Pauli repulsive forces

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-... 

Electrons with the same spin behave as if there is a repulsive force acting between them. This apparent force is sometimes called the Pauli force. However, it is preferable not to speak of Pauli forces, since they are only apparent forces, not real forces like electromagnetic or gravitational forces. In fact, the Pauli principle implies that there is an intimate interconnection between the constituent parts of matter in the universe. Strictly speaking, no part can be isolated from the rest, except in an idealized way. The Pauli force acts at any time and over huge distances, much larger than atomic dimensions, but its effect becomes dramatic only when electrons of the same spin happen to be close to each other. 

The VSEPR model was originally expressed in these terms, but because Pauli repulsions are not real forces and should not be confused with electrostatic forces, it is preferable to express the nonequivalence of electron pairs of different kinds in terms of the size and shape of their domains, as we have done in this chapter. 

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 ... 

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 ... 

It is true that all molecular and atomic forces ultimately find their root in the mutual behavior of the constituent parts of the atoms, viz., the nuclei and the electrons. They may theoretically all be derived from the fundamental wave equations. It is, however, convenient, as in other branches of physics and chemistry, to treat the various forms of mutual interaction of atoms as different forces, acting independently. We shall therefore follow the usual procedure and treat such forces as the nonpolar van der Waals (dispersion) forces, the forces of the electrostatic polarization of atoms or molecules by ions or by dipoles, the mutual attraction or repulsion Coulomb forces of ions and of dipoles, the exchange forces leading to covalent bonds, the repulsion forces due to interpenetration of electronic clouds, together with the Pauli principle, etc., all as different, independently acting forces. 

Since no physisorption well is present, the question has to be considered how the inclusion of a physisorption state would alter the trapping dynamics. Physisorption wells are created by a combination of the attractive van der Waals interaction with Pauli repulsion caused by the overlap of molecular and substrate wave functions. While the former effect is not reproduced by the DFT calculation, the repulsion due to wave function overlap is well described by present DFT functionals. Hence, the calculated PES would only become more attractive if van der Waals forces were correctly included. For a more quantitative description of the trapping process at kinetic energies below 0.05 eV certainly the physisorption channel has to be included. 

The Pauli principle keeps electrons with the same spin spatially apart. This principle applies whether one is dealing with electrons on the same molecule or on different molecules and is the predominant repulsive force (6)that keeps electrons of different molecules from interpenetrating when noncovalent complexes are formed. This repulsive term is often represented by an analytical function of the form... 

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