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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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