Alkali electron affinities, calculation

After cocondensation of SiO (1226 cm 1) with alkali metal atoms like Na or K, new bands are detected at 1014 cm 1 (Na) or 1025 cm 1 (K). They can only be attributed to an SiO" anion because of the red shift of the SiO stretching vibration (with respect to that of uncoordinated SiO) and because of different isotopic splittings (28/29/30SiO, Si16/180) [21]. The formation of an ionic species M+(SiO) (M = Na, K) is in line with the results of quantum chemical calculations for the SiO anion (SiO d = 1.49 A, SiO" d = 1.55 A, "electron affinity" SiO + e + 1.06 eV —> SiO") [20]. Taking simple Coulomb interactions into consideration this species is very likely to have a strongly bent structure. The same situation occurs in gaseous NaCN (<(NaNC) = 81.2°) [22],... 

It is tempting to relate the thermodynamics of electron-transfer between metal atoms or ions and organic substrates directly to the relevant ionization potentials and electron affinities. These quantities certainly play a role in ET-thermo-dynamics but the dominant factor in inner sphere processes in which the product of electron transfer is an ion pair is the electrostatic interaction between the product ions. Model calculations on the reduction of ethylene by alkali metal atoms, for instance [69], showed that the energy difference between the M C2H4 ground state and the electron-transfer state can be... 

A few years ago experimental values were available for Q, S, /, and Z), but not for E the procedure adopted in testing the equation was to use the equation with calculated values of Uq (Equation 13-5) to find E, and as a test of the method to examine the constancy of E for a series of alkali halogenides containing the same halogen. The values obtained in this way were found to be constant to within about 3 kcal/mole. However, later experimental determinations of the values of the electron affinities of the halogen atoms by direct methods have shown that Equation 13-5 for the crystal energy is in general reliable only to about 2 percent. 

Br- (g). The electron affinity of Br (g) is calculable by the method of lattice energies. Selecting the crystal RbBr, because Rb+ and Br have exactly the same nuclear structure, and taking the exponent of the repulsive term to be 10, we have computed, for the reaction, RbBr (c) = Rb+ (g)+Br g), Dz= —151.2 whence the electron affinity of Br (g) becomes 87.9. Using the lattice energies of the alkali bromides as calculated by Sherman,1 we have computed the values 89.6, 85.6, 84.6, 83.6, and 89.6, respectively. Butkow,1 from the spectra of gaseous TIBr, deduced the value 86.5. From data on the absorption spectra of the alkali halides, Lederle1 obtained the value 82. See also Lennard-Jones.2... 

The lattice enthalpy U at 298.20 K is obtainable by use of the Born—Haber cycle or from theoretical calculations, and q is generally known from experiment. Data used for the derivation of the heat of hydration of pairs of alkali and halide ions using the Born—Haber procedure to obtain lattice enthalpies are shown in Table 3. The various thermochemical values at 298.2° K [standard heat of formation of the crystalline alkali halides AHf°, heat of atomization of halogens D, heat of atomization of alkali metals L, enthalpies of solution (infinite dilution) of the crystalline alkali halides q] were taken from the compilations of Rossini et al. (28) and of Pitzer and Brewer (29), with the exception of values of AHf° for LiF and NaF and q for LiF (31, 32, 33). The ionization potentials of the alkali metal atoms I were taken from Moore (34) and the electron affinities of the halogen atoms E are the results of Berry and Reimann (35)4. 

The electron affinities of elements (Chap, 7) that form negative ions may be calculated by considering the formations of compounds containing such negative ions. The formation of such a compound from the elements (the heat of such a reaction being directly measurable) may be broken down into a series of simpler steps. The treatment is again called a Born-Haber cycle and is analogous to the treatment of the conversion of an alkali metal to its hydrated ion (discussed in Chap. 6). Consider the formation of sodium chloride from the elements ... 

This equation permits the calculation of the lattice energy if we know F, the electron affinity of the halogen atom, S, the heat of sublimation of the alkali metal, /, the ionization potential of the metal and Z), the dissociation energy of the molecular halogen. These quantities are known, but to different orders of accuracy, and furthermore, the values should all refer to the same standard temperature, either absolute zero or room temperature, a condition which is not always fulfilled. However, the agreement between the calculated and observed values is sufficiently good to indicate that the theory developed for the lattice energy on the basis of ionic interaction is basically correct. 

It is thus evident from the structure and the electrostatic field calculations that the order of preference for strong cations, such as the alkali and alkaline-earth cations, is Si> Sn> Sm This also suggests that bivalent ions will replace univalent ions at the most preferred sites and that the higher the valence of a cation at a surface site the higher will be both the electron affinity of the cation and the field near the cation. And the stronger the field, the greater will be the polarization of adsorbed molecules and the tendency for reduction of the cation. Some of these questions relate more naturally to the electrostatic potential at a cation site than to the electrostatic field at points near the site. Nevertheless, we have so far dealt with the field, because it is the more important by far for our concept of the carboniogenic activity of the surface cations in catalysis. 

Lattice energies, alkali metal salt values, amides and, 196 azides and, 198-199 bifluorides and, 199 borofluorides and, 203 borohydrides and, 197 chalcogenides and, 192,193 cyanates and, 199-200 cyanides and, 196-197 halides and, 189, 190 hydrides and, 189, 191, 192 hydrosulfides and, 195-196 hydroxides and, 192,194, 195 nitrates and, 201 superoxides and, 197-198 thiocyanates and, 200 alkaline earth salt values, acetylides and, 198 carbonates and, 202-203 chalcogenides and, 192, 193 imides and, 196 peroxides and, 198 calculation uses, absolute enthalpies and, 206 electron affinity determination and, 203-204... 

Popkie, H. E., and Kaufman, Joyce J., "Molecular Calculations with the MODPOT, VRDDO and MODPOT/VRDDO Procedures. III. M0DP0T/SCF + Cl Calculations to Determine Electron Affinities of Alkali Metal Atoms," Chem. Phys. Letts. C1977), 7, 55-58. 

A complete review of the theoretical calculations for the electron affinities of atoms is beyond the scope of this book. The quantum mechanically calculated electron affinities of the first and second row elements—the alkali metals, Ca, Ba, and Sr—support experimental results within their mutual uncertainties. 5 meV has been determined to be the best precision and accuracy of theoretical methods for atoms [13]. For example, the calculated values for Li, Na, K, Rb, and Cs agree with the experimental values to within 5 meV. Thus, the AEa of Fr is 0.491(5) eV calculated theoretically. By the same method, the predicted value for eka-francium (element 119) is 0.663(5) eV [41]. The predicted Ea for Ra is also larger than the experimental value for Ba, 0.145 eV. 

Calculated electron affinities are collected and compared with experiment in Table 16. The power of the intermediate Hamiltonian method is demonstrated by the excellent agreement with experiment. The Fock space values start well for Na, but errors increase to 5%, 7% and 9% for the heavier K, Rb and Cs, respectively. IHFSCC values, on the other hand, are all within 5 meV or 1% of experiment. It should be noted that the FSCC function of the anions includes only one determinant in the P space, whereas the IHFSCC P space includes several thousand. The importance of these additional determinants (and of excitations from them to Q) increases with the size of the alkali anion. 

In these equations, AG is the energy of formation of the indicated species, AGfat is the crystal lattice energy, / is the ionisation potential of the metal and A is the electron affinity of the halide. In sect. 2.11.2 the calculation of AG at and Ai/i t (at 298.15 K) is discussed and in Appendix 2.11.1 values are given for the alkali metal halides and a few other selected salts. 

A major problem associated with the use of 2.11.6 has been the lack of accurate electron affinities. However, recent measurements of A for the halides were made with great precision by Berry and Reimann by u.v. absorption spectra of alkali halide vapours heated by shock waves. With accurate A values, eqns. 2.11.6 probably represent the best method for the evaluation of A/ffit and AGjat since the heats and free energies of formation are known for most of the common salts. " There are several cases for which the thermodynamic data required for the calculation of AGfat are incomplete, and providing A i t is known, the former quantity can be obtained from the relation... 

There are several methods for determining ionic radii from physical characteristics of atoms and crystals. Thus, Fumi and Tosi [209] derived ionic radii (similar to the bonded ones) for alkali halides, using the Born model of crystal lattice energy with experimental interatomic distances, compressibilities and polarizabilities. Rossein-sky [210] calculated ionic radii from ionization potentials and electron affinities of atoms, his results were close to Pauling s. Important conclusions can also be drawn from the behaviour of solids under pressure. Considering metal as an assembly of cations immersed into electron gas, its compressibility at extremely high pressures... 

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