154
5 Complex Reactive Applications: A Forward Look to Open Science
interaction region leveraging on the fact that, at the energies important for a large
variety of gas phase chemical processes, the system spends a significant fraction of
time at large distances.
For most of the systems made of three, or a few more, bodies (the case of many
more bodies will be considered separately later), the long-range overall potential V
is usually partitioned into a strong interaction internal component (named intra)
of the closely aggregated (bonded) atoms and a weaker (longer range) one (named
inter) between the bonded bodies and the loosely interacting ones moving fairly
free either in the entrance or in the exit channel
V = V intra + V inter .
(5.1)
V intra is usually formulated around the equilibrium geometry of the bonded atoms
(e.g., as a combination of Morse potentials) while V inter is usually formulated in
terms of a long-range two-body like “effective” interaction components (the van der
Waals size repulsion plus dispersion attraction) V vdW plus an electrostatic V elect term
[84] as follows:
V inter = V vdW + V elect .
(5.2)
V vdW can be expressed as a bond–bond pairwise interaction (more appropriate than
the atom–atom ones) because it leverages on the additivity of the bond polarizability
in contributing to the overall (molecular) one and accounts indirectly for three-body
like effects [85]. V elect is instead formulated as an electrostatic interaction associated
with an anisotropic distribution of the molecular charge over the two interacting
bodies (say molecule (or atom) a and molecule (or atom) b (sometimes labeled
instead as 1 and 2)) that asymptotically tends to the permanent multipole – permanent
multipole interaction.
Both V vdW and V elect are usually taken as functions of the intermolecular distance
R between the centers of mass of molecule a and molecule b. For the simplest atom–
diatom systems, the internuclear distances are used to formulate the strong interaction
terms of the LEPS PES while the Jacobi coordinates are preferred for the V vdW and
V elect interaction terms (both types of coordinates are illustrated in Fig. 4.2). As a
matter of fact, the N + N 2 reaction already discussed in Chap. 3 is an appropriate
example in order to illustrate how to exploit BO coordinates for three and more atom
systems also for formulating both V vdW and V elect that are instead usually expressed
as a function of the atom to the diatom center of mass distance R [39, 86].
A similar procedure has been adopted also for four N atom systems (in particular
for the N 2 + N 2 diatom–diatom case). The Jacobi coordinates R, θ 1 , and θ 2 formed
by R with the internuclear vectors r 1 and r 2 , respectively, and the angle the
dihedral angle formed by the planes (R, r 1 ) and (R, r 2 ) are illustrated in Fig. 5.1.
The analysis of the interaction and the related fitting is performed by focusing on
some representative configurations like the (θ 1 , θ 2 , ,) = (90
◦ , 90
◦ , 0
◦ ), (90
◦ , 90
◦ ,
90
◦ ), (90
◦ , 0
◦ , 0
◦ ), (0
◦ , 90
◦ , 0
◦ ), and (0
◦ , 0
◦ , 0
◦ ) ones.
The van der Waals term V vdW is then formulated as an improved Lennard-Jones
(ILJ) [87]
5 Complex Reactive Applications: A Forward Look to Open Science
interaction region leveraging on the fact that, at the energies important for a large
variety of gas phase chemical processes, the system spends a significant fraction of
time at large distances.
For most of the systems made of three, or a few more, bodies (the case of many
more bodies will be considered separately later), the long-range overall potential V
is usually partitioned into a strong interaction internal component (named intra)
of the closely aggregated (bonded) atoms and a weaker (longer range) one (named
inter) between the bonded bodies and the loosely interacting ones moving fairly
free either in the entrance or in the exit channel
V = V intra + V inter .
(5.1)
V intra is usually formulated around the equilibrium geometry of the bonded atoms
(e.g., as a combination of Morse potentials) while V inter is usually formulated in
terms of a long-range two-body like “effective” interaction components (the van der
Waals size repulsion plus dispersion attraction) V vdW plus an electrostatic V elect term
[84] as follows:
V inter = V vdW + V elect .
(5.2)
V vdW can be expressed as a bond–bond pairwise interaction (more appropriate than
the atom–atom ones) because it leverages on the additivity of the bond polarizability
in contributing to the overall (molecular) one and accounts indirectly for three-body
like effects [85]. V elect is instead formulated as an electrostatic interaction associated
with an anisotropic distribution of the molecular charge over the two interacting
bodies (say molecule (or atom) a and molecule (or atom) b (sometimes labeled
instead as 1 and 2)) that asymptotically tends to the permanent multipole – permanent
multipole interaction.
Both V vdW and V elect are usually taken as functions of the intermolecular distance
R between the centers of mass of molecule a and molecule b. For the simplest atom–
diatom systems, the internuclear distances are used to formulate the strong interaction
terms of the LEPS PES while the Jacobi coordinates are preferred for the V vdW and
V elect interaction terms (both types of coordinates are illustrated in Fig. 4.2). As a
matter of fact, the N + N 2 reaction already discussed in Chap. 3 is an appropriate
example in order to illustrate how to exploit BO coordinates for three and more atom
systems also for formulating both V vdW and V elect that are instead usually expressed
as a function of the atom to the diatom center of mass distance R [39, 86].
A similar procedure has been adopted also for four N atom systems (in particular
for the N 2 + N 2 diatom–diatom case). The Jacobi coordinates R, θ 1 , and θ 2 formed
by R with the internuclear vectors r 1 and r 2 , respectively, and the angle the
dihedral angle formed by the planes (R, r 1 ) and (R, r 2 ) are illustrated in Fig. 5.1.
The analysis of the interaction and the related fitting is performed by focusing on
some representative configurations like the (θ 1 , θ 2 , ,) = (90
◦ , 90
◦ , 0
◦ ), (90
◦ , 90
◦ ,
90
◦ ), (90
◦ , 0
◦ , 0
◦ ), (0
◦ , 90
◦ , 0
◦ ), and (0
◦ , 0
◦ , 0
◦ ) ones.
The van der Waals term V vdW is then formulated as an improved Lennard-Jones
(ILJ) [87]