Pauli exclusion principle forces

Pascal An SI unit of pressure the pressure exerted by the force of 1 newton on an area of 1 square meter, 104,635 Paschen series, 138 Pasteur, Louis, 601 Pauli exclusion principle, 141-143 Pauling, Linus, 185 Pentyl propionate, 596t Peptide linkage The—C—N—group... 

Although (l)-(4) involve polarization and other terms that are reminiscent of a classical dipole-dipole picture, it must be re-emphasized that the nB-ffAH picture is formulated entirely in the quantal framework (including full consistency with the Pauli exclusion principle). Thus, while vague connections to concepts of classical electrostatics can be drawn, the NBO donor-acceptor picture of H-bonding is essentially based on overlap-type ionic resonance (5.29a), not on ionic forces (or the like) of classical type. 

Short-range repulsive forces are a direct result of the Pauli exclusion principle and are thus quantum mechanical in nature. Kitaigorodskii (1961) has emphasized that such short-range repulsive forces play a major role in determining the packing in molecular crystals. The size and shape of molecules is determined by the repulsive forces, and the molecules pack as closely as is permitted by these forces. 

In addition to the Coulombic forces, there is a repulsive force which operates at short distances between ions as a result of the overlapping of filled orbitals, potentially a violation of the Pauli exclusion principle. This repulsive force may be represented by the equation ... 

Electrons having the same spin strongly repel each other and tend to occupy different regions of space. This is a result of a fundamental law of nature known as the Pauli exclusion principle. It states that total wave functions (including spin) must change their signs on exchange of any pair of electrons in the system. Briefly, this means that if two electrons have the same spin they must have different spatial wave functions (i.e., different orbitals) and if they occupy the same orbital they must have paired spins. The Pauli principle and the so-called Pauli repulsive forces 1 have lar-... 

The nuclei of the atoms in a solid and the inner electrons form ion cores with energy levels little different from corresponding levels in free atoms. The characteristics of the valence electrons arc modified greatly, however. The stale functions of these outer electrons greatly overlap those of neighboring atoms. Restrictions of the Pauli Exclusion Principle and the Uncertainty Principle force modification of the state functions, and the development of a set of split energy levels becomes a quasi-continuous band of levels of width, which are several electron volts for most solids. Importantly, unoccupied levels of the atoms are also split into bands. The electronic characteristics of solids are determined by the relative position in energy of the occupied and unoccupied levels as well as by die characteristics of the electrons within a band. 

The development of quantum theory, particularly of quantum mechanics, forced certain changes in statistical mechanics. In the development of the resulting quantum statistics, the phase space is divided into cells of volume hf. where h is the Planck constant and / is the number of degrees of freedom. In considering the permutations of the molecules, it is recognized that the interchange of two identical particles does not lead to a new state. With these two new ideas, one arrives at the Bose-Einstein statistics. These statistics must be further modified for particles, such as electrons, to which the Pauli exclusion principle applies, and the Fermi-Dirac statistics follow. 

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 ... 

Physical chemistry of the positron and Ps is unique in itself, since the positron possesses its own quantum mechanics, thermodynamics and kinetics. The positron can be treated by the quantum theory of the electron with two important modifications the sign of the Coulomb force and absence of the Pauli exclusion principle with electrons in many electron systems. The positron can form a bound state or scatter when it interacts with electrons or with molecules. The positron wave function can be calculated more accurately than the electron wave function by taking advantage of simplified, no-exchange interaction with electrons. However, positron wave functions in molecular and atomic systems have not been documented in the literature as electrons have. Most researchers perform calculations at certain levels of approximation for specific purposes. Once the positron wave function is calculated, experimental annihilation parameters can be obtained by incorporating the known electron wave functions. This will be discussed in Chapter 2. 

Van der Waals forces The term van der Waals forces denotes the short-range interactions between closed-shell molecules. Van der Waals forces include attractive forces arising from interactions between the partial electric charges and repulsive forces arising from the Pauli exclusion principle and the exclusion of electrons in overlapping orbitals. A very commonly used potential is the so-called Lennard-Jones (6-12) potential to describe the attractive and repulsive components of van der Waals forces. 

The nature of the repulsive force that arises when two closed-shell systems approach each other can be described in many ways, one of which is as follows. At larger distances the electron clouds of two atoms attract each other by dispersion forces, while at short distances the Pauli exclusion principle drives electrons with the same quantum numbers away from the space they are trying to share, so that a local deshielding of the nuclei occurs, and repulsion arises. Note that the Pauli principle does not imply forces , but only the purely quantum mechanical effect of mutual electron avoidance. At equilibrium, which results from a balance between dispersion attraction and nuclear repulsion forces, there is usually a net gain in energy. The parametric potential must therefore consist of a repulsive (the exponential) and an attractive (mostly, m = 6) term. 

The VSEPR model is the least sophisticated it makes practically no use of the mathematical machinery of quantum mechanics. Its emphasis on the influence of interelectronic repulsions is in sharp contrast to the other models, in which repulsions are not explicitly mentioned except perhaps at a secondary stage to refine details of the structural prediction. Nevertheless, this model achieves considerable success and should be regarded as a useful qualitative tool in handling structural problems. It is interesting that the repulsive forces invoked in the VSEPR model may not, in fact, be simple electrostatic ones. Instead, they may be attributable to the combined effects of the orthogonality of orbitals and the Pauli exclusion principle.9... 

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