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At least 757 records · Page 42

Double photoionization of atomic oxygen: Feshbach resonances in the two-electron continuum

In this work, we describe a joint experimental and theoretical investigation on oxygen double photoionization—the emission of two electrons from atomic oxygen following single photon absorption. High-resolution experimental measurements were performed at the Advanced Light Source, revealing sharp resonance structure superimposed on the more familiar Wannier-like, nearly-linear background. These resonance features are attributed to ionization-plus-excitation Feshbach resonances embedded in the double ionization continuum, doubly-excited states that lie above the double-ionization threshold. Such features are absent in the double photoionization cross section of He, or other quasi-two-electron systems, for which the doubly-ionized atomic core remains inert. For a corresponding theoretical analysis, the R-matrix with pseudostates (RMPS) method was invoked by calculating final-state, two-electron resonances-plus-continua wavefunctions and corresponding single-photon absorption cross sections. Overall agreement is found in the direct, background double photoionization cross section. However, the RMPS method, using a small basis due to practical computational limitations, was unable to reproduce quantitatively the smooth background or the sharper resonance features observed in the measurements, showing instead large-scale oscillations about the experimental background, and characteristic pseudoresonance jitter, associated with an insufficient convergence of the pseudostate representation to the true two-electron infinite series of Feshbach resonances embedded in the two-electron continuum. The prominent resonance structure observed highlights the need to consider multiple excitation processes in atoms more complex than He or quasi-two-electron systems.

74 ATOMIC AND MOLECULAR PHYSICS↗

Plasma waves associated with the space shuttle

Water molecules outgassed from the Space Shuttle suffer collisional charge-exchange with ionospheric oxygen ions, thereby forming unstable distributions of pick-up water ions and leading to high levels of plasma waves near the Shuttle. Liouville's equation with a charge-exchange source term is solved for the water ion distribution function as a function of position relative to the Shuttle. The observational characteristics of the near zone Shuttle waves are summarized. A linear theory in which beam like distributions of water ions drive Doppler shifted lower hybrid waves via the modified two stream instability is developed. This theory explains many characteristics of the near zone waves. Further work on the effects of wave nonlinearities and spatial inhomogeneity is required to explain the detailed frequency spectrum of the waves. The observed wave levels apparently satisfy the threshold condition for modulational instability of lower hybrid waves.

Cairns, I. H.↗

Investigation of N2O Production from 266 and 532 nm Laser Flash Photolysis of O3/N2/O2 Mixtures

Tunable diode laser absorption spectroscopy has been employed to measure the amount of N2O produced from laser flash photolysis of O3/N2/O2 mixtures at 266 and 532 nm. In the 532 nm photolysis experiments very little N2O is observed, thus allowing an upper limit yield of 7 x 10(exp -8) to be established for the process O3 + N2 yield N2O + O2, where O3 is nascent O3 that is newly formed via O(3P(sub J)) + O2 recombination (with vibrational excitation near the dissociation energy of O3). The measured upper limit yield is a factor of approx. 600 smaller than a previous literature value and is approximately a factor of 10 below the threshold for atmospheric importance. In the 266 nm photolysis experiments, significant N2O production is observed and the N2O quantum yield is found to increase linearly with pressure over the range 100 - 900 Torr in air bath gas. The source of N2O in the 266 nm photolysis experiments is believed to be the addition reaction O(1D(sub 2)) + N2 + M yields (k(sub sigma)) N2O + M, although reaction of (very short-lived) electronically excited O3 with N2 cannot be ruled out by the available data. Assuming that all observed N2O comes from the O(1D(sub 2)) + N2 + M reaction, the following expression describes the temperature dependence of k(sub sigma) (in its third-order low-pressure limit) that is consistent with the N2O yield data: k(sub sigma) = (2.8 +/- 0.1) x 10(exp -36)(T/300)(sup -(0-88+0.36)) cm(sup 6) molecule(sup -2)/s, where the uncertainties are 2(sigma) and represent precision only. The accuracy of the reported rate coefficients at the 95% confidence level is estimated to be 30 - 40% depending on the temperature. Model calculations suggest that gas phase processes initiated by ozone absorption of a UV photon represent about 1.4% of the currently estimated global source strength of atmospheric N2O. However, these processes could account for a significant fraction of the oxygen mass-independent enrichment observed in atmospheric N2O, and they appear to be the first suggested photochemical mechanism that is capable of explaining the altitude dependence of the observed mass -independent isotopic signature.

Estupinan, E. G.↗

SureTrak Probability of Impact Display

The SureTrak Probability of Impact Display software was developed for use during rocket launch operations. The software displays probability of impact information for each ship near the hazardous area during the time immediately preceding the launch of an unguided vehicle. Wallops range safety officers need to be sure that the risk to humans is below a certain threshold during each use of the Wallops Flight Facility Launch Range. Under the variable conditions that can exist at launch time, the decision to launch must be made in a timely manner to ensure a successful mission while not exceeding those risk criteria. Range safety officers need a tool that can give them the needed probability of impact information quickly, and in a format that is clearly understandable. This application is meant to fill that need. The software is a reuse of part of software developed for an earlier project: Ship Surveillance Software System (S4). The S4 project was written in C++ using Microsoft Visual Studio 6. The data structures and dialog templates from it were copied into a new application that calls the implementation of the algorithms from S4 and displays the results as needed. In the S4 software, the list of ships in the area was received from one local radar interface and from operators who entered the ship information manually. The SureTrak Probability of Impact Display application receives ship data from two local radars as well as the SureTrak system, eliminating the need for manual data entry.

Elliott, John↗

Exploration of Near-Term Potential Routes and Procedures for Urban Air Mobility

Urban air mobility is gaining interest as the need for On Demand Mobility in today's congested traffic is becoming high in metropolitan areas. Urban Air Mobility (UAM) is envisioned as a concept to transport passengers and cargo safely and efficiently using innovative aircraft in the urban areas. It is expected to improve mobility for the general public, decongest road traffic, reduce transport time and reduce the strain on existing public transport networks. There exist several challenges to Urban Air Mobility (UAM) such as integration of procedures with airspace and the airport, noise levels that are acceptable to the general public, public safety, public acceptance, vehicle certification, and more. Most of the research in the United States and European skies (DLR - German Aerospace Center) related to urban areas has focused on small UAS (Unmanned Aircraft Systems) flights (NASA's UTM (UAS Traffic Management) research) and their integration with the airspace and building safe operations in densely populated areas. Previous studies on UAM have focused on fast time simulations of the routes that are separated via a separation service and network of routes. Similarly, research in Europe has focused on the approach profile for these innovative aircraft, vertiports and battery life among others. UAM as a part of the On-Demand Mobility effort has provided some guidelines for operations as shown below: Does not require additional ATC (Air Traffic Control) infrastructure; Does not impose additional workload on ATC; Does not restrict operations of traditional airspace users; Will meet appropriate safety thresholds and requirements; Will prioritize operational scalability; Will allow flexibility where possible and structure where necessary. This paper explores potential routes and procedures in a Human-In-The-Loop (HITL) experiment that could be applied in the near-term to allow integration of UAM flights into the airspace as well as a large airport. The airspace that was explored was Dallas Fort Worth (DFW) airspace managed by the DFW East Tower in South Flow only. In addition, Dallas Love Field (DAL) and Addison (ADS) airspace were also part of the testbed. The initial set of routes investigated in this study were published helicopter routes in the DFW area. Figure 1 shows class B airspace in DFW area and the origin/destination city pairs where UAM flights flew along with helicopter routes shown in blue. The research focused on exploring procedures for integrating UAM flights into Class Bravo and Class Delta airspace. Three different communication procedures, evaluated with three different levels of UAM traffic, are shown in Table 1. The current day routes were evaluated with current day communication procedures were explored as the first condition. The current day routes were also evaluated in the second condition with reduced communications, which was assumed due to the presence of a Letter Of Agreement (LOA). The purpose of the LOA was to reduce the verbiage associated with pilots getting clearance to Class B airspace from the controllers, pre-assigning beacons codes to the UAM flights, separate routes by assigning altitudes and speeds to flights going in any one direction. Flights were expected to automatically change frequency when exiting Class B airspace, thus transition points for entry and exit points were also specified in the LOA.

Urban Air Mobility↗

High Cooperativity Using a Confocal-Cavity–QED Microscope

Cavity quantum electrodynamics (QED) with cooperativity far greater than unity enables high-fidelity quantum sensing and information processing. The high-cooperativity regime is often reached through the use of short single-mode resonators. More complicated multimode resonators, such as the near-confocal optical Fabry-Pérot cavity, can provide intracavity atomic imaging in addition to high cooperativity. This capability has recently proved important for exploring quantum many-body physics in the driven-dissipative setting. In this work, we show that a confocal-cavity–QED microscope can realize cooperativity in excess of 110. This cooperativity is on par with the very best single-mode cavities (which are far shorter) and 21 times greater than single-mode resonators of similar length and mirror radii. The 1.7-µm imaging resolution is naturally identical to the photon-mediated interaction range. We measure these quantities by determining the threshold of cavity superradiance when small optically tweezed BoseEinstein condensates are pumped at various intracavity locations. Transmission measurements of an ex situ cavity corroborate these results. We provide a theoretical description that shows how cooperativity enhancement arises from the dispersive coupling to the atoms of many near-degenerate modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Nonlinear stability of solar type 3 radio bursts. 2: Application to observations near 1 AU

A set of rate equations including strong turbulence effects and anomalous resitivity are solved using parmeters which model several solar type 3 bursts. Exciter distributions observed at 1 AU are excitation of the linear bump-in-tail instability, amplifying Langmuir waves above the threshold for the oscillating two stream instability (OTSI). The OTSI, and the attendant anomalous resistivity produce a rapid spectral transfer of Langmuir waves to short wavelengths, out of resonance with the electron exciter. Further energy loss of the beam is thus precluded. The various parameters needed to model the bursts are extrapolated inside 1 AU with similar results. Again, the OTSI is excited and decouples the electron beam from the Langmuir radiation. Reabsorption of the Langmuir waves by the beam is shown to be unimportant in all cases, even at 0.1 AU. The theory provides a natural explanation for the observed realationship between radio flux, and the electron flux.

Goldstein, M. L.↗

Methods and apparatus for comprehensive characterization of performance attributes and damage thresholds of ultrafast laser optics

It is presently well understood that the operational performance limits of optics are determined by three fundamental attributes: the initiation of laser-induced damage, the growth of damage sites, and the transient (nondamaging) modification of optical parameters. The comprehensive characterization of the performance limitations of ultrafast optics requires consideration of all three fundamental attributes. Here, the vast majority of literature to date, however, has focused primarily on damage-initiation and testing systems that are largely focused on determining the damage-initiation threshold under single- and multipulse excitation. In this work, we discuss a testing apparatus that was designed to offer the capability to adequately characterize all three of these performance attributes under femtosecond, near-infrared laser irradiation. Key aspects of methodology are discussed, including high-dynamic-range energy control, variable beam size, wavelength tunability, B-integral management, and functional performance characterization to explore the true operational limits of the components. Example results for a metal-dielectric mirror demonstrate the test station’s operation.

42 ENGINEERING↗

Canopy damage and recovery following Hurricane Maria using multitemporal lidar data, Mar/2017 - Mar/2020, Puerto Rico

Hurricane Maria (Category 4) snapped and uprooted canopy trees, removed large branches, and defoliated vegetation across Puerto Rico. The magnitude of forest damages and the rates and mechanisms of forest recovery following Maria provide important benchmarks for understanding the ecology of extreme events. We used airborne lidar data acquired before (2017) and after Maria (2018, 2020) to quantify landscape-scale changes in forest structure along a 439-ha elevational gradient (100 to 800 m) in the Luquillo Experimental Forest. Damages from Maria were widespread, with 73% of the study area losing ≥1 m in canopy height (mean = -7.1 m). Taller forests at lower elevations suffered more damage than shorter forests above 600 m. Yet only 13% of the study area had canopy heights ≤2 m in 2018, a typical threshold for forest gaps, highlighting the importance of damaged trees and advanced regeneration on post-storm forest structure. Heterogeneous patterns of regrowth and recruitment yielded shorter and more open forests by 2020. Nearly 45% of forests experienced initial height loss (<-1 m, 2017-2018) followed by rapid height gain (>1 m, 2018-2020), whereas 21.6% of forests with initial height losses showed little or no height gain, and 17.8% of forests exhibited no structural changes >|1| m in either period. Canopy layers <10 m accounted for most increases in canopy height and fractional cover between 2018-2020, with gains split evenly between height growth and lateral crown expansion by surviving individuals. These findings benchmark rates of gap formation, crown expansion, and canopy closure following hurricane damage. Included in the attached zip file are four TIF and four KML files.

54 ENVIRONMENTAL SCIENCES↗

Clustering of DESI galaxies split by thermal Sunyaev-Zeldovich effect

The thermal Sunyaev-Zeldovich (tSZ) effect is associated with galaxy clusters - extremely large and dense structures tracing the dark matter with a higher bias than isolated galaxies. We propose to use the tSZ data to separate galaxies from redshift surveys into distinct subpopulations corresponding to different densities and biases independently of the redshift survey systematics. Leveraging the information from different environments, as in density-split and density-marked clustering, is known to tighten the constraints on cosmological parameters, like $\Omega_m$, $\sigma_8$ and neutrino mass. We use data from the Dark Energy Spectroscopic Instrument (DESI) and the Atacama Cosmology Telescope (ACT) in their region of overlap to demonstrate informative tSZ splitting of Luminous Red Galaxies (LRGs). We discover a significant increase in the large-scale clustering of DESI LRGs corresponding to detections starting from 1-2 sigma in the ACT DR6 + Planck tSZ Compton-$y$ map, below the cluster candidate threshold (4 sigma). We also find that such galaxies have higher line-of-sight coordinate (and velocity) dispersions and a higher number of close neighbors than both the full sample and near-zero tSZ regions. We produce simple simulations of tSZ maps that are intrinsically consistent with galaxy catalogs and do not include systematic effects, and find a similar pattern of large-scale clustering enhancement with tSZ effect significance. Moreover, we observe that this relative bias pattern remains largely unchanged with variations in the galaxy-halo connection model in our simulations. This is promising for future cosmological inference from tSZ-split clustering with semi-analytical models. Thus, we demonstrate that valuable cosmological information is present in the lower signal-to-noise regions of the thermal Sunyaev-Zeldovich map, extending far beyond the individual cluster candidates.

Astronomy data analysis↗

Tracking the Rates and Mechanisms of Canopy Damage and Recovery Following Hurricane Maria Using Multitemporal Lidar Data

Hurricane Maria, a Category 4 storm, snapped and uprooted canopy trees, removed large branches, and defoliated vegetation across Puerto Rico. The magnitude of forest damages and the rates and mechanisms of forest recovery following Maria provide important benchmarks for understanding the ecology of extreme events. We used airborne Lidar data acquired before (2017) and after Maria (2018, 2020) to quantify landscape-scale changes in forest structure along a 439-ha elevational gradient (100–800 m) in the Luquillo Experimental Forest. Damages from Maria were widespread, with 73% of the study area losing ≥ 1 m in canopy height (mean = −7.1 m). Taller forests at lower elevations suffered more damage than shorter forests above 600 m. Yet only 13.5% of the study area had canopy heights ≤ 2 m in 2018, a typical threshold for forest gaps, highlighting the importance of damaged trees and advanced regeneration on post-storm forest structure. Heterogeneous patterns of regrowth and recruitment yielded shorter and more open forests by 2020. Nearly 45% of forests experienced initial height loss > 1 m (2017–2018) followed by rapid height gain > 1 m (2018–2020), whereas 21.6% of forests with initial height losses showed little or no height gain, and 17.8% of forests exhibited no height changes larger than ± 1 m in either period. Canopy layers < 10 m tall accounted for most increases in canopy height and fractional cover between 2018 and 2020, with gains split evenly between height growth and lateral crown expansion by surviving individuals. These findings benchmark rates of gap formation, crown expansion, and canopy closure following hurricane damage and highlight the diversity of ecosystem impacts from heterogeneous spatial patterns and vertical stratification of forest regrowth following a major disturbance event.

forest structure↗

Tracking the Rates and Mechanisms of Canopy Damage and Recovery Following Hurricane Maria Using Multitemporal Lidar Data

Hurricane Maria, a Category 4 storm, snapped and uprooted canopy trees, removed large branches, and defoliated vegetation across Puerto Rico. The magnitude of forest damages and the rates and mechanisms of forest recovery following Maria provide important benchmarks for understanding the ecology of extreme events. We used airborne Lidar data acquired before (2017) and after Maria (2018, 2020) to quantify landscape-scale changes in forest structure along a 439-ha elevational gradient (100–800 m) in the Luquillo Experimental Forest. Damages from Maria were widespread, with 73% of the study area losing ≥ 1 m in canopy height (mean = −7.1 m). Taller forests at lower elevations suffered more damage than shorter forests above 600 m. Yet only 13.5% of the study area had canopy heights ≤ 2 m in 2018, a typical threshold for forest gaps, highlighting the importance of damaged trees and advanced regeneration on post-storm forest structure. Heterogeneous patterns of regrowth and recruitment yielded shorter and more open forests by 2020. Nearly 45% of forests experienced initial height loss > 1 m (2017–2018) followed by rapid height gain > 1 m (2018–2020), whereas 21.6% of forests with initial height losses showed little or no height gain, and 17.8% of forests exhibited no height changes larger than ± 1 m in either period. Canopy layers < 10 m tall accounted for most increases in canopy height and fractional cover between 2018 and 2020, with gains split evenly between height growth and lateral crown expansion by surviving individuals. These findings benchmark rates of gap formation, crown expansion, and canopy closure following hurricane damage and highlight the diversity of ecosystem impacts from heterogeneous spatial patterns and vertical stratification of forest regrowth following a major disturbance event.

forest structure↗

Room Temperature Lasing from Semiconducting Single-Walled Carbon Nanotubes

Miniaturized near-infrared semiconductor lasers that are able to generate coherent light with low energy consumption have widespread applications in fields such as optical interconnects, neuromorphic computing, and deep-tissue optogenetics. With optical transitions at near-infrared wavelengths, diameter-tunable electronic structures, and superlative optoelectronic properties, semiconducting single-walled carbon nanotubes (SWCNTs) are promising candidates for nanolaser applications. However, despite significant efforts in this direction and recent progress toward enhancing spontaneous emission from SWCNTs through Purcell effects, SWCNT-based excitonic lasers have not yet been demonstrated. Leveraging an optimized cavity-emitter integration scheme enabled by a self-assembly process, here we couple SWCNT emission to the whispering gallery modes supported by polymer microspheres, resulting in room temperature excitonic lasing with an average lasing threshold of 4.5 kW/cm 2 . The high photostability of SWCNTs allows stable lasing for prolonged duration with minimal degradation. Finally, this experimental realization of excitonic lasing from SWCNTs, combined with their versatile electronic and optical properties that can be further controlled by chemical modification, offers far-reaching opportunities for tunable near-infrared nanolasers that are applicable for optical signal processing, in vivo biosensing, and optoelectronic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Radiometry Measurements of Mars at 1064 nm Using the Mars Orbiter Laser Altimeter

Measurements by the Mars Orbiter Laser Altimeter (MOLA) on board the Mars Global Surveyor (MGS) may be used to provides a radiometric measurement of Mars in addition to the topographic measurement. We will describe the principle of operation, a mathematical model, and the receiver calibration in this presentation. MOLA was designed primarily to measure Mars topography, surface roughness end the bidirectional reflectance to the laser beam. To achieve the highest sensitivity the receiver detection threshold is dynamically adjusted to be as low as possible while keeping a predetermined false alarm rate. The average false alarm rate 29 monitored in real time on board MOLA via a noise counter, whose output is fed to the threshold control loop. The false alarm rate at a given threshold is a function of the detector output noise which is the sum of the photo detector, shot noise due to the background light seen by the detector and the dark noise. A mathematical model has been developed that can be used to numerically solve for the optical background power given the MOLA threshold setting and the average noise count. The radiance of Mars can then be determined by dividing the optical power by the solid angle subtended by the MOLA receiver, the receiver optical band-width, end the Mars surface area within the receiver field of view. The phase angle which is the sun-Mars-MOLA angle is available from the MGS database. MOLA also measures simultaneously the bidirectional reflectance of Mars vie its 106-lum loser beam at nadir with nearly zero phase angle. The optical bandwidth of the MOLA receiver is 2um full width at half maximum (FWHM) and centered at 106-lum. The receiver field of view is 0.95mrad FWHM. The nominated spacecraft altitude is 100km and the ground track speed is about 3km/s. Under normal operation, the noise counter are read and the threshold levels are updated at 1Hz. The receiver sensitivity is limited by the detector dark noise to about 0.1nW, which corresponds to less than 2% the maximum radiance during daytime from the brightest area on Mars. The results from the mathematical model agree well with the prelaunch measurements at several calibrated optical power levels. The radiance of sunlit Mars estimated with this technique correlates well with the measurement from the MGS. Thermal Emission Spectrometer (TES) and the Hubble Space Telescope at similar wavelength.

Sun, Xiao-Li↗

Performance Thresholds for Application of MEMS Inertial Sensors in Space

We review types of inertial sensors available and current usage of inertial sensors in space and the performance requirements for these applications. We then assess the performance available from micro-electro-mechanical systems (MEMS) devices, both in the near and far term. Opportunities for the application of these devices are identified. A key point is that although the performance available from MEMS inertial sensors is significantly lower than that achieved by existing macroscopic devices (at least in the near term), the low cost, low size, and power of the MEMS devices opens up a number of applications. In particular, we show that there are substantial benefits to using MEMS devices to provide vibration, and for some missions, attitude sensing. In addition, augmentation for global positioning system (GPS) navigation systems holds much promise.

Smit, Geoffrey N.↗

Improving SMAP freeze-thaw retrievals for pavements using effective soil temperature from GEOS-5: Evaluation against in situ road temperature data over the U.S

Seasonal freeze-thaw (FT) affects over half the northern hemisphere and impacts many key processes of the Earth System such as energy exchange, hydrology and vegetation. Nearly all past studies using spaceborne FT retrievals have focused on characterizing FT specifically for natural environments. FT in the built environment is also routinely studied and a topic of great interest, especially with regards to transportation infrastructure. Whereas natural FT process are frequently investigated using spaceborne observations, FT studies of roads are often limited to local scales, using in situ or nearby weather station data only. Comparisons between FT retrievals obtained from NASA's Soil Moisture Active Passive (SMAP) satellite and roads in Alaska (AK) and the Contiguous United States (CONUS) showed that spaceborne FT retrievals had good agreement with road data. But those results also indicated that NASA FT retrievals in CONUS were relatively too warm compared to road data. If SMAP FT retrievals were to be used for identifying FT transition timing for applications by the transportation community, it is also important for frozen conditions to be identified more accurately. This work is primarily concerned with improving frozen retrievals made in CONUS by calculating new Normalized Polarization Ratio (NPR) thresholds as compared to those currently used in SMAP FT. We found that focusing on a temporal subset of October through May for comparisons greatly improved the correlation between NPR and effective soil temperature (Teff, one of SMAP's ancillary datasets), often from about zero to 0.6. We then applied linear regression between NPR and Teff to obtain new NPR thresholds resulting in the FT-Roads (FT-R) product. NASA FT and FT-R were evaluated against road data at about 1000 locations in CONUS and a battery of different tests indicated that FT-R performed better under nearly all conditions compared to NASA FT. Overall, NASA FT accuracies were 69% and 80% for 6 am and 6 pm SMAP retrievals, while FT-R achieved accuracies of 79% and 82%. We also investigated the potential for using Teff for road FT (6 am, only) and found that those comparisons were even more accurate (84%). We've also quantified inter- and intraregional differences of SMAP FT performance and found that accuracy metrics vary over twice as much between geographic subdivisions (9%) as compared to between the states within a subdivision (4%). Most importantly, the main goal of improving the detection of in situ frozen conditions in CONUS was realized, with FT-R accurately detecting frozen conditions >50% more frequently than NASA FT.

Passive microwave↗

An Algorithm for Atom-Centered Lossy Compression of the Atomic Orbital Basis in Density Functional Theory Calculations

Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-ζ (QZ) size are required to adequately converge Kohn–Sham density functional theory (DFT) calculations toward the complete basis set limit. However, incrementing the cardinal number by one nearly doubles the AO basis dimension, and the computational cost scales as the cube of the AO dimension, so this is very computationally demanding. Here, in this work, we develop and test a threshold-based natural atomic orbital (NAO) scheme in which ϵ-NAOs are obtained as eigenfunctions of atomic blocks of the density matrix in a one-center orthogonalized representation. This enables compression of the AO basis that is optimal for a given threshold, 10 –ϵ , by discarding NAOs with occupation numbers below that threshold. Extensive pilot test calculations using the Hartree–Fock functional and taking the converged density matrix as input suggest that a threshold of 10 –5 can yield a compression factor (ratio of AO to compressed ϵ-NAO dimension) between 2.5 and 4.5 for the QZ pc-3 basis. The errors in relative energies are typically less than 0.1 kcal/mol when the compressed basis is used instead of the uncompressed basis. Between 10 and 100 times smaller errors (i.e., usually less than 0.01 kcal/mol) can be obtained with a threshold 10 –7 , while the compression factor is typically between 2 and 2.5.

basis sets↗