ترغب بنشر مسار تعليمي؟ اضغط هنا

Semilocal and Hybrid Meta-Generalized Gradient Approximations Based on the Understanding of the Kinetic-Energy-Density Dependence

46   0   0.0 ( 0 )
 نشر من قبل Jianwei Sun
 تاريخ النشر 2013
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

We present a global hybrid meta-generalized gradient approximation (meta-GGA) with three empirical parameters, as well as its underlying semilocal meta-GGA and a meta-GGA with only one empirical parameter. All of them are based on the new meta-GGA resulting from the understanding of kinetic-energy-density dependence [J. Chem. Phys. 137, 051101 (2012)]. The obtained functionals show robust performances on the considered molecular systems for the properties of heats of formation, barrier heights, and noncovalent interactions. The pair-wise additive dispersion corrections to the functionals are also presented.

قيم البحث

اقرأ أيضاً

We present the self-consistent implementation of current-dependent (hybrid) meta generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to imple ment mGGAs in the framework of Kohn--Sham current density-functional theory (KS-CDFT). A unique feature of the non-perturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 a.u. ($sim 235000$T) in strength. CDFT functionals based on the TPSS and B98 forms are investigated and their performance is assessed by comparison with accurate CCSD(T) data. In the weak field regime magnetic properties such as magnetizabilities and NMR shielding constants show modest but systematic improvements over GGA functionals. However, in strong field regime the mGGA based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity these forms are found to be numerically stable and their accuracy at high field suggests the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations.
The development of semilocal models for the kinetic energy density (KED) is an important topic in density functional theory (DFT). This is especially true for subsystem DFT, where these models are necessary to construct the required non-additive embe dding contributions. In particular, these models can also be efficiently employed to replace the exact KED in meta-Generalized Gradient Approximation (meta-GGA) exchange-correlation functionals allowing to extend the subsystem DFT applicability to the meta-GGA level of theory. Here, we present a two-dimensional scan of semilocal KED models as linear functionals of the reduced gradient and of the reduced Laplacian, for atoms and weakly-bound molecular systems. We find that several models can perform well but in any case the Laplacian contribution is extremely important to model the local features of the KED. Indeed a simple model constructed as the sum of Thomas-Fermi KED and 1/6 of the Laplacian of the density yields the best accuracy for atoms and weakly-bound molecular systems. These KED models are tested within subsystem DFT with various meta-GGA exchange-correlation functionals for non-bonded systems, showing a good accuracy of the method.
Recently a novel approach to find approximate exchange-correlation functionals in density-functional theory (DFT) was presented (U. Mordovina et. al., JCTC 15, 5209 (2019)), which relies on approximations to the interacting wave function using densit y-matrix embedding theory (DMET). This approximate interacting wave function is constructed by using a projection determined by an iterative procedure that makes parts of the reduced density matrix of an auxiliary system the same as the approximate interacting density matrix. If only the diagonal of both systems are connected this leads to an approximation of the interacting-to-non-interacting mapping of the Kohn-Sham approach to DFT. Yet other choices are possible and allow to connect DMET with other DFTs such as kinetic-energy DFT or reduced density-matrix functional theory. In this work we give a detailed review of the basics of the DMET procedure from a DFT perspective and show how both approaches can be used to supplement each other. We do so explicitly for the case of a one-dimensional lattice system, as this is the simplest setting where we can apply DMET and the one that was originally presented. Among others we highlight how the mappings of DFTs can be used to identify uniquely defined auxiliary systems and auxiliary projections in DMET and how to construct approximations for different DFTs using DMET inspired projections. Such alternative approximation strategies become especially important for DFTs that are based on non-linearly coupled observables such as kinetic-energy DFT, where the Kohn-Sham fields are no longer simply obtainable by functional differentiation of an energy expression, or for reduced density-matrix functional theories, where a straightforward Kohn-Sham construction is not feasible.
We present a kinetic-energy density-functional theory and the corresponding kinetic-energy Kohn-Sham (keKS) scheme on a lattice and show that by including more observables explicitly in a density-functional approach already simple approximation strat egies lead to very accurate results. Here we promote the kinetic-energy density to a fundamental variable along side the density and show for specific cases (analytically and numerically) that there is a one-to-one correspondence between the external pair of on-site potential and site-dependent hopping and the internal pair of density and kinetic-energy density. Based on this mapping we establish two unknown effective fields, the mean-field exchange-correlation potential and the mean-field exchange-correlation hopping, that force the keKS system to generate the same kinetic-energy density and density as the fully interacting one. We show, by a decomposition based on the equations of motions for the density and the kinetic-energy density, that we can construct simple orbital-dependent functionals that outperform the corresponding exact-exchange Kohn-Sham (KS) approximation of standard density-functional theory. We do so by considering the exact KS and keKS systems and compare the unknown correlation contributions as well as by comparing self-consistent calculations based on the mean-field exchange for the keKS and the exact-exchange for the KS system, respectively.
69 - Yuri Kornyushin 2008
A concept of Kinetic Energy in Quantum Mechanics is analyzed. Kinetic Energy is not zero in many cases where there are no motion and flux. This paradox can be understood, using expansion of the wave function in Fourier integral, that is on the basis of virtual plane waves.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا