Tao-Perdew-Staroverov-Scuseria Research Articles

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.

The correlation factor model for the exchange-correlation energy and its application to transition metal compounds.

In the recently developed correlation factor (CF) model [Precechtelova et al., J. Chem. Phys. 143, 144102 (2015)], the exchange-correlation (XC) hole is approximated. Since various constraints satisfied by the XC-hole are known, approximations to it can be designed which largely avoid empirical adjustments. In the CF approach, the XC-hole is written as a product of an exchange hole times a CF. An important constraint satisfied by the CF model is that it correctly reproduces the exact exchange energy in the high density limit. This is achieved by employing the exact exchange-energy per particle (ϵXr) as an input variable, i.e., the CF model builds on exact exchange. Variations of the initial CF model are proposed which ensure that the exact answer is obtained in the homogeneous limit. Furthermore, we apply a correction to the depth of the XC-hole that is designed to capture strong correlation. EC functionals that build on exact exchange, such as hybrids, often fail for systems that exhibit sizeable electron correlation. Despite this fact and despite the reduction of empiricism to a single parameter within CF, accurate atomization energies are obtained for strongly-correlated transition metal compounds. The CF model significantly improves upon widely used functionals such as Perdew-Burke-Ernzerhof (PBE), PBE hybrid, and Tao-Perdew-Staroverov-Scuseria (TPSS).

Structural determination of neutral Con clusters (n = 4–10,13) through IR–UV two-color vibrational spectroscopy and DFT calculations

We recorded IR spectra for neutral cobalt clusters via two-color IR-UV ionization, using the Free Electron Laser for intracavity experiments (FELICE). Well-resolved IR spectra are presented for (n = 4–10, 13) and analyzed with the help of Density Functional Theory calculations using two different correlation exchange functionals: the revisited Tao–Perdew–Staroverov–Scuseria (revTPSS) and the frequently used Perdew–Burke–Ernzerhof (PBE) approaches. Although we have not performed an extensive structure search, we tentatively assign the spectra for all cluster sizes except for n = 7, and n = 10. We find that neither of the two functionals chosen clearly outperforms the other in predicting IR spectra, and that relatively low scaling factors of 0.82 (PBE) and 0.8 (revTPSS) are required. In contrast to the magnetic moments, the calculated electric dipole moments fluctuate strongly as a function of cluster size and could therefore be used as an indirect probe to the cluster structure.

Assessing the performance of the recent meta-GGA density functionals for describing the lattice constants, bulk moduli, and cohesive energies of alkali, alkaline-earth, and transition metals

The bulk properties such as lattice constants, bulk moduli, and cohesive energies of alkali, alkaline-earth, and transition metals are studied within the framework of the recently developed meta-GGA (meta-Generalized Gradient Approximation) level semilocal exchange-correlation functionals. To establish the applicability, broadness, and accuracy of meta-GGA functionals, we also put the results obtained using PBE (Perdew-Burke-Ernzerhof) [J. P. Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)] and PBE reparameterized for solid [J. P. Perdew et al., Phys. Rev. Lett. 100, 136406 (2008)] GGA functionals. The interesting feature of the present paper is that it measures the accuracy of the recently developed TM (Tao-Mo), TMTPSS [TM exchange with Tao-Perdew-Staroverov-Scuseria (TPSS)] [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016)] correlation, and strongly constrained and appropriately normed [J. Sun et al., Phys. Rev. Lett. 115, 036402 (2015)] functionals to calculate the aforementioned properties. Not only that, we also include other (popular) meta-GGA functionals in order to have a closer look at the performance of the meta-GGA functionals too. The present systematic investigation shows that the TM functional is accurate in describing the lattice constants while for cohesive energies and bulk moduli, the PBE and modified TPSS perform better compared to others.

Assessing the performance of the Tao-Mo semilocal density functional in the projector-augmented-wave method.

We assess the performance of the recently proposed Tao-Mo (TM) semilocal exchange-correlation functional [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016)] using the projector-augmented-wave method with the plane wave basis set. The meta-generalized gradient approximation level semilocal functional constructed by Tao-Mo is an all-purpose exchange-correlation functional for the quantum chemistry and solid-state physics. The exchange of the TM functional is based on the density matrix expansion technique together with the slowly varying fourth order gradient expansion. The correlation functional corresponding to the exchange is based on the one-electron self-interaction-free Tao-Perdew-Staroverov-Scuseria functional. Our test includes solid-state lattice constants, bulk moduli, bandgaps, cohesive energies, magnetic moments and vacancy-formation energies of transition metals. It is observed that in the plane wave basis, the TM functional performs accurately in predicting all the solid state properties at the semilocal level.

Comparative study of the properties of ionic solids from density functionals

Prediction of ionic-solid properties presents a great challenge to Kohn–Sham conventional density functional theory, due to the fact that there is strong van der Waals interaction between ion cores. In this work, we apply the Tao-Mo (TM) semilocal density functional to calculate lattice constants, bulk moduli, and cohesive energies for ionic solids consisting of alkali halides, silver halides, and other ionic solids. Our calculation shows that the TM functional yields accurate lattice constants, with a mean absolute error (MAE) of 0.087 Å, which is obviously smaller than commonly-used semilocal functionals such as the local spin-density approximation (LSDA) and Perdew–Burke–Ernzerhof generalized gradient approximation (PBE GGA). It is even more accurate than dispersion-corrected density functional PBE + D3 (MAE = 0.116 Å). This is unexpected success. For bulk moduli, TM functional can also yield very good accuracy, with an MAE of 3.02 GPA. Finally, we evaluate the cohesive energies of ionic solids. We find that this functional produces an MAE of 0.13 eV/atom, which is more accurate than the LSDA and PBE GGA, but less accurate than PBE + D3. We have also made a comparison of TM with other semilocal density functional theory (DFT) methods on several other ionic solids. It appears that TM also gives an overall improvement upon other popular semilocal DFT methods such as PBE for solids and Tao–Perdew–Staroverov–Scuseria.

Robustness of surface activity electronic structure-based descriptors of transition metals.

Efficient yet simple electronic structure-based descriptors of transition metal surfaces are key in material design for many scientific fields in research and technology. Density functional theory-based methods provide the framework to systematically explore the performance and transferability of such descriptors. Using appropriate surface models and the Vosko-Wilk-Nussair (VWN), Perdew-Burke-Ernzerhof (PBE), PBE adapted for solids (PBEsol), revised PBE (RPBE), and Tao-Perdew-Staroverov-Scuseria (TPSS) exchange-correlation functionals, we study the transferability of three descriptors: the d-band centre, the width-corrected d-band centre, and the Hilbert transform highest peak, among the low-index Miller surfaces for the metals of transition elements. We show that the d-band centre and the width-corrected d-band centre descriptors are almost independent of the functional used whereas a dependency is seen in the Hilbert transform highest peak. Moreover, it is seen that the differences between the surface descriptor values and predictions from the bulk ones are affected by the presence of surface states. Interestingly, a direct relation between the surface coordination number and the d-band centre electronic descriptor is found when surface states are absent.

Exchange-correlation energies of atoms from efficient density functionals: influence of the electron density

The primary goal of Kohn–Sham density functional theory is to evaluate the exchange-correlation contribution to electronic properties. However, the accuracy of a density functional can be affected by the electron density. Here we apply the nonempirical Tao–Mo (TM) semilocal functional to study the influence of the electron density on the exchange and correlation energies of atoms and ions, and compare the results with the commonly used nonempirical semilocal functionals local spin-density approximation (LSDA), Perdew–Burke–Ernzerhof (PBE), Tao–Perdew–Staroverov–Scuseria (TPSS), and hybrid functional PBE0. We find that the spin-restricted Hartree–Fock density yields the exchange and correlation energies in good agreement with the Optimized Effective Potential method, particularly for spherical atoms and ions. However, the errors of these semilocal and hybrid functionals become larger for self-consistent densities. We further find that the quality of the electron density have greater effect on the exchange-correlation energies of kinetic energy density-dependent meta-GGA functionals TPSS and TM than on those of the LSDA and GGA, and therefore, should have greater influence on the performance of meta-GGA functionals. Finally, we show that the influence of the density quality on PBE0 is slightly reduced, compared to that of PBE, due to the exact mixing.

Accurate excitation energies of molecules and oligomers from a semilocal density functional.

Excitation energy plays an important role in energy conversion, biological processes, and optical devices. In this work, we apply the Tao-Mo (TM) nonempirical meta-generalized gradient approximation and the combination TMTPSS (TMx + TPSSc), with TPSSc being the correlation part of the original TPSS (Tao-Perdew-Staroverov-Scuseria) to study excitation energies of small molecules and oligomers. Our test set consists of 17 molecules with 134 total excited states, including singlet, triplet, valence, and Rydberg excited states. Our calculation shows that both the TMTPSS and TM functionals yield good overall performance, with mean absolute errors (MAEs) of 0.37 eV and 0.42 eV, respectively, outperforming commonly used semilocal functionals LSDA (MAE = 0.55 eV), PBE (MAE = 0.58 eV), and TPSS (MAE = 0.47 eV). In particular, TMTPSS can yield nearly the same accuracy of B3LYP (MAE = 0.36 eV), with lower computational cost. The accuracy for semilocal density functional theory continues to hold for conjugated oligomers, but they become less accurate than hybrid functionals, due to the insufficient nonlocality.

Energetic Study of Clusters and Reaction Barrier Heights from Efficient Semilocal Density Functionals

The accurate first-principles prediction of the energetic properties of molecules and clusters from efficient semilocal density functionals is of broad interest. Here we study the performance of a non-empirical Tao-Mo (TM) density functional on binding energies and excitation energies of titanium dioxide and water clusters, as well as reaction barrier heights. To make a comparison, a combination of the TM exchange part with the TPSS (Tao–Perdew–Staroverov–Scuseria) correlation functional—called TMTPSS—is also included in this study. Our calculations show that the best binding energies of titanium dioxide are predicted by PBE0 (Perdew–Burke–Ernzerhof hybrid functional), TM, and TMTPSS with nearly the same accuracy, while B3LYP (Beck’s three-parameter exchange part with Lee-Yang-Parr correlation), TPSS, and PBE (Perdew–Burke–Ernzerhof) yield larger mean absolute errors. For excitation energies of titanium and water clusters, PBE0 and B3LYP are the most accurate functionals, outperforming the performance of semilocal functionals due to the nonlocality problem suffered by the latter. Nevertheless, TMTPSS and TM functionals are still good accurate semilocal methods, improving upon the commonly-used TPSS and PBE functionals. We also find that the best reaction barrier heights are predicted by PBE0 and B3LYP, thanks to the nonlocality incorporated into these two hybrid functionals, but TMTPSS and TM are obviously more accurate than SCAN (Strongly Constrained and Appropriately Normed), TPSS, and PBE, suggesting the good performance of TM and TMTPSS for physically different systems and properties.

Semilocal exchange hole with an application to range-separated density functionals

Exchange-correlation hole is a central concept in density functional theory. It not only provides justification for an exchange-correlation energy functional, but also serves as a local ingredient in nonlocal range-separation density functional. However, due to the nonlocal nature, modelig the conventional exact exchange hole presents a great challenge to density functional theory. In this work, we propose a semilocal exchange hole underlying the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA functional. The present model is distinct from previous models at small separation between an electron and the hole around the electron. It is also different in the way it interpolates between the rapidly varying iso-orbital density and the slowly varying density, which is determined by the wave vector analysis based on the exactly solvable infinite barrier model for jellium surface. Our numerical tests show that the exchange hole generated from this model mimics the conventional exact exchange hole quite well for atoms. Finally, as a simple application, we apply the hole model to construct a TPSS-based range-separation functional. Our tests show that this TPSS-based range-separation functional can substantially improve TPSS band gaps and barrier heights, without losing much accuracy of molecular atomization energies.

Predicting core level binding energies shifts: Suitability of the projector augmented wave approach as implemented in VASP.

Here, we assess the accuracy of various approaches implemented in Vienna ab initio simulation package code to estimate core-level binding energy shifts (ΔBEs) using a projector augmented wave method to treat core electrons. The performance of the Perdew-Burke-Ernzerhof (PBE) and the Tao-Perdew-Staroverov-Scuseria (TPSS) exchange-correlation density functionals is examined on a dataset of 68 molecules containing B→F atoms in diverse chemical environments, accounting for 185 different 1s core level binding energy shifts, for which both experimental gas-phase X-ray photoemission (XPS) data and accurate all electron ΔBEs are available. Four procedures to calculate core-level shifts are investigated. Janak-Slater transition state approach yields mean absolute errors of 0.37 (0.21) eV at PBE (TPSS) level, similar to highly accurate all electron ΔSCF approaches using same functionals, and close to XPS experimental accuracy of 0.1 eV. The study supports the use of these procedures to assign ΔBEs of molecular moieties on material surfaces of interest in surface science, nanotechnology, and heterogeneous catalysis. © 2017 Wiley Periodicals, Inc.

First-principles calculations of the electronic and structural properties of GaSb

In this paper, we carried out first-principles calculations in order to investigate the structural and electronic properties of the binary compound gallium antimonide (GaSb). This theoretical study was carried out using the Density Functional Theory within the plane-wave pseudopotential method. The effects of exchange and correlation (XC) were treated using the functional Local Density Approximation (LDA), generalized gradient approximation (GGA): Perdew–Burke–Ernzerhof (PBE), Perdew-Burke-Ernzerhof revised for solids (PBEsol), Perdew-Wang91 (PW91), revised Perdew–Burke–Ernzerhof (rPBE), Armiento–Mattson 2005 (AM05) and meta-generalized gradient approximation (meta-GGA): Tao–Perdew–Staroverov–Scuseria (TPSS) and revised Tao–Perdew–Staroverov–Scuseria (RTPSS) and modified Becke-Johnson (MBJ). We calculated the densities of state (DOS) and band structure with different XC potentials identified and compared them with the theoretical and experimental results reported in the literature. It was discovered that functional: LDA, PBEsol, AM05 and RTPSS provide the best results to calculate the lattice parameters (a) and bulk modulus (B 0); while for the cohesive energy (E coh), functional: AM05, RTPSS and PW91 are closer to the values obtained experimentally. The MBJ, Rtpss and AM05 values found for the band gap energy is slightly underestimated with those values reported experimentally.

Density functional theory study of substituent effects on gas‐phase heterolytic Fe–O and Fe–S bond energies of m‐G‐C6H4OFe(CO)2(η5‐C5H5) and m‐G‐C6H4SFe(CO)2(η5‐C5H5)

The knowledge of accurate bond strengths is a fundamental basis for a proper analysis of chemical reaction mechanisms. Quantum chemical calculations at different levels of theory have been used to investigate heterolytic Fe–O and Fe–S bond energies of (meta‐substituted phenoxy)dicarbonyl(η5‐cyclopentadienyl) iron [m‐G‐C6H4OFp (1)] and (meta‐substituted benzenethiolato)dicarbonyl(η5‐cyclopentadienyl) iron [m‐G‐C6H4SFp (2)] complexes. In this study, Fp is (η5‐C5H5)Fe(CO)2, and G is NO2, CN, COMe, CO2Me, CF3, Br, Cl, F, H, Me, MeO, and NMe2. The results show that Tao–Perdew–Staroverov–Scuseria and Becke's power‐series ansatz from 1997 with dispersion corrections functionals can provide the best price/performance ratio and accurate predictions of ΔHhet(Fe–O)'s and ΔHhet(Fe–S)'s. The excellent linear free energy relations [r = 1.00 (g, 1e), 1.00 (g, 2b)] among the ΔΔHhet (Fe–O)'s and δΔG0 of OH bonds of m‐G‐C6H4OH or ΔΔHhet(Fe–S)'s and ΔpKa's of SH bonds of m‐G‐C6H4SH imply that the governing structural factors for these bond scissions are similar. And, the linear correlations [r = −0.97 (g, 1 g), −0.97 (g, 2 h)] among the ΔΔHhet (Fe–O)'s or ΔΔHhet(Fe–S)'s and the substituent σm constants show that these correlations are in accordance with Hammett linear free energy relationships. The inductive effects of these substituents and the basis set effects influence the accuracy of ΔHhet(Fe–O)'s or ΔHhet(Fe–S)'s. The ΔΔHhet(Fe–O)'s(g) (1) and ΔΔHhet(Fe–S)'s(g)(2) follow the capto‐dative Principle. The substituent effects on the Fe–O bonds are much stronger than those on the less polar Fe–S bonds. Insight from this work may help the design of more effective catalytic processes. Copyright © 2016 John Wiley & Sons, Ltd.

Effect of the Exchange-Correlation Potential on the Transferability of Brønsted-Evans-Polanyi Relationships in Heterogeneous Catalysis.

As more and more accurate density functional methods emerge, the transferability of Brønsted-Evans-Polanyi (BEP) relationships obtained with previous models is an open question. In this work, BEP relationships derived from different density functional theory based calculations are analyzed to answer this question. In particular, BEP relationships linking the activation energy of O-H bond breaking reactions taking place on metallic surfaces with the adsorption energy of the reaction products are chosen as a case study. These relationships are obtained with the widely used Perdew-Wang (PW91) generalized gradient approximation (GGA) exchange-correlation functional and with the more accurate meta-GGA Tao-Perdew-Staroverov-Scuseria (TPSS) one. We provide compelling evidence that BEP relationships derived from PW91 and TPSS functionals are essentially coincidental. This finding validates previously published BEP relationships and indicates that the reaction activation energy barrier can be obtained by the determination of the energy reaction descriptor value at the less computationally demanding GGA level; an important aspect to consider in future studies aimed at the computational design of catalysts with improved characteristics.

Performance of the TPSS Functional on Predicting Core Level Binding Energies of Main Group Elements Containing Molecules: A Good Choice for Molecules Adsorbed on Metal Surfaces.

Here we explored the performance of Hartree-Fock (HF), Perdew-Burke-Ernzerhof (PBE), and Tao-Perdew-Staroverov-Scuseria (TPSS) functionals in predicting core level 1s binding energies (BEs) and BE shifts (ΔBEs) for a large set of 68 molecules containing a wide variety of functional groups for main group elements B → F and considering up to 185 core levels. A statistical analysis comparing with X-ray photoelectron spectroscopy (XPS) experiments shows that BEs estimations are very accurate, TPSS exhibiting the best performance. Considering ΔBEs, the three methods yield very similar and excellent results, with mean absolute deviations of ∼0.25 eV. When considering relativistic effects, BEs deviations drop approaching experimental values. So, the largest mean percentage deviation is of 0.25% only. Linear trends among experimental and estimated values have been found, gaining offsets with respect to ideality. By adding relativistic effects to offsets, HF and TPSS methods underestimate experimental values by solely 0.11 and 0.05 eV, respectively, well within XPS chemical precision. TPSS is posed as an excellent choice for the characterization, by XPS, of molecules on metal solid substrates, given its suitability in describing metal substrates bonds and atomic and/or molecular orbitals.

Combinations of coupled cluster, density functionals, and the random phase approximation for describing static and dynamic correlation, and van der Waals interactions

ABSTRACTContrary to standard coupled cluster doubles (CCD) and Brueckner doubles (BD), singlet-paired analogues of CCD and BD (denoted here as CCD0 and BD0) do not break down when static correlation is present, but neglect substantial amounts of dynamic correlation. In fact, CCD0 and BD0 do not account for any contributions from multielectron excitations involving only same-spin electrons at all. We exploit this feature to add – without introducing double counting, self-interaction, or increase in cost – the missing correlation to these methods via meta-GGA (generalised gradient approximation) density functionals (Tao–Perdew–Staroverov–Scuseria and strongly constrained and appropriately normed). Furthermore, we improve upon these CCD0+DFT blends by invoking range separation: the short- and long-range correlations absent in CCD0/BD0 are evaluated with density functional theory and the direct random phase approximation, respectively. This corrects the description of long-range van der Waals forces. Comprehensive benchmarking shows that the combinations presented here are very accurate for weakly correlated systems, while also providing a reasonable description of strongly correlated problems without resorting to symmetry breaking.

Substituent effects on gas‐phase homolytic Fe–O and Fe–S bond energies of m‐G‐C6H4OFe(CO)2(η5‐C5H5) and m‐G‐C6H4SFe(CO)2(η5‐C5H5) studied using Hartree–Fock and density functional theory methods

The thermochemistry of organometallic complexes in solution and in the gas phase has been an area of increasing research interest. In this paper, the Fe–O and Fe–S homolytic bond dissociation energies [ΔHhomo(Fe–O)'s and ΔHhomo(Fe–S)'s] of two series of meta‐substituted phenoxydicarbonyl(η5‐cyclopentadienyl) iron [m‐G‐C6H4OFp (1)] and (meta‐substituted benzenethiolato)dicarbonyl(η5‐cyclopentadienyl) iron [m‐G‐C6H4SFp (2)] were studied using Hartree–Fock and density functional theory methods with large basis sets. In this study, Fp is (η5‐C5H5)Fe(CO)2, and G are NO2, CN, COMe, CO2Me, CF3, Br, Cl, F, H, Me, MeO, and NMe2. The results show that Tao–Perdew–Staroverov–Scuseria and Minnesota 2006 functionals can provide the best price/performance ratio and accurate predictions of ΔHhomo(Fe–O)'s and ΔHhomo(Fe–S)'s. The polar effects of the meta substituents show that the dominant role to the magnitudes of ΔΔHhomo(Fe–O)'s or ΔΔHhomo(Fe–S)'s. σα·, σc· values for meta substituents are all related to polar effects. Spin‐delocalization effects of the meta substituents in ΔΔHhomo(Fe–O)'s and ΔΔHhomo(Fe–S)'s are small but not necessarily zero. Molecular effects rather than ΔΔHhomo(Fe–O)'s and ΔΔHhomo(Fe–S)'s are more suitable indexes for the overall substituent effects on ΔHhomo(Fe–O)'s and ΔHhomo(Fe–S)'s. The meta substituent effects of meta‐electron‐withdrawing groups on the Fe–S bonds are much stronger than those on the Fe–O bonds. For meta‐electron‐donating groups, the meta substituent effects have the comparable magnitudes between series 1 and 2. ΔΔHhomo(Fe–O)'s (1) and ΔΔHhomo(Fe–S)'s (2) conform to the captodative principle. Insight from this work may help the design of more effective catalytic processes. Copyright © 2015 John Wiley & Sons, Ltd.

Influence of the exchange-correlation functional on the quasi-harmonic lattice dynamics of II-VI semiconductors.

We perform a systematic comparison of the finite-temperature structure and properties of four bulk semiconductors (PbS, PbTe, ZnS, and ZnTe) predicted by eight popular exchange-correlation functionals from quasi-harmonic lattice-dynamics calculations. The performance of the functionals in reproducing the temperature dependence of a number of material properties, including lattice parameters, thermal-expansion coefficients, bulk moduli, heat capacities, and phonon frequencies, is evaluated quantitatively against available experimental data. We find that the phenomenological over- and under-binding characteristics of the local-density approximation and the PW91 and Perdew-Burke-Enzerhof (PBE) generalised-gradient approximation (GGA) functionals, respectively, are exaggerated at finite temperature, whereas the PBEsol GGA shows good general performance across all four systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) and revTPSS meta-GGAs provide relatively small improvements over PBE, with the latter being better suited to calculating structural and dynamical properties, but both are considerably more computationally demanding than the simpler GGAs. The dispersion-corrected PBE-D2 and PBE-D3 functionals perform well in describing the lattice dynamics of the zinc chalcogenides, whereas the lead chalcogenides appear to be challenging for these functionals. These findings show that quasi-harmonic calculations with a suitable functional can predict finite-temperature structure and properties with useful accuracy, and that this technique can serve as a means of evaluating the performance of new functionals in the future.

Designing a paradigm for parameter-free double-hybrid density functionals through the adiabatic connection path

It is now well established that the double-hybrid (DH) approximations belong to the most accurate methodologies for various properties and electronic structure calculations in the framework of density functional theory (DFT). In this context, we are lately witnessing the blooming of capable DH functionals derived from the adiabatic connection (AC) formalism. In the present work, through the AC path and by using a cubic integrand (CI) function, a novel DH exchange–correlation model is derived. The mixing coefficients are determined based on several well-known limiting conditions and linearly scaled one-parameter DH approximation. Employing the Perdew–Burke–Ernzerhof (PBE) and Tao–Perdew–Staroverov–Scuseria (TPSS) semilocal functionals as exchange and correlation terms in the underlying expression, the two new functionals free of any empirical parameter, CIDH–PBE and CIDH–TPSS, are developed. Using some benchmark sets on a number of different molecular properties including atomization energies, equilibrium geometries, vibrational frequencies, frontier orbital energies, and dipole polarizabilities, the performance of the CIDH models is compared with recently proposed parameterized, parameter-free, and AC-based DHs. Our numerical results show that the CIDH–PBE functional performs slightly better on average than CIDH–TPSS. Moreover, owing to its significant improvement over its parent functional and Moller–Plesset perturbation calculations, and similar or comparable performance compared to other DHs in some cases, CIDH–PBE can be considered as another promising functional for DH computations. On the whole, as evidenced from this study and other recent efforts in this respect, the development of parameter-free DHs from the route of AC has opened a new outlook in the field of DH–DFT, and more investigations in this direction are desirable.