Cohesive energy defined

The most important quantity for understanding the trends in the formation of fullerene-like molecules is the cohesive energy, defined as the difference of the total molecular energy and the sum of the energies of the isolated atoms. As expected, the cohesive energy decreases considerably from Cso to Pbeo- The maximum HF (B3LYP) value of -15.160 a.u. (-18.503 a.u) corresponds to Ceo, and the minimum value -3.677 a.u. (-5.950 a.u.) corresponds to Pbeo- The other values lie in between and are relatively close to each other. 

Scatchard and Hildebrand defined the cohesive energy density coh-ii of a liquid 1 as the negative molar configurational energy divided by its liquid molar volume, V, ... 

The internal pressure is a differential quantity that measures some of the forces of interaction between solvent molecules. A related quantity, the cohesive energy density (ced), defined by Eq. (8-35), is an integral quantity that measures the total molecular cohesion per unit volume. - p... 

A useful way to approach these individual point defect energies is to define the energy per mole or cohesive energy of perfect material with respect to separated free atoms, Cmoi-We can then arbitrarily divide this between the atoms of type A and B so that ... 

Figure 3.4 shows a fair correlation between vo-2ot and the Hildebrand solubility parameter 8 (linear correlation coefficient = 0.930) which makes intuitive sense. The Hildebrand parameter, which is often used to characterize liquids, is defined as the square root of the cohesive energy density (Barton 1991), while vcr2o( can be viewed as reflecting how strongly a molecule interacts with others of the same kind (Murray et al. 1994). 

The cohesive energy coh of a substance in a condensed state is defined as the increase in internal energy AU per mole of substance if all the intermolecular forces are eliminated. 

Cohesive energies are defined as the difference between the total energy of a system and the sum of the energies of its components. If there is a rearrangement of the separate component densities when the components are brought together, this distortion must be taken into account. 

Figure 1. Viscosity T as a function of temperature. The reduced temperature t is defined as the ratio of thermal energy k T and the heat of vaporization, which is a measure of the fluid cohesive energy density. The subscripts on r indicate the melting point and boiling point, respectively. (Used with permission from Trans Tech Publ. Ltd. W. Kurz and D. J. Fisher, Fundamentals of Solidification, 4th ed., Trans Tech Publ Ltd., Switzerland, 1998.)...

We define the cohesive energy Ecoh (Johansson, Skriver ) as the difference between the energy of an assembly of free atoms in their ground state (see Table 1 of Chap. A) and the energy of the same assembly in the condensed phase (the solid at 0 °K), (this definition yields a positive number for Ecoii). It coincides with the enthalpy of sublimation AHj (see Chap. A) (which is usually extrapolated at room temperature). 

Secondary forces operate at longer distances (.25-50 nm) than covalent bonds. These secondary forces are much weaker than primary covalent bonds, but the forces are cumulative. Thus the cohesive energy of a polymer is equal to the summation of the cohesive energy density (CED) values for each mole of repeating unit ( < 2 kcal) in the chain. The CED of a liquid is defined as the energy of vaporization per unit volume, / E/V. 

Table 6.3 Contributions to the binding energy (in Ry per atom) of sodium, magnesium, and aluminium within the second order real-space representation, eqn (6.73), using Ashcroft empty-core pseudopotentials. L/gf is defined by eqn (6.75). The numbers in brackets correspond to the simple expression, eqn (6.77), for = 0) and to the experimental values of the binding energy and negative cohesive energy respectively.

In linear polymers, cohesion results from weak (compared with covalent bonds) intermolecular attractive forces (Van der Waals) of various types London, Debye, Keesom, and hydrogen bonding. In a first approach, they can be considered undistinguishable, and one can define cohesive energy as the whole energy of intermolecular interactions. For small molecules, cohesive energy is easy to determine from calorimetric measurements since... 

The solubility parameter is defined as the square root of the cohesive energy density. The most common presentation of the solubility parameter is in units of cal1/2cm 3/2. Here, the cohesive energy is expressed per unit volume. A more modem format that is found in some of the literature after 1990 utilizes SI units derived from cohesive pressures. It is possible to convert between the two scales with the following equations ... 

From the chemist s point of view, the cohesive energy of solids is their most important property. The cohesive energy (AEcxp) is defined as the energy required to dissociate one mole of solid M(s) into its constituent gas atoms M(g) ... 

Table III. Minus the total Si crystal valence electron energy per atom with relaxation energy and pseudopotential corrections included, along with the equilibrium lattice constant, bulk modulus, and cohesive energy calculated with four different exchange-correlation functionals (defined in the caption of Table I) are compared with experimental values. The experimental total energy is the sum of Acoh plus the four-fold ionization energy.

The theorem has the important implication that intramolecular interactions can be calculated by the methods of classical electrostatics if the electronic wave function (or charge distribution) is correctly known. The one instance where it can be applied immediately is in the calculation of cohesive energies in ionic crystals. Taking NaCl as an example, the assumed complete ionization that defines a (Na+Cl-) crystal, also defines the charge distribution and the correct cohesive energy is calculated directly by the Madelung procedure. 

---