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Topics in Catalysis

, Volume 61, Issue 1–2, pp 3–19 | Cite as

Activation of CO2 by Gadolinium Cation (Gd+): Energetics and Mechanism from Experiment and Theory

  • Maria Demireva
  • P. B. Armentrout
Original Paper

Abstract

The exothermic and barrierless activation of CO2 by the lanthanide gadolinium cation (Gd+) to form GdO+ and CO is investigated in detail using guided ion beam tandem mass spectrometry (GIBMS) and theory. Kinetic energy dependent product ion cross sections from collision-induced dissociation (CID) experiments of GdCO2 + are measured to determine the energetics of OGd+(CO) and Gd+(OCO) intermediates. Modeling these cross sections yields bond dissociation energies (BDEs) for OGd+–CO and Gd+–OCO of 0.57 ± 0.05 and 0.38 ± 0.05 eV, respectively. The OGd+–CO BDE is similar to that previously measured for Gd+–CO, which can be attributed to the comparable electrostatic interaction with CO in both complexes. The Gd+(OCO) adduct is identified from calculations to correspond to an electronically excited state. The thermochemistry here and the recently measured GdO+ BDE allows for the potential energy surface (PES) of the Gd+ reaction with CO2 to be deduced from experiment in some detail. Theoretical calculations are performed for comparison with the experimental thermochemistry and for insight into the electronic states of the GdCO2 + intermediates, transition states, and the reaction mechanism. Although the reaction between ground state Gd+ (10D) and CO2 (1Σg +) reactants to form ground state GdO+ (8Σ) and CO (1Σ+) products is formally spin-forbidden, calculations indicate that there are octet and dectet surfaces having a small energy gap in the entrance channel, such that they can readily mix. Thereby, the reaction can efficiently proceed along the lowest energy octet surface to yield ground state products, consistent with the experimental observations of an efficient, barrierless process. At high collision energies, the measured GdO+ cross section from the Gd+ reaction with CO2 exhibits a distinct feature, attributed to formation of electronically excited GdO+ products along a single dectet PES in a diabatic and spin-allowed process. Modeling this high-energy feature gives an excitation energy of 3.25 ± 0.16 eV relative to the GdO+ (8Σ) ground state, in good agreement with calculated excitation energies for GdO+ (10Π, 10Σ) electronic states. The reactivity of Gd+ with CO2 is compared with the group 3 transition metal cations and other lanthanide cations and periodic trends are discussed.

Keywords

CO2 activation Lanthanides Gadolinium Guided ion beam Bond energies Potential energy surface 

1 Introduction

The interest in carbon dioxide reactivity has increased in recent years, in part because of the role of CO2 as a greenhouse gas and its potential use as a natural source of carbon in chemical synthesis [1, 2, 3, 4]. Conversion of CO2 to more useful forms requires activation by catalysts, where, for example, reduction of CO2 to CO by O atom transfer can be induced by several metals and their complexes or clusters [4]. Understanding the reactivity and interactions of these metals and complexes with CO2 can provide useful insight for the design of new and improved catalysts. In the gas phase, these interactions can be probed directly, without interference from solvent or substrate molecules, where such studies can offer important thermochemical information and help elucidate mechanistic details.

Gas-phase reactions of metal cations with CO2 have previously been carried out at thermal energies using ion cyclotron resonance (ICR) and selected-ion drift or flow tube techniques [5, 6, 7, 8, 9, 10, 11]. From the ICR studies, thermochemical information has been reported from bracketing experiments that determine whether oxygen atom transfer occurs from an oxidant with a known oxygen affinity [7, 8]. Kinetic information at thermal energies has also been obtained from measurements of the rate coefficients [5, 6, 7, 8]. More recently, Bohme and coworkers have systematically investigated the reactivity of 46 main group and transition metal cations [11] and in a separate study [9] the reactivity of lanthanide metal cations with CO2 using an inductively-coupled plasma selected-ion flow tube (ICP/SIFT) instrument. In these experiments, the rate coefficients for reaction (1) have been measured for the metal cations that react under thermal conditions.
$${{\text{M}}^+}+~{\text{C}}{{\text{O}}_{2~}} \to ~{\text{M}}{{\text{O}}^+}~+{\text{CO}}$$
(1)

Reaction (1) is observed for the early transition metal cations and several of the lanthanide cations, where the kinetics appear to be influenced by both electronic spin conservation and the exothermicity of the reaction [9, 11].

More detailed kinetic and thermochemical information can be obtained from studying the energy dependence of these reactions, where endothermic processes or those exhibiting a barrier can also be investigated. For example, using guided ion beam tandem mass spectrometry (GIBMS) [12, 13], reaction cross sections can be measured over a wide range of energies (thermal—1000 eV, lab) and this technique has previously been used to investigate the gas-phase activation of CO2 by first [14, 15, 16, 17], second [18, 19, 20, 21], and third [22] row transition metal cations, along with Al+ [23], Sm+ [24], and U+ [25]. These experiments have provided the energetics of the potential energy surfaces (PESs) and detailed mechanistic information, including the role of spin conservation and PES crossings, for many of these metal cations.

Few experimental gas-phase studies have focused on the reactivity of lanthanide metal atoms and ions with CO2. These include the study noted above by Bohme and coworkers as well as a systematic study by Campbell [26], who measured the temperature dependent rate coefficients for the lanthanide metal atoms. More recently, the reaction of Sm+ with CO2 has been investigated in great detail by GIBMS [24]. The lanthanide metals are unusual in that many of them have larger metal oxide bond dissociation energies (BDEs) than ionization energies (IEs) and can combine exothermically with atomic oxygen to release an electron and form the metal oxide cation in a chemi-ionization reaction [27, 28, 29, 30]. Thus, many of these lanthanides form stable oxide cations, where the BDEs of these oxides exceed that of OC–O such that reaction (1) is exothermic [9, 27, 31]. Of the lanthanide cations for which reaction (1) is expected to be exothermic, Bohme and coworkers have determined that La+, Ce+, Pr+, Nd+, Gd+, Tb+, and Lu+ react with CO2 at thermal energies, whereas Sm+, Dy+, Er+, and Ho+ do not [9]. These authors suggest that there is a kinetic energy barrier to the reaction of the latter species, where the barrier height correlates inversely with the exothermicity of reaction (1) [9]. Because reaction (1) is not significantly exothermic for Sm+, Dy+, Er+, and Ho+, the barrier height exceeds the reactant asymptote and no reaction occurs at thermal energies [9]. The nature of this barrier for Sm+ has recently been identified to arise from a crossing (which occurs above the reactant asymptote) between the diabatic surface of the Sm+(OCO) intermediate (4f66s1 configuration) in the entrance channel with the diabatic surface of the OSm+(CO) intermediate (4f55d2 configuration) that readily leads to ground state products in the exit channel [24]. Theoretical studies have investigated the activation of CO2 by the early lanthanide metal cations, La+ [32, 33], Ce+ [34], and Pr+ [34], for which reaction (1) is significantly exothermic, and suggest that these lanthanide cations will react according to a two-state reactivity (TSR) [35] mechanism, involving a crossing of two PESs with different spin [32, 33, 34]. Although these theoretical studies provide some information about the PESs and reaction mechanism, the calculations [34] for Ce+ suggest that no reaction will occur at thermal energies, which is at odds with the experiments of Bohme and coworkers [9], where a relatively large rate coefficient is measured for Ce+. Spin–orbit and relativistic effects and the many electronic configurations that are possible from the 4f electrons make these heavy elements challenging to describe theoretically, illustrating the need for good experimental data that can be used as theoretical benchmarks.

In the present study, the gas-phase activation of CO2 by the lanthanide gadolinium cation (Gd+) is investigated in detail using GIBMS and theory. BDEs at 0 K are measured for OGd+(CO) and Gd+(OCO) from collision-induced dissociation (CID) experiments of GdCO2 + precursor ions. Using this thermochemistry and the recently [36] measured BDE for GdO+, a PES for reaction (1) is constructed from experiment. Quantum chemical calculations are performed and tested against the experimental thermochemistry and provide insight into the electronic states of the intermediates and the reaction mechanism. The thermochemistry and reactivity of Gd+ with CO2 is compared with the group 3 metal cations and other lanthanide cations and periodic trends are discussed.

2 Experimental and Theoretical Methods

2.1 Experiments

The guided ion beam tandem mass spectrometer and the experimental procedure have been described in detail previously [12, 13, 37, 38]. Briefly, singly charged Gd+ ions were produced from Gd foil (Sigma-Aldrich, St. Louis, MO) using a direct current discharge flow tube (DC/FT) ion source [39]. A potential of − 1000 to − 1500 V was applied to a cathode consisting of the Gd foil attached to a tantalum holder. A gas mixture of 90% He and 10% Ar was continuously introduced into the source at a pressure of ~ 0.4 Torr. The DC discharge produced Ar+ cations, which were accelerated toward and collided with the cathode, sputtering singly charged Gd+ ions. To form GdCO2 + precursor ions, CO2 gas was leaked into the source about ~ 15 cm downstream from the cathode where Gd+ ions were produced. This yielded the putative Gd+(OCO) adduct. The putative inserted OGd+(CO) precursor ion was formed by introducing O2 and CO gases via separate inlets at ~ 15 and 30 cm downstream from the cathode, respectively. The precursor ions traveled through a meter-long flow tube, undergoing ~ 105 thermalizing collisions with the He/Ar gas mixture. Gd+ precursor ions are assumed to have electronic energies of 0.04 ± 0.03 eV (temperature of 700 ± 400 K) as described elsewhere [36]. GdCO2 + precursor ions are assumed to be thermalized to the flow tube temperature at ~ 300 K. After ions were skimmed and focused, the precursor ion of interest was mass selected using a magnetic momentum analyzer. For sufficient mass separation, the 160Gd isotope, being at least 2 Da heavier than all other naturally occurring isotopes, was used. Ions were decelerated to a specific kinetic energy prior to entering a radio frequency (rf) octopole ion beam guide, a section of which is surrounded by a reaction cell (effective length of ~ 8.26 cm). Xe and CO2 gases were introduced into the cell at pressures of ~ 0.1 to ~ 0.4 mTorr for reaction with the precursor ions. In this pressure regime, single collisions dominate the reactions as was confirmed from cross section measurements at different neutral reactant pressures exhibiting no pressure dependence. Precursor and resulting product ions were extracted from the octopole and subsequently mass analyzed using a quadrupole mass filter and their intensities were measured as a function of precursor ion kinetic energy in the lab frame using a Daly detector [40]. Product ion intensities were corrected for any background reaction that does not occur in the cell and were converted to cross sections as a function of center-of-mass (CM) energy as detailed previously [38]. Precursor ion kinetic energy distributions measured from retarding experiments had a full-width at half maximum of ~ 0.5 eV, and the uncertainty in the energy scale for this instrument was ± 0.1 eV (lab).

2.2 Data Analysis

Threshold energies at 0 K, E0, for the endothermic reactions studied here were obtained by modeling the product ion cross sections with the modified line-of-centers Eq. (2) using the data analysis program CRUNCH as described in detail elsewhere [13, 41].
$${{{\upsigma}}}\left( {\text{E}} \right)~=~{{{{\upsigma}}}_0}\mathop \sum \limits_{i} {{\text{g}}_{\text{i}}}{({\text{E}}~+~{{\text{E}}_{i~}}+~{{\text{E}}_{{\text{el}}}} - ~{{\text{E}}_0})^{\text{n}}}/{\text{E}}$$
(2)
In Eq. (2), E corresponds to the CM collision energy, σ0 is an empirical scaling factor (which describes the efficiency of energy deposition for CID reactions) [41], n is an empirical fitting parameter that determines the shape of the cross section, and Ei is the rotational and vibrational energy of the reactants for state i, having a population degeneracy gi (Σgi = 1). Calculation of Ei utilizes vibrational frequencies and rotational constants for the GdCO2 + reactants that were obtained from theoretical calculations described below. The reactant kinetic energy distributions were convolved with Eq. (2) before comparison with the experimental cross sections. E0, σ0, and n were determined from optimized fits to the experimental cross sections obtained by varying these parameters using a nonlinear least-squares procedure. The uncertainty in E0 was determined from optimized fits to several independent data sets (4–18) and from the range of n parameters that can reproduce the experimental cross section. For exchange reactions between an ion and a neutral, there is a decrease in the product ion cross section at CM energies that exceed the BDE of the neutral because the product ion has sufficient energy to dissociate at these energies. A modified version of Eq. (2) that includes this dissociation probability as described in detail previously [42] was used to model this decrease. For CID experiments, BDEs correspond directly to the measured E0 values, whereas for exchange reactions, M+ + AB → MA+ + B, the BDE was obtained from expression (3), which assumes no barrier in excess of the reaction endothermicity.
$${{\text{D}}_0}\left( {{{\text{M}}^+} - {\text{A}}} \right)~=~{{\text{D}}_0}\left( {{\text{A}} - {\text{B}}} \right)~ - ~{{\text{E}}_0}$$
(3)

2.3 Theoretical Calculations

To determine the ground and low-energy states for the GdCO2 + intermediates investigated experimentally, quantum chemical calculations were performed using the Gaussian09 package [43]. Most calculations, including relaxed potential energy scans where the O–Gd+–CO angle is varied, were performed with density functional theory (DFT) at the B3LYP [44, 45] level. These calculations use the relativistic Stuttgart Dresden [46] (SDD) effective small (28 electron) core potential (ECP) and the atomic natural orbital [47] (ANO) basis set for Gd and the Pople 6-311 + G(3df) basis set for C and O. Theoretical BDEs were obtained from the difference in calculated energies between ground state intact and dissociated GdCO2 + species. BDEs for the GdCO2 + intermediates were additionally calculated at the PBE0 [48, 49] and CCSD(T,full) [50, 51, 52, 53] levels of theory using the same ECP and basis sets. Calculations that utilize the 2nd order Douglas-Kroll-Hess Hamiltonian (DKH2) [54, 55] with the correlation consistent all-electron basis sets (cc-pVXZ-DK3 where X = T and Q) [56] for Gd developed by the Peterson group and corresponding aug-cc-pVXZ-DK basis sets for C and O were also carried out. Single-point energies at the CCSD(T,full) level were computed using the optimized geometries and corresponding frequencies for the zero-point energy correction obtained at the B3LYP/ANO level. Energies reported at all levels of theory include zero-point energy corrections where vibrational frequencies were scaled by 0.989 [57]. Rotational constants and vibrational frequencies for Gd+(OCO) and OGd+(CO) needed in the modeling of the experimental cross sections were obtained from calculations at the B3LYP/ANO level. With the exception of the cc-pVXZ-DK3 basis sets for Gd, which were provided by Professor Peterson, the other basis sets (and SDD ECP) were obtained from the EMSL basis set exchange [58, 59].

3 Experimental and Theoretical Results

3.1 Gd+ Reaction with CO2 to Form GdO+ and CO

In the energy dependent reaction between Gd+ and CO2, three product ions, GdO+, GdCO+, and GdO2 +, are observed as shown recently [36]. The cross section for these product ions as a function of energy in the CM frame are shown here in Fig. 1a. The GdO+ product is formed via reaction (1). At the lowest collision energy (~ 0.02 eV), the cross section exceeds 100 Å2, slightly below the theoretical collision limit according to the Langevin-Gioumousis-Stevenson (LGS) [60] model, which assumes an ion-induced dipole interaction potential, as shown by the black line in Fig. 1a. The experimental cross section decreases with increasing collision energy, indicating that GdO+ is formed in an exothermic and barrierless reaction, as discussed previously [36]. The rate coefficient, k, for reaction (1) can be computed from the cross section as described elsewhere [38]. At the two energies below 0.1 eV, the rate coefficients are 4.9 ± 1.0 and 4.0 ± 0.8 × 10−10 cm3/s, respectively, compared with kLGS = 6.3 × 10−10 cm3/s, indicating that the reaction proceeds with 77 ± 15 and 64 ± 13% efficiency relative to the LGS collision limit at these two energies (corresponding to effective temperatures of 329 ± 167 and 724 ± 167 K, respectively). These coefficients compare fairly well with the rate coefficient of 3.4 ± 1.0 × 10−10 cm3/s reported for this reaction at thermal (295 K) kinetic energies by Bohme and coworkers [61].

Fig. 1

a Experimental product ion cross sections (symbols) as a function of center-of-mass (bottom x-axis) and laboratory (top x-axis) frame kinetic energy for the Gd+ reaction with CO2 at a pressure of ~0.31 mTorr. The black line corresponds to the theoretical collision limit given by the Langevin-Gioumousis-Stevenson (LGS) model, and the black arrows indicate D0(OC–O) = 5.45 eV and the predicted decline in the cross section from the spectator stripping model (SSM) at 12.9 eV. For collision energies above 0.2 eV, an optimized composite fit for the ground and excited state GdO+ products is indicated by the red solid line, see text, where the dashed line corresponds to the 0 K model (i.e., excluding convolution over reactant internal and kinetic energies) for the high-energy feature. An optimized fit for the GdCO+ cross section is indicated by the solid green line, obtained by convolving the reactant kinetic energy distributions with equation (2). The dashed green line indicates the 0 K modeled GdCO+ cross section, excluding convolution over the reactant kinetic and internal energy distributions. b Comparison between the experimental (open circles) and calculated GdO+ cross sections from phase space theory using an exothermicity of 2.24 eV and scaling factor of 0.33 (red solid line) or an exothermicity of 0.19 eV and scaling factor of 0.38 (black solid line). The red and black dashed lines indicate the corresponding phase space theory cross sections for returning to reactants.

A similar efficiency (64%) was also observed for the analogous reaction between CO2 and the group 3 metal cation, Y+, in GIBMS experiments [19]. Disregarding the half-filled 4f shell of Gd+, Y+ is isovalent with Gd+ and has a reaction (1) exothermicity of 1.79 ± 0.18 eV [19], which is slightly smaller but comparable with that for Gd+, 2.24 ± 0.10 eV (determined from D0(Gd+–O) = 7.69 ± 0.10 eV [36] and D0(OC–O) = 5.45 eV [62]). The GdO+ cross section has an energy dependence of E−0.6±0.1 for energies below 0.2 eV and an energy dependence of E−1.0±0.1 for energies in the range of 0.2–1.5 eV (red solid line, Fig. 1a). This contrasts with the behavior of the YO+ cross section, which follows the expected energy dependence of E−0.5 from the LGS model up to 1 eV [19]. The possible origins for these differences in reactivity between Gd+ and Y+ are discussed further below.

To investigate the energy dependent GdO+ cross section from reaction (1) in more detail, phase space theory (PST) calculations were carried out using modified programs based on those developed by Chesnavich and Bowers [63, 64]. The PST cross section calculated using an exothermicity of 2.24 eV is shown by the red line in Fig. 1b. Here, the PST cross section has been scaled by 0.33 to improve the agreement with the experimental data (Fig. 1b). The reduced efficiency of the reaction is also evident from the smaller cross section compared with that predicted from the LGS model. Slightly better agreement can be obtained using an exothermicity of 0.19 eV and a scaling factor of 0.38 (black line, Fig. 1b). These results contrast with PST calculations for the exothermic reaction of Gd+ with O2 to form GdO+ and O, where relatively good agreement between the calculated and experimental GdO+ cross sections was obtained without the need to scale the calculated cross section [65]. The lower exothermicity and scaling factor needed in the PST calculations to reproduce the experimental data suggest that the reaction proceeds less efficiently than what would be expected on the basis of the relatively large reaction (1) exothermicity for Gd+. This could presumably be a result of Gd+(OCO) adducts that do not yield GdO+ and CO products, but preferentially dissociate back to Gd+ and CO2 reactants. As discussed in more detail below, this hypothesis agrees with our observation of an electronically excited Gd+(OCO) adduct for which loss of CO2 is energetically favored over rearrangement to an inserted OGd+(CO) complex that forms GdO+ and CO. Such unreactive adducts that compete and reduce the efficiency of reaction (1) are not explicitly accounted for in the PST calculations and could therefore contribute to the scaling factor needed to reproduce the experimental results in Fig. 1b.

3.2 High-Energy GdO+ Feature

At higher energies, the GdO+ cross section from reaction (1) exhibits a distinct second feature with an apparent threshold near 1 eV and a cross section that exceeds the LGS limit by ~ 20% from ~ 4.5–10 eV (Fig. 1). This feature peaks near D0(OC–O) = 5.45 eV as expected. At higher energies, the GdO+ cross section remains relatively constant and only begins to decline sharply at around 10 eV, much greater than D0(OC–O). A similar delay was observed in the Gd+ reaction with O2 [65], and suggests that the GdO+ product may be formed via an impulsive reaction mechanism at these higher energies. A simple model for an impulsive mechanism is the spectator stripping model (SSM), which assumes that reaction will occur from the interaction of Gd+ with one of the oxygen atoms while the rest of the CO2 molecule (i.e., CO) remains a “spectator” [66]. This constrains the available energy for reaction such that GdO+ will only have sufficient energy to dissociate at significantly higher energies than D0(OC–O). The SSM predicts that GdO+ will have enough energy to dissociate at CM energies exceeding 12.9 eV (Fig. 1a), which is slightly higher than the experimental onset.

The origins of this distinctive high-energy GdO+ feature could be the formation of electronically excited GdO+ products, as also postulated in the reactions of V+ [14], Zr+ [20], and Nb+ [18] with CO2. To estimate the threshold energy for the high-energy GdO+ feature from the data in Fig. 1a, the contribution from the ground state GdO+ product can be subtracted from the data and the remaining cross section can be modeled with Eq. (2). Assuming the cross section for the ground state GdO+ product follows an energy dependence of E−1.0±0.1 above 0.2 eV, modeling the remaining high-energy feature yields an E0 value of 1.01 ± 0.12 eV (dashed line, with the composite cross section shown by the solid line, Fig. 1a). Combining this E0 value with the reaction (1) exothermicity of 2.24 ± 0.10 eV gives an excitation energy of 3.25 ± 0.16 eV relative to the GdO+ ground state. The optimized parameters used in the modeling of this reaction and in all other endothermic reactions here are summarized in Table 1.

Table 1

Optimized parameters of Eq. (2) obtained by modeling the experimental cross sections

Reaction

σ0

n

E0 (eV)

D0 (eV)

Gd+ + CO2 → GdO+ + COa

5.3 ± 1.4

1.7 ± 0.2

1.01 ± 0.12

3.25 ± 0.16

Gd+ + CO2 → GdCO+ + Ob

0.8 ± 0.2

2.0 ± 0.2

4.80 ± 0.06

0.65 ± 0.06

GdO+ + CO → Gd+ + CO2 b, c

0.003 ± 0.002

2.4 ± 0.2

2.16 ± 0.27

2.16 ± 0.27

OGd+(CO) + Xe → GdO+ + CO + Xe

16.0 ± 0.5

1.3 ± 0.2

0.57 ± 0.05

0.57 ± 0.05

Gd+(OCO) + Xe → Gd+ + CO2 + Xe

71 ± 8

1.3 ± 0.2

0.38 ± 0.05

0.38 ± 0.05

Uncertainties correspond to one standard deviation

aHigh-energy feature. The excitation energy relative to the ground state of GdO+ is provided instead of D0, by adding E0 to the exothermicity (2.24 ± 0.10 eV) of reaction (1)

bFrom reference [36]

cThe endothermicity of the reaction, i.e., E0, is provided instead of D0

3.3 Gd+ Reaction with CO2 to Form GdCO+ and O

In the reaction between Gd+ and CO2, the GdCO+ product ion is formed in an endothermic reaction, as shown in Fig. 1a (scaled up by a factor of 10). The cross section has an apparent onset of ~ 4 eV and peaks around 5.5 eV, consistent with the OC–O BDE of 5.45 eV [62]. This cross section declines at higher energies because the GdCO+ product ion has enough energy to dissociate to Gd+ + CO. Modeling these data with Eq. (2) yields a 0 K threshold energy of 4.80 ± 0.06 eV, which gives a BDE for Gd+–CO of 0.65 ± 0.06 using Eq. (3) [36].

3.4 Gd+ Reaction with CO2 to Form GdO2 +

The energy dependent cross section (scaled by a factor of 100) for the GdO2 + product, also observed in the reaction between Gd+ and CO2, is shown in Fig. 1a. This cross section exhibits two distinct features, which do not exceed 10−18 cm2. Examination of the pressure dependence of this cross section demonstrates that the low-energy feature depends linearly on the pressure of CO2, indicating it is formed in a sequential reaction, whereas the higher energy feature has no dependence on pressure. Thus, the low and high energy features can be attributed to reactions (4) and (5), respectively.
$${\text{GdO}}^{ + } ~ + ~{\text{CO}}_{{2~}} \to ~{\text{GdO}}_{2} ^{ + } ~ + ~{\text{CO}}$$
(4)
$${\text{G}}{{\text{d}}^+}~{\text{+}}~{{\text{CO}}_{{\text{2}}}}~ \to ~{\text{Gd}}{{\text{O}}_2}^{+}~{\text{+}}~{\text{C}}$$
(5)

Using D0(OGd+–O) = 2.86 ± 0.08 eV [65] and D0(Gd+–O) = 7.69 ± 0.10 eV [36], reaction (5) is expected to have a threshold of 6.01 ± 0.13 eV with the GdO2 + product having sufficient energy to dissociate at energies exceeding 8.87 ± 0.10 eV. These values are in relatively good agreement with the apparent threshold and decline in the higher energy feature of the experimental data (Fig. 1a).

When GdO2 + is formed sequentially in reaction (4), its cross section is more appropriately envisioned by using the GdO+ product as the precursor ion, as was performed for the dioxides in the Re+, Os+, and Gd+ reactions with O2 [65, 67, 68]. Figure 2 shows the reanalyzed GdO2 + cross section as a function of CM energy, where the energy scale reflects that of the GdO+ + CO2 reactants and includes the 2.24 eV exothermicity for reaction (1). Figure 2 also shows a direct measurement of the cross section for reaction (4). The apparent thresholds of the sequential and direct cross sections are in the same general vicinity, but elevated compared with the thermodynamic threshold of 2.59 ± 0.08 eV = D0(O–CO)−D0(OGd+–O). This indicates that reaction (4) has a substantial barrier, not unlike the recent examination of the Sm+ + CO2 system [24] and previous results for the reaction of YO+ with CO2 to form YO2 + + CO [19]. In both these cases, measurements of the reverse reactions demonstrated the presence of a barrier in excess of the reaction endothermicities. At higher energies, the shapes of the sequential and direct cross sections for GdO2 + differ appreciably (even considering that the higher energy feature is the result of reaction (5), which will not occur in the direct reaction). This result can be attributed to the fact that in the sequential reaction, the GdO+ “reactant” has a very different distribution of internal and kinetic energies than in the better controlled direct reaction.

Fig. 2

Reanalysis of the GdO2 + cross section (open blue circles) from Fig. 1a assuming GdO+ is the precursor ion reacting in a sequential reaction with CO2. The 2.24 eV exothermicity of reaction (1) is included in the CM energy scale. The GdO2 + cross section from a direct reaction between GdO+ and CO2 is shown by the solid blue circles

3.5 Reverse Reaction, GdO+ + CO to Form Gd+ + CO2

Additional insight into the Gd+ reaction with CO2 to form GdO+ and CO can be obtained by investigating the reverse reaction (6), which should be endothermic by 2.24 ± 0.10 eV.
$${\text{Gd}}{{\text{O}}^+}~{\text{+}}~{\text{CO}} \to ~{\text{G}}{{\text{d}}^+}~{\text{+}}~{{\text{CO}}_2}$$
(6)

GdO+ reacts with CO in endothermic reactions to form Gd+ and GdO2 + as shown recently [36]. The resulting energy dependent cross section for Gd+ from this reaction is shown in Fig. 3. The Gd+ cross section exhibits two features: a low-energy feature arising from process (6) and a high-energy feature resulting from CID of GdO+ with an onset consistent with D0(Gd+–O), as modeled and discussed elsewhere [36]. The magnitude of the Gd+ cross section from process (6) does not exceed 2 × 10−18 cm2, indicating that this reaction is relatively inefficient. As shown previously [36], modeling this cross section with Eq. (2) yields a threshold energy of 2.16 ± 0.27 eV, which is consistent with the exothermicity determined for the forward reaction of 2.24 ± 0.10 eV obtained from measurements of D0(GdO+) from several different reactions [36]. The good agreement suggests that ground state Gd+ and CO2 products must be formed, and these results confirm that there is no barrier in excess of the endothermicity of reaction (6), consistent with the cross section for the forward reaction (1), Fig. 1.

Fig. 3

Gd+ cross section as a function of center-of-mass (bottom x-axis) and laboratory (top x-axis) frame kinetic energy resulting from the reaction between GdO+ and CO. The arrow indicates the GdO+ BDE of 7.69 ± 0.10 eV [36]. A combined optimized fit for the two Gd+ features, as described in reference [36], is indicated by the solid line and includes convolution of Eq. (2) over the reactant kinetic energies. The dashed lines correspond to the modeled cross sections at 0 K excluding convolution over the reactant kinetic and internal energies

3.6 CID of Gd+(OCO)

The energetics of the intermediates along the PES for the Gd+ reaction with CO2 can potentially be measured by forming these complexes in the source and dissociating them using Xe as collision gas. CID of GdCO2 + precursor ions formed by introducing CO2 gas into the source resulted in exclusive loss of CO2 to form Gd+ as the only product ion according to process (7).
$${\text{G}}{{\text{d}}^+}{\text{(OCO)}}~{\text{+}}~{\text{Xe}}~ \to ~{\text{G}}{{\text{d}}^+}~{\text{+}}~{\text{C}}{{\text{O}}_2}~{\text{+}}~{\text{Xe}}$$
(7)

This indicates that only a weakly bound Gd+(OCO) adduct is formed. The energy dependent cross section for Gd+ is shown in Fig. 4 and has an apparent threshold near 0 eV. The cross section increases with increasing energy, exceeding 40 Å2 at the highest energies measured, which indicates that process (7) is relatively efficient as a result of the weak interaction between Gd+ and the CO2 molecule. Modeling the cross section with Eq. (2) yields an E0 value and corresponding D0(Gd+–OCO) of 0.38 ± 0.05 eV (dashed line, Fig. 4). Attempts were made to form an inserted OGd+(CO) precursor ion by altering the source conditions, including changing the CO2 pressure and the DC discharge voltage used to generate Gd+. However, the GdO+ product ion corresponding to loss of CO could not be observed even at CM energies up to 8 eV (data not shown). If present, CID of Gd+(OCO) yields GdO+ + CO with a cross section below ~ 0.5 × 10−18 Å2.

Fig. 4

Product ion cross sections as a function of center-of-mass (bottom x-axis) and laboratory (top x-axis) frame kinetic energy for CID of Gd+(OCO) with Xe. This precursor ion is formed by introducing CO2 into the source. An optimized fit for the Gd+ cross section obtained by convolving Eq. (2) with the reactant kinetic energy distributions is indicated by the solid line. The dashed line corresponds to the modeled cross section at 0 K, which excludes convolution over the internal and kinetic energy distributions of the reactants

3.7 CID of OGd+(CO)

The inserted OGd+(CO) precursor ion could be formed by first introducing O2 in the source to form GdO+ and separately introducing CO farther downstream for reaction with GdO+. CID of this GdCO2 + precursor ion resulted in exclusive loss of CO to produce GdO+ according to reaction (8).
$${\text{OG}}{{\text{d}}^+}{\text{(CO)}}~{\text{+}}~{\text{Xe}}~ \to ~{\text{Gd}}{{\text{O}}^+}~{\text{+}}~{\text{CO}}~{\text{+}}~{\text{Xe}}$$
(8)

The cross section for the GdO+ product is shown as a function of CM energy in Fig. 5. The apparent threshold energy is near 0.1 eV. The GdO+ cross section does not exceed 10 Å2 at the highest energies measured, indicating that this process is less efficient than reaction (7), consistent with the slightly larger threshold for process (8). Modeling the cross section yields an E0 and corresponding D0(OGd+–CO) value of 0.57 ± 0.05 eV (Table 1), which is about a factor of two larger than the BDE of the CO2 adduct.

Fig. 5

Product ion cross sections as a function of center-of-mass (bottom x-axis) and laboratory (top x-axis) frame kinetic energy for CID of OGd+(CO) with Xe. This precursor ion is formed by introducing O2 and CO at ~ 15 and 30 cm, respectively, downstream from the cathode, where Gd+ ions are produced. An optimized fit for the GdO+ cross section obtained by convolving Eq. (2) with the reactant kinetic energy distributions is indicated by the solid line. The dashed line corresponds to the modeled cross section at 0 K, which excludes convolution over the internal and kinetic energy distributions of the reactants

3.8 Theoretical Calculations for GdCO2 +

Quantum chemical calculations were performed to determine the electronic states of stable GdCO2 + intermediates for comparison with those probed in the experiments, and to gain insight into the reaction mechanism of process (1). Most of these calculations were carried out at the B3LYP level using the ANO basis set and the SDD ECP for Gd and the 6-311 + G(3df) basis set for O and C. Various geometries and electronic states with multiplicities of 10 and 8 were explored. The energies, bond lengths, angles, and vibrational frequencies from these calculations for various optimized GdCO2 + complexes are summarized in Table S1 in the Electronic Supplementary Material. Molecular orbitals (MOs) that result from the interactions of the valence electrons of Gd+ (4f75d16s1), the two O atoms (2p4), and C (2p2) are shown in Fig. 6 for different GdCO2 + geometries and electronic states. The MOs resulting from the seven 4f valence electrons of Gd+ are omitted for simplicity because these form mostly nonbonding orbitals similar to their atomic orbitals. Representative MOs for the 4f electrons of different GdCO2 + geometries with C∞v and Cs symmetry are shown in Fig. S1 in the Electronic Supplementary Material.

Fig. 6

Electronic states and molecular orbitals resulting from the valence electrons of Gd+, C, and O for various optimized GdCO2 + structures with a C∞ v and b Cs symmetry calculated at the B3LYP/ANO level of theory. The 4f electrons of Gd+ form mainly nonbonding molecular orbitals similar to their atomic orbitals and are omitted (see Fig. S1). Unless otherwise noted, the electronic configurations shown are those for a multiplicity of 8, with electrons indicated in red resulting in states with a multiplicity of 10 if both electrons are high-spin coupled with the seven 4f electrons

The interaction between Gd+ and CO2 in linear Gd+(OCO) adducts (having C∞v symmetry) is primarily electrostatic in nature such that the valence electrons of the two O atoms and C combine to form MOs like those in free CO2. This is demonstrated in Fig. 6a, where the 2pz orbitals of O and C combine in-phase to form a 2σ bonding mo, the 2px and 2py orbitals combine in-phase to form 2π bonding MOs, and the out-of-phase combination of the 2px and 2py orbitals of the O atoms form nonbonding 3π MOs. In these linear Gd+(OCO) structures, the 5d and 6s valence electrons of Gd+ form mainly nonbonding MOs. The lowest energy linear Gd+(OCO) structure is found to have a 8Σ electronic state, where both valence electrons of Gd+ fill the nonbonding 3σ mo comprising primarily the 6s (with some 5dz 2 character) atomic orbital of Gd+. A Gd+(OCO) adduct with a 10Δ electronic state is calculated to be only 0.03 eV higher in energy, where one of the 3σ electrons has moved to occupy a 5d orbital comprising a nonbonding 2δ mo, with both these electrons high-spin coupling with the 4f electrons (Table S1). The electron in the 3σ mo can also be low-spin coupled resulting in a 8Δ electronic state, Fig. 6a, which is 0.64 eV higher in energy than the 8Σ state. Alternatively, the 5d electron of Gd+ can be in a mostly nonbonding 4π orbital to give a Π electronic state. The resulting high-spin coupled 10Π state is 0.16 eV higher in energy than the 8Σ state, whereas the low-spin 8Π state is significantly higher in energy at 0.58 eV above the 8Σ state. Another 8Δ electronic state moves the 5d valence electron of Gd+ to occupy a 4fδ atomic orbital in a low-spin configuration. This 4f8 (7Δ) 6s1 configuration is predicted to be 0.12 and 0.18 eV lower in energy than the 8Δ and 8Π states (with 4f75d16s1 configurations on Gd+), respectively. The B3LYP/ANO calculations likely overestimate the stability of the 4f8 electronic configuration because calculations utilizing the same basis set and level of theory predict the 8F (4f86s1) electronically excited state of Gd+ to have an excitation energy relative to the 10D (4f75d16s1) ground state that is smaller by ~ 0.75 eV compared with experiment [36].

For linear OGd+(CO) geometries (C∞ v symmetry), two stable local minima were identified having multiplicities of 8 and 10 and electronic states of Σ or Δ. In these linear structures, the valence electrons of C and O form 2σ and 2π bonding MOs similar to those in free CO (experimental r = 1.128 Å) resulting in C–O bond lengths of 1.13 Å (Fig. 6a, Table S1). The 2σ mo has some bonding character from the 5dz 2 Gd+ atomic orbital. The MOs formed between Gd+ and O are similar to those in GdO+ [36], where the 2p orbitals of O interact with three 5d orbitals of Gd+ to form 3π and 3σ bonding MOs. Five of the six valence electrons occupy these MOs with one electron remaining unpaired in the 3π MOs, while a single unpaired electron occupies a 4π mo, resulting predominantly from an in-phase combination between a 5d Gd+ orbital and 2p O and C orbitals. Multiplicities of 10 and 8 are obtained by high or low-spin coupling the unpaired 3π electron with the 4f electrons (Fig. 6a). We also located an 8Σ electronic state in which the 3π mo is doubly occupied, but this optimized linear OGd+(CO) structure has two imaginary bending frequencies (Table S1).

The search for stable inserted OGd+(CO) complexes with Cs symmetry yielded a global minimum 8A′′ electronic state with an O–Gd+–CO angle of 87° and Gd+–O and Gd+–CO bond lengths of 1.77 and 2.70 Å, respectively (Fig. 6b). The C–O bond length of the adduct is calculated as 1.12 Å, consistent with the experimental (calculated) bond length of free CO of 1.128 Å (1.124 Å). In this OGd+(CO) complex, two of the 2p atomic orbitals of the CO adduct combine in-phase to form bonding 5a′ and 4a′′ MOs similar to the π bonding MOs in free CO, as shown in Fig. 6b. An in-phase combination of the remaining 2p C and O orbitals in the adduct with a 5d (having 5dz 2 character) atomic orbital of Gd+ gives rise to a σ-type bonding 6a′ mo. Thus, the interaction between Gd+ and CO in this inserted OGd+(CO) structure should be slightly stronger than just electrostatics. The bonding of the O atom in this inserted OGd+(CO) complex is similar to that of GdO+, where effectively a triple bond is formed from the interaction of two 5d valence electrons of Gd+ with the four 2p valence electrons of the O atom [36]. In this structure, two 5d orbitals of Gd+ combine with 2p orbitals of O to form bonding 7a′ and 5a′′ MOs (like the π bonding MOs in GdO+), and the remaining 2p orbital of O combines with a 5d orbital of Gd+ having 5dz 2 character to form a bonding 8a′ mo (like the σ bonding mo in GdO+), Fig. 6b [36]. Several other optimized OGd+(CO) structures resulting in local minima with 10A′, 10A′′, and 8A′ electronic states were also found that were significantly higher in energy at ~ 1.5–3 eV above the global 8A′′ minimum (Table S1). The A′ electronic states have similar MOs as those of the 8A′′ ground state, except that one of the 7a′ electrons has moved to occupy a 6a′′ mo comprising a slightly bonding 5d Gd+ atomic orbital with the 2p C orbital (Fig. 6b). A multiplicity of 10 or 8 results if the 7a′ electron high or low spin-couples with the 6a′′ and 4f electrons. For the 8A′ state, two different geometries yielded local minima, with O–Gd+–CO bond angles of 31 and 96° (Fig. 6b), respectively, where the former corresponds to a CO2 adduct rather than an inserted OGd+(CO) complex (Table S1). For the 10A′ state, a local minimum was located having a similar geometry (O–Gd+–CO angle of 97°) as the inserted OGd+(CO) 8A′ state. The inserted OGd+(CO) complexes with A′ states are about 2.9 eV higher in energy than the 8A′′ ground state, whereas the Gd+(OCO) 8A′ adduct is slightly lower in energy at 2.2 eV above the ground state (Table S1). Three optimized structures with 10A′′ electronic states were obtained where one of the 7a′ electrons has moved to occupy a 9a′ orbital that corresponds to a mostly nonbonding 6s atomic orbital of Gd+ with some 5dz 2 character (Fig. 6b). These structures include a nonlinear CO2 adduct with O–Gd+–CO angle of 29° and two inserted structures with angles of 71° (Fig. 6b) and 129°, respectively. The Gd+(OCO) adduct is 1.6 eV higher in energy than the 8A′′ ground state, whereas both inserted structures are 3.0 eV above the global minimum (Table S1).

3.9 Theoretical Potential Energy Surfaces (PESs)

Reaction (1) between ground state Gd+ (10D) and CO2 (1Σg +) reactants to form ground state GdO+ (8Σ) and CO (1Σ+) products is formally spin-forbidden. Thus, the reaction with CO2 must proceed via a two-state reactivity (TSR) [35] mechanism involving a crossing of potential energy surfaces (PESs) with different spin. This is consistent with the exothermic reaction (1) exhibiting an energy dependence of E−1 (Fig. 1) for ground state products [69, 70], where the deviation from the expected E−0.5 energy dependence of the LGS model can possibly be attributed to the effect of the surface crossing [35]. Additionally, the high-energy GdO+ feature that appears in Fig. 1a can be explained by the formation of an electronically excited GdO+ product in a spin-allowed process, as has been observed for other metal systems [14, 18, 20]. To explore the reaction mechanism, relaxed PES scans were calculated at the B3LYP/ANO level as a function of O–Gd+–CO angle for multiplicities of 10 (reactants) and 8 (products) having A′ and A′′ symmetries. These surfaces are shown in Fig. 7 and have minima that correspond to the optimized GdCO2 + structures already discussed. The geometries, energies, and vibrational frequencies for the stationary points along these surfaces, including the transition states (TS), are listed in Table S1 in the Electronic Supplementary Material. The results in Fig. 7 indicate that the reaction between ground state Gd+ (10D) and CO2 (1Σg +) reactants can be initiated on 10A′ and 10A′′ surfaces by forming linear Gd+(OCO) adducts that are both about ~ 1.1 eV below the reactant asymptote. Interestingly, there is a 8A′′ PES that is even slightly lower in energy than the 10A′ and 10A′′ surfaces for adducts with O–Gd+–CO angles less than ~ 25°. The small energy gap between these octet and dectet surfaces in the entrance channel of the reaction can lead to rapid spin pre-equilibrium [71, 72], such that reaction (1) can proceed efficiently along the 8A′′ surface to form the ground state 8A′′ OGd+(CO) intermediate, which can subsequently dissociate to ground state GdO+ (8Σ) and CO (1Σ+) products. This is consistent with the experimental observation of the relatively efficient exothermic reaction (Fig. 1). The small energy gap between the octet and dectet surfaces is also demonstrated in Fig. S2a, where calculated PES scans are shown for linear Gd+(OCO) adducts as a function of the Gd+ and CO2 separation distance. These PESs have minima corresponding to the stable linear Gd+(OCO) adducts already discussed and indicate that adducts with 10Δ and 8Σ electronic states have wells that are very close in energy (Fig. S2).

Fig. 7

Relaxed potential energy surface scans as a function of OGd+(CO) angle calculated at the B3LYP/ANO level of theory. Surfaces are separated into A′ (solid) and A′′ (dash) symmetry having dectet (black) and octet (red) multiplicities. Horizontal bars indicate the experimental (solid) and calculated (dash-dot) energies for the ground and electronically excited states of the reactants, Gd+ (10D and 8D) + CO2 (1Σg +), and products, GdO+ (8Σ, 10Π) + CO (1Σ+). The red dotted 8A′′ surface was obtained from a relaxed potential energy surface scan that varied the O and CO distance (which essentially changes the O–Gd+–CO angle in this range) because scans that explicitly varied the O–Gd+–CO angle resulted in a break in the 8A′′ surface such that the CO adduct was no longer as closely bound to GdO+

The origin for the shape exhibited by the calculated PESs in Fig. 7 has recently been described for the Sm+ reaction with CO2 [24], where the early barrier at an O–Gd+–CO angle of ~ 25° arises from the need to bend the CO2 adduct such that the metal cation can insert into one of the CO bonds of CO2 (Fig. 7). The transition state (TS) found along this PES (Table S1) can yield intermediates with O–Gd+–CO angles of ~ 30° along the 8A′ and 10A′ surfaces that are stabilized by the additional interaction between Gd+ and C (Fig. 7). As the angle increases further, another TS results along the 8A′, 10A′, and 10A′′ surfaces at ~ 50° corresponding to cleaving the C–O bond, which then leads to the stable inserted OGd+(CO) complexes. The 8A′′ surface begins to deviate from the rest of the PESs after the first TS barrier (Fig. 7), where there is a significant energy drop with increasing angle. This is attributed to the ability of Gd+ to more effectively bind (i.e., form a triple bond) with the O atom in the 8A′′ electronic configuration, which eventually leads to the ground state inserted OGd+(CO) complex (Fig. 6b).

The calculated PESs in Fig. 7 also support the conclusion that the distinct high-energy feature observed for reaction (1) in Fig. 1a results from electronically excited GdO+ products. These can be formed by following either the 10A′ and 10A′′ surfaces in diabatic and spin-allowed processes, and have calculated barriers of ~ 1 eV above the reactant asymptote, consistent with the measured threshold energy of 1.01 ± 0.12 eV for the high-energy GdO+ feature (Table 1). It should also be noted that extraction of an O atom directly from the CO2 molecule by Gd+ to form GdO+ and CO products can proceed along diabatic surfaces and has a calculated barrier of 1–2 eV in excess of the reactant asymptote (Fig. S2b, Electronic Supplementary Material). This process is consistent with an impulsive reaction mechanism, postulated to explain the delayed onset in the decline of the high-energy feature, and thus likely contributes to the high-energy feature (vide supra).

3.10 Comparison Between Experimental and Theoretical Thermochemistry

To determine the electronic states of the GdCO2 + intermediates probed in the CID experiments and the electronically excited GdO+ product formed at higher collision energies in reaction (1), the experimental thermochemistry is compared with theory at the B3LYP, PBE0, and CCSD(T,full) levels of theory using the ANO and all-electron cc-pVXZ-DK3 [56] (where X = T, Q) basis sets for Gd. Because the calculations using the all-electron Gd basis sets are computationally expensive, only single-point energies were calculated for the GdCO2 + complexes. For the B3LYP and PBE0 calculations, single-point energies were calculated from the optimized GdCO2 + geometries obtained with the ANO basis set and SDD ECP for Gd at the corresponding level of theory. At the CCSD(T,full) level, single-point energies were calculated using B3LYP/ANO geometries.

The inserted OGd+(CO) species probed in the CID experiments is easily identified from the calculations as the 8A′′ OGd+(CO) ground state. The measured BDE for CO of 0.57 ± 0.05 eV is in relatively good agreement with the theoretical values calculated at the DFT level ranging from 0.63 to 0.70 eV, summarized in Table 2. At the CCSD(T,full) level, the values obtained with the all-electron cc-pVXZ-DK3 basis sets for Gd are somewhat larger at 0.89 and 1.05 eV for X = T and Q, respectively, in slightly worse agreement with experiment.

Table 2

Comparison between experimental and theoretical energies (in eV) for the Gd+–CO (10Π), Gd+–OCO (8Π), and OGd+–CO (8A′′) BDEs, the exothermicity, ΔrH(1), for reaction (1), and the excitation energies of the GdO+ 10Π and 10Σ states relative to the 8Σ ground state

Level

Basis set

GdO+ (10Π/10Σ)

Gd+–CO

OGd+–CO

Gd+–OCO

ΔrH(1)

Expt

 

3.25 ± 0.16

0.65 ± 0.06a

0.57 ± 0.05

0.38 ± 0.05

− 2.24 ± 0.10

B3LYP

ANO

2.81 (2.75)/2.98

0.87 (0.81)

0.67

0.20 (0.14)

− 1.37 (− 1.25)

cc-pVTZ-DK3

3.00 (2.94)/3.16

0.90b (0.84)

0.63b

0.19b (0.13)

− 1.65 (− 1.53)

cc-pVQZ-DK3

2.99 (2.93)/3.15

0.89b (0.83)

0.63b

0.19b (0.13)

− 1.63 (− 1.51)

PBE0

ANO

2.98 (2.92)/3.13

0.95 (0.89)

0.70

0.11 (0.05)

− 1.24 (− 1.12)

cc-pVTZ-DK3

3.10 (3.04)/3.27

1.04b (0.98)

0.66b

0.06b (0.00)

− 1.49 (− 1.37)

cc-pVQZ-DK3

3.09 (3.03)/3.26

1.03b (0.97)

0.66b

0.06b (0.00)

− 1.48 (− 1.36)

CCSD(T,full)

ANO

3.21 (3.15)/3.28

0.71c (0.65)

0.72c

0.28c (0.22)

− 1.62 (− 1.50)

cc-pVTZ-DK3

3.22 (3.16)/3.28c

0.85c (0.79)

0.89c

0.47c (0.41)

− 1.92 (− 1.80)

cc-pVQZ-DK3

3.32 (3.26)/3.38c

1.12c (1.06)

1.05c

0.76c (0.70)

− 2.20 (− 2.08)

CBSd

3.38 (3.32)/3.44

1.28 (1.22)

1.15

0.92 (0.86)

− 2.37 (− 2.25)

Spin-orbit corrected values are in parentheses and italics

aFrom reference [36]

bSingle-point energy calculation using the geometry and corresponding frequency from the optimization calculation with the ANO basis set

cSingle-point energy calculation using the geometry and corresponding frequency at the B3LYP/ANO level

dComplete basis set limit

The electronic state of the Gd+(OCO) adduct probed in the experiments is more difficult to determine, because the lowest energy adduct with 8Σ electronic state has a calculated BDE of 0.77 eV at the B3LYP/ANO level, which is significantly larger than the experimental value of 0.38 ± 0.05 eV. The calculated BDEs at the B3LYP/ANO level for various linear Gd+(OCO) adducts (Table S1) range from ~ 0.2 to 0.7 eV, suggesting that an electronically excited adduct might be probed in the experiments, as was observed for the Gd+ reaction with O2 [65]. This adduct could correspond to that found along the 8A′ surface in Fig. 7 (having a 8Π state in C∞v symmetry), which is about 0.6 eV higher in energy than those on the 10A′, 10A′′, and 8A′′ surfaces. The calculated BDE for this adduct is 0.20 eV at the B3LYP/ANO level, which is somewhat lower than the value measured experimentally. BDEs calculated at the DFT level for the 8Π electronically excited Gd+(OCO) adduct are generally smaller than experiment (Table 2). Better agreement is obtained at the CCSD(T,full) level of theory with BDEs of 0.28 and 0.47 eV calculated using the ANO and cc-pVTZ-DK3 basis sets, respectively (Table 2). In contrast, the larger all-electron cc-pVQZ-DK3 basis set yields a significantly higher BDE of 0.76 eV. Assignment of the Gd+(OCO) adduct probed in the experiments as the 8Π state is also consistent with the corresponding calculated 8A′ surface (Fig. 7), which is isolated from the 10A′, 10A′′, and 8A′′ surfaces, such that this adduct cannot easily couple with these surfaces to yield the inserted 8A′′ OGd+(CO) ground state. Thus, the Gd+(OCO) adduct on the 8A′ surface will dissociate preferentially by CO2 rather than CO loss upon activation. This is supported by RRKM calculations, which indicate that the rate constant for CO2 loss is at least about two orders of magnitude larger than that to form the inserted OGd+(CO) complex for collision energies up to ~ 2 eV. At higher energies, the barrier for rearrangement can be surmounted, such that an inserted complex might be formed that dissociates via CO loss. This product channel, however, was not observed in the experiments at collision energies of up to 8 eV. In contrast, the 8A′′, 10A′, 10A′′ adducts can readily dissociate to GdO+ and CO because of the relatively shallow well of the OGd+(CO) intermediate (Fig. 7) and high exothermicity of reaction (1). Indeed, RRKM calculations indicate that the ground state Gd+(OCO) adduct can rearrange to OGd+(CO) and dissociate to GdO+ and CO on a time scale that is about ~ 105 faster than the collision frequency in the source, thereby explaining the unsuccessful attempts to form the 8A′′ OGd+(CO) intermediate from reaction with CO2 in the source.

Modeling the high-energy feature in reaction (1) results in an excitation energy of 3.25 ± 0.16 eV for the electronically excited GdO+ product relative to the ground state. Calculations indicate that this high-energy state could correspond to a 10Π or 10Σ state. At the DFT level, slightly lower excitation energies are obtained for the 10Π state compared with experiment, ranging from 2.81 to 3.10 eV (Table 2), while slightly better agreement with experiment is obtained for the 10Σ state, where excitation energies range from 2.98 to 3.27 eV. At the CCSD(T,full) level, the difference in excitation energies between the 10Π and 10Σ states is smaller, with energies for the 10Π state ranging from 3.21 to 3.32 eV and those for the 10Σ state ranging from 3.28 to 3.38 eV for the different basis sets. These results suggest that both the 10Π and 10Σ states likely contribute to the high-energy feature in Fig. 1.

Using the BDEs for the Gd+(OCO) and OGd+(CO) intermediates and the exothermicity for reaction (1) determined from our recent GdO+ BDE measurement [36], an experimental PES can be constructed for Gd+ reacting with CO2 to yield GdO+ and CO. This PES is shown in Fig. 8 and is compared with theoretical values obtained by extrapolating those from the all-electron cc-pVXZ-DK3 basis sets where X = T and Q to the complete basis set (CBS) limit at the CCSD(T,full) level of theory using the formula E[CBS] = 1.577163 E[Q]−0.577163 E[T] [73, 74]. Figure 8 includes theoretical CBS energies for the ground and low-energy octet and dectet Gd+(OCO) adducts and the 8A′′ TS, which could not be probed experimentally, but should be found along the lowest energy pathway to yield ground state GdO+ and CO products. The CBS calculations predict that the linear Gd+(OCO) adduct with a 10Δ electronic state is lower in energy than the 8Σ state by 0.22 eV, which contrasts with the B3LYP/ANO calculations that found the 8Σ state to be lower in energy by 0.03 eV. Thus, the reaction to form ground state products may be limited by a surface crossing from the dectet to the octet surface, which occurs early in the entrance channel and well below the reactant asymptote. A summary of the pathways and thermochemistry for reaction (1) along the octet and dectet surfaces in spin-allowed processes is shown in Scheme 1. The comparison of the CBS values with experiment indicates that the calculations reproduce the experimental exothermicity (which depends on the GdO+ BDE) and the threshold of the electronically excited GdO+ product (Fig. 8). However, the CBS extrapolated calculations perform poorly in reproducing the BDEs of OGd+-CO and Gd+-OCO, predicting larger values of 1.15 and 0.92 eV, compared with experiment of 0.57 ± 0.05 and 0.38 ± 0.05 eV, respectively (Table 2; Fig. 8).

Fig. 8

Potential energy surface for the Gd+ reaction with CO2 to form GdO+ and CO mapped from guided ion beam tandem mass spectrometry measurements (green horizontal lines with error bars). This thermochemistry is compared with theoretical calculations at the CCSD(T,full)/CBS//B3LYP/ANO level of theory, where dectet and octet states are shown by black and red bars, respectively, with the term symbols given in the figure. Included are also the calculated values for the low-energy and ground state octet and dectet Gd+(OCO) adducts and the transition state along the 8A′′ potential energy surface, which are the intermediates along the lowest energy pathway to form ground state GdO+ (8Σ) + CO (1Σ+) products from ground state Gd+ (10D) + CO2 (1Σ g +) reactants

Scheme 1

Schematic of the reaction proceeding along the octet and dectet surfaces to form ground state and electronically excited GdO+ product ions, respectively. Black and red arrows indicate spin-allowed processes along dectet and octet surfaces, respectively

Part of the deviation in the calculated BDEs could potentially arise from spin–orbit effects. The calculated energies for a given state do not reflect the lowest spin–orbit (SO) level, but instead give the energy averaged over all SO levels for that state. The experimental threshold should correspond to the energy difference between the lowest energy SO levels of reactants and products. Thus, for a more accurate comparison between experiment and theory, a first-order semi-empirical SO correction can be applied to the calculated energies to reflect the lowest energy SO levels as described in detail elsewhere [36]. For the Gd+(OCO) adduct, assuming a 8Π excited electronic state, the calculated BDE needs to be corrected by the SO averaged energy of the Gd+ (10D) ground state (0.12 eV) and the 8Π state of the Gd+(OCO) adduct (0.06 eV), resulting in an overall correction which lowers the theoretical BDE by 0.06 eV. This yields a CBS value of 0.86 eV, in better agreement with experiment. For the inserted OGd+(CO) intermediate, the calculated BDE requires no SO correction because OGd+(CO) (8A′′), GdO+ (8Σ), and CO (1Σ+) have zero orbital angular momentum and thus have no first-order SO splittings. The calculated exothermicity for reaction (1) needs to be reduced by only the SO averaged energy for the 10D ground state of Gd+ (0.12 eV), giving an exothermicity of − 2.25 eV at the CCSD(T,full)/CBS level in excellent agreement with experiment (− 2.24 ± 0.10 eV). For the electronically excited GdO+ product, only the calculated energy for the 10Π state needs to be SO corrected, which lowers this state by 0.06 eV, increasing the difference with the 10Σ state slightly. The SO corrected energies are included in Table 2. Generally, these results demonstrate that the SO corrections are not significant and cannot explain the larger deviations observed between experiment and theory at the CCSD(T,full)/CBS//B3LYP/ANO level for the OGd+(CO) and Gd+(OCO) BDEs.

3.11 CO Binding to Gd+ and GdO+

As reported recently [36], the BDE for Gd+(CO) measured from the exchange reaction between Gd+ and CO2 to form GdCO+ and O is 0.65 ± 0.06 eV (Table 2). A 10Π ground state was generally predicted from the calculations for Gd+(CO) where the 6s and 5d valence electrons of Gd+ remain in their respective atomic orbitals to form mostly nonbonding MOs, such that the CO adduct interacts with Gd+ primarily through electrostatics [36]. For the previously reported theoretical BDEs at the B3LYP level, the zero-point energy of CO (0.14 eV) was accidentally omitted. Applying this correction gives slightly larger BDEs of 0.81 and 0.63 eV (including the empirical SO correction) for the ANO and Seg. SDD basis sets, respectively. In the present work, additional BDEs for Gd+(CO) were calculated from single-point energies using the all-electron cc-pVXZ-DK3 (with X = T and Q) basis sets for Gd and are summarized in Table 2. Similar trends in the calculated BDEs are seen for Gd+–CO to those for OGd+–CO (Table 2), where generally larger theoretical BDEs compared with experiment are predicted.

The BDE measured for OGd+–CO (0.57 ± 0.05 eV) is similar but slightly lower than that for Gd+–CO (0.65 ± 0.06 eV). These binding interactions can be envisioned as combinations of electrostatics, σ donation (ligand to metal), and π backbonding (metal to ligand). Qualitatively, the similar bond energies suggest that the interaction is mainly electrostatic for both complexes, which is consistent with the calculated MOs for the ground state OGd+(CO) (Fig. 6b) and Gd+(CO) [36] complexes (although O2‒Gd3+ character would enhance the OGd+–CO interaction). The slightly larger BDE for Gd+(CO) can potentially be explained by an additional π bonding interaction between Gd+ and CO that is possible from the available 5d valence electron of Gd+ [36]. This backbonding interaction is absent for OGd+(CO) because the valence electrons of Gd+ are involved in binding to the additional O atom. The calculations at the B3LYP and PBE0 levels reproduce qualitatively this trend, predicting larger BDEs by 0.14–0.32 eV for Gd+–CO compared with those for OGd+–CO (Table 2), whereas practically the same BDEs for both complexes are obtained at the CCSD(T,full) level (Table 2). Note that the differences calculated at this level using the cc-pVQZ-DK3 and CBS basis sets of 0.01 and 0.07 eV reproduce the experimental difference of 0.08 ± 0.08 eV the best.

3.12 Periodic Trends

Gd+ with its half-filled 4f shell and 5d16s1 ground state valence electron configuration is unusual compared with most lanthanide metal cations, which generally have 4fn6s1 ground state configurations (where n corresponds to the remaining valence electrons). In this regard, Gd+ is similar to the lanthanides La+ (5d2), Ce+ (4f15d2), and Lu+ (4f146s2). Ignoring the 4f electrons, these lanthanides have similar electronic configurations to the group 3 metal cations Sc+ (3d14s1) and Y+ (5s2 with the 4d15s1 state only 0.15 eV higher in energy) with two valence electrons in d or s orbitals. Indeed, all these metal cations react in exothermic, and relatively efficient reactions with CO2 to form MO+ and CO as has been shown from ICP/SIFT experiments [9, 11]. Of these metal cations, the reaction of Y+ with CO2 has previously been investigated in detail with GIBMS, and BDEs for Y+–CO and OY+–CO of 0.31 ± 0.11 and 0.71 ± 0.04 eV, respectively, have been determined [19]. Unlike the GdO+ cross section, the corresponding YO+ cross section does not exhibit a distinct high-energy feature. This difference is likely due to Y+ having a 5s2 ground state, such that the reaction to form ground state products, YO+ (1Σ+) + CO (1Σ+), is spin-allowed and still efficient at high energies, consistent with the YO+ cross section exhibiting the expected LGS E−0.5 energy dependence at collision energies below ~ 1 eV [19]. The weaker bond for Y+–CO (0.31 ± 0.11 eV) compared with Gd+–CO (0.65 ± 0.06 eV) can also be explained by the differences in the ground state electronic configurations of these two metal cations where the 5d valence electron of Gd+ (5d16s1) can form an additional π interaction with the CO adduct, not possible for ground state Y+ (5s2). However, for the OM+(CO) complexes, the available valence electrons for both Gd+ and Y+ are promoted to d orbitals to more effectively bind with the additional O atom, forming essentially a triple bond [36]. Thus, the CO adduct must interact primarily through electrostatics in both complexes, as also evident by the similar BDEs of 0.71 ± 0.04 eV and 0.57 ± 0.05 eV for OY+–CO and OGd+–CO, respectively. An interesting difference between Gd+ and Y+ is that the Gd+(OCO) adduct could be stabilized in reactions with CO2 in the source, but attempts to produce a Y+(OCO) adduct failed and instead yielded only the inserted OY+(CO) complex [19]. This suggests that the Y+(OCO) adduct can readily rearrange to the inserted complex. Thus, the PESs for the Y+ reaction with CO2 must differ somewhat in the entrance channel from those obtained for Gd+ in Fig. 7, presumably a result of the differences in ground state electronic configurations of Gd+ and Y+. The ability to form the inserted OY+(CO) complex from the reaction with CO2 in the source, which was not possible for Gd+, might be aided by the slightly deeper well and lower reaction exothermicity (-1.79 ± 0.18 eV) for Y+. To the best of our knowledge, the energy dependent product ion cross sections for the reactions of Sc+, La+, Ce+, and Lu+ with CO2 have not been measured. However, on the basis of the ground state valence electron configuration of the metal cation and spin-conservation, it seems likely that Sc+ will behave similarly to Gd+, and likewise Lu+ will exhibit comparable behavior to Y+. Because both La+ and Ce+ have a high-spin 5d2 configuration, these metal cations should exhibit similar reactivity with CO2, which should be more similar to that of Sc+ and Gd+ than that of Y+ and Lu+.

The results for Gd+ here can also be compared with recent GIBMS results for Sm+ (4f66s1), which has a ground state electronic configuration typical of most lanthanide cations. The reaction between Sm+ and CO2 to form SmO+ + CO is exothermic, but the GIBMS results [24] indicate that this reaction clearly exhibits a barrier, which is consistent with the failure to observe this reaction in ICP/SIFT experiments [9]. From calculations and comparison with the GIBMS results, this barrier is identified to correspond to the crossings between 8A′′ and 6A′′ surfaces in the entrance channel with the 6A′ surface of the ground state inserted OSm+(CO) complex in the exit channel, which can readily dissociate into ground state products [24]. For Sm+ to achieve effective binding with the O atom in the inserted OSm+(CO) intermediate, promotion of both a 4f electron and the 6s electron to 5d orbitals is required, corresponding to an atomic Sm+ excitation of 2.35 eV [24]. However, for Gd+ only the 6 s electron needs to be promoted. Because this promotion energy cost for Gd+ is not too large (~ 0.55 eV, from the energy difference between the 10D (4f75d16s1) and 10F (4f75d2) states averaged over the spin–orbit levels), a low-energy Gd+(OCO) adduct can be formed along the 8A′′ surface (Fig. 7). This allows the Gd+ reaction with CO2 to proceed entirely along the 8A′′ surface, where the only barrier is well below the reactant asymptote. In contrast, because the promotion energy for Sm+ is significant, the Sm+(OCO) adduct along the 6A′ surface is much higher in energy than the reactant asymptote [24]. Thus, to access the 6A′ surface requires a crossing from the lower energy 8A′′ and 6A′′ surfaces, which occurs above the reactant asymptote and gives rise to the 1.77 ± 0.11 eV barrier observed experimentally [24]. Similar behavior is likely to be exhibited by the other lanthanide cations with 4fn6s1 ground states, for which process (1) is exothermic but no reaction was observed at thermal energies by Bohme and coworkers [9]. Because the 8A′′ and 6A′′ surfaces in the Sm+ reaction are close in energy, they should readily mix, which means that the reaction is probably not limited by spin-conservation [24]. This also appears to be the case for Gd+, as evidenced by the efficient exothermic reaction to ground state products on the octet surface. The pronounced high-energy feature in the Gd+ reaction with CO2 is therefore likely the result of the reaction proceeding along dectet surfaces in diabatic processes that maintain the electronic configurations of the reactants rather than due to spin-conservation. Additionally, direct cleavage of the C–O bond in the CO2 molecule by Gd+ becomes energetically possible at about the same threshold (Fig. S2), which can also proceed along a single diabatic surface.

The BDEs for M+–OCO and OM+–CO should not differ significantly between Gd+ and Sm+ because the interactions of the OCO and CO adducts are primarily electrostatic in these complexes. This is consistent with the measured BDE for ground state Sm+(OCO) of 0.42 ± 0.03 eV [24], which is comparable with that for the electronically excited Gd+(OCO) adduct probed in the CID experiments of 0.38 ± 0.05 eV, where the BDE for the ground state Gd+(OCO) adduct will be somewhat higher. For the inserted OSm+(CO) complex [24], a somewhat larger BDE of 0.97 ± 0.07 eV is measured compared with that for OGd+(CO) of 0.57 ± 0.05 eV. The weaker interaction between CO and GdO+ might result from the much stronger bond that can be formed between the additional O atom and Gd+ than Sm+, where the BDEs for isolated M+–O complexes are 7.69 ± 0.10 eV [36] and 5.725 ± 0.07 eV [75] for Gd+ and Sm+, respectively.

4 Conclusions

The BDEs for OGd+–CO and Gd+–OCO are measured using GIBMS to be 0.57 ± 0.05 and 0.38 ± 0.05 eV, respectively. This thermochemistry is used together with the recently measured BDE of GdO+ to construct an experimental PES for the exothermic reaction between Gd+ (10D) and CO2 (1Σg +). Although the reaction to form ground state GdO+ (8Σ) and CO (1Σ+) products is formally spin-forbidden, the experimental results indicate that this process occurs efficiently without any barriers, as also evident from the measured thermochemistry for the reverse reaction. A more complete picture of the PES is obtained from theory, which also helps elucidate the reaction mechanism in detail. The calculations indicate that low-energy Gd+(OCO) adducts can be formed on 10A′, 10A′′, and 8A′′ surfaces with similar energies such that these states can readily mix. An inserted ground state OGd+(CO) complex that can readily dissociate to ground state GdO+ and CO products is found along the 8A′′ surface. The 8A′′ surface has no barriers exceeding the reactant asymptote and thus the entire reaction from ground state reactants to products can efficiently occur along this surface. A distinct second feature in the measured GdO+ cross section is observed at higher energies and is explained by the formation of electronically excited GdO+ products along single PESs in diabatic processes that maintain the electronic configuration of the reactants. This is further confirmed by the good agreement between the experimentally determined excitation energy of 3.25 ± 0.16 eV from this feature and the values calculated for the 10Π and 10Σ states of GdO+ relative to the 8Σground state.

From theory, the inserted OGd+(CO) complex probed in the CID experiments is identified as the 8A′′ ground state with a calculated O–Gd+–CO angle of ~ 87° and Gd+–O and Gd+–CO bond lengths of 1.8 and 2.7 Å, respectively. Here, the CO adduct primarily binds via electrostatics to GdO+, which forms a triple bond like that in free GdO+. Quantum chemical calculations at the DFT level using various basis sets perform reasonably well in reproducing the experimental BDE for OGd+–CO. In contrast, the electrostatic interaction between GdO+ and CO is significantly overestimated in CCSD(T,full) calculations that use the triple- and quadruple-ζ all-electron basis sets for Gd+. The BDE for OGd+–CO is found to be similar to that previously measured for Gd+–CO of 0.65 ± 0.06 eV [36], where the slightly larger value for the latter complex can potentially be attributed to an additional π interaction between Gd+ and CO that is possible from the available 5d valence electron on Gd+. The Gd+(OCO) adduct probed in the CID experiments is identified from theory to be an electronically excited adduct likely in a 8Π state. This adduct is found along an isolated higher energy 8A′ PES, where formation of an inserted OGd+(CO) complex is not energetically favored over CO2 loss. In contrast, the ground state and other low-energy Gd+(OCO) adducts can readily access the 8A′′ surface to form the ground state inserted OGd+(CO) complex, where CO loss is favored over CO2 loss.

Gd+ with its half-filled 4f shell and 5d16s1 ground state valence electron configuration is different compared with most of the lanthanide cations, which have one 6s valence electron with the rest occupying 4f orbitals. This makes Gd+ more similar to the group 3 metal cations, Sc+ and Y+, and the lanthanides La+, Ce+, and Lu+, which have two valence electrons in d or s orbitals. Comparisons with previous GIBMS results for Y+ and Sm+ reacting with CO2 indicate that Gd+ reacts more similarly to Y+, although there are still some interesting differences that can be attributed to spin-conservation and the different ground state electronic configurations of Gd+ and Y+. The difference with the Sm+ reaction arises primarily as a result of the significant promotion energy cost of the 4f electron to a 5d orbital for Sm+, such that there is a barrier resulting from a crossing between the ground state surface of the Sm+(OCO) adduct in the entrance channel with that of the inserted OSm+(CO) complex in the exit channel. This barrier is not present in the Gd+ reaction because the promotion energy cost from the 6s to 5d orbital is small and both a low-energy Gd+(OCO) adduct and inserted OGd+(CO) complex can be formed along the same PES. Thus, on the basis of this promotion energy argument, similar reactivity is expected for the group 3 metal cations and the lanthanide cations with two s or d electrons as that of Gd+, whereas most other lanthanide cations should exhibit similar behavior to Sm+ and require a crossing between the ground state PESs of the CO2 adduct and inserted complex.

5 Electronic Supplementary Material

Summary of the calculated bond lengths, angles, energies, and vibrational frequencies for various GdCO2 + complexes and potential energy surface scans as a function of the Gd+ and CO2 and GdO+ and CO bond distances obtained at the B3LYP/ANO level of theory.

Notes

Acknowledgements

The authors thank the U.S. Air Force Office of Scientific Research (FA9550-16-1-0095) for financial support, Professor Kirk A. Peterson for providing the all-electron basis sets, and the Center for High Performance Computing at the University of Utah for generous allocation of computer time. Additionally, some of the more computationally demanding calculations were performed on the large shared-memory cluster at the Pittsburgh Supercomputing Center at Carnegie Mellon University via the Extreme Science and Engineering Discovery Environment (XSEDE), under grant number TG-CHE170012. Christopher McNary is thanked for help with using these resources.

Supplementary material

11244_2017_858_MOESM1_ESM.docx (713 kb)
Supplementary material 1 (DOCX 712 KB)

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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of UtahSalt Lake CityUSA

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