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At least 505 records · Page 28

High-dimensional Data-driven Energy optimization for Multi-Modal Transit Agencies (HD-EMMA) (Final Technical Report)

Public bus transit services in the U.S. are responsible for at least 19.7 million metric tons of CO 2 emission annually. Electric vehicles (EVs) can have a much lower environmental impact than comparable internal combustion engine vehicles (ICEVs), especially in urban areas. Unfortunately, EVs are also much more expensive than ICEVs. As a result, many public transit agencies can afford only mixed fleets of transit vehicles, consisting of EVs, hybrids (HEVs), and ICEVs. Transit agencies that operate such mixed fleets of vehicles face a challenging optimization problem: these agencies need to decide which vehicles are assigned to serving which transit trips. Since the advantage of EVs over ICEVs varies depending on the route and time of day (e.g., the benefit of EVs is higher in slower traffic with frequent stops and lower on highways), the assignment can have a significant effect on energy use and, hence, environmental impact. Through this project, we have developed reference data about energy collections and constructed a set of machine learning models that can accurately predict the energy consumption for the whole fleet at the level of each trip. We have used these models to develop a scheduling and assignment strategy that can rotate the different vehicle types across the transit agencies’ routes. The optimization algorithm ensures that the vehicles are matched to trips considering weather patterns, expected congestion, and road gradients to minimize the overall energy usage. We list the key observations from our project for other practitioners below. Details are available in the report, and the list of source code and our publications are included in the appendix. 1. We have demonstrated the feasibility of collecting, merging and analyzing large volumes of high-resolution real-world telemetry data from a mixed vehicle fleet. To mitigate the inherent noise of the recorded GPS points, the team developed an algorithm that filters data and maps the points onto a street. The algorithm considers previous and subsequent location measurements and different characteristics of nearby streets to determine how likely the vehicle travels on them. Then, the team segmented the time series into disjoint contiguous samples based on adjacent road segments and repeated the outlier detection and removal. For each data point, the team added features corresponding to elevation changes within the samples, weather features, such as temperature, and traffic data, such as speed ratio between actual speed and free-flow speed. 2. We have developed two forms of machine learning models that be used to understand and analyze the energy operations of a mixed vehicle transit fleet. The micro prediction model provides estimates of instantaneous energy prediction for all types of buses (diesel, hybrid, and electric). Such a model is important in evaluating the energy impacts of real-time bus operation strategies, but it is challenging due to diversified driving cycles of transit buses. The model can help the drivers understand the impact of their driving behaviors and short-term congestions. The macro prediction models estimate average energy consumption across the whole trip considering the features: distance traveled, various road-type features, elevation change, day of the week, time of day, various weather features (temperature, humidity, etc.), and traffic features (speed ratio and jam factor). 3. We have demonstrated that it is possible to transfer the machine learning models we have developed in this project to other teams and cities by using inductive transfer learning. We also showed that the performance of the macro energy prediction models can be improved using a multi-task learning approach where the learning parameters are shared between the models being developed for different vehicle types. The advantage of this approach is improved learning performance as the models can exploit common spatio-temporal and environmental characteristics. 4. Finally, we have developed trip and vehicle assignment and scheduling algorithms that use the energy prediction models and develop a trip to vehicle type (diesel, electric, hybrid) assignment for the whole operation to reduce overall emissions and cost. We have shown through simulations that the proposed algorithms can save $\$$ 48,910 in energy costs and 175 metric tons of CO 2 emission annually for CARTA.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

94 GHz microplasma sustained by a photonic crystal

A photonic crystal (PhC) with a single vacancy sustains an argon microplasma at 94 GHz. The PhC consists of a 7 × 13 array of small alumina rods, each 250 μm in radius. The PhC has a forbidden bandgap from 70–105 GHz. The vacancy creates an internal electromagnetic resonance at 94 GHz that intensifies the electric field of an incident wave to 5 × 10 5 V m –1 . Breakdown of low-pressure argon gas (80 mbar) occurs and forms a stable, ellipsoidal plasma inside the crystal. The central core of the microplasma is probed using a 200 μm optical fiber inserted into the PhC. The rotational temperature of the CH molecule is estimated from a numerical fit of the plasma emission and is found to increase from 450–650 K with both pressure (200–1000 mbar) and incident wave power (100 mW–1100 mW). Under these conditions, the electron density increases with both power and pressure from 0.5–1.5 × 10 20 m –3 . Furthermore, this plasma density range brackets the electron plasma frequency at 94 GHz. The results are compared with a similar microplasma operating at 44 GHz.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Computer Vision Techniques Used to Monitor the Alignment of Cavities and Solenoids in the PIP-II Prototype SSR1 Cryomodule

The alignment of the SRF PIP-II string components is studied as the acceptable beam deflection, offset and defocusing, which may otherwise cause beam loss. Simulations and measurements established that the maximum deviation of the beam pipe from the reference orbit should not exceed a small fraction of the beam aperture. To observe the translations and rotations of each single component within the cryomodule, optical instruments (H-BCAM) surveying highly reflective targets, installed in the internal assembly of the module were used. The alignment monitoring concept for the PIP II SSR1 prototype cryomodule, along with relevant measurements of the components’ position monitoring during coldmass cooldown is presented in this contribution. This development paves the way to new computer vision applications in the field of cryomodule assemblies in cleanroom environment, in which robotically-assisted operations have the potential to dramatically reduce the risk of chemical and particulate contamination.

43 PARTICLE ACCELERATORS↗

Influence on Structural Loading of a Wave Energy Converter by Controlling Variable-Geometry Components and the Power Take-Off: Preprint

Oceans are a harsh environment and can impose significant loads on deployed structures. Deployment of wave energy converters (WECs) faces a design challenge with apparently contradictory goals. A WEC should be designed to maximize the energy absorbed while ensuring the operating wave condition does not exceed the failure limits of the device itself. Therefore, the loads endured by the support structure are a design constraint for the system. Adaptability to different sea states is, therefore, highly desirable. This work uses a WEC-Sim model of a Variable Geometry Oscillating Wave Energy Converter (VGOSWEC) mounted on a support structure simulated under different wave scenarios. A VGOSWEC resembles a paddle pitching about a fixed hinge perpendicular to the incoming waves-fronts. Therefore, the hinge experiences loads perpendicular to its axis as it maintains its position. The geometry of the VGOSWEC was varied by opening a series of controllable flaps on the pitching paddle when the structure experiences threshold loads. Since opening the flaps lets the waves transmit through the paddle, it is hypothesized that opening the flaps should result in load shedding at the base of the support structure. This load shedding is achieved by reducing the moments about the hinge axis. This work compares the hydrodynamic coefficients, natural periods, and Response Amplitude Operators (RAOs) from completely closed to completely open configurations of the controllable flaps. These comparisons quantify the effects of letting the waves transmit through the VGOSWEC. This work shows that the completely open configuration can reduce the pitch and surge loads on the base of the support structure by as much as 80%. It was observed that at the paddle's resonance frequency, the loads on the structure increased substantially. This increase in loads can be mitigated by a rotational Power Take-off (PTO) damping about the hinge axis. Changing the rotational PTO damping was identified as an additional design parameter that can be used to control the loads experienced by the WEC's support structure.

fixed and floating structures↗

AnisONet: A deep neural operator-based anisotropic permeability upscaler from pore to Darcy scale

Directional permeability variations, which govern directional fluid flow in porous media with anisotropy, are important to accurately predict flow behavior, reactive transport, and fluid–solid interactions for various processes such as enhanced geothermal systems, energy storage devices, and biological systems. However, the intricate architecture of porous media makes it difficult to predict directional permeabilities. In this work, we present a novel machine learning (ML) framework, AnisONet, built upon an integration of a convolutional neural network, Swin transformer, and the deep operator network architecture, designed to predict anisotropic permeability and upscale predictions to larger spatial domains. First, AnisONet was evaluated with three classes of two-dimensional (2D) porous media, including synthetic circular and elliptical grains and natural sandstone grains from micro-computed tomography images. A lattice Boltzmann model (LBM) was used to calculate directional permeabilities at every 10° angle, producing 19 data points per image of porous media. AnisONet is then trained to predict permeability as a function of rotation angle. AnisONet showed strong predictive capability of directional permeability. Second, we tested our model for five upscaling cases with a large image size in the finite-element method (FEM) for 2D Darcy flow with various permeability tensor construction methods. Overall, upscaled permeability tensors in FEM simulations produce a reasonably good match with LBM results, highlighting the importance of selecting appropriate tensor formation strategies for accurate permeability upscaling. AnisONet, as a directional permeability estimator, could be further developed for more complex geometries, with the potential to develop a foundational ML model for various applications in porous media.

42 ENGINEERING↗

Performance evaluation of a Terry GS-2 steam impulse turbine with air-water mixtures

Terry steam turbines are widely used in various industries because of their robust design. Within the nuclear power generation industry, they are used in the Reactor Core Isolation Cooling System to remove decay heat during reactor isolation events. During the Fukushima Daiichi nuclear power station disaster in Japan in 2011, the Reactor Core Isolation Cooling System and associated Terry turbine operated for over 70 hours in Unit 2; this runtime is well beyond the expected operating duration. Theories suggest the turbine was subjected to a two-phase inlet flow, which could degrade the turbine performance. In this work, an experimental test rig was constructed to test a full-scale Terry model GS-2 steam turbine under two-phase air/water flows. Steady-state efficiency and torque performance maps of the turbine were developed over a range of turbine inlet pressures (1.38–4.83 bar or 20–70 psia), air mass fractions (0.05–1.0) and rotational speeds up to 4000 RPM. Furthermore, turbine performance followed expected trends with torque varying linearly and efficiency varying quadratically with rotational speed. In addition, high-speed images of the two-phase flow entering the turbine were also analyzed to understand how changes in inlet pressure and air mass fraction affect the flow regime and homogenization. The present tests with air–water two-phase mixtures are an important step towards providing an understanding of the full-scale Terry turbine’s behavior and performance curves under two-phase conditions. The results of this work will be combined with air/water and steam/water data gathered using a small-scale Terry ZS-1 steam turbine in order to understand the scaling relationship between large and small size Terry turbines and fluid pairs. The combined data set will enable further development of analytical models over a wide range of conditions and may be used to provide technical justification for expanded use of the Terry turbines in nuclear power plant safety systems and other systems.

42 ENGINEERING↗

Comparison of three DWM-based wake models at above-rated wind speeds

In this study we investigate three mid-fidelity wind turbine wake models based on the dynamic wake meandering (DWM) model principle, and compare their performance with a reference dataset, produced with large-eddy simulations using the actuator line model. The models are compared with respect to flow field, power, and loads on a row of four 5MW reference turbines experiencing above-rated wind conditions. In general, the DWM models show fairly good agreement with large-eddy simulation for the time-averaged flow fields, blade forces and power, with increasing differences along the turbine row. Also when comparing fatigue loads of blade root moments, the differences between the models increase further into the row, with deviations up to 25 % of the reference case. However, while the development in blade root moment fatigue along the turbine row is predominantly driven by the energy content at the frequency corresponding to the turbine's rotational period (1 P ) for the DWM models, the large-eddy simulation results suggest that the key drivers for the blade root and tower loads are the increase in meandering and energy at higher frequencies (> 1 P ) deeper into the turbine row. For the tower loads, the DWM models highly underestimate the fatigue for the waked turbines. From these results, we suggest priorities for future model developments so that robust model implementations can be used in wind farm design and operation.

17 WIND ENERGY↗

Specification of EBR-II Contact Profilometry Data

All contact profilometry data stored in FIPD was originally measured using the HFEF vertical contact profilometer, which was an electronic gauge to measure the diameter profile of an element or capsule continuously over the region of interest. The element could be rotated as it passed through the probes if the wire wrap was not to be removed and the element could be returned to reactor for further irradiation. If the wire wrap was removed, the element could be drawn vertically through the probes, rotated, and the process repeated. In this way any cladding ovality could be observed. Figure 1 shows the setup used to measure the fuel pin diameter profile. The ambient temperature during the measurement was ~21-23 ºC. The cladding temperature during the measurement is considered to be similar to the ambient temperature by assuming the fuel decay heat did not impact the cladding temperature. Two documents contain most of the important details about contact profilometry measurements. The first one is the operational manual of the contact profilometer (title: Element contact profilometer operation and maintenance, HFEF/N OMM 4326, DOC. NO. W0202-0007-SA-01). This manual provides: (1) description of the contact profilometer including the functions of each component (support stage, sensing head, control system, and calibration standards, etc.); (2) step-by-step guidance on calibrations, operations, and measurements; and (3) maintenance procedures and other details of the contact profilometer. The second document is a publicly accessible report entitled “A Fuel-element Profilometer for the HFEF.” This report describes the development of the contact profilometer, including the design requirements, features, and details of each component, as well as the acceptance tests for the built system. This document is important because it reports the uncertainties of the measurements with detailed deduction procedures. The reported uncertainties should apply to all hard-copy contact profilometry data in FIPD. Some key information about contact profilometry measurements was extracted from these two documents. Combining the information with other sources, a specification for interpretating the contact profilometry data in FIPD was established.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Transient Multiphysics Simulations with Pin Power Reconstruction in the Griffin Reactor Physics Code

This work introduces the pin power reconstruction capability available in the Griffin reactor physics code. This capability is implemented in an unstructured mesh framework, and the methods introduced are applied to the 2D SIMBA reactor core, which has assemblies and pins arranged in a hexagonal lattice. Since this reactor has a non-Cartesian geometry and also operates in the thermal spectrum, a general approach to pin power reconstruction is adopted, where SPH-based equivalence is leveraged to preserve assembly-wise reaction rates, while computing full-core form functions to preserve pin-wise fission production rates within the fuel pins of the reactor core. In a 2D microreactor benchmark problem, this pin power reconstruction approach was shown to reproduce pin powers compared to the Serpent2 Monte Carlo code for fixed temperature conditions and control drum rotation angles, yielding a core-wide RMS error level of 0.6\% and a maximum absolute pin error of 2.3\%. In addition, a tabulated library of multigroup cross sections, SPH factors, and form functions was generated to demonstrate the applicability of pin power reconstruction to a thermal feedback problem. Finally, a control drum transient was successfully simulated, showcasing the application of pin power reconstruction in a transient multiphysics feedback problem.

97 - MATHEMATICS AND COMPUTING↗

Quantum reactive scattering calculations for the cold and ultracold Li + LiNa → Li 2 + Na reaction

A first-principles based quantum dynamics study of the Li + LiNa(ν = 0, j = 0) → Li 2 (ν', j') + Na reaction is reported for collision energies spanning the ultracold (1 nK) to cold (1 K) regimes. A full-dimensional ab initio potential energy surface for the ground electronic state of Li 2 Na is utilized that includes an accurate treatment of the long-range interactions. The Li + LiNa reaction is barrierless and exoergic and exhibits a deep attractive potential well that supports complex formation. Thus, significant reactivity occurs even for collision temperatures approaching absolute zero. The reactive scattering calculations are based on a numerically exact time-independent quantum dynamics methodology in hyperspherical coordinates. Total and rotationally resolved rate coefficients are reported at 56 collision energies and include all contributing partial waves. Several shape resonances are observed in many of the rotationally resolved rate coefficients and a small resonance feature is also reported in the total rate coefficient near 50 mK. Furthermore, of particular interest, the angular distributions or differential cross sections are reported as a function of both the collision energy and scattering angle. Unique quantum fingerprints (bumps, channels, and ripples) are observed in the angular distributions for each product rotational state due to quantum interference and shape resonance contributions. The Li + LiNa reaction is under active experimental investigation so that these intriguing features could be verified experimentally when sufficient product state resolution becomes feasible for collision energies below 1 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Markov Chain Monte Carlo Parameter Estimation of Deflagration Losses in a Rotating Detonation Engine

One of the practical challenges of the studies of rotating detonation engines (RDEs) is the direct estimation of losses from experimental measurements. This study attempts at resolving this limitation by combining a reduced order model (ROM) of the detonation wave characteristics with a Markov chain Monte Carlo parameter estimation framework. The model considers simple deflagration losses and the overall impact of deflagration on RDE performance. To evaluate this model, a Markov Chain Monte Carlo (MCMC) sampling technique was applied to estimate the loss parameters within the model for a set of conditions operated in hydrogen-air over a range of mass flow rates and equivalence ratios. The MCMC parameter estimation framework allowed for the determination of a posterior distribution of the loss parameters for each test condition, an examination of the correlation between the loss parameters and measured performance metrics of the RDE, and an uncertainty propagation of these parameters. The predicted model loss parameters were then compared to indirect experimental measurements of the deflagration combustion fractions to evaluating the validity of the approach, and shed light on the benefits and drawbacks of the model, measurement techniques, and the estimation framework.

33 ADVANCED PROPULSION SYSTEMS↗

Overview of physics results from MAST upgrade towards core-pedestal-exhaust integration

Recent results from MAST Upgrade are presented, emphasising understanding the capabilities of this new device and deepening understanding of key physics issues for the operation of ITER and the design of future fusion power plants. The impact of MHD instabilities on fast ion confinement have been studied, including the first observation of fast ion losses correlated with Compressional and Global Alfvén Eigenmodes. High-performance plasma scenarios have been developed by tailoring the early plasma current ramp phase to avoid internal reconnection events, resulting in a more monotonic q profile with low central shear. The impact of m/n = 3/2, 2/1 and 1/1 modes on thermal plasma confinement and rotation profiles has been quantified, and scenarios optimised to avoid them have transiently reached values of normalised beta approaching 4.2. In pedestal and ELM physics, a maximum pedestal top temperature of ~350 eV has been achieved, exceeding the value achieved on MAST at similar heating power. Mitigation of type-I ELMs with n = 1 RMPs has been observed. Studies of plasma exhaust have concentrated on comparing conventional and Super-X divertor configurations, while X-point target, X-divertor and snowflake configurations have been developed and studied in parallel. In L-mode discharges, the separatrix density required to detach the outer divertors is approximately a factor 2 lower in the Super-X than the conventional configuration, in agreement with simulations. Detailed analysis of spectroscopy data from studies of the Super-X configuration reveal the importance of including plasma-molecule interactions and D 2 Fulcher band emission to properly quantify the rates of ionisation, plasma-molecule interactions and volumetric recombination processes governing divertor detachment. In H-mode with conventional and Super-X configurations, the outer divertors are attached in the former and detached in the latter with no impact on core or pedestal confinement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Performance prediction applying different reduced turbulence models to the SMART tokamak

The SMall Aspect Ratio Tokamak (SMART) is currently being commissioned at the University of Seville and will be able to compare the performance of positive and negative triangularity plasmas at low aspect ratio. Predictive simulations have been performed for different machine scenarios and heating schemes using the TRANSP code. The objectives of these simulations are to predict the parameters expected in positive triangularity plasmas, to guide diagnostic development, and to validate transport models. Several reduced turbulence models have been used to predict electron and ion temperatures for the operational phase 2. All models provide similar results from approximately mid-radius to the separatrix but important discrepancies are found in the core region. These positive triangularity results are compared with experiments from a similar size machine like GLOBUS-M2. The multi-mode model (MMM) shows the best agreement. Simulations with different boundary conditions have been performed and no strong differences have been observed between them. The impact of neutral beam injection (NBI) on the predicted profiles has also been addressed. Rotation reduces turbulence levels so higher temperatures are achieved when included in the simulations. Studying the different contributions to the thermal diffusivities, it is observed that electron temperature gradient (ETG) turbulence dominates at the plasma core while micro-tearing modes (MTM) dominate at the edge in the electron channel. In the ion channel, the neoclassical contribution is dominant at the core and at the very edge while the Weiland component, which includes ion temperature gradient mode (ITG), trapped electron mode (TEM), kinetic ballooning mode (KBM), peeling mode (PM) and collisionless and collision dominated magnetohydrodynamic (MHD) modes governs the mid-radius region. For phase 3, two plasmas with different electron densities have been studied. The case with lower density matches well a specific discharge of GLOBUS-M2. The higher density plasma shows high performance with β N ≈ 3.8.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Optimizing the HSX stellarator for microinstability by coil-current adjustments

Abstract The optimization of helically symmetric experiment (HSX) for reduced microinstability has been achieved by examining a large set of configurations within a neighborhood of the standard operating configuration. This entailed generating a database of more than 10 6 magnetic-field configurations for HSX by varying the currents in external coils. Using a set of volume-averaged metrics and gyrokinetic simulations, this database has helped to identify a set of configurations that can be used to regulate trapped-electron-mode stability in HSX. This set of configurations is also found to correlate flux-surface elongation and triangularity with an increase in magnetic-well depth, an increase in rotational transform, and low neoclassical heat-flux relative to the standard quasi-helically-symmetric configuration. These results demonstrate sensitivity of plasma behavior in response to changes in a 3D magnetic field to both neoclassical and gyrokinetic models, and the experimental potential in HSX to explore turbulence optimization. This perturbative optimization approach is not unique to HSX, and can readily be deployed on existing fusion devices to identify novel magnetic-fields to be used in turbulence-optimization experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Exploration ToolKit (ExTK)

The Exploration Toolkit (ExTK) is a reusable Extended Reality (XR) system developed for incorporating and exploring 3-Dimensional (3-D) computer aided design (CAD) models in XR, with a primary focus on Augmented Reality (AR). The ExTK consists of a Developer Mode and a User Mode. In Developer Mode, ExTK provides developers with the ability to easily import 3-D CAD models and activate desired exploration functionality and layout. Multiple models can be added to a single instantiation of the ExTK using Unity's Scene capability. Exploration functions include scaling, rotating, explode/contract, animations, hiding parts, submodules, and measurement functions. In User Mode, ExTK provides a menu system that allows users to select models and initiate exploration functions. ExTK is architected for reusability and developers can customize the ExTK layout and functions according to application needs. ExTK is designed to be hardware agnostic, although initial development focused on the Microsoft HoloLens as the primary deployment platform. The ExTK is developed using the Unity Game Engine Development Platform. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. SAND2021-1506 O

Klein, BrandonThorin↗

Exploiting Task Tolerances in Mimicry-based Telemanipulation

We explore task tolerances, i.e., allowable position or rotation inaccuracy, as an important resource to facilitate smooth and effective telemanipulation. Task tolerances provide a robot flexibility to generate smooth and feasible motions; however, in teleoperation, this flexibility may make the user’s control less direct. In this work, we implemented a telema nipulation system that allows a robot to autonomously adjust its configuration within task tolerances. We conducted a user study comparing a telemanipulation paradigm that exploits task tolerances (functional mimicry) to a paradigm that requires the robot to exactly mimic its human operator (exact mimicry), and assess how the choice in paradigm shapes user experience and task performance. Our results show that autonomous adjustments within task tolerances can lead to performance improvements without sacrificing perceived control of the robot. Additionally, we find that users perceive the robot to be more under control, predictable, fluent, and trustworthy in functional mimicry than in exact mimicry.

42 ENGINEERING↗

Mid-infrared Pulsed Upconversion Imaging in a Rotating Detonation Combustor

To meet the challenges associated with performing mid-InfraRed (IR) imaging in Rotating Detonation Combustors (RDCs), a novel pulsed mid-IR UpConversion Imaging (UCI) diagnostic has been implemented. UCI is an alternative to direct mid-IR detection that uses nonlinear optical frequency mixing to shift mid-IR wavelengths carrying a target image to shorter wavelengths that can be imaged with high-performance silicon-based CCD/CMOS cameras. This approach offers several favorable properties including high spectral selectivity, high temporal resolution, and superior low-light detectivity. A hydrogen-air research RDC was operated with carbon dioxide addition to allow pulsed UCI imaging of mid-IR luminosity within the combustion channel from spontaneous thermal emissions. The resulting measurements demonstrate high spatiotemporal resolution capable of imaging small structures near the supersonically propagating detonation wave front. The results show how this technique can be used to observe sharp gradients and millimeter-scale structures in the high-temperature, high-pressure zones RDC flow fields.

White, Logan W.↗

Diagonalizing the Born–Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom

This article describes a method for calculating higher order or nonadiabatic corrections in Born–Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner–Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ 2 , where κ = (m/M)1/4 is the usual Born–Oppenheimer parameter. The lowest order term is the usual Born–Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born–Oppenheimer theory. Here, we show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born–Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗