Development of a Correction Term for the Kinetic Energy Density Functional
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Density functional theory (DFT) is a useful theoretical and computational tool for electronic structure calculations, which form the basis for the classification of materials into conductors, semiconductors or insulators.
DFT started with a crude approximation by Thomas and Fermi (TF theory) which calculated the kinetic energy of electrons using the so-called local density approximation (LDA).
Although TF is computationally inexpensive, it provides a poor numerical result due to a lack of understanding of the density dependence of the kinetic energy.
Another approximation to the kinetic energy is the von-Weizsacker (vW) term, which greatly improves the TF theory, yet the full functional form of the kinetic energy remains unknown.
We seek to develop a supplemental term to the kinetic energy density functional and compute corrections to the Thomas-Fermi-von-Weizsacker kinetic energy of closed shell atoms in order to improve its accuracy.
The quantum mechanics of many-electron systems which have descriptions from time dependent and time-independent Schr¨odinger and Liouville equations, is to a good approximation ostensibly a well-understood subject.
The Schr¨odinger equations present the theoretical bases for the description of both the time evolution and pure stationary states properties of atoms and molecules.
In treating some quantum mechanical systems such as biological molecules and liquids where the individuality of molecules ceases to exist, rather collective effects becomes predominant, it is immaterial to talk of pure states.
However, in each case of pure states and ensemble of non-trivial many-electron systems, the equations involved are not without complicated and complex mathematical parameters with little or no analytical or numerical solutions. equations.
Although, non-relativistic Hamiltonian operators for systems interacting Coulombically can be written explicitly for these equations, understanding a priori, the subtleties of the manybody behavior that ensues from these interactions remains a challenge.
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