Accurate density functional made more versatile

Reworking the Tao-Mo Exchange-Correlation Functional. III. Improved Deorbitalization Strategy and Faithful Deorbitalization

We present a deorbitalization of the recent simplified, regularized Tao-Mo exchange functional ( J. Chem. Phys. 2023, 159, 214102) that is faithful to the parent functional. That is a major gain relative to our earlier deorbitalization which did poorly on molecular heats of formation ( J. Chem. Phys. 2023, 159, 214103). The improvement arises from augmentation of the Mejía-Rodríguez and Trickey deorbitalization strategy ( Phys. Rev. A 2017, 96, 052512) to use a smoothed replacement for the reduced density Laplacian (conventionally denoted q) obtained from that Laplacian itself. The augmentation also rationalizes the improvement obtained from the cutoff of q < 0 that was poorly understood at the time of the previous paper. The new scheme yields deorbitalized chemical region indicators that are much closer to those from the parent, orbital-dependent functional than were obtainable from the previous deorbitalization. It also replicates the good 3d elemental magnetization of the parent functional reasonably well.

Comparing first-principles density functionals plus corrections for the lattice dynamics of YBa2Cu3O6

The enigmatic mechanism underlying unconventional high-temperature superconductivity, especially the role of lattice dynamics, has remained a subject of debate. Theoretical insights have long been hindered due to the lack of an accurate first-principles description of the lattice dynamics of cuprates. Recently, using the r2SCAN meta-generalized gradient approximation (meta-GGA) functional, we have been able to achieve accurate phonon spectra of an insulating cuprate YBa2Cu3O6 and discover significant magnetoelastic coupling in experimentally interesting Cu-O bond stretching optical modes [Ning et al., Phys. Rev. B 107, 045126 (2023)]. We extend this work by comparing Perdew-Burke-Ernzerhof and r2SCAN performances with corrections from the on-site Hubbard U and the D4 van der Waals (vdW) methods, aiming at further understanding on both the materials science side and the density functional side. We demonstrate the importance of vdW and self-interaction corrections for accurate first-principles YBa2Cu3O6 lattice dynamics. Since r2SCAN by itself partially accounts for these effects, the good performance of r2SCAN is now more fully explained. In addition, the performances of the Tao-Mo series of meta-GGAs, which are constructed in a different way from the strongly constrained and appropriately normed (SCAN) meta-GGA and its revised version r2SCAN, are also compared and discussed.

Reworking the Tao-Mo exchange-correlation functional. I. Reconsideration and simplification

The revised, regularized Tao-Mo (rregTM) exchange-correlation density functional approximation (DFA) [A. Patra, S. Jana, and P. Samal, J. Chem. Phys. 153, 184112 (2020) and Jana et al., J. Chem. Phys. 155, 024103 (2021)] resolves the order-of-limits problem in the original TM formulation while preserving its valuable essential behaviors. Those include performance on standard thermochemistry and solid data sets that is competitive with that of the most widely explored meta-generalized-gradient-approximation DFAs (SCAN and r2SCAN) while also providing superior performance on elemental solid magnetization. Puzzlingly however, rregTM proved to be intractable for de-orbitalization via the approach of Mejía-Rodríguez and Trickey [Phys. Rev. A 96, 052512 (2017)]. We report investigation that leads to diagnosis of how the regularization in rregTM of the z indicator functions (z = the ratio of the von-Weizsäcker and Kohn-Sham kinetic energy densities) leads to non-physical behavior. We propose a simpler regularization that eliminates those oddities and that can be calibrated to reproduce the good error patterns of rregTM. We denote this version as simplified, regularized Tao-Mo, sregTM. We also show that it is unnecessary to use rregTM correlation with sregTM exchange: Perdew-Burke-Ernzerhof correlation is sufficient. The subsequent paper shows how sregTM enables some progress on de-orbitalization.

Reworking the Tao-Mo exchange-correlation functional. II. De-orbitalization

In Paper I [H. Francisco, A. C. Cancio, and S. B. Trickey, J. Chem. Phys. 159, 214102 (2023)], we gave a regularization of the Tao-Mo exchange functional that removes the order-of-limits problem in the original Tao-Mo form and also eliminates the unphysical behavior introduced by an earlier regularization while essentially preserving compliance with the second-order gradient expansion. The resulting simplified, regularized (sregTM) functional delivers performance on standard molecular and solid state test sets equal to that of the earlier revised, regularized Tao-Mo functional. Here, we address de-orbitalization of that new sregTM into a pure density functional. We summarize the failures of the Mejía-Rodríguez and Trickey de-orbitalization strategy [Phys. Rev. A 96, 052512 (2017)] when used with both versions. We discuss how those failures apparently arise in the so-called z' indicator function and in substitutes for the reduced density Laplacian in the parent functionals. Then, we show that the sregTM functional can be de-orbitalized somewhat well with a rather peculiarly parameterized version of the previously used deorbitalizer. We discuss, briefly, a de-orbitalization that works in the sense of reproducing error patterns but that apparently succeeds by cancelation of major qualitative errors associated with the de-orbitalized indicator functions α and z, hence, is not recommended. We suggest that the same issue underlies the earlier finding of comparatively mediocre performance of the de-orbitalized Tao-Perdew-Staroverov-Scuseri functional. Our work demonstrates that the intricacy of such two-indicator functionals magnifies the errors introduced by the Mejía-Rodríguez and Trickey de-orbitalization approach in ways that are extremely difficult to analyze and correct.

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.

Reproducibility of density functional approximations: How new functionals should be reported

Density functional theory is the workhorse of chemistry and materials science, and novel density functional approximations are published every year. To become available in program packages, the novel density functional approximations (DFAs) need to be (re)implemented. However, according to our experience as developers of Libxc [Lehtola et al., SoftwareX 7, 1 (2018)], a constant problem in this task is verification due to the lack of reliable reference data. As we discuss in this work, this lack has led to several non-equivalent implementations of functionals such as Becke-Perdew 1986, Perdew-Wang 1991, Perdew-Burke-Ernzerhof, and Becke's three-parameter hybrid functional with Lee-Yang-Parr correlation across various program packages, yielding different total energies. Through careful verification, we have also found many issues with incorrect functional forms in recent DFAs. The goal of this work is to ensure the reproducibility of DFAs. DFAs must be verifiable in order to prevent the reappearance of the above-mentioned errors and incompatibilities. A common framework for verification and testing is, therefore, needed. We suggest several ways in which reference energies can be produced with free and open source software, either with non-self-consistent calculations with tabulated atomic densities or via self-consistent calculations with various program packages. The employed numerical parameters-especially the quadrature grid-need to be converged to guarantee a ≲0.1 μEh precision in the total energy, which is nowadays routinely achievable in fully numerical calculations. Moreover, as such sub-μEh level agreement can only be achieved when fully equivalent implementations of the DFA are used, the source code of the reference implementation should also be made available in any publication describing a new DFA.

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.

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 the 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 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, that depends only on the meta-GGA ingredient α (also known as the Pauli kinetic energy enhancement factor). The model is used subsequently 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.

Improved electronic structure prediction of chalcopyrite semiconductors from a semilocal density functional based on Pauli kinetic energy enhancement factor

The correct treatment ofdelectrons is of prime importance in order to predict the electronic properties of the prototype chalcopyrite semiconductors. The effect ofdstates is linked with the anion displacement parameteru, which in turn influences the bandgap of these systems. Semilocal exchange-correlation functionals which yield good structural properties of semiconductors and insulators often fail to predict reasonableubecause of the underestimation of the bandgaps arising from the strong interplay betweendelectrons. In the present study, we show that the meta-generalized gradient approximation (meta-GGA) obtained from the cuspless hydrogen density (MGGAC) (2019Phys. Rev.B 100 155140) performs in an improved manner in apprehending the key features of the electronic properties of chalcopyrites, and its bandgaps are comparative to that obtained using state-of-art hybrid methods. Moreover, the present assessment also shows the importance of the Pauli kinetic energy enhancement factor,α= (τ-τ^W)/τ^unifin describing thedelectrons in chalcopyrites. The present study strongly suggests that the MGGAC functional within semilocal approximations can be a better and preferred choice to study the chalcopyrites and other solid-state systems due to its superior performance and significantly low computational cost.

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.

Synthesis of Thermally Stable h-BN-CNT Hetero-Structures via Microwave Heating of Ethylene under Nickel, Iron, and Silver Catalysts

Initially, three samples of carbon nanotubes (SWCNTs) were synthesized from neem tree material. Afterward, these samples were coated with hexagonal boron nitride (h-BN) to form h-BN and CNT composite (h-BN-CNT). The essence of using h-BN (being a perfect insulator) with armchair SWCNT (being a conductor) is to create an interface between an insulator and conductor. The samples were treated under three different transition metal nanoparticles; silver, iron, and nickel. Thermogravimetric (TGA) analysis reveals that h-BN/CNT is thermally more stable with silver than iron and nickel nanoparticles. TGA profile showed resistance to mass loss at the beginning due to the higher thermal resistivity by the impurity compounds. The DFT calculation, generalized gradient approximation (GGA), and Perdew–Burke–Ernzerhof (PBE) analysis found engineered bandgap energy of 3.4 eV for the synthesized h-BN-CNT heterostructure. Because of its unique structural and electronic properties such as tunable bandgaps, the h-BN-CNT heterostructure may open new ways for manipulating excitons in the CNTs, and thus can be explored to develop various new electronic devices.