Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDensity-gradient-free variable in exchange-correlation functionals for detecting inhomogeneities in the electron density
246
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
An alternative type of approximation for the exchange and correlation functional in density functional theory is proposed. This approximation depends on a variable $u$ that is able to detect inhomogeneities in the electron density $rho$ without using derivatives of $rho$. Instead, $u$ depends on the orbital energies which can also be used to measure how a system differs from the homogeneous electron gas. Starting from the functional of Perdew, Burke, and Ernzerhof (PBE) [Phys. Rev. Lett. 77, 3865 (1996)], a functional depending on $u$ is constructed. Tests on the lattice constant, bulk modulus, and cohesive energy of solids show that this $u$-dependent PBE-like functional is on average as accurate as the original PBE or its solid-state version PBEsol. Since $u$ carries more nonlocality than the reduced density gradient $s$ used in functionals of the generalized gradient approximation (GGA) like PBE and $alpha$ used in meta-GGAs, it will be certainly useful for the future development of more accurate exchange-correlation functionals.
rate research
Read More
A recent study of Mejia-Rodriguez and Trickey [Phys. Rev. A 96, 052512 (2017)] showed that the deorbitalization procedure (replacing the exact Kohn-Sham kinetic-energy density by an approximate orbital-free expression) applied to exchange-correlation functionals of the meta-generalized gradient approximation (MGGA) can lead to important changes in the results for molecular properties. For the present work, the deorbitalization of MGGA functionals is further investigated by considering various properties of solids. It is shown that depending on the MGGA, common orbital-free approximations to the kinetic-energy density can be sufficiently accurate for the lattice constant, bulk modulus, and cohesive energy. For the band gap, calculated with the modified Becke-Johnson MGGA potential, the deorbitalization has a larger impact on the results.
We introduce a new functional for simulating ground-state and time-dependent electronic systems within density-functional theory. The functional combines an expression for the exact Kohn-Sham (KS) potential in the limit of complete electron localization with a measure of the actual localization. We find accurate self-consistent charge densities, even for systems where the exact exchange-correlation potential exhibits non-local dependence on the density, such as potential steps. We compare our results to the exact KS potential for each system. The self-interaction correction is accurately described, avoiding the need for orbital-dependent potentials.
A curious behavior of electron correlation energy is explored. Namely, the correlation energy is the energy that tends to drive the system toward that of the uniform electron gas. As such, the energy assumes its maximum value when a gradient of density is zero. As the gradient increases, the energy is diminished by a gradient suppressing factor, designed to attenuate the energy from its maximum value similar to the shape of a bell curve. Based on this behavior, we constructed a very simple mathematical formula that predicted the correlation energy of atoms and molecules. Combined with our proposed exchange energy functional, we calculated the correlation energies, the total energies, and the ionization energies of test atoms and molecules; and despite the unique simplicities, the functionals accuracies are in the top tier performance, competitive to the B3LYP, BLYP, PBE, TPSS, and M11. Therefore, we propose that, as guided by the simplicities and supported by the accuracies, the correlation energy is the energy that locally tends to drive the system toward the uniform electron gas.
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 implement 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.
Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between Thomas-Fermi theory as a density functional and as a potential functional is derived. The properties of several recent semiclassical potential functionals are explored, especially in their approach to the large particle number and classical continuum limits. The lack of ambiguity in the energy density of potential functional approximations is demonstrated. The density-density response function of the semiclassical approximation is calculated and shown to violate a key symmetry condition.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
