Modern State of the Conventional DFT Method Studies and the Limits Following from the Quantum State of the System and Its Total Spin

Abstract

At present, the density functional theory (DFT) approach became the most widely used method for study molecules and solids. In the atmosphere of such great popularity, it is particularly important to know the limits of the applicability of DFT methods. In this chapter, I will discuss the modern state of DFT studies basing on the last publications and will consider in detail two cases when the conventional DFT approaches, in which used only electron density and its modifications by gradients, cannot be applied. First, the case related to the total spin S of the state. As I rigorously proved for an arbitrary N-electron state by group theoretical methods, the electron density does not depend on the total spin S of the state. From this follows that the Kohn-Sham equations have the same form for states with different S. The critical survey of elaborated DFT procedures, in which the spin is taken into account, shows that they modified only exchange functionals, and the correlation functionals do not correspond to the spin of the state. The point is that the conception of spin in principle cannot be defined in the framework of the electron density formalism, and this is the main reason of the problems arising in the study by DFT approaches the magnetic properties of the transition metals. The possible way of resolving spin problems can be found in the two-particle reduced density matrix formulation of DFT. In the end, it will be considered the case of the degenerated states, in which, as follows from the adiabatic approximation, the electron density may not be defined, since electronic and nuclear motions cannot be separated, since, the vibronic interaction mixed them.

Effects of Exchange Correlation Functional (Vwdf3) on the Structural, Elastic, and Electronic Properties of Transition Metal Dichalogenides

“…The calculations were performed via ab initio density functional theory (DFT) using plane-wave basis as implemented in the Quantum-ESPRESSO package, this includes the optimization, and determination of equilibrium lattice parameters, and electronic band gaps. An auxiliary package to the quantum ESPRESSO thermo_pw [1] was also used in the calculation of the elastic constants and optical properties. To make an accurate comparison, Kohn-Sham equations were applied by implementing the DFT ab initio quantum computing framework within the Perdiew-Burke-Emzahope (PBE) exchange functional [9], rVV10 and our novel VdW-DF3 functional.…”

“…The optical properties of Mos 2 , MoSe 2 , and MoTe 2 bulk crystals with polarization along x-direction (in-plane) are calculated using independent particle approximation by solving time-dependent density-functional theory (TDDFT) and linear response technique [3], using the Sternheimer approach within Thermo_ pw code [1], a proprietary branch of the quantum ESPRESSO project [4]. The calculated real and imaginary parts of frequency-dependent microscopic dielectric function in the energy range of 0 to 21 eV were plotted.…”

“…5 (2023) 1094 2 affect scientific and high-tech advancement. DFT explanations on how electrons in the many-body systems interact with each other depending on the so-called approximations of the exchange-correlation (XC) functional [1]. Moreover, much of the successes in DFT came from the fact that these functions often produce accurate results.…”