Bond Relaxation in Length and Energy

Bond Relaxation in Length and Energy 11.2.1 Atomic CN-Radius Correlation... 

A set of analytical expressions enables theoretical unification of the size, pressure, temperature, and bond nature dependence of elastic modulus and Raman shift to be reproduced with derivatives of the atomic cohesive energy, binding energy density, Debye temperature, specific heat, and the reference frequency of Raman shift for bulk and nanostructures. The bond relaxation in length and energy determines the correlation between these quantities and their interdependence. The followings conclude ... 

H-0 bond forms a pair of asymmetric, coupled, and H-bridged oscillators with short-range interactions, whose cooperative relaxation in length and energy and the associated entrapment and polarization discriminate water and ice from other usual materials. All detectable properties depend functionally on the performance of either the H-O or the 0 H bond. The involvement of the Coulomb repulsion forms the key to the anomalies of water and ice. 

Cooperative relaxation of the H-bond in length and energy and the associated binding electron entrapment and non-bonding electron polarization determine the... 

The nature, order, length, and energy of the chemical bond determine the properties of a substance. The formation, dissociation, relaxation, and vibration of the bond and non-bond, and the associated dynamics of electron densihcation, localization, entrapment, and polarization are the key of tuning the property change. The underlying mechanism and the consequences of the surface events are useful in practice ... 

As discussed in Chap. 15, the solution to the Hamiltonian of a vibration system is a Fourier series with multiple terms of frequencies being fold of that of the primary mode [36]. Any perturbation to the Hamiltonian causes the Raman frequencies to shift from the initially ideal values. Therefore, applied strain, pressure, temperature, or the atomic CN variation can modulate the length and energy of the involved bonds, or their representative, and hence the phonon frequencies in terms of bond relaxation and vibration. 

Fig. 2.9 The propane potential energy surface as the two HCCC dihedrals are varied (calculated by the AMI method, Chapter 6). Bond lengths and angles were not optimized as the dihedrals were varied, so this is not a relaxed PES however, changes in bond lengths and angles from one propane conformation to another are small, and the relaxed PES should be very similar to this one...

---