Energy attachment

Docherty, R., Clydesdale, G., Roberts, K.J. and Bennema, P., 1991. Application of the Bravais-Freidel-Donnay-Harker attachment energy and Ising models to predicting and understanding the morphology of molecular crystals. Journal of Physics D Applied Physics, 24, 89-99. 

V.I. Vedeneev, L.V. Gurvich, V.N. Kondratyev, et al.. Handbook of Energies of Breaking of Chemical Bonds. Ionization Potential and Electron Attachment Energies, Kondratyev,V.N. (ed.), USSR Acad, of Sci. Publ., Moscow, 1962 (in Russian). 

Figure 1 shows the electron attachment energies (AE) and ionization potentials (IP) of silyl substituted 7t-systems and related compounds [4], AE can be correlated with the energy level of the LUMO (lowest unoccupied molecular orbital) and IP can be correlated with the energy level of the HOMO (highest occupied molecular orbital). For a-substituted 7t-systems, the introduction of a silyl group produces a decrease in the tc -(LUMO) level. This effect is attributed to the interaction between a low-lying silicon-based unoccupied orbital such as the empty d orbital of silicon and the it orbital (d -p interaction) as shown in Fig. 2. Recent investigations on these systems, however, indicate that d orbitals on silicon are not necessarily required for interpreting this effect a-effects of SiR3 can also be explained by the interaction between Si-R a orbitals and the 7r-system.

SiM 3 Fig. 1. Correlation diagram giving electron attachment energies (AE) and ionization potentials (IP) of a-,—SiMe3 and jS-silyl substituted ethylenes... 

A number of investigators (66. 67 have recently employed the critical Ising temperature (transition temperature from smooth to rough interface) to determine the relative importance of F faces. In general, results obtained by this method are quite similar to those obtained from attachment energy calculations. 

A major weakness in the calculations described above is that they can only be used to represent vapor grown crystals. In crystals grown from solution, the solvent can greatly influence the crystal habit as can small amounts of impurities. Several investigators (68. 69 accounted for discrepancies between observed crystal habit and those obtained using attachment energies by assuming preferential solvent (or impurity) adsorption on crystal faces. 

The work discussed in the previous paragraphs provides the framework for the prediction of crystal habit from internal structure. The challenge is to add realistic methods for the calculation of solvent and impurities effects on the attachment energies (hence the crystal habits) to allow this method to provide prediction of crystal habit. Initial attempts of including solvent effects have been recently described (71. 721. The combination of prediction of crystal habit from attachment energies (including solvent and impurity effects) and the development of tailor made additives (based on structural properties) hold promise that practical routine control and prediction of crystal habit in realistic industrial situations could eventually become a reality. 

The ciystal habit of sucrose and adipic add crystals were calculated from their intern structure and from the attachment energies of the various crystal faces. As a first attempt to indude the role of the solvent on the crystal habit, the solvent accessible areas of the faces of sucrose and adipic add and were calculated for spherical solvent probes of difierent sizes. In the sucrose system the results show that this type of calculation can qualitatively account for differences in solvent (water) adsorption hence fast growing and slow growing faces. In the adipic add system results show the presence of solvent sized receptacles that might enhance solvent interadions on various fares. The quantitative use of this type of data in crystal shape calculations could prove to be a reasonable method for incorporation of solvent effeds on calculated crystal shapes. 

Even though still in a prelinainaiy stage, it is hoped that this approach will result in a better solvent - effect corrector to the attachment energy calculations (IS) than the broken hydrogen bond model and a better fit of the predicted sucrose crystal habits with the observed ones. It is already clear that the present model can, at least qualitatively, distinguish between the fast growing ri t pole of the crystal and its slow left pole. 

There are two downsides to the PBC theory the first is that a certain arbitrariness is unavoidable in finding PBCs in real crystal structures, and the second is that PBC analysis is difficult in complicated structures. In answer to the first criticism, Hartman [3] calculated the attachment energy, and correlated this to Jackson s... 

The lattice energy at a half-crystal position (kink site) is defined as the attachment energy and the energy released in forming a slice containing more than two PBCs is denoted by E j These are related to the lattice energy as follows ... 

This section summarizes the variation, across the periods and down the groups of the Periodic Table, of (i) the ionization energies, (ii) the electron attachment energies (electron affinities), (iii) the atomic sizes and (iv) the electronegativity coefficients of the elements. 

Figure 1.4 The first ionization 1.6.2 Variations in Electron Attachment Energies...

The electron attachment energy or electron affinity is defined as the change in internal energy (i.e. A U) that occurs when one mole of gaseous atoms of an element are converted by electron attachment to give one mole of gaseous negative ions ... 

The first electron attachment energies of the first 36 elements are plotted in Figure 1.5 and show the values for H and He followed by a characteristic pattern, the second repetition of which is split by the values for the 10 transition elements. The value for hydrogen is -72.8 kJ mol, which is very different from the Is orbital energy of -1312 kJ mol-1 because of the interelectronic repulsion term amounting to -72.8 -... 

Figure 1.5 The electron attachment energies of the first 36 elements...

The trends in first ionization energies, first electron attachment energies, atomic sizes and electronegativity coefficients of the elements across the groups and down the periods of the periodic classification. 

What general trends are noticeable across the Periodic Table in the values of (a) the first ionization energies, (b) the first electron attachment energies, and (c) the covalent radii of the elements ... 

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