Perdew Zunger Research Articles

Dependence of Structural and Electronic Properties of Uranium Monochalcogenides on Exchange–Correlation Energy Functionals

We study the dependence of the structural properties of uranium monochalcogenides, U X where X = S, Se, and Te, as well as their electronic ones on the exchange–correlation energy functionals within the spin density functional theory, carrying out all electron calculations by the fully relativistic full-potential linear-combination-of-atomic-orbitals method. We employ two functionals of the local spin density approximation (LSDA) and two functionals of the generalized gradient approximations (GGA); the former two are the Perdew–Zunger and Perdew–Wang functionals and the latter two are the Perdew–Burke–Ernzerhof (PBE) and PBEsol functionals. We also examine the effects of the relativistic correction to the LSDA exchange part of each functional. We find that, for lattice constants, bulk moduli, and cohesive energies, the results of the calculations using the PBE functional are in the best agreement with the experimental results. On the contrary, we find that calculated total magnetic moments and one-electro...

First principles lattice dynamical calculation of semiboride Be 2B and its ternary alloys XBeB (X=Na, Mg, Al)

We present results of first principles total energy calculations of the structure, electronic and lattice dynamics for beryllium semiboride and its three ternary alloys using generalized gradient and local density approximations under the framework of density functional theory. The generalized gradient approximation is used for all compounds except MgBeB using the Perdew–Burke–Ernzehorf exchange correlation functional while local density approximations use the Perdew–Zunger ultrasoft exchange correlation functional. The calculated ground state structural parameters are in good agreement with those of experimental and previous theoretical studies. The electronic band structure calculations show that Be 2B may transform to a semiconductor after Al substitution. A linear response approach to density functional theory is used to calculate phonon dispersion curves and vibrational density of states. The phonon dispersion curves of Be 2B and AlBeB are positive indicating a dynamical stablility of the structure for these compounds. The phonon dispersion curves of NaBeB and MgBeB show the imaginary phonons throughout the Brillouin zone, which confirms dynamical instability as indicated in band structures for these alloys. We also present the partial phonon density of states for different species of Be 2B and AlBeB to bring out the details of the participation of different atoms in the total phonon density of state, particularly the role played by Al atom. The first time calculated phonon properties are clearly able to bring out the significant effect of isoelectronic substitution in Be 2B.

First-principles simulations of the electronic density of states for superionic Ag 2CdI 4 crystals

Energy band dispersion calculations have been performed for Ag 2CdI 4 superionic within a framework of local density approximation (Perdew–Zunger parameterization) exploiting the first-principles CASTEP computer code. The ab-initio electronic structure simulations were performed for both ( I4̅ and I4̅2 m) types of ε-Ag 2CdI 4 crystalline structures. Principal optical functions as well as the density of electronic states in the spectral range of inter-band optical transitions (2.5 eV–20 eV) were determined. Theoretically calculated absorption coefficients derived from the obtained band structure are compared with appropriate experimental data.

Ionization potentials and electron affinities in the Perdew–Zunger self-interaction corrected density-functional theory

Using a self-consistent implementation of the Perdew-Zunger self-interaction corrected (PZ-SIC) density-functional theory, we have calculated ionization potentials (IP) and electron affinities (EA) of first- and second-row atoms and a set of small molecules. Several exchange-correlation functionals were tested. IPs and EAs were obtained by two methods: as the difference in self-consistent field (SCF) energies of neutrals and ions (deltaSCF) and as negatives of highest-occupied orbital energies. We found that, except for local spin-density approximation, PZ-SIC worsens DeltaSCF IPs and EAs. On the other hand, PZ-SIC brings orbital eigenvalues into much better agreement with electron removal energies. The Perdew-Zunger SIC seems to over-correct many-electron systems; for molecules it performs worse than for atoms. We also discuss several common approximations to PZ-SIC such as spherical averaging of orbital densities in atoms.

Effect of the Perdew–Zunger self-interaction correction on the thermochemical performance of approximate density functionals

The Perdew-Zunger self-interaction-corrected density functional theory (SIC-DFT) was implemented self-consistently using a quasi-Newton direct minimization method. We calculated SIC-DFT energies for a number of atoms and molecules using various approximate density functionals, including hybrids. Self-interaction errors (SIE) of these functionals were compared and analyzed in terms of contributions from valence and core orbitals. We also calculated enthalpies of formation of the standard G2-1 set of 55 molecules and found that self-interaction-correction (SIC) improves agreement with experiment only for the LSDA functional, while all other functionals show worse performance upon introducing SIC. This is the first systematic study of the effect of SIC on thermochemical properties. We found no direct connection between the magnitude of the SIE contained in a functional and its performance for thermochemistry. Approximate functionals with large self-interaction errors can accurately reproduce enthalpies of formation. Our results do not support the popular belief that a smaller SIE of hybrid functionals is the main reason for their higher accuracy.

Ground state of a quasi-two-dimensional electron gas

The ground state of a quasi-two-dimensional electron gas (Q-2DEG) is investigated within a framework of the local spin density approximation (LSDA) with Perdew–Zunger type exchange-correlation energy. The ground state in a Q-2DEG is given as a function of film thickness and electron density. The Wigner rod ground state in a very thin film with low electron areal density is discussed in detail. In addition, the ground state of a two-dimensional electron gas (2DEG) is investigated using the LSDA with Tanatar–Ceperley and Attaccalite–Moroni–Georgi–Bachelet types of exchange-correlation energy. The ground state is found to show a phase transition from a nonmagnetic fluid to a spin-fully-polarized ferromagnetic Wigner ribbon with decreasing areal density. The difference between a 2DEG and a Q-2DEG with infinitesimal film thickness is discussed.

Ghost- and self-interaction-free ensemble calculations with local exchange–correlationpotential for atoms

Though the exact ensemble energy functional is free from self-interaction andghost-interaction (i.e. self-interaction between the elements of the ensemble),approximations generally suffer from both self- and ghost-interactions. Recently, aghost-interaction-free ensemble Kohn–Sham potential has been proposed. Combining thisnewly proposed method with the self-interaction-free Perdew–Zunger approximation, now aghost- and self-interaction-corrected (GSIC) ensemble Kohn–Sham potential ispresented. Total ensemble energies and excitation energies are obtained withGSIC local Vosko–Wilk–Nusair exchange–correlation potential for some lightatoms.

Magnetic phase diagram in a quasi-two-dimensional electron gas

Using spin density functional theory within the framework of the local spin density approximation with Perdew–Zunger type exchange-correlation energy, ferromagnetism in a quasi-two-dimensional electron gas (Q-2DEG) is studied. The electronic and magnetic structures of a thin film are calculated as a function of film thickness and electron density. Ferromagnetism in the Q-2DEG is found to appear at a higher electron density than in the three-dimensional electron gas. Unless a film is very thin, with decreasing electron density, a magnetic phase transition occurs from a spin-unpolarized fluid to a Wigner film with surface magnetism, in which the spin polarization localizes only in the neighborhood of surfaces. Further decreasing density induces another transition to a fully spin-polarized ferromagnetic Wigner film.

Phosphorus NMR Chemical Shifts with Self-Interaction Free, Gradient-Corrected DFT

We examine the origin of the orbital localization requirement, commonly imposed on effective potential implementations of the Perdew−Zunger (PZ) self-interaction correction (SIC). We demonstrate that the condition arises because of the presence of irreducible off-diagonal Lagrangian multipliers in the coupled PZ eigenequations. Thus, this condition is essential for obtaining an energy-minimizing solution. Further, we report on an implementation of PZ SIC for the generalized gradient approximation (GGA) to the exchange-correlation energy within density functional theory (DFT). The implementation relies on the Krieger−Li−Iafrate (KLI) approximation to the optimized effective potential (OEP), simplifying the evaluation of molecular properties, such as the NMR chemical shifts. We examine several approaches toward incorporating the frozen core orbitals within the SIC−KLI−OEP scheme. To achieve an accurate description of both the energetic and magnetic properties, core orbitals must be included in the KLI potential on an equal footing with the valence orbitals. Implementation of the frozen core orbitals enables incorporation of relativistic effects via the quasirelativistic Pauli Hamiltonian. As the first application of the SIC−GGA approach, we examine 31P NMR chemical shifts of 18 representative small molecules, as well as the previously reported C, H, N, O, and F SIC-LDA (local density approximation) test set. For C, N, O, and F NMR chemical shifts, SIC−GGA performs similarly to SIC−LDA, whereas a significant improvement is observed for hydrogen. Almost identical results, both for the chemical shifts and absolute shieldings, are obtained with different parent GGAs. For the 31P test set, SIC−revPBE (revised Perdew−Burke−Ernzerhof functional of Zhang and Yang) leads to an root-mean-square (RMS) residual error of 23 ppm, compared to 54 ppm for its parent GGA, and 40 ppm for the SIC−VWN (Vosko−Wilk−Nusair) LDA functional. In particular, SIC−revPBE correctly reproduces the experimental trends in the PF3−PCl3−PBr3−PI3 series, which is described qualitatively incorrectly by VWN, revPBE, and SIC−VWN calculations. A similar improvement is observed for the 31P shielding tensor components. The spurious self-interaction, in modern approximate DFT, appears to be a major, and so far largely overlooked, source of errors in calculations of the NMR shielding tensors.

Curing difficult cases in magnetic properties prediction with self-interaction corrected density functional theory

The Perdew–Zunger self-interaction correction (SIC) was implemented self-consistently within a molecular density functional theory (DFT) program, using the Krieger–Li–Iafrate approximation to the optimized effective potential, and the Vosko–Wilk–Nusair (VWN) functional. The computationally efficient implementation relies on the fitting of orbital densities for the evaluation of orbital Coulomb potentials, and allows for routine applications to large molecules. Due to the use of the effective potential approach, the evaluation of the energy derivatives can be handled by standard Kohn–Sham DFT techniques in a straightforward way. The SIC-VWN technique is applied to the calculation of nuclear magnetic resonance (NMR) parameters in representative small molecules, containing C, H, N, O, and F. Removal of self-interaction leads to a substantial improvement in the calculated isotropic chemical shifts for N, O, and F, where SIC-VWN holds an advantage over both local (VWN), and gradient-corrected functionals (Becke 88-Perdew 86, BP86). For C and H isotropic chemical shifts, which are well described by the gradient-corrected functionals, SIC-VWN performs as well as BP86. SIC-VWN also improves the description of the absolute chemical shielding, and of the principal components of the NMR shielding tensors. The changes arise mainly from adjustments in the Kohn–Sham orbital energies, leading to a better description of the paramagnetic contribution to the shielding tensor. For spin–spin coupling constants, SIC-VWN improves the description of the paramagnetic contribution. At the same time, the magnitude of the Fermi contact term is underestimated, yielding mixed overall results. Slow convergence of the spin-spin coupling results with the basis set size prevents a conclusive statistical evaluation for this property. The clear physical origin of the SIC-VWN effect in the prediction of magnetic properties opens the tantalizing possibility that this technique may be effective in solving problems often encountered in the calculations of NMR parameters of heavier nuclei.

Ground-state properties of jellium metals with low electron densities

The ground state of a three-dimensional electron gas is theoretically investigated within the framework of the local spin density approximation with the Perdew–Zunger exchange-correlation energy. The system has been found to be in a one- or two-dimensional crystal state, when the Wigner sphere radius r s has an intermediate value. At r s=60, a triangular lattice with the lattice spacing 96.10 is the lowest energy state among fluids, 1D, 2D, and 3D crystals.

LDA calculations of the Young's moduli of polyethylene and six polyfluoroethylenes

The Young's moduli of the linear chain polymers, polyethylene and six polyfluoroethylenes, constrained to the planar conformation, are calculated by means of the local density approximation (LDA) using the Perdew–Zunger (PZ) correlation potential and a linear combination of Gaussian-type orbitals (LCGTO).

Pencil-case structure in electron distribution of very thin film

The ground-state properties in a very thin film are investigated using the planar uniform jellium model as the positive charge background on the basis of the spin density functional theory treated within the local spin density approximation with the Perdew–Zunger type exchange-correlation energy. For a given electron density, the quasi-two-dimensional system undergoes a transition from a fluid to a one-dimensional electron-self-confined (1D ESC) state with an electron distribution of pencil-case structure, as the film thickness D is decreased. Even in metallic films, a 1D ESC state is always realized in the limit of small D.

Theoretical determination of exact-exchange-mixing parameter employing the ionization energy theorem

The value of Becke's exact-exchange-mixing parameter is determined by purely theoretical considerations by requiring that the ionization energy theorem (−ϵm=I) be satisfied as closely as possible. This method is applied to the case in which the density functional theory approximation to the exchange–correlation energy functional is given by the local spin density approximation with Perdew–Zunger self-interaction correction, which leads to the correct−1/r long-range behavior of the exchange– correlation potential and consequently to accurate highest occupied orbital energy eigenvalues, ϵm. Employing this approach on atoms with Z≤20 self-consistent optimized-effective potential calculations results in the determination of the mixing parameter, which is in good agreement with that of Becke, and the resulting calculations of the ionization potentials and electron affinities for these atoms are on average within 0.10 eV of the experimental results. In addition, the resulting correlation potential for both neon and argon exhibits a positive bump in the region of maximum density of the highest lying p states. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 255–264, 1998

A comparative study of density functional models to estimate molecular atomization energies

In the present study the molecular atomization energies have been computed with some of the recent density functionals and with a semiempirical model developed in the IBM laboratory. In particular, the Lie–Clementi (LC), the Colle–Salvetti (CS), the Gunnarson–Lundqvist (GL), the Vosko, Wilk, and Nusair (VWN), the Perdew–Zunger (PZ), the Becke (B), and the Lee, Yang, and Parr (LYP) functionals have been considered. For GL and VWN the self-interaction correction of Stoll, Pavlidou, and Preuss (SPP) has been included. For the PZ the gradient correction of Perdew has been included. For the LYP a new and simpler form as proposed by Michlich et al. has been implemented. More than 50 small to fairly large molecules have been chosen at test cases. The results obtained with the present semiempirical model are gratifying and indicate that further improvement and calibration is still possible. From the computed data it is concluded that the density functionals in most cases do provide a pragmatic solution to the determination molecular atomization energy.

On the gaussian-type orbitals approach to local density functional theory

Two most pressing practical problems with the linear combination of Gaussian-type orbitals (LCGTO) approach to local density functional (LDF) theory both relate to the treatment of the exchange and correlation potential. They are the problem of (effective or direct) numerical integration on a grid of points and the general LDF problem of the spin dependence of the exchange and correlation functional. We discuss our recent progress in solving the SCF problems associated with a treatment of the la (only) exchange and correlation functional that uses only analytic integrals, thereby avoiding any grid of points. This advance will allow exact analytic gradients; the first derivative expressions are presented. The complete LDF treatment of elemental clusters is an area in which gradients are indispensable. Without such means to optimize the large number of nuclear degrees of freedom in a thirteen-atom cluster, we have studied three highly symmetric thirteen—atom nickel clusters using the la and the Perdew—Zunger approximations to exchange and correlation in order to see if they differ in their predictions of the magnetism of different isomers of clusters, experimental quantities that will likely soon be measured.

A comparison of self-interaction-corrected local correlation energy functionals

A new selfinteraction-corrected local correlation energy functional is constructed to conform with the exact limiting behaviour in both one-electron systems and N-electron systems (N to infinity ) with slowly varying densities. It is combined with an exact treatment of exchange to selfconsistently calculate correlation energies, ionisation potentials, electron affinities, spin and number densities and diamagnetic susceptibilities for a number of atoms and ions. The results are compared with those from the Stoll-Pavlidou-Preuss (SPP) and the Perdew-Zunger (PZ) selfinteraction corrected forms as well as the Kohn-Sham (KS) form. For most of the above properties the new form is either as good as or better than the others. The authors conclude that for physical quantities that can be expressed as differences of energies or differences of spin up/down densities the exact exchange plus local correlation method is a viable and much simpler alternative to large configuration-interaction calculations for atoms and ions, especially for those with N>or=15.