PAULI DEFORMATION

In the second order, the Pauli deformation (cf. Appendix Y available at booksite. elsevier.com/978-0-444-59436-5 on p. el83) of the electronic density in the AB complex results in exchange-based modifications ( ind exch - disp-exch) the induction and dispersion interactions ( ind and Ejisp) that are known from the polarization perturbation theory. 

The Pauli exclusion principle leads to a d ormation of the wave functions describing the two molecules (by projecting the producdike wave function by the antisymmetrizer A) with respect to the producdike wave function. The Pauli deformation (cf. Appendix Y available at booksite.elsevier.com/978-0-444-59436-5) appears already in the zeroth order of perturbation theory, whereas in the polarization approximation, the deformation of the wave function appears in the first order and is not related to the Pauli exelusion prineiple. 

Molecule C interacts electrostatically with the Pauli deformation of molecules A and B (i.e., with the multipoles that represent the d otmation). Such a mixed interaction is called the SE mechanism. 

Fig. 13.12. A scheme of the SE and TE exchange non-additivides. Panels (a), (b), and (cj shew the SE mechamsnL (a) Hiree non-interacting molecules (schematic representation of electron densities), (b) Pauli deformation of molecules A andB. (c) Electrostatic interaction of the Pauli deformation resulting from single electron exchanges between A and B with the dipole mcxneiit of C. (d) The TE mechanism molecules A and B exchange an electron with the mediation of molecule C. All molecular electrcm density distributions undCTgo PauU defmnation.

The Pauli deformation has a local (i.e., short-range) character see Appendix Y available at booksite.elsevier.coin/978-0-444-59436-5. Let us imagine that molecule B is very long and the configuration corresponds to A B C. When C is far from A, the thiee-body effect is extremely small because almost everything in the interaction is of the two-body character. If molecule C approaches A and has some nonzero, low-order multipoles (e.g., a charge), then it may interact by the SE mechanism even from far away. Both mechanisms (SE and TE) operate only at short BA distances. 

Single-Exchange A contribution to the exchange interaction (valence repulsion of molecules) non-additivity effect coming from the interaction of the Pauli deformation of the electron cloud due to two interacting molecules with the electric field created by the third molecule. 

The Pauli deformation may be viewed as a mechanical distortion of both interacting molecules due to their mutual pushing. The reason why two gumballs deform when pushed against each other is the same the electrons of one ball cannot occupy the same space as the electrons (with the same spin coordinates) of the second ball. The most dramatic deformation takes place close to the contact area of these balls. 

Y.l. Comparison of the Pauli deformation for two hydrogen atoms and for two helium atoms, (a) Two hydrogen atoms. Visualization of p — p calculated in the plane containing the nuclei (the net result is zero). One of the protons is located at the... 

In the case of He2, the Pauli exclusion principle makes the electron density decrease in the region between the nuclei and increase close to the nuclei. In the case of the hydrogen molecule, the two atoms smck together, while the two helium atoms deform as if they were gumballs squeezed together (i.e., the Pauli deformation). 

The only thing that has been changed with respect to the hydrogen molecule is the increase of the number of electrons from two to four (we have kept unchanged the orbital exponents equal to 1. as well as the intemuclear distance, which is equal to 4 a.u,). This change resulted in a qualitative difference in the Pauli deformation. 

For two helium atoms, the Pauli deformation means a decrease in the electron density in the region between the nuclei and the corresponding increase of the density on the nuclei. This looks dangerous What if instead of the two helium atoms, we had two closed-shell long molecules A and B, which touch each other by their terminal parts Would the Pauli defonnation be local, or would it extend over the whole system Would the distant parts of the molecules deform as much as the contact regions ... 

This means that the Pauli deformation has a local character it takes place almost exclusively in the region of the contact of both molecules. 

Luty and Eckhardt have highlighted the role of pushing one molecule by another. Let us imagine an atomic probe, e.g., a helium atom. The pushing by the probe deforms the molecular electronic wave function (Pauli deformation), but... 

The product-like wave function has to be made anti mmetric. This causes some changes in the electronic charge distribution (electronic density), which will be called the Pauli deformation. 

In the case of the hydrogen molecule, the two atoms stuck together, while the two hehum atoms deform as if they were rubber balls sque ed together (Pauli deformation). 

If the two systems A and B approach each other in such a way that S = 0, the Pauli deformation is zero. 5 = 0 might occur, e.g., if the two molecules approach along the nodal surfaces of the frontier molecular orbitals. 

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