complicated Lissajous figures (see dot-dash curve on Fig. 3.12). This motion is a
superposition of the symmetric and antisymmetric vibration with different amplitudes and phases. One vibrational mode, one normal oscillation cannot exist. The
anharmonicity of vibrations leads to their mixing.
Let us now try to describe the dissociation of a triatomic molecule using the
image point motion. Suppose a symmetric valence oscillation takes place (motion
along a bisector). In that case, as the distance r OC decreases, the point climbs the
steep slope up to infinity, and when it increases, it ‘crawls’ onto a plateau corresponding to dissociation on O(
3 P) + C(
3
P) + O(
3 P). The author does not know of a
single case when a similar process would have been discovered experimentally.
And the reason is that ‘pure’ symmetric valent oscillations at amplitudes close to
those required for dissociation do not exist. The image point must ‘fall’ into one of
the valleys corresponding to dissociation to O(
1 D) + CO(X
1 R
+
).
Looking at the PES, we must conclude that in the process of ‘pure’ antisymmetric vibrations, dissociation is also impossible, since the image point ‘climbs
onto the wall’. But we can also see that antisymmetric stretching vibrations will
pass into the superposition of oscillations mentioned earlier due to anharmonicity,
and if the energy is large enough, the image point will fall into one of the valleys
along a complex trajectory. The complexity of the trajectory among other things
means that:
– the CO(X
1 R
+
) molecule, the product of the dissociation of CO 2 (ð b
X
1 R
þ
g Þ) must
be vibrationally excited,
– before dissociation, the molecule will make a large number of vibrations.
The author has mentioned in Sects. 2.1 and 2.4.1 that the lifetime of a triatomic
molecule with excitation energy close to the dissociation energy is approximately
equal to the time of 10
3 vibrations. Now we have understood the mechanism of this
phenomenon on the fingers.
And how can we describe the reaction A + BC ! AB + C in terms of the
motion of an image point along the PES. This reaction can be seen on the example
of the reaction O(
1 D) + CO(X
1 R
+
) ! OC(X
1 R
+
) + O(
1 D). Let us accept for definiteness that the horizontal valley (d) corresponds to the products
18 O(
1 D) + C
16
O
(X), and the valley c to
18 OC(X) +
16 O(
1 D), i.e., we describe isotopic exchange in
the CO 2 molecule. It is clear that if the collision of
18
O(
1 D) with the C
16 O(X,v X = 0)
molecule occurs, and the kinetic energy of the relative motion of O and CO is close
to 0, for example, E = 0.03 eV, this point will enter d valley along its bottom.
Then, falling into the wells, it will dangle along it for a long time (various vibrational modes with redistribution of excitation energy will be excited), and finally,
fall out or back, or to valley c, since its height relative to the bottom of the pit is
approximately the same. Apparently, at zero energy
18 O and C
16 O(X, 0), the exit
from the well to the valley is possible only when the velocity vector is strictly
parallel to the axis of the valley, i.e., all vibrational energy is focused on one of the
O À C À O bonds. This is a somewhat rare event, and, therefore, the lifetime of
such a complex has to be quite long. However, the decay of the CO 2 molecule will
66
3 Theory of Elementary Processes
superposition of the symmetric and antisymmetric vibration with different amplitudes and phases. One vibrational mode, one normal oscillation cannot exist. The
anharmonicity of vibrations leads to their mixing.
Let us now try to describe the dissociation of a triatomic molecule using the
image point motion. Suppose a symmetric valence oscillation takes place (motion
along a bisector). In that case, as the distance r OC decreases, the point climbs the
steep slope up to infinity, and when it increases, it ‘crawls’ onto a plateau corresponding to dissociation on O(
3 P) + C(
3
P) + O(
3 P). The author does not know of a
single case when a similar process would have been discovered experimentally.
And the reason is that ‘pure’ symmetric valent oscillations at amplitudes close to
those required for dissociation do not exist. The image point must ‘fall’ into one of
the valleys corresponding to dissociation to O(
1 D) + CO(X
1 R
+
).
Looking at the PES, we must conclude that in the process of ‘pure’ antisymmetric vibrations, dissociation is also impossible, since the image point ‘climbs
onto the wall’. But we can also see that antisymmetric stretching vibrations will
pass into the superposition of oscillations mentioned earlier due to anharmonicity,
and if the energy is large enough, the image point will fall into one of the valleys
along a complex trajectory. The complexity of the trajectory among other things
means that:
– the CO(X
1 R
+
) molecule, the product of the dissociation of CO 2 (ð b
X
1 R
þ
g Þ) must
be vibrationally excited,
– before dissociation, the molecule will make a large number of vibrations.
The author has mentioned in Sects. 2.1 and 2.4.1 that the lifetime of a triatomic
molecule with excitation energy close to the dissociation energy is approximately
equal to the time of 10
3 vibrations. Now we have understood the mechanism of this
phenomenon on the fingers.
And how can we describe the reaction A + BC ! AB + C in terms of the
motion of an image point along the PES. This reaction can be seen on the example
of the reaction O(
1 D) + CO(X
1 R
+
) ! OC(X
1 R
+
) + O(
1 D). Let us accept for definiteness that the horizontal valley (d) corresponds to the products
18 O(
1 D) + C
16
O
(X), and the valley c to
18 OC(X) +
16 O(
1 D), i.e., we describe isotopic exchange in
the CO 2 molecule. It is clear that if the collision of
18
O(
1 D) with the C
16 O(X,v X = 0)
molecule occurs, and the kinetic energy of the relative motion of O and CO is close
to 0, for example, E = 0.03 eV, this point will enter d valley along its bottom.
Then, falling into the wells, it will dangle along it for a long time (various vibrational modes with redistribution of excitation energy will be excited), and finally,
fall out or back, or to valley c, since its height relative to the bottom of the pit is
approximately the same. Apparently, at zero energy
18 O and C
16 O(X, 0), the exit
from the well to the valley is possible only when the velocity vector is strictly
parallel to the axis of the valley, i.e., all vibrational energy is focused on one of the
O À C À O bonds. This is a somewhat rare event, and, therefore, the lifetime of
such a complex has to be quite long. However, the decay of the CO 2 molecule will
66
3 Theory of Elementary Processes