A density matrix approach to multiconfiguration calculations
Density matrix components for multiconfiguration wave functions, constructing N electron /spin free/ Hamiltonian configuration interaction matrix
Harriman, J. E.↗
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Resonance Scattering of Fe XVII X-Ray and EUV Lines
Over the years a number of calculations have been carried out to derive intensities of various X-ray and EUV lines in Fe XVII to compare with observed spectra. The predicted intensities have not agreed with solar observations, particularly for the line at 15.02 Angstroms; resonance scattering has been suggested as the source for much of the disagreement. The atomic data calculated earlier used seven configurations, 2s(sup 2) 2p(sup 6),2s(sup 2) 2p(sup 5)3s, 2s(sup 2) 2p(sup 5)3p, 2s(sup 2)2p(sup 5)3d, 2s2 p(sup 6)3s, 2s2p(sup 6)3p, and 2s2p(sup 6)3d, having n=3 orbitals and the scattering calculations in the distorted wave approximation were carried out only for incident energies above the threshold of the highest fine-structure level. These calculations have now been extended to thirteen configurations by adding six more configurations having n=4 orbitals, namely 2s(sup 2) 2p(sup 5)4s, 2s(sup 2) 2p(sup 5)4p, 2s(sup 2) 2p(sup 5)4d, 2s2p(sup 6)4s, 2s2p(sup 6)4p, and 2s2p(sup 6)4d, giving rise to 73 fine structure levels. The scattering calculations are carried out below as well as above the threshold of the highest fine-structure level. The incident energies below the threshold are 55.8, 65, 70, and 76 Ry and those above are 85, 127.5, 170, 212.5, 255, 340, and 425 Ry. The collision strengths are calculated up to total angular momentum L(sup T) = 33. Level populations and intensity ratios are calculated at various electron temperatures and densities. It is not possible to predict how the ratios would change when configurations with n=5 and 6 orbitals are added but some estimates have been made for a few transitions by Liedhal, who indicates an asymptotic convergence when n=5 and 6 orbitals are added. These improved calculations of Fe XVII change the intensity ratios compared to those obtained earlier, bringing the optically thin F(15.02)/F(16.78) ratio and several other ratios closer to the observed values: However, some disagreement with the solar observations still persists, even though the agreement of the presently calculated optically thin F(15.02)/F(15.26) ratio with the experimental results of Brown et al. and Laming et al. has improved. Some of the remaining discrepancy is still thought to be the effect of opacity, which is consistent with expected physical conditions for solar sources. EUV intensity ratios are also calculated and compared with observations. Level populations and intensity ratios are calculated, as a function of column density of Fe XVII, in the slab and cylindrical geometries. As found previously, the predicted intensities for the resonance lines at 15.02 and 15.26 Angstroms exhibit initial increases in flux relative to the forbidden line at 17.10 Angstroms and the resonance line at 16.78 Angstroms as optical thickness increases. The same behavior is predicted for the lines at 12.262 and 12.122 Angstroms. Predicted intensities for some of the allowed EUV lines are also affected by opacity.
Bhatia, A. K.↗
An improved exceedance theory for combined random stresses
An extension is presented of Rice's classic solution for the exceedances of a constant level by a single random process to its counterpart for an n-dimensional vector process. An interaction boundary, analogous to the constant level considered by Rice for the one-dimensional case, is assumed in the form of a hypersurface. The theory for the numbers of boundary exceedances is developed by using a joint statistical approach which fully accounts for all cross-correlation effects. An exact expression is derived for the n-dimensional exceedance density function, which is valid for an arbitrary interaction boundary. For application to biaxial states of combined random stress, the general theory is reduced to the two-dimensional case. An elliptical stress interaction boundary is assumed and the exact expression for the density function is presented. The equations are expressed in a format which facilitates calculating the exceedances by numerically evaluating a line integral. The behavior of the density function for the two-dimensional case is briefly discussed.
Lester, H. C.↗
Effective Forces Between Colloidal Particles
Colloidal suspensions have proven to be excellent model systems for the study of condensed matter and its phase behavior. Many of the properties of colloidal suspensions can be investigated with a systematic variation of the characteristics of the systems and, in addition, the energy, length and time scales associated with them allow for experimental probing of otherwise inaccessible regimes. The latter property also makes colloidal systems vulnerable to external influences such as gravity. Experiments performed in micro-ravity by Chaikin and Russell have been invaluable in extracting the true behavior of the systems without an external field. Weitz and Pusey intend to use mixtures of colloidal particles with additives such as polymers to induce aggregation and form weak, tenuous, highly disordered fractal structures that would be stable in the absence of gravitational forces. When dispersed in a polarizable medium, colloidal particles can ionize, emitting counterions into the solution. The standard interaction potential in these charged colloidal suspensions was first obtained by Derjaguin, Landau, Verwey and Overbeek. The DLVO potential is obtained in the mean-field linearized Poisson-Boltzmann approximation and thus has limited applicability. For more precise calculations, we have used ab initio density functional theory. In our model, colloidal particles are charged hard spheres, the counterions are described by a continuum density field and the solvent is treated as a homogeneous medium with a specified dielectric constant. We calculate the effective forces between charged colloidal particles by integrating over the solvent and counterion degrees of freedom, taking into account the direct interactions between the particles as well as particle-counterion, counterion-counterion Coulomb, counterion entropic and correlation contributions. We obtain the effective interaction potential between charged colloidal particles in different configurations. We evaluate two- and three-body forces in the bulk as well as study the influence of soft walls. We qualitatively explain the effects of the walls on the forces and demonstrate that many-body effects are negligible in our system. With adjustments in the parameters, the DLVO pair-potential can describe the results quantitatively. Besides electrostatic interactions, entropic depletion effects that arise from (hard-core) exclusion play an important role in determining the behavior of multi-component colloidal suspensions. A standard theory for depletion forces is due to Asakura and Oosawa and is based on the ideal gas approximation. To go beyond this approximation, we have studied entropic forces in molecular dynamics simulations of systems of hard spheres (the effects of the solvent have been ignored). The effective depletion forces for these systems can be found either from equilibrium distribution functions or from direct momentum transfer calculations. Our results obtained by either method show qualitative differences from the Asakura-Oosawa forces, indicating a longer range, higher value at contact and most importantly a more complicated structure, comprising of several maxima and minima. Our calculations include the determination of effective forces between two spheres, a hard sphere and a wall, and the behavior of a hard sphere near a step-edge and a corner. We also demonstrate that such entropic forces do not necessarily satisfy pairwise additivity.
Tehver, Riina↗
Thermal conductivity of comets
The thermal conductivity of two comet models is calculated. Both models assume the comets to be heterogeneous in composition. One model considers the comet to have a nucleus of water-ice mixed with basaltic and meteoritic material in the form of dust and agglomerated particles surrounded by a layer of water-frost. The second model assumes the frost and water-ice layers have sublimated, leaving a porous structure to some depth composed of solid basaltic and meteoritic material with residual gases. K values are calculated as a function of depth, density, temperature and porosity.
Kumar, G. N.↗
Satellite disintegration dynamics
The subject of satellite disintegration is examined in detail. Elements of the orbits of individual fragments, determined by DOD space surveillance systems, are used to accurately predict the time and place of fragmentation. Dual time independent and time dependent analyses are performed for simulated and real breakups. Methods of statistical mechanics are used to study the evolution of the fragment clouds. The fragments are treated as an ensemble of non-interacting particles. A solution of Liouville's equation is obtained which enables the spatial density to be calculated as a function of position, time and initial velocity distribution.
Dasenbrock, R. R.↗
New atomic data of O/2+/
New atomic data are tabulated for the ion O(2+). Collision strengths are calculated for several energies of the exciting electron. The populations of the levels of O(2+) are calculated as a function of electron density under conditions appropriate for the solar atmosphere. The available solar data are compared with theoretical predictions of relative line intensities.
Bhatia, A. K.↗
New atomic data for Fe/+19/
New atomic data are tabulated for Fe(+19). The electron collision strengths are calculated using the 'distorted wave' approximation and results are presented for several energies of the exciting electron. The populations of the ground levels are calculated as a function of electron density under conditions appropriate to solar flares and tokamak plasmas. Theoretical intensity ratios are tabulated for the UV lines.
Bhatia, A. K.↗
Theoretical studies of chromospheres and winds in cool stars
The formation of spectral lines in expanding spherical atmospheres was determined in a physically realistic way, taking into account multilevel atomic processes, partial frequency redistribution, and other non-LTE transfer effects that affect the formation of optically thick lines. The formation of MgII and Ca II circumstellar absorption lines in late type giants and supergiants is investigated. The radiative cooling rate as a function of density and temperature was calculated from the results of plane parallel chromospheric models and these results were used to approximate the radiative cooling in an extended wind. The run of temperature was calculated along with the density and velocity profiles. The most important prediction of these models is that a warm zone in the wind must exist as a result of the wave heating. Within this zone, the Ca II and Mg II atoms can be ionized to Ca III and Mg III, so that the gas is transparent in the resonance transitions.
Dupree, A.↗
Planetary Interior Modeling and Tectonic Implications
A technique is described for estimating spectral admittance functions using Pioneer Venus gravity and topography data. These admittance functions provide a convenient means to carry out systematic geophysical studies over much of the surface of Venus with a variety of interior density models. The admittance functions are calculated in the observation space of line-of-sight (LOS) gravity. Both closed and open system petrological models are considered for the Tharsis region of Mars. An analytic theory for isostatic compensation on one-plate planet is applied, including membrane stresses in the lithosphere, self gravitation, and rotational ellipticity. Crucial to this stress modeling and also to the petrological modeling is the observation that the earliest fracturing seen in the Tharsis region is associated with isostatic stresses. The radial fractures that extend far from Tharsis are associated with an additional and/or a completely different mechanism.
Phillips, R. J.↗
The electronic Hamiltonian for cuprates
A realistic many-body Hamiltonian for the cuprate superconductors should include both copper d and oxygen p states, hopping matrix elements between them, and Coulomb energies, both on-site and inter-site. We have developed a novel computational scheme for deriving the relevant parameters ab initio from a constrained occupation local density functional. The scheme includes numerical calculation of appropriate Wannier functions for the copper and oxygen states. Explicit parameter values are given for La2CuO4. These parameters are generally consistent with other estimates and with the observed superexchange energy. Secondly, we address whether this complicated multi-band Hamiltonian can be reduced to a simpler one with fewer basis states per unit cell. We propose a mapping onto a new two-band effective Hamiltonian with one copper d and one oxygen p derived state per unit cell. This mapping takes into account the large oxygen-oxygen hopping given by the ab initio calculations.
Annett, James F.↗
Resonance Scattering of Fe XVII X-ray and EUV Lines
Over the years a number of calculations have been carried out to derive intensities of various X-ray and EUV lines in Fe XVII to compare with observed spectra. The predicted intensities have not agreed with solar observations, particularly for the line at 1.5.02 Angstroms; resonance scattering has been suggested as the source for much of the disagreement. The atomic data calculated earlier used seven configurations having n=3 orbitals and the scattering calculations were carried out only for incident energies above the threshold of the highest fine-structure level. These calculations have now been extended to thirteen configurations having n=4 orbitals and the scattering calculations are carried out below as well as above the threshold of the highest fine structure level. These improved calculations of Fe XVII change the intensity ratios compared to those obtained earlier, bringing the optically thin F(15.02)/F(16.78) ratio and several other ratios closer to the observed values. However, some disagreement with the solar observations still persists, even thought the agreement of the presently calculated optically thin F(15.02)/F(15.26) ratio with the experimental results of Brown et al. (1998) and Laming et al. (2000) has improved. Some of the remaining discrepancy is still thought to be the effect of opacity, which is consistent with expected physical conditions for solar sources. EUV intensity ratios are also calculated and compared with observations. Level populations and intensity ratios are calculated, as a function of column density of Fe XVII, in the slab and cylindrical geometries. As found previously, the predicted intensities for the resonance lines at 15.02 and 15.26 Angstroms exhibit initial increases in flux relative to the forbidden line at 17.10 Angstroms and the resonance line at 16.78 Angstroms as optical thickness increases. The same behavior is predicted for the lines at 12.262 and 12.122 Angstroms. Predicted intensities for some of the allowed EUV lines are also affected by opacity.
Bhatia, A. K.↗
The Molecular Structure of cis-FONO
The molecular structure of cis-FONO has been determined with the CCSD(T) correlation method using an spdf quality basis set. In agreement with previous coupled-cluster calculations but in disagreement with density functional theory, cis-FONO is found to exhibit normal bond distances. The quadratic and cubic force fields of cis-FONO have also been determined in order to evaluate the effect of vibrational averaging on the molecular geometry. Vibrational averaging is found to increase bond distances, as expected, but it does not affect the qualitative nature of the bonding. The CCSD(T)/spdf harmonic frequencies of cis-FONO support our previous assertion that a band observed at 1200 /cm is a combination band (upsilon(sub 3) + upsilon(sub 4)), and not a fundamental.
Lee, Timothy J.↗
Infrared Spectra of Perdeuterated Naphthalene, Phenanthrene, Chrysene, and Pyrene
Calculations are carried out using density functional theory (DFT) to determine the harmonic frequencies and intensities of perdeuterated naphthalene, phenanthrene, pyrene, and chrysene. We also report matrix- isolation spectra for these four species. The theoretical and experimental frequencies and relative intensities for the perdeuterated species are in generally good agreement. The effect of perdeuteration is to reduce the sum of the integrated intensities by a factor of about 1.75. This reduction occurs for all vibrational motions, except for the weak low frequency ring deformation modes. There is also a significant redistribution of the relative intensities between the out-of-plane C-D bands relative to those found for the out-of-plane C-H bands. The theoretical isotopic ratios provide an excellent diagnostic of the degree of C-H(C-D) involvement in the vibrational bands, allowing in most cases a clear distinction of the type of motion.
Bauschlicher, Charles W., Jr.↗
Infrared Spectra of Substituted Polycyclic Aromatic Hydrocarbons
Calculations are carried out using density functional theory (DFT) to determine the harmonic frequencies and intensities of 1-methylanthracene, 9-methylanthracene, 9-cyanoanthracene, 2-aminoanthracene, acridine, and their positive ions. The theoretical data are compared with matrix-isolation spectra for these species also reported in this work. The theoretical and experimental frequencies and relative intensities for the neutral species are in generally good agreement, whereas the positive ion spectra are only in qualitative agreement. Relative to anthracene, we find that substitution of amethyl or CN for a hydrogen does not significantly affect the spectrum other than to add the characteristic methyl C-H stretch and C-N stretch (near 2200/cm), respectively. However, addition of NH2 dramatically affects the spectrum of the neutral. Not only are the NH2 modes themselves strong, but this electron withdrawing group induces sufficient partial charge on the ring to give the neutral molecule characteristics of the anthracene cation spectrum. The sum of the absolute intensities is about four times larger for 2-aminoanthracene than for 9-cyanoanthracene. Substituting nitrogen in the ring at the nine position (acridine) does not greatly alter the spectrum compared with anthracene.
Bauschlicher, Charles W., Jr.↗
Infrared spectra of substituted polycylic aromatic hydrocarbons
Calculations are carried out using density functional theory (DFT) to determine the harmonic frequencies and intensities of 1-methylanthracene, 9-methylanthracene, 9-cyanoanthracene, 2-aminoanthracene, acridine, and their positive ions. The theoretical data are compared with matrix-isolation spectra for these species also reported in this work. The theoretical and experimental frequencies and relative intensities for the neutral species are in generally good agreement, whereas the positive ion spectra are only in qualitative agreement. Relative to anthracene, we find that substitution of a methyl or CN for a hydrogen does not significantly affect the spectrum other than to add the characteristic methyl C-H and C triple bond N stretches near 2900 and 2200 cm-1, respectively. However, addition of NH2 dramatically affects the spectrum of the neutral. Not only are the NH2 modes themselves strong, but this electron-withdrawing group induces sufficient partial charge on the ring to give the neutral molecule spectra characteristics of the anthracene cation. The sum of the absolute intensities is about four times larger for 2-aminoanthracene than those for 9-cyanoanthracene. Substituting nitrogen in the ring at the nine position (acridine) does not greatly alter the spectrum compared with anthracene.
NASA Discipline Exobiology↗
Very Large Eddy Simulations of a Jet-A Spray Reacting Flow in a Single Element LDI Injector With and Without Invoking an Eulerian Scalar DWFDF Method
This paper presents the very large eddy simulations (VLES) of a Jet-A spray reacting flow in a single element lean direct injection (LDI) injector by using the National Combustion Code (NCC) with and without invoking the Eulerian scalar DWFDF method, in which DWFDF is defined as the density weighted time filtered fine grained probability density function. The flow field is calculated by using the time filtered compressible Navier-Stokes equations (TFNS) with nonlinear subscale turbulence models, and when the Eulerian scalar DWFDF method is invoked, the energy and species mass fractions are calculated by solving the equation of DWFDF. A nonlinear subscale model for closing the convection term of the Eulerian scalar DWFDF equation is used and will be briefly described in this paper. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the Eulerian scalar DWFDF method in both improving the simulation quality and maintaining economic computing cost are observed.
Shih, Tsan-Hsing↗
Short-term time variability of Cygnus X-1
Autocorrelation functions, power-density spectra, and cross-correlation functions were calculated for 71 observations of Cyg X-1 by the Uhuru satellite. The average autocorrelation function and power-density spectrum were found to be independent of energy and consistent with a shot-noise source with a characteristic time constant of 0.45 s. The data in different energy bands were found to be 100 percent correlated.
Weisskopf, M. C.↗