Stefano Falcinelli1, Franco Vecchiocattivi1, James M Farrar2, Fernando Pirani3. 1. Department of Civil and Environmental Engineering, University of Perugia, Via G. Duranti 93, 06125 Perugia, Italy. 2. Department of Chemistry, University of Rochester, 14627 Rochester, New York, United States. 3. Department of Chemistry, Biology and Biotechnologies, University of Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy.
Abstract
A new theoretical method, developed by our laboratory to describe the microscopic dynamics of gas-phase elementary chemi-ionization reactions, has been applied recently to study prototype atom-atom processes involving reactions between electronically excited metastable Ne*(3P2,0) and heavier noble gas atoms. Important aspects of electronic rearrangement selectivity have been emphasized that suggested the existence of two fundamental microscopic reaction mechanisms. The distinct mechanisms, which are controlled by intermolecular forces of chemical and noncovalent nature respectively, emerge under different conditions, and their balance depends on the collision energy regime investigated. The present paper provides the first step for the extension of the method to cases involving molecules of increasing complexity, whose chemi-ionization reactions are of relevance in several fields of basic and applied researches. The focus is here on the reactions of Ne* with simple inorganic molecules as Cl2 and NH3, and the application of the method discloses relevant features of the reaction microscopic evolution. In particular, this study shows that the balance of two fundamental reaction mechanisms depends not only on the collision energy and on the relative orientation of reagents but also on the orbital angular momentum of each collision complex. The additional insights so emphasized are of general relevance to assess in detail the stereodynamics of many other elementary processes.
A new theoretical method, developed by our laboratory to describe the microscopic dynamics of gas-phase elementary chemi-ionization reactions, has been applied recently to study prototype atom-atom processes involving reactions between electronically excited metastable Ne*(3P2,0) and heavier noble gas atoms. Important aspects of electronic rearrangement selectivity have been emphasized that suggested the existence of two fundamental microscopic reaction mechanisms. The distinct mechanisms, which are controlled by intermolecular forces of chemical and noncovalent nature respectively, emerge under different conditions, and their balance depends on the collision energy regime investigated. The present paper provides the first step for the extension of the method to cases involving molecules of increasing complexity, whose chemi-ionization reactions are of relevance in several fields of basic and applied researches. The focus is here on the reactions of Ne* with simple inorganic molecules as Cl2 and NH3, and the application of the method discloses relevant features of the reaction microscopic evolution. In particular, this study shows that the balance of two fundamental reaction mechanisms depends not only on the collision energy and on the relative orientation of reagents but also on the orbital angular momentum of each collision complex. The additional insights so emphasized are of general relevance to assess in detail the stereodynamics of many other elementary processes.
The weakly bound adducts formed by colliding
reagents play an important
role in the kinetics of elementary processes, serving as precursor
states opening the passage to the transition state (TS) of several
chemical–physical phenomena occurring in gaseous and condensed
phases and at the gas–solid, gas–liquid interphases.[1−4] The valence electrons quantum confinement of reagents in such adducts
and the selectivity of electronic rearrangements, promoting the stereodynamical
evolution of the systems toward the final products, is still today
a topic of general interest.Recently, we developed and applied
a new/original method[5−7] to the detailed investigation of chemi-ionization
reactions (CHEMI),
promoted by collisions of atoms electronically excited in metastable
states with other atoms, that are prototypical of barrierless processes
leading to the formation of ionic products plus electrons.[8−10] The study of them remains of great interest for fundamental and
applied research, since it allows a definition of the role of the
barrierless reactions in cold chemistry[11−13] and an opportunity to
model energy-transfer phenomena occurring in flames, plasmas, and
electric discharges.[14,15]If CHEMI involving Ng atoms
are important, especially from the
point of view of basic research, those involving molecules are of
a more general interest, especially in highlighting the role of electronic
transfer, that is, the redox nature of this type of process.[6,7] Indeed, they control the balance of phenomena occurring in interstellar
environments, in combustion and flames, where CHEMI are considered
as the primary initial step,[14,15] in molecular plasmas
and nuclear fusion. They also govern interstellar chemistry and planetary
ionospheres[16−18] affecting the transmission of radio and satellite
signals.[18] These reactions are also implicated
in soft-ionization mass spectrometry techniques,[19,20] since the controlled internal degrees excitation of the molecular
ionic products limits the number of fragmentation channels.In the present study we attempt to take the first step toward the
extension/generalization of our approach to atom-molecule CHEMI, where
the intermolecular interactions driving the dynamics are usually stronger
and more anisotropic with respect to atom–atom CHEMI and often
include further components. The combination of these interaction features
can strongly vary the relative role of two basic (direct and indirect) mechanisms, initially demonstrated
for atom–atom CHEMI reactions.[5−7]In the next sections,
after a comparison of the experimental total
ionization cross sections, with their different magnitudes and collision
energy dependence, the focus is on some prototypical CHEMI of molecules.
The special case of Cl2 emphasizes how the typical harpooning
effect can affect the reaction precursor state. The detailed study
of NH3 reaction stereodynamics shows how the two basic
mechanisms, first revealed for atom–atom CHEMI, are modulated
by molecular orientation and by the orbital angular momentum of the
collision complex, controlling the centrifugal component of the total
interaction potential.
Methods
Our investigation, based
on a new semiclassical treatment fully
described in recent papers,[5−7] focused on Ne*(3P2,0)-Ng (Ng = Ar, Kr, Xe) systems, and the analysis provided
an internally consistent rationalization of available experimental
findings, such as Penning ionization electron spectra (PIES), total
and partial ionization cross sections, and their branching ratios
(BRs). The detailed characterization of the atom–atom reaction
dynamics revealed new insights into the role of rearrangement and
the angular momentum coupling of valence electrons in chemical kinetics
that must be considered of general interest for many other reactions.
In particular, the application of the method[5−7] suggests thatThe optical potential
model, formally
introduced to describe nuclear reactions dynamics and applied also
to CHEMI,[9,10] is defined as a combination of a real and
an imaginary part. We have demonstrated[5−7] that the two parts—that
control, respectively, the collision dynamics and the “opacity”
or probability of CHEMI—must be interdependent, since they
arise from the same interaction components.The different balance of such components
originates two competitive microscopic reaction mechanisms. They have
been identified, respectively, as a direct mechanism, dominant at short separation distances of reagents being driven
by chemical forces, and an indirect mechanism, prevalent
at large separation distances and originating from noncovalent forces,
such as dispersion, induction-polarization contributions, and those
promoting spin–orbit and centrifugal-Coriolis effects.[5−7] In particular, the direct mechanism is triggered
by effective charge (electron) transfer (CT) effects between reagents
favored by the overlap of valence orbitals. The indirect mechanism describes ionization that occurs also by a concerted emission-absorption
of a “virtual” photon exchanged by reagents within the
confines of the weakly bound collision complex. Therefore, while the direct mechanism controls the evolution of prototype elementary oxidation reactions, the indirect mechanism triggers typical radiative (photo)-ionization
processes.[7]The reactivity depends on the collision
energy (Ecoll), separation distance R, and relative alignment of valence orbitals, important
factors that affect the structure and stability of the adducts formed
by collision of reagents and then of the reaction TS.Twelve reaction channels, ascribed
to specific passages from a quantum state of reagents to that of products,
have been characterized, where each one is affected by a different
relative role of the two basic mechanisms mentioned above.[7]
Results and Discussion
General
Trends
According to the pioneering work of
Beijerinck and co-workers,[21] molecular
systems giving CHEMI, all experimentally investigated in detail in
the gas phase under single collision conditions with the molecular
beam technique, can be distinguished in two groups: CHEMI systems
showing a pronounced increase in the total ionization cross section
as Ecoll increases and CHEMI systems showing,
contrariwise, cross sections with a decreasing trend. The energy dependence
of the total ionization cross section has been measured in our laboratory
in an internally consistent way for several systems involving Ne*;[22−25] therefore, a direct and quantitative comparison of obtained results
is straightforward. Some prototype examples are reported in Figure a,b.
Figure 1
Total ionization cross
sections in some Ne*-molecule systems, as
a function of collision energy. The curves are interpolating 3rd degree
polynomials of experimental data.[22,25] (a) The case
of some inorganic molecules. (b) The case of the simplest saturated
and unsaturated hydrocarbons.
Total ionization cross
sections in some Ne*-molecule systems, as
a function of collision energy. The curves are interpolating 3rd degree
polynomials of experimental data.[22,25] (a) The case
of some inorganic molecules. (b) The case of the simplest saturated
and unsaturated hydrocarbons.The differing behaviors, exhibited by the various partners of the
Ne* reagent, must selectively depend on their fundamental chemical
physical properties, as depicted in Figure for three cases of inorganic molecules.
The present focus is on Ne*-Cl2, where the formation by
harpooning of an effective ion pair is expected to increase the binding
energy in the collision complex, at least 2 orders of magnitude with
respect to that in Ne*-N2, favoring a closer approach of
reagents. However, in addition to specific features of Ne*-Cl2, here we also analyze in detail the Ne*-NH3 system
for which the intermolecular interaction is strongly anisotropic,
exhibits an intermediate strength between Ne*-Cl2 and Ne*-N2, and has been recently provided in analytical form (see below).
Figure 2
Fundamental
features of Cl2, NH3, and N2 molecules
associated with different electronic charge distribution
around their molecular axis. The chlorine molecule exhibits two σ-holes
collinear with the bond axis. This justifies the large and positive
quadrupole moment of Cl2. The ammonia molecule exhibits
a large dipole moment. The nitrogen molecule exhibits a large and
negative quadrupole moment. The positive charge density increase is
approximately indicated by the increased extent of the red color;
the corresponding change in negative charge density is likewise indicated
in blue.
Fundamental
features of Cl2, NH3, and N2 molecules
associated with different electronic charge distribution
around their molecular axis. The chlorine molecule exhibits two σ-holes
collinear with the bond axis. This justifies the large and positive
quadrupole moment of Cl2. The ammonia molecule exhibits
a large dipole moment. The nitrogen molecule exhibits a large and
negative quadrupole moment. The positive charge density increase is
approximately indicated by the increased extent of the red color;
the corresponding change in negative charge density is likewise indicated
in blue.
The Ne*-Cl2 Case
To cast light on the critical
role of the interaction components that are expected to selectively
modulate the relative weight of the two basic microscopic mechanisms
indicated above as a function of collision energy, we make a preliminary
attempt to rationalize the phenomenology observed for the Ne*-Cl2 system shown in Figure a. In particular, in the thermal range of Ecoll, Ne*-Cl2 is one of the systems showing
the highest cross-section value. For the Cl2 reagent this
behavior must relate to the electronic features of its structure.
The potential curves for the ground and excited states of the chlorine
molecule as well as of its positive and negative ions have been calculated
by Peyerimhoff and Buenker using the MRD-CI method,[26] to which the interested reader can refer. Specifically,
this molecule exhibits a high permanent electric quadrupole moment
(+3.8 au),[27] a high electron affinity (2.44
eV),[28] and is characterized by a σ-hole,[29] with a positive electrostatic potential confined
along the outer parts of the Cl–Cl bond (see Figure ). An extended discussion on
the σ-hole topic, in terms of electron density plots of Cl2 molecule in its ground electronic state, is presented in
ref (29) (see also
references therein).These unique features of Cl2 are indeed responsible of the formation of the intermolecular halogen
bond even with lighter Ng atoms in their ground electronic state.[29] Therefore, during the approach to Cl2, the “floppy” outer electronic cloud of Ne* tends
to be polarized by the long-range intermolecular interaction field.
This electron transfer is primarily triggered in the collinear approach
by the σ-hole presence. The newly formed Cl2– anion tends further to align with its axis along the
interatomic Ne···Cl···Cl separation R, and the Coulomb attraction in the nascent ion-pair Ne+-Cl2– favors the trapping of
reagents, shown schematically in Figure . Indeed, in Cl2– the added electron, populating the outer 3σu* antibonding
orbital, confined in the external part of the Cl–Cl bond, completely
fills the σ-hole and strongly reduces the molecular bond strength
making Cl2– a highly unstable species,
especially in the presence of Ne+.
Figure 3
A schematic diagram representing
the microscopic dynamics for Ne*-Cl2 CHEMI reaction. Redox 1 (upper panel)
At a large distance (∼6 Å) and with collinear Cl2 the Rydberg electron of Ne* can go to fill the σ-hole of Cl2 with subsequent Ne+-Cl2– ion pair formation. The extra electron in Cl2– is located in the antibonding 3σu* orbital. Redox 2 (middle panel) At shorter distances the ionization
can take place involving a pair of electrons from the 3σ molecular
orbitals. In this case, the Cl2+ ion is then
formed in the dissociative B2Σg+. (lower panel) In case of a perpendicular approach, the Ne* atom
is polarized, and the ionization can take place essentially through
a radiative (physical-photoionization) mechanism at a large distance,
or by an exchange (chemical-redox) mechanism at a short distance.
The positive charge density increase is approximately indicated by
the increased extent of the red color; the corresponding change in
negative charge density is likewise indicated in blue.
A schematic diagram representing
the microscopic dynamics for Ne*-Cl2CHEMI reaction. Redox 1 (upper panel)
At a large distance (∼6 Å) and with collinear Cl2 the Rydberg electron of Ne* can go to fill the σ-hole of Cl2 with subsequent Ne+-Cl2– ion pair formation. The extra electron in Cl2– is located in the antibonding 3σu* orbital. Redox 2 (middle panel) At shorter distances the ionization
can take place involving a pair of electrons from the 3σ molecular
orbitals. In this case, the Cl2+ ion is then
formed in the dissociative B2Σg+. (lower panel) In case of a perpendicular approach, the Ne* atom
is polarized, and the ionization can take place essentially through
a radiative (physical-photoionization) mechanism at a large distance,
or by an exchange (chemical-redox) mechanism at a short distance.
The positive charge density increase is approximately indicated by
the increased extent of the red color; the corresponding change in
negative charge density is likewise indicated in blue.The increased attraction arising from ion pair formation
and the
instability of Cl2– stimulates the formation
of a highly excited NeCl* adduct that autoionizes leading to Ne +
Cl+ + e– products. At a short R, an additional electronic rearrangement process become
possible, illustrated in the middle panel in Figure , triggered by the overlap between the half-filled
orbital of Ne+ and the populated 3σ molecular orbitals
of Cl2. Specifically, this overlap promotes a single electron
transfer from the outer 3σu* of Cl2– to the half-filled orbital of the Ne+ core,
which is accompanied by an energy release sufficient to eject one
of two electrons populating the 3σg bonding molecular
orbital of Cl2. As a consequence, the product Cl2+ shows a propensity to be formed in the dissociative
B2Σg+ state with a bond order
of 0.5. Since electrons populating both 3σu* and
3σg molecular orbitals are mostly confined in the
σ hole region, this peculiar feature of the chlorine molecule
can be assimilated to a reaction catalyst. However, the formation
of the fragment Cl+ requires a synchronization between
the time required by an interacting complex to give an electronic
rearrangement and the typical collision time. This synchronization
is partially and totally relaxed with increasing Ecoll. Therefore, the Cl2+ production
is predicted to increase with Ecoll, consistent
with the experimental findings by Kischlat and Morgner[30] and by our laboratory.[23]It is intriguing to note that, under such conditions, the
chemical
(direct) mechanism is dominant and that it occurs
through two basic steps: first, Cl2 undergoes a reduction
to Cl2– by CT in which the resulting
neon behaves as an alkali atom (i.e., Na) as reducing agent (Redox
1 in Figure ); in
the second step, the Coulomb attraction promotes the trapping of the
Ne+-Cl2– ion pair at closer
distances, where a concerted CT involving both internal 3σg and external 3σu* populated molecular orbitals
of Cl2– (with the outer electron filling
the p-orbital of the Ne and the other innermost electron being ejected)
(Redox 2 in Figure ), accompanied by molecular dissociation, determines the oxidation
to the final state of Cl+. In this second case the Ne+ behaves like a halogen atom (i.e., F) as an oxidizing agent.However, with increasing collision energy, the effectiveness of
such a global mechanism, triggered by the Cl2 with the
molecular axis aligned along R, decreases, since the collision time
shortens, the passage through the crossing between neutral and ionic
states assumes a less adiabatic character,[31] and alignment effects are less probable. Under such conditions,
collisions become statistically possible for all relative orientations
of both partners, including the Cl2 molecule perpendicular
approach to the Ne* atom and the global reactivity decreases. Here,
in the perpendicular configuration of the formed adduct, rather unstable
because of the absence of strong attractive components, both indirect (including possible radiative effects[9,32−34]) and direct (chemical or exchange)
mechanisms become competitive, and above all an electron removal from
the outer 3πu* molecular orbital becomes effective,
leading to the single-step formation of Cl2+ in its ground electronic state X2Πg.
This new channel increases the formation probability of Cl2+ with respect to Cl+.
The NH3 Reaction
Stereodynamics
A system
useful for the generalization of our approach is Ne*-NH3, for which a multidimensional potential energy surface (PES) given
in analytical form[35] assists in the formulation
of the real part of the optical potential. A previous study,[25] adopting a radial dependent imaginary part,
whose average strength is modulated only by the NH3 orientation
defined by the polar coordinates R, θ, ϕ
given in the lower panel of Figure , suggested that CHEMI occurs exclusively on the N-side
of the molecular frame. Specifically, while the Ne* approach within
an angular cone confined around the C3 ammonia axis promotes the formation of NH3+ in the X ground electronic state, the broadside approach
in the vicinity of the perpendicular configuration leads to the formation
of the electronically excited NH3+(A) ion that
dissociates to NH2+ + H.[25] The approach toward the hydrogen end of the molecule, along
the C3 ammonia axis,
is accompanied by the strong polarization of the “floppy”
cloud of 3s1 valence electron of Ne* that enhances the
propensity to give an intermolecular hydrogen bond with a consequent
reduction of the redox reaction effectiveness.[35]
Figure 4
(lower panel) The polar coordinate system used to define the orientation
of NH3 with respect to Ne*. (upper and intermediate panels)
Two relevant configurations giving redox-reactive and nonreactive
events. The metastable Ne* atom is differently polarized, accordingly
to the NH3 dipole orientation. The positive charge density
increase is approximately indicated by the increased extent of the
red color; the corresponding change in negative charge density is
likewise indicated in blue.
(lower panel) The polar coordinate system used to define the orientation
of NH3 with respect to Ne*. (upper and intermediate panels)
Two relevant configurations giving redox-reactive and nonreactive
events. The metastable Ne* atom is differently polarized, accordingly
to the NH3 dipole orientation. The positive charge density
increase is approximately indicated by the increased extent of the
red color; the corresponding change in negative charge density is
likewise indicated in blue.The optical potential formulation, including also an effective
angular-dependent imaginary Γ component, permitted us to estimate
the acceptance of two angular cones where the reactions mainly occur.
Details on the acceptance angular cones have been discussed in details
in ref (25). However,
no information has been provided on the relative role of direct and indirect mechanisms and therefore on partial
ionization cross sections associated with the different reaction paths.The present study, exploiting the analytical PES,[35] attempts to deconvolve the effective imaginary part,[25] separating the contributions from chemical and
physical components of intermolecular forces, in order to identify
the relative role of the two direct and indirect (basic) mechanisms. This preliminary objective is fundamental for
characterizing the dependence of the relative role of the two basic
reaction mechanisms on Ecoll and therefore
on the orbital angular momentum quantum number of the collision
complex that, in a classical
picture, relates to the impact parameter b. Here,
we analyze in detail two geometries of reagents approach, the one
close to the C3 molecular
axis and the one in proximity of the perpendicular to this axis, that
control the formation of NH3+ in the ground
and first excited electronic states, respectively. Note that the two
selected geometries are representative of the most probable configurations
within the acceptance angular cones where the reaction occur, leading
to the formation of a different type of ionic products. This allows
the use of the same function for the imaginary Γ1 and Γ2 components, triggering direct and indirect mechanisms, respectively, whose general
exponential formulation is borrowed from the atom–atom CHEMI
reactions[6,7] to describe direct and indirect mechanisms with their state-to-state dependence.
In the present analysis, only the pre-exponential factors are adjusted
to reproduce the magnitude and energy dependence of the total and
partial ionization cross sections. Note also that any averaging over
the angular acceptance cones is expected to change the pre-exponential
factor values but not their ratios. The methodological choice of two
selected configurations within the angular cones allows to highlight
the different role of the centrifugal potential respect to the intermolecular
interaction.In previous work, the imaginary part of the optical
potential was
usually represented by a single effective radial component.[9,10,25] Here, it is decomposed into two
terms that control, as noted above, the selectivity and efficiency
of the two basic direct and indirect mechanisms. Accordingly, the term Γ1 is related
to the efficiency of the direct mechanism (exchange-redox), while
Γ2 indicates the opacity function in the case of
the indirect (radiative-photoionization) mechanism.
Analogous symbolism is used for the cross sections calculated from
the relative Γ1 and Γ2 functions
as shown in Figure (see below). Their separated formulation has been obtained according
to the following guidelines:
Figure 5
Collision energy dependence of partial (σ1, σ2) and total (σtot) cross sections
evaluated
from individual (Γ1, Γ2) and total
(Γtot) components of the imaginary part (see Table
1) and referred to the two selected geometries. The subscripts 1 and
2 indicate the direct and indirect reaction mechanism contributions separately, respectively.
the quantities Γ1 and Γ2 must be related to intermolecular forces
of a specific nature, whose strength scales in a different way with R. In particular, while chemical components, depending on
the overlap integral between orbitals exchanging the electron, emerge
at short separation distances and are strongly varying with R, those of physical origin show a much less radial dependence.
Accordingly, completely different exponential functions have been
adopted for the two imaginary terms, formulated as suggested from
the detailed study of atom–atom reactions.[6,7]Their relative and absolute
strengths
have been modeled in order to reproduce total and partial ionization
cross sections in the right scale of experimental determinations.
Considering the results provided by our[25] and by another laboratory,[36] cross sections
represent a critical test of predicted values, since they cover 1–2
orders of magnitude and the probed Ecoll varies for subthermal (∼0.1 meV) up to hyper-thermal values
(−103 meV), a changing of ∼4 orders of magnitude.
More specifically, total ionization cross sections measured by the
Losanna group[36] vary from 300 to 400 Å2 (Ecoll = 01 meV) up to ≃100
Å2 (Ecoll = 10 meV), while
those obtained in our laboratory cover a complementary range and are
shown in Figure a.Collision energy dependence of partial (σ1, σ2) and total (σtot) cross sections
evaluated
from individual (Γ1, Γ2) and total
(Γtot) components of the imaginary part (see Table
1) and referred to the two selected geometries. The subscripts 1 and
2 indicate the direct and indirect reaction mechanism contributions separately, respectively.Details of the selected geometries and on the formulation
of the
imaginary components are given in Table .
Table I
Angular Coordinates
Referred to the
Two Selected Geometries and Formulation of the Individual and Total
Imaginary Γ Components (in meV) as a Function of the Separation
Distance R (in Å)a
θ = 90°; ϕ = 220°
θ = 15°; ϕ = 270°
Γ1 (R)
3.0 × 105 exp(−4.1 R)
3.0 × 105 exp(−4.1 R)
Γ2 (R)
60.0
exp(−1.4R)
60.0 exp(−1.4R)
Γtot(R)
Γ1 (R) + Γ2 (R)
Γ1 (R) + Γ2 (R)
The Γ1 and Γ2 components for the two selected geometries of the approach
of reagents within the acceptance angular cones (see text) have the
same analytical formulation in order to highlight the different role
of the centrifugal potential with respect to the intermolecular interaction
potential.
The Γ1 and Γ2 components for the two selected geometries of the approach
of reagents within the acceptance angular cones (see text) have the
same analytical formulation in order to highlight the different role
of the centrifugal potential with respect to the intermolecular interaction
potential.The total and
partial (i.e., referred to each mechanism) ionization
cross sections predicted by our method, and calculated within the
semiclassical treatment, whose details can be found in refs (6) and (7), are shown in Figure . The results show
that the role of two mechanisms and their energy dependence are completely
different for the two geometries here considered, since the combination
of the intermolecular potential and the centrifugal barrier selectively
modulates the range of intermolecular distances probed so exalting
the different role of direct and indirect mechanisms. In particular, for the geometry close to the C3 NH3 axis (“collinear”),
producing the NH3+(X) ground state, the direct mechanism is dominant at all Ecoll values. However, for the “broadside” geometry,
which gives rise to the formation of the NH3+(A) excited state with its subsequent dissociation into NH2+ + H, the direct mechanism becomes dominant
only at hyper-thermal values of Ecoll.
The contrasting behavior is ascribable to the different stability
of the adduct formed in the two selected geometries for collision
of reagents. Therefore, the detailed characterization of the dynamical
evolution of the two types of collision complexes, leading to the
turning points, which represent the most critical intermolecular distances
where the reaction manifests the highest probability to occur, provides
additional insight into critical features of the reaction stereodynamics.
In particular, understanding the dependence of the turning points
on b or on , that have
been characterized, as emphasized
in Figure , by a critical
comparison between sum of real potential and centrifugal contribution
with Ecoll, is of great interpretational
value.
Figure 6
(upper panels) The dependence on the intermolecular distance R of the effective potential given as sum of the real component Vθφ(R) and of the
centrifugal contribution . (lower panels)
The turning point dependence
on the impact parameter b, or in the quantum picture
on , evaluated
for the two geometries at selected Ecoll values that cover 4 orders of magnitude.
(upper panels) The dependence on the intermolecular distance R of the effective potential given as sum of the real component Vθφ(R) and of the
centrifugal contribution . (lower panels)
The turning point dependence
on the impact parameter b, or in the quantum picture
on , evaluated
for the two geometries at selected Ecoll values that cover 4 orders of magnitude.From the data reported in Figure emerges the important selective role of the centrifugal
barrier that generates, at collision energies lower than a critical Ecoll value, turning points confined in well-separated
ranges of values, where the reaction probability is completely different,
while for higher collision energies a unique extended range of turning
points becomes effective. As depicted in Figure , for the “collinear” geometry
the critical Ecoll value is ∼100
meV, while for the “broadside” geometry it amounts to
∼10 meV, and this variation arises from the different strength
of the real potential that drives the collision. In particular, the
centrifugal potential vanishes the trapping effect of the interaction
more easily for the side approach because of the weaker attraction.The striking selectivity feature is that, for Ecoll lower than the critical value, only a limited range
of b or values controls
the reactivity. Moreover,
under such conditions the collision time is sufficiently long, the
phase accumulation along each reaction path depends on a similar passage
from long to short R values, and then the relative
role of the two mechanisms is approximately constant, as shown in Figure . Along these trajectories,
the chemical reactivity can be also enhanced by the possible orientation
of the polar molecule within the strong and anisotropic intermolecular
field probe, favored by the low Ecoll and
by the long collision time. At higher Ecoll, in contrast, the range of turning points effective for reaction
enlarges significantly, since the selective role of the centrifugal
barrier (see upper panels in Figure ), which separates short and large turning points,
disappears. This is confirmed by the results in Figure , where, as a function of Ecoll, are plotted the total cross section (due to all b or values contributions)
and the partial cross
section, determined exclusively by b or lower than b or values determining
the absolute maximum
of centrifugal barrier associated at each Ecoll (bmax or ,
and for values
see Table ). In
particular, at Ecoll lower than the critical
value, the centrifugal barrier
completely separates the ranges of b or driving the
collisions (see Figure ), making ineffective turning
points determined by b > bmax or , since they occur at
too large R values.
Figure 7
Total, σtot, and partial, σpar, ionization cross sections
determined by all values and
by ,
respectively.
Table II
For the
Two Selected Geometries,
the Dependence of ,
Defining the Absolute Maximum of the Centrifugal
Barrier, at Each Collision Energy
θ = 90°; ϕ = 220°
θ = 15°; ϕ = 270°
Ecoll (meV)
0.1
10
10
0.3
15
15
1
23
23
3
34
34
10
52
37
30
78
44
100
114
55
300
140
110
1000
190
115
Total, σtot, and partial, σpar, ionization cross sections
determined by all values and
by ,
respectively.Obtained cross-section values
and their ratios demonstrate that
the contribution from highest b or values becomes
appreciable only for Ecoll larger than
the critical value. Accordingly,
the selective role of the centrifugal barrier tends to disappear,
and a unique interval of b or values promotes
the reaction, making effective
also those larger than bmax or ,
since determining turning points at intermediate
and moderately large R.
Conclusions
It
is important to stress that all stereodynamical effects emphasized
for the CHEMI of Cl2 and NH3 must be considered
averaged over all fine structure states accessible to the open-shell
Ne*(3PJ) reagent, identified for atom–atom
reactions by J and Ω quantum numbers. Note
that Ω provides the absolute value of the projection of the
total (sum of the orbital and spin components) electronic angular
momentum J along R, and it indirectly defines
also the alignment degree of the half-filled p-orbital of Ne*(3PJ) reagent respect to R. As demonstrated
for atom–atom CHEMIs,[6,7] both real and imaginary
parts of the optical potential are depending on J and Ω, and this determines the opening of different state-to-state
reaction channels. Figure summarizes some basic differences between CHEMI reaction
dynamics involving molecules in terms of a qualitative scheme of the
potential energy curves that characterizes (see previous sections)
two limiting cases for the direct mechanism. Figure a concerns molecules
with positive electron affinity (e.g., Cl2 and O2), while Figure b
concerns the other cases (e.g., NH3, N2, and
CO).
Figure 8
Scheme of the potential energy curves characterizing the two limiting
cases for the direct mechanism. (a) CHEMI involving
molecules with positive electron affinity (e.g., Cl2 and
O2); (b) other cases mentioned in the text (e.g., NH3, N2, and CO).
Scheme of the potential energy curves characterizing the two limiting
cases for the direct mechanism. (a) CHEMI involving
molecules with positive electron affinity (e.g., Cl2 and
O2); (b) other cases mentioned in the text (e.g., NH3, N2, and CO).For CHEMIs of molecules, the characterization of state-to-state
reaction channels, with their dependence on both atomic alignment
and molecular orientation, will be the target of a future extension
of our methodology. Particular attention must be further addressed
to the N2 and O2 reagents for which differences
in the collinear and perpendicular approach of the diatomic molecule
to Ne* are expected to emphasize a new selectivity in the reaction
dynamics. In particular, while N2, from a phenomenological
point of view (see Figure ), behaves similarly to CO and CH4, with a total
ionization cross section that increases with Ecoll, under thermal collision energies the cross section of
O2 is at least a factor 3 larger with respect to that of
N2, and it decreases with Ecoll as for Cl2 and C2H2. The present
paper suggests that the different behavior in the ionization cross
sections of CHEMI involving molecules probably arises from a different
balance of the intermolecular forces involved, which selectively depend
on the fundamental physical/chemical properties of the molecules.
In particular, while the electronic polarizability is comparable for
N2 and O2, the electric quadrupole moment (that
of N2, depicted in Figure , is approximately a factor 4 larger with respect to
that of O2), energetics, and symmetry of highest occupied
molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO)
molecular orbitals are completely different in the two cases.Finally, it is interesting to note for Ne*-N2 important
features of the isotropic optical potential were obtained from a multiproperty
analysis of several experimental findings.[37] In such a study the use of a combination of two imaginary components
was necessary to reproduce simultaneously all analyzed experimental
observables, which were probing complementary details of the interaction.
According to the suggestions of this paper and our recent studies,[6,7] this necessity probably relates to the occurrence of two competitive
reaction mechanisms.Therefore, the investigation from a phenomenological
point of view
of CHEMI reactions of prototype diatomic and polyatomic molecules
emphasizes again the importance of experiments performed under single
collision conditions and addressed to measure both ionization cross
sections and PIES. The combined analysis of the experimental findings,
that must be carried out adopting a proper formulation of the leading
interaction components driving the collision dynamics, is then crucial
to define the relative role of direct and indirect reaction mechanisms as a function of the geometry
of the reagents approach and of the collision energy. The analysis
of the reaction stereodynamics has allowed us to highlight important
details on the microscopic redox mechanism of CHEMI, which is strongly
dependent on the fundamental intrinsic characteristics of the target
molecule and on the specific intermolecular interactions existing
between the colliding partners, both crucial aspects in determining
the formation of the transition state of the reaction. Our treatment
is able to fully describe such reactions passing over the range from
high temperature to ultracold collisions. This highlights the fact
that that the “canonical” chemical oxidation process,
dominant at a high collision energy, changes its nature in the subthermal
regime to a pure direct photoionization process.[7] It also points out differences between the cold chemistry of terrestrial and interstellar environments and the hot one of combustion and flames.[11−13,38,39]
Authors: Justin Jankunas; Benjamin Bertsche; Krzysztof Jachymski; Michał Hapka; Andreas Osterwalder Journal: J Chem Phys Date: 2014-06-28 Impact factor: 3.488
Authors: Fernando Pirani; David Cappelletti; Stefano Falcinelli; Diego Cesario; Francesca Nunzi; Leonardo Belpassi; Francesco Tarantelli Journal: Angew Chem Int Ed Engl Date: 2019-02-20 Impact factor: 15.336