Valentin V. Karasiev

Issues and challenges in orbital-free density functional calculations

a b s t r a c t 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 allelectron and pseudopotential calculations and, if the latter, construction of the pseudopotential. 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.

Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations

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 lowand high-T asymptotic limits, and is well-behaved beyond the range of the RPIMC data, suggestive of broad utility.

Properties of constraint-based single-point approximate kinetic energy functionals

We present an analysis and extension of our constraint-based approach to orbital-free OF kinetic-energy KE density functionals intended for the calculation of quantum-mechanical forces in multiscale moleculardynamics simulations. Suitability for realistic system simulations requires that the OF-KE functional yield accurate forces on the nuclei yet be computationally simple. We therefore require that the functionals be based on density-functional theory constraints, be local, be dependent at most upon a small number of parameters fitted to a training set of limited size, and be 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 generalized-gradient-approximation-type functionals in that they gave semiquantitative 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 and analyze the consequences. We give a simple illustration of such a functional and a few tests of it.

Nonempirical generalized gradient approximation free-energy functional for orbital-free simulations

(Received 6 August 2013; published 28 October 2013)We report a purely nonempirical generalized gradient approximation for the noninteracting free energyfunctionaloforbital-freedensityfunctionaltheoryobtainedviaanovelconstraint-basedparametrizationscheme.Weusethatfunctionaltoprovideforcesforfinite-temperaturemoleculardynamicssimulationsinthewarmdensematter(WDM)regimeanddemonstrategood-to-excellentagreementwithreferenceKohn-Shamcalculationsun-derWDMconditionsataminusculefractionofthecomputationalcostofcorrespondingorbital-basedsimulations.DOI: 10.1103/PhysRevB.88.161108 PACS number(s): 71

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

Abstract 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 2000 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.

Local-Scaling Transformation Version of Density Functional Theory: Application to Atoms and Diatomic Molecules

Applications of the local‐scaling transformation version of density functional theory, LS‐DFT, to atoms and diatomic molecules are presented. In the case of atoms, explicit kinetic‐ and exchange‐energy functionals for first‐ and second‐row atoms at the Hartree–Fock level are constructed. The emphasis given in LS‐DFT to the symmetry problem, namely, to the inclusion of spin and angular momentum restrictions in energy density functionals, is illustrated by the construction of explicit energy functionals (at the Hartree–Fock level) for the 1S, 3P and 1D terms of the 1s22s22p2 configuration of the carbon atom. Also, applications of LS‐DFT that go beyond the Hartree–Fock method are presented. In this respect, the decomposition of the electron correlation energy into its dynamical and nondynamical parts is analyzed for the case of four‐electron atoms and ions. It is shown that a “reference wave function”—differing from the exact one only in the dynamical correlation energy component—can always be found. Based on this wave function, the correlation energy is partitioned into “long‐range” and “short‐range” contributions. A method based on a cluster‐expansion technique is advanced for the purpose of treating the dynamical “short‐range” correlation component. In the case of diatomic molecules, the derivation of coupled first‐order integral equations for density transformations of prolate‐spheroidal coordinates is discussed. Applications of these density transformations to molecular orbitals involving single ζ atomic functions are carried out and a comparison is made between the energies coming from the original and the locally scaled orbitals. Also, the minimization of the kinetic energy at fixed Hartree–Fock density is discussed as this procedure is equivalent to solving the Kohn–Sham x‐only equations. Finally, some extensions of LS‐DFT to polyatomic systems (molecules and solids) are discussed. In particular, the possibility of generating a molecular energy density functional as a collection of atom‐centered functionals and of applying nonisotropic density transformations to solids is considered. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 155–183, 1999

Frank Discussion of the Status of Ground-State Orbital-Free DFT

Abstract 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 in single-point functionals since our original paper (2006). Then we focus on the advantages and limitations of generalized gradient approximation (GGA) noninteracting kinetic energy (KE) 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 noninteracting KE for a modest-sized set of molecules with 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.

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 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 that are valid for lithium densities up to at least 80 g/cm{3}.

Functional sets in quantum chemistry as fundamental elements of parametric methods

Abstract The idea of understanding the basic foundations of parametric quantum chemistry methods is the motivation of this work. The main purpose is to analyze, in a general way, the set of basic functionals (SBF) employed to express the energy functional of the Born-Oppenheimer Hamiltonian. The SBF is described according with addition and scalar multiplication properties of its subsets (SSBF) that must be obeyed by parametric SBF (PSBF). The minimax and variational principles (MMP and VP) are defined in terms of the SBF. A MMP is proposed for parametric methods given an optimal PSBF.

PADE APPROXIMATION FOR THE POLYNOMIAL REPRESENTATION OF THE CORRELATION ENERGY DENSITY FUNCTIONAL

Abstract Polynomials in the one-third power of the density were recently proposed to represent approximately the correlation energy density functional [S. Liu and R.G. Parr, Phys. Rev. A 53 (1996) 2211]. Studied in the present work is a Pade-approximant in that same variable which overcomes weaknesses in the polynomial form. Numerical results for atoms and molecules show that Pade forms fairly reproduce the experimental values, and are comparable in accuracy with other commonly used local functionals for the correlation energy.