Yue Wang

Bio: Yue Wang is an academic researcher from Tulane University. The author has contributed to research in topics: Energy (signal processing) & Density functional theory. The author has an hindex of 12, co-authored 18 publications receiving 27297 citations. Previous affiliations of Yue Wang include University of North Carolina at Chapel Hill.

Accurate and simple analytic representation of the electron-gas correlation energy

Abstract: We propose a simple analytic representation of the correlation energy ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$ for a uniform electron gas, as a function of density parameter ${\mathit{r}}_{\mathit{s}}$ and relative spin polarization \ensuremath{\zeta}. Within the random-phase approximation (RPA), this representation allows for the ${\mathit{r}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}3/4}$ behavior as ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}\ensuremath{\infty}. Close agreement with numerical RPA values for ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,0), ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,1), and the spin stiffness ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$)=${\mathrm{\ensuremath{\partial}}}^{2}$${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$, \ensuremath{\zeta}=0)/\ensuremath{\delta}${\mathrm{\ensuremath{\zeta}}}^{2}$, and recovery of the correct ${\mathit{r}}_{\mathit{s}}$ln${\mathit{r}}_{\mathit{s}}$ term for ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0, indicate the appropriateness of the chosen analytic form. Beyond RPA, different parameters for the same analytic form are found by fitting to the Green's-function Monte Carlo data of Ceperley and Alder [Phys. Rev. Lett. 45, 566 (1980)], taking into account data uncertainties that have been ignored in earlier fits by Vosko, Wilk, and Nusair (VWN) [Can. J. Phys. 58, 1200 (1980)] or by Perdew and Zunger (PZ) [Phys. Rev. B 23, 5048 (1981)]. While we confirm the practical accuracy of the VWN and PZ representations, we eliminate some minor problems with these forms. We study the \ensuremath{\zeta}-dependent coefficients in the high- and low-density expansions, and the ${\mathit{r}}_{\mathit{s}}$-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential ${\mathrm{\ensuremath{\mu}}}_{\mathit{c}}^{\mathrm{\ensuremath{\sigma}}}$(${\mathit{r}}_{\mathit{s}}$,\ensuremath{\zeta}) is evaluated for use in self-consistent density-functional calculations.

Generalized gradient approximation for the exchange-correlation hole of a many-electron system

Abstract: We construct a generalized gradient approximation (GGA) for the density ${\mathit{n}}_{\mathrm{xc}}$(r,r+u) at position r+u of the exchange-correlation hole surrounding an electron at r, or more precisely for its system and spherical average 〈${\mathit{n}}_{\mathrm{xc}}$(u)〉=(4\ensuremath{\pi}${)}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\int}d${\mathrm{\ensuremath{\Omega}}}_{\mathit{u}}$ ${\mathit{N}}^{\mathrm{\ensuremath{-}}1}$\ensuremath{\int}${\mathit{d}}^{3}$r n(r)${\mathit{n}}_{\mathrm{xc}}$(r,r+u). Starting from the second-order density gradient expansion, which involves the local spin densities ${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$(r),${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$(r) and their gradients \ensuremath{ abla}${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$(r),\ensuremath{ abla}${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$(r), we cut off the spurious large-u contributions to restore those exact conditions on the hole that the local spin density (LSD) approximation respects. Our GGA hole recovers the Perdew-Wang 1991 and Perdew-Burke-Ernzerhof GGA's for the exchange-correlation energy, which therefore respect the same powerful hole constraints as LSD. When applied to real systems, our hole model provides a more detailed test of these energy functionals, and also predicts the observable electron-electron structure factor. \textcopyright{} 1996 The American Physical Society.

Correlation hole of the spin-polarized electron gas, with exact small-wave-vector and high-density scaling

Abstract: For a uniform electron gas of density n=${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$+${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$=3/4\ensuremath{\pi}${\mathit{r}}_{\mathit{s}}^{3}$=\ensuremath{\pi}${\mathit{k}}_{\mathit{s}}^{6}$/192 and spin polarization \ensuremath{\zeta}=(${\mathit{n}}_{\mathrm{\ensuremath{\uparrow}}}$-${\mathit{n}}_{\mathrm{\ensuremath{\downarrow}}}$)/n, we study the Fourier transform \ensuremath{\rho}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{c}}$(k,${\mathit{r}}_{\mathit{s}}$,\ensuremath{\zeta}) of the correlation hole, as well as the correlation energy ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,\ensuremath{\zeta})=${\mathcal{F}}_{0}^{\mathrm{\ensuremath{\infty}}}$dk \ensuremath{\rho}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{c}}$/\ensuremath{\pi}. In the high-density (${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0) limit, we find a simple scaling relation ${\mathit{k}}_{\mathit{s}}$\ensuremath{\rho}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{c}}$/\ensuremath{\pi}${\mathit{g}}^{2}$\ensuremath{\rightarrow}f(z,\ensuremath{\zeta}), where z=k/${\mathit{gk}}_{\mathit{s}}$, g=[(1+\ensuremath{\zeta}${)}^{2/3}$+(1-\ensuremath{\zeta}${)}^{2/3}$]/2, and f(z,1)=f(z,0). The function f(z,\ensuremath{\zeta}) is only weakly \ensuremath{\zeta} dependent, and its small-z expansion -3z/${\mathrm{\ensuremath{\pi}}}^{2}$+4 \ensuremath{\surd}3 ${\mathrm{z}}^{2}$/${\mathrm{\ensuremath{\pi}}}^{2}$+... is also the exact small-wave-vector (k\ensuremath{\rightarrow}0) expansion for any ${\mathit{r}}_{\mathit{s}}$ or \ensuremath{\zeta}. Motivated by these considerations, and by a discussion of the large-wave-vector and low-density limits, we present two Pad\'e representations for \ensuremath{\rho}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{c}}$ at any k, ${\mathit{r}}_{\mathit{s}}$, or \ensuremath{\zeta}, one within and one beyond the random-phase approximation (RPA). We also show that \ensuremath{\rho}\ifmmode\bar\else\textasciimacron\fi{} $_{\mathit{c}}^{\mathrm{RPA}}$ obeys a generalization of Misawa's spin-scaling relation for ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}^{\mathrm{RPA}}$, and that the low-density (${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}\ensuremath{\infty}) limit of ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}^{\mathrm{RPA}}$ is \ensuremath{\sim}${\mathit{r}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}3/4}$.

Pair-distribution function and its coupling-constant average for the spin-polarized electron gas

Abstract: The pair-distribution function g describes physical correlations between electrons, while its average g\ifmmode\bar\else\textasciimacron\fi{} over coupling constant generates the exchange-correlation energy. The former is found from the latter by g=(1-${\mathit{a}}_{0}$\ensuremath{\partial}/\ensuremath{\partial}${\mathit{a}}_{0}$)g\ifmmode\bar\else\textasciimacron\fi{}, where ${\mathit{a}}_{0}$ is the Bohr radius. We present an analytic representation of g\ifmmode\bar\else\textasciimacron\fi{} (and hence g) in real space for a uniform electron gas with density parameter ${\mathit{r}}_{\mathit{s}}$ and spin polarization \ensuremath{\zeta}. This expression has the following attractive features: (1) The exchange-only contribution is treated exactly, apart from oscillations we prefer to ignore. (2) The correlation contribution is correct in the high-density (${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0) and nonoscillatory long-range (R\ensuremath{\rightarrow}\ensuremath{\infty}) limits. (3) The value and cusp are properly described in the short-range (R\ensuremath{\rightarrow}0) limit. (4) The normalization and energy integrals are respected. The result is found to agree with the pair-distribution function g from Ceperley's quantum Monte Carlo calculation. Estimates are also given for the separate contributions from parallel and antiparallel spin correlations, and for the long-range oscillations at a high finite density.

Spin scaling of the electron-gas correlation energy in the high-density limit.

Abstract: Expression de l'energie de correlation de l'etat fondamental par particule dans un gaz d'electrons uniformes avec des densites de spin n↑ et n↓. Etablissement d'une expression analytique pour le facteur d'echelle de spin dans la limite de haute densite r s →0

Density‐functional thermochemistry. III. The role of exact exchange

Abstract: Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.

A New Mixing of Hartree-Fock and Local Density-Functional Theories

Abstract: Previous attempts to combine Hartree–Fock theory with local density‐functional theory have been unsuccessful in applications to molecular bonding. We derive a new coupling of these two theories that maintains their simplicity and computational efficiency, and yet greatly improves their predictive power. Very encouraging results of tests on atomization energies, ionization potentials, and proton affinities are reported, and the potential for future development is discussed.

Toward reliable density functional methods without adjustable parameters: The PBE0 model

Abstract: We present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amount of exact exchange. The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.

From molecules to solids with the DMol3 approach

Abstract: Recent extensions of the DMol3 local orbital density functional method for band structure calculations of insulating and metallic solids are described. Furthermore the method for calculating semilocal pseudopotential matrix elements and basis functions are detailed together with other unpublished parts of the methodology pertaining to gradient functionals and local orbital basis sets. The method is applied to calculations of the enthalpy of formation of a set of molecules and solids. We find that the present numerical localized basis sets yield improved results as compared to previous results for the same functionals. Enthalpies for the formation of H, N, O, F, Cl, and C, Si, S atoms from the thermodynamic reference states are calculated at the same level of theory. It is found that the performance in predicting molecular enthalpies of formation is markedly improved for the Perdew–Burke–Ernzerhof [Phys. Rev. Lett. 77, 3865 (1996)] functional.

Harmonic Vibrational Frequencies: An Evaluation of Hartree−Fock, Møller−Plesset, Quadratic Configuration Interaction, Density Functional Theory, and Semiempirical Scale Factors

Abstract: Scaling factors for obtaining fundamental vibrational frequencies, low-frequency vibrations, zero-point vibrational energies (ZPVE), and thermal contributions to enthalpy and entropy from harmonic frequencies determined at 19 levels of theory have been derived through a least-squares approach. Semiempirical methods (AM1 and PM3), conventional uncorrelated and correlated ab initio molecular orbital procedures [Hartree−Fock (HF), Moller−Plesset (MP2), and quadratic configuration interaction including single and double substitutions (QCISD)], and several variants of density functional theory (DFT: B-LYP, B-P86, B3-LYP, B3-P86, and B3-PW91) have been examined in conjunction with the 3-21G, 6-31G(d), 6-31+G(d), 6-31G(d,p), 6-311G(d,p), and 6-311G(df,p) basis sets. The scaling factors for the theoretical harmonic vibrational frequencies were determined by a comparison with the corresponding experimental fundamentals utilizing a total of 1066 individual vibrations. Scaling factors suitable for low-frequency vib...