Semi-local Density Functional Theory Approximations Research Articles

Revisiting Understanding of Electrochemical CO2 Reduction on Cu(111): Competing Proton-Coupled Electron Transfer Reaction Mechanisms Revealed by Embedded Correlated Wavefunction Theory.

Copper (Cu) electrodes, as the most efficacious of CO2 reduction reaction (CO2RR) electrocatalysts, serve as prototypes for determining and validating reaction mechanisms associated with electrochemical CO2 reduction to hydrocarbons. As in situ electrochemical mechanism determination by experiments is still out of reach, such mechanistic analysis typically is conducted using density functional theory (DFT). The semilocal exchange-correlation (XC) approximations most often used to model such catalysis unfortunately engender a basic error: predicting the wrong adsorption site for CO (a key CO2RR intermediate) on the most ubiquitous facet of Cu, namely, Cu(111). This longstanding inconsistency casts lingering doubt on previous DFT predictions of the attendant CO2RR kinetics. Here, we apply embedded correlated wavefunction (ECW) theory, which corrects XC functional error, to study the CO2RR on Cu(111) via both surface hydride (*H) transfer and proton-coupled electron transfer (PCET). We predict that adsorbed CO (*CO) reduces almost equally to two intermediates, namely, hydroxymethylidyne (*COH) and formyl (*CHO) at -0.9 V vs the RHE. In contrast, semilocal DFT approximations predict a strong preference for *COH. With increasing applied potential, the dominance of *COH (formed via potential-independent surface *H transfer) diminishes, switching to the competitive formation of both *CHO and *COH (both formed via potential-dependent PCET). Our results also demonstrate the importance of including explicitly modeled solvent molecules in predicting electron-transfer barriers and reveal the pitfalls of overreliance on simple surface *H transfer models of reduction reactions.

Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage.

The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH4···(H2O)20, is a stringent test for approximate methods, including density functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here, we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA), which uses approximate Kohn-Sham orbitals as its input. The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of the many-body expansion. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the many-body expansion. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.

Critical assessment of Co-Cu phase diagram from first-principles calculations

Using first-principles alloy theory, we perform a systematic study of the Co-Cu phase diagram. Calculations are carried out for ferromagnetic and paramagnetic ${\mathrm{Co}}_{1\ensuremath{-}x}{\mathrm{Cu}}_{x}$ solid solutions with face-centered-cubic (fcc) crystal structure. We find that the equilibrium volumes and magnetic states are crucial for a quantitative description of the thermodynamics of the Co-Cu system at temperatures up to 1400 K. In particular, the paramagnetic state of Cu-rich alloys with persisting local magnetic moments is shown to be responsible for the solubility of a small amount of Co in fcc Cu whereas the excess entropy in the ferromagnetic Co-rich region critically depends on the adopted lattice parameters. None of the common local or semilocal density functional theory approximations have the necessary accuracy for the lattice parameters when compared to the experimental data. The predicted ab initio Co-Cu phase diagram is in good agreement with the measurements and CALPHAD data, making it possible to gain a deep insight into the various contributions to the Gibbs free energy. The present study provides an atomic-level description of the thermodynamic quantities controlling the limited mutual solubility of Co and Cu and highlights the importance of high-temperature magnetism.

Electron Confinement and Magnetism of (LaTiO3)1/(SrTiO3)5 Heterostructure: A Diffusion Quantum Monte Carlo Study.

We have applied the diffusion quantum Monte Carlo (DMC) method to study the electron confinement and magnetic structure in the (LaTiO3)1/(SrTiO3)5 heterostructure. The DMC results were compared with various density functional theory (DFT) methods, including local density approximation (LDA), generalized gradient approximation (GGA), LDA+U, and GGA+U, as well as the recently proposed strongly constrained appropriately normed (SCAN) and van der Waals-Bayesian error estimation functional (vdW-BEEF). We found that many-body correlations are crucial to accurately describe the localization of the two-dimensional (2D) electron gas around the lanthanum planes. DMC predicts 20% more electron density within the first interfacial titanium layer in (LaTiO3)1/(SrTiO3)5 than LDA+U, suggesting that the degree of confinement of the 2D electron gas in the interfacial region is underestimated with semilocal DFT approximations. DMC yields the ferromagnetic (FM) state as the ground state of (LaTiO3)1/(SrTiO3)5 and the antiferromagnetic (AFM) and nonmagnetic (NM) states that are higher in energy by 37(15) and 238(15) meV per lanthanum atom at the interface, respectively. Most DFT methods yield the FM and NM states within less than 25 meV in energy and could not find the AFM state.

Diffusion quantum Monte Carlo calculations of SrFeO3 and LaFeO3.

The equations of state, formation energy, and migration energy barrier of the oxygen vacancy in SrFeO3 and LaFeO3 were calculated with the diffusion quantum Monte Carlo (DMC) method. Calculations were also performed with various Density Functional Theory (DFT) approximations for comparison. DMC reproduces the measured cohesive energies of these materials with errors below 0.23(5) eV and the structural properties within 1% of the experimental values. The DMC formation energies of the oxygen vacancy in SrFeO3 and LaFeO3 under oxygen-rich conditions are 1.3(1) and 6.24(7) eV, respectively. Similar calculations with semi-local DFT approximations for LaFeO3 yielded vacancy formation energies 1.5 eV lower. Comparison of charge density evaluated with DMC and DFT approximations shows that DFT tends to overdelocalize the electrons in defected SrFeO3 and LaFeO3. Calculations with DMC and local density approximation yield similar vacancy migration energy barriers, indicating that steric/electrostatic effects mainly determine migration barriers in these materials.

Accuracy of density functional theory in the prediction of carbon dioxide adsorbent materials

Density functional theory (DFT) has become the computational method of choice for modeling and characterization of carbon dioxide adsorbents, a broad family of materials which at present are urgently sought after for environmental applications. The description of polar carbon dioxide (CO(2)) molecules in low-coordinated environments like surfaces and porous materials, however, may be challenging for local and semi-local DFT approximations. Here, we present a thorough computational study in which the accuracy of DFT methods in describing the interactions of CO(2) with model alkali-earth-metal (AEM, Ca and Li) decorated carbon structures, namely anthracene (C(14)H(10)) molecules, is assessed. We find that gas-adsorption energies and equilibrium structures obtained with standard (i.e. LDA and GGA), hybrid (i.e. PBE0 and B3LYP) and van der Waals exchange-correlation functionals of DFT dramatically differ from the results obtained with second-order Møller-Plesset perturbation theory (MP2), an accurate computational quantum chemistry method. The major disagreements found can be mostly rationalized in terms of electron correlation errors that lead to wrong charge-transfer and electrostatic Coulomb interactions between CO(2) and AEM-decorated anthracene molecules. Nevertheless, we show that when the concentration of AEM atoms in anthracene is tuned to resemble as closely as possible the electronic structure of AEM-decorated graphene (i.e. an extended two-dimensional material), hybrid exchange-correlation DFT and MP2 methods quantitatively provide similar results.

A scalable and accurate algorithm for the computation of Hartree–Fock exchange

Hartree–Fock exchange and hybrid density functionals have recently attracted renewed interest in electronic structure theory for the description of periodic systems, overcoming some of the limitations of local and semi-local approximations of density-functional theory (DFT). However, their use in plane-wave calculations for extended systems remains limited by poor convergence behavior regarding Brillouin-zone sampling and by a high overall computational cost. We present a computational approach that achieves quadratic convergence of exchange integrals with respect to Brillouin zone discretization, while using a compact representation of the exchange operator during non-self-consistent iterations. The computational cost is mitigated by an efficient parallel implementation. The method is applied to computations of Hartree–Fock and hybrid DFT (PBE0) band structures and structural parameters for bulk silicon and diamond.

Accurate prediction of defect properties in density functional supercell calculations

The theoretical description of defects and impurities in semiconductors is largely based on density functional theory (DFT) employing supercell models. The literature discussion of uncertainties that limit the predictivity of this approach has focused mostly on two issues: (1) finite-size effects, in particular for charged defects; (2) the band-gap problem in local or semi-local DFT approximations. We here describe how finite-size effects (1) in the formation energy of charged defects can be accurately corrected in a simple way, i.e. by potential alignment in conjunction with a scaling of the Madelung-like screened first order correction term. The factor involved with this scaling depends only on the dielectric constant and the shape of the supercell, and quite accurately accounts for the full third order correction according to Makov and Payne. We further discuss in some detail the background and justification for this correction method, and also address the effect of the ionic screening on the magnitude of the image charge energy. In regard to (2) the band-gap problem, we discuss the merits of non-local external potentials that are added to the DFT Hamiltonian and allow for an empirical band-gap correction without significantly increasing the computational demand over that of standard DFT calculations. In combination with LDA + U, these potentials are further instrumental for the prediction of polaronic defects with localized holes in anion-p orbitals, such as the metal-site acceptors in wide-gap oxide semiconductors.

Order-Nimplementation of exact exchange in extended insulating systems

Exact (Hartree-Fock) exchange is needed to overcome some of the limitations of local and semilocal approximations of density-functional theory. So far, however, computational cost has limited the use of exact exchange in plane-wave calculations for extended systems. We show that this difficulty can be overcome by performing a unitary transformation from Bloch to maximally localized Wannier functions in combination with an efficient technique to compute real-space Coulomb integrals. The resulting scheme scales linearly with system size. We validate the scheme with representative applications.