Atomic hybrid polarizability

The average polarizability a, defined by equation 9, is a global property, which pertains to a molecule as a whole. It is a measure, to the first order, of the overall effect of an external electric field upon the charge distribution of the molecule. We are unaware of any experimentally determined a for the molecules that are included in this chapter. However, they can be estimated using equation 12 and the atomic hybrid polarizabilities, and corresponding group values, that were derived empirically by Miller. These were found to reproduce experimental molecular a with an average error of 2.8%. The relevant data, taken from his work, are in Table 7. 

Table E-3. Atomic polarizability values 1. Kang-Jhon atomic hybrid polarizabilities aA(ahp) 2. Miller-Savchik average atomic polarizabilities aX(ahc) 3. No-Cho-Jhon-Sheraga atomic polarizabilities a,, o and linear charge coefficient a,y.

The next step towards increasing the accuracy in estimating molecular properties is to use different contributions for atoms in different hybridi2ation states. This simple extension is sufficient to reproduce mean molecular polarizabilities to within 1-3 % of the experimental value. The estimation of mean molecular polarizabilities from atomic refractions has a long history, dating back to around 1911 [7], Miller and Sav-chik were the first to propose a method that considered atom hybridization in which each atom is characterized by its state of atomic hybridization [8]. They derived a formula for calculating these contributions on the basis of a theoretical interpretation of variational perturbation results and on the basis of molecular orbital theory. 

In Section 7.1.2 a method for the calculation of mean molecular polarizability was presented. Mean molecular polarizability can be calculated from additive contributions of the atoms in their various hybridization states in a molecule (see Eq. (6)). Mean molecular polarizability, a, expresses the magnitude of the dipole moment, fi, induced into a molecule imder the influence of an external field, E (Eq. (15))... 

These interactions (dd, di, ii) are a function of dipole moment and polarizability. It has been shown that the dipole moment cannot be replaced entirely by the use of electrical effect substituent constants as parameters52. This is because the dipole moment has no sign. Either an overall electron donor group or an overall electron acceptor group may have the same value of /x. It has also been shown that the bond moment rather than the molecular dipole moment is the parameter of choice. The dipole moments of MeX and PhX were taken as measures of the bond moments of substituents bonded to sp3- and sp2-hybridized carbon atoms, respectively, of a skeletal group. Application to substituents bonded to sp-hybridized carbon atoms should require a set of dipole moments for substituted ethynes. 

Miller and Savchik (12) have given Equation 1 for estimating the mean polarizability, a, of a molecule, where N is the total number of electrons in the molecule, and x.is a polarizability contribution for each atom i, characteristic of the atom type and its hybridization state. 

TABLE 8. Estimated average molecular polarizabilities, based ou empirical hybrid atom aud group values (Table 7) ... 

High polarizibility of atoms or ions requires easy hybridization and/or large size. We see that for both copper and bismuth we have ample opportunity for hybridization that could lead to high polarizibility. For copper, it is 3d-4s hybridization for bismuth, it is 6s-6p hybridization. We expect this polarizibility to be more pronounced for the lower oxidation states of bismuth and copper. Oxygen polarizibility (2s-2p) may also be significant. 

Chemical Properties. The chemistry of ketenes is dominated by the strongly electrophilic -hybridized carbon atom and alow eneigy lowest unoccupied molecular orbital (LUMO). Therefore, ketenes are especially prone to nucleophilic attack at Cl and to [2 + 2] cycloadditions. Less frequent reactions are the so-called ketene insertion, a special case of addition to substances with strongly polarized or polarizable single bonds (37), and the addition of electrophiles at C2. For a review of addition reactions of ketenes see Reference 8. 

Since the suggestion of the sequential QM/MM hybrid method, Canuto, Coutinho and co-authors have applied this method with success in the study of several systems and properties shift of the electronic absorption spectrum of benzene [42], pyrimidine [51] and (3-carotene [47] in several solvents shift of the ortho-betaine in water [52] shift of the electronic absorption and emission spectrum of formaldehyde in water [53] and acetone in water [54] hydrogen interaction energy of pyridine [46] and guanine-cytosine in water [55] differential solvation of phenol and phenoxy radical in different solvents [56,57] hydrated electron [58] dipole polarizability of F in water [59] tautomeric equilibrium of 2-mercaptopyridine in water [60] NMR chemical shifts in liquid water [61] electron affinity and ionization potential of liquid water [62] and liquid ammonia [35] dipole polarizability of atomic liquids [63] etc. 

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