136
4 The Treatment of Few-Body Reactions
in which Q trans (T ) and Q rot (T ) are the translational and rotational partition functions of the system while the correlation function C f f is defined as C f f (t) =
R f f (t)C f f (0) that is in terms of a static factor C f f (0) (that can be evaluated as
a partition function in the asymptotic region then mapped into the interaction region)
and a dynamic one R f f (t) (that can be evaluated by replacing the exact time evolution propagator with the Herman and Kluk (HK) one). In order to evaluate C f f (t)
therefore one can define a coordinate x along which locates a surface s(x) separating
the reactant configurations from the product ones.
4.4 Basic Features of Atom–Diatom Reactions
4.4.1 Energy Dependence of the Detailed Probabilities
As already mentioned, the possibility of carrying out accurate quantum calculations
of the S matrix elements of the atom–diatom reactions provides us with a picture of the
corresponding elementary processes that can hardly be paralleled by the experiment
in terms of details. The key feature of such calculations is that they can be extended
to conditions in which either the experiment cannot be performed or its outcomes are
mixed with those of other intervening processes. Moreover, the computational study
has the advantage of making explicit all the relationships and interactions between
the intervening particles and the produced results allowing so far a rationalization of
the computed outcomes.
In order to illustrate some important features of the atom–diatom reactions, we
consider here the outcomes of reduced dimensionality calculations performed on a
few emblematic cases of this type of systems. For this purpose, we consider here
first the N + N 2 (nitrogen atom nitrogen molecule) system. Typically, nitrogen is
quite inactive at normal conditions and scarce experimental information is available
about related processes. However, the N + N 2 (v, j) → N + N 2 (v
, j
) reaction for
a large variety of vibrational and rotational numbers are the dominant processes in
the modeling of reentering spacecrafts and some plasmas. In these processes, the
temperature is large and involves so far reactive transitions from/to a large number
of vibrotational states and collision energies (the corresponding temperatures around
reentering spacecrafts can be, for example, as high as several ten thousand degrees).
Electronic structure calculations of the N 3 system have been performed in the past
and a potential energy surface of the LEPS type has been fitted to the calculated
points [67]. As a matter of fact, the contours of the LEPS plotted in Fig. 4.1 for the
collinear geometry ( = 180
◦ ) show that the reaction channel is indeed symmetric
(entrance and exit have the same shape and contours) and that the barrier separating
the entrance and exit channel is right in the middle (more recent calculations and
fitting show that the barrier hosts on its top a little well). The dependence of the height
of the MEP on the angle expressing its evolution from the reactant to the product
channel (whose maximum is the barrier to reaction) for different values of for
4 The Treatment of Few-Body Reactions
in which Q trans (T ) and Q rot (T ) are the translational and rotational partition functions of the system while the correlation function C f f is defined as C f f (t) =
R f f (t)C f f (0) that is in terms of a static factor C f f (0) (that can be evaluated as
a partition function in the asymptotic region then mapped into the interaction region)
and a dynamic one R f f (t) (that can be evaluated by replacing the exact time evolution propagator with the Herman and Kluk (HK) one). In order to evaluate C f f (t)
therefore one can define a coordinate x along which locates a surface s(x) separating
the reactant configurations from the product ones.
4.4 Basic Features of Atom–Diatom Reactions
4.4.1 Energy Dependence of the Detailed Probabilities
As already mentioned, the possibility of carrying out accurate quantum calculations
of the S matrix elements of the atom–diatom reactions provides us with a picture of the
corresponding elementary processes that can hardly be paralleled by the experiment
in terms of details. The key feature of such calculations is that they can be extended
to conditions in which either the experiment cannot be performed or its outcomes are
mixed with those of other intervening processes. Moreover, the computational study
has the advantage of making explicit all the relationships and interactions between
the intervening particles and the produced results allowing so far a rationalization of
the computed outcomes.
In order to illustrate some important features of the atom–diatom reactions, we
consider here the outcomes of reduced dimensionality calculations performed on a
few emblematic cases of this type of systems. For this purpose, we consider here
first the N + N 2 (nitrogen atom nitrogen molecule) system. Typically, nitrogen is
quite inactive at normal conditions and scarce experimental information is available
about related processes. However, the N + N 2 (v, j) → N + N 2 (v
, j
) reaction for
a large variety of vibrational and rotational numbers are the dominant processes in
the modeling of reentering spacecrafts and some plasmas. In these processes, the
temperature is large and involves so far reactive transitions from/to a large number
of vibrotational states and collision energies (the corresponding temperatures around
reentering spacecrafts can be, for example, as high as several ten thousand degrees).
Electronic structure calculations of the N 3 system have been performed in the past
and a potential energy surface of the LEPS type has been fitted to the calculated
points [67]. As a matter of fact, the contours of the LEPS plotted in Fig. 4.1 for the
collinear geometry ( = 180
◦ ) show that the reaction channel is indeed symmetric
(entrance and exit have the same shape and contours) and that the barrier separating
the entrance and exit channel is right in the middle (more recent calculations and
fitting show that the barrier hosts on its top a little well). The dependence of the height
of the MEP on the angle expressing its evolution from the reactant to the product
channel (whose maximum is the barrier to reaction) for different values of for