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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Photoelectric sheath formation around small spherical objects in space

The formation of a photoelectron sheath around positively charged small (∼cm) spherical objects roaming in near earth space due to the solar radiation (with continuous spectrum) and the solar wind plasma has been investigated. The sheath structure has been derived, taking into account anisotropic photoelectron flux with the Poisson equation, spherical geometry of the object, and half Fermi Dirac distribution of photoelectron velocities. Two cases, viz., when the object is illuminated by (i) isotropic or (ii) unidirectional (parallel beam) radiation, have been analyzed. The analysis predicts a spherically symmetric sheath in case of isotropic illumination, while a symmetry in sheath about a θ=π/4 is seen in case of parallel beam illumination; θ is the angle of incidence which is the angle made by the normal to a surface element with the direction of incidence of solar radiation. The radial and angular profiles of the electric potential and electron density in the photoelectron sheath have been evaluated and illustrated graphically; the dependence of the sheath structure on the solar wind plasma parameters, material properties of the spherical object, and its size have been discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Linear and nonlinear optical absorption coefficients and refractive index changes in GaN/Al{sub x}Ga{sub (1−x)}N double quantum wells operating at 1.55 μm

In the present paper, the linear and nonlinear optical absorption coefficients and refractive index changes between the ground and the first excited states in double GaN/Al{sub x}Ga{sub (1−x)}N quantum wells are studied theoretically. The electronic energy levels and their corresponding wave functions are obtained by solving Schrödinger-Poisson equations self-consistently within the effective mass approximation. The obtained results show that the optical absorption coefficients and refractive index changes can be red- and blue-shifted through varying the left quantum well width and the aluminum concentration x{sub b2} of the central barrier, respectively. These structural parameters are found to present optimum values for carrying out the transition of 0.8 eV (1.55 μm). Furthermore, we show that the desired transition can also be achieved by replacing the GaN in the left quantum well with Al{sub y}Ga{sub (1−y)}N and by varying the aluminum concentration y{sub Al}. The obtained results give a new degree of freedom in optoelectronic device applications such as optical fiber telecommunications operating at (1.55 μm)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Resonant tunneling of interacting electrons in an AC electric field

The problem of the effect of electron-electron interaction on the static and dynamic properties of a double-barrier nanostructure (resonant tunneling diode (RTD)) is studied in terms of a coherent tunneling model, which includes a set of Schrödinger and Poisson equations with open boundary conditions. Explicit analytical expressions are derived for dc and ac potentials and reduced (active and reactive) currents in the quasi-classical approximation over a wide frequency range. These expressions are used to analyze the frequency characteristics of RTD. It is shown that the interaction can radically change the form of these expressions, especially in the case of a hysteretic I-V characteristic. In this case, the active current and the ac potentials can increase sharply at both low and high frequencies. For this increase to occur, it is necessary to meet quantum regime conditions and to choose a proper working point in the I-V characteristic of RTD. The possibility of appearance of specific plasma oscillations, which can improve the high-frequency characteristics of RTD, is predicted. It is found that the active current can be comparable with the resonant dc current of RTD.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

An efficient algorithm for incompressible N-phase flows

We present an efficient algorithm within the phase field framework for simulating the motion of a mixture of N (N⩾2) immiscible incompressible fluids, with possibly very different physical properties such as densities, viscosities, and pairwise surface tensions. The algorithm employs a physical formulation for the N-phase system that honors the conservations of mass and momentum and the second law of thermodynamics. We present a method for uniquely determining the mixing energy density coefficients involved in the N-phase model based on the pairwise surface tensions among the N fluids. Our numerical algorithm has several attractive properties that make it computationally very efficient: (i) it has completely de-coupled the computations for different flow variables, and has also completely de-coupled the computations for the (N−1) phase field functions; (ii) the algorithm only requires the solution of linear algebraic systems after discretization, and no nonlinear algebraic solve is needed; (iii) for each flow variable the linear algebraic system involves only constant and time-independent coefficient matrices, which can be pre-computed during pre-processing, despite the variable density and variable viscosity of the N-phase mixture; (iv) within a time step the semi-discretized system involves only individual de-coupled Helmholtz-type (including Poisson) equations, despite the strongly-coupled phase–field system of fourth spatial order at the continuum level; (v) the algorithm is suitable for large density contrasts and large viscosity contrasts among the N fluids. Extensive numerical experiments have been presented for several problems involving multiple fluid phases, large density contrasts and large viscosity contrasts. In particular, we compare our simulations with the de Gennes theory, and demonstrate that our method produces physically accurate results for multiple fluid phases. We also demonstrate the significant and sometimes dramatic effects of the gravity, density ratios, pairwise surface tensions, and drop sizes on the N-phase configurations and dynamics. The numerical results show that the method developed herein is capable of dealing with N-phase systems with large density ratios, large viscosity ratios, and pairwise surface tensions, and that it can be a powerful tool for studying the interactions among multiple types of fluid interfaces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Atom-partitioned multipole expansions for electrostatic potential boundary conditions

Applications such as grid-based real-space density functional theory (DFT) use the Poisson equation to compute electrostatics. However, the expected long tail of the electrostatic potential requires either the use of a large and costly outer domain or Dirichlet boundary conditions estimated via multipole expansion. We find that the oft-used single-center spherical multipole expansion is only appropriate for isotropic mesh domains such as spheres and cubes. In this work, we introduce a method suitable for high aspect ratio meshes whereby the charge density is partitioned into atomic domains and multipoles are computed for each domain. While this approach is moderately more expensive than a single-center expansion, it is numerically stable and still a small fraction of the overall cost of a DFT calculation. The net result is that when high aspect ratio systems are being studied, form-fitted meshes can now be used in lieu of cubic meshes to gain computational speedup.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Vertical electron transport in van der Waals heterostructures with graphene layers

We propose and analyze an analytical model for the self-consistent description of the vertical electron transport in van der Waals graphene-layer (GL) heterostructures with the GLs separated by the barriers layers. The top and bottom GLs serve as the structure emitter and collector. The vertical electron transport in such structures is associated with the propagation of the electrons thermionically emitted from GLs above the inter-GL barriers. The model under consideration describes the processes of the electron thermionic emission from and the electron capture to GLs. It accounts for the nonuniformity of the self-consistent electric field governed by the Poisson equation which accounts for the variation of the electron population in GLs. The model takes also under consideration the cooling of electrons in the emitter layer due to the Peltier effect. We find the spatial distributions of the electric field and potential with the high-electric-field domain near the emitter GL in the GL heterostructures with different numbers of GLs. Using the obtained spatial distributions of the electric field, we calculate the current-voltage characteristics. We demonstrate that the Peltier cooling of the two-dimensional electron gas in the emitter GL can strongly affect the current-voltage characteristics resulting in their saturation. The obtained results can be important for the optimization of the hot-electron bolometric terahertz detectors and different devices based on GL heterostructures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Excitation and evolution of finite-amplitude plasma wave

The evolution of a small spatially periodic perturbation in the electron velocity distribution function in collisionless plasma is reconsidered by numerically solving the Vlasov and Poisson equations. The short as well as long time behaviors of the excited oscillations and damping/modulation are followed. In the small but finite-amplitude excited plasma wave, resonant electrons become trapped in the wave potential wells and their motion affects the low-velocity electrons participating in the plasma oscillations, leading to modulation of the latter at an effective trapping frequency. It is found that the phase space of the resonant and low-velocity electrons becomes chaotic, but then self-organization takes place but remains fine-scale chaotic. It is also found that as long as particles are trapped, there is only modulation and no monotonic damping of the excited plasma wave. The modulation period/amplitude increases/decreases as the magnitude of the initial disturbance is reduced. For the initial and boundary conditions used here, linear Landau damping corresponds to the asymptotic limit of the modulation period becoming infinite, or no trapping of the resonant electrons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Electrostatics of proteins in dielectric solvent continua. II. Hamiltonian reaction field dynamics

In Paper I of this work [S. Bauer, G. Mathias, and P. Tavan, J. Chem. Phys. 140, 104102 (2014)] we have presented a reaction field (RF) method, which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of polarizable molecular mechanics (MM) force fields. Building upon these results, here we suggest a method for linearly scaling Hamiltonian RF/MM molecular dynamics (MD) simulations, which we call “Hamiltonian dielectric solvent” (HADES). First, we derive analytical expressions for the RF forces acting on the solute atoms. These forces properly account for all those conditions, which have to be self-consistently fulfilled by RF quantities introduced in Paper I. Next we provide details on the implementation, i.e., we show how our RF approach is combined with a fast multipole method and how the self-consistency iterations are accelerated by the use of the so-called direct inversion in the iterative subspace. Finally we demonstrate that the method and its implementation enable Hamiltonian, i.e., energy and momentum conserving HADES-MD, and compare in a sample application on Ac-Ala-NHMe the HADES-MD free energy landscape at 300 K with that obtained in Paper I by scanning of configurations and with one obtained from an explicit solvent simulation.

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

Hybrid immersed interface-immersed boundary methods for AC dielectrophoresis

Dielectrophoresis, a nonlinear electrokinetic transport mechanism, has become popular in many engineering applications including manipulation, characterization and actuation of biomaterials, particles and biological cells. In this paper, we present a hybrid immersed interface–immersed boundary method to study AC dielectrophoresis where an algorithm is developed to solve the complex Poisson equation using a real variable formulation. An immersed interface method is employed to obtain the AC electric field in a fluid media with suspended particles and an immersed boundary method is used for the fluid equations and particle transport. The convergence of the proposed algorithm as well as validation of the hybrid scheme with experimental results is presented. In this paper, the Maxwell stress tensor is used to calculate the dielectrophoretic force acting on particles by considering the physical effect of particles in the computational domain. Thus, this study eliminates the approximations used in point dipole methods for calculating dielectrophoretic force. A comparative study between Maxwell stress tensor and point dipole methods for computing dielectrophoretic forces are presented. The hybrid method is used to investigate the physics of dielectrophoresis in microfluidic devices using an AC electric field. The numerical results show that with proper design and appropriate selection of applied potential and frequency, global electric field minima can be obtained to facilitate multiple particle trapping by exploiting the mechanism of negative dielectrophoresis. Our numerical results also show that electrically neutral particles form a chain parallel to the applied electric field irrespective of their initial orientation when an AC electric field is applied. This proposed hybrid numerical scheme will help to better understand dielectrophoresis and to design and optimize microfluidic devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Expansion techniques for collisionless stellar dynamical simulations

We present graphics processing unit (GPU) implementations of two fast force calculation methods based on series expansions of the Poisson equation. One method is the self-consistent field (SCF) method, which is a Fourier-like expansion of the density field in some basis set; the other method is the multipole expansion (MEX) method, which is a Taylor-like expansion of the Green's function. MEX, which has been advocated in the past, has not gained as much popularity as SCF. Both are particle-field methods and optimized for collisionless galactic dynamics, but while SCF is a 'pure' expansion, MEX is an expansion in just the angular part; thus, MEX is capable of capturing radial structure easily, while SCF needs a large number of radial terms. We show that despite the expansion bias, these methods are more accurate than direct techniques for the same number of particles. The performance of our GPU code, which we call ETICS, is profiled and compared to a CPU implementation. On the tested GPU hardware, a full force calculation for one million particles took ∼0.1 s (depending on expansion cutoff), making simulations with as many as 10{sup 8} particles fast for a comparatively small number of nodes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Mechanisms of dust grain charging in plasma with allowance for electron emission processes

The process of dust grain charging is described with allowance for secondary, ion-induced, photoelectric, and thermal electron emission from the grain surface. The roughness of the grain surface is taken into account. An intermediate charging regime involving ion–atom collisions and electron ionization in the perturbed plasma region is analyzed using the moment equations and Poisson’s equation. A calculation method is proposed that allows one to take into account the influence of all the above effects and determine the radius of the plasma region perturbed by the dust grain.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Capacitance enhancement via electrode patterning

The necessity of increasing the energy density in electric double layer capacitors to meet current demand is fueling fundamental and applied research alike. We report here molecular dynamics simulation results for aqueous electrolytes near model electrodes. Particular focus is on the effect of electrode patterning on the structure of interfacial electrolytes, and on the potential drop between the solid electrodes and the bulk electrolytes. The latter is estimated by numerically integrating the Poisson equation using the charge densities due to water and ions accumulated near the interface as input. We considered uniform and patterned electrodes, both positively and negatively charged. The uniformly charged electrodes are modeled as graphite. The patterned ones are obtained by removing carbon atoms from the top-most graphene layer, yielding nanoscopic squares and stripes patterns. For simplicity, the patterned electrodes are effectively simulated as insulators (the charge remains localized on the top-most layer of carbon atoms). Our simulations show that the patterns alter the structure of water and the accumulation of ions at the liquid-solid interfaces. Using aqueous NaCl solutions, we found that while the capacitance calculated for three positively charged electrodes did not change much, that calculated for the negatively charged electrodes significantly increased upon patterning. We find that both water structure and orientation, as well as ion accumulation affect the capacitance. As electrode patterning affects differently water structure and ion accumulation, it might be possible to observe ion-specific effects. These results could be useful for advancing our understanding of electric double layer capacitors, capacitive desalination processes, as well as of fundamental interfacial electrolytes properties.

36 MATERIALS SCIENCE↗
DOE OSTI2013

Studies of photoconductivity and field effect transistor behavior in examining drift mobility, surface depletion, and transient effects in Si-doped GaN nanowires in vacuum and air

Variable intensity photoconductivity (PC) performed under vacuum at 325 nm was used to estimate drift mobility ({mu}) and density ({sigma}{sub s}) of negative surface charge for c-axis oriented Si-doped GaN nanowires (NWs). In this approach, we assumed that {sigma}{sub s} was responsible for the equilibrium surface band bending ( Empty-Set ) and surface depletion in the absence of illumination. The NWs were grown by molecular beam epitaxy to a length of approximately 10 {mu}m and exhibited negligible taper. The free carrier concentration (N) was separately measured using Raman scattering which yielded N = (2.5 {+-} 0.3) Multiplication-Sign 10{sup 17} cm{sup -3} for the growth batch studied under 325 nm excitation. Saturation of the PC was interpreted as a flatband condition whereby Empty-Set was eliminated via the injection of photogenerated holes. Measurements of dark and saturated photocurrents, N, NW dimensions, and dimensional uncertainties, were used as input to a temperature-dependent cylindrical Poisson equation based model, yielding {sigma}{sub s} in the range of (3.5 to 7.5) Multiplication-Sign 10{sup 11} cm{sup -2} and {mu} in the range of (850 to 2100) cm{sup 2}/(V s) across the (75 to 194) nm span of individual NW diameters examined. Data illustrating the spectral dependence and polarization dependence of the PC are also presented. Back-gating these devices, and devices from other growth batches, as field effect transistors (FETs) was found to not be a reliable means to estimate transport parameters (e.g., {mu} and {sigma}{sub s}) due to long-term current drift. The current drift was ascribed to screening of the FET back gate by injected positive charge. We describe how these gate charging effects can be exploited as a means to hasten the otherwise long recovery time of NW devices used as photoconductive detectors. Additionally, we present data illustrating comparative drift effects under vacuum, room air, and dry air for both back-gated NW FETs and top-gated NW MESFETs.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Multi-shell model of ion-induced nucleic acid condensation

We present a semi-quantitative model of condensation of short nucleic acid (NA) duplexes induced by trivalent cobalt(III) hexammine (CoHex) ions. The model is based on partitioning of bound counterion distribution around single NA duplex into “external” and “internal” ion binding shells distinguished by the proximity to duplex helical axis. In the aggregated phase the shells overlap, which leads to significantly increased attraction of CoHex ions in these overlaps with the neighboring duplexes. The duplex aggregation free energy is decomposed into attractive and repulsive components in such a way that they can be represented by simple analytical expressions with parameters derived from molecular dynamic simulations and numerical solutions of Poisson equation. The attractive term depends on the fractions of bound ions in the overlapping shells and affinity of CoHex to the “external” shell of nearly neutralized duplex. The repulsive components of the free energy are duplex configurational entropy loss upon the aggregation and the electrostatic repulsion of the duplexes that remains after neutralization by bound CoHex ions. The estimates of the aggregation free energy are consistent with the experimental range of NA duplex condensation propensities, including the unusually poor condensation of RNA structures and subtle sequence effects upon DNA condensation. The model predicts that, in contrast to DNA, RNA duplexes may condense into tighter packed aggregates with a higher degree of duplex neutralization. An appreciable CoHex mediated RNA-RNA attraction requires closer inter-duplex separation to engage CoHex ions (bound mostly in the “internal” shell of RNA) into short-range attractive interactions. The model also predicts that longer NA fragments will condense more readily than shorter ones. The ability of this model to explain experimentally observed trends in NA condensation lends support to proposed NA condensation picture based on the multivalent “ion binding shells.”.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2013

Optimal width of barrier region in X/{gamma}-ray Schottky diode detectors based on CdTe and CdZnTe

The spectral distribution of quantum detection efficiency of X- and {gamma}-ray Schottky diodes based on semi-insulating CdTe or Cd{sub 0.9}Zn{sub 0.1}Te crystals is substantiated and obtained in analytical form. It is shown that the width of the space charge region (SCR) of 6-40 {mu}m at zero bias in CdTe (Cd{sub 0.9}Zn{sub 0.1}Te) Schottky diode is optimal for detecting radiation in the photon energy range above 5-10 keV. Based on the Poisson equation, the relationship between the SCR width and the composition of impurities and the degree of their compensation are investigated. It is shown that the presence of deep levels in the bandgap leads to a considerable increase in space charge density and electric field strength near the crystal surface. However, this effect contributes a small error in the determination of the SCR width using the standard formula for the Schottky diode. It is also shown that the concentration of uncompensated impurities in CdTe and Cd{sub 0.9}Zn{sub 0.1}Te crystals within the 4 Multiplication-Sign 10{sup 11}-10{sup 13} cm{sup -3} range is optimal for the detection efficiency of X- and {gamma}-rays in the photon high-energy range. The record-high values of energy resolution have been obtained in the spectra of {sup 241}Am, {sup 57}Co, {sup 133}Ba and {sup 137}Cs isotopes measured using CdTe crystals with Schottky diodes because the concentration of uncompensated donors in the CdTe crystals (1-2) Multiplication-Sign 10{sup 12} cm{sup -3} falls on an interval of maximum detection efficiency. In the spectrum of {sup 57}Co isotope, the limiting energy resolution has been achieved.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Modern gyrokinetic particle-in-cell simulation of fusion plasmas on top supercomputers

The Gyrokinetic Toroidal Code at Princeton (GTC-P) is a highly scalable and portable particle-in-cell (PIC) code. It solves the 5D Vlasov-Poisson equation featuring efficient utilization of modern parallel computer architectures at the petascale and beyond. Motivated by the goal of developing a modern code capable of dealing with the physics challenge of increasing problem size with sufficient resolution, new thread-level optimizations have been introduced as well as a key additional domain decomposition. GTC-P's multiple levels of parallelism, including inter-node 2D domain decomposition and particle decomposition, as well as intra-node shared memory partition and vectorization have enabled pushing the scalability of the PIC method to extreme computational scales. In this paper, we describe the methods developed to build a highly parallelized PIC code across a broad range of supercomputer designs. This particularly includes implementations on heterogeneous systems using NVIDIA GPU accelerators and Intel Xeon Phi (MIC) co-processors and performance comparisons with state-of-the-art homogeneous HPC systems such as Blue Gene/Q. New discovery science capabilities in the magnetic fusion energy application domain are enabled, including investigations of Ion-Temperature-Gradient (ITG) driven turbulence simulations with unprecedented spatial resolution and long temporal duration. Performance studies with realistic fusion experimental parameters are carried out on multiple supercomputing systems spanning a wide range of cache capacities, cache-sharing configurations, memory bandwidth, interconnects and network topologies. Furthermore, these performance comparisons using a realistic discovery-science-capable domain application code provide valuable insights on optimization techniques across one of the broadest sets of current high-end computing platforms worldwide.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

A cosmological exclusion plot: towards model-independent constraints on modified gravity from current and future growth rate data

Most cosmological constraints on modified gravity are obtained assuming that the cosmic evolution was standard ΛCDM in the past and that the present matter density and power spectrum normalization are the same as in a ΛCDM model. Here we examine how the constraints change when these assumptions are lifted. We focus in particular on the parameter Y (also called G{sub eff}) that quantifies the deviation from the Poisson equation. This parameter can be estimated by comparing with the model-independent growth rate quantity fσ{sub 8}(z) obtained through redshift distortions. We reduce the model dependency in evaluating Y by marginalizing over σ{sub 8} and over the initial conditions, and by absorbing the degenerate parameter Ω{sub m,0} into Y. We use all currently available values of fσ{sub 8}(z). We find that the combination Y-circumflex =YΩ{sub m,0}, assumed constant in the observed redshift range, can be constrained only very weakly by current data, Y-circumflex =0.28{sub −0.23}{sup +0.35} at 68% c.l. We also forecast the precision of a future estimation of Y-circumflex in a Euclid-like redshift survey. We find that the future constraints will reduce substantially the uncertainty, Y-circumflex =0.30{sub −0.09}{sup +0.08} , at 68% c.l., but the relative error on Y-circumflex around the fiducial remains quite high, of the order of 30%. The main reason for these weak constraints is that Y-circumflex is strongly degenerate with the initial conditions, so that large or small values of Y-circumflex are compensated by choosing non-standard initial values of the derivative of the matter density contrast. Finally, we produce a forecast of a cosmological exclusion plot on the Yukawa strength and range parameters, which complements similar plots on laboratory scales but explores scales and epochs reachable only with large-scale galaxy surveys. We find that future data can constrain the Yukawa strength to within 3% of the Newtonian one if the range is around a few Megaparsecs. In the particular case of f(R) models, we find that the Yukawa range will be constrained to be larger than 80 Mpc/h or smaller than 2 Mpc/h (95% c.l.), regardless of the specific f(R) model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Electrostatics of proteins in dielectric solvent continua. I. An accurate and efficient reaction field description

We present a reaction field (RF) method which accurately solves the Poisson equation for proteins embedded in dielectric solvent continua at a computational effort comparable to that of an electrostatics calculation with polarizable molecular mechanics (MM) force fields. The method combines an approach originally suggested by Egwolf and Tavan [J. Chem. Phys. 118, 2039 (2003)] with concepts generalizing the Born solution [Z. Phys. 1, 45 (1920)] for a solvated ion. First, we derive an exact representation according to which the sources of the RF potential and energy are inducible atomic anti-polarization densities and atomic shielding charge distributions. Modeling these atomic densities by Gaussians leads to an approximate representation. Here, the strengths of the Gaussian shielding charge distributions are directly given in terms of the static partial charges as defined, e.g., by standard MM force fields for the various atom types, whereas the strengths of the Gaussian anti-polarization densities are calculated by a self-consistency iteration. The atomic volumes are also described by Gaussians. To account for covalently overlapping atoms, their effective volumes are calculated by another self-consistency procedure, which guarantees that the dielectric function ε(r) is close to one everywhere inside the protein. The Gaussian widths σ{sub i} of the atoms i are parameters of the RF approximation. The remarkable accuracy of the method is demonstrated by comparison with Kirkwood's analytical solution for a spherical protein [J. Chem. Phys. 2, 351 (1934)] and with computationally expensive grid-based numerical solutions for simple model systems in dielectric continua including a di-peptide (Ac-Ala-NHMe) as modeled by a standard MM force field. The latter example shows how weakly the RF conformational free energy landscape depends on the parameters σ{sub i}. A summarizing discussion highlights the achievements of the new theory and of its approximate solution particularly by comparison with so-called generalized Born methods. A follow-up paper describes how the method enables Hamiltonian, efficient, and accurate MM molecular dynamics simulations of proteins in dielectric solvent continua.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗