Solid Bandgap Research Articles

M11pz: A Nonlocal Meta Functional with Zero Hartree-Fock Exchange and with Broad Accuracy for Chemical Energies and Structures.

The accuracy of Kohn-Sham density functional theory depends strongly on the approximation to the exchange-correlation functional. In this work, we present a new exchange-correlation functional called M11pz (M11 plus rung-3.5 terms with zero Hartree-Fock exchange) that is built on the M11plus functional with the goal of using its rung-3.5 terms without a Hartree-Fock exchange term, especially to improve the accuracy for strongly correlated systems. The M11pz functional is optimized with the same local and rung-3.5 ingredients that are used in M11plus but without any percentage of Hartree-Fock exchange. The performance of M11pz is compared with eight local functionals, and M11pz is found to be in top three when the errors or ranks are averaged over eight grouped and partially overlapping databases: AME418/22, atomic and molecular energies; MGBE172, main-group bond energies; TMBE40, transition-metal bond energies; SR309, single-reference systems; MR54, multireference systems; BH192, barrier heights; NC579, noncovalent interaction energies; and MS20, molecular structures. For calculations of band gaps of solids, M11pz is the second best of the nine tested functionals that have zero Hartree-Fock exchange.

Investigation of the Optoelectronic and Photovoltaic Properties of YxIN1-xP Alloys using First Principles Calculations

Abstract Structural stability, electronic, optical, and photovoltaic properties of pure and doped InP were evaluated by using first principles calculations via the density functional theory (DFT). The exchange-correlation potential is treated with generalized gradient approximation (GGA-PBE). Additionally, the Tran Blaha modified Becke-Johnson exchange potential (TB-mBJ) is employed, because it gives very accurate results of the band gap in solids. Our results reveal that all compounds are energetically and mechanically stable. It is found that for Y concentrations less than 30%, the favored structure is a Zinc blende-like one, while for Y concentrations greater than 30%, the favored structure is a NaCl-like structure. The substitution of In by Y is found to be able to enlarge the direct bandgap of about 34% (from 1.43 eV to 2.17 eV) and confirms the semiconductor behavior for zinc blende stable structures. The absorption coefficient is reasonably exceeding 105 cm −1 for YxIn1-xP alloys in the case (x=0 and x=25%). The reflectivity shows less than 30% around the energy value of 2 eV and an efficiency of solar cell of 18% can be achieved for Y0.25In0.75P. Also, a thickness of L = 1μm is enough to confirm the experimental data. Regarding to the matching of lattice parameters (a mismatch < 4%) of InP and Y0.25In0.75P and the band gap energy difference made Y0.25In0.75P suitable for optoelectronic and photovoltaic devices in particularity as Tandem solar cells (Y0.25In0.75P/InP) and quantum well (Y0.25In0.75P/InP/Y0.25In0.75P) applications. In the absence of experimental works, our results can be useful for further studies.

Hardness of molecules and bandgap of solids from a generalized gradient approximation exchange energy functional.

The deviations from linearity of the energy as a function of the number of electrons that arise with current approximations to the exchange-correlation (XC) energy functional have important consequences for the frontier eigenvalues of molecules and the corresponding valence-band maxima for solids. In this work, we present an analysis of the exact theory that allows one to infer the effects of such approximations on the highest occupied and lowest unoccupied molecular orbital eigenvalues. Then, we show the importance of the asymptotic behavior of the XC potential in the generalized gradient approximation (GGA) in the case of the NCAPR functional (nearly correct asymptotic potential revised) for determining the shift of the frontier orbital eigenvalues toward the exact values. Thereby we establish a procedure at the GGA level of refinement that allows one to make a single calculation to determine the ionization potential, the electron affinity, and the hardness of molecules (and its solid counterpart, the bandgap) with an accuracy equivalent to that obtained for those properties through energy differences, a procedure that requires three calculations. For solids, the accuracy achieved for the bandgap lies rather close to that which is obtained through hybrid XC energy functionals, but those also demand much greater computational effort than what is required with the simple NCAPR GGA calculation.

Should We Gain Confidence from the Similarity of Results between Methods?

Confirming the result of a calculation by a calculation with a different method is often seen as a validity check. However, when the methods considered are all subject to the same (systematic) errors, this practice fails. Using a statistical approach, we define measures for reliability and similarity, and we explore the extent to which the similarity of results can help improve our judgment of the validity of data. This method is illustrated on synthetic data and applied to two benchmark datasets extracted from the literature: band gaps of solids estimated by various density functional approximations, and effective atomization energies estimated by ab initio and machine-learning methods. Depending on the levels of bias and correlation of the datasets, we found that similarity may provide a null-to-marginal improvement in reliability and was mostly effective in eliminating large errors.

Accurate bandgap predictions of solids assisted by machine learning

The bandgap of the material is a primary property, which affects their performance and applications. Recently, with the emergence of high-throughput simulations, various materials databases are developed based on the density functional theory (DFT). However, for existing databases, the bandgaps are often underestimated since the exchange-correlation functional is treated by the generalized gradient approximation (GGA) with Perdew-Burke-Ernzerh (PBE) approach during the DFT calculations. To better describe the bandgaps, more accurate approach should be employed, such as Heyd-Scuseria-Ernzerh (HSE) hybrid functional. However, this method is extremely time-consuming, which limits its applications. In this work, we employ the machine learning (ML) approach to predict the bandgaps of solids at the HSE level. We first develop a classifier model to identify nonmetals from the database, which shows excellent performance with the area under curve (AUC) up to 0.99. To predict the bandgaps of nonmetals, three ML models are trained and tested based on the selection of different features. These models can accurately predict the HSE bandgaps of solids, with the cross-validation score of 96% and root mean square error (RMSE) of 0.28 eV. Moreover, we apply these ML models to predict the bandgaps from Materials Project database at the HSE level, which contain 126324 inorganic compounds. These data are fully accessible from our newly released code for further study. Thus, our work not only provides an efficient approach to accurately predict the bandgaps of solids, but also accelerates the discovery and development of functional materials.

First-principles calculations to investigate structural, elastic, electronic and magnetic properties of novel d0 half metallic half Heusler alloys XSrB (X=Be, Mg)

The structural, elastic, electronic properties and magnetism of new d0 half Heusler alloys XSrB (X = Be, Mg) were investigated by means of first-principles calculation based on the density functional theory (DFT). The exchange-correlation functional is treated by the generalized gradient approximation proposed by Perdew–Burke–Ernzerhof (GGA-PBE). The Tran-Blaha modified Becke-Johnson (TB-mBJ) exchange potential, which can compute accurately the band gap of solids, is adopted to improve the calculations of the electronic structure and magnetic properties. We found that the two alloys are energetically and mechanically stable in the α phase presenting ductile nature with negative cohesive energies. It was found that MgSrB compound can be experimentally synthesized because of its negative formation energy. The two compounds are half-metallic ferromagnets with total magnetic moment of 1.000 μB per formula unit, in well agreement with Slater-Pauling rule (Mtot = (8 – Ztot) μB). Our calculations show that BeSrB and MgSrB have majority band gaps of 1.024 eV (1.387 eV) and 0.831 eV (1.277 eV) with half-metallic gaps of 0.165 eV (0.613 eV) and 0.311 eV (0.626 eV), respectively, by GGA-PBE (TB-mBJ). The origin of these gaps is well discussed. It was also found that BeSrB and MgSrB are robust half-metallic alloys with respect to the variation of lattice constants. They kept their half-metallicity in relatively wide range of lattice constants of 5.90–7.00 Å and 6.18–7.28 Å, respectively. The obtained results reveal also that BeSrB and MgSrB compounds are considered as nearly gapless half-metallic ferromagnets for lattice parameters range of 7.03–7.88 Å and 7.50–8.40 Å, respectively, which makes them promising candidates for potential applications.

Effectively improving the accuracy of PBE functional in calculating the solid band gap via machine learning

Band gap is one of the most important parameters determining the electronic, optoelectronic, and other applications of a wide range of materials including semiconductors and insulators. However, the accurate prediction of the band gap of these materials has been a persistent difficulty in quantum chemistry. Numerous studies have attempted to improve the accuracy of the predicted band gap from standard density functional theory (DFT) calculations with local density approximation (LDA) and generalized gradient approximation (GGA), which are well-known to underestimate the band gap severely. With the rapid development of material databases from both experimental and theoretical studies, herein, we develop a correction model to improve the prediction accuracy for the band gap by combing the widely used Perdew-Burke-Ernzerh (PBE-GGA) functional with machine learning approach. The correction model introduces physically meaningful but computationally efficient descriptors to fit the experimental dataset, and an artificial neural network (ANN) model is established to improve the prediction accuracy of computational results from DFT-PBE functional. The new method brings a highly accurate model for the prediction of the band gaps at high-precision G0W0 level without increasing computational cost at DFT-PBE level. Further, the error distribution of the predicted band gaps is more in line with the normal distribution compared with DFT-PBE and G0W0 methods. The band gap correction model provides a practical way to obtain GW-like quality results from standard DFT calculations, and should be valuable to perform accurate high-throughput screening of semiconductors and insulators for which GW calculations become unfeasible.

Distinct rhodamine B derivatives exhibiting dual effect of anticancer activity and fluorescence property

Design and application of novel Rhodamine B amide derivatives achieved especially with simple secondary amines, and furthermore exhibiting fluorescence property and anticancer activity is not reported elsewhere. Further functionalization of rhodamine B at the carboxylic acid group with selected secondary amines generated amides, avoiding cyclization and simultaneously sustaining fluorescence. Currently, we have designed and developed three well defined novel rhodamine B amide derivatives by reacting rhodamine B (RHB) with thiomorpholine, bis-(2-chloroethyl) amine and morpholine (the side chains of several anticancer drugs) via rhodamine B acid chloride which resulted in fluorophores namely rhodamine B thiomorpholine amide (1), rhodamine B bis(2-chloroethyl)amine amide (2) and rhodamine B morpholine amide (3). All the three RHB amides were thoroughly characterized using analytical techniques like FT-IR, Mass, 1H NMR, 13C NMR spectroscopy and HPLC. Obtained compounds displayed molecular material attributes as well as anticancer activity. The wavelength of maximum absorption and emission of solutions occurred at ~560 nm and ~583 nm. Quantum yields (Φf = 0.40) and average fluorescence decay (~1.60 ns) of amides was comparable to RHB (1.72 ns). Optical bandgap of solids revealed semiconducting property (~ 2.9 eV). Acquired rhodamine B amides were found to be insensitive over a wide range of pH i.e. from 2 to 10 suggesting their plausible utility in biological labeling, moreover, showed potential anticancer activity against B16F10 (murine melanoma cells), MDA-MB231 (human breast cancer cells), A549 (human lung cancer cells) while they displayed less toxicity to normal HEK 293 (human embryonic kidney) cells. Interestingly, the cellular uptake study manifested that more quantity of the compound were taken up by the cancer cells compared to normal cells which indicate that these amides might become potential candidates to be developed as theranostic agents.

Investigation of the photovoltaic properties of BaHf1-xZrxS3 ([formula omitted]) chalcogenide perovskites using first principles calculations

Electronic, optical, and photovoltaic properties of BaHf1-xZrxS3 (x = 0.00, 0.25, 0.50, 0.75, and 1.00) alloys were evaluated using first principles calculations via the density functional theory. The exchange-correlation potential is treated with generalized gradient approximation. Additionally, the Tran–Blaha modified Becke–Johnson exchange potential is employed, because it gives very accurate results of the band gap in solids. The band structure calculations reveal that these compounds exhibit a semiconductor behavior with a small band gap (Eg < 2 eV). To investigate the optical transitions in these compounds, the real and imaginary parts of the dielectric function are examined. The coefficient absorption (α) is calculated and discussed as well. We found a remarkable α exceeding 105 cm−1 near Eg, which is suitable for the absorption of visible light. To exploit the high photo-absorptivity and evaluate the photovoltaic performance of these alloys, the power conversion efficiency is computed using the spectroscopic limited maximum efficiency method. Our predicted alloys have the characteristics required for photovoltaic applications with a maximum photovoltaic efficiency (η) between 22.22% and 30.09% for thickness L = 500 nm. Particularly, BaHf0.75Zr0·25S3 reveals a performance comparable to that of the best-known photovoltaic materials such as CH3NH3PbI3.

First-principles approach with a pseudohybrid density functional for extended Hubbard interactions

For fast and accurate calculations of band gaps of solids, we present an {\it ab initio} method that extends the density functional theory plus on-site Hubbard interaction (DFT+$U$) to include inter-site Hubbard interaction ($V$). This formalism is appropriate for considering various interactions such as a local Coulomb repulsion, covalent hybridizations, and their coexistence in solids. To achieve self-consistent evaluations of $U$ and $V$, we adapt a recently proposed Agapito-Curtarolo-Buongiorno Nardelli pseudohybrid functional for DFT$+U$ to implement a density functional of $V$ and obtain band gaps of diverse bulk materials as accurate as those from $GW$ or hybrid functionals methods with a standard DFT computational cost. Moreover, we also show that computed band gaps of few layers black phosphorous and Si(111)-($2\times1$) surface agree with experiments very well, thus meriting the new method for large-scale as well as high throughput calculations with higher accuracy.

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.

Electronic band structure of layers within meta generalized gradient approximation of density functionals

Semilocal exchange functionals are propitious in describing several properties of solids due to computational competence. For calculating band gaps of solids, the underestimation of generalized gradient approximation (GGA) functionals is known. The next rung of GGA in Jacob's ladder, i.e., meta-GGA, is expected to improve the band-gap calculation. In this regard, exchange-only potentials are very effective in producing accurate band gaps of solids. But, due to the presence of lattice-dependent parameters, these methods are incompetent for monolayers or slabs. Here, we show the potency of advance meta-GGA energy functionals in elucidating the band gaps of different layered structures. The recently proposed MGGAC meta-GGA functional by Patra et al. Phys. Rev. B 100, 155140 (2019) has proved to be very promising for band gaps within the semilocal treatment of density-functional theory. This conclusion is acquired by applying these functionals to encouraging examples of doped graphene, graphane, and halogenated graphene having insulating band gaps. Also, the improved values of energies of hydrogen-terminated Si(111) surface states are demonstrated with this meta-GGA functional.

Exchange-correlation functionals for band gaps of solids: benchmark, reparametrization and machine learning

We conducted a large-scale density-functional theory study on the influence of the exchange-correlation functional in the calculation of electronic band gaps of solids. First, we use the large materials data set that we have recently proposed to benchmark 21 different functionals, with a particular focus on approximations of the meta-generalized-gradient family. Combining these data with the results for 12 functionals in our previous work, we can analyze in detail the characteristics of each approximation and identify its strong and/or weak points. Beside confirming that mBJ, HLE16 and HSE06 are the most accurate functionals for band gap calculations, we reveal several other interesting functionals, chief among which are the local Slater potential approximation, the GGA AK13LDA, and the meta-GGAs HLE17 and TASK. We also compare the computational efficiency of these different approximations. Relying on these data, we investigate the potential for improvement of a promising subset of functionals by varying their internal parameters. The identified optimal parameters yield a family of functionals fitted for the calculation of band gaps. Finally, we demonstrate how to train machine learning models for accurate band gap prediction, using as input structural and composition data, as well as approximate band gaps obtained from density-functional theory.

Validation of Pseudopotential Calculations for the Electronic Band Gap of Solids.

Nowadays pseudopotential (PP) density functional theory calculations constitute the standard approach to tackle solid-state electronic problems. These rely on distributed PP tables that were built from all-electron atomic calculations using few popular semilocal exchange-correlation functionals, while PPs based on more modern functionals, such as meta-generalized gradient approximation and hybrid functionals, or for many-body methods, such as GW, are often not available. Because of this, employing PPs created with inconsistent exchange-correlation functionals has become a common practice. Our aim is to quantify systematically the error in the determination of the electronic band gap when cross-functional PP calculations are performed. To this end, we compare band gaps obtained with norm-conserving PPs or the projector-augmented wave method with all-electron calculations for a large data set of 473 solids. We focus, in particular, on density functionals that were designed specifically for band gap calculations. On average, the absolute error is about 0.1 eV, yielding absolute relative errors in the 5–10% range. Considering that typical errors stemming from the choice of the functional are usually larger, we conclude that the effect of choosing an inconsistent PP is rather harmless for most applications. However, we find specific cases where absolute errors can be larger than 1 eV or others where relative errors can amount to a large fraction of the band gap.

Investigations of electronic, structural and optical properties of cubic A2ZnTeO6 (A = Ca, Sr, Ba) compounds via first-principles approaches

Theoretical calculations are performed to investigate the electronic, structural and optical properties of double perovskite oxide A2ZnTeO6 (A = Ca, Sr, Ba). The calculations are based on the Density Functional Theory (DFT) using the WIEN2k code. The exchange–correlation potential is treated with generalized gradient approximation (GGA-PBE). Additionally, the Tran Blaha modified Becke-Johnson exchange potential (TB-mBJ) is employed for electronic and optical calculations due to that it gives very accurate results of band gap in solids. In order to estimate the ground state parameters, total energies are calculated with respect to cell volume. Also, the energies are fitted with Murnaghan equation of state. The estimated ground state parameters are comparable with the available experimental data. The band structure calculations reveal that these compounds exhibit semiconducting behavior with a direct band gap. To explore the optical transitions in these compounds, the real and imaginary parts of the dielectric function are analyzed at ambient conditions and the important optical constants are calculated and discussed.

On the calculation of the bandgap of periodic solids with MGGA functionals using the total energy.

During the last few years, it has become more and more clear that functionals of the meta generalized gradient approximation (MGGA) are more accurate than GGA functionals for the geometry and energetics of electronic systems. However, MGGA functionals are also potentially more interesting for the electronic structure, in particular, when the potential is nonmultiplicative (i.e., when MGGAs are implemented in the generalized Kohn-Sham framework), which may help to get more accurate bandgaps. Here, we show that the calculation of bandgap of solids with MGGA functionals can also be done very accurately in a non-self-consistent manner. This scheme uses only the total energy and can, therefore, be very useful when the self-consistent implementation of a particular MGGA functional is not available. Since self-consistent MGGA calculations may be difficult to converge, the non-self-consistent scheme may also help to speed up the calculations. Furthermore, it can be applied to any other types of functionals, for which the implementation of the corresponding potential is not trivial.

Large-Scale Benchmark of Exchange-Correlation Functionals for the Determination of Electronic Band Gaps of Solids.

We compile a large data set designed for the efficient benchmarking of exchange–correlation functionals for the calculation of electronic band gaps. The data set comprises information on the experimental structure and band gap of 472 nonmagnetic materials and includes a diverse group of covalent-, ionic-, and van der Waals-bonded solids. We used it to benchmark 12 functionals, ranging from standard local and semilocal functionals, passing through meta-generalized-gradient approximations, and several hybrids. We included both general purpose functionals, like the Perdew–Burke–Ernzerhof approximation, and functionals specifically crafted for the determination of band gaps. The comparison of experimental and theoretical band gaps shows that the modified Becke–Johnson is at the moment the best available density functional, closely followed by the Heyd–Scuseria–Ernzerhof screened hybrid from 2006 and the high-local-exchange generalized-gradient approximation.

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.

First principles study on structural, electronic and optical properties of Ga1−xBxP ternary alloys (x = 0, 0.25, 0.5, 0.75 and 1)

The structural, electronic and optical properties of GaP, BP binary compounds and their ternary alloys Ga1−xBxP (x=0.25, 0.5 and 0.75) have been studied by full-potential linearized augmented plane wave (FP-LAPW) method within the framework of density functional theory (DFT) as implemented in WIEN2k package. Local density approximation (LDA) and generalized gradient approximation (GGA) as proposed by Perdew–Burke–Ernzerhof (PBE), Wu–Cohen (WC) and PBE for solid (PBESol) were used for treatment of exchange-correlation effect in calculations. Additionally, the Tran–Blaha modified Becke–Johnson (mBJ) potential was also employed for electronic and optical calculations due to that it gives very accurate band gap of solids. As B concentration increases, the lattice constant reduces and the energy band gap firstly decreases for small composition x and then it shows increasing trend until pure BP. Our results show that the indirect–direct band gap transition can be reached from x=0.33. The linear optical properties, such as reflectivity, absorption coefficient, refractive index and optical conductivity of binary compounds and ternary alloys were derived from their calculated complex dielectric function in wide energy range up to 30 eV, and the alloying effect on these properties was also analyzed in detail.

Nonempirical hybrid functionals for band gaps and polaronic distortions in solids

We construct hybrid functionals in a nonempirical way by fixing the fraction of Fock exchange through either the long-range screening or the generalized Koopmans' condition applied to defect charge-transition levels. These functionals not only give band gaps of solids as accurate as state-of-the-art $GW$ calculations, but are also capable of describing polaronic distortions. The Koopmans' condition is found to be satisfied across a series of defects, to the point of achieving accurate band gaps through a hydrogen probe. Extension to range-separated functionals demonstrates the robustness of the present approach.