Natural orbitals for H sub 2.
Natural orbital expansion coefficients of LCAO-MO-SCF-CI wave functions for ground state of H molecule
Barker, W. H.↗
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General contraction of Gaussian basis sets. Part 2: Atomic natural orbitals and the calculation of atomic and molecular properties
A recently proposed scheme for using natural orbitals from atomic configuration interaction (CI) wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outmost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital (ANO) sets.
Almloef, Jan↗
General contraction of Gaussian basis sets. II - Atomic natural orbitals and the calculation of atomic and molecular properties
A recently proposed scheme for using natural orbitals from atomic configuration interaction wave functions as a basis set for linear combination of atomic orbitals (LCAO) calculations is extended for the calculation of molecular properties. For one-electron properties like multipole moments, which are determined largely by the outermost regions of the molecular wave function, it is necessary to increase the flexibility of the basis in these regions. This is most easily done by uncontracting the outermost Gaussian primitives, and/or by adding diffuse primitives. A similar approach can be employed for the calculation of polarizabilities. Properties which are not dominated by the long-range part of the wave function, such as spectroscopic constants or electric field gradients at the nucleus, can generally be treated satisfactorily with the original atomic natural orbital sets.
Almlof, Jan↗
Nonorthogonal natural orbitals from open-shell configuration-interaction calculations.
Natural orbitals calculated from spin free one density matrix of open shell limited configuration-interaction wave function constructed from nonorthogonal basis
Heaton, M.↗
Atomic Natural Orbital Basis Sets for Transition Metals
We show that atomic natural orbitals are an excellent way to contract transition-metal basis sets, even though the different low-lying electronic states may have very different basis set requirements.
Bauschlicher, Charles W., Jr.↗
Large Atomic Natural Orbital Basis Sets for the First Transition Row Atoms
Large atomic natural orbital (ANO) basis sets are tabulated for the Sc to Cu. The primitive sets are taken from the large sets optimized by Partridge, namely (21s 13p 8d) for Sc and Ti and (20s 12p 9d) for V to Cu. These primitive sets are supplemented with three p, one d, six f, and four g functions. The ANO sets are derived from configuration interaction density matrices constructed as the average of the lowest states derived from the 3d(sup n)4s(sup 2) and 3d(sup n+1)4s(sup 1) occupations. For Ni, the 1S(3d(sup 10)) state is included in the averaging. The choice of basis sets for molecular calculations is discussed.
Bauschlicher, Charles W., Jr.↗
Unoccupied natural orbitals of two-electron wave-functions.
Functions complementing set of occupied natural orbitals on two-electron wave functions
Nazaroff, G. V.↗
Natural orbital environment definition guidelines for use in aerospace vehicle development
This document provides definitions of the natural near-Earth space environment suitable for use in the initial development/design phase of any space vehicle. The natural environment includes the neutral atmosphere, plasma, charged particle radiation, electromagnetic radiation (EMR), meteoroids, orbital debris, magnetic field, physical and thermal constants, and gravitational field. Communications and other unmanned satellites operate in geosynchronous-Earth orbit (GEO); therefore, some data are given for GEO, but emphasis is on altitudes from 200 km to 1000 km (low-Earth orbit (LEO)). This document does not cover the induced environment of other effects resulting from presence of the space vehicle. Manmade factors are included as part of the ambient natural environment; i.e., orbital debris and radio frequency (RF) noise generated on Earth, because they are not caused by the presence of the space vehicle but form part of the ambient environment that the space vehicle experiences.
Anderson, B. Jeffrey↗
COMPARISON OF THE HARTREE-FOCK ORBITAL WITH THE FIRST NATURAL SPIN ORBITAL FOR TWO-ELECTRON SYSTEMS
Comparison of hartree-fock orbital with first natural spin orbital for two-electron system
GROUND STATE↗
Symmetry and equivalence restrictions in electronic structure calculations
A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalnece restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction.
Bauschlicher, Charles W., Jr.↗
Analytical and experimental vibration studies of a 1/8-scale shuttle orbiter
Natural frequencies and mode shapes for four symmetric vibration modes and four antisymmetric modes are compared with predictions based on NASTRAN finite-element analyses. Initial predictions gave poor agreement with test data; an extensive investigation revealed that the major factors influencing agreement were out-of-plane imperfections in fuselage panels and a soft fin-fuselage connection. Computations with a more refined analysis indicated satisfactory frequency predictions for all modes studied, within 11 percent of experimental values.
Pinson, L. D.↗
On the 3d2 4s2, 3d3 4s1, and 3d4 states of Ti
The energies of the 3F (3d2 4s2), 5F (3d3 4s1) and 5D (3d4) states of Ti are investigated on the basis of MCSCF and CI calculations. Following SCF calculations using a basis set including the primitive set of Wachters (1970) and the diffuse d function of Hay (1977), four full-electron CI calculations involving the 3d and 4s electrons were performed to obtain the natural orbitals, and the full CI calculations were repeated. MCSCF calculations then performed using the most important configurations of the natural orbital basis are found to be in agreement with those of Dunning (1980), but to differ from CI results. CI(SD) calculations including single and double excitations from the MCSCF reference are found to be in agreement with the full CI but differ from experimental energy separations. Further calculations reveal that Dunning's MCSCF description is an oversimplication of the problem, and that the 5F-5D separation at the CI(SD) level is in good agreement with experiment for all basis sets but the 3F state is too low relative to the 5F and 5D states.
Bauschlicher, C. W., Jr.↗
Natural and orbital debris particles on LDEF's trailing and forward-facing surfaces
Approximately 1000 impact craters on the Chemistry of Meteoroid Experiment (CME) have been analyzed by means of Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Analysis (EDXA) to determine the compositional make-up of projectile residues. This report completes our systematic survey of gold and aluminum surfaces exposed at the trailing-edge (A03) and forward-facing (A11) LDEF sites, respectively. The major categories for the projectile residues were (1) natural, with diverse subgroups such as chondritic, monomineralic silicates, and sulfides, and (2) man made, that were classified into aluminum (metallic or oxide) and miscellaneous materials (such as stainless steel, paint flakes, etc). On CME gold collectors on LDEF's trailing edge approximately 11 percent of all craters greater than 100 micron in diameter were due to man-made debris, the majority (8.6 percent) caused by pure aluminum, approximately 31.4 percent were due to cosmic dust, while the remaining 58 percent were indeterminate via the analytical techniques utilized in this study. The aluminum surfaces located at the A11 forward-facing site did not permit analysis of aluminum impactors, but approximately 9.4 percent of all craters were demonstratably caused by miscellaneous debris materials and approximately 39.2 percent were the result of natural particles, leaving approximately 50 percent which were indeterminate. Model considerations and calculations are presented that focus on the crater-production rates for features greater than 100 micron in diameter, and on assigning the intermediate crater population to man-made or natural particles. An enhancement factor of 6 in the crater-production rate of natural impactors for the 'forward-facing' versus the 'trailing-edge' CME collectors was found to best explain all observations (i.e., total crater number(s), as well as their computational characteristics). Enhancement factors of 10 and 4 are either too high or too low. It is also suggested that approximately 45 percent of all craters greater than 100 micron in diameter are caused by man-made impactors on the A11 surfaces. This makes the production rate for craters greater than 100 micron in diameter, resulting from orbital debris, a factor of 40 higher on the forward-facing sides as opposed to the trailing-edge direction.
Hoerz, Friedrich↗
Toward immersive spacecraft trajectory design: Mapping user drawings to natural periodic orbits
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Dhathri H. Somavarapu↗
A simultaneous estimation of the mass of Mars and its natural satellites, Phobos and Deimos, from the orbital perturbations on the Mariner 9, Viking 1, and Viking 2 orbiters
The natural satellites of Mars, Phobos and Deimos, caused perturbations on the orbits of the Mariner 9, and the Viking spacecraft that were used to estimate the satellite masses. The Viking spacecraft were specifically targeted to make close flybys (within a few hundred kilometers) of Phobos in February 1977 and of Deimos in October 1977. These close encounters were used to estimate the moon's gravitational constant, GM (the universal constant of gravitation multiplied by the satellite mass). However, the Viking and Mariner 9 spacecraft made numerous flybys of Phobos and Deimos at distances of a few thousand kilometers. The tracking data from these more 'distant' encounters were processed to estimate the masses of Mars, Phobos, and Deimos.
Lemoine, F. G.↗
Large manned systems/environment interactions in Low Earth Orbit (LEO)
With the advent of the NASA Space Transportation System, regular flights of a large manned spacecraft, the Space Shuttle Orbiter, became a reality. From the earliest mission containing space science instruments as a payload on the third flight of the Orbiter (STS-3), it became apparent that the disturbance caused by the interaction of this orbiting system with the low Earth orbit (LEO) environment resulted in adverse conditions for the performance of scientific observations of the Orbiter natural environment and for certain high sensitivity optical observations. The interaction of the Space Shuttle Orbiter system can be divided into two parts, the structure-environment interaction, and the outgas cloud-environment interaction. These interaction are briefly discussed.
Raitt, W. J.↗
Analyzing the Impacts of Natural Environments on Launch and Landing Availability for NASA's Eploration Systems Development Programs
NASA is developing new capabilities for human and scientific exploration beyond Earth orbit. Natural environments information is an important asset for NASA's development of the next generation space transportation system as part of the Exploration Systems Development Program, which includes the Space Launch System (SLS) and MultiPurpose Crew Vehicle (MPCV) Programs. Natural terrestrial environment conditions - such as wind, lightning and sea states - can affect vehicle safety and performance during multiple mission phases ranging from prelaunch ground processing to landing and recovery operations, including all potential abort scenarios. Space vehicles are particularly sensitive to these environments during the launch/ascent and the entry/landing phases of mission operations. The Marshall Space Flight Center (MSFC) Natural Environments Branch provides engineering design support for NASA space vehicle projects and programs by providing design engineers and mission planners with natural environments definitions as well as performing custom analyses to help characterize the impacts the natural environment may have on vehicle performance. One such analysis involves assessing the impact of natural environments to operational availability. Climatological time series of operational surface weather observations are used to calculate probabilities of meeting or exceeding various sets of hypothetical vehicle-specific parametric constraint thresholds.
Altino, Karen M.↗
Analyzing the Impacts of Natural Environments on Launch and Landing Availability for NASA's Exploration Systems Development Programs
The National Aeronautics and Space Administration (NASA) is developing new capabilities for human and scientific exploration beyond Earth orbit. Natural environments information is an important asset for NASA's development of the next generation space transportation system as part of the Exploration Systems Development (ESD) Programs, which includes the Space Launch System (SLS) and Multi-Purpose Crew Vehicle (MPCV) Programs. Natural terrestrial environment conditions - such as wind, lightning and sea states - can affect vehicle safety and performance during multiple mission phases ranging from pre-launch ground processing to landing and recovery operations, including all potential abort scenarios. Space vehicles are particularly sensitive to these environments during the launch/ascent and the entry/landing phases of mission operations. The Marshall Space Flight Center (MSFC) Natural Environments Branch provides engineering design support for NASA space vehicle projects and programs by providing design engineers and mission planners with natural environments definitions as well as performing custom analyses to help characterize the impacts the natural environment may have on vehicle performance. One such analysis involves assessing the impact of natural environments to operational availability. Climatological time series of operational surface weather observations are used to calculate probabilities of meeting/exceeding various sets of hypothetical vehicle-specific parametric constraint thresholds. Outputs are tabulated by month and hour of day to show both seasonal and diurnal variation. This paper will discuss how climate analyses are performed by the MSFC Natural Environments Branch to support the ESD Launch Availability (LA) Technical Performance Measure (TPM), the SLS Launch Availability due to Natural Environments TPM, and several MPCV (Orion) launch and landing availability analyses - including the 2014 Orion Exploration Flight Test 1 (EFT-1) mission.
Altino, Karen M.↗