Volume dependence similarity principles

Further, if the wave function depends also on the electron spins, spin variables over all electrons should also be integrated we will see this below, in the calculation of exchange hole. The expression in the curly brackets above is exactly the XC hole PxCM(r, r ) defined in Equation 7.17. A comparison with Equation 7.19a shows that adding the hole to the density is similar to subtracting the density of one electron p(r )/N from it. The hole thus represents a deficit of one electron from the density. This is easily verified by integrating p tM(V, r ) over the volume dr, which gives a value of — 1. However, the structure of the hole is not simple and this is because of the motion of different electrons correlated due to the Pauli exclusion principle and the Coulomb interaction between them. Finally we note that the product p(r)p cM(r, r ) is symmetric with respect to an exchange in the variables... 

The fact that matrix elements of the fundamental band are dependent on the rotational quantum numbers j, f cannot be ignored. As a consequence, many more B coefficients must now be evaluated which, in principle, poses no special problem. The volume of data needed renders the task awkward. Molecular spectroscopists have for generations coped with similar problems which were solved with the so-called Dunham expansion in terms of j(j+1). Specifically, for our purpose, the lowest-order expansion for the fundamental band looks like [63]... 

Gases dissolve in liquids to an extent dependent on the similarity of the gas molecules and the solvent molecules. Polar gas molecules dissolve to a greater extent in polar solvents than nonpolar molecules do. Pressure also affects gas solubility. At higher pressure more gas dissolves in a given volume of liquid than at lower pressure. When the pressure is lowered, gas will be evolved from a gas-in-Uquid solution. The behavior of a carbonated beverage when the cap is removed is a common illustration of this principle. 

Application of Eq. (20.4-12) to highly supercritical gases is somewhat ambiguous since the effective molecular volume of sorbed gases under these conditions is not estimated easily. A similar problem exists in a priori estimates of partial molar volumes of supercritical components even in low-molecular-weight iiqui. The principle on which Eq. (20.4-12) is ba remains valid, however, and while the total amount of unrelaxed volume may be available for a penetrant, the magnitude of Cj, depends strongly on how condensable the penetrant is, since this factor determines the relative efficiency with which the component can use the available volume. 

Hence the volume of a mixture of heterogenous molecules interacting by the vdW mechanism exceeds the additive value, and according to the Le Chatelier principle such mixture under high pressure will be separated. It follows that the diamond cluster size depends on the separation extent of components of the detonation cloud. In this context, it seemed reasonable to perform a detonation synthesis of c-BN under similar conditions (in a large chamber). No attempt in this direction has been... 

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