Hardly polarizable molecules

THE EXCITONIC PICTURE A MODEL FOR HARDLY POLARIZABLE MOLECULES... 

This term breaks down tire excitonic approximation mixing up states whose exciton number differs by two units. This so called non-Heitler-London term has negligible effects for systems with J 2wo [47]. So the excitonic approximation is expected to work well for clusters of molecules with large excitation energies and not too large transition dipole moments, i.e. for hardly polarizable molecules. 

The reliability of mf approximation for the calculation of static linear and nonlinear susceptibilities is another important result that is expected to hold for mm with negligible intermolecular overlap and not too near to charge instabilities (i.e. to phase transitions or to precursor of phase transitions in finite size systems). This is related to the uncorrelated nature of the gs in these materials, that is fairly well captured within mf. On the opposite, EM does not properly account for tlie molecular polarizability it can possibly describe low-lying excited states in clusters of weakly interacting and hardly polarizable molecules, but it is for sure inadequate to calculate linear and non-linear susceptibilities for mm of interest for applications. 

To rationalize observations such as these, Pearson presented the concept of hard and soft acids and bases (HSABs), designating polarizable acids and bases as soft and nonpolarizable acids and bases as hard. Much of the hard-soft distinction depends on polarizability, the degree to which a molecule or ion is distorted by interaction with other molecules or ions. Electrons in polarizable molecules can be attracted or repelled by charges on other molecules, forming slightly polar species that can then interact with the other molecules. The HSAB concept is a nseful gnide to explain acid-base chemistry and other chemical phenomena. Pearson stated, Hard acids prefer to bind to hard bases, and... 

One way to measure softness and hardness of molecules is the polarizability of the electron shell. A first criterion is the number of a- and jr-electrons. With an increasing number of 7i-electrons, the polarizability and the soft character usually increase. 

Ghanty TIC, Ghosh SK (1996) A density functional approach to hardness, polarizability, and valency of molecules in chemical reactions. J Phys Chem 100(30) 12295-12298... 

The borderlines between the different classes are not hard and fast, depending as they do both on the shape of the pores and on the nature (especially the polarizability) of the adsorptive molecule. Thus, the highest value of w (and therefore of p/p ) at which the enhancement of adsorption occurs, i.e. the upper limit of the micropore range, will vary from one adsorptive to another (cf. Chapter 4). 

The concepts of electronegativity, hardness, and polarizability are all interrelated. For the kind of qualitative applications we will make in discussing reactivity, the concept that initial interactions between reacting molecules can be dominated by either partial electron transfer by bond formation (soft reactants) or by electrostatic interaction (hard reactants) is a useftxl generalization. 

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. By means of Koopmann s theorem (Section 3.4) the hardness is related to the HOMO-LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large contribution to the polarizability (Section 10.6), i.e. softness is a measure of how easily the electron density can be distorted by external fields, for example those generated by another molecule. In terms of the perturbation equation (15.1), a hard-hard interaction is primarily charge controlled, while a soft-soft interaction is orbital controlled. Both FMO and HSAB theories may be considered as being limiting cases of chemical reactivity described by the Fukui ftinction. 

It is shown that the stabilities of solids can be related to Parr s physical hardness parameter for solids, and that this is proportional to Pearson s chemical hardness parameter for molecules. For sp-bonded metals, the bulk moduli correlate with the chemical hardness density (CffD), and for covalently bonded crystals, the octahedral shear moduli correlate with CHD. By analogy with molecules, the chemical hardness is related to the gap in the spectrum of bonding energies. This is verified for the Group IV elements and the isoelec-tronic III-V compounds. Since polarization requires excitation of the valence electrons, polarizability is related to band-gaps, and thence to chemical hardness and elastic moduli. Another measure of stability is indentation hardness, and it is shown that this correlates linearly with reciprocal polarizability. Finally, it is shown that theoretical values of critical transformation pressures correlate linearly with indentation hardness numbers, so the latter are a good measure of phase stability. 

Earlier it was described how PH3 is a much weaker base than NH3. That is certainly true when the interaction of these molecules with H+ is considered. However, if the electron pair acceptor is Pt2+, the situation is quite different. In this case, the Pt2+ ion is large and has a low charge, so it is considered to be a soft (polarizable) Lewis acid. Interaction between Pt2+ and PH3 provides a more stable bond that when NH3 bonds to Pt2+. In other words, the soft electron acceptor, Pt2+, bonds better to the softer electron donor, PH3, than it does to NH3. The hard-soft interaction principle does not say that soft Lewis acids will not interact with hard Lewis bases. In fact, they will interact, but this is not the most favored type of interaction. 

As was discussed in Chapter 6, the electronic polarizability, a, of species is very useful for correlating many chemical and physical properties. Values of a are usually expressed in cm3 per unit (atom, ion, or molecule). Because atomic dimensions are conveniently expressed in angstroms, the polarizability is also expressed as A3, so lCT24cm3 = 1 A3. The polarizability gives a measure of the ability of the electron cloud of a species to be distorted so it is also related to the hard-soft character of the species in a qualitative way. Table 9.6 gives the polarizabilities for ions and molecules. 

This chapter aims to present the fundamental formal and exact relations between polarizabilities and other DFT descriptors and is organized as follows. For pedagogical reasons, we present first the polarizability responses for simple models in Section 24.2. In particular, we introduce a new concept the dipole atomic hardnesses (Equation 24.20). The relationship between polarizability and chemical reactivity is described in Section 24.3. In this section, we clarify the relationship between the different Fukui functions and the polarizabilities, we introduce new concepts as, for instance, the polarization Fukui function, and the interacting Fukui function and their corresponding hardnesses. The formulation of the local softness for a fragment in a molecule and its relation to polarization is also reviewed in detail. Generalization of the polarizability and chemical responses to an arbitrary perturbation order is summarized in Section 24.4. 

The hardness h are intimately related to the linear and nonlinear electronic responses as shown explicitly in Equation 24.18. In particular, h is simply the inverse of the linear polarizability it is well known in chemistry that a hard atom has a low polarizability. The nonlinear terms hn/, could allow to better quantify the hardness/softness and polarizability relations (see Section 24.2.2). Note that for an atom in a molecule, the contribution of a2 has to be considered as well in Equation 24.12 through Equation 24.18. On the other hand, Equation 24.18 shows that all the polarizabilities can be formulated in terms of the linear one, if the derivatives hn, which are function of p, are known ... 

For instance, in structure 12-e, the C-X and C-0 dipole moments are additive, leading to a destabilization of the molecule by increasing the energy. In structure 12-a, offset of the C-X and C-0 dipole moments minimizes electrostatic interactions, thus leading to a more stable conformation. This electrostatic model was supported by the observed increase of the percentage of the equatorial conformation of 2-methoxy tetrahydropyran (14) when moving from a non-polar to a polar solvent (Table 3).12 In this model, the polar groups are not polarizable and lead to dipole/dipole (hard/hard) interactions. 

An inner-sphere complex is formed between Lewis acids and bases, while an outer-sphere complex involves a water molecule interposed between the acid and the base. A hard Lewis acid is a molecular unit of small size, high oxidation state, high electronegativity, and low polarizability whereas a soft Lewis acid is a molecular unit of relatively large size, characterized by low oxidation state, low electronegativity, and high polarizability. Based on this characterization, hard bases prefer to complex hard acids, and soft bases prefer to complex soft acids, under similar conditions of acid-base strength. 

The extent to which an atom or molecule s charge distribution is affected by an external electric field E (which could be due to an approaching reactant) is governed, to first order, by its polarizability a. It was really a to which Pearson was referring in his hard and soft acid-base theory, which rationalizes a large number of chemical reactions. The terms hard and soft refer, respectively, to low and high polarizability. 

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