Semilocal Density Functionals Research Articles

How Does HF-DFT Achieve Chemical Accuracy for Water Clusters?

Bolstered by recent calculations of exact functional-driven errors (FEs) and density-driven errors (DEs) of semilocal density functionals in the water dimer binding energy [Kanungo, B. J. Phys. Chem. Lett. 2024, 15, 323-328], we investigate approximate FEs and DEs in neutral water clusters containing up to 20 monomers, charged water clusters, and alkali- and halide-water clusters. Our proxy for the exact density is r2SCAN 50, a 50% global hybrid of exact exchange with r2SCAN, which may be less correct than r2SCAN for the compact water monomer but importantly more correct for long-range electron transfers in the noncompact water clusters. We show that SCAN makes substantially larger FEs for neutral water clusters than r2SCAN, while both make essentially the same DEs. Unlike the case for barrier heights, these FEs are small in a relative sense and become large in an absolute sense only due to an increase in cluster size. SCAN@HF, short for SCAN evaluated on the Hartree-Fock (HF) density, produces a cancellation of errors that makes it chemically accurate for predicting the absolute binding energies of water clusters. Likewise, adding a long-range dispersion correction to r2SCAN@HF, as in the composite method HF-r2SCAN-DC4, makes its FE more negative than in r2SCAN@HF, permitting a near-perfect cancellation of FE and DE. r2SCAN by itself (and even more so, r2SCAN evaluated on the r2SCAN 50 density), is almost perfect for the energy differences between water hexamers, and thus probably also for liquid water away from the boiling point. Thus, the accuracy of composite methods like SCAN@HF and HF-r2SCAN-DC4 is not due to the HF density being closer to the exact density, but to a compensation of errors from its greater degree of localization. We also give an argument for the approximate reliability of this unconventional error cancellation for diverse molecular properties. Finally, we confirm this unconventional error cancellation for the SCAN description of the water trimer via Kohn-Sham inversion of the CCSD(T) density.

Combining Local Range Separation and Local Hybrids: A Step in the Quest for Obtaining Good Energies and Eigenvalues from One Functional.

Some of the most successful exchange-correlation approximations in density functional theory are "hybrids", i.e., they rely on combining semilocal density functionals with exact nonlocal Fock exchange. In recent years, two classes of hybrid functionals have emerged as particularly promising: range-separated hybrids on the one hand, and local hybrids on the other hand. These functionals offer the hope to overcome a long-standing "observable dilemma", i.e., the fact that density functionals typically yield either a good description of binding energies, as obtained, e.g., in global and local hybrids, or physically interpretable eigenvalues, as obtained, e.g., in optimally tuned range-separated hybrids. Obtaining both of these characteristics from one and the same functional with the same set of parameters has been a long-standing challenge. We here discuss combining the concepts of local range separation and local hybrids as part of a constraint-guided quest for functionals that overcome the observable dilemma.

Nonempirical semilocal density functionals for correcting the self-interaction of polaronic states

Through the use of the piecewise-linearity condition of the total energy, we correct the self-interaction for the study of polarons by constructing nonempirical functionals at the semilocal level of theory. We consider two functionals, the γDFT and μDFT functionals, both of which are based on the addition of a weak local potential to the semilocal Hamiltonian to enforce the piecewise-linearity condition. We show that the resulting polaron properties are in good agreement with reference hybrid functional calculations. This supports the use of semilocal functionals for calculating polaron properties.

Assessing r2SCAN meta-GGA functional for structural parameters, cohesive energy, mechanical modulus, and thermophysical properties of 3d, 4d, and 5d transition metals.

The recent development of accurate and efficient semilocal density functionals on the third rung of Jacob's ladder of density functional theory, such as the revised regularized strongly constrained and appropriately normed (r2SCAN) density functional, could enable rapid and highly reliable prediction of the elasticity and temperature dependence of thermophysical parameters of refractory elements and their intermetallic compounds using the quasi-harmonic approximation (QHA). Here, we present a comparative evaluation of equilibrium cell volumes, cohesive energy, mechanical moduli, and thermophysical properties (Debye temperature and thermal expansion coefficient) for 22 transition metals using semilocal density functionals, including the local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE) and PBEsol generalized gradient approximations (GGAs), and the r2SCAN meta-GGA. PBEsol and r2SCAN deliver the same level of accuracies for structural, mechanical, and thermophysical properties. PBE and r2SCAN perform better than LDA and PBEsol for calculating cohesive energies of transition metals. Among the tested density functionals, r2SCAN provides an overall well-balanced performance for reliably computing cell volumes, cohesive energies, mechanical properties, and thermophysical properties of various 3d, 4d, and 5d transition metals using QHA. Therefore, we recommend that r2SCAN could be employed as a workhorse method to evaluate thermophysical properties of transition metal compounds and alloys in high throughput workflows.

Machine learning molecular dynamics simulations of liquid methanol

As the simplest hydrogen-bonded alcohol, liquid methanol has attracted intensive experimental and theoretical interest. However, theoretical investigations on this system have primarily relied on empirical intermolecular force fields or ab initio molecular dynamics with semilocal density functionals. Inspired by recent studies on bulk water using increasingly accurate machine learning force fields, we report a new machine learning force field for liquid methanol with a hybrid functional revPBE0 plus dispersion correction. Molecular dynamics simulations on this machine learning force field are orders of magnitude faster than ab initio molecular dynamics simulations, yielding the radial distribution functions, self-diffusion coefficients, and hydrogen bond network properties with very small statistical errors. The resulting structural and dynamical properties are compared well with the experimental data, demonstrating the superior accuracy of this machine learning force field. This work represents a successful step toward a first-principles description of this benchmark system and showcases the general applicability of the machine learning force field in studying liquid systems.

Electronic excitations of the charged nitrogen-vacancy center in diamond obtained using time-independent variational density functional calculations

Elucidation of the mechanism for optical spin initialization of point defects in solids in the context of quantum applications requires an accurate description of the excited electronic states involved. While variational density functional calculations have been successful in describing the ground state of a great variety of systems, doubts have been expressed in the literature regarding the ability of such calculations to describe electronic excitations of point defects. A direct orbital optimization method is used here to perform time-independent, variational density functional calculations of a prototypical defect, the negatively charged nitrogen-vacancy center in diamond. The calculations include up to 511 atoms subject to periodic boundary conditions and the excited state calculations require similar computational effort as ground state calculations. Contrary to some previous reports, the use of local and semilocal density functionals gives the correct ordering of the low-lying triplet and singlet states, namely {}^{3}A_2 < {}^{1}E < {}^{1}A_1 < {}^{3}E3A2<1E<1A1<3E. Furthermore, the more advanced meta generalized gradient approximation functionals give results that are in remarkably good agreement with high-level, many-body calculations as well as available experimental estimates, even for the excited singlet state which is often referred to as having multireference character. The lowering of the energy in the triplet excited state as the atom coordinates are optimized in accordance with analytical forces is also close to the experimental estimate and the resulting zero-phonon line triplet excitation energy is underestimated by only 0.15 eV. The approach used here is found to be a promising tool for studying electronic excitations of point defects in, for example, systems relevant for quantum technologies.

Origin of Structural Anomaly in Cuprous Halides.

Cuprous halides (CuX; X = Cl, Br, or I) have been extensively investigated in the literature, but many of their fundamental properties are still not very well understood. For example, debate about their crystal stability, i.e., whether the ground-state structures of CuX are zinc-blende, still exists. By performing rigorous first-principles calculations for CuX using an accurate hybrid functional, we unambiguously demonstrate that CuX are indeed stable in the zinc-blende structure, but their accurate description requires careful treatment of the exchange interaction. Previous calculations based on local or semilocal density functionals underestimated the important contributions from exchange interactions and thus underestimated the energy separation between the unoccupied 4s and occupied 3d orbitals in Cu, resulting in an overestimation of the s-d coupling and the energy reduction of distorted CuX. Our study clarifies a long-standing and highly debated issue with regard to ground-state structures of CuX and advances the physics of phase stability and the importance of s-d coupling in semiconductors.

Correct and Accurate Polymorphic Energy Ordering of Transition-Metal Monoxides Obtained from Semilocal and Onsite-Hybrid Exchange-Correlation Approximations

The relative energetic stability of the structural phases of common antiferromagnetic transition-metal oxides (MnO, FeO, CoO, and NiO) within the semilocal and hybrid density functionals are fraught with difficulties. In particular, MnO is known to be the most difficult case for almost all common semilocal and hybrid density approximations. Here, we show that the meta-generalized gradient approximation (meta-GGA) constructed from the cuspless hydrogen model and Pauli kinetic energy density (MGGAC) can lead to the correct phase as the ground-state of MnO. The relative energy differences of zinc blende (zb) and rock salt (rs) structures as computed using MGGAC are found to be in nice agreement with those obtained from high-level correlation methods like the random phase approximation or quantum Monte Carlo techniques. Besides, we have also applied the onsite hybrid functionals (closely related to DFT+U) based on GGA and meta-GGA functionals, and it is shown that a relatively high amount of Hartree–Fock exchange is necessary to obtain rs as the ground-state phase. Our present investigation suggests the semilocal MGGAC and onsite hybrids, both being computationally cheap, as methods of choice for the calculation of the relative stability of antiferromagnetic transition-metal oxides having potential applications in solid-state physics and structural chemistry.

Numerically stable inversion approach to construct Kohn-Sham potentials for given electron densities within a Gaussian basis set framework.

We present a Kohn-Sham (KS) inversion approach to construct KS exchange-correlation potentials corresponding to given electron densities. This method is based on an iterative procedure using linear response to update potentials. All involved quantities, i.e., orbitals, potentials, and response functions, are represented by Gaussian basis functions. In contrast to previous KS inversion methods relying on Gaussian basis sets, the method presented here is numerically stable even for standard basis sets from basis set libraries due to a preprocessing of the auxiliary basis used to represent an exchange-correlation charge density that generates the exchange-correlation potential. The new KS inversion method is applied to reference densities of various atoms and molecules obtained by full configuration interaction or CCSD(T) (coupled cluster singles doubles perturbative triples). The considered examples encompass cases known to be difficult, such as stretched hydrogen or lithium hydride molecules or the beryllium isoelectronic series. For the stretched hydrogen molecule, potentials of benchmark quality are obtained by employing large basis sets. For the carbon monoxide molecule, we show that the correlation potential from the random phase approximation (RPA) is in excellent qualitative and quantitative agreement with the correlation potential from the KS inversion of a CCSD(T) reference density. This indicates that RPA correlation potentials, in contrast to those from semi-local density-functionals, resemble the exact correlation potential. Besides providing exchange-correlation potentials for benchmark purposes, the proposed KS inversion method may be used in density-partition-based quantum embedding and in subsystem density-functional methods because it combines numerical stability with computational efficiency.

Ab-Initio Investigation of Finite Size Effects in Rutile Titania Nanoparticles with Semilocal and Nonlocal Density Functionals

In this work, we employ hybrid and generalized gradient approximation (GGA) level density functional theory (DFT) calculations to investigate the convergence of surface properties and the electronic gap of rutile titania (TiO2) nanoparticles with particle size. The surface energies and electronic gaps are calculated for cuboidal particles with minimum dimension ranging from 3.7 Å (24 atoms) to 10.3 Å (384 atoms) using a highly parallel real-space DFT code to enable hybrid-level DFT calculations of larger nanoparticles than are typically practical. We deconvolute the geometric and electronic finite size effects in surface energy and evaluate the influence of defects on the electronic gap and density of states (DOS). The electronic finite size effects in surface energy vanish when the minimum length scale of the nanoparticles becomes greater than 10 Å. We show that this length scale is consistent with a computationally efficient numerical analysis of the characteristic length scale of electronic interactions. The surface energy of nanoparticles having a minimum dimension beyond this characteristic length can be approximated using slab calculations that account for the geometric defects. In contrast, the finite size effects on the electronic gap and DOS are highly dependent on the shape and size of these particles. The DOS for cuboidal particles and more realistic particles constructed using the Wulff algorithm reveal that defect states within the electronic gap play a key role in determining the eigenvalue distribution of nanoparticles and the electronic gap does not converge to the bulk limit for the particle sizes investigated.

Hidden Hemibonding in the Aqueous Hydroxyl Radical.

The existence of a two-center, three-electron hemibond in the first solvation shell of •OH(aq) has long been a matter of debate. The hemibond manifests in ab initio molecular dynamics simulations as a small-r feature in the oxygen radial distribution function (RDF) for H2O···•OH, but that feature disappears when semilocal density functionals are replaced with hybrids, suggesting a self-interaction artifact. Using periodic simulations at the PBE0+D3 level, we demonstrate that the hemibond is actually still present (as evidenced by delocalization of the spin density) but is obscured by the hydrogen-bonded feature in the RDF due to a slight elongation of the hemibond. Computed electronic spectra for •OH(aq) are in excellent agreement with experiment and confirm that hemibond-like configurations play an outsized role in the spectroscopy due to an intense charge-transfer transition that is strongly attenuated in hydrogen-bonded configurations. Apparently, 25% exact exchange (as in PBE0) is insufficient to eliminate delocalization of unpaired spins.

Defect levels from SCAN and MBJ meta-GGA exchange-correlation potentials

For more than a decade the HSE06 hybrid exchange-correlation functional developed by Heyd, Scuseria and Ernzerhof has provided a tool for reliable defect level calculations in density functional theory for which postprocessing tools are not necessary, in contrast to previous calculations using semilocal density functionals. One of the main reasons for its reliability is the high precision of HSE06 for band gap calculations. Recently, other functionals from the meta-generalized gradient approximation (meta-GGA) class have been used extensively to calculate the electronic properties of solids. In particular, band gaps can be accurately evaluated with the modified Becke-Johnson (MBJ) potential, and relaxed atomic structures close to experimental findings can be obtained with the strongly constrained and appropriately normed (SCAN) exchange-correlation functional. Both approaches are computationally cheaper than HSE06, and we consider here their performance for defect level calculations. We compare results for the $\ensuremath{\epsilon}(+/0)$ transition levels of seven donors and $\ensuremath{\epsilon}(0/\ensuremath{-})$ transition levels of four acceptors in group IV semiconductors. We conclude that in certain situations where HSE06 cannot be applied because of excessive computational costs, SCAN and MBJ might provide a good alternative.

Opening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations

The quasiparticle band structure can be properly described by Hedin's GW approximation (GW), at a high computational cost. For band gaps, semilocal density functionals up to the generalized gradient approximation (GGA) level cannot compete with the accuracy of hybrid-based approximations or GW. Meta-GGA density functionals with a strong dependence on the kinetic energy density ingredient can potentially give wider band gaps compared with GGAs. The recent TASK meta-GGA density functional from Aschebrock and K\"ummel [Phys. Rev. Research 1, 033082 (2019)], is constructed with an enhanced nonlocality in the generalized Kohn-Sham scheme and therefore harbors great opportunities for band gap prediction. Although this approximation was found to yield excellent band gaps of bulk solids, this accuracy cannot be straightforwardly transferred to low-dimensional materials. The reduced screening of these materials results in larger band gaps compared with their bulk counterparts, as an additional barrier to overcome. In this paper we demonstrate how the alteration of this functional affects the band gaps of monolayers and nanoribbons and present accurate band gaps competing with the revised Heyd-Scuseria-Ernzerhof (HSE06) approximation. In order to achieve this goal, we have modified the TASK functional (a) by changing the tight upper bound for one- or two-electron systems (${h}_{X}^{0}$) from 1.174 to 1.29 and (b) by changing the limit of the interpolation function ${f}_{X}(\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$) of the TASK functional that interpolates the exchange enhancement factor ${F}_{X}(s,\ensuremath{\alpha})$ from $\ensuremath{\alpha}=0$ to 1. The resulting modified TASK (mTASK) was tested for various materials from three dimensions to two dimensions to one dimension (nanoribbons) and was compared with the results of the higher-level hybrid functional HSE06 or with the ${\mathrm{G}}_{0}{\mathrm{W}}_{0}$ approximation within many-body perturbation theory. We find that mTASK systematically improves the band gaps and band structures of two-dimensional (2D) and 1D systems, without significantly affecting the accuracy of the original TASK for the bulk 3D materials, when compared with the Perdew-Burke-Ernzerhof (PBE) GGA and the strongly constrained and appropriately normed (SCAN) meta-GGA. We further demonstrate the applicability of mTASK by assessing the band structures of transition metal dichalcogenide nanoribbons with respect to various bending curvatures.

Efficient Band Structure Calculation of Two-Dimensional Materials from Semilocal Density Functionals.

The experimental and theoretical realization of two-dimensional (2D) materials is of utmost importance in semiconducting applications. Computational modeling of these systems with satisfactory accuracy and computational efficiency is only feasible with semilocal density functional theory methods. In the search for the most useful method in predicting the band gap of 2D materials, we assess the accuracy of recently developed semilocal exchange–correlation (XC) energy functionals and potentials. Though the explicit forms of exchange–correlation (XC) potentials are very effective against XC energy functionals for the band gap of bulk solids, their performance needs to be investigated for 2D materials. In particular, the LMBJ [J. Chem. Theory Comput.2020, 16, 265432097004] and GLLB-SC [Phys. Rev. B82, 2010, 115106] potentials are considered for their dominance in bulk band gap calculation. The performance of recently developed meta generalized gradient approximations, like TASK [Phys. Rev. Res.1, 2019, 033082] and MGGAC [Phys. Rev. B. 100, 2019, 155140], is also assessed. We find that the LMBJ potential constructed for 2D materials is not as successful as its parent functional, i.e., MBJ [Phys. Rev. Lett.102, 2009, 22640119658882] in bulk solids. Due to a contribution from the derivative discontinuity, the band gaps obtained with GLLB-SC are in a certain number of cases, albeit not systematically, larger than those obtained with other methods, which leads to better agreement with the quasi-particle band gap obtained from the GW method. The band gaps obtained with TASK and MGGAC can also be quite accurate.

Van der Waals corrected density functionals for cylindrical surfaces: Ammonia and nitrogen dioxide adsorbed on a single-walled carbon nanotube

We extend the damped Zaremba-Kohn model (dZK) for long-range dispersion interaction between a molecule and a planar surface [J. Tao, H. Tang, A. Patra, P. Bhattarai, and J. P. Perdew, Phys. Rev. B 97, 165403 (2018)] to molecules adsorbed on a curved cylindrical surface, and employ this extended model as an additive correction to the semilocal density functionals PBE (Perdew-Burke-Ernzerhof) and SCAN (strongly constrained and appropriately normed). The resulting PBE+vdW (van der Waals)-dZK and SCAN+vdW-dZK are applied to two systems, $\mathrm{N}{\mathrm{H}}_{3}$ and $\mathrm{N}{\mathrm{O}}_{2}$ molecules adsorbed on a single-wall carbon nanotube (CNT), for calculations of binding energies and equilibrium distances. For comparison, the results from vdW nonlocal functionals, such as SCAN+rVV10 and PBE+rVV10, are also presented. The binding energies from PBE+rVV10 (Vydrov and Van Voorhis), SCAN+rVV10, PBE+vdW-dZK, and SCAN+vdW-dZK are about 70--115 meV for the system of $\mathrm{CNT}+\mathrm{N}{\mathrm{H}}_{3}$ and 300--500 meV for the system of $\mathrm{CNT}+\mathrm{N}{\mathrm{O}}_{2}$. The results from PBE+vdW-dZK and SCAN+vdW-dZK are closer to each other than those from PBE+rVV10 and SCAN+rVV10 are. The relatively closer results from PBE+vdW-dZK and SCAN+vdW-dZK indicate the consistency of our developed vdW\ensuremath{-}dZK model for cylindrical surfaces. All methods, including PBE, SCAN, PBE+rVV10, SCAN+rVV10, PBE+vdW-dZK, and SCAN+vdW-dZK, give approximately the same binding energy differences between two adsorption configurations (types I and II) for the two systems. This implies that the two adsorption sites have approximately the same adsorption stability. The exponent of the vdW interaction power law from our vdW-dZK model for the two systems is about 0 at short distance, largely due to the damping factor, and tends slowly to \ensuremath{-}4 to \ensuremath{-}4.5 at distances $D$ about 20--50 \AA{}. At even larger distances, the vdW power-law exponent approaches \ensuremath{-}5. This feature is very similar to the one calculated with random-phase approximation and renormalization group approaches, supporting the applicability of our methods. Our developed vdW-dZK method provides a highly efficient and reliable method for large systems with cylindrical surfaces, such as vdW interactions with nanotubes.

Assessment of Performance of Density Functionals for Predicting Potential Energy Curves in Hydrogen Storage Applications.

The availability of accurate computational tools for modeling and simulation is vital to accelerate the discovery of materials capable of storing hydrogen (H2) under given parameters of pressure swing and temperature. Previously, we compiled the H2Bind275 data set consisting of equilibrium geometries and assessed the performance of 55 density functionals over this data set (Veccham, S. P.; Head-Gordon, M. J. Chem. Theory Comput. 2020, 16, 4963-4982). As it is crucial for computational tools to accurately model the entire potential energy curve (PEC), in addition to the equilibrium geometry, we extended this data set with 389 new data points to include two compressed and three elongated geometries along 78 PECs for H2 binding, forming the H2Bind78 × 7 data set. By assessing the performance of 55 density functionals on this significantly larger and more comprehensive H2Bind78 × 7 data set, we identified the best performing density functionals for H2 binding applications: PBE0-DH, ωB97X-V, ωB97M-V, and DSD-PBEPBE-D3(BJ). The addition of Hartree-Fock exchange improves the performance of density functionals, albeit not uniformly throughout the PEC. We recommend the usage of ωB97X-V and ωB97M-V density functionals as they offer good performance for both geometries and energies. In addition, we also identified B97M-V and B97M-rV as the best semilocal density functionals for predicting H2 binding energy at its equilibrium geometry.

Performance of SCAN Meta-GGA Functionals on Nonlinear Mechanics of Graphene-Like g-SiC

Although meta-generalized-gradient approximations (meta-GGAs) are believed potentially the most accurate among the efficient first-principles calculations, the performance has not been accessed on the nonlinear mechanical properties of two-dimensional nanomaterials. Graphene, like two-dimensional silicon carbide g-SiC, has a wide direct band-gap with applications in high-power electronics and solar energy. Taken g-SiC as a paradigm, we have investigated the performance of meta-GGA functionals on the nonlinear mechanical properties under large strains, both compressive and tensile, along three deformation modes using Strongly Constrained and Appropriately Normed Semilocal Density Functional (SCAN) as an example. A close comparison suggests that the nonlinear mechanics predicted from SCAN are very similar to that of Perdew-Burke-Ernzerhof (PBE) formulated functional, a standard Density Functional Theory (DFT) functional. The improvement from SCAN calculation over PBE calculation is minor, despite the considerable increase of computing demand. This study could be helpful in selection of density functionals in simulations and modeling of mechanics of materials.

New insights into the 1D carbon chain through the RPA.

We investigated the electronic and structural properties of the infinite linear carbon chain (carbyne) using density functional theory (DFT) and the random phase approximation (RPA) to the correlation energy. The studies are performed in vacuo and for carbyne inside a carbon nano tube (CNT). In the vacuum, semi-local DFT and RPA predict bond length alternations of about 0.04 Å and 0.13 Å, respectively. The frequency of the highest optical mode at the Γ point is 1219 cm-1 and about 2000 cm-1 for DFT and the RPA. Agreement of the RPA to previous high level quantum chemistry and diffusion Monte-Carlo results is excellent. For the RPA we calculate the phonon-dispersion in the full Brillouine zone and find marked quantitative differences to DFT calculations not only at the Γ point but also throughout the entire Brillouine zone. To model carbyne inside a carbon nanotube, we considered a (10,0) CNT. Here the DFT calculations are even qualitatively sensitive to the k-points sampling. At the limes of a very dense k-points sampling, semi-local DFT predicts no bond length alternation (BLA), whereas in the RPA a sizeable BLA of 0.09 Å prevails. The reduced BLA leads to a significant red shift of the vibrational frequencies of about 350 cm-1, so that they are in good agreement with experimental estimates. Overall, the good agreement between the RPA and previously reported results from correlated wavefunction methods and experimental Raman data suggests that the RPA provides reliable results at moderate computational costs. It hence presents a useful addition to the repertoire of correlated wavefunction methods and its accuracy clearly prevails for low dimensional systems, where semi-local density functionals struggle to yield even qualitatively correct results.

Plane-wave many-body corrections to the conductance in bulk tunnel junctions

The conductance of bulk metal--insulator--metal junctions is evaluated by the Landauer formula using an \textit{ab initio} electronic structure calculated using a plane-waves basis set within density-functional theory (DFT) and beyond, i.e.\ including exact non-local exchange using hybrid functional (HSE) or many-body $G_0W_0$ and COHSEX quasiparticle (QP) schemes. We consider an Ag/MgO/Ag heterostructure model and we focus on the evolution of the zero-bias conductance as a function of the MgO film thickness. Our study shows that the correction of the electronic structure beyond semi-local density functionals goes in the right direction to improve the agreement with experiments, significantly reducing the zero-bias conductance. This effect becomes more evident at larger MgO thickness, that is in increasing tunneling regime. We also observe that the reduction of the conductance seems more related to the correction of wavefunctions rather than energies, and thus not directly related to the correction of the band-gap of bulk MgO. $G_0W_0$ and HSE both provide a correct band-gap in agreement with experiments, but only HSE gives a significant reduction of the conductance. COHSEX, while overestimating the band-gap, gives a reduction of the conductance very close to HSE.

Ab initio calculations of the rate of carrier trapping and release at dopant sites in NaI: Tl beyond the harmonic approximation

We present ab initio calculations of electron capture and release coefficients as a function of temperature for Tl dopants in the widely used scintillator NaI, which is a soft ionic crystal. The modeled capture and release events occur by transitions mediated by multiple phonon absorption and emission between states with significantly different local geometries around the trapping site. We demonstrate that such transitions are not well-described by the normal harmonic approximation to the nuclear dynamics. We go beyond the harmonic approximation by numerically solving the vibrational Schr\odinger equation for the motion along/of a single effective phonon coordinate. The localized trapped state is not correctly described by semilocal density functionals, so we employ a global hybrid functional tuned to reproduce the band gap and lattice constant of the host material. Our calculations, which combine plane-wave and embedded cluster electronic structure methods are in reasonable agreement with available experimental data for detrapping and predict an unusual temperature dependence for trapping rates.