Ion Chemistry of Carbon Dioxide in Nonthermal Reaction with Molecular Hydrogen.

The exothermic hydrogen transfer from H2 to CO2·+ leading to H and HCO2+ is investigated in a combined experimental and theoretical work. The experimental mass/charge ratios of the ionic product (HCO2+) and the ionic reactant (CO2·+) are recorded as a function of the photoionization energy of the synchrotron radiation. Theoretical density functional calculations and variational transition state theory are employed and adapted to analyze the energetic and the kinetics of the reaction, which turns out to be barrierless and with nonthermal rate coefficients controlled by nonstatistical processes. This study aims to understand the mechanisms and energetics that drive the reactivity of the elementary reaction of CO2·+ with H2 in different processes.

Introduction

Carbon dioxide, CO2, is one of the trace gases present in the Earth’s atmosphere and is uniformly distributed in its layers. This molecule is also the main component of the Mars and Venus atmospheres,[1,2] and it is also present in the interstellar medium as neutral (CO2) and ionic (CO2·+, HCO2+) species.[3,4] CO2 and other trace gases such as methane, CH4, nitrous oxide, N2O, and water, H2O, absorb infrared light coming from the Earth’s surface and consequently increase the temperature of the planet, producing the so-called “atmospheric greenhouse effect”. The increase of CO2 in the atmosphere is also the main factor for the increased acidity of the sea.[5] The need for rapid reduction of fossil fuel emission and the requirement of “negative CO2 emissions” are pushing for the development of new approaches and technologies to produce energy (renewable sources)[6,7] and remove CO2 from the atmosphere (carbon geoengineering).[8] Indeed, CO2 conversion into suitable chemicals and fuels such as methanol, formaldehyde, and formic acid is one of the great challenges of the 21st century.[9] The transformation of CO2 requires a coreactant that acts as a hydrogen source (like CH4, H2, or H2O) or the splitting of CO2 into CO and O2.[10] Among the different emerging and novel technologies for the activation and conversion of CO2, the plasma-based approach has recently received much attention.[11] In this strategy, carbon dioxide is activated by energetic electrons and the experimental conditions are mild, clean, and upscaling. Plasma is an ionized gas containing also neutral species, for example, atoms, molecules, radicals, and excited species that can emit light. All these species create a complex network of chemical reactions that can produce a system of interest for many potential different applications[12] and, in the best cases, used on an industrial scale. The plasma is in “local thermodynamic equilibrium” (LTE) if all the species are at the same temperature (thermal plasma), which is otherwise called nonthermal plasma.[13] Here, highly energetic electrons can activate the inert carbon dioxide[14] at room temperature, which then can react with species such as CH4, H2O, or H2, leading to an efficient conversion of CO2 despite the low selectivity in the correspondent products. However, this undesired effect can be overcome by employing plasma catalysis, which can lead to a more selective production of specific compounds.[15] Although there are several setups for the plasma-based CO2 conversion, the mechanistic insights into CO2 transformation are not well understood, and this prevents the prediction of a realistic trend on product yields and selectivity. Hence, an accurate experimental and theoretical analysis at the molecular level of the reactions of the “internally excited” CO2·+ with these neutrals is undoubtedly relevant.[16−21] The reaction of carbon dioxide cation with molecular hydrogen has been already studied at low temperatures (15–300 K) under thermal conditions by Gerlich and co-workers.[22] Instead, in the present study, we report an experimental and theoretical study of the same reaction with different internal energy of the carbon dioxide cation: the tunable synchrotron radiation has been used to excite vibrationally the reagent ions and the experimental results has been analyzed by developing a theoretical model based on the variational transition state theory (VTST).[23] The VTST is a powerful tool to study barrierless reactions,[24] and it can be modeled to study theoretical reactions under nonthermal conditions and with nonstatistical energy distribution among the different degrees of freedom. Specific theoretical models have been developed to describe nonstatistical reactions, and adaptations of statistical theories are of fundamental importance to explain specific experimental reactions.[25,26,17]

The results of this work unravel the mechanistic details of this ion-molecule reaction of multidisciplinary interest spanning from the nonthermal plasma technology for CO2 conversion to the chemical processes occurring in the space.

Methods

Synchrotron Experiments

The monochromatized radiation from the beamline CiPo (Circular Polarization) at ELETTRA (Trieste), described in detail in our previous studies,[27−30] has been used to produce carbon dioxide radical cations with different internal energies. The beamline, equipped with an electromagnetic elliptical undulator/wiggler, works in the vacuum ultraviolet (VUV) region, and a normal incidence monochromator (NIM) provides photons in the 8–40 eV energy range. The aluminum grating of the NIM, operating in the energy range 8–17 eV and providing a photon flux of about 109–1010 photon/s with an energy resolution of about 10–20 meV, has been used. The photon energy was calibrated against the autoionization features observed in the Ar total photoionization cross-section between the 3p spin orbit components.[31] The effusive molecular beam of carbon dioxide has been introduced in the ion source through a leak valve and ionized by synchrotron radiation at a pressure of about 10–6–10–5 mbar. The generated CO2·+ ions were guided with several optical lenses into the octupole reaction cell at the nominal collision energy (CE) of 0 eV with an energy spread of about 150 meV. This value has been obtained by measuring the CO2+ yield as a function of the retarding field at the entrance of the octupole. The reactants H2 or D2 were inserted into the reaction cell (octupole) at different nominal pressures from 9.0 × 10–6 to 9.0 × 10–5 mbar and at room temperature. Mass spectra in the mass over charge (m/z) range 10–48 were acquired at 14.0 eV photon energy without and with neutral gases in the reaction cell at the nominal pressures of 9.0 × 10–6 and 3.0 × 10–5 mbar and with acquisition time ranging from 1 to 5 s/point. The areas of the signals acquired at m/z = 44 (CO2·+), 45 (HCO2+), and 46 (DCO2+) were fitted by Gaussian profiles with the OriginPro 2015 software to evaluate the isotopic effect. The intensities of the reagent and product ions in the ion-molecule reactions of CO2·+ with H2 or D2 were measured by scanning the photon energy in the range of 13.7–15.0 eV with a step of 0.10 eV and an acquisition time of 30 s/point at several pressure values in the reaction cell, namely, 0.9 × 10–5, 1.2 × 10–5, 3.0 × 10–5, 6.0 × 10–5, and 8.6 × 10–5 mbar. The pressure measurements are affected by an error of about 30%. For the sake of clarity, the · in CO2·+ is omitted in the following sections.

Materials

All the samples were used at room temperature. Carbon dioxide CO2 was from SIAD with purity >99.99%. The H2 and D2 gases were purchased from Sigma-Aldrich with purity >99.99% and with a 99.8 atom % D.

Theoretical Calculations and Methodology

Reactive Potential Energy Surface

The interaction between the ionized CO2+ and the neutral hydrogen molecule has been studied by means of ab initio calculations based on density functional theory (DFT) double-hybrid approach, which takes into account the radical nature of the species during the reaction. The functional used through all the calculations is the B2PLYP of Grimme,[32] and the basis set is the valence double-zeta Pople polarization and diffuse functions 6-31++G**.[33] All the frequency calculations have been carried on in the harmonic approximation. The electronic structure calculations have been done using the Gaussian code.[34] The accuracy of the calculation has been verified by comparing the reaction enthalpy of 121.36 kJ/mol[35] with the theoretical value of 121.9 kJ/mol obtained in this work. The open shell radical nature of the present reaction is properly accounted for with the employed level of calculation, as shown by the partial charge and spin analysis presented in the next section. The reactive potential energy surface (PES) has been calculated by scanning both the O–H and H–H coordinates with a variable step whose minimum value has been taken as 0.02 Å in the regions near the reactive complex. During the scan, all the other geometrical coordinates, except the scanning ones, have been optimized. The charge and spin population are based on the Mulliken analysis of the electron density.[36] The geometries and the normal coordinates of the species are reported in the Supporting Information (SI) in Table S1–S3.

Nonthermal Rate Coefficient

The VTST[23] has been adopted to calculate the rate coefficient of the present reaction, following a nonthermal (NT) approach, which resembles the experimental conditions where the ionized CO2+ is not in thermal equilibrium with the H2 neutral molecule and the energy flow within the reactive complex does not follow a statistical distribution. Hence, the rate coefficient has been obtained by averaging over the translational and rotational energy, whereas the vibrational energy of CO2+ is not used in Boltzmann thermalization because its vibrational population is controlled by the amount of energy adsorbed during the photoionization process. The microcanonical nonthermal rate coefficient (kμNT) is given bywhere kμ is the standard bimolecular microcanonical rate coefficient, EV is the vibrational energy of CO2+, σ the rotational symmetry factor, and ETR is the translational-rotational energy of the reactants (the translational energy is referred to the center of the mass frame in which the translational energy of the TS is zero). Prea is the distribution probability of the reactants at temperature T:and ρrea is the density of states of the reactants. We have considered only the vibrational energy of CO2+ because the vibrational partition function of H2 is unity for all temperatures of the present theoretical study (T ≤ 300 K) due to the high vibrational frequency of H2 (4381 cm–1).

The number of states of the reactants arewhere NH is considered to be equal to 1 because at T ≤ 300 K, only the first vibrational level is populated due to the high vibrational frequency of H2.

Since ρ(E) = ∂N(E)/∂E, the reactant density of state is:where ρreaTR(ETR) is the translational-rotational density of states for the reactants and is given byand NTRrea is the translational-rotational number of states of the reactants

The integral at the denominator of eq is

Equation can be simplified by using the Laplace transform of the density and number of states:where QRrea(T) is the rotational and QTrea(T) the translational molecular partition function of the reactants at temperature T.

The vibrational number of states is much greater than the density number of states up to T = 300 K; hence, the term ρVCO(EVCO) · KBT in eq can be neglected.

Equation then can be rewritten as follows:where ETR = ETRCO + ETRH.

The microcanonical rate coefficient can be written aswhere the number of states of the transition state (NTS), in the reference frame of the center of mass of the reactants, depends on the vibrational (NTSV) and rotational (NTSR) number of states:

By substituting the eqs and 9 into eq , the translational-rotational averaged nonthermal rate coefficient can be rewritten as:and because , eq became

We consider TS as divided into two vibrational subsystems (a and b) not interacting with each other. System a is referred to the frequencies associated with the CO2+ modes not thermalized, and b to the intermolecular vibrations thermally averaged. Then, the vibrational number of states of TS can be written as

that gives the nonthermal rate coefficient:where QRTS(T) is the rotational partition function for the VTS complex, QTrea(T) is the relative translation molecular partition function of the reagents, QRVH is the rovibrational partition function of H2, QRCO is the rotational partition function of CO2+, and NVCO is the number of vibrational states of CO2+. QVbTS is the vibrational partition function of the VTS complex relative to the set Vb, NTSVa is the number of vibrational states of the VTS complex relative to the set Va. The number of vibrational states have been calculated by direct count (Beyer–Swinehart algorithm).[37]

Moreover, to calculate the rate coefficient of the reaction, it is relevant to know the energy, named ETS, acquired by the reactive complex when moving along the barrierless minimum energy path (MEP) from reagents to the VTS geometry. ETS can be distributed among the internal degrees of freedom of the VTS complex as well as in the relative kinetic energy of the two products. The dynamics that control such energy “flow” are subtle and depend on several factors, such as the internal energy content of the reagents and the timescales of the internal vibration rearrangement (IVR) within the VTS complex. In thermal equilibrium conditions, the canonical rate coefficient iswhere Qrea(T) is the molecular partition function for the reagents, E is the rovibrational energy of the system, NTS(E) is the rovibrational number of states of the VTS complex, and X(T) is the fraction of the ETS, which goes into all the degrees of freedom of the VTS complex, except that of the reaction coordinate. X(T) is defined as a parameter which controls the energy flow during the reaction. The increase in X(T) pushes the reaction energy flow toward the internal degrees of freedom of the reaction complex, vice versa, when X(T) goes to zero, all the reaction energy remains in the reaction coordinate and eventually goes into the relative kinetic energy of the products. Equation can be solved to give the standard canonical form of the rate coefficient with an exponential part depending on the X(T)ETS:

In the nonthermal condition of the present experiments, eq cannot be applied, while eq should be used after accounting properly the effect of X(T) within the VTS complex.

The nonthermal rate coefficient (eq ) is transformed as follows:where Xb·X(T)·ETS is the energy flow going into the intermolecular vibrations (Vb) of the VTS complex, whereas the Xa·X(T)·ETS is the energy flow going into the vibrations (Va) of the VTS complex associated with CO2. The sum of Xa and Xb is always equal to 1.

Results and Discussion

In the explored photon energy range from 13.7 to 15.0 eV, the carbon dioxide is ionized (ionization energy = 13.777 ± 0.001 eV)[38] and vibrationally excited in its ionic ground state X2Π3/2,1/2g[39] without dissociation, as several spectroscopic studies of CO2+ have demonstrated.[40] The mass spectrum of CO2 measured at 14.0 eV photon energy in the range 10 < m/z < 48 is shown in Figure a, where neither fragment ions nor water traces are observed. The introduction of the H2 molecule in the reaction cell at a pressure of 9.0 × 10–5 mbar induces the hydrogen atom transfer (HAT) reaction that generates the protonated form of carbon dioxide (inset in Figure a) HCO2+ detected at m/z = 45,

Figure 1

(a) Mass spectrum of CO2 at 14.0 eV photon energy. The CO2 pressure in the ion source was 1.8 × 10–5 mbar and no H2 gas in the reaction cell. In the inset, the mass spectrum acquired with H2 in the reaction cell at the nominal pressure of 9.0 × 10–5 mbar and nominal CE = 0 eV. (b) Comparison of the mass spectra acquired at the 14.0 eV photon energy, at a nominal pressure of about 3.0 × 10–5 mbar, and nominal CE = 0 eV for the reaction of CO2+ with D2 (red line) and H2 (blue line).

To evaluate the isotopic effect, the reaction was also performed with D2 and, as expected, a peak at m/z = 46 due to the CO2D+ ion was recorded. In Figure b, the spectra obtained at the photon energy 14.0 eV with H2 (D2) in the reaction cell at the nominal pressure of 3.0 × 10–5 mbar are shown. By fitting the area of the peaks at m/z = 44, 45 and 46, the obtained ratios CO2+/HCO2+ = 1.3 and CO2+/DCO2+ = 2.12 give an isotopic effect of 1.6.

The reactions were also studied at fixed photon energy (hv = 14 eV) to verify the linear increase of the H(D)CO2+/CO2+ ratio with the pressure of H2(D2) in the reaction cell (Figure a) and by scanning the photon energy from 13.7 to 15.0 eV to measure the H(D)CO2+/CO2+ ratio as a function of photon energy at a fixed H2(D2) pressure (Figure b).

Figure 2

(a) Trend of HCO2+/CO2+ ratio vs H2 pressure in the CO2+/H2 ion-molecule reaction. (b) H(D)CO2+/CO2+ ratio vs photon energy for the reaction of CO2+ with H2 (black line) and D2 (red line) at nominal CE = 0 eV and at H2 (D2) nominal pressure of about 6.0 × 10–5 mbar in both cases.

The experimental data in Figure b show that the reaction is not favored by the increase of the vibrational energy of the CO2+. Literature data[41] at room temperature (298 K) and at low pressure report rate coefficients k of 5.80 × 10–10 ± 10% and 4.10 × 10–10 ± 10% molecule–1 s–1 cm3 for the reaction with H2 and D2 respectively, whereas the rate coefficients reported by Gerlich and co-workers[22] at high pressure are 9.5 × 10–10 ± 20% and 4.9 × 10–10 ± 20% molecule–1 s–1 cm3 for reaction with H2 and D2, respectively. Consequently the calculated isotopic effect (kH/kD) at low pressure is 1.4 ± 0.3 which is in quite good agreement with our low pressure experimental result of 1.6 obtained from data shown in Figure b. Moreover, the Langevin rate coefficients[42]kL 1.53 × 10–9 and 1.09 × 10–9 molecule–1 s–1 cm3 for the reaction with H2 and D2, respectively, demonstrate that the reaction efficiency relative to collision rate, (kH(D)/kL), is about 38% at low pressure[41] and it is 62% (kH/kL) and 45% (kD/kL) when Gerlich’s data are considered.[22]

The mechanism of this reaction is unveiled by the theoretical calculations performed at the DFT level of theory to compute the MEP, and by VTST to calculate the rate coefficients. All energies reported here after are corrected for zero point energy (ZPE).

The MEP reported in Figure shows that reaction is barrierless, with a minimum (blue arrow) at −134 kJ/mol (−142 kJ/mol for D2) that has a dissociation energy of 12.1 kJ/mol (13.3 kJ/mol for D2) to form the products HCO2+ + H.

Figure 3

Minimum Energy Path of the reaction between CO2+ and H2 molecule. The zero energy is referred to the entrance channel of the reactants. The red arrow points to the geometry of the VTS Complex, whereas the blue arrow points to the minimum (MIN) of the MEP. The level of calculation is B2PLYP/6-31++G** with ZPE correction.

The reactive complex at MIN of the MEP has the two hydrogen atoms separated by 1.55 Å, while the interatomic distance between O and H is 1.02 Å. This structure shows that the reaction has almost already occurred with the atomic hydrogen weakly bound to the ionic product HCO2+, which remains quasi-linear, as well as the O–H–H group. From a dynamical perspective, the reaction proceeds with the H–H approaching one of the oxygen lone pair while the outgoing H atom bounces back along the direction over which the H–H has entered the reaction region. The geometry of the transition state is calculated by variational minimization of the number of vibrational states of the reactive complex along the reactive coordinate. In Figure , the position of VTS is indicated by a red arrow, and its energy is about 16 kJ/mol (19 kJ/mol for D2) higher than MIN, about 4 kJ/mol (5 kJ/mol for D2) above the energy of the products. In this VTS, the H–H bond is partially broken (1.12 Å), and the O–H bond is quasi-formed (1.22 Å).

The electronic nature of the VTS can be analyzed in terms of the partial charges q (see Figure a), where the outgoing hydrogen atom (5H) has a q of 0.3e, while the q value of CO2 is 0.47e, which is almost the value (0.5e) it reaches in the final products.

Figure 4

(a) Mulliken partial charges along the MEP. (b) Atomic partial spin along the MEP. Red dashed lines indicate the position of the VTS, while the blue dashed lines point to the MIN complex. 4H is the H bound to the oxygen atom and 5H the outgoing hydrogen atom.

It is noteworthy that the positions along the MEP of the minimum of the q of CO2, as well as of the maximum of the q of the outgoing H, are very close in the VTS: the partially positive charged outgoing hydrogen (5H) has to be filled with half an electron charge to became neutral and to reach the final product region. The partial spins of the reactive systems are also interesting especially when considering the hydrogen atom which is transferred from H2 to CO2+: in the reactant region as well as in the final product region, this hydrogen has a zero net value of its partial spin; meanwhile, a maximum value of about 0.2ℏ is reached in the neighborhood of the VTS.

From a dynamical point of view, the maximum of the partial charge of the outgoing hydrogen and the corresponding maximum of the partial spin of the “transferred” hydrogen are correlated to a slowing down of the speed of the reaction: in this region of the MEP, where the VTS is located, the system decelerates its way toward the products. The break of the strongly bound H2 molecule is the key factor in the determination of the rate coefficient and the electron density of both H atoms is strongly shaken up during the reaction.

As for the energetics of the reaction, the low-pressure experimental conditions of the present study are such that the CO2+ and the VTS complex are not in thermal equilibrium in their internal degrees of freedom as well as with the surrounding molecules. The hydrogen molecule is at room temperature, as well as the roto-translation degrees of freedom of the CO2+ ion. Instead, the CO2+ vibrational states are excited by the energy absorbed during the photoionization and hence, not in thermal equilibrium with the surrounding. Furthermore, the H2 molecule plays a peculiar role with its high vibrational energy (4381 cm–1), which is poorly coupled with the other lower energy vibrations of the VTS complex, leading to a nonthermalized system. Hence, the vibrations of the transition state (see Table S4 in the Supporting Information) have been classified according to the following scheme: four frequencies form the set (Va) associated with the CO2 ion (578, 608, 1283, 2386 and578, 585, 1270, 2383 cm–1 in the reaction with H2 and D2, respectively), the negative frequency at −245 cm–1 for H2 (−181 cm–1 for D2) is associated with the reactive coordinate, and the other four vibrations (311, 909, 1068, 1170 and 232, 650, 776, 882 cm–1 in the reaction with H2 and D2, respectively) are classified as the set (Vb) of intermolecular modes. These last frequencies are not considered when computing the number (N) of vibrational states of the VTS complex, which depends only on the frequencies associated with the CO2+ ion excited in photoionization, whereas the intermolecular vibrational modes of the VTS are considered to compute the corresponding vibrational molecular partition function (see eqs and 14).

ETS is the difference between the energy of VTS (EVTS) and reagents (Erea) and its values are −118.2 and −124.0 kJ/mol for H2 (Figure ) and D2, respectively. In order to obtain the fraction X of ETS (see eq ), which goes into the VTS complex, we used the experimental reaction rates obtained by Gerlich and co-workers in the temperature range between 15 and 300 K for reaction .[22] By equating eq with the k(T) obtained by Gerlich and co-workers,[22] the fraction X(T) as a function of T can be derived, and it is shown in Figure .

Figure 5

Energy flow fraction X(T) versus temperature. A fraction X of the energy ETS(XETS) is transferred to the vibrational degrees of freedom of the TS. In blue is reported the energy fraction obtained by using the experimental rate coefficients for H2 measured by Gerlich and co-workers.[22] The brown area shows the uncertainty due to the 20% error on the experimental rate coefficients. The cyan line represents similar data for reaction with D2.

X(T) at 15 K is 4.5 × 10–4 and 14.5 × 10–4 for H2 and D2, respectively, showing that at low temperature, the ETS remains along the reaction coordinate and goes to the relative kinetic energy of the products. X(T) slowly increases with temperature, up to 6.1 × 10–2 and 6.6 × 10–2 for H2 and D2, respectively, at room temperature. The X(T) obtained in the temperature range 15–300 K has been fitted with the function X(T) whose parameters are reported in Table .

Table 1

Parameters of the Function X(T) = αe–β + δ for the Reaction of CO2+ with H2 and D2. (T is in K)

	α	β	γ	δ
H2	1.7667	22.4123	0.3320	3.3205 × 10–4
D2	1.5483	19.4790	0.3176	1.2225 × 10–3

Hence, we have calculated the nonthermal rate coefficients (eq ) at different energies for several values of the “XaXb pair” at room temperature (300 K) when X(300 K) = 0.0612. Figure reports such calculations for H2 (Similar data for the reaction with D2 are reported in Figure S2 of the Supporting Information) when Xa is 0.1 and Xb 0.9.

Figure 6

Rate coefficients as a function of the internal energy of CO2+ when vibrational energy distributions inside the VTS has a “XaXb pair” equal to 0.1 and 0.9. The data are referred to X(300 K) = 0.0612. In the inset are reported the rate coefficients for different values of the internal energy of CO2+ and as a function of Xa. See further details in the main text.

Rate coefficients presented in Figure show that the reaction slows down when the internal energy increases and that below 1.0 eV the rate coefficients oscillate because of a competition between the population of the vibrational levels of CO2+ and that of the VTS complex. The increase in the population of the vibrations of the VTS complex produces an increase in the rate coefficient, while the increase in the population of the vibrations of the CO2+ induces a decrease in the rate coefficients. The rate coefficient is higher when the energy flow goes to the intermolecular vibrations (Vb) of the VTS complex without exciting the vibrations of the VTS complex associated with CO2+ normal modes (Va) (see the low values of Xa in the inset of Figure ). The rate coefficient decreases up to below 10–10 cm3 s–1 molecule–1 when the energy flow does not go to the intermolecular vibrations (Vb) of the VTS complex (see the high values of Xa the inset of Figure ). This trend can be rationalized considering how the vibrations that mainly favor the reaction are those associated with the formation of the O–H bond, and hence, all the four intermolecular vibrations (Vb) of the VTS complex. Vice versa when the energy flow goes to the four vibrations (Va) of the VTS complex that come from CO2+, then the reaction is not favored because these vibrations are not relevant for the hydrogen transfer from H2 to CO2+. From a theoretical point of view, it is not so simple to provide a quantitative scenario describing the real energy flow between the two vibrational subsystem Va and Vb of the VTS complex even if it could be expected that low values of Xa, and complementary high values of Xb should correspond to the real dynamical description of the reaction. In order to verify such hypothesis, we have transformed the HCO2+/CO2+ ratio vs photon-energy data of Figure b in rate coefficients vs internal energy, following the procedure described in the paragraph 3 of the Supporting Information. The average internal energy of the CO2+ ion as a function of photon energy (Figure S1) allows to plot the experimental rate coefficients as a function of the internal energy of the CO2+ ion, and hence to compare the theoretical and experimental rate coefficients (see Figure a for H2 and Figure S3 for D2).

Figure 7

(a) Theoretical and experimental rate coefficients as a function of the internal energy of the system. The green points represent the experimental data, while the blue line is the theoretical rate coefficients calculated when X(300 K) = 0.0612 and Xa = 0.1. The red area shows the uncertainty due to the 20% error on the experimental rate coefficient from Gerlich.[22] See main text for further details; (b) rate coefficients for the hydrogen transfer reaction between CO2+ and H2 as a function of the internal energy acquired during the photoionization of the CO2+ at different temperature T. T is the temperature of the roto-translations of the CO2+ and of the vibro-roto-translation of the H2 reagent. X(300 K) = 0.0612, and Xa = 0.1.

It is noteworthy that the “XaXb pair” is a relevant parameter to select a theoretical rate coefficient in agreement with the experimental data. The Xa(Xb) = 0.1(0.9) is the best pair of parameters which is able to correctly reproduce the reaction kinetic at T = 300 K for reaction with H2, whereas the Xa(Xb) = 0.0(1.0) seems to better reproduce the reaction with D2 (see Figure S3 of the Supporting Information). In terms of energy flow, this means that for the reaction with H2 (ETS = −118.2 kJ/mol), only Xa·X(300 K)·ETS = 0.7 kJ/mol is the energy that flows into the “CO2-like” vibrational levels (Va) of the VTS complex, while Xb·X(300 K)·ETS = 6.5 kJ/mol is the energy that goes to the intermolecular vibrations (Vb) of the VTS complex. For the reaction with D2 (ETS = −124.0 kJ/mol), all the energy goes to the intermolecular modes of the VTS, and Xb·X(300 K)·ETS = 8.1 kJ/mol. Hence, the relative kinetic energy of the two products H and HCO2+ is 111.0 kJ/mol, while for D and DCO2+ it is 115.9 kJ/mol. This means that the reaction occurs so quickly that there is no much time to share the reaction energy with the internal degrees of freedom of the VTS complex.

Because of the small amount of energy X(T)·ETS transferred to the VTS complex at T = 300 K, which will be even smaller at lower T (see Figure ), it is reasonable to assume that the “XaXb pair” is independent from the temperature itself. Hence, in the temperature range between 15 and 300 K, where the X(T) is known, the rate coefficients can be calculated (see Figure b for H2 and Figure S4 for D2). The rate coefficients increase when the T decreases (see Figure S5 of the Supporting Information), and at T = 15 K, the reaction accelerates up to about 1.5 × 10–9 molecule–1 s–1 cm3 for H2 reaction (the collision limit), keeping the decreasing oscillating trend with energy at every T between 15 and 300 K (see Figure b). The general decreasing trend of the rate coefficient with the increase in the vibrational energy of CO2+ has the same decreasing behaviors of the Gerlich’s rates with temperature, where only the populations of the translational and rotational levels are involved. Hence, this reaction is not favored when either vibrational or roto-translational energy content are increased as generally expected in the barrierless reactions.

For reaction with D2, the temperature trend of the rate coefficient (see Figure S6 of the Supporting Information) has a maximum at about 55 K for all the energies up to 2 eV, and k = 6.5 × 10–10 molecule–1 s–1 cm3 is reached for E = 0 eV. The reason for the different temperature trend of the rate coefficients for H2 and D2 is the different fraction X(T): for both reactions, X(T) decreases with the temperature, but in the reaction with D2, the energy flow fraction at low T is greater than the one for the reaction with H2 (see Figure ). Hence, the exponential part of eq (), which makes the rate coefficient decreasing with decreasing T, is more effective in decreasing the rate coefficient below 55 K for the reaction with D2 then in the case of the reaction with H2. The rate coefficients for D2 at low temperatures have a different behavior in the present work with respect to thermal Gerlich’s data, and this can be explained with the nonstatistical energy distribution in the experimental conditions in our work.

Conclusions

The reaction of CO2+ with hydrogen molecules has been studied as a function of the CO2+ internal energy by using tunable synchrotron radiation to perform photoionization mass-resolved experiments, which have been analyzed and rationalized by means of the energetic and kinetics theoretical model. The reaction proceeds via hydrogen transfer from H2 to CO2+ with HCO2+ and H as final products. The experimental ratio of the charged product over the charged reactant shows a decrease in the reaction rate with increasing photon energy, confirmed also by the reaction of CO2+ with D2. The DFT minimum energy path of the reaction is barrierless and exothermic, and the variational transition state is located near the minimum of the energy along the reaction coordinate. Charge and spin population analysis clearly marks a strong reshuffle of the electron density when the reactive complex reaches the VTS geometry. The rate coefficient has been evaluated taking into account the nonthermal experimental conditions because of the low pressures in the reaction chamber. Moreover, the kinetic calculations considered the decoupling of the high energy vibration of H2 with respect to the lower energy vibrations of CO2+, and this is reflected in two vibrational sets of the VTS complex, which give different contribution to the overall reaction rate. The energy produced along the reaction coordinate is parameterized in terms of flows toward either the relative kinetic energy of the products or the internal degrees of freedom of the reactive complex. The present theoretical model gives an interpretation of the experimental data in terms of energy flow, revealing a decreasing trend of the rate coefficients with the photoionization energy. Furthermore, calculations of the reaction rates at different temperatures of the reactants confirm that the reaction at lower temperature reaches almost its Langevin upper limit of 1.53 × 10–9 molecule–1 s–1 cm3 . This study provides kinetic information that deserves to be considered within the network of the chemical reactions occurring where CO2 and H2 are present.