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NASA NTRS1999

Man-Made Debris In and From Lunar Orbit

During 1966-1976, as part of the first phase of lunar exploration, 29 manned and robotic missions placed more than 40 objects into lunar orbit. Whereas several vehicles later successfully landed on the Moon and/or returned to Earth, others were either abandoned in orbit or intentionally sent to their destruction on the lunar surface. The former now constitute a small population of lunar orbital debris; the latter, including four Lunar Orbiters and four Lunar Module ascent stages, have contributed to nearly 50 lunar sites of man's refuse. Other lunar satellites are known or suspected of having fallen from orbit. Unlike Earth satellite orbital decays and deorbits, lunar satellites impact the lunar surface unscathed by atmospheric burning or melting. Fragmentations of lunar satellites, which would produce clouds of numerous orbital debris, have not yet been detected. The return to lunar orbit in the 1990's by the Hagoromo, Hiten, Clementine, and Lunar Prospector spacecraft and plans for increased lunar exploration early in the 21st century, raise questions of how best to minimize and to dispose of lunar orbital debris. Some of the lessons learned from more than 40 years of Earth orbit exploitation can be applied to the lunar orbital environment. For the near-term, perhaps the most important of these is postmission passivation. Unique solutions, e.g., lunar equatorial dumps, may also prove attractive. However, as with Earth satellites, debris mitigation measures are most effectively adopted early in the concept and design phase, and prevention is less costly than remediation.

Johnson, Nicholas L.↗

NASA NTRS2002

Orbit Determination Support for the Microwave Anisotropy Probe (MAP)

The Microwave Anisotropy Probe (MAP) is a Medium Class Explorers (MIDEX) mission produced in partnership between Goddard Space Flight Center (GSFC) and Princeton University. The main science objective of the MAP mission is to produce an accurate full-sky map of the cosmic microwave background temperature fluctuations anisotropy. MAP was launched from the Cape Canaveral Air Force Station Complex 17 aboard a Delta II 7425-10 expendable launch vehicle at exactly 19:46:46.183 UTC on June 30, 2001. The spacecraft received a nominal direct insertion by the Delta into a 185 km circular orbit. MAP was then maneuvered into a sequence of phasing loops designed to set up a lunar swingby (gravity-assisted acceleration) of the spacecraft onto a transfer trajectory to a Lissajous orbit about the Earth-Sun L2 point. The mission duration is approximately 27 months with 3 to 4 months of transfer time to the final mission orbit about L2. The MAP transfer orbit consisted of 3.5 phasing loops: the first loop has a 7-day period, the second and third loops have a 9-day period, and the last half loop has a 4-day period as illustrated in Figure 1, which also indicates the placement of maneuvers. A Pfinal correction maneuver was performed 18 hours after the last perigee to more closely achieve the targeted lissajous orbit. The lunar encounter or swingby took place approximately 30 days after launch. After the lunar encounter, the spacecraft will cruise for approximately 120 days before it arrives at L2. A Mid-Course Correction (MCC) maneuver was executed seven days after the swingby to further refine the trajectory. Once the MAP satellite is injected into the L2 Lissajous orbit, it will perform occasional stationkeeping maneuvers to maintain the Lissajous orbit for a minimum of two years (and a goal of four years). Because of its complex orbital characteristics, the mission provided a unique challenge to orbit determination (OD) support in many orbital regimes. Extensive trajectory error covariance analysis was performed to predict ephemeris accuracy for the OD process using a Bayesian least-squares technique. The orbit determination error analysis is essential for maneuver planning and maneuver recovery study. Several tracking scenarios were investigated for each phase of the mission. This paper provides a summary of the premission trajectory covariance error analysis, as well as actual real-time OD results. The use and impact of the various tracking stations, systems, and measurements will be discussed. Details of the operational OD support and the inferred OD accuracy will be presented, and the results will be compared to the premission covariance analysis, In addition, there will be a discussion of the challenges presented to OD support including delta-Vs at apogee as well as perigee, and effects due to spacecraft attitude mode, in light of their implications to the OD accuracy and covariance analysis.

Truong, Son H.↗

NASA NTRS2006

TRMM On-Orbit Performance Re-Accessed After Control Change

The Tropical Rainfall Measuring Mission (TRMM) spacecraft, a joint mission between the U.S. and Japan, launched onboard an HI1 rocket on November 27,1997 and transitioned in August, 2001 from an average operating altitude of 350 kilometers to 402.5 kilometers. Due to problems using the Earth Sensor Assembly (ESA) at the higher altitude, TRMM switched to a backup attitude control mode. Prior to the orbit boost TRMM controlled pitch and roll to the local vertical using ESA measurements while using gyro data to propagate yaw attitude between yaw updates from the Sun sensors. After the orbit boost, a Kalman filter used 3-axis gyro data with Sun sensor and magnetometers to estimate onboard attitude. While originally intended to meet a degraded attitude accuracy of 0.7 degrees, the new control mode met the original 0.2 degree attitude accuracy requirement after improving onboard ephemeris prediction and adjusting the magnetometer calibration onboard. Independent roll attitude checks using a science instrument, the Precipitation Radar (PR) which was built in Japan, provided a novel insight into the pointing performance. The PR data helped identify the pointing errors after the orbit boost, track the performance improvements, and show subtle effects from ephemeris errors and gyro bias errors. It also helped identify average bias trends throughout the mission. Roll errors tracked by the PR from sample orbits pre-boost and post-boost are shown in Figure 1. Prior to the orbit boost the largest attitude errors were due to occasional interference in the ESA. These errors were sometime larger than 0.2 degrees in pitch and roll, but usually less, as estimated from a comprehensive review of the attitude excursions using gyro data. Sudden jumps in the onboard roll show up as spikes in the reported attitude since the control responds within tens of seconds to null the pointing error. The PR estimated roll tracks well with an estimate of the roll history propagated using gyro data. After the orbit boost, the attitude errors shown by the PR roll have a smooth sine-wave type signal because of the way that attitude errors propagate with the use of gyro data. Yaw errors couple at orbit period to roll with '/4 orbit lag. By tracking the amplitude, phase, and bias of the sinusoidal PR roll error signal, it was shown that the average pitch rotation axis tends to be offset from orbit normal in a direction perpendicular to the Sun direction, as shown in Figure 2 for a 200 day period following the orbit boost. This is a result of the higher accuracy and stability of the Sun sensor measurements relative to the magnetometer measurements used in the Kalman filter. In November, 2001 a magnetometer calibration adjustment was uploaded which improved the pointing performance, keeping the roll and yaw amplitudes within about 0.1 degrees. After the boost, onboard ephemeris errors had a direct effect on the pitch pointing, being used to compute the Earth pointing reference frame. Improvements after the orbit boost have kept the the onboard ephemeris errors generally below 20 kilometers. Ephemeris errors have secondary effects on roll and yaw, especially during high beta angle when pitch effects can couple into roll and yaw. This is illustrated in figure 3. The onboard roll bias trends as measured by PR data show correlations with the Kalman filter's gyro bias error. This particularly shows up after yaw turns (every 2 to 4 weeks) as shown in Figure 3, when a slight roll bias is observed while the onboard computed gyro biases settle to new values. As for longer term trends, the PR data shows that the roll bias was influenced by Earth horizon radiance effects prior to the boost, changing values at yaw turns, and indicated a long term drift as shown in Figure 4. After the boost, the bias variations were smaller and showed some possible correlation with solar beta angle, probably due to sun sensor misalignment effects.

Bilanow, Steve↗

NASA NTRS2003

Mars orbits with daily repeating ground traces

This paper derives orbits at Mars with ground traces that repeat at the same times every solar day (sol). A relay orbiter in such an orbit would pass over insitu probes at the same times every sol, ensuring consistent coverage and simplifying mission design and operations. 42 orbits in five classes are characteried: 14 cicular equatorial prograde orbits; 14 circular equatorial retrograde orbits; 11 circular sun synchrounous orbits; 2 eccentroc equatorial orbits; 1 eccentric critcally inclined orbit. the paper reports on the performance of a relay orbiter in some of the orbits.

Mars↗

NASA NTRS1992

Method of delivering lunar generated fluid to earth orbit using an external tank

A method and apparatus are provided for delivering lunar generated fluid to Earth orbit from lunar orbit. Transport takes place in an external tank of a shuttle which has been suitably outfitted in Earth orbit for reusable travel between Earth orbit and a lunar orbit. The outfitting of the external tank includes the adding of an engine, an electrical system, a communication system, a guidance system, an aerobraking device, and a plurality of interconnected fluid storage tanks to the hydrogen and oxygen tanks of the external tank. The external tank is then propelled to lunar orbit the first time using Earth-based propellant. In lunar orbit, the storage tanks are filled with the lunar generated fluid with the remainder tank volumes filled with lunar generated liquid oxygen and hydrogen which serve as propellants for returning the tank to Earth orbit where the fluid is off-loaded. The remaining lunar generated oxygen and hydrogen is then sufficient to return the external tank to lunar orbit so that a subsequent cycle of fluid delivery is repeated. A space station in a higher Earth orbit is preferably used to outfit the external tank, and a lunar node in lunar orbit is used to store and transfer the fluid and liquid oxygen and hydrogen to the external tank. The lunar generated fluid is preferably .sup.3 He.

Butterfield, Ansel J.↗

NASA NTRS2009

Orbital Debris Quarterly News, Volume 13, Issue 4

Although NASA has conducted research on orbital debris since the 1960s, the NASA Orbital Debris Program Office is now considered to have been established in October 1979, following the recognition by senior NASA officials of orbital debris as a space environmental issue and the allocation by NASA Headquarters Advanced Programs Office to the Lyndon B. Johnson Space Center (JSC) of funds specifically dedicated for orbital debris investigations. In the 30 years since, the NASA Orbital Debris Program Office has pioneered the characterization of the orbital debris environment and its potential effects on current and future space systems, has developed comprehensive orbital debris mitigation measures, and has led efforts by the international aerospace community in addressing the challenges posed by orbital debris. In 1967 the Flight Analysis Branch at the Manned Spacecraft Center (renamed the Lyndon B. Johnson Space Center in 1973) evaluated the risks of collisions between an Apollo spacecraft and orbital debris. Three years later the same group calculated collision risks for the forthcoming Skylab space station, which was launched in 1973. By 1976, the nucleus of NASA s yet-to-be-formed orbital debris research efforts, including Andrew Potter, Burton Cour-Palais, and Donald Kessler, was found in JSC s Environmental Effects Office, examining the potential threat of orbital debris to large space platforms, in particular the proposed Solar Power Satellites (SPS).

Liou, Jer-Chyi↗

NASA NTRS2011

Orbit Determination of the SELENE Satellites Using Multi-Satellite Data Types and Evaluation of SELENE Gravity Field Models

The SELENE mission, consisting of three separate satellites that use different terrestrial-based tracking systems, presents a unique opportunity to evaluate the contribution of these tracking systems to orbit determination precision. The tracking data consist of four-way Doppler between the main orbiter and one of the two sub-satellites while the former is over the far side, and of same-beam differential VLBI tracking between the two sub-satellites. Laser altimeter data are also used for orbit determination. The contribution to orbit precision of these different data types is investigated through orbit overlap analysis. It is shown that using four-way and VLBI data improves orbit consistency for all satellites involved by reducing peak values in orbit overlap differences that exist when only standard two-way Doppler and range data are used. Including laser altimeter data improves the orbit precision of the SELENE main satellite further, resulting in very smooth total orbit errors at an average level of 18m. The multi-satellite data have also resulted in improved lunar gravity field models, which are assessed through orbit overlap analysis using Lunar Prospector tracking data. Improvements over a pre-SELENE model are shown to be mostly in the along-track and cross-track directions. Orbit overlap differences are at a level between 13 and 21 m with the SELENE models, depending on whether l-day data overlaps or I-day predictions are used.

Goossens, S.↗

NASA NTRS2012

The Effect of Geocenter Motion on Jason-2 Orbits and the Mean Sea Level

We compute a series of Jason-2 GPS and SLR/DORIS-based orbits using ITRF2005 and the std0905 standards (Lemoine et al. 2010). Our GPS and SLR/DORIS orbit data sets span a period of 2 years from cycle 3 (July 2008) to cycle 74 (July 2010). We extract the Jason-2 orbit frame translational parameters per cycle by the means of a Helmert transformation between a set of reference orbits and a set of test orbits. We compare the annual terms of these time-series to the annual terms of two different geocenter motion models where biases and trends have been removed. Subsequently, we include the annual terms of the modeled geocenter motion as a degree-1 loading displacement correction to the GPS and SLR/DORIS tracking network of the POD process. Although the annual geocenter motion correction would reflect a stationary signal in time, under ideal conditions, the whole geocenter motion is a non-stationary process that includes secular trends. Our results suggest that our GSFC Jason-2 GPS-based orbits are closely tied to the center of mass (CM) of the Earth consistent with our current force modeling, whereas GSFC's SLR/DORIS-based orbits are tied to the origin of ITRF2005, which is the center of figure (CF) for sub-secular scales. We quantify the GPS and SLR/DORIS orbit centering and how this impacts the orbit radial error over the globe, which is assimilated into mean sea level (MSL) error, from the omission of the annual term of the geocenter correction. We find that for the SLR/DORIS std0905 orbits, currently used by the oceanographic community, only the negligence of the annual term of the geocenter motion correction results in a 4.67 plus or minus 3.40 mm error in the Z-component of the orbit frame which creates 1.06 plus or minus 2.66 mm of systematic error in the MSL estimates, mainly due to the uneven distribution of the oceans between the North and South hemisphere.

Melachroinos, S. A.↗

NASA NTRS2012

The Precise Orbit and the Challenge of Long Term Stability

The computation of a precise orbit reference is a fundamental component of the altimetric measurement. Since the dawn of the modern altimeter age, orbit accuracy has been determined by the quality of the GPS, SLR, and DORIS tracking systems, the fidelity of the measurement and force models, and the choice of parameterization for the orbit solutions, and whether a dynamic or a reduced-dynamic strategy is used to calculate the orbits. At the start of the TOPEX mission, the inaccuracies in the modeling of static gravity, dynamic ocean tides, and the nonconservative forces dominated the orbit error budget. Much of the error due to dynamic mismodeling can be compensated by reduced-dynamic tracking techniques depending on the measurement system strength. In the last decade, the launch of the GRACE mission has eliminated the static gravity field as a concern, and the background force models and the terrestrial reference frame have been systematically refined. GPS systems have realized many improvements, including better modeling of the forces on the GPS spacecraft, large increases in the ground tracking network, and improved modeling of the GPS measurements. DORIS systems have achieved improvements through the use of new antennae, more stable monumentation, and of satellite receivers that can track multiple beacons, and as well as through improved modeling of the nonconservative forces. Many of these improvements have been applied in the new reprocessed time series of orbits produced for the ERS satellites, Envisat, TOPEX/Poseidon and the Jason satellites, and as well as for the most recent Cryosat-2 and HY2A. We now face the challenge of maintaining a stable orbit reference for these altimetric satellites. Changes in the time-variable gravity field of the Earth and how these are modelled have been shown to affect the orbit evolution, and the calibration of the altimetric data with tide gauges. The accuracy of the reference frame realizations, and their projection into the future remains a source of error. Other sources of omission error include the geocenter for which no consensus model is as of yet applied. Although progress has been made in nonconservative force modeling through the use of detailed satellite-specific models, radiation pressure modeling, and atmospheric density modeling remain a potential source of orbit error. The longer term influence of variations in the solar and terrestrial radiation fields over annual and solar cycles remains principally untested. Also the long term variation in optical and thermal properties of the space vehicle surfaces would contribute to biases in the orbital frame if ignored. We review the status of altimetric precision orbit determination as exemplified by the recent computations undertaken by the different analysis centers for ERS, Envisat, TOPEX/Poseidon, Jason, Cryosat2 and HY2A, and we provide a perspective on the challenges for future missions such as the Jason-3, SENTINEL-3 and SWOT.

Lemoine, Frank G.↗

NASA NTRS2013

Orbital Transfer Techniques for Round-Trip Mars Missions

The human exploration of Phobos and Deimos or the retrieval of a surface sample launched to low-Mars orbit presents a highly constrained orbital transfer problem. In general, the plane of the target orbit will not be accessible from the arrival or departure interplanetary trajectories with an (energetically optimal) tangential burn at periapsis. The orbital design is further complicated by the addition of a high-energy parking orbit for the relatively massive Deep Space Vehicle to reduce propellant expenditure, while the crew transfers to and from the target orbit in a smaller Space Exploration Vehicle. The proposed strategy shifts the arrival and departure maneuvers away from periapsis so that the apsidal line of the parking orbit lies in the plane of the target orbit, permitting highly efficient plane change maneuvers at apoapsis of the elliptical parking orbit. An apsidal shift during the arrival or departure maneuver is approximately five times as efficient as maneuvering while in Mars orbit, thus significantly reducing the propellant necessary to transfer between the arrival, target, and departure orbits.

human missions↗

NASA NTRS2015

Small Orbital Stereo Tracking Camera Technology Development

On-Orbit Small Debris Tracking and Characterization is a technical gap in the current National Space Situational Awareness necessary to safeguard orbital assets and crew. This poses a major risk of MOD damage to ISS and Exploration vehicles. In 2015 this technology was added to NASA's Office of Chief Technologist roadmap. For missions flying in or assembled in or staging from LEO, the physical threat to vehicle and crew is needed in order to properly design the proper level of MOD impact shielding and proper mission design restrictions. Need to verify debris flux and size population versus ground RADAR tracking. Use of ISS for In-Situ Orbital Debris Tracking development provides attitude, power, data and orbital access without a dedicated spacecraft or restricted operations on-board a host vehicle as a secondary payload. Sensor Applicable to in-situ measuring orbital debris in flux and population in other orbits or on other vehicles. Could enhance safety on and around ISS. Some technologies extensible to monitoring of extraterrestrial debris as well to help accomplish this, new technologies must be developed quickly. The Small Orbital Stereo Tracking Camera is one such up and coming technology. It consists of flying a pair of intensified megapixel telephoto cameras to evaluate Orbital Debris (OD) monitoring in proximity of International Space Station. It will demonstrate on-orbit optical tracking (in situ) of various sized objects versus ground RADAR tracking and small OD models. The cameras are based on Flight Proven Advanced Video Guidance Sensor pixel to spot algorithms (Orbital Express) and military targeting cameras. And by using twin cameras we can provide Stereo images for ranging & mission redundancy. When pointed into the orbital velocity vector (RAM), objects approaching or near the stereo camera set can be differentiated from the stars moving upward in background.

Bryan, Tom↗

NASA NTRS2016

Small Orbital Stereo Tracking Camera Technology Development

On-Orbit Small Debris Tracking and Characterization is a technical gap in the current National Space Situational Awareness necessary to safeguard orbital assets and crew. This poses a major risk of MOD damage to ISS and Exploration vehicles. In 2015 this technology was added to NASA's Office of Chief Technologist roadmap. For missions flying in or assembled in or staging from LEO, the physical threat to vehicle and crew is needed in order to properly design the proper level of MOD impact shielding and proper mission design restrictions. Need to verify debris flux and size population versus ground RADAR tracking. Use of ISS for In-Situ Orbital Debris Tracking development provides attitude, power, data and orbital access without a dedicated spacecraft or restricted operations on-board a host vehicle as a secondary payload. Sensor Applicable to in-situ measuring orbital debris in flux and population in other orbits or on other vehicles. Could enhance safety on and around ISS. Some technologies extensible to monitoring of extraterrestrial debris as well To help accomplish this, new technologies must be developed quickly. The Small Orbital Stereo Tracking Camera is one such up and coming technology. It consists of flying a pair of intensified megapixel telephoto cameras to evaluate Orbital Debris (OD) monitoring in proximity of International Space Station. It will demonstrate on-orbit optical tracking (in situ) of various sized objects versus ground RADAR tracking and small OD models. The cameras are based on Flight Proven Advanced Video Guidance Sensor pixel to spot algorithms (Orbital Express) and military targeting cameras. And by using twin cameras we can provide Stereo images for ranging & mission redundancy. When pointed into the orbital velocity vector (RAM), objects approaching or near the stereo camera set can be differentiated from the stars moving upward in background.

Bryan, Tom↗

NASA NTRS2003

Mars orbits with daily repeating ground traces

This paper derives orbits at Mars with ground traces that repeat at the same times every solar day (sol). A relay orbiter in such an orbit would pass over in-situ probes at the same times every sol, ensuring consistent coverage and simplifying mission design and operations. 42 orbits in five dasses are characterized: 14 circular equatorial prograde orbits 14 circular equatorial retrograde orbits 11 circular sun synchronous orbits 2 eccentric equatorial orbits 1 eccentric critically inclined orbit The paper reports on the performance of a relay orbiter in some of the orbits.

Turner, Andrew↗

NASA NTRS2021

OSIRIS-REx Orbit Trim Strategy

One of the more challenging aspects of the trajectory design for the OSIRIS-REx (Origins, Spectral Interpretation, Resource Identification, and Security-Regolith Explorer) mission at asteroid Bennu was maneuvering while in orbit. The orbital dynamics were highly perturbed by various sources, most notably solar radiation pressure, which degraded accuracy of long term predictions of the spacecraft’s location in orbit. Generally, the Navigation team had to solve three separate issues: correcting a perturbed orbit, changing to a different orbit, or phasing the or bitto place the spacecraft at a specific location at a specific time. The team composed a common framework using up to two maneuvers that could solve all of these problems using an identical schedule that allowed for consistent planning long before the final trajectory could be designed. This orbit trim strategy was successfully used for the first time in the Orbital B phase of the mission to maximize the duration of usable observing geometry in a time-variable orbit with strict operational limits. It was used an additional 3 times throughout the mission to adjust and/or change the orbit, most notably altering the orbit in the weeks prior to the successful Touch-And-Go (TAG)sample collection attempt. This same strategy was used to phase the orbit a total 10 times in preparation for each of the science sorties over potential sample sites, the TAG Rehearsals, and TAG. The trim strategy was demonstrated to be robust and performed exceptionally well in all aspects, which proved critical to a successful sample collection.

Daniel R. Wibben↗

NASA NTRSDate not supplied

Uranus Flagship-class Orbiter and Probe Using Aerocapture

Exploration of the Ice Giants, especially Uranus, via orbiter and atmospheric probes, is required to answer pressing science questions that have been raised in the latest National Academies of Sciences Planetary Decadal Survey. Since the Ice Giants are the farthest planets from Earth, traditional fully-propulsive orbit insertion missions have transit times to the planetary bodies bordering 13-15 years and require a large amount of propellant (wet mass percentages of around 60-70%) for the orbit insertion maneuver, leaving less mass for the scientific payload and a planetary probe. Aerocapture uses aerodynamic forces generated by flight within a planetary atmosphere to decelerate and achieve orbit insertion. Aerocapture has been considered for several past missions but it has not been demonstrated. However, recent developments in thermal protection systems (TPS), guidance and control (G&C), and interplanetary navigation capabilities show the potential for using rigid, heritage entry vehicle configurations already flown at other planetary bodies for Ice Giants aerocapture. Aerocapture can robustly deliver spacecraft to Ice Giant orbits, while substantially increasing on-orbit payload mass (more than 40%) that can be used for a robust atmospheric entry probe. Additionally, the aerocapture maneuver would reduce the interplanetary transit time by 2-5 years (15-30%) relative to fully-propulsive orbit insertion. Recent work has shown that a flagship-class mission can be conducted in a shorter time than fully-propulsive missions if using aerocapture. This paper will consider the merits of including aerocapture as the orbit-insertion mechanism for a Uranus mission. Specifically, the implications of aerocapture orbit insertion for in-situ atmospheric probes will be discussed. The Uranus Orbiter and Probe concept mission study [3] is considered as the potential payload. Results from a recent NASA Space Technology Mission Directorate (STMD)-funded activity that is designing an aerocapture mission for a Uranus orbiter will be presented.

Soumyo Dutta↗

NASA NTRSDate not supplied

Uranus Flagship-class Orbiter and Probe Using Aerocapture

Soumyo Dutta↗

DOE OSTI2020

Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets

Natural orbitals are often used to achieve a more compact representation of correlated wave-functions. Using natural orbitals computed as eigenstates of the virtual–virtual block of the state density matrix instead of the canonical Hartree–Fock orbitals results in smaller errors when the same fraction of virtual space is frozen. This strategy, termed frozen natural orbital (FNO) approach, is effective in reducing the cost of regular coupled-cluster (CC) calculations and some multistate methods, such as EOM-IP-CC (equation-of-motion CC for ionization potentials). This contribution extends the FNO approach to the EOM-SF-CC ansatz (EOM-CC with spin-flip). In contrast to EOM-IP-CCSD, EOM-SF-CCSD relies on high-spin open-shell references. Using FNOs computed for an open-shell reference leads to an erratic behavior of the EOM-SF-CC energies and properties due to an inconsistent truncation of the α and β orbital spaces. A general solution to problems arising in the EOM-CC calculations utilizing open-shell references, termed OSFNO (open-shell FNO), is proposed. Furthermore, by means of singular value decomposition (SVD) of the overlap matrix of the α and β orbitals, the OSFNO algorithm identifies the corresponding orbitals and determines virtual orbitals corresponding to the singly occupied space. This is followed by SVD of the singlet part of the state density matrix in the remaining virtual orbital subspace. The so-computed FNOs preserve the spin purity of the open-shell orbital subspace to the extent allowed by the original reference, thus facilitating a safe truncation of the virtual space. The performance of OSFNO is benchmarked for selected diradicals and triradicals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Cartesian equivariant representations for learning and understanding molecular orbitals

Qualitative and quantitative orbital properties such as bonding/antibonding character, localization, and orbital energies are critical to how chemists understand reactivity, catalysis, and excited-state behavior. Despite this, representations of orbitals in deep learning models have been very underdeveloped relative to representations of molecular geometries and Hamiltonians. Here, we apply state-of-the-art equivariant deep learning architectures to the task of assigning global labels to orbitals, namely energies characterizations, given the molecular coefficients from Hartree–Fock or density functional theory. The architecture we have developed, the Cartesian Equivariant Orbital Network (CEONET), shows how molecular orbital coefficients are readily featurized as equivariant node features common to all graph-based machine-learned potentials. We find that CEONET performs well at predicting difficult quantitative labels such as the orbital energy and orbital entropy. Furthermore, we find that the CEONET representation provides an intuitive latent space for differentiating orbital character for the qualitative assignment of e.g. bonding or antibonding character. In addition to providing a useful representation for further integrating deep learning with electronic structure theory, we expect CEONET to be useful for automatizing and interpreting the results of advanced electronic structure methods such as complete active space self-consistent field theory. In particular, the ability of CEONET to infer multireference character via the orbital entropy paves the way toward the machine-learned selection of active spaces.

chemical reactions↗