(Fig. 5.2b). Nevertheless, the interaction of translational and rotational degrees of
freedom can often be neglected. These models give the correct dependencies of the
rate of V $ T processes on molecular constants and collision conditions. To some
extent, this is because that all theories of V $ T processes are semi-empirical since
the exact interaction potentials of even an atom and a diatomic molecule are
unknown. And by fitting the parameters to achieve the coincidence of the calculation results with experimental data, it is often possible to eliminate these errors
implicitly. Usually, but not always, and then you must take into account other types
of interaction, namely, V $ R, V $ V, if molecules collide, or nonadiabatic processes occur during collisions (see below).
Qualitatively, we already considered the problem of the V $ T process when
discussing the semiclassical description of the collinear collision of an atom and a
diatomic particle by moving an image point on the PES (see Sect. 3.5 and Fig. 3.11).
The solution of this problem in this way is quite difficult since it is necessary to know
the PES; besides, it can only be solved numerically. There are simpler approaches.
The vibrational and rotational energies are quantized, and it is not always
possible to use the semiclassical or adiabatic approximations when considering their
relaxation (excitation). Here, as in some other cases, the so-called adiabatic
principle can be applied, according to which the process is adiabatic, i.e., a process
without changing the quantum states of particles in a collision process, if the rate of
change of the perturbing action of the collision is negligible compared to the rate
of periodic quantized motion corresponding to internal degrees of freedom, i.e.,
1=s ( x
ð5:3:1aÞ
or the collision time leading to a change of periodic motion is much longer than the
period of the latter. Here s is the time of the ‘productive’ collision, x is the angular
frequency of the periodic motion. Otherwise, this principle can be expressed as
follows:
DE ) h s;
ð5:3:1bÞ
since DE = ħx.
If we consider T-V processes, then (5.3.1b) means that the probability of
transformation of the translational energy 1/s (s
−1 ) is much less than the ‘transition
frequency’ corresponding to the internal energy DE/ħx (s
−1 ), and far from every
collision, this process takes place. If the quantized energy is high, for example,
when we are dealing with vibrational excitation, then the classical approach for
describing a change in a quantized state is not applicable, but the probability of this
change in a single collision is small, (5.3.1a, 5.3.1b) are valid; the adiabatic principle is also true with them. This principle is also applicable when considering other
energy transfer processes. The above considerations relate to the transfer of the
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5 Energy Transfer in Collisions
freedom can often be neglected. These models give the correct dependencies of the
rate of V $ T processes on molecular constants and collision conditions. To some
extent, this is because that all theories of V $ T processes are semi-empirical since
the exact interaction potentials of even an atom and a diatomic molecule are
unknown. And by fitting the parameters to achieve the coincidence of the calculation results with experimental data, it is often possible to eliminate these errors
implicitly. Usually, but not always, and then you must take into account other types
of interaction, namely, V $ R, V $ V, if molecules collide, or nonadiabatic processes occur during collisions (see below).
Qualitatively, we already considered the problem of the V $ T process when
discussing the semiclassical description of the collinear collision of an atom and a
diatomic particle by moving an image point on the PES (see Sect. 3.5 and Fig. 3.11).
The solution of this problem in this way is quite difficult since it is necessary to know
the PES; besides, it can only be solved numerically. There are simpler approaches.
The vibrational and rotational energies are quantized, and it is not always
possible to use the semiclassical or adiabatic approximations when considering their
relaxation (excitation). Here, as in some other cases, the so-called adiabatic
principle can be applied, according to which the process is adiabatic, i.e., a process
without changing the quantum states of particles in a collision process, if the rate of
change of the perturbing action of the collision is negligible compared to the rate
of periodic quantized motion corresponding to internal degrees of freedom, i.e.,
1=s ( x
ð5:3:1aÞ
or the collision time leading to a change of periodic motion is much longer than the
period of the latter. Here s is the time of the ‘productive’ collision, x is the angular
frequency of the periodic motion. Otherwise, this principle can be expressed as
follows:
DE ) h s;
ð5:3:1bÞ
since DE = ħx.
If we consider T-V processes, then (5.3.1b) means that the probability of
transformation of the translational energy 1/s (s
−1 ) is much less than the ‘transition
frequency’ corresponding to the internal energy DE/ħx (s
−1 ), and far from every
collision, this process takes place. If the quantized energy is high, for example,
when we are dealing with vibrational excitation, then the classical approach for
describing a change in a quantized state is not applicable, but the probability of this
change in a single collision is small, (5.3.1a, 5.3.1b) are valid; the adiabatic principle is also true with them. This principle is also applicable when considering other
energy transfer processes. The above considerations relate to the transfer of the
158
5 Energy Transfer in Collisions