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6 Molecular Systems
that emphasizes the connections between heat capacity and inelastic collisional
transitions between molecular internal energy levels characterized by quantum
numbers r and r . Such an interpretation arises from our knowledge, for an ideal
gas, for example, that the mechanism through which a new thermal equilibrium state
is established following a change of system temperature (via energy exchange with
the ‘surroundings’) is that of binary collisions between molecules or of collisions
between molecules and container walls. In particular, we shall see that this provides
an interesting and useful interpretation of the temperature dependence of C V ,int (T ).
The normal procedure in dealing with internal molecular states is to treat
diatomic molecules first, both because they represent the simplest molecules, and
because they represent an important special class of molecules with which we
deal on a frequent basis. Only when the diatomic molecular expressions are well
understood are the more general polyatomic molecules considered. We shall follow
tradition here, and do the same thing.
6.2 Diatomic Molecules
When we consider diatomic molecules we have to visualize the various degrees of
freedom possessed by such molecules. We can split the types of degrees of freedom
into four separate classes. In the first place we have three translational degrees of
freedom, as for the monatomic case, then we have molecular rotational degrees of
freedom (essentially the two end-over-end tumbling motions of the molecules), one
vibrational degree of freedom, and electronic degrees of freedom (similar to those
of monatomics, but often lying at lower energies). The latter three types of degree
of freedom have so far been lumped together as the ‘internal’ degrees of freedom,
as opposed to the ‘translational’ degrees of freedom.
6.2.1 Setting the Stage
In order to treat the internal degrees of freedom we shall make some simplifying
approximations, but ones that are nonetheless very good approximations from the
point of view of thermodynamic calculations. Some of these approximations would
not be considered good ones to make from the point of view of spectroscopy,
however: we must always bear in mind the applications that we wish to consider
prior to introducing simplifying approximations.
The first approximation that we shall make is to assume that the electronic
and nuclear motions are decoupled. In its simplest terms this assumption means
that the motions of the electrons in the molecule are unaffected by the motions
of the much heavier, and slower, nuclei, so that we can in principle solve the
Schrödinger equation for the electronic motion in the Coulomb field of fixed nuclei.
This approximation is based upon the fact that electrons are about 2000 times less
6 Molecular Systems
that emphasizes the connections between heat capacity and inelastic collisional
transitions between molecular internal energy levels characterized by quantum
numbers r and r . Such an interpretation arises from our knowledge, for an ideal
gas, for example, that the mechanism through which a new thermal equilibrium state
is established following a change of system temperature (via energy exchange with
the ‘surroundings’) is that of binary collisions between molecules or of collisions
between molecules and container walls. In particular, we shall see that this provides
an interesting and useful interpretation of the temperature dependence of C V ,int (T ).
The normal procedure in dealing with internal molecular states is to treat
diatomic molecules first, both because they represent the simplest molecules, and
because they represent an important special class of molecules with which we
deal on a frequent basis. Only when the diatomic molecular expressions are well
understood are the more general polyatomic molecules considered. We shall follow
tradition here, and do the same thing.
6.2 Diatomic Molecules
When we consider diatomic molecules we have to visualize the various degrees of
freedom possessed by such molecules. We can split the types of degrees of freedom
into four separate classes. In the first place we have three translational degrees of
freedom, as for the monatomic case, then we have molecular rotational degrees of
freedom (essentially the two end-over-end tumbling motions of the molecules), one
vibrational degree of freedom, and electronic degrees of freedom (similar to those
of monatomics, but often lying at lower energies). The latter three types of degree
of freedom have so far been lumped together as the ‘internal’ degrees of freedom,
as opposed to the ‘translational’ degrees of freedom.
6.2.1 Setting the Stage
In order to treat the internal degrees of freedom we shall make some simplifying
approximations, but ones that are nonetheless very good approximations from the
point of view of thermodynamic calculations. Some of these approximations would
not be considered good ones to make from the point of view of spectroscopy,
however: we must always bear in mind the applications that we wish to consider
prior to introducing simplifying approximations.
The first approximation that we shall make is to assume that the electronic
and nuclear motions are decoupled. In its simplest terms this assumption means
that the motions of the electrons in the molecule are unaffected by the motions
of the much heavier, and slower, nuclei, so that we can in principle solve the
Schrödinger equation for the electronic motion in the Coulomb field of fixed nuclei.
This approximation is based upon the fact that electrons are about 2000 times less