Local Exchange-correlation Potential Research Articles

Self-Consistent Range-Separated Density-Functional Theory with Second-Order Perturbative Correction via the Optimized-Effective-Potential Method.

We extend the range-separated double-hybrid RSH+MP2 method (Ángyán, J. G.; et al. Phys. Rev. A 2005, 72, 012510), combining long-range HF exchange and MP2 correlation with a short-range density functional to a fully self-consistent version using the optimized-effective-potential technique in which the orbitals are obtained from a local potential including the long-range HF and MP2 contributions. We test this approach, that we name RS-OEP2, on a set of small closed-shell atoms and molecules. For the commonly used value of the range-separation parameter μ = 0.5 bohr-1, we find that self-consistency does not seem to bring any improvement for total energies, ionization potentials, and electronic affinities. However, contrary to the non-self-consistent RSH+MP2 method, the present RS-OEP2 method gives a LUMO energy which physically corresponds to a neutral excitation energy and gives local exchange-correlation potentials which are reasonably good approximations to the corresponding Kohn-Sham quantities. At a finer scale, we find that RS-OEP2 gives largely inaccurate correlation potentials and correlated densities, which points to the need of further improvement of this type of range-separated double hybrids.

Simple correction to bandgap problems in IV and III–V semiconductors: an improved, local first-principles density functional theory

We report results from a fast, efficient, and first-principles full-potential Nth-order muffin-tin orbital (FP-NMTO) method combined with van Leeuwen–Baerends correction to local density exchange-correlation potential. We show that more complete and compact basis set is critical in improving the electronic and structural properties. We exemplify the self-consistent FP-NMTO calculations on group IV and III–V semiconductors. Notably, predicted bandgaps, lattice constants, and bulk moduli are in good agreement with experiments (e.g. we find for Ge 0.86 eV, 5.57 , 75 GPa versus measured 0.74 eV, 5.66 , 77.2 GPa). We also showcase its application to the electronic properties of 2-dimensional h-BN and h-SiC, again finding good agreement with experiments.

A local environment descriptor for machine-learned density functional theory at the generalized gradient approximation level.

We propose a grid-based local representation of electronic quantities that can be used in machine learning applications for molecules, which is compact, fixed in size, and able to distinguish different chemical environments. We apply the proposed approach to represent the external potential in density functional theory with modified pseudopotentials and demonstrate its proof of concept by predicting the Perdew-Burke-Ernzerhof and local density approximation electronic density and exchange-correlation potentials by kernel ridge regression. For 16 small molecules consisting of C, H, N, and O, the mean absolute error of exchange-correlation energy was 0.78 kcal/mol when trained for individual molecules. Furthermore, the model is shown to predict the exchange-correlation energy with an accuracy of 3.68 kcal/mol when the model is trained with a small fraction (4%) of all 16 molecules of the present dataset, suggesting a promising possibility that the current machine-learned model may predict the exchange-correlation energies of an arbitrary molecule with reasonable accuracy when trained with a sufficient amount of data covering an extensive variety of chemical environments.

Efficient and Linear-Scaling Seminumerical Method for Local Hybrid Density Functionals.

Local hybrid functionals, that is, functionals with local dependence on the exact exchange energy density, generalize the popular class of global hybrid functionals and extend the applicability of density functional theory to electronic structures that require an accurate description of static correlation. However, the higher computational cost compared to conventional Kohn-Sham density functional theory restrained their widespread application. Here, we present a low-prefactor, linear-scaling method to evaluate the local hybrid exchange-correlation potential as well as the corresponding nuclear forces by employing a seminumerical integration scheme. In the seminumerical scheme, one integration in the electron repulsion integrals is carried out analytically and the other one is carried out numerically, employing an integration grid. A high computational efficiency is achieved by combining the preLinK method [ J. Kussmann and C. Ochsenfeld, J. Chem. Phys. 2013 138, 134114 ] with explicit screening of integrals for batches of grid points to minimize the screening overhead. This new method, denoted as preLinX, provides an 8-fold performance increase for a DNA fragment containing four base pairs as compared to existing S- and P-junction-based methods. In this way, our method allows for the evaluation of local hybrid functionals at a cost similar to that of global hybrid functionals. The linear-scaling behavior, efficiency, accuracy, and multinode parallelization of the presented method is demonstrated for large systems containing more than 1000 atoms.

An Empirical, yet Practical Way To Predict the Band Gap in Solids by Using Density Functional Band Structure Calculations

Band structure calculations based on density functional theory (DFT) with local or gradient-corrected exchange-correlation potentials are known to severely underestimate the band gap of semiconducting and insulating materials. Alternative approaches have been proposed: from semiempirical setups, such as the so-called DFT+U, to hybrid density functionals using a fraction of nonlocal Fock exchange, to modifications of semilocal density functionals. However, the resulting methods appear to be material dependent and lack theoretical rigor. The rigorous many-body perturbation theory based on GW methods provides accurate results but at a very high computational cost. Hereby, we show that a linear correlation between the electronic band gaps obtained from standard DFT and GW approaches exists for most materials and argue that (1) this is a strong indication that the problem of predicting band gaps from standard DFT calculation arises from the assignment of a physical meaning to the Kohn–Sham energy levels rather...

English

In this paper a theoretical studies of the space separation of electron and hole wave functions in the quantum well ZnO/Mg0.27Zn0.73O are presented. For this aim the self-consistent solution of the Schrodinger equations for electrons and holes and the Poisson equations at the presence of spatially varying quantum well potential due to the piezoelectric effect and local exchange-correlation potential is found. The one-dimensional Poisson equation contains the Hartree potential which includes the one-dimensional charge density for electrons and holes along the polarization field distribution. The three-dimensional Poisson equation contains besides the one-dimensional charge density for electrons and holes the exchange-correlation potential which is built on convolutions of a plane-wave part of wave functions in addition. In ZnO/(Zn,Mg)O quantum well the electron-hole pairing leads to the exciton insulator states. An exciton insulator states with a gap 3.4 eV are predicted. If the electron and hole are separated, their energy is higher on 0.2 meV than if they are paired. The particle-hole pairing leads to the Cooper instability.

Particle-hole pair and beelectron states in ZnO/(Zn,Mg)O quantum wells and Dirac materials.

In this paper a theoretical studies of the space separation of electron and hole wave functions in the quantum well ZnO/Mg(0.27)Zn(0.73)O are presented. For this aim the self-consistent solution of the Schrödinger equations for electrons and holes and the Poisson equations at the presence of spatially varying quantum well potential due to the piezoelectric effect and local exchange-correlation potential is found. The one-dimensional Poisson equation contains the Hartree potential which includes the one-dimensional charge density for electrons and holes along the polarization field distribution. The three-dimensional Poisson equation contains besides the one-dimensional charge density for electrons and holes the exchange-correlation potential which is built on convolutions of a plane-wave part of wave functions in addition. The shifts of the Hartree valence band spectrums and the conduction band spectrum with respect to the flat band spectrums as well as the Hartree-Fock band spectrums with respect to the Hartree ones are found. An overlap integrals of the wave functions of holes and electron with taking into account besides the piezoelectric effects the exchange-correlation effects in addition is greater than an overlap integral of Hartree ones. The Hartree particles distribute greater on edges of quantum well than Hartree-Fock particles. It is found that an effective mass of heavy hole of Mg(0.27)Zn(0.73)O under biaxial strain is greater than an effective-mass of heavy hole of ZnO. It is calculated that an electron mass is less than a hole mass. It is found that the Bohr radius is grater than the localization range particle-hole pair, and the excitons may be spontaneously created.Schrödinger equation for pair of two massless Dirac particles when magnetic field is applied in Landau gauge is solved exactly. In this case the separation of center of mass and relative motion is obtained. Landau quantization $\epsilon=\pm\,B\sqrt{l}$ for pair of two Majorana fermions coupled via a Coulomb potential from massless chiral Dirac equation in cylindric coordinate is found. The root ambiguity in energy spectrum leads into Landau quantization for beelectron, when the states in which the one simultaneously exists are allowed. The tachyon solution with imaginary energy in Cooper problem ($\epsilon^{2}<0$) is found.

Non Local Corrections to the Electronic Structure of Non Ideal Electron Gases: The Case of Graphene and Tyrosine

We introduce a formal definition of a non local functional and show that the non local exchange-correlation potential functional, derived within Density-Functional Theory, is non local in the space of electronic densities. A previously developed non local exchange-correlation potential term, is introduced to approach the exact density-functional potential. With this approach, the electronic structure of the graphene surface and the tyrosine amino acid are calculated.

Role of nonlocal exchange in the electronic structure of correlated oxides

We present a systematic study of the electronic structure of several prototypical correlated transition-metal oxides: VO${}_{2}$, V${}_{2}$O${}_{3}$, Ti${}_{2}$O${}_{3}$, LaTiO${}_{3}$, and YTiO${}_{3}$. In all these materials, in the low-temperature insulating phases the local and semilocal density approximations (LDA and GGA, respectively) of density-functional theory yield a metallic Kohn-Sham band structure. Here we show that, without invoking strong-correlation effects, the role of nonlocal exchange is essential to cure the LDA/GGA delocalization error and provide a band-structure description of the electronic properties in qualitative agreement with the experimental photoemission results. To this end, we make use of hybrid functionals that mix a portion of nonlocal Fock exchange with the local LDA exchange-correlation potential. Finally, we discuss the advantages and the shortcomings of using hybrid functionals for correlated transition-metal oxides.

Ab initio DFT – the seamless connection between WFT and DFT

Orbital-dependent exchange-correlation functionals and potentials play an increasingly important role in Density Functional Theory (DFT). Methods which use explicit orbital-dependent functionals can be viewed as a natural extension to the standard Kohn–Sham (KS) procedure in DFT, that traditionally have used functionals with explicit density-dependence but only implicit orbital-dependence. Ab initio DFT, invented at the Quantum Theory Project, is the method which could define rigorous orbital-dependent exchange-correlation functionals and potentials in the context of KS DFT theory. The local and multiplicative exchange-correlation potentials are derived from a general theoretical framework based on the density condition in KS theory and from coupled-cluster theory and many-body perturbation theory. Ab initio DFT guarantees to converge to the right answer in the correlation and basis set limit, just as does ab initio Wave Function Theory (WFT) and solves in a rigorous way most of the shortcomings of standard density-dependent KS DFT. It is also the route toward understanding the relationships between traditional ab initio WFT and DFT. The Optimized Effective Potential ‘journey’ on the borderline of WFT and DFT was inspired and possible only because of the Quantum Theory Project where we stayed as postdocs in 1999–2001. It seems to us then we were in the right place and at the right time, and certainly with the right people. The QTP scientific melting pot and Sanibel's meetings gave us an excellent possibility to work together, learn and hopefully solve many important scientific problems.

The role of the reference state in long-range random phase approximation correlation

We recently presented a combination of a short-range density functional approximation with long-range random phase approximation (RPA) correlation [B. G. Janesko, T. M. Henderson, and G. E. Scuseria, J. Chem. Phys. 130, 081105 (2009)]. Here we explore how this approximation's performance is affected by the choice of reference state, i.e., the orbitals and orbital energy differences entering the RPA energy expression. Our previous results built the reference state using a nonlocal exchange potential. Rescaling the RPA correlation energy by an empirical factor >1 gave very accurate results for a wide range of properties. We show here that reference states constructed from approximate local exchange-correlation potentials give their best results with smaller rescaling factors approximately 1. However, the tested potentials yield artifacts in some systems.

Improving approximate-optimized effective potentials by imposing exact conditions: Theory and applications to electronic statics and dynamics

We develop a method that can constrain any local exchange-correlation potential to preserve basic exact conditions. Using the method of Lagrange multipliers, we calculate for each set of given Kohn-Sham orbitals a constraint-preserving potential which is closest to the given exchange-correlation potential. The method is applicable to both the time-dependent (TD) and independent cases. The exact conditions that are enforced for the time-independent case are Galilean covariance, zero net force and torque, and Levy-Perdew virial theorem. For the time-dependent case we enforce translational covariance, zero net force, Levy-Perdew virial theorem, and energy balance. We test our method on the exchange (only) Krieger-Li-Iafrate (xKLI) approximate-optimized effective potential for both cases. For the time-independent case, we calculated the ground state properties of some hydrogen chains and small sodium clusters for some constrained xKLI potentials and Hartree-Fock (HF) exchange. The results (total energy, Kohn-Sham eigenvalues, polarizability, and hyperpolarizability) indicate that enforcing the exact conditions is not important for these cases. On the other hand, in the time-dependent case, constraining both energy balance and zero net force yields improved results relative to TDHF calculations. We explored the electron dynamics in small sodium clusters driven by cw laser pulses. For each laser pulse we compared calculations from TD constrained xKLI, TD partially constrained xKLI, and TDHF. We found that electron dynamics such as electron ionization and moment of inertia dynamics for the constrained xKLI are most similar to the TDHF results. Also, energy conservation is better by at least one order of magnitude with respect to the unconstrained xKLI. We also discuss the problems that arise in satisfying constraints in the TD case with a non-cw driving force.

First-principles study of electronic structure and insulating properties of uranium and plutonium dioxides

First-principles density functional theory calculations were carried out to investigate the electronic structure and the degree of 5f states localization of the Mott–Hubbard type insulators UO 2 and PuO 2. We used the fully relativistic cluster discrete variational method (RDV) with the local exchange-correlation potential. The energies of one-electron transition between occupied and vacant 5f 5/2 states of neighboring actinide atoms were evaluated on the base of the ground state and the excited state calculations. It is found that in UO 2 and PuO 2 the energy difference between 5f 5/2 levels of nearest metal sites in the lattice are close to 1.0 eV and 0.9 eV, despite the results of conventional band structure approach predicting that both oxides are good conductors.

Electronic structure of grain boundaries in the Fe86-Mn12.7-C1.3alloy

The importance of studying Fe-Mn-C alloys is related to their wide use as constructional materials in mechanical engineering. In this work an effort has been made to elucidate the physical origin of the magnetization in austenitic steels by calculating the electronic structure of grain boundaries. To theoretically investigate the magnetic properties of a crystal of ferromagnetic bcc iron, the wave functions of the iron atom calculated in view of the spin polarization of a core by the Hartree-Fock method with local exchange-correlation potentials have been used as base functions. This has made it possible to optimize the choice of a zero approximation for the description of the electronic states of ferromagnetic iron and to attain good agreement with the experimental values of the magnetic moment (μ theor = 2.23μ B , μ exp = 2.218μ B ), of the exchange splitting of the crystal term P 4 (Δ theor = Δ exp = 0.112 Ry), and of the cross-sections of the Fermi surface. A similar approach has been used to investigate the magnetic states of clusters (nanoclusters) based on the method of scattered waves. The approach developed for clusters of the alloy under investigation makes it possible to calculate the alloy magnetic properties in relation to the cluster size for a varied lattice parameter.

Nuclear shielding constants from localized local hybrid exchange-correlation potentials

Localized local hybrid (LLH) potentials derived from corresponding local hybrid functionals with position-dependent exact-exchange admixture governed by appropriate local mixing functions (LMFs) have been tested for the first time in calculations of nuclear shielding constants for main-group molecules. Two different types of LMFs have been evaluated, based either on the kinetic energy density or on the dimensionless density gradient. LLH potentials provide comparable quality shielding constants as the localized hybrid potentials from global hybrid functionals. However, this is achieved (a) without generalized gradient corrections, and (b) with LMFs providing also excellent thermochemical performance and built-in correct long-range asymptotic behavior.

The effective local potential method: Implementation for molecules and relation to approximate optimized effective potential techniques

We have recently formulated a new approach, named the effective local potential (ELP) method, for calculating local exchange-correlation potentials for orbital-dependent functionals based on minimizing the variance of the difference between a given nonlocal potential and its desired local counterpart [V. N. Staroverov et al., J. Chem. Phys. 125, 081104 (2006)]. Here we show that under a mildly simplifying assumption of frozen molecular orbitals, the equation defining the ELP has a unique analytic solution which is identical with the expression arising in the localized Hartree-Fock (LHF) and common energy denominator approximations (CEDA) to the optimized effective potential. The ELP procedure differs from the CEDA and LHF in that it yields the target potential as an expansion in auxiliary basis functions. We report extensive calculations of atomic and molecular properties using the frozen-orbital ELP method and its iterative generalization to prove that ELP results agree with the corresponding LHF and CEDA values, as they should. Finally, we make the case for extending the iterative frozen-orbital ELP method to full orbital relaxation.

Effect of spatial nonlocality on the density functional band gap

We show that for a large class of exchange-correlation functionals the local exchange-correlation potential obtained within an optimized effective potential severely underestimates the band gap. On the other hand, the corresponding nonlocal potential obtained from a generalized Kohn-Sham scheme provides a much better description of the band gap, in good agreement with experiments. These results strongly indicate that a local exchange-correlation potential, however good the exchange-correlation approximation, cannot capture the delicate interplay between correlation effects and spatial localization in the KS band structure, unless the (cumbersome) contribution from the derivative discontinuity of the exchange-correlation energy functional is considered.

Effective local potentials for orbital-dependent density functionals

Practicality of the Kohn-Sham density functional scheme for orbital-dependent functionals hinges on the availability of an efficient procedure for constructing local exchange-correlation potentials in finite basis sets. We have shown recently that the optimized effective potential (OEP) method, commonly used for this purpose, is not free from difficulties. Here we propose a robust alternative to OEPs, termed effective local potentials (ELPs), based on minimizing the variance of the difference between a given nonlocal potential and its desired local counterpart. The ELP method is applied to the exact-exchange-only problem and shown to be promising for overcoming troubles with OEPs.

Orbital- and state-dependent functionals in density-functional theory

Shortcomings of present density-functional methods are considered. Kohn-Sham and time-dependent density-functional methods using orbital- and state-dependent functionals for exchange-correlation energies, potentials, and kernels are discussed as possible remedy for some of these shortcomings. A view on the Kohn-Sham formalism is presented which differs somewhat from the one conventionally taken. The crucial step of constructing local multiplicative exchange-correlation potentials in Kohn-Sham methods based on orbital- and state-dependent functionals is discussed. The description of open-shell systems via a symmetrized Kohn-Sham formalism employing state-dependent exchange-correlation functionals is elucidated. The generalized adiabatic connection Kohn-Sham approach for the self-consistent treatment of excited states within a density-functional framework is considered. In the latter approach orbital- and state-dependent exchange-correlation functionals occur in a density-functional framework which is no longer based on the Hohenberg-Kohn theorem but on a more general relation between electron densities and local multiplicative potentials.

The exchange-correlation potential in ab initio density functional theory

From coupled-cluster theory and many-body perturbation theory we derive the local exchange-correlation potential of density functional theory in an orbital dependent form. We show the relationship between the coupled-cluster approach and density functional theory, and connections and comparisons with our previous second-order correlation potential [OEP-MBPT(2) (OEP-optimized effective potential)] [I. Grabowski, S. Hirata, S. Ivanov, and R. J. Bartlett, J. Chem. Phys. 116, 4415 (2002)]. Starting from a general theoretical framework based on the density condition in Kohn-Sham theory, we define a rigorous exchange-correlation functional, potential and orbitals. Specifying initially to second-order terms, we show that our ab initio correlation potential provides the correct shape compared to those from reference quantum Monte Carlo calculations, and we demonstrate the superiority of using Fock matrix elements or more general infinite-order semicanonical transformations. This enables us to introduce a method that is guaranteed to converge to the right answer in the correlation and basis set limit, just as does ab initio wave function theory. We also demonstrate that the energies obtained from this generalized second-order method [OEP-MBPT2-f] and [OEP-MBPT2-sc] are often of coupled-cluster accuracy and substantially better than ordinary Hartree-Fock based second-order MBPT=MP2.