( -) reactions have been determined, revealing the dominance of σ CT (v + ) over σ HT (v + ) at E cm =0.04-8.00 eV. The E cm dependence of σ CT (v + ) at low E cm <1.00 eV is consistent with the long-range ion-dipole and ion-induced dipole CT mechanism. Minor vibrational inhibition is observed for the σ CT (v + ) at low E cm 0.30 eV, which can be rationalized by the near-resonance CT mechanism. While the σ HT (v + ) values are consistent with previous measurements, the σ CT (v + ) obtained here resolve a hump at E cm =1.0-5.0 eV, which is not observed previously. This feature is attributed to the formation of excited H 2 O + (B 2 B 2 ) ions via the collision-assisted CT mechanism. The branching ratio for product H 2 O + [BR(H 2 O + )] is found to be constant (0.82 ± 0.05) at E cm =0.04-1.00 eV, and is independent of v + vibrational state. As E cm is increased from 1.0 eV, the BR(H 2 O + ) reaches a maximum of 0.93 at E cm ≈3.00 eV, followed by the decline to 0.20 at E cm 9.0 eV, where σ HT (v + ) becomes dominant compared to σ CT (v + ). The v v v
PT 1 2 3 s 1. Introduction
Nitrogen (N 2 ) and water (H 2 O) molecules and their cations (N 2 + and H 2 O + ) are some of the main molecular species in planetary atmospheres and astrochemical environments, where chemical reactions involving N N 2 2 + and H 2 O + /H 2 O play an important role in determining the chemical compositions as well as the chemical evolutions (Giguere & Huebner 1978;Huntress et al. 1980;Semo & Koski 1984;Smith 1992;Smith & Spanel 1995;Herbst 2001;Williams et al. 2002;Snow & Bierbaum 2008;Larsson et al. 2012). Since N 2 + and H 2 O + cations are mostly produced by electron impact and solar vacuum ultraviolet (VUV) photoionization of atmospheric N 2 and H 2 O neutrals, long-lived rovibronically excited N 2 + and H 2 O + ions are expected to be produced in abundance in planetary environments. We have pointed out previously that long-lived N 2 + and H 2 O + ions thus produced in different quantum states can have different chemical reactivity toward the same neutral reactants (Chang et al. 2012;Xu et al. 2013b). Hence, it is highly desirable to take into account quantumrovibronic-state effects on σ values of relevant ion-molecule reactions involving N 2 + and H 2 O + ions in order to achieve realistic modeling of the chemistry occurring in planetary atmospheres and astrochemical environments.
Most ion-molecule reactions of relevance to astrophysics are known to take place at near thermal energies with center-of-mass collision energies of E cm 30-40 meV. However, suprathermal ion-molecule collisions in the E cm range of a few eV also occur. In such cases, reactants may originate from solar VUV or electron impact photodissociation and photoionization processes with high kinetic energy releases. Dressler and coworkers have shown that the fluorescence glow observed near the surface of the space shuttle during its exit of or entry into the Earth's atmosphere can involve supra-thermal reactions of N H O 2 2 + + (Dressler et al. 1990a). After taking into account of the velocities of space vehicles, ion-molecule collisions between N 2 + and H 2 O associated with contaminant clouds of the space vehicles can reach supra-thermal energies of a few eV.
With the goal to establish a reliable database of quantumstate-selected σ values for chemical modeling of planetary atmospheres, we have developed unique ion-molecule reaction facilities for ion-molecule collisional studies. By combining the vacuum ultraviolet laser pulsed field ionization-photoion (VUV-PFI-PI) ion source with the DQDO radio-frequency (rf) ion-guided mass spectrometer (Chang et al. 2011(Chang et al. , 2012)), we have recently succeeded in recording σ values for an array of quantum-rovibronic-state-selected ion-molecule reactions in the E cm range of 0.03-10.00 eV, which are relevant to chemical modeling of planetary atmospheres. These reactions include (Chang et al. 2011(Chang et al. , 2012;;Xu et al. 2012Xu et al. , 2016Xu et al. , 2017aXu et al. , 2017bXu et al. , 2013aXu et al. , 2013b;;Li et al. 2014;Song et al. 2016;Xiong et al. 2017aXiong et al. , 2017b)). The current vibrational state-selected σ-measurements on the X N :
reactions represent a continuation of this effort. In addition to providing reliable quantum-state-selected cross sections for chemical modeling, which are mostly not available previously, the σ values and product branching ratios (BRs) obtained here can also serve as valuable benchmarks for first-principle theoretical quantum reaction dynamics calculations.
Because of the importance of the N H O 2 2 + + reaction, many kinetic and dynamic studies on this reaction have been reported in past decades (Shahin 1967;Turner & Rutherford 1968;Howard et al. 1970;Dreyer & Perner 1971;Bolden & Twiddy 1972;Howorka et al. 1974;Karpas et al. 1978;Smith et al. 1978;Tichý et al. 1979;Huntress et al. 1980;Parent et al. 1985;Dressler et al. 1990bDressler et al. , 1993;;Yuan et al. 2011
The ΔE values for the N 2 + (v + =1 and 2)+H 2 O reactions can be calculated using the respective vibrational energies of 2181 and 4312 cm -1 . Here, the σ values for the formation of H 2 O + via the charge transfer (CT) and N 2 H + via the H-atom transfer (HT) product channels are referred to as σ CT (v + ) and σ HT (v + ), respectively. The most interesting observation of this study is the hump at E cm =1.0-5.0 eV resolved in the We also reported on σ-measurements for the X B H O :
and 100)+N 2 reactions at E cm =0.30-8.00 eV, which can be considered the reverse reaction of reaction (1). In the E cm range of 0.04-10.0 eV, we have only observed and determined the v v v + + in the collision of H 2 O + (X 2 B 1 : 000 and 100)+N 2 , are too weak to be measured. Although the σ PT (000 and 100) values are low, we are still able to measure the σ PT (000 and 100) curves. The comparison of these curves reveals strong vibrational enhancement for excitation of the (100) symmetric stretching vibrational mode of reactant H 2 O + (X 2 B 1 ) ion. Furthermore, the σ PT (000 and 100) curves observed here exhibit distinct E cm thresholds, which are found to be in accord with their thermochemical thresholds.
The VUV-PFI-PI DQDO ion-molecule reaction apparatus and experimental procedures employed in this study have been described in detail previously (Chang et al. 2012;Xu et al. 2013b;Xiong et al. 2017a). This apparatus consists of a molecular beam source for the generation of a pulsed supersonic N 2 (H 2 O) beam, a VUV laser PFI-PI ion source for the preparation of quantum-state-selected reactant
and 100; N 0 Ka Kc 00
)] ions with narrow laboratory kinetic energy (E lab ) spreads (ΔE lab ≈ ± 0.05 eV), and a DQDO mass spectrometer for σ measurements. A set of dual rf-octopole ion guides was used for guiding the reactant and product ions in and out of the reactant gas cell. The measurements of reactant and product ion intensities were made by using the product quadrupole mass spectrometer (QMS) along with a Daly-type ion detector.
For the
and 100)+N 2 ] reaction study, the tunable VUV laser radiation was generated by resonance-enhanced four-wave sum-frequency (2ω 1 +ω 2 ) mixing schemes using a Kr (Xe) jet as the nonlinear medium. The fundamental frequencies ω 1 and ω 2 were generated by two independently tunable dye lasers pumped by an identical Nd:YAG laser operated at 15 Hz. While the laser ω 1 output was set to match the p p p p 5 4 6 5 ¬ ¬ (
) resonance-enhanced two-photon transition of Kr (Xe) atom, the laser ω 2 output was scanned to generate the VUV (2ω 1 +ω 2 ) sum-frequency range required for the experiment, i.e., photoionizing N 2 (H 2 O) molecules into selected quantum rovibrational states of
B 1 : 000 and 100)] reactant ions. We introduce the precursor N 2 (H 2 O) molecules into the photoionization/photoexcitation (PI/PEX) region in the form of a supersonic molecular beam, traveling along the central axis of the DQDO mass spectrometer to intersect the VUV laser beam perpendicularly at the PI/PEX center. By employing the sequential electric field pulse scheme to generate VUV-PFI-PIs, we achieved narrow kinetic energy spreads (ΔE lab ≈ ±0.05 eV) as well as high detection sensitivity for VUV-PFI-PIs. The most essential elements of the VUV-PFI-PI ion source consist of three ion lenses, E1, I1, and I2, where the space between E1 and I1 defines the PI/PEX region; and I2 is the ion lens used to block out the prompt ions from exiting the ion source. The high-n Rydberg neutral species N 2
as well as prompt N 2 + (H 2 O + ) ions are produced by VUV laser excitation of the N 2 (H 2 O) molecular beam at the PI/PEX center, where n represents the principal quantum number. At a delay of 100 ns with respect to the VUV laser pulse, the first electric field pulse [amplitude=2 V/cm, duration=2 μs] is applied at lens I1. This first electric field pulse serves to retard and thus separate the prompt ions spatially from the neutral N 2 * (n) [H 2 O * (n)] Rydberg species. At a delay of 300 ns with respect to the termination of the separation electric field pulse, the second electric field pulse (amplitude=14 V/cm, duration=0.5 μs) is applied to lens E1. This second electric field pulse serves to PFI neutral N 2
Rydberg species, and to extract PFI-PIs thus formed along with prompt ions out of the PI/PEX region, traveling toward the rf-octopole reaction gas cell. Since the prompt ions have lower kinetic energies than that of the PFI-PIs because of the prompt ion retarding effect, we were able to apply a potential energy barrier at lens I2 to cleanly block out the prompt ions, passing only the PFI-PIs to the reaction gas cell. This capability allows the quantum-rovibronic-state-selection of small molecular ions, such as N 2 + and H 2 O + , with essentially 100% purity. The key for achieving high kinetic energy resolution (i.e., narrow ΔE lab spread) for the PFI-PIs is to turn off the second electric field pulse before the PFI-PIs exit the PI/PEX region, such that all PFI-PIs produced in the PI/PEX region gain the same momentum. In this study, for each PFI-PI vibrational band, N 2 + ions were prepared by setting the VUV laser sumfrequency at the strongest rotational peak position, i.e., the Q branch. Thus, the vibrationally selected v N N 0 2;
VUV-PFI-PIs are in a distribution of low N + =0-9 rotational states. (Chang et al. 2012) For the PFI-PI H 2 O + (X 2 B 1 : 000 and 100) vibrational bands, single 0 00 , 1 11 , and 2 11 rotational states are also selected. However, no observable rotational effects are found for the σ values of the H 2 O + (X 2 B 1 : 000 and 100)+N 2 reactions.
The reaction gas cell is situated between the first and second rf-octopoles, such that slow CT product H 2 O + ions can be effectively extracted out of the reaction gas cell by applying a small dc electric field between the two rf-octopoles. In this study, we fill the neutral H 2 O (N 2 ) reactant gas in the rf-octopole reaction gas cell in the pressure range from 1.0×10 -5 to 1.0×10 -4 Torr as monitored by an MKS Baratron. After passing through the reaction gas cell, the intensity of the attenuated reactant N 2 + (H 2 O + ) PFI-PI beam is measured by the product QMS. Product ions resulting from the collisions between the PFI-PI beam and neutral reactant molecules in the reaction gas cell are also guided into the product QMS for intensity measurements. The ion intensities thus measured allow the determination of σ values for the ionmolecule reactions of interest based on the Beer-Lambert Law.
We have pointed out in previous studies (Xu et al. 2012(Xu et al. , 2013b(Xu et al. , 2017a(Xu et al. , 2017b) ) that in an ion-beam gas cell study, such as in this experiment, the thermal motions of neutral H 2 O (N 2 ) molecules in the reaction gas cell can be the main contribution to the uncertainty of E cm (i.e., ΔE cm ; Chantry 1971). For the reaction of
[H 2 O + (000 and 100)+N 2 ], the estimated uncertainties for E cm =0.05, 0.10, and 0.5 eV are 0.09, 0.13, and 0.29 eV (0.07, 0.10, and 0.23 eV), respectively. The ΔE cm spreads have the effect of smoothing the integral cross section curves, particularly at low E cm values; but the general trends for the σ curves are not expected to be seriously affected. For the conversion of E lab into E cm , we use the formula
where m + and M represent the mass of the reactant ion and that of the neutral molecule, respectively.
All σ values presented in this study are based on the average of at least three independent and reproducible measurements. The standard deviations are generally 5%-10%, which represent the reproducibility of independent measurements. However, the systematic error limits for absolute σ determinations are significantly larger due to the lack of accurate calibration parameters used as well as the variation of experimental conditions and procedures used in different individual experiments. The σ values presented here have been calibrated to those determined previously for the formation of (Tanaka et al. 1981;Ervin & Armentrout 1985;Qian et al. 2003); and we have assigned error limits of ≈30% (Chang et al. 2012;Xu et al. 2013b) for the absolute values of
The current σ and BR measurements are mainly concerned with the X N 2 2 g
( ; v + =0-2)+H 2 O reaction. The inclusion of the σ measurement of the H 2 O + (X 2 B 1 : 000 and 100)+N 2 reaction is aimed to gain additional insight into the reaction mechanisms of the ion-molecule reaction system involving the neutral and ionic species N N ) +H 2 O at E cm =0.40 eV observed without and with H 2 O gas filled in the rf-octupole reaction gas cell. Without H 2 O filled in the reaction gas cell, the mass spectrum of Figure 1(a) reveals only two ion peaks at m/z=28 and 29 with the intensity ratio of I(m/z=29):I(m/z=28)=0.0074. Since this ratio is in excellent accord with that deduced using the known natural isotope abundances of 15 N/ 14 N, the observed ion peaks at m/z=28 and 29 can be confidently assigned as 14 N 14 N + and 15 N 14 N + ions, respectively. When the gas cell is filled by neutral reactant H 2 O gas at a pressure of 4.0×10 -5 Torr, two additional ion peaks at m/z=18 and 19 are discernible in the mass spectrum of Figure 1 1(a) and (b), we can correct for the contribution of isotropic 15 N 14 N + ions and obtain the actual intensity of product N 2 H + ions. Without filling H 2 O vapor in the reaction gas cell, we have carefully examined the intensity ratio of I(m/z=29):I(m/z=28) as a function of E cm in the range of 0.05-10.0 eV, and we found that this ratio remains constant at 0.0074 throughout this E cm range. This observation shows that the 15 N 14 N + ion intensity correction for product N 2 H + ion can be reliably determined based on the I(m/z=28 and 29) measurements with H 2 O filled in the reaction gas cell, along with the isotopic ratio I(m/z=29):I(m/z=28) of 0.0074 calculated based on the known natural isotopic abundances for 14 N/ 15 N.
Absolute Integral Cross Sections:By using the measured intensity for reactant N 2 + PFI-PIs and the corrected intensities for product H 2 O + and N 2 H + ions, quantum-vibrational-stateselected σ CT (v + =0-2) and σ HT (v + =0-2) values can be determined based on the Beer-Lambert law, as described in detail previously (Chang et al. 2012;Xu et al. 2013bXu et al. , 2016)).
The k r values of previous measurements are converted into σ values by using the approximated relation, k r s n = á ñ, where n á ñ is the averaged ion-molecule collision velocity calculated using the E cm . This relation is also used to convert the σ values obtained here and in previous experiments into k r values. This conversion scheme enables the comparison of experimental results obtained in dynamics and kinetics measurements as well as in theoretical predictions.
In order to confirm that the σ CT (v + ) and σ HT (v + ) determined in our experiment are not affected by secondary reactions, we have carefully examined the σ CT (v + =0) and σ HT (v + =0) at E cm =0.04-10.00 eV for reactions (1) and (2) occurring in the reaction gas cell at H 2 O gas pressures ranging from 1.0×10 -5 to 1.0×10 -4 Torr. We found that the σ CT (v + =0) and σ HT (v + =0) curves observed in this H 2 O pressure range are in excellent agreement. As an example, we show the comparison of the σ CT (v + =0) curves obtained at 4×10 -5 and 1.0×10 -4 Torr in Figure 2(a), and those of the σ HT (v + =0) curves in Figure 2(b). The fact that the σ CT (v + =0) and σ HT (v + =0) determined at these pressures are in excellent accord supports the conclusion that the σ CT (v + =0-2) and σ HT (v + =0-2) curves obtained here are reliable and are only negligibly affected by secondary collision processes.
The σ CT (v + =0-2) and σ HT (v + =0-2) curves measured in the E cm range of 0.04-10.00 eV are shown in Figures 3(a) and (b), respectively. As shown below, the general trend of the σ CT (v + =0-2) curves [σ CT (v + =0-2) versus E cm plots] observed at E cm =0.04-1.00 eV is consistent with the longrange near resonant CT mechanism. The σ CT (v + ) is very high (≈200 Å 2 ) at near thermal collision energies (E cm ≈0.03-0.04 eV), and it decreases monotonically as E cm is increased to ≈1.00 eV. Most interestingly, the σ CT (v + =0-2) curves exhibit a hump at E cm 1.0-5.0 eV, which has not been observed in previous experiments. The σ CT (v + =0-2) decreases from the peak of the hump at E cm ≈3.0 eV to near the background level at E cm =9.0-10.0 eV. At E cm 8.0 eV, the formation of H 2 O + via CT is the overwhelming product channel with σ CT (v + )>σ HT (v + ). However, at E cm 9.0 eV, σ CT (v + ) becomes smaller than σ HT (v + ). This observation suggests that the reaction mechanism may switch from near resonant CT to more direct collisional pathways. The decreasing trend for σ HT (v + =0-2) observed as E cm is increased, as shown in Figure 3(b), which is in accordance with an exothermic barrier-less reaction process.
The vibrational effects on σ CT (v + ) and σ HT (v + ) can be examined based on the comparison of the σ CT (v + =0-2) and σ HT (v + =0-2) curves in Figures 3(a ( : v + =0-2) toward H 2 O can be measured by the sum σ SUM (v + )=σ CT (v + )+ σ HT (v + ), v + =0-2. The σ SUM (v + =0-2) curves in the range of E cm =0.04-10.00 eV are depicted in Figure 4. The CT channel being the dominant product channel, the E cm and v + -vibrational dependences observed for σ SUM (v + ) are expected to be similar to those for σ CT (v + ). The humps resolved in the σ CT (v + 0-2) curves at E cm =1.0-5.0 eV are also evident in the σ SUM (v + =0-2) curves of Figure 4. We have included in Figures 3(a),(b), and 4 all previous available experimental σand k r -measurements for comparison with the σ CT (v + ), σ HT (v + ), and σ SUM (v + ) values obtained in our study here. However, we note that all previous σ and k r measurements are not state-selected studies.
To facilitate the discussion below, we show in ( : v + =0, 1, and 2)+H 2 O and the possible product states H ( ; v + =0-2)+H 2 O reaction at E cm =0.04-10.00 eV. Results from previous kinetics studies near thermal energies and dynamics studies using the crossed-ion-neutral-beam and the rf-octopole ionguided techniques are also included in the figures. We note that all previous experiments are not state-selected measurements. ( ; v + =0-2)+H 2 O reactions obtained at E cm =0.04-10.00 eV in our study with those reported previously. Results from previous kinetics studies at near thermal energies and dynamics studies using the crossed-ion-neutral-beam and the rf-octopole ion-guided techniques are also included in the figures. All previous experiments are not state-selected measurements. We have also depicted in the figure the recent rf-ion-trap kinetics measurements obtained at the rotational temperatures of=222-298 K for comparison with the theoretical σ(ADO) and σ(LGS) predictions.
scale normalized to the heat-of-formation scale. This He I spectrum covers the formation of the H 2 O (X, A, and B) states. The intensities for the vibronically resolved photoelectron bands are measures of the Franck-Condon factors (FCFs) for the corresponding photoionization transitions to form the latter ion states from the H 2 O(X) neutral ground state. As shown in Figure 5, at low E cm values, the near energy-resonance CT mechanism is expected to favor the production of excited ( )+H 2 O CT collisions has been observed in the chemi-luminescence experiment of Dressler and coworkers (Dressler et al. 1990a). Based on the energy diagram of Figure 5, the FCF for the formation of near resonant H
) vibrationally excited states, and thus giving rise to minor vibrational inhibition for σ CT (v + ), i.e., σ CT (v + =0)>σ CT (v + =1)>σ CT (v + =2) observed at low E cm 0.3 eV, as shown in Figures 3(a) and4.
According to known energetic data (Kimura 1981;Reutt et al. 1986;Truong et al. 2009), the energetic threshold for the formation of the
reactant state. This value coincides with the onset at E cm ≈1-2 eV observed for the hump resolved in the σ CT (v + =0-2) curves of Figure 3(a). Based on this observation, we have identified this hump at E cm ≈1.0-5.0 eV to arise from the formation of excited ions in the H
The hump is found to decline at E cm 4.0 eV. Two reasons may contribute to the decline: one is the possible dissociation of internally excited H 2 O + (B 2 B 2 ) ions, and the other is that the near energyresonance CT pathway becomes less important at higher E cm 4.0 eV. Excited H 2 O + (B 2 B 2 ) ions with internal energies above the OH + and H + dissociation thresholds are known to result in prompt dissociation (Lorquet & Lorquet 1974;Suárez et al. 2015). The E cm threshold for the lowest dissociation channel, i.e., the formation of OH + (X)+H+N 2 (X) from the
, is known to be at 2.54 eV. At higher E cm 3.12 eV, the dissociation to form H + +OH(X)+N 2 (X) can also occur. However, as a result of the low OH + and H + fragment ion intensities, the OH + and H + ions were not measured in our experiment. Interestingly, a recent lifetime study has shown that at internal excitation below but near the ion dissociation thresholds for the formation of these product ions, the radiative lifetimes of H 2 O + (B 2 B 2 : v v v 1 2 3 + + + ) ions are surprisingly long with a value of ≈200 μs (Harbo et al. 2014). We note that this lifetime value is within the timescale of our experimental measurements. Therefore, the decline of σ CT (v + =0-2) observed here may be mainly ascribed to the fast weakening of the near energy-resonance CT processes when E cm 4.0 eV.
Previous studies of the N H O 2 2 + + reaction were mostly concerned with k r measurements near thermal energies (E cm =30-40 meV; Shahin 1967;Turner & Rutherford 1968;Howard et al. 1970;Dreyer & Perner 1971;Bolden & Twiddy 1972;Howorka et al. 1974;Karpas et al. 1978;Smith et al. 1978;Tichý et al. 1979;Huntress et al. 1980;Parent et al. 1985;Dressler et al. 1990bDressler et al. , 1993;;Yuan et al. 2011). The σ values obtained in previous dynamics studies (Shahin 1967;Turner & Rutherford 1968;Howard et al. 1970;Dreyer & Perner 1971;Bolden & Twiddy 1972;Howorka et al. 1974;Karpas et al. 1978;Smith et al. 1978;Tichý et al. 1979;Huntress et al. 1980;Parent et al. 1985;Dressler et al. 1990bDressler et al. , 1993;;Yuan et al. 2011) or converted from previous reported k r measurements are included in Figures 3(a + + collision pair, the σ CT (v + ) values for this reaction are expected to be very high, as confirmed by the experimental measurements of Gerlich and coworkers (Yuan et al. 2011).
Using the crossed-ion-neutral beam method, Turner and Rutherford (Turner & Rutherford 1968) have earlier measured the σ CT and the σ HT as a function of E cm and found that these σ values are nearly independent of E cm in the range of 1-10 eV. The σ CT and σ HT curves measured in the E cm range of 0.06-10 eV have also been reported by Dressler and coworkers (Dressler et al. 1990b(Dressler et al. , 1993) ) using the guided ion-beam mass spectrometric technique. These σ CT and σ HT curves thus determined are in fair agreement with the σ values obtained by the crossed-beam experiment at E cm =1-10 eV. As shown in Figures 3(a), (b), and 4, the σ CT , σ HT , and σ SUM curves reported by Turner and Rutherford and Dressler and coworkers are in reasonable agreement with the σ CT (v + =0-2) σ HT (v + =0-2) and σ SUM (v + =0-2) curves observed in our experiment. However, the hump resolved at E cm =1.0-5.0 eV in the σ CT (v + =0-2) and σ SUM (v + =0-2) curves was not observed in previous studies. As discussed above, we have tentatively assigned this hump to the formation of excited H 2 O + (B 2 B 2 ) ions by the collision-assisted CT mechanism.
Ion-dipole and Ion-induced Dipole Models:In addition to experimental σ values, theoretical σ predictions based on the Langevin-Gioumousis-Stevenson (LGS; Gioumousis & Stevenson 1958) and the averaged dipole orientation (ADO) models (Su & Bowers 1973a, 1973b) are also depicted in Figure 4 as the black dotted and blue dashed curves, respectively. We found that the σ SUM (v + =0-2) curves obtained in this experiment are in reasonable agreement with the σ(ADO) predictions. Two times of the σ(ADO) predictions, i.e., 2×σ(ADO), obtained at near thermal energies (E cm ≈30-40 meV) are found to be in excellent agreement with the recent k r measurements of Gerlich and coworkers (Yuan et al. 2011), and thus the 2×σ(ADO) curve (shown as the red dashed curve) is also shown in Figure 4 for comparison with other experimental results.
Since the ADO model includes the prediction of the LGS model, we only list the interaction potential formula (Israelachvili 2011;in SI units) for the ADO model below:
V r e r e r
Here V r ( ), r, ε 0 , e μ D , Θ, and α represent the interaction potential, the center-of-mass distance between N 2 + and H 2 O, the vacuum permittivity constant, the electron charge, the permanent dipole moment of H 2 O molecule, the angle between D m and r, and the average polarizability of H 2 O molecule, respectively, where μ D =1.8546 D or 6.19×10 -30 mC and α=1.61×10 -40 kg -1 s 2 C 2 are known (Nelson et al. 1967;Miller & Bederson 1978). The angle-averaged cos á Q ñ ( ) value is taken to be 0.5. The first potential term is the interaction between a charge and a permanent dipole, and the second term is for the interaction between a charge and an induced dipole. We note that the LGS model only has the second term.
The σ(ADO) determined based on V(r) can be expressed as follows:
where b c is the critical impact parameter. The second term in Equation ( 5) is the expression of σ(LGS). Equation (5) readily shows that both σ(ADO) and σ(LGS) are predicted to be enhanced dramatically as E cm approaches zero. This increasing trend as E cm is decreased predicted by the σ(ADO) and σ(LGS) models is in fair agreement with the experimental σ SUM (v + ) values shown in Figure 4. The majority of previous experimental σ values are found to fall in between the σ (ADO) (blue dashed) and σ(LGS) (black dotted) curves. The kinetics results obtained from the recent study (Yuan et al. 2011) employing the rf-ring trap technique are larger than the ADO predictions at thermal energies by about a factor of two, which might indicate that a more complicated reaction mechanism is involved. We note that only the CT channel was measured in the rf-ring trap study. As shown in Figure 4, the σ SUM (v + =0-2) curves at low E cm <1.0 eV are similar to the curve of the σ(ADO) predictions.
The σ HT (v + ) decreases smoothly, resulting in a switch of the dominant reaction channel from the CT to the HT channel at E cm 9.00 eV. At higher E cm region, the direct collision reaction pathways are expected to become more important, which may be responsible for the observed switching of the dominant reaction channels.
Products Branching Ratios:We list in Table 1 detailed BRs for the CT and HT product channels of the X N 2 2 g
( ; v + =0-2)+H 2 O reaction obtained in our study, which were determined by the intensities of product H 2 O + and N 2 H + ions measured in the E cm range from 0.04 to 10.00 eV. At E cm = 0.04-8.00 eV, the dominant product channel is the CT channel for all vibrational states N 2 + (v + =0-2). It is interesting to find that the BRs of the CT and HT channels are essentially independent of E cm and v + at E cm =0.04-1.00 eV with the v + -averaged BR(H 2 O + )=0.82±0.05. As E cm is increased from 1.00 eV, the BR(H 2 O + ) is found to increase and peak at 0.93 at E cm =3.00 eV. The BR(H 2 O + ) drops as E cm is increased beyond 4.00 eV. At E cm 9.00 eV, the HT product channel, which corresponds to the formation of N 2 H + , becomes dominant compared to the CT channel for all N 2 + (v + =0-2) vibrational states.
Table 2 (Karpas et al. 1978;Smith et al. 1978;Tichý et al. 1979;Huntress et al. 1980;Dressler et al. 1993) + are expected to serve as valuable experimental benchmarks for state-of-the-art theoretical chemical dynamics calculations as well as for chemical modeling of planetary atmospheres. Since the intensities of different product ions can be measured simultaneously, the error limits (±5%) achieved for BR measurements are significantly smaller than those (±30%) for σ CT (v + =0-2) and σ HT (v + =0-2) measurements. Thus, BR data determined here are expected to be better experimental benchmarks for theoretical predictions than σ CT (v + ) and σ HT (v + ) measurements.
: 000 As shown in the potential energy diagram of Figure 5, the energy of the H 2 O + (X 2 B 1 : 000)+N 2 reactant state is the lowest (or most stable) of all the possible open product states. Because of the endothermic constraint, the formation of these product states from the H 2 O + (X 2 B 1 : 000, 100)+N 2 reactant state is low. Thus, we have only measured the σ PT (000 and 100) curves as depicted in Figure 6 for the formation of N 2 H + from the H 2 O + (X 2 B 1 : 000 and 100)+N 2 reaction. The endothermicity of the process involved means that the σ PT (000 and 100) values are ten to hundred times lower than those for σ CT (v + ) and σ HT (v + ), v + =0-2, for the N 2 + (v + = 0-2)+H 2 O reaction. As shown in the figure, the σ PT (000 and 100) curves reveal distinct E cm thresholds at 0.90±0.10 and 0.60±0.10 eV, which can be considered in good agreement with the known thermochemical thresholds of 1.05±0.01and 0.65±0.01 eV, respectively. The profile of the σ PT (000 and that of the σ PT (100) curves are similar, appearing as a broad peak located at ≈3 eV above the E cm threshold. Most interestingly, the σ PT (100) value is found to be greatly enhanced (by about six times) compared to the σ PT (000) value. This observation indicates that excitation to the (100) symmetric stretching mode of H 2 O + (X 2 B 1 ) reactant ion is highly effective in driving the endothermic PT reaction channel of the H 2 O + (X 2 B 1 )+N 2 reaction. Rigorous theoretical dynamics studies based on high level ab initio potential energy This work d 0.82±0.05 0.18±0.05 580 K Ref. (Karpas et al. 1978) 0.78 0.22 298 K Ref. (Smith et al. 1978) 0.82 0.18 298 K Ref. (Tichý et al. 1979) 0.81 0.19 298 K Ref. (Huntress et al. 1980) 0.71 0.29 298 K Ref. (Dressler et al. 1993) 0.73 0.27 700 K Notes. a T≈580 K is converted from E cm =0.05 eV. b T=298 K is obtained by assuming that the kinetic measurements were performed at room temperature. c T≈700 K is converted from E cm =0.06 eV. d The BR(H 2 O + ) and BR(N 2 H + ) are found to be constant at the E cm range of 0.05-1.00 eV. The values of BR(H 2 O + )=0.82±0.05 and BR(N 2 H + )= 0.18±0.05 are obtained by averaging the values obtained for the N 2 (v + =0, 1, and 2) vibrational states as shown in Table 1. surface calculations are called for to gain further understanding on the reaction mechanism of the titled ion-molecule reaction systems.
We have obtained detailed quantum-vibrational-state-selected σ CT (v + =0-2) and σ HT (v + =0-2) measurements for the CT and HT reaction channels of the ion-molecule reaction X N 2 2 g S + +
( ; v + =0-2)+H 2 O at E cm =0.04-10.00 eV. Minor vibrational inhibition is observed for the σ CT (v + =0-2) at E cm =0.04-0.30 eV. The high σ CT (v + =0-2) values along with their decreasing trend observed as E cm is increased suggest that the long-range energy-resonance CT mechanism is operative at low E cm values. We have compared σ CT (v + =0-2) obtained in our experiment with previous dynamics and kinetics measurements and theoretical predictions based on the LGS and ADO models. The σ CT (v + ) and σ SUM (v + ) measurements resolve a hump in the region of E cm =1.0-5.0 eV, which was not observed in previous studies. We have tentatively identified this feature to arise from the formation of excited H 2 O + (B 2 B 2 ) ions via the collision-assisted CT excitation mechanism, which is known to have the energetic threshold at E cm =1.60 eV. The BR(H 2 O + ) and BR(N 2 H + ) values measured as a function of both E cm and v + vibrational state of reactant N 2 + ion are also presented and compared with previous measurements. At E cm =0.04-1.00 eV, the dominant product ion is H 2 O + and the BR(H 2 O + ) is found to be independent of E cm and v + -vibrational state with the v + -averaged value BR(H 2 O + )=0.82±0.05. As E cm is increased from 1.00 eV, the BR(H 2 O + ) increases to the peak value of 0.93 at E cm =3.00 eV. At E cm >4.00 eV, the BR(H 2 O + ) further decreases as E cm is increased, and eventually becomes lower than the BR(N 2 H + ) at E cm 9.00 eV, where direct collision reaction dynamics may play a more dominant role.
In order to gain further insights into the titled reaction systems, we have also performed σ measurements for the H 2 O + (X 2 B 1 : 000 and 100) + N 2 reaction. In the E cm range of interest, only the formation of N 2 H + from the PT reaction channel of the latter reaction is observed. The σ PT (000 and 100) curves thus obtained exhibit distinct E cm thresholds, which agree with the corresponding thermochemical thresholds. Furthermore, the σ PT (100) values are found to be nearly six times higher than the σ PT (000) values, which is indicative of a significant vibrational enhancement effect for excitation to the (100) symmetric stretching mode of H 2 O + (X 2 B 1 ). The detailed σ CT (v + =0-2), σ HT (v + =0-2), σ SUM (v + =0-2) and σ PT (000 and 100) as well as branching ratios BR(H 2 O + ):BR(N 2 H + ) reported here are expected to serve as valuable benchmarks for the development of a state-of-the-art theoretical chemical dynamics package. This material is based upon work supported by the National Science Foundation under CHE-1462172 and CHE-1763319. C.Y.N. is also grateful to Dr. Huie Tarng Liou for his generous donation of research support for the Ng Laboratory.
Cheuk-Yiu Ng https:/ /orcid.org/0000-0003-4425-5307
The Astrophysical Journal, 861:17 (9pp), 2018 July 1 Xu et al.