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At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Numerical methods for the simulation of complex multi-body flows with applications for the integrated Space Shuttle vehicle

This project forms part of the long term computational effort to simulate the time dependent flow over the integrated Space Shuttle vehicle (orbiter, solid rocket boosters (SRB's), external tank (ET), and attach hardware) during its ascent mode for various nominal and abort flight conditions. Due to the limitations of experimental data such as wind tunnel wall effects and the difficulty of safely obtaining valid flight data, numerical simulations are undertaken to supplement the existing data base. This data can then be used to predict the aerodynamic behavior over a wide range of flight conditions. Existing computational results show relatively good overall comparison with experiments but further refinement is required to reduce numerical errors and to obtain finer agreements over a larger parameter space. One of the important goals of this project is to obtain better comparisons between numerical simulations and experiments. In the simulations performed so far, the geometry has been simplified in various ways to reduce the complexity so that useful results can be obtained in a reasonable time frame due to limitations in computer resources. In this project, the finer details of the major components of the Space Shuttle are modeled better by including more complexity in the geometry definition. Smaller components not included in early Space Shuttle simulations will now be modeled and gridded.

Chan, William M.↗
NASA NTRS1992

Parameterization of solar cells

The aggregation (sorting) of the individual solar cells into an array is commonly based on a single operating point on the current-voltage (I-V) characteristic curve. An alternative approach for cell performance prediction and cell screening is provided by modeling the cell using an equivalent electrical circuit, in which the parameters involved are related to the physical phenomena in the device. These analytical models may be represented by a double exponential I-V characteristic with seven parameters, by a double exponential model with five parameters, or by a single exponential equation with four or five parameters. In this article we address issues concerning methodologies for the determination of solar cell parameters based on measured data points of the I-V characteristic, and introduce a procedure for screening of solar cells for arrays. We show that common curve fitting techniques, e.g., least squares, may produce many combinations of parameter values while maintaining a good fit between the fitted and measured I-V characteristics of the cell. Therefore, techniques relying on curve fitting criteria alone cannot be directly used for cell parameterization. We propose a consistent procedure which takes into account the entire set of parameter values for a batch of cells. This procedure is based on a definition of a mean cell representing the batch, and takes into account the relative contribution of each parameter to the overall goodness of fit. The procedure is demonstrated on a batch of 50 silicon cells for Space Station Freedom.

Appelbaum, J.↗
NASA NTRS1933

Wind-tunnel tests on model wing with Fowler flap and specially developed leading-edge slot

An investigation was made in the NACA 7 by 10 foot wind tunnel to find the increase in maximum lift coefficient which could be obtained by providing a model wing with both a Fowler trailing-edge extension flap and a Handley Page type leading-edge slot. A conventional Handley page slot proportioned to operate on the plain wing without a flap gave but a slight increase with the flap; so a special form of slot was developed to work more effectively with the flap. With the best combined arrangement the maximum lift coefficient based on the original area was increased from 3.17, for the Fowler wing, to 3.62. The minimum drag coefficient with both devices retracted was increased in approximately the same proportion. Tests were also made with the special-type slot on the plain wing without the flap. The special slot, used either with or without the Fowler flap, gave definitely higher values of the maximum lift coefficient than the slots of conventional form, with an increase of the same order in the minimum drag coefficient.

WING SLOTS & FLAPS, FOWLER↗
NASA NTRS1994

Deep VLA imaging of twelve extended 3CR quasars

A representative sample of 12 extended quasars from the 3CR catalog has been imaged at 4.9 GHz using the Very Large Array (VLA). These full synthesis observations typically achieve an rms noise of 20 micro-Jy per beam. Jets are detected on at least one side of every source. The jets are well collimated compared with those in less powerfull sources, but spreading is detected in most of them. The opening angles of several jets are not constant, but show recollimation after an initial regime of rapid spreading. Many of the jets contain quasiperiodic strings of knots, of which the knot closest to the central feature is usually the brightest (until the jet nears its hot spot). The degrees of linear polarization at the jet knots range from less than 5% to approx. 50%, but show no common trend with distance along the jets. In knots that are elongated in directions close to that of the jet, the E vectors tend to be orthogonal to the jet axis. The prominence of the inner, straighter jet segments relative to the extended lobes correlates significantly with the prominence of the milliarcsecond-scale central features, but the prominence of the more bent jet segments does not. Candidates for counterjet emission are detected in seven sources, but there is no unambiguous, continuous counterjet in any of them. Estimates of the flux density ratios between the straighter jet segments and the counterjets based on these tentative detections range from 1.2:1 to greater than 175:1. There is no evidence in this sample that counterjet detectability correlates with such putative inclination indicators as central feature prominence or projected linear size. There is also no evidence that the prominence of the counterjets anticorrelates with that of the jets as predicted by simple relativistic-beaming models for the jet/counterjet asymmetry. There is, however, strong evidence that large bends in the main jet favor counterjet detection, and there are no counterjet candidates opposite long, uninterrupted straight segments of the main jets. The detectability of the counterjets in these quasars may therefore be strongly influenced by interactions between the underlying beams and inhomogeneities in the surrounding material. We offer a new empirical definition of the term 'hot spot' that is intended to improve the distinction between such features and 'jet knots.' Both the compactness of hot spots and their position in the lobe are affected by whether they are fed by a detectable jet. When the hot spots differ significantly in compactness, the more compact one is always on the jetted side. Jetted hot spots are also more likely to be recessed deeply from the outer edge of their lobes than are their counterjetted counterparts. The jetted hot spot is less prominent relative to other extended emission if the jet bends through a large angle, particularly if a large bend occurs abruptly. The counterjetted hot spot is also less well defined if the jet is more bent. The lobes of several sources show considerable inhomogeneity, including filamentation.

Bridle, Alan H.↗
NASA NTRS1993

MASTRE trajectory code update to automate flight trajectory design, performance predictions, and vehicle sizing for support of shuttle and shuttle derived vehicles: Programmers manual

The information required by a programmer using the Minimum Hamiltonian AScent Trajectory Evaluation (MASTRE) Program is provided. This document enables the programmer to either modify the program or convert the program to computers other than the VAX computer. Documentation for each subroutine or function based on providing the definitions of the variables and a source listing are included. Questions concerning the equations, techniques, or input requirements should be answered by either the Engineering or User's manuals. Three appendices are also included which provide a listing of the Root-Sum-Square (RSS) program, a listing of subroutine names and definitions used in the MASTRE User Friendly Interface Program, and listing of the subroutine names and definitions used in the Mass Properties Program. The RSS Program is used to aid in the performance of dispersion analyses. The RSS program reads a file generated by the MASTRE Program, calculates dispersion parameters, and generates output tables and output plot files. UFI Program provides a screen user interface to aid the user in providing input to the model. The Mass Properties Program defines the mass properties data for the MASTRE program through the use of user interface software.

Source record↗
NASA NTRS2009

Distribution and Radiative Forcing of Tropical Thin Cirrus Clouds

To understand the radiative impact of tropical thin cirrus clouds, the frequency of occurrence and optical depths of these clouds have been derived. Thin cirrus clouds are defined here as being those that are not detected by the operational Moderate Resolution Imaging Spectroradiometer (MODIS) cloud mask, corresponding to an optical depth value of approximately 0.3 or smaller, but that are detectable in terms of the cirrus reflectance product based on the MODIS 1.375-micron channel. With such a definition, thin cirrus clouds were present in more than 40% of the pixels flagged as clear sky by the operational MODIS cloud mask algorithm. It is shown that these thin cirrus clouds are frequently observed in deep convective regions in the western Pacific. Thin cirrus optical depths were derived from the cirrus reflectance product. Regions of significant cloud fraction and large optical depths were observed in the Northern Hemisphere during the boreal spring and summer and moved southward during the boreal autumn and winter. The radiative effects of tropical thin cirrus clouds were studied on the basis of the retrieved cirrus optical depths, the atmospheric profiles derived from the Atmospheric Infrared Sounder (AIRS) observations, and a radiative transfer model in conjunction with a parameterization of ice cloud spectral optical properties. To understand how these clouds regulate the radiation field in the atmosphere, the instantaneous net fluxes at the top of the atmosphere (TOA) and at the surface were calculated. The present study shows positive and negative net forcings at the TOA and at the surface, respectively. The positive (negative) net forcing at the TOA (surface) is due to the dominance of longwave (shortwave) forcing. Both the TOA and surface forcings are in a range of 0-20 W/sq m, depending on the optical depths of thin cirrus clouds.

THIN CIRRUS CLOUDS↗
NASA NTRSDate not supplied

Medical Risk Estimates and Clinical Capability Needs for A Long Duration Artemis Mission

BACKGROUND Human exploration spaceflight missions to the Moon and Mars present unprecedented challenges for in-mission medical care. Compared with the ISS, the greater distance from Earth will mean increased mission durations, communication delays, limited to no resupply opportunities, and significant limitations on the evacuation of ill or injured crew. Spacecraft mass, volume, and power will be curtailed while higher demands will be placed on the crew’s knowledge, skills, and abilities. In this higher risk environment, it is important to: a) quantitatively estimate human system risk attributable to medical conditions, a process known as Probabilistic Risk Analysis, and b) use these estimates to inform medical system design. IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces) is a PRA and medical trade space analysis tool developed by NASA to advance exploration mission medical system design. IMPACT v1.0 improves upon and will soon replace NASA’s existing tool, the Integrated Medical Model, with: a novel evidence base baselined to exploration environments; an expanded list of 119 medical conditions; a significant increase in the number of medical resources that can be utilized and in the flexibility of their use; and the modelling of time lost performing mission-specific tasks due to medical conditions. DISCUSSION: This abstract will present IMPACT estimates of medical system risk and clinical capability needs for an extended duration Artemis mission of approximately 9 months, with phases including outbound transit, 3 months on the Lunar Gateway space station, 3 months on the Lunar surface with EVAs, 3 months on Gateway (simulating the return phase of a Mars mission), and transit back to Earth. Medical system risk estimates include loss of crew life (LOCL), consideration of medical evacuation (known as return to definitive care – RTDC), and an estimate of crew time lost due to medical conditions (Task Time Lost – TTL). The presentation will also describe the medical conditions that are the greatest drivers of risk as well as the clinical capabilities and resources that have the largest effect on risk.

W Thompson↗
NASA NTRS2022

Medical Risk Estimates and Clinical Capability Needs for a Late Artemis Mission

BACKGROUND Human exploration spaceflight missions to the Moon and Mars present unprecedented challenges for in-mission medical care. Compared with the ISS, the greater distance from Earth will mean increased mission durations, communication delays, limited to no resupply opportunities, and significant limitations on the evacuation of ill or injured crew. Spacecraft mass, volume, and power will be curtailed while higher demands will be placed on the crew’s knowledge, skills, and abilities. In this higher risk environment, it is important to: a) quantitatively estimate human system risk attributable to medical conditions, a process known as Probabilistic Risk Analysis, and b) use these estimates to inform medical system design. IMPACT (Informing Mission Planning via Analysis of Complex Tradespaces) is a PRA and medical trade space analysis tool developed by NASA to advance exploration mission medical system design. IMPACT v1.0 improves upon and will soon replace NASA’s existing tool, the Integrated Medical Model, with: a novel evidence base baselined to exploration environments; an expanded list of 119 medical conditions; a significant increase in the number of medical resources that can be utilized and in the flexibility of their use; and the modelling of time lost performing mission-specific tasks due to medical conditions. DISCUSSION: This abstract will present IMPACT estimates of medical system risk and clinical capability needs for an extended duration Artemis mission of approximately 9 months, with phases including outbound transit, 3 months on the Lunar Gateway space station, 3 months on the Lunar surface with EVAs, 3 months on Gateway (simulating the return phase of a Mars mission), and transit back to Earth. Medical system risk estimates include loss of crew life (LOCL), consideration of medical evacuation (known as return to definitive care –RTDC), and an estimate of crew time list due to medical conditions (Task Time Lost –TTL). The presentation will also describe the medical conditions that are the greatest drivers of risk as well as the clinical capabilities and resources that have the largest effect on risk.

A Anderson↗
DOE OSTI2024

Mesoscale Convective Systems Represented in High Resolution E3SMv2 and Impact of New Cloud and Convection Parameterizations

Mesoscale convective systems (MCSs) play an important role in modulating the global hydrological cycle, general circulation, and radiative energy budget. In this study, we evaluate MCS simulations in the second version of U.S. Department of Energy (DOE) Energy Exascale Earth System Model (E3SMv2). E3SMv2 atmosphere model (EAMv2) is run at the uniform 0.25? horizontal resolution. We track MCSs consistently in the model and observations using the PyFLEXTRKR algorithm, which defines MCS based on both cloud-top brightness temperature (Tb) and surface precipitation. Results from using Tb only to define MCS, commonly used in previous studies, are also discussed. Furthermore, sensitivity experiments are performed to examine the impact of new cloud and convection parameterizations developed for EAMv3 on simulated MCSs. Our results show that EAMv2 simulated MCS precipitation is largely underestimated in the tropics and contiguous United States. This is mainly attributed to the underestimated precipitation intensity in EAMv2. In contrast, the simulated MCS frequency becomes more comparable to observations if MCSs are defined only based on cloud-top Tb. The Tb-based MCS tracking method, however, includes many cloud systems with very weak precipitation which conflicts with the MCS definition. This result illustrates the importance of accounting for precipitation in evaluating simulated MCSs. We also find that the new physics parameterizations help increase the relative contribution of convective precipitation to total precipitation in the tropics, but the simulated MCS properties are generally not improved. This suggests that simulating MCSs will remain a challenge for the next version of E3SM.

Zhang, Meng↗
DOE OSTI2022

How Can Probabilistic Solar Power Forecasts Be Used to Lower Costs and Improve Reliability in Power Spot Markets? A Review and Application to Flexiramp Requirements

Net load uncertainty in electricity spot markets is rapidly growing. There are five general approaches by which system operators and market participants can use probabilistic forecasts of wind, solar, and load to help manage this uncertainty. These include operator situation awareness, resource risk hedging, reserves procurement, definition of contingencies, and explicit stochastic optimization. We review these approaches, and then provide a case study in which a method for using probabilistic solar forecasts to define needs for reserves is developed and evaluated. The case study has three parts. First, we describe building blocks for enhancing the Watt-Sun solar forecasting system to produce probabilistic irradiance and power forecasts. Second, relationships between Watt-Sun forecasts for multiple sites in California and the system's need for flexible ramp capability (flexiramp) are defined by machine learning and statistical methods. Third, the performance of present methods to defining flexiramp requirements, which are not conditioned on weather and renewables forecasts, is compared with that of probabilistic solar forecast-based requirements, using a multi-timescale production costing model with an 1820-bus representation of the WECC power system. Significant potential savings in fuel and flexiramp procurement costs from using solar-informed reserve requirements are found.

14 SOLAR ENERGY↗
NASA NTRS1997

The Optical Counterpart to Gamma-Ray Burst GRB 970228 Observed Using the Hubble Space Telescope

Although more than 2,000 astronomical gamma-ray bursts (GRBS) have been detected, and numerous models proposed to explain their occurrence, they have remained enigmatic owing to the lack of an obvious counterpart at other wavelengths. The recent ground-based detection of a transient optical source in the vicinity of GRB970228 may therefore have provided a breakthrough. The optical counterpart appears to be embedded in an extended source which, if a galaxy, as has been suggested would lend weight to those models that place GRBs at cosmological distances. Here we report, observations using the Hubble Space Telescope of the transient counterpart and extended source 26 and 39 days after the initial gamma-ray outburst. We find that the counterpart has faded since the initial detection (and continues to fade), but the extended source exhibits no significant change in brightness between the two dates of the observations reported here. The size and apparent constancy of the extended source imply that it is extragalactic, but its faintness makes a definitive statement about its nature difficult. Nevertheless, the decay profile of the transient source is consistent with a popular impulsive-fireball model13, which assumes a merger between two neutron stars in a distant galaxy.

Sahu, K. C.↗
NASA NTRS2015

Connecting Requirements to Architecture and Analysis via Model-Based Systems Engineering

In traditional systems engineering practice, architecture, concept development, and requirements development are related but still separate activities. Concepts for operation, key technical approaches, and related proofs of concept are developed. These inform the formulation of an architecture at multiple levels, starting with the overall system composition and functionality and progressing into more detail. As this formulation is done, a parallel activity develops a set of English statements that constrain solutions. These requirements are often called "shall statements" since they are formulated to use "shall." The separation of requirements from design is exacerbated by well-meaning tools like the Dynamic Object-Oriented Requirements System (DOORS) that remained separated from engineering design tools. With the Europa Clipper project, efforts are being taken to change the requirements development approach from a separate activity to one intimately embedded in formulation effort. This paper presents a modeling approach and related tooling to generate English requirement statements from constraints embedded in architecture definition.

Cole, Bjorn F.↗
NASA NTRSDate not supplied

Lunar Water Extraction Via Lunar Auger Dryer ISRU (LADI)

In 2009, the Lunar Reconnaissance Orbiter (LRO) and Lunar Crater Observation and Sensing Satellite (LCROSS) provided definitive proof of water in the Lunar’s southern permanently shadowed region (PSR)1. Both the 2020 NASA Technology Taxonomy2 and the Lunar Surface Innovation Initiative (LSII) team identified capability gaps in icy regolith transfer and reactor processing in Permanently Shadowed Region (PSR) environmental conditions. A water processing plant operating inside the PSR can continuously process water (and volatiles) for both breathable air and propellant. NASA’s Johnson Space Center (JSC) fabricated a unique breadboard test stand for validating the feasibility of this concept,developed a lunar auger dryer sizing tool, and identified the physical flow and thermal models required to design an Engineering Development Unit (EDU) for environmental testing. Over the two years this project was active, models were developed including: a) a sizing tool that scales the auger parameters based on production targets, b) accurate thermal models in both lab and lunar conditions, c) a Discreet Element Model (DEM) for observing particle effects in low-g, and d) incorporated these subsystem models into a MATLAB parametric Modular Open System Approach (MOSA) system model. These models were validated by testing the auger in both a mechanical and thermal system configuration. The results of this testing increased the Technology Readiness Level (TRL) of the Lunar Auger Dryer ISRU (LADI) system to TRL 4.

Lunar↗
NASA NTRS2024

Preventing Camera Clipping Through Varied Terrain and Other Planetary Objects

Within the scope of computer visualization systems and technologies, camera objects allow users to navigate three-dimensional (3D) scenes much like a person would navigate the real world. As such, when one seeks to model a scene or environment based on real-world laws, the camera must often follow these same conventions. Accomplishing this in the world of computer renderings presents unique challenges for defining space, spatial relations, depth, distance, and height. Therefore, movement for a camera must be specifically designated and processed by the program in order to achieve accurate movement representations. Although this thought process involves each aspect of camera movement, one specific aspect of camera movement is the primary focus of this report: ensuring that the camera does not clip through an object and appear subsurface. This is important to mimic real-world movements because people in the real world would not go beneath the solid-surface terrain unless they intended to do so. By working with numerical definitions, equations, and variables, a computer can relate an object to its existence in space. Thus, such challenges in camera movements with computationally rendered 3D spaces can be mitigated.

Kristie O'Brien↗
NASA NTRS1996

Mission simulation as an approach to develop requirements for automation in Advanced Life Support Systems

This paper examines mission simulation as an approach to develop requirements for automation and robotics for Advanced Life Support Systems (ALSS). The focus is on requirements and applications for command and control, control and monitoring, situation assessment and response, diagnosis and recovery, adaptive planning and scheduling, and other automation applications in addition to mechanized equipment and robotics applications to reduce the excessive human labor requirements to operate and maintain an ALSS. Based on principles of systems engineering, an approach is proposed to assess requirements for automation and robotics using mission simulation tools. First, the story of a simulated mission is defined in terms of processes with attendant types of resources needed, including options for use of automation and robotic systems. Next, systems dynamics models are used in simulation to reveal the implications for selected resource allocation schemes in terms of resources required to complete operational tasks. The simulations not only help establish ALSS design criteria, but also may offer guidance to ALSS research efforts by identifying gaps in knowledge about procedures and/or biophysical processes. Simulations of a planned one-year mission with 4 crewmembers in a Human Rated Test Facility are presented as an approach to evaluation of mission feasibility and definition of automation and robotics requirements.

NASA Discipline Number 61-10↗
NASA NTRS2000

Preliminary Results From NASA's Space Solar Power Exploratory Research and Technology Program

Large solar power satellite (SPS) systems that might provide base load power into terrestrial markets were examined extensively in the 1970s by the US Department of Energy (DOE) and the National Aeronautics and Space Administration (NASA). Following a hiatus of about 15 years, the subject of space solar power (SSP) was reexamined by NASA from 1995-1997 in the "fresh look" study, and during 1998 in an SSP "concept definition study". As a result of these efforts, during 1999-2000, NASA has been conducting the SSP Exploratory Research and Technology (SERT) program. The goal of the SERT activity has been to conduct preliminary strategic technology research and development to enable large, multi-megawatt SSP systems and wireless power transmission (WPT) for government missions and commercial markets (in-space and terrestrial). In pursuing that goal, the SERT: (1) refined and modeled systems approaches for the utilization of SSP concepts and technologies, ranging from the near-term (e.g., for space science, exploration and commercial space applications) to the far-term (e.g., SSP for terrestrial markets), including systems concepts, architectures, technology, infrastructure (e.g. transportation), and economics; (2) conducted technology research, development and demonstration activities to produce "proof-of-concept" validation of critical SSP elements for both nearer and farther-term applications; and (3) engendered the beginnings of partnerships (nationally and internationally) that could be expanded, as appropriate, to pursue later SSP technology and applications. Through these efforts, the SERT should allow better informed future decisions regarding further SSP and related technology research and development investments by both NASA and prospective partners, and guide further definition of technology roadmaps - including performance objectives, resources and schedules, as well as "multi-purpose" applications (e.g., commerce, science, and government). This paper presents preliminary results from the SERT effort at a summary level, including the study approach, SPS concepts, applications findings, and concludes with a revised assessment of the prospects for solar power satellites using SSP technologies and systems.

Howell, Joe T.↗
NASA NTRS2004

Theoretical and Observational Determination of Global and Regional Radiation Budget, Forcing and Feedbacks at the Top-of-Atmosphere and Surface

Report consists of: 1. List of accomplishments 2. List of publications 3. Abstracts of published or submitted papers and 4. Subject invention disclosure. The accomplishments of the grant listed are: 1. Improved the third-order turbulence closure in cloud resolving models to remove the liquid water oscillation. 2. Used the University of California-Los Angeles (UCLA) large-eddy simulation (LES) model to provide data for radiation transfer testing. 3. Revised shortwave k-distribution models based on HITRAN 2000. 4. Developed a gamma-weighted two-stream radiative transfer model for radiation budget estimate applications. 5. Estimated the effect of spherical geometry to the earth radiation budget. 6. Estimated top-of-atmosphere irradiance over snow and sea ice surfaces. 7. Estimated the aerosol direct radiative effect at the top of the atmosphere. 8. Estimated the top-of-atmosphere reflectance of the clear-sky molecular atmosphere over ocean. 9. Developed and validated new set of Angular Distribution Models for the CERES TRMM satellite instrument (tropical) 10. Developed and validated new set of Angular Distribution Models for the CERES Terra satellite instrument (global) 11. Quantified the top-of-atmosphere direct radiative effect of aerosols over global oceans from merged CERES and MODIS observations 12 Clarified the definition of TOA flux reference level for radiation budget studies 13. Developed new algorithm for unfaltering CERES measured radiances 14. Used multiangle POLDER measurements to produce narrowband angular distribution models and examine the effect of scene identification errors on TOA albedo estimates 15. Developed and validated a novel algorithm called the Multidirectional Reflectance Matching (MRM) model for inferring TOA albedos from ice clouds using multi-angle satellite measurements. 16. Developed and validated a novel algorithm called the Multidirectional Polarized Reflectance Matching (MPRM) model for inferring particle shapes from ice clouds using multi-angle polarized satellite measurements. 17. Developed 4 advanced light scattering models including the three-dimensional (3D) uniaxial perfectly matched layer (UPML) finite-difference time-domain (FDTD) model. 18. Develop sunglint in situ measurement and study reflectance distribution in the sunglint area. 19. Lead a balloon-borne radiometer TOA albedo validation effort. 20. Developed a CERES surface UVB, UVA, and UV index product.

Loeb, Norman G.↗
DOE OSTI2025

Fermi’s Golden Rule Rate Expression for Transitions Due to Nonadiabatic Derivative Couplings in the Adiabatic Basis

Starting from a general molecular Hamiltonian expressed in the basis of adiabatic electronic and nuclear position states, where a compact and complete expression for the nonadiabatic derivative coupling (NDC) Hamiltonian term is obtained, we provide a general analysis of the Fermi’s golden rule (FGR) rate expression for nonadiabatic transitions between adiabatic states. We then consider a quasi-adiabatic approximation that uses crude adiabatic states and NDC couplings, both evaluated at the minimum potential energy configuration of the initial adiabatic state, for the definition of the zeroth and first-order terms of the Hamiltonian. Although the application of this approximation is rather limited, it allows deriving a general FGR rate expression without further approximation while accounting for non-Condon contribution to the FGR rate arising from momentum operators of NDC terms and its coupling with vibronic displacements. For a generic and widely used model where all nuclear degrees of freedom and environmental effects are represented as linearly coupled harmonic oscillators, we derive a closed-form FGR rate expression that requires only Fourier transform. The resulting rate expression includes quadratic contributions of NDC terms and their couplings to Franck–Condon modes, which require evaluation of two additional bath spectral densities in addition to the conventional one that appears in a typical FGR rate theory based on the Condon approximation. Model calculations for the case where nuclear vibrations consist of both a sharp high-frequency mode and an Ohmic bath spectral density illustrate new features and implications of the rate expression. We then apply our theoretical expression to the nonradiative decay from the first excited singlet state of azulene, which illustrates the utility and implications of our theoretical results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗