Electron spin Pauli exclusion principle

A maximum of 2 electrons can be placed in an orbital, but they must have opposite spins (Pauli Exclusion Principle). 

We can now explain something that puzzled Lewis-—the fact that a bond normally consists of a pair of electrons. The Pauli exclusion principle allows only two electrons (with paired spins) to occupy any one molecular orbital. Hence, a single bond between two atoms consists of two paired electrons in a bonding orbital. 

Vcore(v) is the potential associated with the interaction between valence and core electrons and VexchangeC-v) is the exchange potential between valence electrons. The exchange potential accounts for the repulsive interaction between electrons of like spin (Pauli exclusion principle) and electrons of either spin (correlation interaction). Both of these potentials are experienced in the bulk as well as at the surface. Vdipoie(v) is specific to the surface and arises from charge redistribution at the asymmetric surface. 

Analyze and Plan Because oxygen has an atomic number of 8, each oxygen atom has 8 electrons. Figure 6.24 shows the ordering of orbitals. The electrons (represented as arrows) are placed in the orbitals (represented as boxes) beginning with the lowest-enei orbital, the Is. Each orbital can hold a maximum of two electrons (the Pauli exclusion principle). Because the 2p orbitals are degenerate, we place one electron in each of these orbitals (spin-up) before pairing any electrons (Hund s rule). 

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... 

Electrons act as if they were spinning around an axis, in much the same way that the earth spins. This spin can have two orientations, denoted as up T and down i. Only two electrons can occupy an orbital, and they must be of opposite spin, a statement called the Pauli exclusion principle. 

Pauli exclusion principle (Section 1.3) No more than two electrons can occupy the same orbital, and those two must have spins of opposite sign. 

The Pauli exclusion principle has an implication that is not obvious at first glance. It requires that only two electrons can fit into an orbital, since there are only two possible values of m,. Moreover, if two electrons occupy the same orbital, they must have opposed spins. Otherwise they would have the same set of four quantum numbers. 

The wave function, constructed from the atomic orbitals must be antisymmetric with respect to interchange of electrons in order to satisfy the Pauli exclusion principle, having different spin quantum numbers (a and J3) for two electrons which are in the same orbital. 

The spins of two electrons are said to be paired if one is T and the other 1 (Fig. 1.43). Paired spins are denoted Tl, and electrons with paired spins have spin magnetic quantum numbers of opposite sign. Because an atomic orbital is designated by three quantum numbers (n, /, and mt) and the two spin states are specified by a fourth quantum number, ms, another way of expressing the Pauli exclusion principle for atoms is... 

Introduction of the half-integral spin of the electrons (values h/2 and —fe/2) alters the above discussion only in that a spin coordinate must now be added to the wavefunctions which would then have both space and spin components. This creates four vectors (three space and one spin component). Application of the Pauli exclusion principle, which states that all wavefunctions must be antisymmetric in space and spin coordinates for all pairs of electrons, again results in the T-state being of lower energy [equations (9) and (10)]. 

Electron configurations of transition metal complexes are governed by the principles described in Chapters. The Pauli exclusion principle states that no two electrons can have identical descriptions, and Hund s rule requires that all unpaired electrons have the same spin orientation. These concepts are used in Chapter 8 for atomic configurations and in Chapters 9 and 10 to describe the electron configurations of molecules. They also determine the electron configurations of transition metal complexes. 

The last rule needed to generate electron configurations for all the atoms in the periodic table came from a German scientist named Friedrich Hund. Hund s rule can be expressed in several ways. The most precise definition is that atoms in a higher total spin state are more stable than those in a lower spin state. Thus, the sixth electron in carbon-12 must have the same spin as the fifth one. The Pauli exclusion principle then requires that it fill an empty p orbital. 

For over a decade, the topological analysis of the ELF has been extensively used for the analysis of chemical bonding and chemical reactivity. Indeed, the Lewis pair concept can be interpreted using the Pauli Exclusion Principle which introduces an effective repulsion between same spin electrons in the wavefunction. Consequently, bonds and lone pairs correspond to area of space where the electron density generated by valence electrons is associated to a weak Pauli repulsion. Such a property was noticed by Becke and Edgecombe [28] who proposed an expression of ELF based on the laplacian of conditional probability of finding one electron of spin a at t2, knowing that another reference same spin electron is present at ri. Such a function... 

The connection between the Pauli exclusion principle and the more general Pauli principle can be understood as follows. If two electrons with the same spin a were to occupy the same orbital ip, the total wave function for the system would be written yi, zO (/ "to, yi,... 

The Pauli exclusion principle requires that no two electrons can occupy the same spin-orbital is a consequence of the more general Pauli antisymmetry principle ... 

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 relative size of atomic orbitals, which is found to increase as their energy level rises, is defined by the principal quantum number, n, their shape and spatial orientation (with respect to the nucleus and each other) by the subsidiary quantum numbers, Z and m, respectively. Electrons in orbitals also have a further designation in terms of the spin quantum number, which can have the values +j or — j. One limitation that theory imposes on such orbitals is that each may accommodate not more than two electrons, these electrons being distinguished from each other by having opposed (paired) spins, t This follows from the Pauli exclusion principle, which states that no two electrons in any atom may have exactly the same set of quantum numbers. 

A spinning electron also has a spin quantum number that is expressed as 1/2 in units of ti. However, that quantum number does not arise from the solution of a differential equation in Schrodinger s solution of the hydrogen atom problem. It arises because, like other fundamental particles, the electron has an intrinsic spin that is half integer in units of ti, the quantum of angular momentum. As a result, four quantum numbers are required to completely specify the state of the electron in an atom. The Pauli Exclusion Principle states that no two electrons in the same atom can have identical sets of four quantum numbers. We will illustrate this principle later. 

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