156
5 Complex Reactive Applications: A Forward Look to Open Science
expansion is then estimated from the abovementioned selected configurations further
refined by computing high-level ab initio electronic structure. The comparison of
computed cross sections and second virial coefficient values with beam experiments
are also used for further refinements.
5.1.3 Four-Atom Many-Process Expansion
The additional flexibility built-in into the accurate description of the above discussed
functional formulation of the PES of the four body systems sheds new light on the
richness of its interaction components that have not yet found completely their way
into LM-LS fitting methods for four-atom collisions. For the four-atom N 2 + N 2
processes the investigation of the interaction has focused initially only on the inelastic channel. Accordingly, the PES was initially formulated as a sum of the two N 2
intramolecular interactions and of an intermolecular component (i.e., that of two
separated nitrogen molecules with their internuclear distances close to equilibrium)
described in terms of isotropic and anisotropic contributions using expansions in
spherical harmonics (see for example Refs. [90–95]) later formulated as a bond–bond
pairwise additive interaction (see Ref. [96]). In order to overcome the bias of such
formulation of the PES (that prevents the description of atom exchange processes
and the fragmentation of one (or both) molecule(s)), extensive additional ab initio
studies were performed for a wide set of molecular geometries aimed at obtaining
a full-dimensional more rigorous description of the interaction governing the N 2 +
N 2 collisions. The first work along this direction was reported in Ref. [97]. A more
complete effort to deal with the problem of describing the processes in which the
initial N 2 molecules deform to the extent of reaching the situation of either forming
new bonds or breaking old bonds and allowing the newly formed atoms and molecules to fly away, was made by the authors of Ref. [98] by carrying out ab initio
computations for 16 435 geometries describing nine N 2 + N 2 and three N + N 3
arrangements. Then, this set of potential energy values was fitted both to a polynomial of bond-order variables [98, 99] (Paukku PES) and to a statistically localized,
permutationally invariant, local moving least squares interpolating function [100].
The same set of data was used to build a PES as a sum of bond, valence angle, torsion
angle, van der Waals and Coulombic energy interaction terms among all atom pairs
[101]. More recently, based on the same set of ab initio values, a new polynomial
function (Bender PES) was proposed including in the definition of the bond-order
variables a Gaussian contribution [102]. This feature provides the Bender PES with
significant flexibility that improves the fitting quality of the ab initio values. What
is more important, however, is that both the Paukku and the Bender PESs validly
describe high energy processes (including dissociation) and consistently formulate
(using polynomials) two-, three-, and four-body components (e.g., reproduce the
double barrier structure of the triatomic N + N 2 subsystem when one nitrogen atom
is displaced to very large distances).
5 Complex Reactive Applications: A Forward Look to Open Science
expansion is then estimated from the abovementioned selected configurations further
refined by computing high-level ab initio electronic structure. The comparison of
computed cross sections and second virial coefficient values with beam experiments
are also used for further refinements.
5.1.3 Four-Atom Many-Process Expansion
The additional flexibility built-in into the accurate description of the above discussed
functional formulation of the PES of the four body systems sheds new light on the
richness of its interaction components that have not yet found completely their way
into LM-LS fitting methods for four-atom collisions. For the four-atom N 2 + N 2
processes the investigation of the interaction has focused initially only on the inelastic channel. Accordingly, the PES was initially formulated as a sum of the two N 2
intramolecular interactions and of an intermolecular component (i.e., that of two
separated nitrogen molecules with their internuclear distances close to equilibrium)
described in terms of isotropic and anisotropic contributions using expansions in
spherical harmonics (see for example Refs. [90–95]) later formulated as a bond–bond
pairwise additive interaction (see Ref. [96]). In order to overcome the bias of such
formulation of the PES (that prevents the description of atom exchange processes
and the fragmentation of one (or both) molecule(s)), extensive additional ab initio
studies were performed for a wide set of molecular geometries aimed at obtaining
a full-dimensional more rigorous description of the interaction governing the N 2 +
N 2 collisions. The first work along this direction was reported in Ref. [97]. A more
complete effort to deal with the problem of describing the processes in which the
initial N 2 molecules deform to the extent of reaching the situation of either forming
new bonds or breaking old bonds and allowing the newly formed atoms and molecules to fly away, was made by the authors of Ref. [98] by carrying out ab initio
computations for 16 435 geometries describing nine N 2 + N 2 and three N + N 3
arrangements. Then, this set of potential energy values was fitted both to a polynomial of bond-order variables [98, 99] (Paukku PES) and to a statistically localized,
permutationally invariant, local moving least squares interpolating function [100].
The same set of data was used to build a PES as a sum of bond, valence angle, torsion
angle, van der Waals and Coulombic energy interaction terms among all atom pairs
[101]. More recently, based on the same set of ab initio values, a new polynomial
function (Bender PES) was proposed including in the definition of the bond-order
variables a Gaussian contribution [102]. This feature provides the Bender PES with
significant flexibility that improves the fitting quality of the ab initio values. What
is more important, however, is that both the Paukku and the Bender PESs validly
describe high energy processes (including dissociation) and consistently formulate
(using polynomials) two-, three-, and four-body components (e.g., reproduce the
double barrier structure of the triatomic N + N 2 subsystem when one nitrogen atom
is displaced to very large distances).