Ab initio (aka First Principle) calculations are based on the basic laws of physics without any empirical parameters or fitting models. Simulations originating from the First Principles have played a more important role in studies in condensed matter physics and chemistry.
A solid system comprises electrons and nuclei, and interactions among them determine the total energy of the system. Also, the outer shell electrons have great influences on the electronic and optic properties of solids. As there are many particles inside a real solid system, “single-electron” approximation is essential to make simulation possible.
The Density Functional Theory is a promising approach to compute the electronic structure of matter. It determines the properties of a system at the ground state by using functionals (i.e. functions of another function) of electron density.
The construction of the theory starts with elementary quantum mechanics and the theory is later generalized to fit different situations.
A Schrodinger equation describes how the quantum state of a system varies with time. However, it would be really complex for solid system consisting of many nuclei and electrons. It would be much better if a time-independent, non-relativistic Schrodinger equation can be acquired.
H ̂Ψ_i (x ⃑_1,x ⃑_2,…,x ⃑_N,R ⃑_1,R ⃑_2,…,R ⃑_M )=E_i Ψ_i (x ⃑_1,x ⃑_2,…,x ⃑_N,R ⃑_1,R ⃑_2,…,R ⃑_M )
Ĥ is the Hamiltonian for a system consisting M nuclei and N electrons, and it governs the dynamics of the quantum system.
H ̂=-1/2 ∑_(i=1)^N▒∇_i^2 -1/2 ∑_(A=1)^M▒〖1/M_A ∇_i^2 〗-∑_(i=1)^N▒∑_(A=1)^M▒Z_A/r_iA +∑_(i=1)^N▒∑_(j>1)^N▒1/r_ij +∑_(A=1)^M▒∑_(B>A)^M▒(Z_A Z_B)/R_AB where the first two terms are describing the kinetic energy of electrons and nuclei, th...
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...ctron gas. This is a system in which electrons move on a positive background charge distribution such that the total ensemble is neutral. The central idea of LDA is the assumption that we can write EXC in the following form [eq43]
Here, εXC(ρ(⃗r)) is the exchange-correlation energy per particle of an uniform electron gas of density ρ(⃗r). This energy per particle is weighted with the probability ρ(⃗r) that there is an electron at this position. The quantity εXC(ρ(⃗r)) can be further split into exchange and correlation contributions, εXC(ρ(⃗r)) = εX(ρ(⃗r)) + εC(ρ(⃗r)). (44)
The exchange part, εX , which represents the exchange energy of an electron in a uniform electron gas of a particular density, was originally derived by Bloch and Dirac in the late 1920’s
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Works Cited
J. C. Cuevas, “Introduction to Density Functional Theory,” Universitat Karlsruhe(Germany).
In "Energy Story" uses an explanation of atoms and tells us the parts of an atom and its structure. In the text it
A theory can lead to the development of a model which provides a visual representation and explanation of the scientists’ understanding. A model can assist in predicting what could happen if a particular incident occurs. An example of a model is the Niels Bohr model of the atom.
The amazing transformation the study of physics underwent in the two decades following the turn of the 20th century is a well-known story. Physicists, on the verge of declaring the physical world “understood”, discovered that existing theories failed to describe the behavior of the atom. In a very short time, a more fundamental theory of the ...
In the 1920s the new quantum and relativity theories were engaging the attentions of science. That mass was equivalent to energy and that matter could be both wavelike and corpuscular carried implications seen only dimly at that time. Oppenheimer's early research was devoted in particular to energy processes of subatomic particles, including electrons, positrons, and cosmic rays. Since quantum theory had been proposed only a few years before, the university post provided him an excellent opportunity to devote his entire career to the exploration and development of its full significance. In addition, he trained a whole generation of U.S. physicists, who were greatly affected by his qualities of leadership and intellectual independence.
The Pauli exclusion principle is defined by Dr. Steven S. Zumdahl, "In a given atom no two electrons can have the same set of four quantum numbers." Due to this principle, only two electrons can inhabit a single energy level. The electrons that share the same energy level have opposite intrinsic angular momentums which is more commonly known as "spin". To determine the direction of the spin the angular momentum vector is analyzed.
The molar specific heats of most solids at room temperature and above are nearly constant, in agreement with the Law of Dulong and Petit. At lower temperatures the specific heats drop as quantum processes become significant. The Einstein-Debye model of specific heat describes the low temperature behavior.
21. Partoens, B., and F. M. Peeters. "From graphene to graphite: Electronic structure around the K point." Physical Review B 74.7 (2006): 075404.
Quantum mechanics was pioneered by Max Planck, who developed the formula E = hv—which is the base for much of the quantum mechanical field. Quantum theory (the origin of quantum mechanics), as described in Talking Tech, was, at its early core, a handful of theories and hypotheses regarding energy quantization and wave-particle duality (Rheingold and Levine). The book goes on to explain how this realm of science is basically an extension of physics attempting to derive a mathematical specification of how the entirety of the universe operates and behaves at the subatomic level. Conversely, it also describes how quantum theory also diverges from classical physics in that it stipulates that the only...
Strassler, Matthew. “Fermions And Bosons.” Of Particular Significance. WordPress, 12 Aug. 2011. Web. 13 Oct. 2013.
Serway, Raymond A, and Robert J Beichner. Physics: For Scientists and Engineers. United States of
Mann, M., 2013. Mind Action Series Physical Sciences 12 Textbook and Workbook. Sanlamhof: Allcopy Publishers.
sort of 3D map of the places that the electron is likely to be found.
American Institute of Physics. Vol. 1051 Issue 1 (2008). Academic Search Premier.> 224. http://login.ezproxy1.lib.asu.edu/login?url=http://search.ebscohost.com.ezproxy1.lib.asu.edu/login.aspx?direct=true&db=aph&AN=34874307&site=ehost-live.
states strikes an excited atom, the atom is stimulated, as it falls back to a
2. A He and H atom collide elastically in a head-on collision. (a). If they have the same kinetic energy (KE) to begin with, which one gains KE? Answer this by calculating the amount gained and lost for both, relative to their initial value. (b). Suppose the atoms had the same mass but different kinetic energies? Do not do a detailed calculation here, but instead make a physical argument as to why the “slower” thus “cooler” atoms would slow down the faster, hotter atoms. This is one process for the moderation of hot neutrons in a nuclear fission reactor by the water used as its coolant.