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5 Complex Reactive Applications: A Forward Look to Open Science
simplicity of a trajectory treatment (that, though being a more recently developed
computational procedure than those developed for electronic structure calculations,
have already reached a similar robustness and popularity) can make the problem easily solvable. Using classical mechanics and cartesian coordinates, in fact, the time
evolution of the system can be easily followed by integrating numerically the firstorder ordinary differential Hamilton equations given in Eq. 1.29 for each ith body
of the ensemble of the atoms to be treated once initial positions and momenta are
defined. As already discussed for three atom systems, the possibility of both associating simple formulations of the reactant vibrational quantum states and sampling
of the corresponding interatomic distances allows us to deal with four-atom systems
(diatom–diatom in particular) and to determine related product (reactive and non
reactive) states with a limited amount of extra work and little loss of accuracy.
A clear illustration of the potentialities of the collaborative molecular simulator
named GEMS [107] (grid empowered molecular simulator whose detailed description will be given later) in supporting the rationalization of crossed molecular beams
(CMB) experiments using classical trajectories is given below by discussing the
investigation of the OH + CO reaction [108]. In this case, GEMS has been able
to handle a reactive diatom–diatom study all the way through from first principle
treatments to measured data reproduction (the so-called “last mile”) of the intensity
of the CO 2 product. In the CMB experiment the product number density N lab ((, t)
was measured in the laboratory frame as a function of the scattering angle, , and
time of flight, t, for OH and CO beams colliding with a narrow distribution of the
reactant collision energy (E c ) around its nominal value and a single or a small set of
reactant vibrotational states (v, j).
In most CMB experimental studies N lab ((, t) is converted (using when necessary mechanistic model assumptions) into the center of mass, CM, differential cross
section that corresponds to the CM product flux ICM(θ, u). In principle, it is possible
to directly convert the measured N lab ((, t) into ICM(θ, u) if a sufficiently fine grid of
measured points is available and experimental measurements are sufficiently clean.
However, the use of such direct inversion procedure is impracticable due to the finite
resolution of experimental conditions (i.e., finite angular and velocity spread of the
reactant beams and angular resolution of the detector). For this reason the analysis
of the laboratory data is usually carried out by a forward convolution trial-and-error
procedure, in which tentative (model) CM angular and velocity distributions are
assumed, averaged and transformed to the lab distributions for comparison with the
experimental data, until the best fit is achieved (with this procedure it is trivial to
account for the averaging over the experimental conditions). Moreover, ICM(θ, u)
is usually expressed in terms of a product angular (PAD) and a product translational
energy (PTD) Distribution under the assumption that they are substantially uncoupled. The best-fit CM PAD and PTD are then usually compared with other measured
data obtained under different experimental conditions and interpreted by associating their shapes with the reaction mechanism of some known models. The same
quantities are then compared as well with the outcomes of theoretical calculations.
Yet, using the computational techniques illustrated so far ICM(θ, u) can be evaluated directly from first principles if one knows the experimental conditions and
5 Complex Reactive Applications: A Forward Look to Open Science
simplicity of a trajectory treatment (that, though being a more recently developed
computational procedure than those developed for electronic structure calculations,
have already reached a similar robustness and popularity) can make the problem easily solvable. Using classical mechanics and cartesian coordinates, in fact, the time
evolution of the system can be easily followed by integrating numerically the firstorder ordinary differential Hamilton equations given in Eq. 1.29 for each ith body
of the ensemble of the atoms to be treated once initial positions and momenta are
defined. As already discussed for three atom systems, the possibility of both associating simple formulations of the reactant vibrational quantum states and sampling
of the corresponding interatomic distances allows us to deal with four-atom systems
(diatom–diatom in particular) and to determine related product (reactive and non
reactive) states with a limited amount of extra work and little loss of accuracy.
A clear illustration of the potentialities of the collaborative molecular simulator
named GEMS [107] (grid empowered molecular simulator whose detailed description will be given later) in supporting the rationalization of crossed molecular beams
(CMB) experiments using classical trajectories is given below by discussing the
investigation of the OH + CO reaction [108]. In this case, GEMS has been able
to handle a reactive diatom–diatom study all the way through from first principle
treatments to measured data reproduction (the so-called “last mile”) of the intensity
of the CO 2 product. In the CMB experiment the product number density N lab ((, t)
was measured in the laboratory frame as a function of the scattering angle, , and
time of flight, t, for OH and CO beams colliding with a narrow distribution of the
reactant collision energy (E c ) around its nominal value and a single or a small set of
reactant vibrotational states (v, j).
In most CMB experimental studies N lab ((, t) is converted (using when necessary mechanistic model assumptions) into the center of mass, CM, differential cross
section that corresponds to the CM product flux ICM(θ, u). In principle, it is possible
to directly convert the measured N lab ((, t) into ICM(θ, u) if a sufficiently fine grid of
measured points is available and experimental measurements are sufficiently clean.
However, the use of such direct inversion procedure is impracticable due to the finite
resolution of experimental conditions (i.e., finite angular and velocity spread of the
reactant beams and angular resolution of the detector). For this reason the analysis
of the laboratory data is usually carried out by a forward convolution trial-and-error
procedure, in which tentative (model) CM angular and velocity distributions are
assumed, averaged and transformed to the lab distributions for comparison with the
experimental data, until the best fit is achieved (with this procedure it is trivial to
account for the averaging over the experimental conditions). Moreover, ICM(θ, u)
is usually expressed in terms of a product angular (PAD) and a product translational
energy (PTD) Distribution under the assumption that they are substantially uncoupled. The best-fit CM PAD and PTD are then usually compared with other measured
data obtained under different experimental conditions and interpreted by associating their shapes with the reaction mechanism of some known models. The same
quantities are then compared as well with the outcomes of theoretical calculations.
Yet, using the computational techniques illustrated so far ICM(θ, u) can be evaluated directly from first principles if one knows the experimental conditions and