Search NASA⌕ Search

SEARCH · Search NASA

Results for “WAVE FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Optical Imaging and Radiometric Modeling and Simulation

OPTOOL software is a general-purpose optical systems analysis tool that was developed to offer a solution to problems associated with computational programs written for the James Webb Space Telescope optical system. It integrates existing routines into coherent processes, and provides a structure with reusable capabilities that allow additional processes to be quickly developed and integrated. It has an extensive graphical user interface, which makes the tool more intuitive and friendly. OPTOOL is implemented using MATLAB with a Fourier optics-based approach for point spread function (PSF) calculations. It features parametric and Monte Carlo simulation capabilities, and uses a direct integration calculation to permit high spatial sampling of the PSF. Exit pupil optical path difference (OPD) maps can be generated using combinations of Zernike polynomials or shaped power spectral densities. The graphical user interface allows rapid creation of arbitrary pupil geometries, and entry of all other modeling parameters to support basic imaging and radiometric analyses. OPTOOL provides the capability to generate wavefront-error (WFE) maps for arbitrary grid sizes. These maps are 2D arrays containing digital sampled versions of functions ranging from Zernike polynomials to combination of sinusoidal wave functions in 2D, to functions generated from a spatial frequency power spectral distribution (PSD). It also can generate optical transfer functions (OTFs), which are incorporated into the PSF calculation. The user can specify radiometrics for the target and sky background, and key performance parameters for the instrument s focal plane array (FPA). This radiometric and detector model setup is fairly extensive, and includes parameters such as zodiacal background, thermal emission noise, read noise, and dark current. The setup also includes target spectral energy distribution as a function of wavelength for polychromatic sources, detector pixel size, and the FPA s charge diffusion modulation transfer function (MTF).

Ha, Kong Q.↗
NASA NTRS2003

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

Shertzer, Janine↗
NASA NTRS1992

The optimization of single mode basis functions for polyatomic vibrational problems with application to the water molecule

The optimization of the wave functions is considered for coupled vibrations represented by linear combinations of products of functions depending only on a single vibrational coordinate. The functions themselves are optimized as well as configuration list. For the H2O molecule highly accurate results are obtained for the lowest 15 levels using significantly shorter expansions than would otherwise be possible.

Schwenke, David W.↗
NASA NTRS1985

Modeling of pressure-induced far-infrared absorption spectra Molecular hydrogen pairs

Meyer et al. (1985) have calculated the accurate induced dipole moment function of H2-H2 from first principles, using highly correlated wave functions for the first time in such work. The present paper is concerned with the collision-induced translational-rotational absorption coefficient for molecular hydrogen pairs, taking into account computations on the basis of the fundamental theory considered by Meyer et al. Data have been obtained for temperatures in the range from 40 to 300 K. Criteria are developed for choosing among various model line shapes. It is found that certain models are capable of approximating the quantum profiles closely, with rms errors of only a few percent.

Borysow, J.↗
NASA NTRS2002

First Principle Predictions of Isotopic Shifts in H2O

We compute isotope independent first and second order corrections to the Born-Oppenheimer approximation for water and use them to predict isotopic shifts. For the diagonal correction, we use icMRCI wavefunctions and derivatives with respect to mass dependent, internal coordinates to generate the mass independent correction functions. For the non-adiabatic correction, we use scaled SCF/CIS wave functions and a generalization of the Handy method to obtain mass independent correction functions. We find that including the non-adiabatic correction gives significantly improved results compared to just including the diagonal correction when the Born-Oppenheimer potential energy surface is optimized for H2O-16. The agreement with experimental results for deuterium and tritium containing isotopes is nearly as good as our best empirical correction, however, the present correction is expected to be more reliable for higher, uncharacterized levels.

Schwenke, David W.↗
NASA NTRS1979

Sound radiation from hyperboloidal inlet ducts

This paper presents rigorous solutions for the problem of sound radiation from various inlet ducts including hyperboloidal (or hyperbolic) inlet ducts and circular ducts with wide flange. The numerical results include the complex conversion (or reflection) coefficients and the radiation directivity for the various incident wave modes - spinning modes as well as axisymmetric modes. The analysis utilizes hyperboloidal wave functions which are defined here as a class of eigensolutions of the wave equation for oblate spheroidal coordinates, and is valid for the whole frequency range including frequencies above and below the cutoff frequencies of duct modes involved.

Cho, Y. C.↗
NASA NTRS1985

The exact eigenfunctions and eigenvalues of a two-dimensional rigid rotor obtained using Gaussian wave packet dynamics

Exact eigenfunctions for a two-dimensional rigid rotor are obtained using Gaussian wave packet dynamics. The wave functions are obtained by propagating, without approximation, an infinite set of Gaussian wave packets that collectively have the correct periodicity, being coherent states appropriate to this rotational problem. This result leads to a numerical method for the semiclassical calculation of rovibrational, molecular eigenstates. Also, a simple, almost classical, approximation to full wave packet dynamics is shown to give exact results: this leads to an a posteriori justification of the De Leon-Heller spectral quantization method.

Reimers, J. R.↗
DOE OSTI2025

Electronic structure and exchange interactions in altermagnetic MnGeP 2 in the quasiparticle self-consistent G W approach

The quasiparticle self-consistent 𝐺⁡𝑊 method is used to study the electronic band structure, optical dielectric function, and exchange interactions in chalcopyrite, 𝐼⁢ ‾ 4 ⁢2⁢𝑑, structure MnGeP 2 . The material is found to be an antiferromagnetic semiconductor with a lowest direct gap of 2.44 eV at the Γ point and a lower indirect gap of 1.87 eV from Γ to 𝑀. The material is an altermagnet because the two magnetic atoms of opposite spin are related by a twofold rotation operation perpendicular to the main fourfold rotation inversion axis. The spin splittings along a low symmetry line like 𝑃⁢𝑁 is sizable while at k points on the diagonal mirror planes or on the twofold symmetry axes the spin splitting is zero. The exchange interactions are calculated using a linear response approach. The antiferromagnetic exchange interaction between nearest neighbors in the primitive unit cell is dominating and found to be slightly decreasing upon carrier doping but not sufficiently to change the interaction to become ferromagnetic. The bare (noninteracting) and interacting transverse spin susceptibilities, which provide interatomic site exchange interactions after averaging over the muffin-tin spheres, are calculated from the 𝐺⁡𝑊 band structure and wave functions. From these exchange interactions, the spin wave spectra are obtained along the high symmetry lines and the Néel temperature is calculated using the mean-field and Tyablikov estimations. The dielectric function and the optical absorption spectra are calculated including excitonic effects using the Bethe Salpeter equation. The exchange interactions around Mn Ge defect sites is also studied. While we find it can generate ferromagnetic interactions with neighboring spins, we did not find direct evidence of producing an overall ferromagnetic phase. First, if Mn antisites are introduced by exchanging Mn with a nearby Ge, the interactions stay largely antiferromagnetic. Second, when we add additional Mn, in other words in Mn-rich stoichiometry, the Mn Ge antisites produce a strong ferromagnetic interaction primarily with the Mn in the same basal plane but weaker ferromagnetic interaction with adjacent plane Mn. The interactions between regular lattice Mn stay antiferromagnetic as before and thus favor keeping the antiferromagnetic order along the [001] direction. Adding Mn antisites, however, does lead to a metallic band structure.

36 MATERIALS SCIENCE↗
NASA NTRS1985

Photodetachment of the positronium negative ion

The photodetachment cross section of the negative positronium ion is calculated. The description of the initial bound state is simplified by representing it by an asymptotic form whose normalization comes from the most accurate Hylleraas wave function of the ion. The final state is assumed to be a plane wave.

Bhatia, A. K.↗
NASA NTRS1984

Experimental Determination of the 1 Sigma(+) State Electric-Dipole-Moment Function of Carbon Monoxide up to a Large Internuclear Separation

Experimental intensity information is combined with numerically obtained vibrational wave functions in a nonlinear least squares fitting procedure to obtain the ground electronic state electric-dipole-moment function of carbon monoxide valid in the range of nuclear oscillation (0.87 to 1.01 A) of about the V = 38th vibrational level. Mechanical anharmonicity intensity factors, H, are computed from this function for delta V + = 1, 2, 3, with or = to 38.

Chackerian, C., Jr.↗
NASA NTRS1984

Experimental determination of the 1 Sigma(+) state electric dipole moment function of carbon monoxide up to a large internuclear separation

Experimental intensity information is combined with numerically obtained vibrational wave functions in a nonlinear least-squares fitting procedure to obtain the ground electronic state electric dipole moment function of carbon monoxide valid in the range of nuclear oscillation (0.87-1.91 A) of about the V = 38th vibrational level. Vibrational transition matrix elements are computed from this function for Delta V = 1, 2, 3 with V not more than 38.

Chackerian, C., Jr.↗
NASA NTRS1983

Theoretical study of NH2 - Potential curves, transition moments, and photodissociation cross sections

Photodissociation cross sections from the ground state of NH2 have been calculated using a pseudodiatomic model. The potential curves needed in these calculations, functions of one NH bond length, were obtained by ab initio MCSCF calculations on the five lowest doublet states of NH2 using a contracted Gaussian basis set of double zeta quality augmented by polarization and Rydberg functions. Transition dipole moments between the ground and excited states were evaluated using MCSCF wave functions.

Saxon, R. P.↗
NASA NTRSDate not supplied

Metal Hydroxide and Oxyhydroxide Gas Database

In a high temperature combustion situation such as a gas turbine or rocket engine, combustion products include water vapor. This water vapor reacts with oxides in the hot-gas-path to form volatile hydroxides and oxyhydroxides. The oxides may be structural oxide components or protective oxides on alloys or non-oxide ceramics. In either case, this enhanced volatilization leads to degradation of components. Reliable thermochemical data for many metal hydroxides and oxyhydroxides has not been available. We review a database put together at NASA over many years based on experimental and ab initio computations for thermochemical data of Al, Si, Ti, Cr, Mn, Y, Zr, La, Ta, Gd, and Yb hydroxides and oxyhydroxides. Experimental methods for measuring thermodynamic quantities of metal hydroxides and oxyhydroxides are limited since the required high temperatures and high pressures preclude many conventional methods. Nonetheless, transpiration has proven a valuable tool in our laboratories for the Si-O-H, Cr-O-H, and Ti-O-H systems. Data are analyzed with second and third law methods. These data can be leveraged with quantum chemistry to provide reliable free energy functions for the third law calculation and comparison to the derived enthalpies of formation. Both wave function and DFT methods can be utilized for deriving the thermodynamic functions for the various metal hydroxides and oxyhydroxides. We have found that, in general, reasonable molecular geometries and spectroscopic data can be derived with a relatively low level of theory, i.e. DFT with the B3LYP functional. Accurate calculations of the enthalpy of formation require higher levels of theory, such as the Coupled Cluster, Singles, Doubles, and perturbative Triples CCSD(T) approach with complete basis sets (CBS). Also, corrections for hindered rotations and anharmonicity are necessary. For some symmetries, the anharmonic correction has proven to be a challenge and we have found that this is only treated properly by certain codes. The database lists the fHo(298), So(298), and Cp in the form Cp = A + BT + CT2 + D/T + E/T2, where A, B, C, D, and E are the fitting constants. Thus, it can be easily used in any of the common computational thermochemistry codes. To date, the database contains 51 gaseous species of the formula MOx(OH)y.

Metal Hydroxides↗
DOE OSTI2024

Quantum tensor network algorithms for evaluation of spectral functions on quantum computers

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we call a quantum tensor network (QTN), we demonstrate algorithms to prepare ground and excited states on a quantum computer and apply them to molecular nanomagnets (MNMs) as a paradigmatic example. In this setting, we develop two approaches for extracting the spectral correlation functions measured in neutron-scattering experiments: (a) a generalization of the SWAP test for computing wave function overlaps and, (b) a generalization of the notion of matrix product operators to the QTN setting which generates a linear combination of unitaries. The latter method is discussed in detail for translationally invariant spin-half systems, where it is shown to reduce the qubit resource requirements compared with the SWAP method and may be generalized to other systems. We demonstrate the versatility of our approaches by simulating spin-1/2 and spin-3/2 MNMs, with the latter being an experimentally relevant model of a Cr$^{3+}_{8}$ ring. Here, our approach has qubit requirements that are independent of the number of constituents of the many-body system and scale only logarithmically with the bond dimension of the MPS representation, making them appealing for implementation on near-term quantum hardware with mid-circuit measurement and reset.

Neutron scattering↗
NASA NTRS1981

A theoretical study of selected singlet and triplet states of CO molecule

The results of the configuration calculations of six singlet electronic states and one triplet electronic state of CO are presented. The potential energy curves, spectroscopic constants, and electron transition moments are calculated, along with electronic dipole moment functions for three states. The self consistent field and configuration calculations used to obtain the electronic wave functions are described. The theoretical results are found to be in good agreement with the experimental measurements, and in the case of the dipole moment function calculations, preferable to them.

Cooper, D. M.↗
NASA NTRS1983

A comment on some drawbacks of monostatic radars

All Mesosphere, Stratosphere, Troposphere (MST) radars now in operation or under construction use the monostatic mode, that is to say, the same antenna for both transmitting and receiving. Consequently, it is never possible to determine more than one component of the atmospheric velocity at one point in space. Two important properties of gravity waves which are difficult if not impossible to determine by the monostatic method are discussed. The first of these is the polarization of the gravity waves; that is, the complex ratio of the wave functions of vertical and horizontal motion. A second quantity of importance is the horizontal wavelength of gravity waves. Both of these problems could be overcome by use of a bistatic system. Such a system has the additional advantage of making it possible to measure at very low altitudes, and to look away from the transmitter (for example to make a horizontal section through a thunderstorm). However, bistatic operation, in the practical sense, requires not only an additional highly directive antenna, but also that both the transmitting and receiving antennas should be fully steerable.

Bowhill, S. A.↗