Valence repulsion

The attractive resonance interaction for the Ilg state overcomes the valence repulsion at large R and causes the formation of a second minimum, which is not found in the triplet state [88]. The resonance interaction in the triplet state is instead repulsive which further strengthens the valence repulsion at large internuclear distances. The second minimum for the state is found at 8.14 a.u. 

Another effect which should be considered is the relativistic shrinkage of the ns valence shell of the metal. This can contribute to the valence repulsion (making it weaker), although, on the other hand, this may also reduce the overlap between the boron 2p orbital and the ns orbital of the... 

Distinguished Role of the Valence Repulsion and Electrostatic Interaction... 

In the most commonly encountered interaction of closed shell molecules, the term represents the valence repulsion. 

The symbol 0(5 ) stands for all the terms that vanish with the fourth power of the overlap integrals or faster. The valence repulsion already appears in the first order of the perturbation theory (besides the electrostatic energy as a result of the Pauli exclusion principle. ... 

If this were true, we could not exist. Indeed, sitting safely in a chair, we have an equilibrium of the gravitational force and..., well, and what First of all, the force coming from the valence repulsion that we are talking about. It is claimed sometimes that quanmm effects are peculiar to small objects (electrons, nuclei, atoms, molecules) and are visible when dealing with such... 

Here is an intriguing idea the polarization approximation should be an extremely good approximation for the interaction of a molecule with an antimolecule (built from antimatter). Indeed, in the molecule we have electrons in the antimolecule positrons, and no antisjmunetrization (between the systems) is needed. Therefore, a product wave function should be a very good starting point. No valence repulsion will appear, and the two molecules will penetrate like ghosts. Soon after the annihilation takes place and the system disappear . 

Fig. 13.11. Interaction eneigy of Na+ and Cl (scheme). The polarization approximation gives an absurdity for small separatirais the sub stems attract veiy strongly (mainly because of the electrostatic interaction), while they have had to repel very strtmgly. (a) The absurdity is removed when the valence repulsion is taken into account. Panel(b) shows the valence repulsion alone modeled by the term A exp (-BR), where A and B are positive constants.

Valence repulsion removes the absurdity of the polarization approximation, which made the collapse of the two subsystems possible. 

We recognize on the right side (the first two terms) the complete first-order contribution i.e., the electrostatic energy (Feist) and the valence repulsion energy (F pj,). From the definition of the induction and dispersion energies [Eqs. (13.13) on p. 808], as well as fi-om the reduced resolvent Rq of Eq. (10.76) on p. 644. (applied here to the individual molecules), one may write... 

S-exch associated with a modification of polarization (due to the valence repulsion) of B by A and a similmpart for polarization modification of A by B. 

In the first order, due to the Pauli exclusion principle (i.e., to the antisymmetrization) the electrostatic energy eist that is known from the polarization approximation is supplemented by the valence repulsion energy... 

Thus, any realistic deformation of the electron clouds has to take into account simultaneously the exchange interaction (valence repulsion, or the Pauh principle). Because of this, we have introduced what is called the deformation-exchange interaction energy ... 

Although the intermolecular interactions are non-additive, we may ask whether individual contributions to the interaction energy (electrostatic, induction, dispersion, or valence repulsion) are additive ... 

The eist(ABC) term in SAPT represents only part of the first-order correction to the energy (the rest being the valence repulsion"). 

The expression for the three-body non-additivity of the valence repulsion is given by Eq. (13.42), based on Eq. (13.39) of the first-order correction in SAPT and Eq. (13.70) of the three-body contribution ... 

Molecules at long distances interact through the mediation of the electric fields created by them. The valence repulsion is of a different character, since it results from the Pauli exclusion... 

The valence repulsion plays the role of a hard wall (covered by a soft blanket ) that forbids the closed-shell molecules to approach too closely (this represents a very important factor, since those molecules that do not fit together receive an energy penalty). 

The induction and dispersion contributions are negative (almost independent of the mutual orientation of the molecules), and we may say, as a rule of thumb, that their role is to stabilize the structure already determined by the valence repulsion and the electrostatics. 

Table 13.5. Energy contributions to the interaction energy jjjj in the systemHO-H... OH2 (hydrogen bond) calculated" within the SAPT method electrostatic energy feist, valence repulsion energy f xch induction energy fjmi and dispersion energy (jisp for three 0...0 distances erjuilibrium distance = 3.00 and two distances a little larger medium 3.70 A and large 4.76 A.

This is quite a peculiar type of interaction, which appears mainly (but not only) in water solutions. The hydrophobic interaction does not represent any particular new interaction (beyond those we have already considered), because at least potentially, they could be explained by the electrostatic, induction, dispersion, valence repulsion, and other interactions already discussed. 

Elimination of some potential convex reactants guest molecules ) to enter a reaction center inside a eoneave pocket of the host molecule, just because their shape makes the contact impossible (due to the steric hindrance i.e., an excessive valence repulsion, as shown in Fig. 13.23al). 

The most important contributions electrostatic, valence repulsion, induction, and dispersion lead to a richness of supramolecular structures. 

Also, valence repulsion is one of the most important energy contributions because it controls how the interacting molecules fit together in space. 

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 accuracy of this interpretation is confirmed by a glance at conditions in the hydrogen sulfide molecule. By reason of the greater diameter of the sulfur atom, the distance between the substituent H atoms is already 1.91 A at normal valence angle, so that only a very small deformation of 2° 20 is necessary for a state of equilibrium to be established in the molecule with a distance of 1.95 A between the two hydrogen atoms. The other data in Table 6 are to be interpreted in the same way and together they afford a very clear and instructive picture of the interaction between primary valence attraction and secondary valence repulsion within the molecule. 

Both approaches have then their practical defects. As far as the wavefunction is dominated by a few VB determinants or configurations (a Rydberg configuration crossing a valence repulsive curve, for instance), one may of course restrict the problem to this space and give an approximate elegant diabatic picture of the problem. ... 

Distinguished role of the electrostatic interaction and the valence repulsion... 

We will see later that taking the zero-order wave function with the proper symmetry leads to the first order energy containing what is called the valence repulsion, besides the term. 

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