Debye correlation energy

As shown by Debye and Hiickel, due to the strong electrostatic interaction between the ions in a solution, the positions of the ions are correlated in such a way that a counterion atmosphere appears aronnd each ion, thns screening its Coulomb potential. The energy of formation of the counterion atmospheres contribntes to the free energy of the system called correlation energy. ... 

Therefore, the macroscopically measurable B and Aco connect directly to the bond length and energy of the specimen and their response to the intrinsic coordination imperfection and the applied stimuli through the BOLS correlation and the LBA approach. Exercises lead to derived information of the cohesive energy and Debye temperature, energy density, compressibility, the bulk modulus and their first-order derivatives, and the analytical correlation between the B and Aco. 

Table 4.3. Water dimer properties the interaction energy (Ei t) in kcal/mol, the intermolecular distance (R00) in A, and the dipole moment p. in Debye, calculated using the B88/P86 exchange-correlation functional and different basis sets.

Debye screening parameter X using variational method with correlated basis functions. The numerical results show that the energy diminishes continuously with respect to increased screening and finally becomes zero, giving instability in the system at X 2.0. Later on several authors showed their interest in studying the behavior of energy of two-electron systems in... 

Wang and Winkler [185] used correlated basis sets to study variationally the stability of the ground state energy of the H- ion and He and also the behavior of several excited states of He under Debye screening. A general study of the stability of the excited states of the He isoelectronic sequence... 

A considerable solvent dependence has been reported by Debye and coworkers32 33 in their already mentioned study of a-monoglycerides in benzene, chlorobenzene, and chloroform. The authors found a correlation between the cohesive energy densities of the solvents and the clustering tendency of the nonionic surfactants with decreasing cohesive energy the aggregation increased. In chloroform no micelles were found. 

In the following we outline the method of Ref. [18] which attempts to retain the simplicity of the PB theory but also accommodates correlation effects within a local density approximation (LDA) where all the relevant interactions are included at the level of the free energy density. One starts out with the free energy density of the PB approach and adds an appropriate correlational correction to the mean-field free energy density. One attempt at the level of the Debye-Hiickel theory (DH) is called DH plus Hole (DHH)... 

Electron spin resonance (ESR) studies of radical probe species also suggest complexity. Evans et al. [250] study the temperature dependence of IL viscosity and the diffusion of probe molecules in a series of dissimilar IL solvents. The results indicate that, at least over the temperature range studied, the activation energy for viscous flow of the liquid correlates well with the activation energies for both translational and rotational diffusion, indicative of Stoke-Einstein and Debye-Stokes-Einstein diffusion, respectively. Where exceptions to these trends are noted, they appear to be associated with structural inhomogeneity in the solvent. However, Strehmel and co-workers [251] take a different approach, and use ESR to study the behavior of spin probes in a homologous series of ILs. In these studies, comparisons of viscosity and probe dynamics across different (but structurally similar) ILs do not lead to a Stokes-Einstein correlation between viscosity and solute diffusion. Since the capacities for specific interactions are... 

Driven by a Boltzmann thermal-energy source kT and measured in kT units, coupled by a number of effective mobile ionic charges rs from Gibbs, the monopole-monopole correlation force is screened by Xnebye across the length 21, back and forth between point particles. At the same time its power-law dependence on length is measured in the natural thermal unit >.Bj. Boltzmann, Gibbs, Debye, Bjerrum—all at the same time. Can it get any prettier ... 

Hill, 1986). We have emphasized that fluctuation contributions, e.g. Eq. (4.71) p. 90, have a definite sign. This Debye-Hiickel theory treats correlations between ionic species, and here we observe again that treatment of correlations lowers this free energy. 

Figure 9.15. Typical trajectories of a Gaussian stochastic process x(t) with zero mean and Gaussian (a) or exponential (i>) correlation function. Circles are crossing points of x = 0. Trajectories were generated by regular sampling in the frequency domain, (c) corresponds to the Debye relaxation spectrum with a cutoff frequency. Reorganization energy of the discarded part of the spectrum is 7% of the total. The sampling pattern was the same as in (b).

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