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In [[computational chemistry]], '''orbital-free density functional theory''' is a quantum mechanical approach to [[electronic structure]] determination which is based on [[Functional (mathematics)|functional]]s of the [[electronic density]]. It is most closely related to the [[Thomas–Fermi model]]. Orbital-free density functional theory is, at present, less accurate than [[Kohn–Sham equations|Kohn–Sham density functional theory]] models, but has the advantage of being fast, so that it can be applied to large systems.
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==The Kinetic Energy of Electrons==
 
The Hohenberg-Kohn theorems<ref>{{cite journal|last=Hohenberg|first=P|coauthors=Kohn, W|title=Inhomogeneous Electron Gas|journal=Physical Review|year=1964|volume=136|pages=B864-B871|doi=10.1103/PhysRev.136.B864}}</ref>  guarantee that, for a system of atoms, there exists a functional of the electron density that yields the total energy. Minimization of this functional with respect to the density gives the ground-state density from which all of the system's properties can be obtained. Although the Hohenberg-Kohn theorems tell us that such a functional exists, they do not give us guidance on how to find it. In practice, the density functional is known exactly except for two terms. These are the electronic kinetic energy and the [[exchange-correlation]] energy. The lack of the true exchange-correlation functional is a well known problem in DFT and there exists a huge variety of approaches to approximate this crucial component.
 
The fact that there is no known density functional for the electron kinetic energy is generally circumvented in another way. The traditional approach of density functional theory is to assume that the system can be treated as electrons residing in single-particle states (called orbitals). The total wave function can then be written as a Slater determinant of these single-particle orbitals. The orbitals themselves are found by diagonalizing the effective Kohn-Sham Hamiltonian. The kinetic energy of an electron in a single-particle state can be written exactly in terms of the orbital, <math>|\phi_i\rangle</math>, as (in atomic units)
 
<math> E_{kinetic}=-\frac{1}{2}\langle\phi_i|\nabla^2|\phi_i\rangle</math>.
 
The problem with this approach is that it requires diagonalization of the Kohn-Sham Hamiltonian to find the single-particle orbitals. Further, since the Hamiltonian itself depends on these orbitals, the problem must be solved self-consistently. This is, in general, a computationally expensive process. If one could write the electron kinetic energy as a density functional, the problem of diagonalizing a large matrix could be replaced with a relatively straight-forward functional optimization problem. Thus, finding an accurate density functional for the kinetic energy is the key focus of the so called "orbital free" methods.
 
One of the first attempts to do this was the [[Thomas-Fermi model]], which wrote the kinetic energy as<ref>{{cite book|last=Ligneres|first=Vincent L.|title=Handbook of Materials Modeling|year=2005|publisher=Springer Netherlands|pages=137–148|coauthors=Emily A. Carter|editor=Syndey Yip|chapter=An Introduction to Orbital Free Density Functional Theory}}</ref>
 
<math>E_{TF}=\frac{3}{10}\left(3\pi^2\right)^{\frac{2}{3}}\int{\left[n\left(\vec{r}\right)\right]^{\frac{5}{3}}d^3r}</math>.
 
This expression is based on the homogeneous electron gas and, thus, is not very accurate for most physical systems. Finding more accurate and transferable kinetic energy density functionals is the focus of ongoing research.
 
==References==
<references/>
 
[[Category:Density functional theory]]
[[Category:Computational chemistry]]

Latest revision as of 17:41, 31 December 2014



The very best combat knives are created particularly for military use and are the ultimate hand to hand close combat weapons. If you have any inquiries concerning exactly where and how to use Leatherman 315 Knife Review, you can get in touch with us at our own webpage. While it can serve as a self defense weapon too, it's main use is for fighting purposes (i.e, combat).

Tactical folding knives became well-liked in the US in the early 1990s. This was the time when custom knife makers developed knives with liner locks or locking mechanisms for opening and closing the knife. And mainly because the demand elevated rapidly, production providers collaborated with some of these tactical knife makers to mass-generate these knives. Nonetheless, noted knife makers such as Chris Reeve and Ernest Emerson later decided to open their personal knife factories. Variables when Purchasing Tactical Knives

As you can see deciding on the best tactical knife is surely something that needs a terrific deal of research. The knife that you really should pick will be entirely dependent upon your specific requires and how much you intend to use the knife. Lots of uncommon Asian weapons followed the exact same trail, from origins as farmer's tools to defense weapons of monks and travelers, and then sometimes to the qualified military. Typical of these intriguing and complicated combat weapons, the Shaolin Monk's Spade has a history as intriguing as its shape. The Kabar Becker BK9 is for anyone seeking to have a fantastic tool at their side while on their weekend camping, hunting, fishing trip or though obtaining themselves in survival mode or in a critical combat scenario. Blade length

There's at least a single Special Forces team that I know of where a single of them ordered a Busse Boss Jack for every single of the members. The knife is pricy, but then once more the steel, craftmanship and abuse resistance are outstanding. I know that Busse knives are typically chosen by both SF and SEAL guys that know a thing or two about knives and appreciate the good quality. I've reviewed the Boss Jack ahead of so check my youtbube videos if interested. Have you ever trained with a knife? Yes, a knife is a actually fantastic offensive weapon for even untrained assailants, butsimply because of the element of surprise. this knife could be beat point very first through sheet metal and suffer nothing but dulling. Smith and Wesson Homeland Security Survival Knife Crappy acting, crappier knives.

Our leather is USA vegetable tanned steer hide that is just the ideal funds can obtain. We have a face-to-face connection with our supplier, Hermann Oak Leather, who is primarily based appropriate right here in ourhome town of St. Louis, Missouri. All the big parts of our sheaths are built with 11 ounce thick leather, which is hard to work with in parts of the crafting procedure, but we adore its iron-like durability. By the time we dye, tool, burnish and situation our leather it appears like a tank and will final like a single too.

This is the ghost of the old "shooting him in the leg" misconception so several individuals had. People today would shoot an intruder and then inform the police that they have been only attempting to wound him. This left them open to all sorts of criminal charges and civil litigation - from the individual they had shot. There is a all-natural hesitation to take a further human life. However, when this manifests in in search of to "wound" an individual in order to make them "go away" you end up in a incredibly risky legal grey area. And the reality that you have been even in a situation where a knife was utilized is going to make that grey region more harmful. Remember, a knife is considered a thug's weapon.