2.1. AIMD simulations
Research on collision-induced O2 dissociation can be
dated back to the 60s when the dissociation of O2 was
driven by argon collisions in a shock-tube apparatus and the reduction
of its optical absorption intensity was detected.[23] This seminal
work confirmed that under such a macroscopic collision arrangement, the
condition of near-thermal-equilibrium is satisfied and the rate constant
of O2 dissociation is governed by a simple Arrhenius
equation such that the dissociation probability scales exponentially
with -5.1eV/kBT , where 5.1eV is the well-known
dissociation energy of O2. In shock-tube experiments,T of 5000 to 18000K and kBT for argon
rated at 0.65 to 2.35eV are practical. As such, simulations of such
collision-induced dissociation are typically performed with classical or
semi-classical methods.[24] However, the collision-induced
O2 dissociation in the present work is conducted with a
condition far from thermal equilibrium and must be treated
microscopically, with a diligent attention of each collision event in an
atomic scale.
The advances in computational hardware and software now indeed support
such microscopic tracks of collisions and collision-induced
dissociations. In brief, ab initio calculations of the electronic
structures of all collision partners in each collision event by solving
the Schrödinger equation as a function of the evolution-time with a
time-division as short as 0.2fs are practically conducted. The snapshots
of the coordinates, rotational/vibrational states and electronic
structures of the collision partners are commonly referred as ab initio
molecular dynamics (AIMD). In accord to the practical experimental
setup, AIMD of some 200 representative collision events are performed by
adopting O+ to model the oxygen ion extracted from an
ECR oxygen plasma into a cloud of O2. Although
O2+ ions are also extracted, the
practical operation of the experimental AO generator always injects
oxygen ions at 300eV into a cloud of O2 and a 300eV
O2+ collides with O2is expected to effectively converted all injected
O2+ into O+ and O.
Hence, AIMD with O+ as bullets is reasonable. Some
exemplary collision events tracked by AIMD are depicted inFigures 2-3 , with more exemplars shown in Figure S1 .
For example, the AIMD computational results for 300eV
O+ colliding O2 along the molecular
axis of O2 (collision angle at 0o) are
summarized in Figure 2(a) . Briefly, the closest encounter
between the projectile and the OI atom of
O2 occurs near 6fs, and prior to that the projectile is
traveling with not any force influence until the weak van de Waals
interactions prior to 3.5fs. At 3.5fs, the wavefunction of
O+ starts interacting with that of O2and charge exchange occurs, with an electron from the highest occupied
states of O2 tunneling to the lowest unoccupied state of
O+. This process leads to a transfer of potential
energy between the projectile and its colliding partner via electron
tunneling, and virtually induces no change of the kinematics. Then,
shortly after this, the encounter of O and
O2+ becomes repulsive and the
wavefunction of O starts mixing with that of
O2+, to form a transient molecular
species which retains a configuration of
O3+ in the time duration of about 5.5
– 7fs. In this duration, kinetic energy and molecular potential
interchange in a rather peculiar way. Apparently, at about 6.7fs, the
most stable O3+ species is formed and
it flies with a kinetic energy of 300eV. Still, this most stable
O3+ is repulsive in nature and quickly
dissociates into O-OI+ and OII at
about 7.5fs. Hence, although the collision is violent, the process ends
with one AO and an O2+, with no
generation of any additional AO.
To further illustrate the collision events in an atomic scale, the
isosurface evolutions of the spin density distributions of this system
comprising three oxygen atoms are tracked and depicted inFigures 2. For example, Figure 2(a) shows, at 0fs, two
blue isosurfaces signifying the presence of two spin-identical electrons
in the px and py orbitals of the spin-polarized oxygen molecule. The
spatial distributions of spin density undergo significant changes
throughout the collision process.
Although the violent head-on collision with a collision angle of
0o does not yield any AO generation, a slight change
in collision angle causes some surprising changes. For example, when the
collision angle is changed merely by 5 degrees, the shear-like
adjustment of the violent collision effectively causes the dissociation
of the transient repulsive molecular species of
O3+ into 2AOs and an
O+. Additional AIMD calculations reveal that the
production of AOs in this collision configuration of “5 degrees” can
proceed as long as the incoming O+ carries a kinetic
energy more than 36eV, as shown in Figure 2(b) . In this case,
the O+ bullet of 36eV changes to O at about 9fs and merges with the
resultant O2+ to form a transient
O3+ which survives in the duration of
about 12fs – 17fs. At 20fs, an AO and a highly excited
O2+ are formed. At 25fs, the excited
O2+ dissociates into O and
O+. Clearly, the inset of Figure 2(b)illustrates that the separations among all three atomic centers are all
increasing with time.
In the collision configuration when an 14eV O+ flies
head-on towards the OI atom of O2 with
a velocity perpendicular to the O2 molecular axis
((collision angle at 90o), a repulsive and transient
O3+is formed and survived for the
duration of about 28fs – 50fs. But the three atomic centers slowly move
away from each other and eventually dissociates into 2AOs and an
O+. The threshold kinetic energy of the bullet
O+ for collision-induced dissociation of
O2 is 14eV for this particular collision configuration.
The AIMD results are summarized in Figure 3(a) . By moving the
flight path of O+ merely 0.04nm away from the
OI center of O2, the slightly change
in the collision impact parameter (therein referred as IP) causes a
large increase from 14 to 54eV in the dissociation threshold in
reference to the kinetic energy of the O+ bullet, as
shown in Figure 3(b) . A comparison of the head-on case inFigure 3(a) and the IP at 0.04nm case in Figure 3(b)validates the intuitive expectation that the kinematic changes of
OI which is the principal collision partner hit by the
O+ bullet is less “sloppy” in the case of the
head-on collision case.
In short, the AO-generation thresholds critically depend on the exact
collision configurations and some representative values are summarized
in Table 1 . Consequently, this results strongly support the
likelihood of the following reaction kinematics involving
charge-transfer and dissociative collisions (with a label of * to denote
the hyperthermal nature of a reactant):
\(\text{\ O}^{+*}+\ O_{2}\ =\ O^{+*}\ +\ O^{*}\ +\ O^{*}\)(R1)
\(\ O^{*}+\ O_{2}\ =\ O^{*}\ +\ O^{*}\ +\ O^{*}\) (R2)
\(\text{\ O}^{+*}\ +\ O_{2}\ =\ O^{*}+O_{2}^{\ +*}\ \) (R3)
\(\text{\ O}_{2}^{\ +*}\ +\ O_{2}\ =\ \text{\ O}_{2}^{\ *}+O_{2}^{\ +*}\ \)(R4)
\(\text{\ O}_{2}^{\ +*}\ +\ O_{2}\ =\ O^{+*}+O^{*}+O^{*}+O^{*}\ \ \)(R5)
\(\text{\ O}_{2}^{\ +*}\ +\ O_{2}\ =\ \text{\ O}_{2}^{\ +*}+O^{*}+O^{*}\ \ \)(R6)
\(\text{\ O}_{2}^{\ *}\ +\ O_{2}\ =\ O^{*}+O^{*}+O^{*}+O^{*}\ \ \)(R7)
\(\text{\ O}_{2}^{\ *}\ +\ O_{2}\ =\ O_{2}^{\ *}+O^{*}+O^{*}\ \ \)(R8)
For example, in R1, a hyperthermal O+ with 300eV
violently collides with an O2 and this leads to the
dissociation of O2 into two hyperthermal AOs. With a
sufficiently high kinetic energy, a resultant hyperthermal atomic oxygen
may again cause the collision-induced dissociation of an
O2, a reaction which yields three hyperthermal AOs. In
R3, charge transfer between O+ and O2is noted, together with kinetic energy transfer. Similarly, charge
transfer between an \(O_{2}^{\ +*}\) and an O2 is
noted in R4, together with kinetic energy transfer. In R5, an\(O_{2}^{\ +*}\) with a sufficiently high kinetic energy causes an
extremely violent collision-induced dissociation of itself and the
collided O2, with the production of four hyperthermal
AOs. In comparison, R6 depicts a less violent event with only one case
of dissociation. R7 and R8 are counterparts of R5 and R6, with\(\text{\ O}_{2}^{\ *}\) replacing \(O_{2}^{\ +*}\) as the “bullet”.
The present work tracks all these reactions and statistically sizes up
the essences in the AO generation by injecting 300eV O+ into a cloud of
O2 at 0.14Pa.