Potential Density Functional Theory Research Articles

Efficient Gaussian process regression for prediction of molecular crystals harmonic free energies

We present a method to accurately predict the Helmholtz harmonic free energies of molecular crystals in high-throughput settings. This is achieved by devising a computationally efficient framework that employs a Gaussian Process Regression model based on local atomic environments. The cost to train the model with ab initio potentials is reduced by starting the optimization of the framework parameters, as well as the training and validation sets, with an empirical potential. This is then transferred to train the model based on density-functional theory potentials, including dispersion-corrections. We benchmarked our framework on a set of 444 hydrocarbon crystal structures, comprising 38 polymorphs and 406 crystal structures either measured in different conditions or derived from these polymorphs. Superior performance and high prediction accuracy, with mean absolute deviation below 0.04 kJ mol−1 per atom at 300 K is achieved by training on as little as 60 crystal structures. Furthermore, we demonstrate the predictive efficiency and accuracy of the developed framework by successfully calculating the thermal lattice expansion of aromatic hydrocarbon crystals within the quasi-harmonic approximation, and predict how lattice expansion affects the polymorph stability ranking.

Progress at the interface of wave-function and density-functional theories

The Kohn-Sham (KS) potential of density-functional theory (DFT) emerges as the minimizing effective potential in a variational scheme that does not involve fixing the unknown single-electron density. Using Rayleigh Schr\"odinger (RS) perturbation theory (PT), we construct ab initio approximations for the energy difference, the minimization of which determines the KS potential directly---thereby bypassing DFT's traditional algorithm to search for the density that minimizes the total energy. From second-order RS PT, we obtain variationally stable energy differences to be minimized, solving the severe problem of variational collapse of orbital-dependent exchange-correlation functionals based on second-order RS PT.

Resolving controversy about the correlation potential of density-functional theory far outside a finite system

The correlation potential, determined recently by Ginzburg [Theor. Math. Phys. 146, 275 (2006)] in the region far outside a finite many-electron system, differs significantly from the potential determined previously by Almbladh and von Barth (AvB) [Phys. Rev. B 31, 3231 (1985)]\char22{}the two versions sum to zero. We demonstrate that the arguments of Ginzburg for accepting his result (rather than that of AvB) as the correct one are inconsistent. We also find an error in the derivation of Ginzburg (some terms are omitted without explanation). After our correction, the Ginzburg result becomes identical with that of AvB.

Comment on “Asymptotic form of the Kohn-Sham correlation potential”

For finite systems that have the energetically highest-occupied molecular orbital (HOMO) with an asymptotic nodal surface, Joubert demonstrated recently [Phys. Rev. A 76, 012501 (2007)] strongly anisotropic behavior (in the asymptotic large-r region) of the exact correlation potential of density-functional theory. As is shown by us, this result is a direct and simple consequence of the strong anisotropy of the exact exchange potential obtained by Della Sala and Goerling [Phys. Rev. Lett. 89, 033003 (2002); Della Sala and GoerlingJ. Chem. Phys. 116, 5374 (2002)] and the assumption about the asymptotic isotropy of the Kohn-Sham (KS) potential (based on the investigation of Almbladh and von Barth [Phys. Rev. B 31, 3231 (1985)] for atoms). Joubert's result remains a hypothesis only, because the last assumption is in contradiction with the asymptotic strong anisotropy of the KS potential for systems with asymptotic nodal surface of the HOMO, demonstrated by Wu, Ayers, and Yang [J. Chem. Phys. 119, 2978 (2003)]. The correlation potential in the asymptotic region, stemming from their results, is given.

Multilayer relaxation and search for ferromagnetic order at the (100) surface of bulk paramagnetic vanadium

Low-energy-electron-diffraction (LEED) intensity measurements and multiple-scattering analysis for V(100), supported by accurate characterization of surface impurity concentrations based on Auger-electron spectroscopy, are used to obtain a meaningful extrapolation of the first-layer relaxation to the clean surface value: ${d}_{12}=1.36\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, corresponding to ${\ensuremath{\Delta}}_{12}=\ensuremath{-}10%\ifmmode\pm\else\textpm\fi{}3%$ relative to the bulk value ${d}_{0}=1.514\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$. A high-sensitivity probe for surface magnetism based on magneto-optic Kerr effect polarimetry using the cleanest surfaces achieved in the LEED experiment $(\ensuremath{\sim}5%\phantom{\rule{0.3em}{0ex}}\mathrm{C})$ yields a (sensitivity limited) null result with an estimated upper limit of $0.05\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{B}$/surface atom. These results are discussed within the framework of related experiments and in relation to the predictive accuracy of ab initio calculations that explore the surface structure and magnetism of V(100) both of which are sensitive to different approximations for the exchange-correlation potential in density-functional theory.

Spectral density functionals for electronic structure calculations

We introduce a spectral density-functional theory which can be used to compute energetics and spectra of real strongly correlated materials using methods, algorithms, and computer programs of the electronic structure theory of solids. The approach considers the total free energy of a system as a functional of a local electronic Green function which is probed in the region of interest. Since we have a variety of notions of locality in our formulation, our method is manifestly basis-set dependent. However, it produces the exact total energy and local excitational spectrum provided that the exact functional is extremized. The self-energy of the theory appears as an auxiliary mass operator similar to the introduction of the ground-state Kohn-Sham potential in density-functional theory. It is automatically short ranged in the same region of Hilbert space which defines the local Green function. We exploit this property to find good approximations to the functional. For example, if electronic self-energy is known to be local in some portion of Hilbert space, a good approximation to the functional is provided by the corresponding local dynamical mean-field theory. A simplified implementation of the theory is described based on the linear muffin-tin orbital method widely used in electronic structure calculations. We demonstrate the power of the approach on the long standing problem of the anomalous volume expansion of metallic plutonium.

Density-functional theory calculations with correct long-range potentials

A variational method for forcing the exchange-correlation potential in density-functional theory (DFT) to have the correct asymptotic decay is developed. The resulting exchange-correlation potentials are much improved while the total energies remain essentially the same, compared with conventional density-functional theory calculations. The highest occupied orbital energies from the asymptotically corrected exchange-correlation potentials are found to provide significantly more accurate approximations to the ionization potential (for a neutral molecule) and the electron affinity (for an anion) than those from conventional calculations, although the results are usually inferior to direct methods by computing energy differences. Extending recent results from exchange-only DFT, we show that exact exchange-correlation potential is nonuniform asymptotically. Correcting the asymptotic decay of approximate exchange-correlation potentials towards the exact functional form binds the highest occupied orbitals for atomic and molecular anions, which supports the use of DFT calculations for negatively charged molecular species. With this technique, even hybrid functionals have local exchange-correlation potentials, effectively removing the largest objection to including these functionals in the panoply of Kohn–Sham DFT methods.

Direct method for optimized effective potentials in density-functional theory.

The conventional optimized effective potential method is based on a difficult-to-solve integral equation. In the new method, this potential is constructed as a sum of a fixed potential and a linear combination of basis functions. The energy derivatives with respect to the coefficients of the linear combination are obtained. This enables calculations by optimization methods. Accurate atomic and molecular calculations with Gaussian basis sets are presented for exact exchange functionals. This efficient and accurate method for the optimized effective potential should play an important role in the development and application of density functionals.

Path-integral analysis of the exchange-correlation energy and potential in density-functional theory: Unpolarized systems.

The present work is a demonstration of how the exchange and correlation in density-functional theory can be studied using path-integral techniques. Compact and formally exact expressions for the exchange-correlation functional and potential are derived in terms of the functional integrals. The local density approximation is obtained in the limit of slowly varying density. A perturbative analysis of the exchange-correlation energy and potential via the semiclassical expansion of the effective action is presented. \textcopyright{} 1996 The American Physical Society.

THEOREMS FOR EXACT LOCAL EXCHANGE POTENTIAL

Theorems for the exact local Kohn-Sham exchange potential in density-functional theory are reviewed. Trial exchange potentials based on these theorems are illustrated.

Exchange potentials in density-functional theory.

The Harbola-Sahni exchange potential is the work needed to move an electron against the electric field of its hole charge distribution. We prove that it is not the exact exchange potential of density-functional theory, by showing that it yields the wrong second-order gradient expansion in the slowly varying limit. But we also discover that it yields the correct local-density approximation. Thus the Harbola-Sahni potential is a more physically correct version of the Slater potential, one that is better suited for molecular and solid-state applications. As a step in our derivation, we present the third-order gradient expansion of the exchange hole density, and discuss its structure. We also describe a new version of the Harbola-Sahni potential which corrects its path dependence. The exact exchange potential for an atom is given by the optimized potential model (OPM) of Talman and Shadwick. By using enhanced numerics, we confirm that the OPM potential satisfies the Levy-Perdew virial relation and exhibits correct -1/r behavior at large r. Numerical calculations also show that the intershell maxima in the exact exchange potential are needed to lower the total energy. These ``bumps'' are missing from the Harbola-Sahni and Slater potentials.

Effective potentials in density-functional theory.

Effective potentials in density-functional theory.