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14 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

The utilization of abelian point group symmetry in the graphical unitary group approach to the calculation of correlated electronic wavefunctions

A procedure is described for the utilization of abelian point group symmetry in the graphical unitary group approach (GUGA) to calculations of correlated electronic wavefunctions. The procedure is based on a recursively computed set of symmetry dependent counting indices, and results in the separate numbering, without gaps, of the Gelfand states (configuration functions) belonging to each symmetry species

Shavitt, I.↗
NASA NTRS1979

Crystallography of decahedral and icosahedral particles. I - Geometry of twinning

The crystal structure of the tetrahedral twins in multiply-twinned particles with decahedral and icosahedral point group symmetries has been examined and correlated with the face-centered cubic structure. Details on the crystal structure as well as the geometrical relationships among twins in each particle are presented. These crystallographic facts serve as a basis for the interpretation of small particle images obtained with advanced methods of transmission electron microscopy.

Yang, C. Y.↗
NASA NTRS1982

Electronic levels and charge distribution near the interface of nickel

The energy levels in clusters of nickel atoms were investigated by means of a series of cluster calculations using both the multiple scattering and computational techniques (designated SSO) which avoids the muffin-tin approximation. The point group symmetry of the cluster has significant effect on the energy of levels nominally not occupied. This influences the electron transfer process during chemisorption. The SSO technique permits the approaching atom or molecule plus a small number of nickel atoms to be treated as a cluster. Specifically, molecular levels become more negative in the O atom, as well as in a CO molecule, as the metal atoms are approached. Thus, electron transfer from the nickel and bond formation is facilitated. This result is of importance in understanding chemisorption and catalytic processes.

Waber, J. T.↗
NASA NTRSDate not supplied

Using Anharmonic PAH Vibrational Spectra to Simulate Fully Anharmonic Cascade Emission Spectra

In recent years, we have developed vibrational second-order perturbation theory (VPT2) approaches that can be applied to very large molecules, such as polycyclic aromatic hydrocarbon (PAH) molecules. One of the main difficulties in applying standard VPT2 methods to PAHs is the large number of Fermi resonances that occur, especially in the C-H stretching region of the infrared spectrum. In order to properly account for these resonances, it is necessary to set up resonance polyads for each irreducible representation of the symmetry point group to which the molecule belongs, and for specific wavenumber regions, such as the C-H stretching region. Diagonalization of the polyads allows us to determine vibrational band positions, the intensity sharing due to the resonances, and hence there will be many more vibrational bands present than there are C-H bonds. Using these data, a library of fully anharmonic temperature-dependent spectra, with proper treatment of polyad resonances, can be determined and subsequently used to model the cascade emission spectra of PAH molecules – the type of spectra directly observed by astronomers. The theoretical approach will be described, with comparison to experiment where possible, and the latest fully anharmonic PAH cascade emission spectra will be discussed.

Timothy J Lee↗
NASA NTRS1988

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.↗
NASA NTRS1997

Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

Liu, Yen↗
NASA NTRS1994

Some Aspects of the Implementation of Double Group Symmetry and Electron Correlation in Molecular 4-Component Calculations

The efficient implementation of method for electron correlation in molecular 4-component calculations demands that symmetry be exploited where possible. Algorithms for the construction of matrices and the transformation of integrals over symmetry-adapted basis functions, where the point group is restricted to D(sub 2h) and subgroups, will be presented. The merits of keeping the primitive integrals in the scalar basis will be compared with those of transforming them to the 2-spinor basis.

Dyall, Kenneth G.↗
NASA NTRS1992

Interconversion of diborane(4) isomers

Highly correlated electronic structure computations using many-body perturbation theory and coupled-cluster gradient techniques are used to study the reaction pathway that links the two forms (C2u and D2d) of diborane(4). The results obtained indicate that a low-energy pathway exists for interconversion of the two low-lying isomers of diborane(4). The proposed mechanism consists of a single concerted but nonsynchronous rotation of the BH2 groups. The pathway first follows an idealized reaction coordinate which preserves C2 symmetry, but then bifurcates at a branch point, leading to two equivalent transition states which lack nontrivial elements of symmetry.

Stanton, John F.↗
NASA NTRS2012

Conditions for Symmetries in the Buckle Patterns of Laminated-Composite Plates

Conditions for the existence of certain symmetries to exist in the buckle patterns of symmetrically laminated composite plates are presented. The plates considered have a general planform with cutouts, variable thickness and stiffnesses, and general support and loading conditions. The symmetry analysis is based on enforcing invariance of the corresponding eigenvalue problem for a group of coordinate transformations associated with buckle patterns commonly exhibited by symmetrically laminated plates. The buckle-pattern symmetries examined include a central point of inversion symmetry, one plane of reflective symmetry, and two planes of reflective symmetry.

Nemeth, Michael P.↗
NASA NTRS2002

Nucleation and Growth According to Lysozyme

How does one take a molecule, strongly asymmetric in both shape and charge distribution, and assemble it into a crystal? We propose a model for the nucleation and crystal growth process for tetragonal lysozyme that may be very germane to other monomeric proteins. The first species formed is postulated to be a dimer. Through repeating associations involving the same intermolecular interactions this becomes the 4(sub 3) helix, that in turn serves as the basic unit for nucleation and crystal growth. High salt attenuates surface charges while promoting hydrophobic interactions. Symmetry facilitates helix self-association. Assembly stability is enhanced when a four helix structure is obtained, with each bound to two neighbors. Only two unique interactions are required. The first are those for helix formation, where the dominant interaction is the intermolecular bridging anion. The second is the anti-parallel side-by-side helix-helix interaction, guided by alternating pairs of symmetry related salt bridges along each side. At this stage all eight unique positions of the P4(sub 3)2(sub 1)2(sub 1) unit cell are filled. From the above, the process is one of a) attenuating the most strongly interacting groups, such that b) the molecules begin to self-associate in defined patterns, so that c) symmetry is obtained, which d) propagates as a growing crystal. Simple and conceptually obvious in hindsight, this tells much about what we are empirically doing when we crystallize macromolecules. By adjusting the solution parameters we are empirically balancing the intermolecular interactions, preferentially attenuating the dominant strong (for lysozyme the charged groups) while strengthening the lesser strong (hydrophobic) interactions. Lysozyme is atypical in the breadth of its crystallization conditions; many proteins only crystallize under narrowly defined conditions, pointing to the criticality of the empirical balancing process. Lack of a singularly defined association pathway leads to formation of multiple species, i.e., amorphous precipitation. Weak interactions, such as hydrogen bonds, are promiscuous, serving to strengthen rather than define specific interactions. Participation in an interaction sequesters that surface from subsequent interactions, and we expect the strongest bonds to form first. When two molecules self associate the resulting species will have an axis of symmetry. Subsequent interactions between two associated species having equivalent interactions will also have symmetry. Only a few unique sets of interactions are required to give any of the commonly found space groups for monomeric proteins. This model and what it suggests will be discussed.

Pusey, Marc L.↗
NASA NTRS1993

Dynamics and control of coherent structures in the turbulent wall layer: An overview

We expand the velocity field in the vicinity of the wall in empirical eigenfunctions obtained from experiment. Truncating our system and using Galerkin projection, we obtain a closed set of non-linear ordinary differential equations with ten degrees of freedom. We find a rich dynamical behavior, including in particular a heteroclinic attracting orbit giving rise to intermittency. The intermittent jump from one attracting point to the other resembles in many respects the bursts observed in experiments. Specifically, the time between jumps and the duration of the jumps, is approximately that observed in a burst; the jump begins with the formation of a narrowed and intensified updraft, like the ejection phase of a burst, and is followed by a gentle, diffuse downdraft like the sweep phase of a burst. The magnitude of the Reynolds stress spike produced during a burst is limited by our truncation. The behavior is quite robust, much of it being due to the symmetries present (Aubry's group has examined dimensions up to 128 with persistence of the global behavior). We have examined eigenvalues and coefficients obtained from experiment, and from exact simulation, which differ in magnitude. Similar behavior is obtained in both cases; in the latter case, the heteroclinic orbits connect limit cycles instead of fixed points, corresponding to cross-stream waving of the streamwise rolls. The bifurcation diagram remains structurally similar, but somewhat distorted. The role of the pressure term is made clear - it triggers the intermittent jumps, which otherwise would occur at longer and longer intervals, as the system trajectory is attracted closer and closer to the heteroclinic cycle. The pressure term results in the jumps occurring at essentially random times, and the magnitude of the signal determines the average timing. Stretching of the wall region shows that the model is consistent with observations of polymer drag reduction. Change of the third order coefficients, corresponding to acceleration or deceleration of the mean flow, changes the heteroclinic cycles from attracting to repelling, increasing or decreasing the stability, in agreement with observations. The existence of fixed points is an artifact introduced by the projection; however, a decoupled model still displays the rich dynamics. Numerous assumptions made in Aubry et al. (1988) can now be proved exactly. Feeding back eigenfuncitons with the proper phase can delay the bursting, (the heteroclinic jump to the other fixed point), decreasing the drag. It is also possible to speed up the bursting, increasing mixing to control separation. Our approach is optimal for short time tracking in control.

Berkooz, Gal↗
NASA NTRS1998

Molecular Static Third-Order Polarizabilities of Carbon-Cage Fullerene and Their Correlation with Three Geometric Properties: Symmetry, Aromaticity, and Size

The static third-order polarizabilities (gamma) of C60, C70, five isomers of C78 and two isomers of C84 were analyzed in terms of three properties, from a geometric point of view: symmetry, aromaticity and size. The polarizability values were based on the finite field approximation using a semiempirical Hamiltonian (AM1) and applied to molecular structures obtained from density functional theory calculations. Symmetry was characterized by the molecular group order. The selection of 6-member rings as aromatic was determined from an analysis of bond lengths. Maximum interatomic distance and surface area were the parameters considered with respect to size. Based on triple linear regression analysis, it was found that the static linear polarizability (alpha) and gamma in these molecules respond differently to geometrical properties: alpha depends almost exclusively on surface area while gamma is affected by a combination of number of aromatic rings, length and group order, in decreasing importance. In the case of alpha, valence electron contributions provide the same information as all-electron estimates. For gamma, the best correlation coefficients are obtained when all-electron estimates are used and when the dependent parameter is ln(gamma) instead of gamma.

Moore, C. E.↗
NASA NTRS1977

Corrections for atmospheric refractivity in satellite laser ranging

The effects of departures from the spherical symmetry assumption are investigated by describing the refractivity profile on the earth's surface as a generalized function of the surface coordinates. Aspects of satellite ranging geometry are considered and the representation of the true group refractivity of the atmosphere at any point on the earth's surface is discussed. Surface meteorological data obtained from a few east coast weather stations are analyzed to obtain typical values of the higher order bias terms.

Iyer, R. S.↗
NASA NTRS2000

Cross-Linking Studies of Lysozyme Nucleation

Tetragonal chicken egg white crystals consist of 4(sub 3) helices running in alternating directions, the helix rows having a two fold symmetry with each other. The unit cell consists of one complete tetrameric turn from each of two adjacent helices (an octamer). PBC analysis indicates that the helix intermolecular bonds are the strongest in the crystal, therefore likely formed first. AFM analysis of the (110) surface shows only complete helices, no half steps or bisected helices being found, while AFM line scans to measure the growth step increments show that they are multiples of the 4(sub 3) helix tetramer dimensions. This supports our thesis that the growth units are in fact multiples of the four molecule 4(sub 3) helix unit, the "average" growth unit size for the (110) face being an octamer (two turns about the helix) and the (101) growth unit averaging about the size of a hexamer. In an effort to better understand the species involved in the crystal nucleation and growth process, we have initiated an experimental program to study the species formed in solution compared to what is found in the crystal through covalent cross-linking studies. These experiments use the heterobifunctional cross-linking agent aminoethyl-4-azidonitroanaline (AEANA). An aliphatic amine at one end is covalently attached to the protein by a carbodiimide-mediated reaction, and a photo reactive group at the other can be used to initiate crosslinking. Modifications to the parent structure can be used to alter the distance between the two reactive groups and thus the cross-linking agents "reach". In practice, the cross-linking agent is first coupled to the asp101 side chain through the amine group. Asp101 lies within the active site cleft, and previous work with fluorescent probes had shown that derivatives at this site still crystallize in the tetragonal space group. This was also found to be the case with the AEANA derivative, which gave red tetragonal crystals. The protein now has a reactive group that can be photoactivated at a specific point in the nucleation or crystal growth process to "capture" protein molecules bound within reach of the crosslinking agent. If those bound protein molecules have a defined geometric relationship with the capturing molecule, such as would be found in a crystal, then the photoreacted cross-linking site should be consistent. Random protein interactions, typical of an amorphous precipitate or interaction, would show a random cross-linking reaction. The results of these and other experiments will be presented.

Forsythe, Elizabeth↗