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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.

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At least 1,315 records · Page 73
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DOE OSTI2014

Analytic representations of bath correlation functions for ohmic and superohmic spectral densities using simple poles

We present a scheme to express a bath correlation function (BCF) corresponding to a given spectral density (SD) as a sum of damped harmonic oscillations. Such a representation is needed, for example, in many open quantum system approaches. To this end we introduce a class of fit functions that enables us to model ohmic as well as superohmic behavior. We show that these functions allow for an analytic calculation of the BCF using pole expansions of the temperature dependent hyperbolic cotangent. We demonstrate how to use these functions to fit spectral densities exemplarily for cases encountered in the description of photosynthetic light harvesting complexes. Finally, we compare absorption spectra obtained for different fits with exact spectra and show that it is crucial to take properly into account the behavior at small frequencies when fitting a given SD.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Analytical solutions to matrix diffusion problems

We report an analytical method to solve in a few cases of practical interest the equations which have traditionally been proposed for the matrix diffusion problem. In matrix diffusion, elements dissolved in ground water can penetrate the porous rock surronuding the advective flow paths. In the context of radioactive waste repositories this phenomenon provides a mechanism by which the area of rock surface in contact with advecting elements is greatly enhanced, and can thus be an important delay mechanism. The cases solved are relevant for laboratory as well for in situ experiments. Solutions are given as integral representations well suited for easy numerical solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Analytical solutions of a generalized non-central potential in N-dimensions

We present that N-dimensional non-relativistic wave equation for the generalized non-central potential with arbitrary angular momentum is analytically solvable in the hyperspherical coordinates. Asymptotic iteration method as a different approach is applied to obtain N-dimensional energy eigenvalues and the corresponding eigenfunctions. In hyperspherical coordinates, the wave function solutions are obtained in terms of hypergeometric functions and Jacobi polynomials. The bound states of quantum systems under consideration for some special cases, such as Hartmann and Makarov potentials, have been discussed in N-dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Analytic derivative couplings in time-dependent density functional theory: Quadratic response theory versus pseudo-wavefunction approach

We revisit the formalism for analytic derivative couplings between excited states in time-dependent density functional theory (TDDFT). We derive and implement these couplings using quadratic response theory, then numerically compare this response-theory formulation to couplings implemented previously based on a pseudo-wavefunction formalism and direct differentiation of the Kohn-Sham determinant. Numerical results, including comparison to full configuration interaction calculations, suggest that the two approaches perform equally well for many molecular systems, provided that the underlying DFT method affords accurate potential energy surfaces. The response contributions are found to be important for certain systems with high symmetry, but can be calculated with only a moderate increase in computational cost beyond what is required for the pseudo-wavefunction approach. In the case of spin-flip TDDFT, we provide a formal proof that the derivative couplings obtained using response theory are identical to those obtained from the pseudo-wavefunction formulation, which validates our previous implementation based on the latter formalism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Shear deformable deformation of carbon nanotubes based on a new analytical nonlocal Timoshenko beam nodel

According to Hamilton’s principle, a new mathematical model and analytical solutions for nonlocal Timoshenko beam model (ANT) is established based on nonlocal elastic continuum theory when shear deformation and nonlocal effect are considered. The new ANT equilibrium equations and boundary conditions are derived for bending analysis of carbon nanotubes (CNTs) with simply supported, clamped and cantilever. The ANT deflection solutions demonstrate that the CNT stiffness is enhanced by the presence of nonlocal stress effects. Furthermore, the new ANT model concluded verifiable bending behaviors for a cantilever CNT with point load at the free end, which depends on the strength of nonlocal stress. Therefore, this new model will gives a better prediction for mechanical behaviors of nanostructures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Trigonometric and hyperbolic functions method for constructing analytic solutions to nonlinear plane magnetohydrodynamics equilibrium equations

In this paper, we present a solution method for constructing exact analytic solutions to magnetohydrodynamics (MHD) equations. The method is constructed via all the trigonometric and hyperbolic functions. The method is applied to MHD equilibria with mass flow. Applications to a solar system concerned with the properties of coronal mass ejections that affect the heliosphere are presented. Some examples of the constructed solutions which describe magnetic structures of solar eruptions are investigated. Moreover, the constructed method can be applied to a variety classes of elliptic partial differential equations which arise in plasma physics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Nonlinear dynamics of the ion Weibel-filamentation instability: An analytical model for the evolution of the plasma and spectral properties

We present a predictive model of the nonlinear phase of the Weibel instability induced by two symmetric, counter-streaming ion beams in the non-relativistic regime. This self-consistent model combines the quasilinear kinetic theory of Davidson et al. [Phys. Fluids 15, 317 (1972)] with a simple description of current filament coalescence. It allows us to follow the evolution of the ion parameters up to a stage close to complete isotropization, and is thus of prime interest to understand the dynamics of collisionless shock formation. Its predictions are supported by 2-D and 3-D particle-in-cell simulations of the ion Weibel instability. The derived approximate analytical solutions reveal the various dependencies of the ion relaxation to isotropy. In particular, it is found that the influence of the electron screening can affect the results of simulations using an unphysical electron mass.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Communication: A simple full range analytical potential for H{sub 2} b{sup 3}∑{sub u}{sup +}, H–He {sup 2}∑{sup +}, and He{sub 2} {sup 1}∑{sub g}{sup +}

The Tang-Toennies potential for the weakly interacting systems H{sub 2} b{sup 3}Σ{sub u}{sup +}, H–He {sup 2}Σ{sup +}, and He{sub 2} {sup 1}Σ{sub g}{sup +} is extended down to the united atom limit of vanishing internuclear distance. A simple analytic expression connects the united atom limiting potential with the Tang-Toennies potential in the well region. The new potential model is compared with the most recent ab initio calculations for all three systems. The agreement is better than 20% (H{sub 2} and He{sub 2}) or comparable with the differences in the available ab initio calculations (H–He) over six orders of magnitude corresponding to the entire range of internuclear distances.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Ground state analytical ab initio intermolecular potential for the Cl{sub 2}-water system

The chlorine/water interface is of crucial importance in the context of atmospheric chemistry. Modeling the structure and dynamics at this interface requires an accurate description of the interaction potential energy surfaces. We propose here an analytical intermolecular potential that reproduces the interaction between the Cl{sub 2} molecule and a water molecule. Our functional form is fitted to a set of high level ab initio data using the coupled-cluster single double (triple)/aug-cc-p-VTZ level of electronic structure theory for the Cl{sub 2} − H{sub 2}O complex. The potential fitted to reproduce the three minima structures of 1:1 complex is validated by the comparison of ab initio results of Cl{sub 2} interacting with an increasing number of water molecules. Finally, the model potential is used to study the physisorption of Cl{sub 2} on a perfectly ordered hexagonal ice slab. The calculated adsorption energy, in the range 0.27 eV, shows a good agreement with previous experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Analytical model of wall forces produced by kink perturbations in tokamaks

Analytical model of the electromagnetic forces produced by kink modes on the tokamak wall [H. R. Strauss et al., Phys. Plasmas 17, 082505 (2010)] is revisited. One of the main conclusions of the mentioned paper is that the largest force occurs at γτ{sub w}≈1, where γ is the kink growth rate and τ{sub w} is the wall penetration time. In the present study, a similar approach is developed under less restrictive assumptions on the plasma and dynamics of perturbation, and a different result is obtained: the force increases with γ and must be maximal at γτ{sub w}→∞. Additionally, the dependence of its amplitude on the plasma parameters is clarified. All distinctions and their reasons are explained in detail. The analysis is performed in the cylindrical model incorporating a resistive wall treated without traditional thin-wall constraints and covering therefore a full range in γτ{sub w}. It is applicable to either locked or rotating modes. Estimates of the sideways force are presented and compared with earlier forecasts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Analytical energy gradient for the two-component normalized elimination of the small component method

The analytical gradient for the two-component Normalized Elimination of the Small Component (2c-NESC) method is presented. The 2c-NESC is a Dirac-exact method that employs the exact two-component one-electron Hamiltonian and thus leads to exact Dirac spin-orbit (SO) splittings for one-electron atoms. For many-electron atoms and molecules, the effect of the two-electron SO interaction is modeled by a screened nucleus potential using effective nuclear charges as proposed by Boettger [Phys. Rev. B 62, 7809 (2000)]. The effect of spin-orbit coupling (SOC) on molecular geometries is analyzed utilizing the properties of the frontier orbitals and calculated SO couplings. It is shown that bond lengths can either be lengthened or shortened under the impact of SOC where in the first case the influence of low lying excited states with occupied antibonding orbitals plays a role and in the second case the jj-coupling between occupied antibonding and unoccupied bonding orbitals dominates. In general, the effect of SOC on bond lengths is relatively small (≤5% of the scalar relativistic changes in the bond length). However, large effects are found for van der Waals complexes Hg{sub 2} and Cn{sub 2}, which are due to the admixture of more bonding character to the highest occupied spinors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Reference interaction site model with hydrophobicity induced density inhomogeneity: An analytical theory to compute solvation properties of large hydrophobic solutes in the mixture of polyatomic solvent molecules

Reference interaction site model (RISM) has recently become a popular approach in the study of thermodynamical and structural properties of the solvent around macromolecules. On the other hand, it was widely suggested that there exists water density depletion around large hydrophobic solutes (>1 nm), and this may pose a great challenge to the RISM theory. In this paper, we develop a new analytical theory, the Reference Interaction Site Model with Hydrophobicity induced density Inhomogeneity (RISM-HI), to compute solvent radial distribution function (RDF) around large hydrophobic solute in water as well as its mixture with other polyatomic organic solvents. To achieve this, we have explicitly considered the density inhomogeneity at the solute-solvent interface using the framework of the Yvon-Born-Green hierarchy, and the RISM theory is used to obtain the solute-solvent pair correlation. In order to efficiently solve the relevant equations while maintaining reasonable accuracy, we have also developed a new closure called the D2 closure. With this new theory, the solvent RDFs around a large hydrophobic particle in water and different water-acetonitrile mixtures could be computed, which agree well with the results of the molecular dynamics simulations. Furthermore, we show that our RISM-HI theory can also efficiently compute the solvation free energy of solute with a wide range of hydrophobicity in various water-acetonitrile solvent mixtures with a reasonable accuracy. We anticipate that our theory could be widely applied to compute the thermodynamic and structural properties for the solvation of hydrophobic solute.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Soft mean spherical approximation for dusty plasma liquids: Level of accuracy and analytic expressions

The soft mean spherical approximation is employed for the study of the thermodynamics of dusty plasma liquids, the latter treated as Yukawa one-component plasmas. Within this integral theory method, the only input necessary for the calculation of the reduced excess energy stems from the solution of a single non-linear algebraic equation. Consequently, thermodynamic quantities can be routinely computed without the need to determine the pair correlation function or the structure factor. The level of accuracy of the approach is quantified after an extensive comparison with numerical simulation results. The approach is solved over a million times with input spanning the whole parameter space and reliable analytic expressions are obtained for the basic thermodynamic quantities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Analytic energy gradient of excited electronic state within TDDFT/MMpol framework: Benchmark tests and parallel implementation

The time-dependent density functional theory (TDDFT) has become the most popular method to calculate the electronic excitation energies, describe the excited-state properties, and perform the excited-state geometric optimization of medium and large-size molecules due to the implementation of analytic excited-state energy gradient and Hessian in many electronic structure software packages. To describe the molecules in condensed phase, one usually adopts the computationally efficient hybrid Quantum Mechanics/Molecular Mechanics (QM/MM) models. Here, we extend our previous work on the energy gradient of TDDFT/MM excited state to account for the mutual polarization effects between QM and MM regions, which is believed to hold a crucial position in the potential energy surface of molecular systems when the photoexcitation-induced charge rearrangement in the QM region is drastic. The implementation of a simple polarizable TDDFT/MM (TDDFT/MMpol) model in Q-Chem/CHARMM interface with both the linear response and the state-specific features has been realized. Several benchmark tests and preliminary applications are exhibited to confirm our implementation and assess the effects of different treatment of environmental polarization on the excited-state properties, and the efficiency of parallel implementation is demonstrated as well.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Analytic ab initio-based molecular interaction potential for the BrO⋅H{sub 2}O complex

Radical halogen oxide species play important roles within atmospheric processes, specifically those responsible for the removal of O{sub 3}. To facilitate future investigations on this family of compounds, RCCSD(T)/aug-cc-pVQZ-level electronic structure calculations were employed to generate individual-molecule optimized geometries, as well as to determine the global minimum energy structure for the BrO⋅H{sub 2}O complex. This information facilitated the generation of several one-dimensional potential energy surface (PES) scans for the BrO⋅H{sub 2}O complex. Scans were performed for both the ground state and the first excited state; this inclusion is due to a low-lying first electronic excited-state energy. These rigid-geometry PES scans were used both to generate a novel analytic interaction potential by modifying the existing Thole-type model used for water and to the fitted potential function. This interaction potential features anisotropic atomic polarizabilities facilitating appropriate modeling of the physics regarding the unpaired electron residing within the p-orbitals of the oxygen atom of the bromine oxide radical. The intention of this work is to facilitate future molecular dynamics simulations involving the interaction between the BrO radical and water clusters as a first step in devising possible novel chemistries taking place at the water interface of clouds within the atmosphere.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Communication: Analytical optimal pulse shapes obtained with the aid of genetic algorithms: Controlling the photoisomerization yield of retinal

We recently proposed a Quantum Optimal Control (QOC) method constrained to build pulses from analytical pulse shapes [R. D. Guerrero et al., J. Chem. Phys. 143(12), 124108 (2015)]. This approach was applied to control the dissociation channel yields of the diatomic molecule KH, considering three potential energy curves and one degree of freedom. In this work, we utilized this methodology to study the strong field control of the cis-trans photoisomerization of 11-cis retinal. This more complex system was modeled with a Hamiltonian comprising two potential energy surfaces and two degrees of freedom. The resulting optimal pulse, made of 6 linearly chirped pulses, was capable of controlling the population of the trans isomer on the ground electronic surface for nearly 200 fs. The simplicity of the pulse generated with our QOC approach offers two clear advantages: a direct analysis of the sequence of events occurring during the driven dynamics, and its reproducibility in the laboratory with current laser technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Analytic second derivative of the energy for density-functional tight-binding combined with the fragment molecular orbital method

The analytic second derivative of the energy is developed for the fragment molecular orbital (FMO) method combined with density-functional tight-binding (DFTB), enabling simulations of infrared and Raman spectra of large molecular systems. The accuracy of the method is established in comparison to full DFTB without fragmentation for a set of representative systems. The performance of the FMO-DFTB Hessian is discussed for molecular systems containing up to 10 041 atoms. The method is applied to the study of the binding of α-cyclodextrin to polyethylene glycol, and the calculated IR spectrum of an epoxy amine oligomer reproduces experiment reasonably well.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Approximate explicit analytic solution of the Elenbaas-Heller equation

The Elenbaas-Heller equation describing the temperature field of a cylindrically symmetrical non-radiative electric arc has been solved, and approximate explicit analytic solutions are obtained. The radial distributions of the heat-flux potential and the electrical conductivity have been figured out briefly by using some special simplification techniques. The relations between both the core heat-flux potential and the electric field with the total arc current have also been given in several easy explicit formulas. Besides, the special voltage-ampere characteristic of electric arcs is explained intuitionally by a simple expression involving the Lambert W-function. The analyses also provide a preliminary estimation of the Joule heating per unit length, which has been verified in previous investigations. Helium arc is used to examine the theories, and the results agree well with the numerical computations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗