Coulson charges

Yrs are two-centre two-electron repulsion energies. For aromatic ions, the onsite electron pair densities, i.e., the diagonal elements of the spinless second order density matrix are lower than those of any classical structure. For radicals, however, the pair densities are increased relative to those in the corresponding classical structures. Thus the resonance energy of the ion exceeds that of the radical by 21 Ec I [33]. FIMO and PMO do not differentiate between the formation of an arylmethyl radical and its carbocation. Empirically, radicals are better described by these methods this has been related to the constant Coulson charge order Q = 1 for arylmethyl radicals as opposed to the variable rt-charge order 1 on arylmethyl cations [16,39]. The actual PPP values of Ec have been correlated to an excellent accuracy to their PMO-o) counterparts [16]. 

Population anaiysis methods of assigning charges rely on the LCAO approximation and express the numbers of electrons assigned to an atom as the sum of the populations of the AOs centered at its nucleus. The simplest of these methods is the Coulson analysis usually used in semi-empirical MO theory. This analysis assumes that the orbitals are orthogonal, which leads to the very simple expression for the electronic population of atom i that is given by Eq. (53), where Natomic orbitals centered... 

A consequence of these findings is that the jr-electron charges are all exactly equal to 1, for the ground state of every alternant hydrocarbon. (Coulson and Rushbrooke, 1940). 

The usual multipole expansion is inappropriate for the treatment of London energies associated with the interatomic charge oscillation. However, London23 has given an appropriate method, known as the monopole method. Coulson and Davies7 and Haugh and Hirschfelder16 have applied the monopole method to the inter-... 

Coulson concluded that the most important contribution to H-bonding is ionic resonance (5.29a). However, generations of empirical modelers have found it convenient to employ simple pairwise-additive Coulombic formulas with empirically fitted point charges to model H-bonds, and such empirical models have tended to encourage uncritical belief in the adequacy of a classical electrostatic picture of H-bonding. 

A simple modification of the IAM model, referred to as the K-formalism, makes it possible to allow for charge transfer between atoms. By separating the scattering of the valence electrons from that of the inner shells, it becomes possible to adjust the population and radial dependence of the valence shell. In practice, two charge-density variables, P , the valence shell population parameter, and k, a parameter which allows expansion and contraction of the valence shell, are added to the conventional parameters of structure analysis (Coppens et al. 1979). For consistency, Pv and k must be introduced simultaneously, as a change in the number of electrons affects the electron-electron repulsions, and therefore the radial dependence of the electron distribution (Coulson 1961). 

G. C. Pimentel (Berkeley) In discussing the excess dipole-moment induced by the formation of an H bond, Professor Coulson has noted that the necessary value of Z e9 the effective proton charge, is 2-3. I wonder if this is a rather high estimate of the necessary effective charge because the centre of gravity of the non-bonding electrons is closer to the proton than is the oxygen atom ... 

A. Coulson This is a complicated calculation to attempt because the field varies with position. In any event it does not seem that this could account for more than a factor of 2 in the estimate of We should need a factor of about 10 to get plausible values of net charges on the atoms. 

A few hardy souls may say it doesn t matter. A molecule is a collection of nuclei and electrons, with a certain charge and spin multiplicity. One might stop there and say that this defines the molecule. This austere view was expressed by Charles Coulson, a pioneer of, of all things, valence ...a bond does not really exist at all it is a most convenient fiction... [4], However, the bond concept... 

More generally, one has to consider the weights of VB structures, which are quantitatively related to physical properties like electron densities, net charges, and so on. According to the popular Chirgwin—Coulson formula (5), the weight of a given structure, d>x, is defined as the square of the coefficient plus one-half of the overlap population terms with all the other structures ... 

Because Equation 6.53, which is sometimes called the Coulson scheme for net atomic charges, is based on the NDDO approximation, it cannot be applied properly for ab initio methods. Here, a standard scheme to quantify net atomic charges is Mulliken population analysis (Mulliken, 1955 1962), despite some well-known deflciences such as its strong dependence on the basis set and its apparent lack of convergence with increasing basis set size. Nonetheless, Mulliken charges may... 

The net atomic charge statistics in Table 6.4 reveal surprisingly large differences between the individual methods, and in particular between the semiempirical results based on the Coulson scheme (Section IV.E, Equation 6.53) and the ab initio results derived through the Mulliken... 

We can elaborate this VB formulation for the cycloaddition by replacing the nearest-neighbour active-space AOs in VB structures 50 and 51 with Coulson-Fischer orbitals [34(b)]. Thus if a and b are now the singly-occupied carbon and oxygen AOs of HCNO, and c and d are the singly-occupied carbon AOs of HCCH, the c and d AOs in structure 50 can be replaced by the Coulson-Fischer MOs c + k d and d + k"c. In structure 51, a + Ad, b + Ac, c + K b and d + K"a can replace the a, b c and d AOs. Use of these orbitals permits additional canonical Lewis VB structures to be included in the equivalent Lewis structure resonance scheme. The mechanism can then accommodate some charge transfer between the HCNO and HCCH reactants. The more-flexible wavefunction of Eq.(13),... 

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