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The homogeneous electron gas (HEG) is a key ingredient in the construction of most exchange-correlation functionals of density-functional theory. Often, the energy of the HEG is parameterized as a function of its spin density $n$, leading to the local density approximation (LDA) for inhomogeneous systems. However, the connection between the electron density and kinetic energy density of the HEG can be used to generalize the LDA by evaluating it on a weighted geometric average of the local spin density and the spin density of a HEG that has the local kinetic energy density of the inhomogeneous system, with a mixing ratio $x$. This leads to a new family of functionals that we term meta-local density approximations (meta-LDAs), which are still exact for the HEG, which are derived only from properties of the HEG, and which form a new rung of Jacobs ladder of density functionals. The first functional of this ladder, the local $tau$ approximation (LTA) of Ernzerhof and Scuseria that corresponds to $x=1$ is unfortunately not stable enough to be used in self-consistent field calculations, because it leads to divergent potentials as we show in this work. However, a geometric averaging of the LDA and LTA densities with smaller values of $x$ not only leads to numerical stability of the resulting functional, but also yields more accurate exchange energies in atomic calculations than the LDA, the LTA, or the tLDA functional ($x=1/4$) of Eich and Hellgren. We choose $x=0.50$ as it gives the best total energy in self-consistent exchange-only calculations for the argon atom. Atomization energy benchmarks confirm that the choice $x=0.50$ also yields improved energetics in combination with correlation functionals in molecules, almost eliminating the well-known overbinding of the LDA and reducing its error by two thirds.
The many-body polarization energy is the major source of non-additivity in strongly polar systems such as water. This non-additivity is often considerable and must be included, if only in an average manner, to correctly describe the physical properti
During compression of a water dimer calculated with high-precision first-principles methods, the trends of H-bond and O-H bond lengths show quantum effect of the electronic structure. We found that the H-bond length keeps decreasing, while the O-H bo
Kernel ridge regression is used to approximate the kinetic energy of non-interacting fermions in a one-dimensional box as a functional of their density. The properties of different kernels and methods of cross-validation are explored, and highly accu
The stationary nonempirical simulations of Na+(H2O)n clusters with n in a range of 28 to 51 carried out at the density functional level with a hybrid B3LYP functional and the Born-Oppenheimer molecular dynamics modeling of the size selected clusters
Chirped-Pulse millimetre-Wave (CPmmW) rotational spectroscopy provides a new class of information about photolysis transition state(s). Measured intensities in rotational spectra determine species-isomer-vibrational populations, provided that rotatio