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The accuracy of charge-transfer excitation energies, solvatochromic shifts and other environmental effects calculated via various density embedding techniques depend critically on the approximations employed for the non-additive non-interacting kinetic energy functional, $T_{scriptscriptstylerm s}^{scriptscriptstylerm nad}[n]$. Approximating this functional remains an important challenge in electronic structure theory. To assist in the development and testing of approximations for $T_{scriptscriptstylerm s}^{scriptscriptstylerm nad}[n]$, we derive two virial relations for fragments in molecules. These establish separate connections between the non-additive kinetic energies of the non-interacting and interacting systems of electrons, and quantities such as the electron-nuclear attraction forces, the partition (or embedding) energy and potential, and the Kohn-Sham potentials of the system and its parts. We numerically verify both relations on diatomic molecules.
The idea of using fragment embedding to circumvent the high computational scaling of accurate electronic structure methods while retaining high accuracy has been a long-standing goal for quantum chemists. Traditional fragment embedding methods mainly
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
We present the first implementation of a density matrix renormalization group algorithm embedded in an environment described by density functional theory. The frozen density embedding scheme is used with a freeze-and-thaw strategy for a self-consiste
With the development of low order scaling methods for performing Kohn-Sham Density Functional Theory, it is now possible to perform fully quantum mechanical calculations of systems containing tens of thousands of atoms. However, with an increase in t
Although many equations of state of hard-disk fluids have been proposed, none is capable of reproducing the currently calculated or estimated values of the first eighteen virial coefficients at the same time as giving very good accuracy when compared