Pauling correlation model

Lockman JW, Paul NM, Parquette JR. The role of dynamically correlated conformational equilibria in the folding of macromolecular structures. A model for the design of folded dendrimers. Prog Polym Sci 2005 30 423-452. 

E. R. Lippincott The proposed model is certainly empirical. However, the internuclear potential function used for the terms V1 and F2 may be derived from a quantum mechanical model which lends support to their use in such a treat-ment of hydrogen bond systems. Professor Pauling is quite right in suggesting that the terms Vx and F2 may include some electrostatic contribution, since it is known that the internuclear potential function used correlates properties fairly well for partial polar bonds. Nevertheless the fact that additional terms of the electrostatic type are not needed to describe a number of the important properties of hydrogen bond systems, suggests that the covalent, repulsion and dispersions energy contributions are more important than the electrostatic contribution. 

The chemist is accustomed to think of the chemical bond from the valence-bond approach of Pauling (7)05), for this approach enables construction of simple models with which to develop a chemical intuition for a variety of complex materials. However, this approach is necessarily qualitative in character so that at best it can serve only as a useful device for the correlation and classification of materials. Therefore the theoretical context for the present discussion is the Hund (290)-Mulliken (4f>7) molecular-orbital approach. Nevertheless an important restriction to the application of this approach must be emphasized at the start viz. an apparently sharp breakdown of the collective-electron assumption for interatomic separations greater than some critical distance, R(. In order to illustrate the theoretical basis for this breakdown, several calculations will be considered, the first being those for the hydrogen molecule. 

The number of electrons available for empirical evaluation of metal-metal bonding has been taken as the Pauling metallic valence less the number of H ions per metal. In this connection the valence numbers of Borelius (6) give somewhat better correlations—e.g., in differentiating Pd from Ag (valences 7 and 1, respectively). Heats of formation calculated from the lattice energies by the Born-Haber cycle are not yet sufficiently accurate to be useful numerically, but they provide an interesting rationalization of the formation of many hydrides. This is the principal reason for considering such a naive model. 

The idea of correlating momentary multipoles stands behind the customary modeling of dispersion interaction in the form of a multipole expansion, including dipole-dipole (D-D), dipole-quadrupole (D-Q), quadrupole-quadrupole (Q-Q), and so on, terms. We owe the earliest variational treatments of this problem not only to Slater and Kirkwood [34], but also to Pauling and Beach [35], However, when the distance R decreases and reaches the Van der Waals minimum separation, the assumption that electrons of A and B never cross their trajectories in space becomes too crude. The calculation of the intermonomer electron... 

Another remarkable feature of the presented plots is that the smooth curves are not just correlation curves of any arbitrary form drawn to fit the data as well as possible, but are derived from a simple model of bonding. The model is based on three assumptions. The first is Pauling s relation between bond length and bond number [24] ... 

The correlation curves shown in Fig. 5 are not just smooth curves drawn to fit the experimental points as well as possible. They have a special analytical form derived from a simple model of chemical bonding, based on Pauling s relationship [45] for the bond number n of a fractional bond of distance d ... 

Capone [219] has summarized more recent analysis of the diffusion behavior, and an example is the work by Baojin et al. [249]. The rate of diffusion is modeled from cylindrical coordinates again based on Pick s law. The composition of actual filaments from the spin bath was analyzed, and the coagulant was a DMP water system. Correlations are presented for diffusion coefficients and flux ratios as functions of jet stretch, polymer solution concentration, and coagulation temperature. The flux ratios, they reported, are similar to those reported in Paul s data, 20 years earlier. The diffusion coefficients are in the same range of 4-10 X lO cm /s that Paul found for DMAC-H2O systems. 

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