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16 where ti and Sri are the components of 5 and of small deviations from 50, respectively. A close examination of this expression will show a whole world of applications to energy calculations of mole- cular properties. Molecular and Crystal Energies and the CorreSponding Thermodyanic Functions Vtotal(30), the first term in the Taylor expansion (Equation (18)), is the molecular energy at equilibrium. The corresponding experimental, meaSurable property is the heat of atomization (or ' some related functions such as the heat of formation,or'the heat of combustion) of the system. In comparing the two, we have to take into consideration their differences. The heat (or enthalpy) of atomization is a thermodynamic function related to thermal agitation and temperature, while Vtotal(go) represents the energy of a single microscopically defined state.. The heat of atomization's major component is the quantum mechanical energy of formation (or dis— sociation) of the chemical bonds, which is represented by Morse potentials for the various types of bonds (Equation (13)) as well as by other terms of intramolecular interactions included in Vtotal. It includes, however, other contributions which must be taken into account. First, there is the zero—point energy, which is the vib- rational energy of the lowest vibrational quantum state corresponding to zero absolute temperature. Then there are the energies of mole- cular translations, rotations and vibrations in the gas phase, or the packing energy of the crystal lattice and the molecular and lattice vibrations in the solid phase. These quantities are functions of thermodynamic variables such as temperature. They can be calculated from Vtotal, as we shall see below. In many instances we are interested in the changes in energy accompanying conformational or structural changes in the molecular system. Examples are the cis—trans difference of the peptide bond, the chairuhalf—chair-boat conformational transitions of sugar rings, or the trans—gauche transition in alkanes. In such cases, the zero~ point energy and the other thermodynamic contributions may cancel out to a good approximation, and the correspondence to experiment is then Simpler. When intermolecular interactions are included in Vtotal, it is possible to consider Vtot31Ct) as representing macroscopic condensed phases, i.e. solids, liquids and solutions.A very useful and simple example is the lattice energy of crystals, or the sublimation energy, i.e. the energy of crystal—to—gas transition. For rigid molecules, which maintain the same structure in gas and solid phases, the sublimation process involves work against inter~molecular forces only. The intramolecular energy and the enthalpy of molecular

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