arXiv subjects

S. B. Trickey

Publications and source records attributed to S. B. Trickey.

36 records · Page 2Linked to original sources

arXiv2017

Deorbitalization strategies for meta-GGA exchange-correlation functionals

We explore the simplification of widely used meta-generalized-gradient approximation (mGGA) exchange-correlation functionals to the Laplacian level of refinement by use of approximate kinetic energy density functionals (KEDFs). Such deorbitalization is motivated by the prospect of reducing computational cost while recovering a strictly Kohn-Sham local potential framework (rather than the usual generalized Kohn-Sham treatment of mGGAs). A KEDF that has been rather successful in solid simulations proves to be inadequate for deorbitalization but we produce other forms which, with parametrization to Kohn-Sham results (not experimental data) on a small training set, yield rather good results on standard molecular test sets when used to deorbitalize the meta-GGA made very simple, TPSS, and SCAN functionals. We also study the difference between high-fidelity and best-performing deorbitalizations and discuss possible implications for use in ab initio molecular dynamics simulations of complicated condensed phase systems.

physics.chem-ph↗

arXiv2017

Accurate Anisotropic Gaussian Type Orbital Basis Sets for Atoms in Strong Magnetic Fields

In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic ($B$ field) confinement. However, the best available {\it a priori} procedure for composing highly accurate AGTO sets for atoms in a strong $B$ field [Phys.\ Rev. A {\bf 90}, 022504 (2014)] yields very large basis sets. Their size is problematical for use in any calculation with unfavorable computational cost scaling. Here we provide an alternative constructive procedure. It is based upon analysis of the underlying physics of atoms in $B$ fields that allows identification of several principles for the construction of AGTO basis sets. Aided by numerical optimization and parameter fitting, followed by fine tuning of fitting parameters, we devise formulae for generating accurate AGTO basis sets in an arbitrary $B$ field. For the hydrogen iso-electronic sequence, a set depends on $B$ field strength, nuclear charge, and upon orbital quantum numbers. For multi-electron systems, the basis set formulae also include adjustment to account for orbital occupations. Tests of the new basis sets for atoms H through C ($1 \le Z \le 6$), and ions Li$^+$, Be$^+$, and B$^+$, in a wide $B$ field range ($0 \le B \le 2000$ a.u.), show an accuracy better than a few $μ$H for single-electron systems, and a few hundredths to a few mHs for multi-electron atoms. The relative errors are similar for different atoms and ions in a large $B$ field range, from a few to a couple of tens of millionths, thereby confirming rather uniform accuracy across the nuclear charge $Z$ and $B$ field strength values. Residual basis set errors are two to three orders of magnitude smaller than the electronic correlation energies in muti-electron atoms ...

physics.comp-ph↗

arXiv2017

On the Kubo-Greenwood Model for Electron Conductivity

Currently, the most common method to calculate transport properties for materials under extreme conditions is based on the phenomenological Kubo-Greenwood method. The results of an inquiry into the justification and context of that model are summarized here. Specifically, the basis for its connection to equilibrium DFT and the assumption of static ions are discussed briefly.

cond-mat.stat-mech↗

arXiv2017

Kubo-Greenwood Electrical Conductivity Formulation and Implementation for Projector Augmented Wave Datasets

As the foundation for a new computational implementation, we survey the calculation of the complex electrical conductivity tensor based on the Kubo-Greenwood (KG) formalism (J.\ Phys.\ Soc.\ Jpn. \textbf{12}, 570 (1957); Proc.\ Phys.\ Soc.\ \textbf{71}, 585 (1958)), with emphasis on derivations and technical aspects pertinent to use of projector augmented wave datasets with plane wave basis sets (Phys.\ Rev.\ B \textbf{50}, 17953 (1994)). New analytical results and a full implementation of the KG approach in an open-source Fortran 90 post-processing code for use with Quantum Espresso (J.\ Phys.\ Cond.\ Matt.\ \textbf{21}, 395502 (2009)) are presented.Named KGEC ([K]ubo [G]reenwood [E]lectronic [C]onductivity), the code calculates the full complex conductivity tensor (not just the average trace). It supports use of either the original KG formula or the popular one approximated in terms of a Dirac delta function. It provides both Gaussian and Lorentzian representations of the Dirac delta function (thoughthe Lorentzian is preferable on basic grounds). KGEC provides decomposition of the conductivity into intra- and inter-band contributions as well as degenerate state contributions. It calculates the dc conductivity tensor directly. It is MPI parallelized over k-points, bands, and plane waves, with an option to recover the plane wave processes for their use in band parallelization as well. It is designed to provide rapid convergence with respect to $\mathbf k$-point density. Examples of its use are given.

cond-mat.mes-hall↗

arXiv2016

Finite Temperature Scaling in Density Functional Theory

A previous analysis of scaling, bounds, and inequalities for the non-interacting functionals of thermal density functional theory is extended to the full interacting functionals. The results are obtained from analysis of the related functionals from the equilibrium statistical mechanics of thermodynamics for an inhomogeneous system. Their extension to the functionals of density functional theory is described.

cond-mat.stat-mech↗

arXiv2016

Revised Thomas-Fermi Approximation for Singular Potentials

Approximations to the many-fermion free energy density functional that include the Thomas-Fermi (TF) form for the non-interacting part lead to singular densities for singular external potentials (e.g. attractive Coulomb). This limitation of the TF approximation is addressed here by a formal map of the exact Euler equation for the density onto an equivalent TF form characterized by a modified Kohn-Sham potential. It is shown to be a "regularized" version of the Kohn-Sham potential, tempered by convolution with a finite-temperature response function. The resulting density is non-singular, with the equilibrium properties obtained from the total free energy functional evaluated at this density. This new representation is formally exact. Approximate expressions for the regularized potential are given to leading order in a non-locality parameter and the limiting behavior at high and low temperatures is described. The non-interacting part of the free energy in this approximation is the usual Thomas-Fermi functional. These results generalize and extend to finite temperatures the ground-state regularization by Parr and Ghosh (Proc. Nat. Acad. Sci. 83, 3577 (1986)) and by Pratt, Hoffman, and Harris (J. Chem. Phys. 92, 1818 (1988)) and formally systematize the finite-temperature regularization given by the latter authors.

cond-mat.stat-mech↗

arXiv2016

The importance of finite-temperature exchange-correlation for warm dense matter calculations

Effects of explicit temperature dependence in the exchange-correlation (XC) free-energy functional upon calculated properties of matter in the warm dense regime are investigated. The comparison is between the KSDT finite-temperature local density approximation (TLDA) XC functional [Phys.\ Rev.\ Lett.\ \textbf{112}, 076403 (2014)] parametrized from restricted path integral Monte Carlo data on the homogeneous electron gas (HEG) and the conventional Monte Carlo parametrization ground-state LDA XC functional (Perdew-Zunger, "PZ") evaluated with $T$-dependent densities. Both Kohn-Sham (KS) and orbital-free density functional theory (OFDFT) are used, depending upon computational resource demands. Compared to the PZ functional, the KSDT functional generally lowers the direct-current (DC) electrical conductivity of low density Al, yielding improved agreement with experiment. The greatest lowering is about 15\% for T= 15 kK. Correspondingly, the KS band structure of low-density fcc Al from KSDT exhibits a clear increase in inter-band separation above the Fermi level compared to the PZ bands. In some density-temperature regimes, the Deuterium equations of state obtained from the two XC functionals exhibit pressure differences as large as 4\% and a 6\% range of differences. However, the Hydrogen principal Hugoniot is insensitive to explicit XC $T$-dependence because of cancellation between the energy and pressure-volume work difference terms in the Rankine-Hugoniot equation. Finally, the temperature at which the HEG becomes unstable is $T\geq$ 7200 K for $T$-dependent XC, a result that the ground-state XC underestimates by about 1000 K.

cond-mat.mtrl-sci↗

arXiv2015

Frank Discussion of the Status of Ground-state Orbital-free DFT

F.E. Harris has been a significant partner in our work on orbital-free density functional approximations for use in ab initio molecular dynamics. Here we mention briefly the essential progress on single-point functionals since our original paper (2006). Then we focus on the advantages and limitations of generalized gradient approximation (GGA) non-interacting kinetic-energy functionals. We reconsider the constraints provided by near-origin conditions in atomic-like systems and their relationship to regularized versus physical external potentials. Then we seek the best empirical GGA for the non-interacting KE for a modest-sized set of molecules with a well-defined near-origin behavior of their densities. The search is motivated by a desire for insight into GGA limitations and for a target for constraint-based development.

physics.chem-ph↗

arXiv2014

Improved analytical representation of combinations of Fermi-Dirac integrals for finite-temperature density functional calculations

Smooth, highly accurate analytical representations of Fermi-Dirac (FD) integral combinations important in free-energy density functional calculations are presented. Specific forms include those that occur in the local density approximation (LDA), generalized gradient approximation (GGA), and fourth-order gradient expansion of the non-interacting free energy as well as in the LDA and second-order gradient expansion for exchange. By construction, all the representations and their derivatives of any order are continuous on the full domains of their independent variables. The same type of technique provides an analytical representation of the function inverse to the FD integral of order $1/2$. It plays an important role in physical problems related to the electron gas at finite temperature. From direct evaluation, the quality of these improved representations is shown to be substantially superior to existing ones, many of which were developed before the era of large-scale computation or early in the era.

physics.comp-ph↗

arXiv2014

Finite-temperature orbital-free DFT molecular dynamics: coupling Profess and Quantum Espresso

Implementation of orbital-free free-energy functionals in the Profess code and the coupling of Profess with the Quantum Espresso code are described. The combination enables orbital-free DFT to drive ab initio molecular dynamics simulations on the same footing (algorithms, thermostats, convergence parameters, etc.) as for Kohn-Sham (KS) DFT. All the non-interacting free-energy functionals implemented are single-point: the local density approximation (LDA; also known as finite-T Thomas-Fermi, ftTF), the second-order gradient approximation (SGA or finite-T gradient-corrected TF), and our recently introduced finite-T generalized gradient approximations (ftGGA). Elimination of the KS orbital bottleneck via orbital-free methodology enables high-T simulations on ordinary computers, whereas those simulations would be costly or even prohibitively time-consuming for KS molecular dynamics (MD) on very high-performance computer systems. Example MD simulations on H over a temperature range 2,000 K <= T <=4,000,000 K are reported, with timings on small clusters (16-128 cores) and even laptops. With respect to KS-driven calculations, the orbital-free calculations are between a few times through a few hundreds of times faster.

cond-mat.mtrl-sci↗

arXiv2014

Local Spin-density Approximation Exchange-correlation Free-energy Functional

An accurate analytical parametrization for the exchange-correlation free energy of the homogeneous electron gas, including interpolation for partial spin-polarization, is derived via thermodynamic analysis of recent restricted path integral Monte-Carlo (RPIMC) data. This parametrization constitutes the local spin density approximation (LSDA) for the exchange-correlation functional in density functional theory. The new finite-temperature LSDA reproduces the RPIMC data well, satisfies the correct high-density and low- and high-$T$ asymptotic limits, and is well-behaved beyond the range of the RPIMC data, suggestive of broad utility.

physics.chem-ph↗

arXiv2013

Non-empirical Generalized Gradient Approximation Free Energy Functional for Orbital-free Simulations

We report the first wholly non-empirical generalized gradient approximation, non-interacting free energy functional for orbital-free density functional theory and use that new functional to provide forces for finite-temperature molecular dynamics simulations in the warm dense matter (WDM) regime The new functional provides good-to-excellent agreement with reference Kohn-Sham calculations under WDM conditions at a minuscule fraction of the computational cost of corresponding orbital-based simulations.

cond-mat.mtrl-sci↗

arXiv2012

Comparison of Density Functional Approximations and the Finite-temperature Hartree-Fock Approximation in Warm Dense Lithium

We compare the behavior of the finite-temperature Hartree-Fock model with that of thermal density functional theory using both ground-state and temperature-dependent approximate exchange functionals. The test system is bcc Li in the temperature-density regime of warm dense matter (WDM). In this exchange-only case, there are significant qualitative differences in results from the three approaches. Those differences may be important for Born-Oppenheimer molecular dynamics studies of WDM with ground-state approximate density functionals and thermal occupancies. Such calculations require reliable regularized potentials over a demanding range of temperatures and densities. By comparison of pseudopotential and all-electron results at ${\mathrm T} = 0$K for small Li clusters of local bcc symmetry and bond-lengths equivalent to high density bulk Li, we determine the density ranges for which standard projector augmented wave (PAW) and norm-conserving pseudopotentials are reliable. Then we construct and use all-electron PAW data sets with a small cutoff radius which are valid for lithium densities up to at least 80 g/cm$^3$.

cond-mat.mtrl-sci↗

arXiv2012

Issues and Challenges in Orbital-free Density Functional Calculations

Solving the Euler equation which corresponds to the energy minimum of a density functional expressed in orbital-free form involves related but distinct computational challenges. One is the choice between all-electron and pseudo-potential calculations and, if the latter, construction of the pseudo-potential. Another is the stability, speed, and accuracy of solution algorithms. Underlying both is the fundamental issue of satisfactory quality of the approximate functionals (kinetic energy and exchange-correlation). We address both computational issues and illustrate them by some comparative performance testing of our recently developed modified-conjoint generalized gradient approximation kinetic energy functionals. Comparisons are given for atoms, diatomic molecules, and some simple solids.

cond-mat.mtrl-sci↗

arXiv2011

Temperature-Dependent Behavior of Confined Many-electron Systems in the Hartree-Fock Approximation

Many-electron systems at substantial finite temperatures and densities present a major challenge to density functional theory. Very little is known about the free-energy behavior over the temperature range of interest, for example, in the study of warm dense matter. As a result, it is difficult to assess the validity of proposed approximate free-energy density functionals. Here we address, at least in part, this need for detailed results on well-characterized systems for purposes of testing and calibration of proposed approximate functionals. We present results on a comparatively simple, well-defined, but computationally feasible model, namely thermally occupied Hartree-Fock states for eight one-electron atoms at arbitrary positions in a hard-walled box. We discuss the main technical tasks (defining a suitable basis and evaluation of the required matrix elements) and discuss the physics which emerges from the calculations.

cond-mat.mtrl-sci↗

arXiv2011

Finite Temperature Scaling, Bounds, and Inequalities for the Non-interacting Density Functionals

Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is construction of the corresponding functionals for non-interacting particles in an arbitrary external potential. That problem is posed here in the context of the equilibrium statistical mechanics of an inhomogeneous system. The density functionals are defined and shown to be equal to the extremal state for a functional of the reduced one-particle statistical operators. Convexity of the latter functionals implies a class of general inequalities. First, it is shown that the familiar von Weizsäcker lower bound for zero temperature functionals applies at finite temperature as well. An upper bound is obtained in terms of a single-particle statistical operator corresponding to the Thomas-Fermi approximation. Next, the behavior of the density functionals under coordinate scaling is obtained. The inequalities are exploited to obtain a class of upper and lower bounds at constant temperature, and a complementary class at constant density. The utility of such constraints and their relationship to corresponding results at zero temperature are discussed.

cond-mat.stat-mech↗

arXiv2008

Tightened Lieb-Oxford bound for systems of fixed particle number

The Lieb-Oxford bound is a constraint upon approximate exchange-correlation functionals. We explore a non-empirical tightening of that bound in both universal and electron-number-dependent form. The test functional is PBE. Regarding both atomization energies (slightly worsened) and bond lengths (slightly bettered), we find the PBE functional to be remarkably insensitive to the value of the Lieb-Oxford bound. This both rationalizes the use of the original Lieb-Oxford constant in PBE and suggests that enhancement factors more sensitive to sharpened constraints await discovery.

physics.chem-ph↗

arXiv2008

Constraint-based, Single-point Approximate Kinetic Energy Functionals

We present a substantial extension of our constraint-based approach for development of orbital-free (OF) kinetic-energy (KE) density functionals intended for the calculation of quantum-mechanical forces in multi-scale molecular dynamics simulations. Suitability for realistic system simulations requires that the OF-KE functional yield accurate forces on the nuclei yet be relatively simple. We therefore require that the functionals be based on DFT constraints, local, dependent upon a small number of parameters fitted to a training set of limited size, and applicable beyond the scope of the training set. Our previous "modified conjoint" generalized-gradient-type functionals were constrained to producing a positive-definite Pauli potential. Though distinctly better than several published GGA-type functionals in that they gave semi-quantitative agreement with Born-Oppenheimer forces from full Kohn-Sham results, those modified conjoint functionals suffer from unphysical singularities at the nuclei. Here we show how to remove such singularities by introducing higher-order density derivatives. We give a simple illustration of such a functional used for the dissociation energy as a function of bond length for selected molecules.

cond-mat.mtrl-sci↗