaller than the MP2 ones, due to the fact that the former produces shorter elongations (ΔR) of the respective hydrogen bonded OH lengths from the monomer value with respect to the latter. Both the MP2 and CCSD(T) results for the hydrogen bonded frequencies were found to closely follow the relation - Δω = s · ΔR, with a rate of s = 20.3 cm -1 / 0.001 Å. The CCSD(T) harmonic frequencies, when corrected using the MP2 anharmonicities obtained from second order vibrational perturbation theory (VPT2), produce anharmonicCCSD(T) estimates that are within < 60 cm -1 from the measured infrared (IR) active bands of the n=2-6 clusters and furthermore trace the observed red shifts with respect to the monomer (Δν) quite accurately. The energetic order between the various hexamer isomers on the PES (prism has the lowest energy) previously reported at MP2 was found to be preserved at the CCSD(T) level, whereas the inclusion of anharmonic corrections further stabilizes the cage among the hexamer isomers.

Miliordos, Evangelos↗

DOE OSTI2014

The effect of classical and quantum dynamics on vibrational frequency shifts of H{sub 2} in clathrate hydrates

Vibrational frequency shifts of H{sub 2} in clathrate hydrates are important to understand the properties and elucidate details of the clathrate structure. Experimental spectra of H{sub 2} in clathrate hydrates have been measured for different clathrate compositions, temperatures, and pressures. In order to establish reliable relationships between the clathrate structure, dynamics, and observed frequencies, calculations of vibrational frequency shifts in different clathrate environments are required. In this study, a combination of classical molecular dynamics simulations, electronic structure calculations, and quantum dynamical simulation is used to calculate relative vibrational frequencies of H{sub 2} in clathrate hydrates. This approach allows us to assess dynamical effects and simulate the change of vibrational frequencies with temperature and pressure. The frequency distributions of the H{sub 2} vibrations in the different clathrate cage types agree favorably with experiment. Also, the simulations demonstrate that H{sub 2} in the 5{sup 12} cage is more sensitive to the details of the environment and to quantum dynamical effects, in particular when the cage is doubly occupied. We show that for the 5{sup 12} cage quantum effects lead to frequency increases and double occupation is unlikely. This is different for the 5{sup 12}6{sup 4} cages for which higher occupation numbers than one H{sub 2} per cage are likely.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗