Dóra Papp1, Gábor Czakó1. 1. MTA-SZTE Lendület Computational Reaction Dynamics Research Group, Interdisciplinary Excellence Centre and Department of Physical Chemistry and Materials Science, Institute of Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary.
Abstract
We perform rotational mode-specific quasi-classical trajectory simulations using a high-quality ab initio analytical potential energy surface for the Cl(2P3/2) + C2H6 → HCl + C2H5 reaction. As ethane, being a prolate-type symmetric top, can be characterized by the J and K rotational quantum numbers, the excitation of two rotational modes, the tumbling (J, K = 0) and spinning (J, K = J) rotations of the reactant is carried out with J = 10, 20, 30, and 40 at a wide range of collision energies. The impacts of rotational excitation on the reactivity, the mechanism, and the post-reaction distribution of energy are investigated: (1) exciting both rotational modes enhances the reactivity with the spinning rotation being more effective due to its coupling to the C-H stretching vibrational normal modes (C-H bond elongating effect) and larger rotational energies, (2) rotational excitation increases the dominance of direct rebound over the stripping mechanism, while collision energy favors the latter, (3) investing energy in tumbling rotation excites the translational motion of the products, while the excess spinning rotational energy readily flows into the internal degrees of freedom of the ethyl radical or, less significantly, into the HCl vibration, probably due to the pronounced rovibrational coupling in this case. We also study the relative efficiency of vibrational and rotational excitation on the reactivity of the barrierless and thus translationally hindered title reaction.
We perform rotational mode-specific quasi-classical trajectory simulations using a high-quality ab initio analytical potential energy surface for the Cl(2P3/2) + C2H6 → HCl + C2H5 reaction. As ethane, being a prolate-type symmetric top, can be characterized by the J and K rotational quantum numbers, the excitation of two rotational modes, the tumbling (J, K = 0) and spinning (J, K = J) rotations of the reactant is carried out with J = 10, 20, 30, and 40 at a wide range of collision energies. The impacts of rotational excitation on the reactivity, the mechanism, and the post-reaction distribution of energy are investigated: (1) exciting both rotational modes enhances the reactivity with the spinning rotation being more effective due to its coupling to the C-H stretching vibrational normal modes (C-H bond elongating effect) and larger rotational energies, (2) rotational excitation increases the dominance of direct rebound over the stripping mechanism, while collision energy favors the latter, (3) investing energy in tumbling rotation excites the translational motion of the products, while the excess spinning rotational energy readily flows into the internal degrees of freedom of the ethyl radical or, less significantly, into the HCl vibration, probably due to the pronounced rovibrational coupling in this case. We also study the relative efficiency of vibrational and rotational excitation on the reactivity of the barrierless and thus translationally hindered title reaction.
The relative efficiency of different forms of the energy invested
in a chemical reaction has been widely studied both experimentally
and theoretically in the past decades. For the smallest A + BC atom
+ diatom reactions, the first rules of thumb of energy efficiency
have been established:[1] translational energy
promotes such a reaction if the reactants have to surmount an early
barrier, that is, the reaction has a reactant-like transition state
(TS), while vibrational energy enhances a late-barrier reaction having
a product like TS structure with an elongated B–C bond. In
the case of more complex chemical reactions involving a polyatomic
molecule, the question of mode-specificity naturally rises: which
vibrational mode of the polyatomic reactant should be excited to promote
(or inhibit) the reaction? Or, even more specifically, how can one
reach the selective cleavage of a chemical bond? These issues have
also been extensively investigated,[2−25] involving even 7- and 9-atomic systems, as well.[26−33]However, a somewhat less studied phenomenon is when the rotational
motion of a polyatomic reactant molecule is excited. In atom + diatom
reactions, where the rotation of the diatom can be characterized by
the J rotational quantum number, rotational excitation
effects have been the focus of several experimental, classical, and
quantum dynamics studies.[34−41] Stepping forward, in the case of polyatomic reactants, rotational
mode-specificity can also be defined and investigated, as a symmetric/asymmetric
polyatomic rotor can also be characterized by K/KaKc quantum number/labels,
the projections of the J total rotational angular momentum
to the body-fixed axes. Thus, the K/KaKc quantum number/labels,
which can adopt values in the [0, ±1, ..., ±J] interval, necessarily introduce rotational mode-specificity as
their different values correspond to different rotational modes (states)
of the reactant molecule. Accordingly, rotational mode-specific studies
for the H2O+ + H2/D2,[42,43] H/F/Cl + H2O,[44−46] F/Cl/OH + CH4,[47−50] H/Cl/O + CHD3,[51−54] and the F– + CH3F/CH3Cl/CH3I[55,56] reactions involving
asymmetric, spherical, and symmetric top polyatomic reactants have
been carried out.Experiments found significant rotational promotion
in the case
of the H2O+(J, Ka, Kc) + D2 reaction,[42] which was later explained by simulations as
the facilitated reorientation of the H2O+ molecule
due to rotational excitation.[43] In the
case of the H + CHD3 reaction, a seven-dimensional quantum
dynamics study found basically no effect of rotational excitation
up to J = 2;[51] however,
for Cl + CHD3(v1 = 1) →
HCl + CD3, a joint crossed-beam, quasi-classical, and quantum
dynamics investigation showed that the tumbling rotation (J, K = 0) of CHD3 significantly
enhances the reactivity, while the spinning rotation of the reactant
around the C–H axis (K = J) has only a minor effect.[52] It was shown
for this,[52] and also for the O(3P) + CHD3(v1 = 0,1) →
OH + CD3,[54] reaction that rotational
excitation does not affect the scattering angle distribution of the
products, but the initial attack angle distributions indicated the
enlargement of the reactive cone of acceptance with increasing J. Interestingly, for the OH + CH3 → O
+ CH4 reaction, quantum dynamics simulations found that
the rotational excitation of both of reactants hinders the reaction.[57,58] Rotational mode-specific computations involving the F– + CH3F/CH3Cl bimolecular nucleophilic substitution
(SN2) reactions observed substantial rotational inhibition
as well.[55] In the former case, both the
spinning (K = J) and the tumbling
(K = 0) rotation of the CH3F reactant
had a similar inhibiting effect, whereas for the latter reaction,
the tumbling rotation was found to be less effective in hindering
reactivity.[55] Very recently, the F– + CH3I reaction was also studied and showed
considerable rotational hindrance in the case of the SN2 channel for both tumbling and spinning excitations, whereas the
proton-transfer reaction was noticeably promoted with increasing J by exciting the spinning reactant rotational mode; however,
it was left unaffected by tumbling excitation.[56]In the present work, we study the effect of rotational
excitations
for a 8-atomic reactant molecule, namely, ethane, in the Cl(2P3/2) + C2H6 → HCl + C2H5 reaction by performing quasi-classical trajectory
(QCT) simulations on our recently developed high-quality ab initio
full-dimensional potential energy surface (PES).[59] Ethane is a prolate-type symmetric top, characterized by
the J and K rotational quantum numbers,
and we focus on the two limiting cases, (1) K = 0,
referring to the rotation around the axis perpendicular to the C–C
bond, that is tumbling rotation, and (2) K = ±J, denoting the spinning rotation around the C–C bond. We investigate the different
rotational-mode excitations on the reactivity, the mechanism, and
the energy flow during the reactions. We also compare the relative
efficacy of rotational, translational, and even vibrational[31] form of energy investments.
Methods
In the Cl + C2H6 →
HCl + C2H5 reaction, the reactant ethane molecule
within the rigid-rotor
approximation is a prolate-type symmetric top; thus, it can be characterized
by two rotational quantum numbers, J and K. The J quantum number is related to the j length of the j classical total angular momentum
vector aswhere j iswhere jα (α = x, y, z) are the three components of the j total angular momentum
vector in the body-fixed coordinate system (principal axis system)
and the K quantum number is identified as the projection
of j on the body-fixed x axis, that
is, K = j (this latter convention applies only for the prolate-type
case).During the QCT simulations, after setting j to the K quantum number
and j according to eq , j and j are randomly sampled based
on the expressionswhere R ∈ [0,1] is
a real random number. Then, the j vector is transformed
to the space-fixed Cartesian coordinate system defined in the QCT
computations. The initial angular momentum is tuned by standard modifications
of the v velocity vector
of each atom[60]wherewhere Ω is the angular
velocity vector, q are the
Cartesian coordinates of the ith atom, I is the moment of inertia tensor, and j0 is
the preexisting angular momentum vector corresponding to the v0 initial velocities.In quantum dynamics,
the initial JK-specific state
of the reactant can also be selected as was done in ref (52) in the case of the Cl
+ CHD3 reaction. In QCT simulations, an assembly of trajectories
with different R values (j directions,
precessing around the principal axis) corresponds to a specific initial
rotational quantum state.
Computational Details
We carry out quasi-classical computations using our recently developed
PES[59] for the Cl + C2H6 → HCl + C2H5 reaction by applying different
rotational excitations of the reactant ethane molecule. We examine
the two limiting cases of rotational mode-, that is, K-quantum-number dependency: the K = 0 and the K = J cases, while the J quantum number adopts the following values: 0, 10, 20, 30, and 40.
These J, K pairs correspond to 0.21,
0.80, 1.76, and 3.11 kcal/mol rotational energies when K = 0 and to 0.79, 3.11, 6.96, and 12.36 kcal/mol rotational energies
when K = J for J = 10, 20, 30, and 40, respectively.The initial orientation
of the reactants is random, and the initial
vibrational state, the zero-point energy (ZPE), of ethane is set using
standard normal-mode sampling.[60] The initial
distance of the reactants is , where x = 16 bohr and
the b impact parameter is varied between 0 and bmax (where the reactivity vanishes) with a step
size of 1 bohr. The simulations are carried out at the following collision
energies: 1.0, 3.0, 5.5, and 10.0 kcal/mol. We run 500 trajectories
for each b–J, K pair−collision energy combination. The setting of the initial J and K quantum numbers of ethane is described
in Section in detail.The integral cross sections (ICSs) for the title reaction at different
collision energies and for different J, K settings are calculated by using a b-weighted numerical
integration of the P(b) opacity
functions (the reaction probabilities as a function of the impact
parameter). We apply different ZPE constraints for the ICSs: (1) soft: the sum of the classical vibrational energy of the
ethyl radical product and the classical internal energy of the HCl
product must be larger than the sum of the harmonic ZPE of the ethyl
radical and the anharmonic ZPE of HCl corresponding to its actual
rotational state. The variationally determined anharmonic rovibrational
levels of HCl are taken from ref (6), (2) hard: the above constraints
are set for each product separately, (3) ethyl ZPE: the ZPE constraint is only applied for the ethyl radical. The scattering
angle distribution of the products is obtained by binning the cosine
of the angle θ of the relative velocity vector of the reactants
and that of the products into 5 equidistant bins, where backward scattering
corresponds to cos(θ) = −1.The initial attack
angle of the reactants is considered to be the
included angle of the initial C–C vector and the initial velocity
vector of the center of mass of the ethane molecule. The rotational
quantum number of the HCl product is determined as described in detail
in ref (59), and the
vibrational quantum number of HCl is identified as that of the anharmonic
rovibrational energy level nearest to the classical internal energy
of HCl corresponding to its rotational state.As it has been
shown previously for the rovibrationally unexcited
and the v1 = 1 vibrationally excited Cl
+ C2H6(v = 0,v1 = 1) → HCl + C2H5 reactions,[31] where QCT data obtained from 500 trajectories
per collision energy—vibrational mode—impact parameter
(1 bohr step size) combination were tested against QCT data computed
from 1000 trajectories per collision energy—vibrational mode—impact
parameter (0.5 bohr step size),[59] the relative
uncertainties of ICSs, product angular distributions, and opacity
functions turned out to be less than 10% (4% for the non-constrained
ICSs), while the average (maximum) absolute deviations of the reaction
probabilities and the hard-constrained HCl vibrational-state probabilities
were 0.01 (0.04) and 0.03 (0.07), respectively.
Results
and Discussion
We perform rotational mode-specific (QCT)
computations for the
Cl(2P3/2) + C2H6(J, K) → HCl + C2H5 reaction using our recent full-dimensional analytical PES
fitted on high-quality spin-orbit-corrected ab initio energy points
applying the monomial symmetrization approach[61] and developed by using the Robosurfer program system.[62] The PES, whose energetics is shown in Figure , features a slightly
late barrier for the reaction, with a classical/adiabatic height of
2.21/–2.12 kcal/mol, and the reaction has a classical/adiabatic
2.04/–3.06 kcal/mol endothermicity/exothermicity, with a shallow
entrance-channel well and a relatively deep exit-channel minimum.
Thus, with the ZPE-correction included, the title reaction is barrierless
and exothermic; however, the H-abstraction process covers only about
a 5 kcal/mol energy range. Rotational excitation energies, calculated
aswhere A ≫ B are the non-equal rotational constants
of ethane determined
on the PES, are 0.21, 0.80, 1.76, and 3.11 kcal/mol corresponding
to J, K = 0 (tumbling rotation)
and are 0.79, 3.11, 6.96, and 12.36 kcal/mol when K = J (spinning rotation) for J =
10, 20, 30, and 40, respectively. Due to the smaller moment of inertia
in the K = J case, based on theexpression, the same J quantum
number results in larger angular velocity (Ω) and
therefore larger rotational energy. The K = J energies are commeasurable with some of the fundamental
vibrational energies of ethane;[31] thus,
their effect on the reaction can be readily compared.
Figure 1
Schematic representation
of the classical and adiabatic PES[59] of
the Cl(2P3/2) + C2H6(J, K) →
HCl + C2H5 reaction including rotational energy
levels for different J values when K = 0 (tumbling rotation) and when K = J (spinning rotation) determined on the PES.
Schematic representation
of the classical and adiabatic PES[59] of
the Cl(2P3/2) + C2H6(J, K) →
HCl + C2H5 reaction including rotational energy
levels for different J values when K = 0 (tumbling rotation) and when K = J (spinning rotation) determined on the PES.We run trajectories for different rotational quantum numbers (J and K) of the prolate-type symmetric
top reactant ethane molecule at collision energies 1.0, 3.0, 5.5,
and 10.0 kcal/mol. As seen in Figure , rotational excitation promotes the title reaction
in almost all cases, slight inhibition can only be observed for J = 10, K = 0, and J = K = 20. It is also clear from Figure that higher J values usually
enhance reactivity more and more for both rotational modes. The shape
of the excitation functions, that is, the ICSs as a function of collision
energy, is not affected significantly by rotational excitation, however,
a slightly faster decay can be seen at higher J values
when K = 0, except for the J = K = 20, where an interesting drop in the cross section at
low collision energies can be observed. The decaying shape of the
excitation function is originated from the submerged barrier, which
makes reaction time itself a promoting effect. The reactivity enhancement
due to the spinning rotation excitation is much stronger than that
caused by exciting the tumbling mode, which can be explained by the
above-mentioned larger angular velocity in the former case, and the
corresponding centrifugal force, which may cause a significant elongation
of the C–H bonds and thereby facilitates the abstraction of
one of the H atoms. A similar observation could be made for the F– + CH3I proton-transfer reaction as well.[56] Also in line with this, exciting the spinning
rotation around the C–H bond in the X + CHD3 →
HX + CD3 [X = Cl, O] reactions is found to have only a
minor effect on reactivity.[52,54] In the title reaction,
tumbling rotational excitation might rather induce the elongation
of the C–C bond, which is almost a spectator during H-abstraction[31] and only mildly influences the C–H-bond
elongation. From the rotational reactivity enhancements relative to
the unexcited reaction, shown in Figure , the slow decay of the K = 0 promotion can be observed with increasing collision energy,
whereas exciting the K = J mode
leads to a stronger boosting of the reaction at higher collision energies
(except for J = 10) with small maxima at 6–8
kcal/mol. Surprisingly, in contrast to vibrational[52] and tumbling rotational excitation, the impact of the spinning
rotational excitations on reactivity strengthens as collision energy
increases. This might be explained by the time scales (few tenths
of picoseconds) of collisions and the excited spinning rotation (4
times faster than tumbling rotation) approaching each other as collision
energy increases, thereby making the rotational effect enhanced. Moreover,
probably due to the higher K = J rotational energies and their higher growth with increasing J, exciting spinning rotation enhances reactivity much more
effectively than tumbling rotation: in the K = J case, even a 1.6 increasing factor is reached at J = 40.
Figure 2
ICSs of the Cl + C2H6(J, K) → HCl + C2H5 reaction
and
their enhancement factors relative to the rotationally unexcited reaction
as a function of collision energy for different J, K pairs.
ICSs of the Cl + C2H6(J, K) → HCl + C2H5 reaction
and
their enhancement factors relative to the rotationally unexcited reaction
as a function of collision energy for different J, K pairs.As to the relative efficiency of rotational and vibrational energy
invested in the title reaction, in Figure , we plot the ICSs of the title reaction
in the case of five different vibrationally[31] and four different spinning-rotationally excited cases as a function
of the total initially available energy (collision energy + vibrational/rotational
excitation energy). Note that due to the narrow range of the small
rotational energies corresponding to the tumbling rotation, we omit
it from this comparison. If we take a look at the panels of Figure at 10 kcal/mol total
energy, we can see an almost triple increase in the ICSs relative
to the unexcited reaction when the C–H-stretching modes (v = 1 [x =
1,5,7]) are excited, in which case, 90% of the total energy is in
the vibrational degree of freedom. At the same total energy, the J = K = 20 and 30 rotational excitations
lead to approximately 25 and 40% reactivity enhancement with the rotational
energy being 30 and 70% of the total energy. Furthermore, at 15 kcal/mol
total energy, we observe 50% C–H-stretching-caused (60% of
the total energy in the vibrational modes) vibrational and 30/75% J = K = 30/40 rotational increment (45/80%
in rotation) in the ICSs. Based on the above, we can conclude that
the vibrational excitation (of the CH-stretching modes) can result
in a somewhat more effective reactivity enhancement, especially at
low collision energies, than rotational excitation, with the latter
being still significant and competitive with the former as collision
energy increases.
Figure 3
ICSs as a function of total energy for the Cl + C2H6 → HCl + C2H5 reaction
computed
on our PES from ref (59) with C2H6(v = 0) and C2H6(v = 1) [x = 1, 3, 5, 6, 7] vibrationally and C2H6(J, K = J) [J = 0, 10, 20, 30, 40] rotationally
excited reactants. The unexcited ICS value at a 20 kcal/mol collision
energy in the lower panel is taken from ref (31). The upper panel is adapted
with permission from ref (31). Copyright 2021 American Institute of Physics.
ICSs as a function of total energy for the Cl + C2H6 → HCl + C2H5 reaction
computed
on our PES from ref (59) with C2H6(v = 0) and C2H6(v = 1) [x = 1, 3, 5, 6, 7] vibrationally and C2H6(J, K = J) [J = 0, 10, 20, 30, 40] rotationally
excited reactants. The unexcited ICS value at a 20 kcal/mol collision
energy in the lower panel is taken from ref (31). The upper panel is adapted
with permission from ref (31). Copyright 2021 American Institute of Physics.From the reaction probabilities and the product scattering
angle
distributions shown in Figure , we can see that rotational enhancement is the most pronounced
at small impact parameters since the bmax values do not change considerably upon the rotational excitation
of ethane, while the probabilities rise significantly with increasing J at smaller b values. This results in
a small drop in the otherwise basically isotropic (except for the
highest collision energy where the products are mainly forward scattered)
angular distributions near cos(θ) = 1 with increasing J for both tumbling and spinning rotations, which indicates
a slightly increased backward scattering as J increases,
the signature of the direct rebound mechanism, dominant at small b values. As collision energy increases, the stripping mechanism,
occurring at larger impact parameters, becomes prevalent, causing
the clearly forward scattered pattern at 10 kcal/mol (dropping also
at cos(θ) = 1 with increasing J). The more
intense promoting effect of the spinning excitations is also clear
from the reaction probabilities compared to the tumbling rotation,
and therefore, the drop in the normalized product angular distributions
near the forward direction is also more pronounced in the K = J case.
Figure 4
Reaction probabilities
(upper rows) and normalized product scattering
angle distributions (lower rows) of the Cl + C2H6(J, K) → HCl + C2H5 reaction at different collision energies in the K = 0 and K = J limiting
cases for different values of J.
Reaction probabilities
(upper rows) and normalized product scattering
angle distributions (lower rows) of the Cl + C2H6(J, K) → HCl + C2H5 reaction at different collision energies in the K = 0 and K = J limiting
cases for different values of J.If we inspect the distributions of the initial attack angle (α)
of the reactants of reactive trajectories, defined as the angle between
the initial C–C vector and the initial velocity vector of the
center of mass of C2H6, shown in Figure S1 in
the Supporting Information, we cannot observe
significant J-dependency, similarly to the F– + CH3X [X = Cl, I] SN2 reactions.[55,56] However, this finding is in sharp contrast to the behavior of the
O/Cl + CHD3 reactions[52,54] upon rotational
excitation: in these cases, the tumbling rotation (K = 0) enhances the reactivity of H-abstraction by enlarging the reactive
cone of acceptance, while the attack angles corresponding to the K = J excitation (spinning around the C–H
axis) are less dependent on J. For the title reaction,
due to the D3d symmetry of ethane, the
attack angle distributions are supposed to be symmetric with respect
to cos(α) = 0, which is shown in Figure S1, within statistical accuracy. The essentially isotropic
distributions suggest that both the front-side (along the C3 axis) and side-on (along the axis perpendicular
to the C–C bond) reactivities are basically the same; however,
a very slight preference in the spinning-excited cases can be seen
for the perpendicular direction. In the case of spinning rotation,
occurring around the C–C bond, the Cl atom approaching the
front side of ethane along the C3 axis
finds a H atom with similar probability if b is small,
independent of the intensity of the rotation, while when it is approaching
from the side-on direction, the excited rotational motion of the H
atoms around the C–C axis increases the probability of Cl finding
a H atom to react with. This phenomenon is basically independent of
the change in collision energy and becomes more apparent with increasing J.As to the impact of rotational excitation on the
energy flow during
the title reaction, the difference between the two rotational modes
is clearly shown in Figure : the excess rotational energy excites the relative translational
motion of the products, while the internal energy of the ethyl radical
is basically unaffected during tumbling rotation, whereas the energy
of the excited spinning rotational mode is mostly fueled into the
internal degrees of freedom of C2H5, while only
negligible rotational energy flows into the translational motion in
this case. These effects are present at all collision energies (of
course, the ones corresponding to the tumbling rotation are smaller
due to the smaller rotational energies) and are more and more pronounced
as J increases. In addition, higher collision energies
also induce stronger translational excitation of the products upon
the increase of J in the case of spinning rotation.
Interestingly, in the F– + CH3I →
HF + CH2I– reaction, the spinning rotation
around the C–I axis, leading to C–H elongation, gave
rise to a hotter translational distribution of the products.[56] The translational energy distributions of the
unexcited reaction widen with increasing collision energy accompanied
by only minor changes in the internal energy distributions. The fundamentally
different behavior of the two rotational modes in the title reaction
might be explained, on one hand, by the stronger coupling of the spinning
rotation with the C–H stretching vibrational modes of ethane,
and thereby of the ethyl radical product, due to the elongation of
the C–H bonds induced by the spinning-generated centrifugal
force. At the same time, tumbling rotation basically changes only
the relative orientation of the reactants; therefore, the excess energy
in this mode might more easily flow into the relative translational
degree of freedom of the products. On the other hand, the spinning
rotational excitation of ethane is more likely to contribute to the
internal energy of the ethyl radical product because the C–C
bond does not break during the H-abstraction reaction and the shape
of the ethyl radical is not very different from that of ethane (with
respect to the spinning rotation), while the force acting due to the
tumbling rotational motion on the H atoms causes the recoil of the
fragments after reaction. It is also apparent from the internal energy
distributions of the ethyl radical that a significant amount of the
trajectories is ZPE-violating, which is the reason for applying different
ZPE constraints on the cross sections (see Figures S2 and S3 of the Supporting Information).
Figure 5
Normalized internal energy
distribution of the ethyl radical where
vertical black lines refer to the ZPE of the ethyl radical (37.4 kcal/mol)
(upper rows) and normalized relative translational energy distributions
of the products (lower rows) of the Cl + C2H6(J, K) → HCl + C2H5 reaction at different collision energies in the K = 0 and K = J limiting
cases for different values of J.
Normalized internal energy
distribution of the ethyl radical where
vertical black lines refer to the ZPE of the ethyl radical (37.4 kcal/mol)
(upper rows) and normalized relative translational energy distributions
of the products (lower rows) of the Cl + C2H6(J, K) → HCl + C2H5 reaction at different collision energies in the K = 0 and K = J limiting
cases for different values of J.The vibrational state distributions of the HCl product molecule,
shown in Figure ,
suggest that the excess energy in the spinning rotation is more likely
to excite the HCl vibration at low collision energies, while at the
highest 10 kcal/mol energy, this effect is equalized between the spinning
and tumbling rotations. The vHCl = 1 relative
populations increase with increasing J due to spinning
rotational excitation; even the vHCl =
2 state emerges in a few cases, while such a tendency cannot be clearly
observed when the tumbling rotation is excited. The rotational influence
on the HCl vibration is quite moderate overall, especially compared
to vibrational effects, where the CH-stretching excitation energies
readily convert into diatomic product vibration in the Cl/F + C2H6 → HCl/HF + C2H5 reactions.[31,32] Translational effects are commeasurable
for the title reaction with the rotational ones as the rotationally
unexcited reaction also develops some vibrational excitation of HCl
as the collision energy increases.
Figure 6
Vibrational state distributions of the
HCl product of the Cl +
C2H6(J, K)
→ HCl(vHCl) + C2H5 reaction at different collision energies in the K = 0 and K = J limiting cases for
different values of J.
Vibrational state distributions of the
HCl product of the Cl +
C2H6(J, K)
→ HCl(vHCl) + C2H5 reaction at different collision energies in the K = 0 and K = J limiting cases for
different values of J.We also applied different ZPE constraints for the products in the
case of the different rotational excitations, and their impact on
reactivity is shown in Figures S2 and S3 for the tumbling and the spinning rotational cases, respectively.
As these figures show, all the applied restrictions provide smaller
reactivities than the unrestricted results; nevertheless, the qualitative
features of the excitation functions remain similar. The largest changes
in magnitude are induced by the hard constraint, where each product
must have a larger vibrational energy than its ZPE, with these effects
being much clearly present in the case of the tumbling rotations.
As seen in Figures and 6, when K = J, the excess rotational energy remains mostly in the internal
motions of the ethyl radical, while the HCl vibration becomes also
more excited in this case, which is more and more apparent with increasing J; therefore, less trajectories are discarded due to the
ZPE constraints, which results in larger increments in reactivity
as J increases. Accordingly, the rotational effects
are especially intensified when the hard constraint is applied: in
this case, the spinning rotational enhancement reaches even a factor
of 15 at K = J = 40 at 1 kcal/mol
collision energy. An analogous observation can be made for K = 0 as well, however, on a smaller scale. The soft and
“ethyl ZPE” constraints give very similar results for
both rotational modes. From the ICSs plotted as a function of the
total available initial energy (collision energy + rotational excitation
energy, first row of Figures S2 and S3),
the rotational reactivity enhancement is clear, as at a constant total
energy, higher J values lead to higher reactivity
(except for some rare occasions of inhibition).
Conclusions
We carry out a comprehensive rotational mode-specific study for
the negative-barrier Cl(2P3/2) + C2H6 → HCl + C2H5 reaction
by performing QCT simulations using our recently developed high-quality
ab initio analytic PES. The reactant ethane molecule, being a prolate-type
symmetric top, can be characterized by the J and K rotational quantum numbers within the rigid rotor approximation.
We examine the two limiting cases of rotational excitation of ethane:
the tumbling (J, K = 0) and the
spinning (J, K = J) rotational modes, with J = 10, 20, 30, and 40.
We find considerable rotational reaction promotion in almost all cases,
with the spinning rotational excitation having a more pronounced impact,
on one hand, by making the C–H bonds more and more elongated
as J increases, and, on the other hand, due to larger
rotational energies. The decaying shape of the excitation function
(caused by the submerged barrier) of the unexcited reaction does not
change significantly upon rotational excitation; however, the rotational
effects get stronger with increasing collision energy in the case
of spinning excitation, while the enhancement factors decrease with
increasing collision energy when tumbling rotation is excited. Comparing
the relative efficiency of (spinning) rotational and vibrational excitation
on the title reaction, we find that they are commensurable, with vibrational
reactivity enhancement, especially in the case of the C–H normal
modes, being more significant at low collision energies. Exciting
both rotational modes of ethane leads to increased reactivity mainly
at small impact parameters (more markedly in the case of spinning
rotation), where the backward-scattering direct rebound mechanism
is dominant, while increasing collision energy makes the stripping
mechanism prevalent, resulting in mostly forward-scattered products.
The mainly isotropic initial attack angle distributions show a slight
preference for side-on attack for spinning rotational excitations.
The excess tumbling rotational energy turns out to flow mainly into
the relative translational mode of the products, whereas the energy
invested to excite the spinning rotational mode tends to flow into
the internal degrees of freedom of the ethyl radical, which might
be explained by stronger rovibrational coupling in the latter case
(elongated C–H bonds induced by rotational excitation). Rotational
excitation has, in general, a minor role in populating the excited
vibrational states of the HCl product, falling in the magnitude of
translational excitation, and much less significant than vibrational
excitation; however, probably due to the above-mentioned rovibrational
coupling, the spinning rotational energy can more easily flow to HCl
vibration. Since a fair amount of the trajectories is ZPE-violating,
we applied three different ZPE restrictions on the ICSs of the title
reaction. Finally, we conclude that the present study demonstrates
that the reactions of rotationally state-selected polyatomic molecules
may open new mode-specific research directions, thereby advancing
our fundamental knowledge on chemical reaction dynamics.
Authors: Michael Y Hayes; Michael P Deskevich; David J Nesbitt; Kaito Takahashi; Rex T Skodje Journal: J Phys Chem A Date: 2006-01-19 Impact factor: 2.781