A novel density functional theory for atoms, molecules, and solids

Abstract

A theorem is proved stating that in atoms, molecules, and solids, only the set of the spherical parts of the density around each nucleus determines uniquely the external potential. Therefore, the induced Kohn and Sham (KS) potential has spherical symmetry around each nucleus, and furthermore, it has the symmetry of the external potential. In this way, the inconsistencies of standard density functional theory (DFT) concerning the asymmetry of the KS potential are remedied. As a result of the above, the ground state is uniquely determined by this set of spherical densities. In the case of a symmetry group of a Hamiltonian, the minimizing subspace of the Hamiltonian for each irreducible representation of G is uniquely determined by this set of spherical densities. Thus, the present theory opens the way for new density functionals and more accurate molecular calculations as it exploits local symmetries. Moreover, the theory of "Atoms in Molecules" formulated by Bader, by using the open quantum mechanics theory, can be explained in terms of DFT [R. F. W. Bader, Atoms in Molecules. A Quantum Theory (Oxford University Press, Oxford, 1990)].

Synthesis, Cytotoxic Activity, Crystal Structure, DFT Studies and Molecular Docking of 3-Amino-1-(2,5-dichlorophenyl)-8-methoxy-1H-benzo[f]chromene-2-carbonitrile

“…The AIM "atoms in molecule theory" was utilized routinely to assess H-bond formation [55]. QTAIM "Bader's quantum theory of atoms" was applied using AIMAll [56], to detect the contribution of the intramolecular-forces of the molecular conformation inside the studied systems.…”

Параметризованный Эффективный Потенциал Для Возбужденных Состояний И Его Применение К Расчету Дипольных Моментов Перехода

“…r) не обладает симметрией внешнего потенциала из-за асимметрии электронной плотности. Подробное обсуждение проблемы асимметрии в ТФП и ее последствий можно найти в работах [8][9][10][11][12]. B недавней работе A.K.…”

“…B недавней работе A.K. Theophilou [12] доказал теорему, которая утверждает, что в атомах, молекулах и твердых телах только набор сферических частей плотности вокруг каждого ядра однозначно определяет внешний потенциал. Другими словами (см.…”

“…Другими словами (см. теорему 2 в [12]), полный потенциал V KS (r) представляет собой сумму потенциалов, каждый из которых сферически симметричен относительно вращения вокруг соответствующих ядер. Альтернативное доказательство этой теоремы было дано A. Nagy [13].…”

Localizing electron density errors in density functional theory

“…Furthermore, it has been suggested that only cer-tain subspaces of ρ(r) are relevant in DFT. 11,12 On the reverse, different energy-based modifications of DFAs, such as corrections for self-interaction errors, have been shown to affect the density in a similar way in localized regions. 13,14 Considering this, there is a possibility -and hope -that energy-based parametrization strategies indirectly improve the density in specially meaningful regions of space.…”