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From its definition, the electron density is a non-negative function integrating to the total number of electrons. Further, for a system with kinetic energy T , the density satisfies the inequalities [ 7 ]
Using this theory, the properties of a many-electron system can be determined by using functionals - that is, functions that accept a function as input and output a single real number. [1] In the case of DFT, these are functionals of the spatially dependent electron density.
where () is the electron density. The Fukui function itself has two finite versions of this change which can be defined by the following two functions. The form of the function will depend on whether or not an electron was removed from or added to the molecule.
The electron probability density for the first few hydrogen atom electron orbitals shown as cross-sections. These orbitals form an orthonormal basis for the wave function of the electron. Different orbitals are depicted with different scale.
The co-motion functions can be obtained from the integration of this equation. An analytical solution exists for 1D systems, [3] [4] but not for the general case. The interaction energy of the SCE system for a given density () can be exactly calculated in terms of the co-motion functions as [6]
In quantum chemistry, the quantum theory of atoms in molecules (QTAIM), sometimes referred to as atoms in molecules (AIM), is a model of molecular and condensed matter electronic systems (such as crystals) in which the principal objects of molecular structure - atoms and bonds - are natural expressions of a system's observable electron density distribution function.
Charge carrier density, also known as carrier concentration, denotes the number of charge carriers per volume. In SI units, it is measured in m −3. As with any density, in principle it can depend on position. However, usually carrier concentration is given as a single number, and represents the average carrier density over the whole material.
Given a Fermi gas of density , the highest occupied momentum state (at zero temperature) is known as the Fermi momentum, . Then the required relationship is described by the electron number density as a function of μ, the internal chemical potential. The exact functional form depends on the system.