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.