First step toward a parameter-free, nonlocal kinetic energy density functional for semiconductors and simple metals.

The accuracy of orbital-free density functional theory depends on the approximations made for a Kinetic Energy (KE) functional. Until now, the most accurate KEDFs are based on non-local kernels constructed from the linear response theory of homogeneous electron gas. In this work, we explore beyond the HEG by employing a more general kernel based on the jellium-with-gap model (JGM). The proposed functional incorporates several new features, such as (i) having the correct low momentum(q) limit of the response function for metals and semiconductors without any modeling term, (ii) the underlying kernel is density-independent, and most importantly, (iii) parameter-free. The accuracy and efficiency of the proposed JGM NL-KEDF have been demonstrated for several semiconductors and metals. The encouraging results indicate the utility and predictive power of the JGM kernel for NL KEDF developments. This approach is also physically appealing and practically useful as we have presented a general formalism to incorporate the gap kernel in all existing Lindhard-based functionals.

Semilocal Meta-GGA Exchange-Correlation Approximation from Adiabatic Connection Formalism: Extent and Limitations.

The incorporation of a strong-interaction regime within the approximate semilocal exchange-correlation functionals still remains a very challenging task for density functional theory. One of the promising attempts in this direction is the recently proposed adiabatic connection semilocal correlation (ACSC) approach [Constantin, L. A.; Phys. Rev. B 2019, 99, 085117] allowing one to construct the correlation energy functionals by interpolation of the high and low-density limits for the given semilocal approximation. The current study extends the ACSC method to the meta-generalized gradient approximations (meta-GGA) level of theory, providing some new insights in this context. As an example, we construct the correlation energy functional on the basis of the high- and low-density limits of the Tao-Perdew-Staroverov-Scuseria (TPSS) functional. Arose in this way, the TPSS-ACSC functional is one-electron self-interaction free and accurate for the strictly correlated and quasi-two-dimensional regimes. Based on simple examples, we show the advantages and disadvantages of ACSC semilocal functionals and provide some new guidelines for future developments in this context.

Density functional applications of jellium with a local gap model correlation energy functional.

We develop a realistic density functional approximation for the local gap, which is based on a semilocal indicator that shows good screening properties. The local band model has remarkable density scaling behaviors and works properly for the helium isoelectronic series for the atoms of the Periodic Table, as well as for the non-relativistic noble atom series (up to 2022 e-). Due to these desirable properties, we implement the local gap model in the jellium-with-gap correlation energy, developing the local-density-approximation-with-gap correlation functional (named LDAg) that correctly gives correlation energies of atoms comparable with the LDA ones but shows an improvement for ionization potential of atoms and molecules. Thus, LDAg seems to be an interesting and useful tool in density functional theory.

Cathodoluminescence and optical absorption spectroscopy of plasmonic modes in chromium micro-rods.

Manipulating light at the sub-wavelength level is a crucial feature of surface plasmon resonance (SPR) properties for a wide range of nanostructures. Noble metals like Au and Ag are most commonly used as SPR materials. Significant attention is being devoted to identify and develop non-noble metal plasmonic materials whose optical properties can be reconfigured for plasmonic response by structural phase changes. Chromium (Cr) which supports plasmon resonance, is a transition metal with shiny finished, highly non-corrosive, and bio-compatible alloys, making it an alternative plasmonic material. We have synthesized Cr micro-rods from a bi-layer of Cr/Au thin films, which evolves from face centered cubic to hexagonal close packed (HCP) phase by thermal activation in a forming gas ambient. We employed optical absorption spectroscopy and cathodoluminescence (CL) imaging spectroscopy to observe the plasmonic modes from the Cr micro-rod. The origin of three emission bands that spread over the UV-Vis-IR energy range is established theoretically by considering the critical points of the second-order derivative of the macroscopic dielectric function obtained from density functional theory (DFT) matches with interband/intraband transition of electrons observed in density of states versus energy graph. The experimentally observed CL emission peaks closely match thes-dandd-dband transition obtained from DFT calculations. Our findings on plasmonic modes in Cr(HCP) phase can expand the range of plasmonic material beyond noble metal with tunable plasmonic emissions for plasmonic-based optical technology.

Accurate band gaps from exchange potentials designed from a cuspless hydrogen density-based exchange hole model.

The explicit forms of exchange-correlation (XC) potentials, which are not functional derivatives of any XC energy functional, are reasonably efficient in predicting the band gap of materials. The most successful example in this genre is the MBJ [F. Tran et al., Phys. Rev. Lett., 2009 102, 226401] exchange potential, which is based on the asymptotically correct Becke-Roussel (BR) exchange potential. We employ the cuspless hydrogen density and corresponding exchange hole to construct a BR like potential. The modified BR potential is again utilized in the framework of MBJ for band gap calculations. Also, we employ a Laplacian free model of the exchange hole in the framework of MBJ. These methods are analyzed by calculating band gaps of various test sets containing narrow, intermediate, and wide bandgap materials. Besides, we apply these potentials to eighteen ternary semiconductors with a chalcopyrite structure, exciting materials for photovoltaic applications. By comparing them with MBJ, we find that the band gaps obtained using the new potentials are not uniformly larger values than the MBJ potential in all cases. But, in many instances where MBJ overestimates the gap, the new potentials' band gaps are comparatively smaller and closer to the experimental ones. We also show that these potentials can correctly predict the band structure of three-dimensional topological insulators.

Phase evolution in thermally annealed Ni/Bi multilayers studied by X-ray absorption spectroscopy.

The thin films of Ni and Bi are known to form NiBi3 and NiBi compounds spontaneously at the interface, which become superconducting below 4.2 K and show ferromagnetism either intrinsically or due to Ni impurities. Formation of NiBi3 and NiBi is a slow diffusion reaction, which means the local environment around Ni and Bi atoms may vary with time and temperature. In this report, we assess the feasibility of using X-ray Absorption Spectroscopy (XAS) as a tool to track the changes in local bonding environment in NiBi3 and NiBi. Thermal annealing at temperatures up to 500 °C was used to induce changes in the local environment in NiBi3 system. Consequent decomposition of NiBi3 into NiO and Bi has been tracked through changes in structural and magnetization behavior, which matched well with the findings of XAS. In addition, the magnetic hysteresis measurements indicated that NiO should be the dominant phase when NiBi3 is annealed at 500 °C. This was corroborated from XAS and was found to be >90%. The shift in K-edge of Ni in annealed samples was attributed to increasing charge state on Ni atom, which was ascertained by Bader charge analysis using Density Functional Theory (DFT). This study correlating macroscopic properties of NiBi3 with local bonding environment of the system indicates that XAS can be a very reliable tool for studying dynamics of diffusion in the NiBi3 system.

Solid-state performance of a meta-GGA screened hybrid density functional constructed from Pauli kinetic enhancement factor dependent semilocal exchange hole.

The semilocal form of an exchange hole is highly useful in developing non-local range-separated hybrid density functionals for finite and extended systems. The way to construct the conventional exact exchange hole model is based on either the Taylor series expansion or the reverse engineering technique from the corresponding exchange energy functional. Although the latter technique is quite popular in the context of generalized gradient approximation (GGA) functionals, the same for the meta-GGA functionals is not so much explored. Thus, in this study, we propose a reverse-engineered semilocal exchange hole of a meta-GGA functional, which only depends on the meta-GGA ingredient α (also known as the Pauli kinetic energy enhancement factor). The model is subsequently used to design the short-range-separated meta-GGA hybrid density functional. We show that the present method can be successfully applied for several challenging problems in the context of solids, especially for which the GGA based hybrid fails drastically. This assessment proves that the present functional is quite useful for materials sciences. Finally, we also use this method for several molecular test cases, where the results are also as comparative as its base semilocal functional.

Efficient and improved prediction of the band offsets at semiconductor heterojunctions from meta-GGA density functionals: A benchmark study.

Accurate theoretical prediction of the band offsets at interfaces of semiconductor heterostructures can often be quite challenging. Although density functional theory has been reasonably successful to carry out such calculations, efficient, accurate semilocal functionals are desirable to reduce the computational cost. In general, the semilocal functionals based on the generalized gradient approximation (GGA) significantly underestimate the bulk bandgaps. This, in turn, results in inaccurate estimates of the band offsets at the heterointerfaces. In this paper, we investigate the performance of several advanced meta-GGA functionals in the computational prediction of band offsets at semiconductor heterojunctions. In particular, we investigate the performance of r2SCAN (two times revised strongly constrained and appropriately normed functional), rMGGAC (revised semilocal functional based on cuspless hydrogen model and Pauli kinetic energy density functional), mTASK (modified Aschebrock and Kümmel meta-GGA functional), and local modified Becke-Johnson exchange-correlation functionals. Our results strongly suggest that these meta-GGA functionals for supercell calculations perform quite well, especially, when compared to computationally more demanding GW calculations. We also present band offsets calculated using ionization potentials and electron affinities, as well as band alignment via the branch point energies. Overall, our study shows that the aforementioned meta-GGA functionals can be used within the density functional theory framework to estimate the band offsets in semiconductor heterostructures with predictive accuracy.

Accurate density functional made more versatile.

We propose a one-electron self-interaction-free correlation energy functional compatible with the order-of-limit problem-free Tao-Mo (TM) semilocal functional (regTM) [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016) and Patra et al., J. Chem. Phys. 153, 184112 (2020)] to be used for general purpose condensed matter physics and quantum chemistry. The assessment of the proposed functional for large classes of condensed matter and chemical systems shows its improvement in most cases compared to the TM functional, e.g., when applied to the relative energy difference of MnO2 polymorphs. In this respect, the present exchange-correction functional, which incorporates the TM technique of the exchange hole model combined with the slowly varying density correction, can achieve broad applicability, being able to solve difficult solid-state problems.

Benchmark test of a dispersion corrected revised Tao-Mo semilocal functional for thermochemistry, kinetics, and noncovalent interactions of molecules and solids.

In the density functional theory, dispersion corrected semilocal approximations are often used to benchmark weekly interacting finite and extended systems. Here, the focus is on providing a broad overview of the performance of D3 dispersion corrected revised Tao-Mo (revTM) semilocal functionals [A. Patra et al., J. Chem. Phys. 153, 084 117 (2020)] for thermochemistry and kinetics of molecules, molecular crystals, ice polymorphs, metal-organic systems, atom/molecular adsorption on solids, water interacting with nano-materials, binding energies of layered materials, and properties of weekly and strongly bonded solids. We show that the most suitable "optimized power" function for the revTM functional needs a modification to make it suitable for properties related to the diverse nature of finite and extended systems. The present work is an extension of the previously proposed revTM+D3 method with the motivation to design and benchmark the dispersion corrected cost-effective method based on this semilocal approximation. We show that the revised revTM+D3 functional provides various general purpose molecular and solid properties with the closest to experimental findings than its predecessor. The present assessment and benchmarking can be practically useful for performing cost-effective method based simulations of various molecular and solid-state properties.

Bandgap of two-dimensional materials: Thorough assessment of modern exchange-correlation functionals.

The density-functional theory (DFT) approximations that are the most accurate for the calculation of bandgap of bulk materials are hybrid functionals, such as HSE06, the modified Becke-Johnson (MBJ) potential, and the GLLB-SC potential. More recently, generalized gradient approximations (GGAs), such as HLE16, or meta-GGAs, such as (m)TASK, have also proven to be quite accurate for the bandgap. Here, the focus is on two-dimensional (2D) materials and the goal is to provide a broad overview of the performance of DFT functionals by considering a large test set of 298 2D systems. The present work is an extension of our recent studies [T. Rauch, M. A. L. Marques, and S. Botti, Phys. Rev. B 101, 245163 (2020); Patra et al., J. Phys. Chem. C 125, 11206 (2021)]. Due to the lack of experimental results for the bandgap of 2D systems, G0W0 results were taken as reference. It is shown that the GLLB-SC potential and mTASK functional provide the bandgaps that are the closest to G0W0. Following closely, the local MBJ potential has a pretty good accuracy that is similar to the accuracy of the more expensive hybrid functional HSE06.

A way of resolving the order-of-limit problem of Tao-Mo semilocal functional.

It has been recently shown that the Tao-Mo (TM) [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016)] semilocal exchange-correlation energy functional suffers from the order-of-limit problem, which affects the functional performance in phase transition pressures [Furness et al., J. Chem. Phys. 152, 244112 (2020)]. The root of the order-of-limit problem of the TM functional is inherent within the interpolation function, which acts as a switch between the compact density and the slowly varying density. This paper proposes a different switch function that avoids the order-of-limit problem and correctly interpolates the compact density and the slowly varying fourth-order density correction. By circumventing the order-of-limit problem, the proposed form enhances the applicability of the original TM functional on the diverse nature of solid-state properties. Our conclusion is ensured by examining the functional in predicting properties related to general-purpose solids, quantum chemistry, and phase transition pressure. Besides, we discuss the connection between the order-of-limit problem, phase transition pressure, and bandgap of solids.

Efficient yet accurate dispersion-corrected semilocal exchange-correlation functionals for non-covalent interactions.

The meta-generalized-gradient approximation (meta-GGA) of the exchange-correlation energy functional can provide appealing performance for the wide range of quantum chemistry and solid-state properties. So far, several meta-GGAs are proposed by fitting to the test sets or/and satisfying as many as known exact constraints. Although the density overlap is treated by meta-GGA functionals efficiently, for non-covalent interactions, a long-range dispersion correction is essential. In this work, we assess the benchmark performance of different variants of the Tao-Mo meta-GGA semilocal functional, i.e., TM [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016)] and revTM [S. Jana, K. Sharma, and P. Samal, J. Phys. Chem. A 123, 6356 (2019)], with Grimme's D3 correction for several non-covalent interactions, including hydrogen-bonded systems. We consider the zero, Becke-Johnson (BJ), and optimized power (OP) damping functions within the D3 method with both TM and revTM functionals. It is observed that the overall performance of the functionals gradually improved from zero to BJ and to OP damping. However, the constructed "OP" corrected (rev)TM + D3(OP) functionals perform considerably better compared to other well-known dispersion corrected functionals. Based on the accuracy of the proposed functionals, the future applicability of these methods is also discussed.

Insights from the density functional performance of water and water-solid interactions: SCAN in relation to other meta-GGAs.

Accurate prediction of water properties in its gas and condensed phases, including the interaction of water with surfaces, is of prime importance for many scientific disciplines. However, accurate simulation of all water properties together within semilocal approximations of the density functional theory possesses great challenges. The Strongly Constrained and Appropriately Normed semilocal density functional, which satisfies 17 known exact constraints and includes the intermediate range van der Waals interaction, performs quite well for different properties of water including the correct energy ordering of isomers. Despite its impressive performance, the energy overestimation for water isomers, ice lattice energies, and volume underestimation for ice are noticeable. However, it is recently shown that [S. Jana et al., J. Chem. Theory Comput. 16(2), 974-987 (2020)] meta-generalized gradient approximations based on the density matrix expansion [i.e., Tao-Mo (TM) and revised TM (revTM)] can achieve quite a good accuracy for the diverse properties of water. In this paper, we assess the performance of the dispersion corrected counterparts of the TM and revTM functionals. It is shown that the dispersion corrected counterparts of both methods are also quite accurate for diverse water properties, especially for the water-solid interactions. Moreover, the extent of accuracy of TM-based functionals is also analyzed from the viewpoint of the density and functional-driven error. Finally, a comparison in the performance of the dispersion corrected functionals is exhibited. It is shown that the "Optimized Power" damping function together with Grimme's D3 correction and revTM functional is in excellent agreement for the water adsorption on carbon nanostructure materials and ice-lattice mismatch problem without deviating accuracy of other water properties compared to its bare functional.

Improved transition metal surface energies from a generalized gradient approximation developed for quasi two-dimensional systems.

Nonuniform density scaling in the quasi-two-dimensional (quasi-2D) regime is an important and challenging aspect of the density functional theory. Semilocal exchange-correlation energy functionals, developed by solving the dimensional crossover criterion in the quasi-2D regime, have great theoretical and practical importance. However, the only semilocal generalized gradient approximation (GGA) that has been designed to satisfy this criterion is the Q2D-GGA [L. Chiodo et al., Phys. Rev. Lett. 108, 126402 (2012)]. Here, we establish the applicability, broadness, and accuracy of the Q2D-GGA functional by performing an extensive assessment of this functional for transition metal surface energies. The important characteristic of the surface density localization and oscillation due to the rearrangement of the d electrons is also shown for different metal surfaces.

Screened range-separated hybrid by balancing the compact and slowly varying density regimes: Satisfaction of local density linear response.

Due to their quantitative accuracy and ability to solve several difficulties, screened range-separated hybrid exchange-correlation functionals are now a standard approach for ab initio simulation of condensed matter systems. However, the screened range-separated hybrid functionals proposed so far are biased either toward compact or slowly varying densities. In this paper, we propose a screened range-separated hybrid functional, named HSEint, which can well describe these density regimes, achieving good accuracy for both molecular and solid-state systems. The semilocal part of the proposed functional is based on the PBEint generalized gradient approximation [E. Fabiano et al., Phys. Rev. B 82, 113104 (2010)], constructed for hybrid interfaces. To improve the functional performance, we employ exact or nearly exact constraints in the construction of range-separated hybrid functional, such as recovering of the local density linear response and semiclassical atom linear response.

Screened hybrid meta-GGA exchange-correlation functionals for extended systems.

Screened Hartree-Fock exchange integrated with semilocal exchange-correlation functionals often proficiently predict several solid-state properties. This is due to the inclusion of the desired non-locality within the density functional approximations. The screened Hartree-Fock is included within the semilocal functional to compensate the short-range semilocal part which is subtracted from the base semilocal functional. The central task for constructing the screened exchange-correlation functional is to design the short-range semilocal functional. In designing the screened hybrid functionals the exchange hole plays the prime role. In this work, we propose a meta-generalized gradient approximation (meta-GGA) level screened hybrid functional based on the local density approximation based exchange hole and the Tao-Mo semilocal functional. We extensively make an assessment of the newly proposed functional for several solid-state properties which include lattice constants, bulk moduli, band gaps, and cohesive energies. A comparison of the results for the present functional to those for the GGA-based hybrid functional HSE06 confirms that several solid-state properties can be substantially improved by going beyond the GGA level.

Correction: Long-range corrected density functional through the density matrix expansion based semilocal exchange hole.

Correction for 'Long-range corrected density functional through the density matrix expansion based semilocal exchange hole' by Bikash Patra et al., Phys. Chem. Chem. Phys., 2018, 20, 8991-8998.

Laplacian free and asymptotic corrected semilocal exchange potential applied to the band gap of solids.

It is well known that the modified semilocal exchange potentials explicitly designed for the study of solid-state band gaps are very successful in describing these properties. These exchange potentials are in principle designed either from a spherically averaged exchange hole or by satisfying the exact asymptotic conditions. In this present attempt, we use the recently developed novel technique of density matrix expansion to construct the model exchange hole potential. The proposed exchange hole potential is free from the Laplacian of density and generalized through the coordinate transformation. An improvement in the exchange energies of atoms using this potential is shown. The salient feature of the proposed semilocal potential is that it can be used within generalized Kohn-Sham formalism because of its Laplacian free representation. This modified potential is used in the framework of TBMBJ [Phys. Rev. Lett., 2009, 102, 226401] to calculate the band gaps of materials. The comparison and assessment of the newly constructed Laplacian free, asymptotically corrected semilocal potential to address the band gap problem show good agreement with the experimental band gaps and diversify the studies done in the same direction.

Improving the Performance of Tao-Mo Non-empirical Density Functional with Broader Applicability in Quantum Chemistry and Materials Science.

A revised version of the semilocal exchange-correlation functional [Tao, J.; Mo, Y. Phys. Rev. Lett. 2016, 117, 073001] (TM) is proposed by incorporating the modifications to its correlation content obtained from the full high-density second-order gradient expansion as proposed in the case of the revised Tao-Perdew-Staroverov-Scuseria (revTPSS) [Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Constantin, L. A.; Sun, J. Phys. Rev. Lett. 2009, 103, 026403] functional. The present construction improves the performance of the TM functional over a wide range of quantum chemical and solid-state properties (thermochemical and structural). More specifically, the cohesive energies, jellium surface exchange-correlation energies, and real metallic surface energies are improved by preserving the accuracy of the solid-state lattice constants and bulk moduli. The present proposition is not only physically motivated but also enhances the applicability of the TM functional. New physical insights with the proper exemplification of the present modification, which is presented here, can further help in constructing more realistic non-empirical density functionals.