Fractional bonds, molecules

We would like to recall that Xa p) is the fraction of molecules not bonded at an associative site now it is a function of the averaged density p(r). A generalization of the perturbational theory allows us to define Xa p) similar to the case of bulk associating fluids. Namely... 

Some molecules exist where the bonding electrons cannot be assigned to atom pairs, but belong to more than two cores, e.g. in the polyboranes. In these cases the model concept of covalently bound atom pairs as a rep-resention basis for chemical constitution using binary relations can be sustained by the assignment of fractional bond orders. 

The light causes a bonded molecule in its ground state to undergo a transition into an excited state. In this new state, the atoms repel one another, causing the molecule to break apart. The fraction of light absorbed, as measured spectroscopically, depends on the population of molecules in the initial state. 

In a few molecules and crystals it is convenient to describe the interactions between the atoms in terms of the one-electron bond and the three-electron bond. Each of these bbnds is about half as strong as a shared-electron-pair bond each might be described as a half-bond.1 There are also many other molecules and crystals with structures that may be described as involving fractional bonds that result, from the resonance of bonds between two or more positions. Moat of these molecules and crystals have a smaller number of valence electrons than of stable bond orbitals. Substances of this type are called electron-deficient substances. The principal types of electron-deficient substances are discussed in the following sections (and in the next chapter, on metals). 

Transition state theory (Chapter 2, section A) was derived for chemical bonds that obey quantum theory. An equation analogous to that for transition state theory may be derived even more simply for protein folding because classical low energy interactions are involved and we can use the Boltzmann equation to calculate the fraction of molecules in the transition state i.e., = exp(— AG -D/RT), where A G D is the mean difference in energy between the conformations at the saddle point of the reaction and the ground state. Then, if v is a characteristic vibration frequency along the reaction coordinate at the saddle point, and k is a transmission coefficient, then... 

C) In Ref. 79 the phenomenon of ion rattling motions was supposed to influence the recorded absorption band at v > 200 cm-1. It seems that without a theory capable of describing the whole 0- to 1000-cm 1 band it is hardly possible to assign the measured alteration of absorption due to a number of specific physical factors. The model, presented above, can be used as a basis for this purpose. However, to achieve this aim, a few important factors should additionally be accounted for. (a) It appears that first of all it is reasonable to introduce an additional fraction containing water molecules of a hydration sheath around an ion. The dielectric response of this fraction should differ from that of bulk water, (b) A model of an ion-dipole system suggested by the authors in GT, p. 318, could possibly be employed for this studies, (c) Another important task concerns development of a model describing the specific loss mechanism due to vibration of H-bonded molecules. 

The bond order in a diatomic molecule is defined as one-half the difference between the number of electrons in bonding orbitals and the number of antibonding orbitals. The factor one-half preserves the concept of the electron pair and makes the bond order correspond to the multiplicity in the valence-bond formulation one for a single bond, two for a double bond, and three for a triple bond. Fractional bond orders are allowed, but are not within the scope of this discussion. 

On the other hand, the effective collision concept can explain the Arrhenius term on the basis of the fraction of molecules having sufficient kinetic energy to destroy one or more chemical bonds of the reactant. More accurately, the formation of an activated complex (i.e., of an unstable reaction intermediate that rapidly degrades to products) can be assumed. Theoretical expressions are available to compute the rate of reaction from thermodynamic properties of the activated complex nevertheless, these expression are of no practical use because the detailed structure of the activated complexes is unknown in most cases. Thus, in general the kinetic parameters (rate constants, activation energies, orders of reaction) must be considered as unknown parameters, whose values must be adjusted on the basis of the experimental data. 

To make this precise, we define a cut in a molecule to be the conceptual dissection of a covalent connectivity a cut of a covalent bond of formal order n is counted as being n cuts. In some molecules the formal order of certain covalent bonds is not an integer. In such cases one can either approximate the bond order by an integer, or use a fractional bond order consistently for counting the cuts the genus for such molecules may therefore be not an integer in the latter case. With these concepts, we can make the precise... 

The Fraction of Molecules with i Intact Bonds in MeOH andEtOHataS C"... 

The first such extension is the introduction of double and triple bonds, where four or six valence electrons are shared. Then there are coordinate bonds, where both electrons are donated by one of the two atoms, instead of a formal donation of one from each atom. There are resonance structures and fractional bonds—to explain why the unusually stable benzene molecule, CeH, has a ring structure that has hexagonal rather than triangular symmetry, or why the acetate ion, CH3COO, has two symmetrically... 

---