Pauli exclusion principle In a given

Pauli exclusion principle in a given atom no two electrons tan have the same set of four quantum numbers. (12.10) Penetration effect the effect whereby a valence electron penetrates the core electrons, thus reducing the shielding effect and increasing the effective nuclear charge. (12.14)... 

Pauli exclusion principle in a given atom, no two electrons can occupy the same atomic orbital and have the same spin. 

In the free electron model, the electrons are presumed to be loosely bound to the atoms, making them free to move throughout the metal. The development of this model requires the use of quantum statistics that apply to particles (such as electrons) that have half integral spin. These particles, known as fermions, obey the Pauli exclusion principle. In a metal, the electrons are treated as if they were particles in a three-dimensional box represented by the surfaces of the metal. For such a system when considering a cubic box, the energy of a particle is given by... 

In this chapter we give a brief review of some of the basic concepts of quantum mechanics with emphasis on salient points of this theory relevant to the central theme of the book. We focus particularly on the electron density because it is the basis of the theory of atoms in molecules (AIM), which is discussed in Chapter 6. The Pauli exclusion principle is also given special attention in view of its role in the VSEPR and LCP models (Chapters 4 and 5). We first revisit the perhaps most characteristic feature of quantum mechanics, which differentiates it from classical mechanics its probabilistic character. For that purpose we go back to the origins of quantum mechanics, a theory that has its roots in attempts to explain the nature of light and its interactions with atoms and molecules. References to more complete and more advanced treatments of quantum mechanics are given at the end of the chapter. 

At shorter distances the repulsive forces start to dominate. The repulsive interaction between two molecules can be described by the power-law potential l/rn (n>9) caused by overlapping of electron clouds resulting in a conflict with the Pauli exclusion principle. For a completely rigid tip and sample whose atoms interact as 1/r12, the repulsion would be described by W-l/D7. In practice, both the tip and the sample are deformable (Fig. 3d). The tip-sample attraction is balanced by mechanical stress which arises in the contact area. From the Hertz theory [77,79], the relation between the deformation force Fd and the contact radius a is given by ... 

For our purposes, the main significance of electron spin is connected with the postulate of Austrian physicist Wolfgang Pauli (1900-1958) In a given atom no two electrons can have the same set of four quantum numbers ( , , ntf, and m). This is called the Pauli exclusion principle. Since electrons In the same orbital have the same values of n, t, and this postulate says that they must have different values of m. Then, since only two values of are allowed, an orbital can hold only two electrons, and they must have opposite spins. This principle will have important consequences as we use the atomic model to account for the electron arrangements of the atoms in the periodic table. 

The application of the quantum mechanics to the interaction of more complicated atoms, and to the non-polar chemical bond in general, is now being made (45). A discussion of this work can not be given here it is, however, worthy of mention that qualitative conclusions have been drawn which are completely equivalent to G. N. Lewis s theory of the shared electron pair. The further results which have so far been obtained are promising and we may look forward with some confidence to the future explanation of chemical valence in general in terms of the Pauli exclusion principle and the Heisenberg-Dirac resonance phenomenon. 

Pauli exclusion principle no two electrons in a given atom can have the same set of four quantum numbers. 

The phenomenon of electron pairing is a consequence of the Pauli exclusion principle. The physical consequences of this principle are made manifest through the spatial properties of the density of the Fermi hole. The Fermi hole has a simple physical interpretation - it provides a description of how the density of an electron of given spin, called the reference electron, is spread out from any given point, into the space of another same-spin electron, thereby excluding the presence of an identical amount of same-spin density. If the Fermi hole is maximally localized in some region of space all other same-spin electrons are excluded from this region and the electron is localized. For a closed-shell molecule the same result is obtained for electrons of p spin and the result is a localized a,p pair [46]. 

Equation 4.49 defines the exchange or Fermi hole. It is as if an electron of a given spin digs a hole around itself in space in order to exclude another electron of the same spin from coming near it (Pauli exclusion principle). The integrated hole charge is unity, i.e., there is exactly one electron inside the hole. Likewise, the correlation energy functional can be defined as... 

Quantum mechanics may be used to determine the arrangement of the electrons within an atom if two specific principles are applied the Pauli exclusion principle and the Aufbau principle. The Pauli exclusion principle states that no two electrons in a given atom can have the same set of the four quantum numbers. For example, if an electron has the following set of quantum numbers n = 1, l = 0, m = 0, and ms= +1/2, then no other electron may have the same set. The Pauli exclusion principle limits all orbitals to only two electrons. For example, the ls-orbital is filled when it has two electrons, so that any additional electrons must enter another orbital. 

A ground-state helium atom has two paired electrons in the Is orbital (Is2). The electrons with paired spin occupy the lowest of the quantised orbitals shown below (the Pauli exclusion principle prohibits any two electrons within a given quantised orbital from having the same spin quantum number) ... 

Using the above definitions for the four quantum numbers, we can list what combinations of quantum numbers are possible. A basic rule when working with quantum numbers is that no two electrons in the same atom can have an identical set of quantum numbers. This rule is known as the Pauli Exclusion Principle named after Wolfgang Pauli (1900-1958). For example, when n = 1,1 and mj can be only 0 and m can be + / or -1/ This means the K shell can hold a maximum of two electrons. The two electrons would have quantum numbers of 1,0,0, + / and 1,0,0,- /, respectively. We see that the opposite spin of the two electrons in the K orbital means the electrons do not violate the Pauli Exclusion Principle. Possible values for quantum numbers and the maximum number of electrons each orbital can hold are given in Table 4.3 and shown in Figure 4.7. 

Exact solutions such as those given above have not yet been obtained for the usual many-electron molecules encountered by chemists. The approximate method which retains tile idea of orbitals for individual electrons is called molecular-orbital theory (M. O. theory). Its approach to the problem is similar to that used to describe atomic orbitals in the many-electron atom. Electrons are assumed to occupy the lowest energy orbitals with a maximum population of two electrons per orbital (to satisfy the Pauli exclusion principle). Furthermore, just as in the case of atoms, electron-electron repulsion is considered to cause degenerate (of equal energy) orbitals to be singly occupied before pairing occurs. 

In helium, the para-state is one group or system of terms in the spectrum of helium that is due to atoms in which the spin of the two electrons are opposing each other. Another group of spectral terms, the orthohelium terms, is given by those helium atoms whose two electrons have parallel spins. Because of the Pauli Exclusion Principle, a helium atom in its ground state must be in a para-state. 

As discussed in Section 5.1, the structure of many-electron atoms can be understood only by assuming that no more than two electrons can occupy each separate orbital. Taking account of the electron spin allows a deeper interpretation of this fact. One way of expressing the Pauli exclusion principle is no two electrons can have the same values of all four quantum numbers, n, l, m, and ms. As only two values of ms are permitted, it follows that each orbital, specified by a given set of values of n, l, and m, can hold... 

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