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At least 1,045 records · Page 58

Development of the self-consistent approximation and its application to the problem of magnetoelastic resonance in an inhomogeneous medium

Our previously proposed approximation involving both the first and second terms of the expansion of the vertex function is generalized to the system of two interacting wavefields of different physical nature. A system of self-consistent equations for the matrix Green’s function and matrix vertex function is derived. On the basis of this matrix generalization of the new self-consistent approximation, a theory of magnetoelastic resonance is developed for a ferromagnetic model, where the magnetoelastic coupling parameter ε(x) is inhomogeneous. Equations for magnetoelastic resonance are analyzed for one-dimensional inhomogeneities of the coupling parameter. The diagonal and off-diagonal elements of the matrix Green’s function of the system of coupled spin and elastic waves are calculated with the change in the ratio between the average value ε and rms fluctuation Δε of the coupling parameter between waves from the homogeneous case (ε ≠ 0, Δε = 0) to the extremely randomized case (ε = 0, Δε ≠ 0) at various correlation wavenumbers of inhomogeneities k{sub c}. For the limiting case of infinite correlation radius (k{sub c} = 0), in addition to approximate expressions, exact analytical expressions corresponding to the summation of all diagrams of elements of the matrix Green’s function are obtained. The results calculated for an arbitrary k{sub c} value in the new self-consistent approximation are compared to the results obtained in the standard self-consistent approximation, where only the first term of the expansion of the vertex function is taken into account. It is shown that the new approximation corrects disadvantages of the Green’s functions calculated in the standard approximation such as the dome shape of resonances and bends on the sides of resonance peaks. The appearance of a fine structure of the spectrum in the form of a narrow resonance on the Green’s function of spin waves and a narrow antiresonance on the Green’s function of elastic waves, which was previously predicted in the standard self-consistent approximation, is confirmed. With an increase in the parameter k{sub c}, the Green’s functions calculated in the standard and new approximations approach each other and almost coincide with each other at k{sub c}/k ≥ 0.5. At the same time, the results of this work indicate that the new self-consistent approximation has a certain advantage for studying the problems of stochastic radiophysics in media with long-wavelength inhomogeneities (small k{sub c} values), because it describes both the shape and width of peaks much better than the standard approximation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it is shown that (i) the empirical formula for the secondary electron emission is not consistent with a MDF due to the presence of super-thermal particles, (ii) the super-thermal particles can replace a diffusion parameter in the Langmuir probe current formula, and (iii) the entropy can explicitly decrease in presence of sources only for the introduced INMDF without violating the second law of thermodynamics. Moreover, the first order entropy of an infinite number of super-thermal tails stays the same as the entropy of a MDF. The latter demystifies the Maxwell's demon by statistically describing non-isolated systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Iterated projected position algorithm for constructing exponentially localized generalized Wannier functions for periodic and nonperiodic insulators in two dimensions and higher

Localized bases play an important role in understanding electronic structure. In periodic insulators, a natural choice of localized basis is given by the Wannier functions which depend on a choice of unitary transform known as a gauge transformation. Over the past few decades, there have been many works that have focused on optimizing the choice of the gauge so that the corresponding Wannier functions are maximally localized or reflect some symmetry of the underlying system. In this work, we consider fully nonperiodic materials where the usual Wannier functions are not well defined and gauge optimization is impractical. To tackle the problem of calculating exponentially localized generalized Wannier functions in both periodic and nonperiodic systems, we discuss the ‘iterated projected position (IPP)” algorithm. Here, the IPP algorithm is based on matrix diagonalization and therefore unlike optimization-based approaches, it does not require initialization and cannot get stuck at a local minimum. Furthermore, the IPP algorithm is guaranteed by a rigorous analysis to produce exponentially localized functions under certain mild assumptions. We numerically demonstrate that the IPP algorithm can be used to calculate exponentially localized bases for the Haldane model, the Kane-Mele model (in both Z 2 invariant even and Z 2 invariant odd phases), and the p x + ip y model on a quasicrystal lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Lateral organization, bilayer asymmetry, and inter-leaflet coupling of biological membranes

Understanding of cell membrane organization has evolved significantly from the classic fluid mosaic model. It is now recognized that biological membranes are highly organized structures, with differences in lipid compositions between inner and outer leaflets and in lateral structures within the bilayer plane, known as lipid rafts. These organizing principles are important for protein localization and function as well as cellular signaling. However, the mechanisms and biophysical basis of lipid raft formation, structure, dynamics and function are not clearly understood. One key question, which we focus on in this review, is how lateral organization and leaflet compositional asymmetry are coupled. Detailed information elucidating this question has been sparse because of the small size and transient nature of rafts and the experimental challenges in constructing asymmetric bilayers. Resolving this mystery will require advances in both experimentation and modeling. We discuss here the preparation of model systems along with experimental and computational approaches that have been applied in efforts to address this key question in membrane biology. Furthermore, we seek to place recent and future advances in experimental and computational techniques in context, providing insight into in-plane and transverse organization of biological membranes.

59 BASIC BIOLOGICAL SCIENCES↗

The galactic contribution to IceCube's astrophysical neutrino flux

High energy neutrinos have been detected by IceCube, but their origin remains a mystery. Determining the sources of this flux is a crucial first step towards multi-messenger studies. Here, we systematically compare two classes of sources with the data: Galactic and extragalactic. We assume that the neutrino sources are distributed according to a class of Galactic models. We build a likelihood function on an event by event basis including energy, event topology, absorption, and direction information. We present the probability that each high energy event with deposited energy E dep >60 TeV in the HESE sample is Galactic, extragalactic, or background. Lastly, for Galactic models considered the Galactic fraction of the astrophysical flux has a best fit value of 1.3% and is <9.5% at 90\% CL. A zero Galactic flux is allowed at <1σ.

79 ASTRONOMY AND ASTROPHYSICS↗

Spin–Orbit Coupling Constants in Atoms and Ions of Transition Elements: Comparison of Effective Core Potentials, Model Core Potentials, and All-Electron Methods

The spin–orbit coupling constants (SOCC) in atoms and ions of the first- through third-row transition elements were calculated for the low-lying atomic states whose main electron configuration is [ n d] q ( q = 1–4 and 6–9, n = the principal quantum number), using four different approaches: (1) a nonrelativistic Hamiltonian used to construct multiconfiguration self-consistent field (MCSCF) wave functions utilizing effective core potentials and their associated basis sets within the framework of second-order configuration interaction (SOCI) to calculate spin–orbit couplings (SOC) using one-electron Breit–Pauli Hamiltonian (BPH), (2) a nonrelativistic Hamiltonian used to construct MCSCF wave functions utilizing model core potentials and their associated basis sets within the framework of SOCI to calculate SOC using the full BPH, (3) nonrelativistic and spin-independent relativistic Hamiltonians used to construct MCSCF wave functions utilizing all-electron (AE) basis sets within the framework of SOCI to calculate SOC using the full BPH, and (4) a relativistic Hamiltonian given by the exact two-component (X2C) transformation for construction of Kramers-restricted relativistic configuration interaction wave functions. In this investigation, these four approaches are referred to as ECP, MCP, AE, and X2C methods, respectively. The ECP, MCP, and AE methods are so-called two-step approaches (TSA), while the X2C method is a one-step approach (OSA). In the AE method, three different calculations—relativistic elimination of small components (RESC), third-order Douglas–Kroll–Hess (DKH3), and infinite-order two-component (IOTC) relativistic correction—were performed for the estimation of the scalar relativistic components in addition to those of the nonscalar relativistic (NSR) contributions. The calculated SOCC are compared to the available experimental data via the Landé interval rule. Although there are several exceptions, including states whose main configuration is [ n d] 5 , the average differences between the ECP and AE (IOTC) SOCC and between the ECP and the X2C SOCC are mostly less than 20%. The differences between the ECP and the experimental SOCC are even smaller. No serious discrepancy was found between the TSA and OSA predictions of SOCC for the first- and second-row transition elements in comparison to experiment. For atoms and ions of the third-row transition elements, the SOCC calculated through the Landé interval rule are not reliable. The low-energy spin-mixed (SM) states originating from a [5d]q configuration ( q = 2–4) have a larger energy lowering due to the SOC effects, in comparison with those for atoms and ions of the first- and second-row transition elements. For the spin-mixed (SM) states originating from a [5d]q configuration ( q = 6–8), the energy lowering of all 4 F 7/2 , 5 D 1 , and 5 D 3 states due to the SOC effects is smaller than those of the other SM states. Furthermore this difficulty, which also arises for the MCP, AE, and X2C (OSA) approaches, suggests that the LS-coupling scheme is inappropriate.

74 ATOMIC AND MOLECULAR PHYSICS↗

A new ab initio potential energy surface and infrared spectra for the Ar–CS{sub 2} complex

We report a new three-dimensional potential energy surface for Ar–CS{sub 2} involving the Q{sub 3} normal mode for the υ{sub 3} antisymmetric stretching vibration of the CS{sub 2} molecule. The potential energies were calculated using the supermolecular method at the coupled-cluster singles and doubles level with noniterative inclusion of connected triples, using augmented correlation-consistent quadruple-zeta basis set plus midpoint bond functions. Two vibrationally averaged potentials with CS{sub 2} at both the ground (υ = 0) and the first excited (υ = 1)υ{sub 3} vibrational states were generated from the integration of the three-dimensional potential over the Q{sub 3} coordinate. Each potential was found to have a T-shaped global minimum and two equivalent linear local minima. The radial discrete variable representation /angular finite basis representation method and the Lanczos algorithm were applied to calculate the rovibrational energy levels. The calculated band origin shift of the complex (0.0622 cm{sup −1}) is very close to the observed one (0.0671 cm{sup −1}). The predicted infrared spectra and spectroscopic parameters based on the two averaged potentials are in excellent agreement with the available experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Unlocking the Future of Aircraft Manufacturing: The Environmental Benefits of Laser Patterning for Surface Enhancement of Aircraft-Certified Alloys

Surface protection and functional modification of aircraft-certified aluminum alloys are essential for corrosion resistance, durability, and long-term airworthiness. At the same time, increasingly restrictive environmental regulations motivate the development of alternatives to legacy wet-chemical surface treatments. This study presents an integrated assessment of ultrafast femtosecond laser surface texturing as a surface functionalization approach for Aluminum 6061 alloys within an aerospace manufacturing and sustainability context. Ultrashort-pulse laser processing enables controlled micro- and nano-scale surface topographical modification with limited thermal impact, allowing adjustment of wettability and surface functionality while preserving bulk material integrity. As a dry and contactless process, femtosecond laser treatment eliminates the use of hazardous chemicals, reduces consumable inputs, and generates minimal secondary waste. A streamlined cradle-to-gate life cycle assessment conducted in accordance with ISO 14040/14044 indicates a lower global-warming potential per functional unit compared with conventional surface treatments, including anodization, plasma-assisted coatings, and organic coating systems. Complementary qualitative analyses addressing environmental health and safety, supply-chain risk, and ESG alignment indicate potential advantages related to occupational safety, regulatory compliance, waste management, and end-of-life recyclability. The investigation is performed on planar Aluminum 6061 reference surfaces with a treated area of 25 mm 2 , providing a controlled laboratory-scale basis for analyzing process behavior, functional surface modification, and associated environmental metrics. Within this defined scope, the results support further evaluation of femtosecond laser surface texturing as a surface engineering option for future aerospace manufacturing.

corrosion resistance↗

A novel Gaussian-Sinc mixed basis set for electronic structure calculations

A Gaussian-Sinc basis set methodology is presented for the calculation of the electronic structure of atoms and molecules at the Hartree–Fock level of theory. This methodology has several advantages over previous methods. The all-electron electronic structure in a Gaussian-Sinc mixed basis spans both the “localized” and “delocalized” regions. A basis set for each region is combined to make a new basis methodology—a lattice of orthonormal sinc functions is used to represent the “delocalized” regions and the atom-centered Gaussian functions are used to represent the “localized” regions to any desired accuracy. For this mixed basis, all the Coulomb integrals are definable and can be computed in a dimensional separated methodology. Additionally, the Sinc basis is translationally invariant, which allows for the Coulomb singularity to be placed anywhere including on lattice sites. Finally, boundary conditions are always satisfied with this basis. To demonstrate the utility of this method, we calculated the ground state Hartree–Fock energies for atoms up to neon, the diatomic systems H{sub 2}, O{sub 2}, and N{sub 2}, and the multi-atom system benzene. Together, it is shown that the Gaussian-Sinc mixed basis set is a flexible and accurate method for solving the electronic structure of atomic and molecular species.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Backbone and Ile-δ1, Leu, Val Methyl 1H, 13C and 15N NMR chemical shift assignments for human interferon-stimulated gene 15 protein

Human interferon-stimulated gene 15 protein (ISG15), also called ubiquitin cross-reactive protein (UCRP), is the first identified ubiquitin-like protein containing two ubiquitin-like domains fused in tandem. The active form of ISG15 is conjugated to target proteins via the C-terminal glycine residue through an isopeptide bond in a manner similar to ubiquitin. The biological role of ISG15 is strongly associated with the modulation of cell immune function, and there is mounting evidence suggesting that many viral pathogens evade the host innate immune response by interfering with ISG15 conjugation to both host and viral proteins in a variety of ways. Here we report nearly complete backbone 1HN, 15N, 13CO, and 13Ca, as well as side chain 13Cb, methyl (Ile-d1, Leu, Val), amide (Asn, Gln), and indole NH (Trp) NMR resonance assignments for the 157-residue human ISG15 protein. These resonance assignments provide the basis for future structural and functional solution NMR studies of the biologically important human ISG15 protein.

59 BASIC BIOLOGICAL SCIENCES↗

Prediction of Redox Potentials for U, Np, Pu, and Am in Aqueous Solution

The redox properties of the actinides in aqueous solution are important for fuel production/reprocessing and understanding the environmental impact of nuclear waste. The redox potentials for U, Np, Pu, and Am in oxidation states from 0 up to VII (as appropriate) in aqueous solutions have been predicted at the density functional theory level with the B3LYP functional, Stuttgart small core pseudopotential basis sets for the actinides, and explicit (30H 2 O molecules)/implicit treatment of the aqueous solvent using the self-consistent reaction field COSMO and SMD approaches for the implicit solvation. The predictions of the structural parameters of clusters incorporating first and second solvation shells are consistent with the available experimental data., Our results are typically within 0.2 V of the available experimental data using two explicit solvation shells with an implicit solvent model. The use of the PW91 functional substantially improved the prediction of the Pu(VI/V) redox couple. The redox couples for An(VI/IV) and An(V/IV) which involve the addition of protons and removal of the actinyl oxygens led to slightly larger differences from experiment. Here, the An(IV/0) and An(III/0) couples were reliably predicted with our approach. Predictions of the unknown An(II/I) redox potentials were negative, consistent with expectations, and predictions for unknown An(VII/VI), An(III/II), and An(II/0) redox couples improve prior estimates.

Actinides↗

Correction Scheme for Comparison of Computed and Experimental Optical Transition Energies in Functionalized Single-Walled Carbon Nanotubes

We present that covalent functionalization of single-walled carbon nanotubes (SWCNTs) introduces red-shifted emission features in the near-infrared spectral range due to exciton localization around the defect site. Such chemical modifications increase their potential use as near-infrared emitters and single-photon sources in telecommunications applications. Density functional theory (DFT) studies using finite-length tube models have been used to calculate their optical transition energies. Predicted energies are typically blue-shifted compared to experiment due to methodology errors including imprecise self-interaction corrections in the density functional and finite-size basis sets. Furthermore, artificial quantum confinement in finite models cannot be corrected by a constant-energy shift since they depend on the degree of exciton localization. Herein, we present a method that corrects the emission energies predicted by time-dependent DFT. Confinement and methodology errors are separately estimated using experimental data for unmodified tubes. Finally, corrected emission energies are in remarkable agreement with experiment, suggesting the value of this straightforward method toward predicting and interpreting the optical features of functionalized SWCNTs.

36 MATERIALS SCIENCE↗

Non-perturbative geometries for planar $ \mathcal{N} $ = 4 SYM amplitudes

There is a remarkable well-known connection between the G(4, n) cluster algebra and n-particle amplitudes in $ \mathcal{N} $ = 4 SYM theory. For n ≥ 8 two long-standing open questions have been to find a mathematically natural way to identify a finite list of amplitude symbol letters from among the infinitely many cluster variables, and to find an explanation for certain algebraic functions, such as the square roots of four-mass-box type, that are expected to appear in symbols but are not cluster variables. In this letter we use the notion of “stringy canonical forms” to construct polytopal realizations of certain compactifications of (the positive part of) the configuration space Conf n (P k–1 ) ≅ G(k, n)/T that are manifestly finite for all k and n. Some facets of these polytopes are naturally associated to cluster variables, while others are naturally associated to algebraic functions constructed from Lusztig’s canonical basis. For (k, n) = (4, 8) the latter include precisely the expected square roots, revealing them to be related to certain “overpositive” functions of the kinematical invariants.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Spectroscopic and thermodynamic properties of L-ornithine monohydrochloride

L-Ornithine Monohydrochloride (LOMHCL) has been investigated with the help of B3LYP density functional theory with 6-31 G (d, p) basis set. Fourier transform infrared and Fourier transform Raman spectra is to identify the various functional groups. The theoretical frequencies showed very good agreement with experimental values. On the basis of the thermodynamic properties of the title compound at different temperatures have been calculated, revealing the correlations between standard heat capacities (C) standard entropies (S), and standard enthalpy changes (H) and temperatures. Second harmonic generation (SHG) efficiency of the grown crystal has been studied.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Character of intermolecular interaction in pyridine-argon complex: Ab initio potential energy surface, internal dynamics, and interrelations between SAPT energy components

The pyridine-Ar (PAr) van der Waals (vdW) complex is studied using a high level ab initio method. Its structure, binding energy, and intermolecular vibrational states are determined from the analytical potential energy surface constructed from interaction energy (IE) values computed at the coupled cluster level of theory with single, double, and perturbatively included triple excitations with the augmented correlation consistent polarized valence double-ζ (aug-cc-pVDZ) basis set complemented by midbond functions. The structure of the complex at its global minimum with Ar at a distance of 3.509 Å from the pyridine plane and shifted by 0.218 Å from the center of mass towards nitrogen agrees well with the corresponding equilibrium structure derived previously from the rotational spectrum of PAr. The PAr binding energy D{sub e} of 392 cm{sup −1} is close to that of 387 cm{sup −1} calculated earlier at the same ab initio level for the prototypical benzene-Ar (BAr) complex. However, under an extension of the basis set, D{sub e} for PAr becomes slightly lower than D{sub e} for BAr. The ab initio vdW vibrational energy levels allow us to estimate the reliability of the methods for the determination of the vdW fundamentals from the rotational spectra. To disclose the character of the intermolecular interaction in PAr, the symmetry-adapted perturbation theory (SAPT) is employed for the analysis of different physical contributions to IE. It is found that SAPT components of IE can be approximately expressed in the binding region by only two of them: the exchange repulsion and dispersion energy. The total induction effect is negligible. The interrelations between various SAPT components found for PAr are fulfilled for a few other complexes involving aromatic molecules and Ar or Ne, which indicates that they are valid for all rare gas (Rg) atoms and aromatics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Quantum optimal control for pure-state preparation using one initial state

This paper presents a framework for solving the pure-state preparation problem using numerical optimal control. As an example, we consider the case where a number of qubits are dispersively coupled to a readout cavity. Herein, we model open system quantum dynamics using the Markovian Lindblad master equation driven by external control pulses. The main result of this paper develops a basis of density matrices (a parameterization) where each basis element is a density matrix by itself. Utilizing a specific objective function, we show how an ensemble of the basis elements can be used as a single initial state throughout the optimization process—independent of the system dimension. We apply the general framework to the specific application of ground-state reset of one and two qubits coupled to a readout cavity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

LONG TERM OPERATION ISSUES FOR ELECTRICAL CABLE SYSTEMS IN NUCLEAR POWER PLANTS

Nuclear power plants contain hundreds of kilometers of electrical cables including cables used for power, for instrumentation, and for control. It is essential that safety-related cable systems continue to perform following a design-basis event. Wholesale replacement of electrical cables in existing plants facing licensing period renewal is both impractical and cost-prohibitive. It is therefore important to understand the long term aging of cable materials to have confidence that aged cables will perform when needed. It is equally important in support of cable aging management to develop methods to evaluate the health of installed cables and inform selective cable replacement decisions. The most common insulation materials for electrical cables in nuclear power plants are cross-linked polyethylene and ethylene-propylene rubber. The mechanical properties of these materials degrade over time in the presence of environmental stresses including heat, gamma irradiation, and moisture. Mechanical degradation of cable insulation beyond a certain threshold is unacceptable because it can lead to insulation cracking, exposure of energized conductors, arcing and burning or loss of the ability of the cable system to function during a design-basis accident. While thermal-, radiation-, and moisture-related degradation of polymer insulation materials has been extensively studied over the last few decades, questions remain regarding the long-term performance of cable materials in nuclear plant-specific environments. Identified knowledge gaps include an understanding of the temperature-dependence of activation energies for thermal damage and an understanding of the synergistic effects of radiation and thermal stress on polymer degradation. Many of the outstanding questions in the aging behavior of cable materials relate to the necessity of predicting long-term field degradation using accelerated aging results from the laboratory. Materials degrade faster under more extreme conditions, but extension of behavior to long term degradation under more mild conditions, such as those experienced by most installed cables in nuclear power plants, is complicated by the fact that different degradation mechanisms may be involved in extreme and mild scenarios. The discrepancy in predicted results from short term, more extreme exposure and actual results from longer term, more mild exposures can be counter intuitive. For instance, due to the attenuation of oxidation penetration in material samples rapidly aged through exposure to high temperatures, the bulk of the samples may be artificially protected from thermal aging. In another example, simultaneous exposure of cable insulation material to heat and radiation may actually lead to less damage at higher temperatures than may be observed at lower temperatures. The Light Water Reactor Sustainability program of the United States (US) Department of Energy Office (DOE) of Nuclear Energy is funding research to increase the predictive understanding of electrical cable material aging and degradation in existing nuclear power plants in support of continued safe operation of plants beyond their initial license periods. This research includes the evaluation and development of methods to assess installed cable condition.

Fifield, Dr Leonard S↗

Free-energy orbital-free density functional theory: recent developments, perspective, and outlook

By summarizing the constraint-based development of orbital-free free-energy density functional approximations, we provide a perspective on progress over the last 15 years, the limitations of existing functionals, and the challenges awaiting resolution. We outline the chronology of the development of noninteracting and exchange-correlation free-energy orbital-free functionals and summarize the theoretical basis of existing local density approximation, second-order approximation, generalized gradient approximation (GGA), and meta-GGAs. We discuss limitations and challenges such as problems with thermodynamic derivatives, free-energy nonadditivity and the closely related issue of all-electron versus valence-only local pseudo-potential performance.

74 ATOMIC AND MOLECULAR PHYSICS↗