Exclusion principle, of Pauli

This statement, as applied to electrons, provides the basis for the exclusion principle of Pauli. ... 

We assume that nearly all the negative-energy states are occupied, with one electron in each state in accordance with the exclusion principle of Pauli. 

The fundamental basis for the VSEPR model is provided by the Pauli principle and not by electrostatics. The fundamental assumption of the model is that the electron pairs in the valence shell of an atom keep as far apart as possible, in other words they appear to repel each other. Electrons exhibit this behavior as a consequence of the Pauli exclusion principle of same spin electrons and not primarily as a consequence of their electrostatic repulsion. The role of the Pauli principle was clearly stated in the first papers on the VSEPR model (Gillespie Nyholm, 1957 Gillespie Nyholm, 1958) but this role has sometimes been ignored and the model has been incorrectly presented in terms of electrostatics. 

The extended formulation of the exclusion principle embraces Pauli s original statement, without invalidating it in any way... 

Pauli exclusion principle The Pauli exclusion principle states that an orbital can hold a maximum of two electrons if they are of opposite spins. In other words, every electron has a unique set of quantum numbers. 

Electrons are found only in certain allowed regions of space the particular locus in which some electron can move is referred to as its orbital. In the 1920s Pauli noted that, when an electron is in a given atomic orbital, a second electron having its spin in the same direction is excluded from that orbital. This led to the enunciation of the Pauli exclusion principle of quantum mechanics When two electrons are in the same orbital, their spins must be in opposite directions. When a molecule has all of its electrons paired in orbitals with their spins in opposite directions, the total spin of the molecule is zero (5 = 0), and the molecule is in a singlet state (25 + 1 = 1 Fig. 4-7a). 

Electrons interchanged. When the many-electron function of a molecule is written in the form of a determinant, the fundamental antisymmetry principle (the Pauli exclusion principle) of quantum mechanics is satisfied. According to that principle an A-electron function must be antisymmetric, i.e. it must change sign whenever spatial and spin variables of any two electrons are interchanged ... 

This sentence is a statement of the Pauli exclusion principle. W. Pauli (Austrian physicist, 1900-1959) was the first man to notice that an electron excludes another electron with the same spin orientation from the orbital it occupies. Only two electrons can occupy one orbital, and they must have opposite spins. Two electrons with opposed spins occupying the same orbital are called an electron pair. 

The first term in brackets in Equation 3.94 represents a strong repulsion of atoms at short range, attributable to their overlapping electron densities. It follows from the Pauli exclusion principle of quantum mechanics. The functional form used for this term (a is empirical. The attractive long-range term corresponds to dispersion or van der Waals forces. It has the functional form a r. In the equation above, ey represents the depth of the potential at the minimum rniin = and ay is the point at which Uu = 0. 

Note that the way of writing the ELF in Equation 5.6 makes it clear that it is a function which indicates some density, not necessarily the total density. It may be also applicable to any distribution of charges obeying the Pauli Exclusion Principle. Of course, the evaluation of the ELF with the total electron density of a molecule is not... 

The resolution of this issue is based on the application of the Pauli exclusion principle and Femii-Dirac statistics. From the free electron model, the total electronic energy, U, can be written as... 

The state F) is such that the particle states a, b, c,..., q are occupied and each particle is equally likely to be in any one of the particle states. However, if two of the particle states a, b, c,...,q are the same then F) vanishes it does not correspond to an allowed state of the assembly. This is a characteristic of antisynmietric states and it is called the Pauli exclusion principle no two identical fennions can be in the same particle state. The general fimction for an assembly of bosons is... 

The average kinetic energy per particle at J= 0, is of the Fenni energy p. At constant A, the energy increases as the volume decreases smce fp Due to the Pauli exclusion principle, the Fenni energy gives... 

Themiodynamic stability requires a repulsive core m the interatomic potential of atoms and molecules, which is a manifestation of the Pauli exclusion principle operating at short distances. This means that the Coulomb and dipole interaction potentials between charged and uncharged real atoms or molecules must be supplemented by a hard core or other repulsive interactions. Examples are as follows. 

Because single-electron wave functions are approximate solutions to the Schroe-dinger equation, one would expect that a linear combination of them would be an approximate solution also. For more than a few basis functions, the number of possible lineal combinations can be very large. Fortunately, spin and the Pauli exclusion principle reduce this complexity. 

In addition to being negatively charged electrons possess the property of spin The spin quantum number of an electron can have a value of either +5 or According to the Pauli exclusion principle, two electrons may occupy the same orbital only when... 

Pauli exclusion principle (Section 1 1) No two electrons can have the same set of four quantum numbers An equivalent expression is that only two electrons can occupy the same orbital and then only when they have opposite spins PCC (Section 15 10) Abbreviation for pyndimum chlorochro mate C5H5NH" ClCr03 When used in an anhydrous medium PCC oxidizes pnmary alcohols to aldehydes and secondary alcohols to ketones... 

Because of the quantum mechanical Uncertainty Principle, quantum mechanics methods treat electrons as indistinguishable particles. This leads to the Pauli Exclusion Principle, which states that the many-electron wave function—which depends on the coordinates of all the electrons—must change sign whenever two electrons interchange positions. That is, the wave function must be antisymmetric with respect to pair-wise permutations of the electron coordinates. 

Again, for the filled orbitals L = 0 and 5 = 0, so we have to consider only the 2p electrons. Since n = 2 and f = 1 for both electrons the Pauli exclusion principle is in danger of being violated unless the two electrons have different values of either or m. For non-equivalent electrons we do not have to consider the values of these two quantum numbers because, as either n or f is different for the electrons, there is no danger of violation. 

Intrinsic Semiconductors. For semiconductors in thermal equiHbrium, (Ai( )), the average number of electrons occupying a state with energy E is governed by the Fermi-Dirac distribution. Because, by the Pauli exclusion principle, at most one electron (fermion) can occupy a state, this average number is also the probabiHty, P E), that this state is occupied (see Fig. 2c). In equation 2, K... 

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