Subrata Jana

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.

Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems: A Step Beyond Generalized Gradient Approximations

Semilocal density functionals for the exchange-correlation energy of electrons are extensively used as they produce realistic and accurate results for finite and extended systems. The choice of techniques plays a crucial role in constructing such functionals of improved accuracy and efficiency. An accurate and efficient semilocal exchange energy functional in two dimensions is constructed by making use of the corresponding hole which is derived based on the density matrix expansion. The exchange hole involved is localized under the generalized coordinate transformation and satisfies all the relevant constraints. Comprehensive testing and excellent performance of the functional is demonstrated versus exact exchange results. The accuracy of results obtained by using the newly constructed functional is quite remarkable as it substantially reduces the errors present in the local and nonempirical exchange functionals proposed so far for two-dimensional quantum systems. The underlying principles involved in the functional construction are physically appealing and hold promise for developing range separated and nonlocal exchange functionals in two dimensions.

A Parameter-Free Semilocal Exchange Energy Functional for Two-Dimensional Quantum Systems

The method of constructing semilocal density functional for exchange in two dimensions using one of the premier approaches, i.e., density matrix expansion, is revisited, and an accurate functional is constructed. The form of the functional is quite simple and includes no adjustable semiempirical parameters. In it, the kinetic energy dependent momentum is used to compensate nonlocal effects of the system. The functional is then examined by considering the very well-known semiconductor quantum dot systems. And despite its very simple form, the results obtained for quantum dots containing a higher number of electrons agrees pretty well with that of the standard exact exchange theory. Some of the desired properties relevant for the two-dimensional exchange functional and the lower bound associated with it are also discussed. It is observed that the above parameter-free semilocal exchange functional satisfies most of the discussed conditions.

Inhomogeneity induced and appropriately parameterized semilocal exchange and correlation energy functionals in two-dimensions

The construction of meta generalized gradient approximations based on the density matrix expansion (DME) is considered as one of the most accurate techniques to design semilocal exchange energy functionals in two-dimensional density functional formalism. The exchange holes modeled using DME possess unique features that make it a superior entity. Parameterized semilocal exchange energy functionals based on the DME are proposed. The use of different forms of the momentum and flexible parameters is to subsume the non-uniform effects of the density in the newly constructed semilocal functionals. In addition to the exchange functionals, a suitable correlation functional is also constructed by working upon the local correlation functional developed for 2D homogeneous electron gas. The non-local effects are induced into the correlation functional by a parametric form of one of the newly constructed exchange energy functionals. The proposed functionals are applied to the parabolic quantum dots with a varying number of confined electrons and the confinement strength. The results obtained with the aforementioned functionals are quite satisfactory, which indicates why these are suitable for two-dimensional quantum systems.

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.

Exploration of near the origin and the asymptotic behaviors of the Kohn-Sham kinetic energy density for two-dimensional quantum dot systems with parabolic confinement

The behaviors of the positive definite Kohn-Sham kinetic energy density near the origin and at the asymptotic region play a major role in designing meta-generalized gradient approximations (meta-GGAs) for exchange in low-dimensional quantum systems. It is shown that near the origin of the parabolic quantum dot, the Kohn-Sham kinetic energy differs from its von Weizsäcker counterpart due to the p orbital contributions, whereas in the asymptotic region, the difference between the above two kinetic energy densities goes as ∼ρ(r)r2. All these behaviors have been explored using the two-dimensional isotropic quantum harmonic oscillator as a test case. Several meta-GGA ingredients are then studied by making use of the above findings. Also, the asymptotic conditions for the exchange energy density and the potential at the meta-GGA level are proposed using the corresponding behaviors of the two kinetic energy densities.

Efficient lattice constants and energy bandgaps for condensed systems from a meta-GGA level screened range-separated hybrid functional

A meta-generalized gradient approximation (meta-GGA) level screened hybrid functional is developed for the solid-state electronic structure calculations. Assessment of the proposed functional for the solid-state lattice constants and bandgaps indicates that it is quite efficient in describing those properties. Specifically, the improvement in the bandgap performance of the presently proposed meta-GGA level screened hybrid functional is noticeable. From the construction point of view, the present screened hybrid functional is one step forward to the density functional screened hybrid functional rung by adding extra ingredients in its functional form. The most appealing feature of the present screened functional is that it is constructed upon an accurate semilocal functional by adopting a simple modification on the top of that functional.