Total intermolecular potential energy

Classical statistical mechanics views fluids (i.e., gases and liquids) as a collection of N mutually interacting molecules confined to a volume V at a temperature T and specifies the system by a total intermolecular potential energy U, U (xi,X2,..., xn) = U( 1,. , N), where Xi stands for a set of generalized coordinates of molecule i. Not only for convenience and simplicity, but as an utmost necessity if a tractable theory is to be ultimately applied, the assumption of pairwise additivity is made at this stage, and U is simplified to... 

This is valid for T,V,N constant and under the assumption of a cancellation of contributions to the free energy other than U. U(N NJ stands for the total intermolecular potential energy of the system, and U N) for that of the pure solvent. The integration is carried out within the phase space accessible to solvent configurations. The denominator is simply equal to... 

The third basic approximation usually introduced is that the total intermolecular potential energy V(r, of) is simply the sum of the intermolecular potentials for isolated pairs ij of molecules, i.e.. 

TABLE 10.2 Contributions from attractive forces to the total intermolecular potential energy of selected molecules, calculated at the equilibrium center of mass separation. 

Based on the following parameters, estimate in kj mol the total intermolecular potential energy for attraction between freely rotating HI and CO at a separation of 4.0 A and a temperature of 298 K ... 

PPE, in J/mole, as in equation 8.10, is then the energy required for the creation of a mole of holes within the crystal, each at infinite distance from the others a rather impractical concept. Consider instead the real process of condensing one mole of gas-phase molecules into one mole of molecules in the crystal. The total intermolecular potential energy (PE) involved in this process is the sum of the interactions of all molecules to all other molecules ... 

As usual, the relevant quantities are expressed in terms of the intermolecular potential energy of the whole system. Accordingly, we begin with a discussion of the total energy of a system composed of molecules and ions. 

Here the number of molecules in the th cluster is n the total number of molecules N, and the number of ways of allocating N molecules to a given partition n,. U, is the cluster formation energy of the cluster j, which consists of n, molecules U, is the sum of each intermolecular potential. S( n, ) is the allocation entropy of partition [21]. 

The L (R) matrix is chosen such that the matrix L (R)TF L (R) = Q (R) is diagonal with elements iv. The eigenvectors of F are arranged as columns in the L (R) matrix. It should also be noticed that V B sol(S (R), R) can no longer be written as a sum of an intramolecular (gas-phase potential) and an intermolecular part as in Eq. (10.18), because the harmonic expansion of the potential around the saddle point is based on the total potential energy surface and not just on the intramolecular part. By combining Eqs (10.19), (10.21), and (10.23) we see that the absolute position coordinates of the atoms in the activated complex around the saddle point of the total potential energy surface can be written as... 

All of the energy contributions described above play a role in the intra-and intermolecular interactions which determine the most stable conformations of crystals of small molecules. If the parameters of the various energy contributions are regarded as unknowns, to be determined by the requirement that the total potential energy be a minimum at the known equilibrium conformation of the crystal, then it should be possible to obtain refined energy functions for use in conformational energy calculations. 

The magnitudes of the three attractive components of the intermolecular energy per mole of gas of some simple molecules are compared in Table 4.4.2, along with the bond energy of the polyatomic species and the enthalpy of sublimation (AH°). The calculation is based on the assumption that the molecules interact in pairs at a separation 8 where the total potential energy U(8) = 0. 

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