Ion pair calculated

These fis must be distinguished from the fis in ion pair calculations where p is used to describe the fraction of metal ion or ligand associated to the ion pair. 

The interaction energy curves for the ion pairs calculated along the lines indicated are quite shallow, which means that there will be thermal vibration of the cation about the minimum of the potential well. For the ions considered reasonable agreement is found with experimental data. The experimentally observed shift of the maximum of the longest wavelength band is in the predicted direction. 

It is important to evaluate the surface distortion associated with the assymetric field at the surface, a difficult task often simplified by assuming that distortion is limited to the direction normal to the plane [64, 6S]. Benson and co-workers [6S] calculated displacements for the first five planes in the (100) face of sodium chloride and found the distortion correction to of about 100 ergs/cm or about half of itself The displacements show a tendency toward ion pair formation, suggesting that lateral displacements to produce ion doublets should be considered [66] however, other calculations yielded much smaller displacements [67]. 

The thennodynamic properties are calculated from the ion-ion pair correlation fimctions by generalizing the expressions derived earlier for one-component systems to multicomponent ionic mixtures. For ionic solutions it is also necessary to note that the interionic potentials are solvent averaged ionic potentials of average force ... 

A simple example would be in a study of a diatomic molecule that in a Hartree-Fock calculation has a bonded cr orbital as the highest occupied MO (HOMO) and a a lowest unoccupied MO (LUMO). A CASSCF calculation would then use the two a electrons and set up four CSFs with single and double excitations from the HOMO into the a orbital. This allows the bond dissociation to be described correctly, with different amounts of the neutral atoms, ion pair, and bonded pair controlled by the Cl coefficients, with the optimal shapes of the orbitals also being found. For more complicated systems... 

The pA of 1,3-dithiane is 36.5 (Cs" ion pair in THF). The value for 2-phenyl-1,3-dithiane is 30.5. There are several factors which can contribute to the anion-stabilizing effect of sulfur substituents. Bond dipole effects contribute but carmot be the dominant factor because oxygen substituents do not have a comparable stabilizing effect. Polarizability of sulfur can also stabilize the carbanion. Delocalization can be described as involving 3d orbitals on sulfur or hyperconjugation with the a orbital of the C—S bond. MO calculations favor the latter interpretation. An experimental study of the rates of deprotonation of phenylthionitromethane indicates that sulfur polarizability is a major factor. Whatever the structural basis is, there is no question that thio substituents enhance... 

The ab initio methods used by most investigators include Hartree-Fock (FFF) and Density Functional Theory (DFT) [6, 7]. An ab initio method typically uses one of many basis sets for the solution of a particular problem. These basis sets are discussed in considerable detail in references [1] and [8]. DFT is based on the proof that the ground state electronic energy is determined completely by the electron density [9]. Thus, there is a direct relationship between electron density and the energy of a system. DFT calculations are extremely popular, as they provide reliable molecular structures and are considerably faster than FFF methods where correlation corrections (MP2) are included. Although intermolecular interactions in ion-pairs are dominated by dispersion interactions, DFT (B3LYP) theory lacks this term [10-14]. FFowever, DFT theory is quite successful in representing molecular structure, which is usually a primary concern. 

Kittelberger and Elm measured the rate of diffusion of sodium chloride through a number of paint films. Calculations based on their results showed clearly that the rate of diffusion of ions was very much smaller than the rate of diffusion of either water or oxygen. Furthermore, they found that there was a linear relationship between the rate of diffusion and the reciprocal of the resistance of the film. This relationship suggests that the sodium chloride diffused through the membrane as ions and not as ion pairs, since the diffusion through the film of un-ionised material would not affect the resistance, because if a current is to flow, either ions of similar charge... 

The saturated solution of potassium iodate in water at 25°C has a molality equal to 0.43. Taking the activity coefficient y in this saturated solution to be 0.52, find the conventional free energy of solution at 25°C, and calculate in electron-volts per ion pair the value of L for the removal of tho ions K+ and (IOs) into water at 25°C. 

The electrostatic free energy associated with the separation of the ion pair and the recombination of the neutral pair can be easily calculated with Coulomb s law and a large dielectric constant, (e.g., s = 40, which is the... 

A is the manufacturer s rated activity based on calorimetric measurement of the heat evolved by the source. Since one 3-m.e.v. alpha particle produces 3 X 104 ion pairs in air of 1 mg. sq. cm. 1 density we calculate 7, the number of ion pairs produced per second above the leak in 1 cc. air at p torr pressure as ... 

Application to Ethylene Radiolysis. The predominant ions in the mass spectrum of ethylene (1) are ethylene, vinyl, and acetylene ions, which together account for over 85% of the total ionization. A total of 38% of all ions are C2H4+, and since kF(ethylene) = 25.9 e.v./ion pair, the parent ion should be produced with a yield of at least 1.5 ions/100 e.v. absorbed in ethylene. Similar calculations for the probable yields of the other major ions lead to estimates of 0.96 vinyl ions/100 e.v. and 0.94 acetylene ions/100 e.v. Successive dissociations are relatively unimportant in ethylene. 

During this, the electrons of the partial X—Z multiple bond are used. Experiments show that the ester can be further active in the polymerization. Its reactivity, however, is reduced in comparison with ion pairs. From a mechanistical point of view, the chain propagation should proceed in the manner of a SN2 reaction, that is with the monomer as nucleophile and the ester as substrate. With the assistance of quantum chemical calculations using the CNDO/2 method, the differences between covalent species and free ions should be examined. The following contains the three types of anions used ... 

Molecular orbital calculations made on t-BuCl show that the C—Cl distance in the intimate ion pair is 2.9 A and the onset of the solvent-separated ion pair takes place at 5.5 A (cf. the C—Cl bond length of 1.8 A). 

The investigations indicate that, in agreement with the calculations on the cations, the push-pull substituted diphosphenes tend to form a bridged structure of one ligand the other substituent can easily depart under formation of an ion pair structure. 

Theoretical calculations by Mixon and Cioslowski (1991) suggested that a push-pull substituted ethane (H2N)3C—C(N02)3 exists as an ion pair (H2N)3C C(N02)3. Recently, a similar hexamethylguanidinium-... 

Okada et al. have found that internal mohilities are strongly related to the separating motion of unlike ion pairs defined by the self-exchange velocity, which can be easily calculated from MD simulation ... 

Bjerrum s theory of ion pairs qualitatively correctly explains a number of experimental data, but cannot be used to the full extent in quantitative calculations, particularly because of the provisional character of quantities a and (the integration limits). 

Diffusion of ions can be observed in multicomponent systems where concentration gradients can arise. In individnal melts, self-diffnsion of ions can be studied with the aid of radiotracers. Whereas the mobilities of ions are lower in melts, the diffusion coefficients are of the same order of magnitude as in aqueous solutions (i.e., about 10 cmVs). Thus, for melts the Nemst relation (4.6) is not applicable. This can be explained in terms of an appreciable contribntion of ion pairs to diffusional transport since these pairs are nncharged, they do not carry cnrrent, so that values of ionic mobility calculated from diffusion coefficients will be high. 

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