basins, V 2 (O1) and V(H6). The creation of the monosynaptic basin V(H6) involves
an intermediate structure in which the hydrogen is detached, and transfers electron
density (dressed proton) toward one of the lone pairs of O5. It is worth noting that
the presence of the V(H6) is observed in both SSD-II and SSD-III. Later, the
passage from SSD-II to SSD-III reveals another cusp-type catastrophe. The disynaptic basins V 1,2 (C2,O4) associated with the double bond C2=O4 are transformed
into single disynaptic basin V(C2,O4). Subsequently, when the system reaches the
SSD-IV, the monosynaptic basins V(H6) and V 1 (O5) are replaced by a single
disynaptic basin V(O5,H6) (cusp-type of catastrophe). The latter topological change
allows thus the formation of a water molecule which is coordinated to C3. Next, the
turning point between SSD-IV and SSD-V is associated with a fold-type catastrophe. Herein, the disynaptic basin V(C3,O5) becomes monosynaptic V(O5).
Thus, the water molecule coordinated to C3 and formed by O5, H6 and H7 departs
from the rest of the system. It is important to remark that according to the ELF
topological point of view when the system reaches the TS1, no breaking/forming
processes are observed. After TS1, when the system reaches the SSD-VI, the
disynaptic basin V(C2,O1) is replaced by a pair of disynaptic basins V 1,2 (C2,O1).
From a chemical point of view, this cusp-type of catastrophe may be interpreted as
a change of topological signature of the single bond C2–O1 to double bond C2=O1.
Finally, when SSD-VII is reached, the ELF scalar field undergoes a fold-type
catastrophe and the creation of the disynaptic basin V(C3,O4) is observed giving
rise to the formation of the lactone intermediate.
Snapshots of the ELF basins for some selected points along the IRC, representing the different SSDs found, are depicted in Fig. 10.7.
The snapshots (a), (b), (c) and (d) of Fig. 10.2 clearly describe the proton transfer
from O1 to O5. The snapshots (d) and (e) show the changes taking place between
C3 and O5: at SSD-IV there is a disynaptic V(C3,O5) basin (see the green basin
between these two atoms in Fig. 10.2d) while when the turning point between
SSD-IV and SSD-V is reached the disynaptic basin V(C3,O5) becomes monosynaptic V(O5) (see the red basin in Fig. 10.2e). Subsequently, the water molecule
release precedes the final cyclization of the intermediate while the last chemical
event accounts for the lactone closure. In Fig. 10.7g the small bonding basin V(C3,
O4) between C3 and O4 is observed.
To complete the topological description of the process, an analysis of the population evolution of the basins directly related with the changes taking place can be
done. These data are reported in Fig. 10.8.
As can be seen in Fig. 10.8, by the end of SSD-I the population of the disynaptic
basin V(O1,H6) diminishes concomitantly with an increase in the population of the
disynaptic basin V(C2,O1). Therefore, the departure of the H6 from O1 initially
makes the population of the basin corresponding to the C2–O1 bond increase.
However, when the basin V(O1,H6) disappears at the turning point between
SSDD-I and SSD-II, its population is not assumed by the disinaptic basin V(C2,
O1), but principally by a new monosynaptic basin V(O1). In Fig. 10.8 we have
represented the population of the monosynaptic basins on O1 as a whole, and
therefore a sudden increase in the V(O1) populations is noticed when the new
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an intermediate structure in which the hydrogen is detached, and transfers electron
density (dressed proton) toward one of the lone pairs of O5. It is worth noting that
the presence of the V(H6) is observed in both SSD-II and SSD-III. Later, the
passage from SSD-II to SSD-III reveals another cusp-type catastrophe. The disynaptic basins V 1,2 (C2,O4) associated with the double bond C2=O4 are transformed
into single disynaptic basin V(C2,O4). Subsequently, when the system reaches the
SSD-IV, the monosynaptic basins V(H6) and V 1 (O5) are replaced by a single
disynaptic basin V(O5,H6) (cusp-type of catastrophe). The latter topological change
allows thus the formation of a water molecule which is coordinated to C3. Next, the
turning point between SSD-IV and SSD-V is associated with a fold-type catastrophe. Herein, the disynaptic basin V(C3,O5) becomes monosynaptic V(O5).
Thus, the water molecule coordinated to C3 and formed by O5, H6 and H7 departs
from the rest of the system. It is important to remark that according to the ELF
topological point of view when the system reaches the TS1, no breaking/forming
processes are observed. After TS1, when the system reaches the SSD-VI, the
disynaptic basin V(C2,O1) is replaced by a pair of disynaptic basins V 1,2 (C2,O1).
From a chemical point of view, this cusp-type of catastrophe may be interpreted as
a change of topological signature of the single bond C2–O1 to double bond C2=O1.
Finally, when SSD-VII is reached, the ELF scalar field undergoes a fold-type
catastrophe and the creation of the disynaptic basin V(C3,O4) is observed giving
rise to the formation of the lactone intermediate.
Snapshots of the ELF basins for some selected points along the IRC, representing the different SSDs found, are depicted in Fig. 10.7.
The snapshots (a), (b), (c) and (d) of Fig. 10.2 clearly describe the proton transfer
from O1 to O5. The snapshots (d) and (e) show the changes taking place between
C3 and O5: at SSD-IV there is a disynaptic V(C3,O5) basin (see the green basin
between these two atoms in Fig. 10.2d) while when the turning point between
SSD-IV and SSD-V is reached the disynaptic basin V(C3,O5) becomes monosynaptic V(O5) (see the red basin in Fig. 10.2e). Subsequently, the water molecule
release precedes the final cyclization of the intermediate while the last chemical
event accounts for the lactone closure. In Fig. 10.7g the small bonding basin V(C3,
O4) between C3 and O4 is observed.
To complete the topological description of the process, an analysis of the population evolution of the basins directly related with the changes taking place can be
done. These data are reported in Fig. 10.8.
As can be seen in Fig. 10.8, by the end of SSD-I the population of the disynaptic
basin V(O1,H6) diminishes concomitantly with an increase in the population of the
disynaptic basin V(C2,O1). Therefore, the departure of the H6 from O1 initially
makes the population of the basin corresponding to the C2–O1 bond increase.
However, when the basin V(O1,H6) disappears at the turning point between
SSDD-I and SSD-II, its population is not assumed by the disinaptic basin V(C2,
O1), but principally by a new monosynaptic basin V(O1). In Fig. 10.8 we have
represented the population of the monosynaptic basins on O1 as a whole, and
therefore a sudden increase in the V(O1) populations is noticed when the new
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