The bond energy of ReO+: Guided ion-beam and theoretical studies of the reaction of Re+ (7S) with O2

The kinetic-energy dependence of the Re+ + O2 reaction is examined using guided ion-beam mass spectrometry. The cross section for ReO+ formation from ground state Re+ (7S) is unusual, exhibiting two endothermic features. The kinetic energy dependence for ReO+ formation is analyzed to determine D0(Re+-O) = 4.82 ± 0.05 eV, with the higher energy feature having a threshold 1.35 ± 0.28 eV higher in energy. This bond energy is consistent with much less precise values determined in the literature. Formation of ReO2 + is also observed with a pressure dependent cross section, establishing that it is formed in an exothermic reaction of ReO+ with O2. The nature of the bonding for ReO+ and ReO2 + is discussed and analyzed primarily using theoretical calculations at the B3LYP/def2-TZVPPD level of theory. The ground state of ReO+ is identified as either 5 or 3, with the latter favored once estimates of spin-orbit splitting are included. Bond energies for ground state ReO+ are calculated at this level as well as BP86 and CCSD(T,full) levels using several different basis sets. BP86 theoretical bond energies are higher than the experimental value, whereas B3LYP and CCSD(T,full) values are lower, although estimated spin-orbit corrections increase the latter close to experiment. Potential energy surfaces for the reaction of Re+ with O2 are also calculated at the B3LYP/def2-TZVPPD level of theory and reveal that ground state Re+ (7S) inserts into O2 by forming a Re+(O2) (5A) complex which can then couple with additional surfaces to form ground state ReO2 + (3B1). Several explanations for the unusual dual endothermic features are explored, with no unambiguous explanation being evident. As such, this heavy metal system provides a very interesting experimental phenomenon of both adiabatic and nonadiabatic behavior.

The bond energy of ReO+: Guided ion-beam and theoretical studies of the reaction of Re+ (7S) with O2 P. B. Armentrout Citation: The Journal of Chemical Physics 139, 084305 (2013); doi: 10.1063/1.4818642 View online: http://dx.doi.org/10.1063/1.4818642 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/139/8?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Guided ion beam and theoretical study of the reactions of Os+ with H2, D2, and HD J. Chem. Phys. 135, 234302 (2011); 10.1063/1.3669425 Guided ion beam and theoretical study of the reactions of Hf + with H 2 , D 2 , and HD J. Chem. Phys. 133, 124307 (2010); 10.1063/1.3482663 Guided ion beam and theoretical studies of the reaction of Ag + with CS 2 : Gas-phase thermochemistry of AgS + and AgCS + and insight into spin-forbidden reactions J. Chem. Phys. 132, 024306 (2010); 10.1063/1.3285837 Activation of methane by gold cations: Guided ion beam and theoretical studies J. Chem. 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The cross section for ReO+ formation from ground state Re+ (7S) is unusual, exhibit-ing two endothermic features. The kinetic energy dependence for ReO+ formation is analyzed to determine D0(Re+-O) = 4.82 ± 0.05 eV, with the higher energy feature having a threshold 1.35 ± 0.28 eV higher in energy. This bond energy is consistent with much less precise values determined in the literature. Formation of ReO2 + is also observed with a pressure dependent cross section, es-tablishing that it is formed in an exothermic reaction of ReO+ with O2. The nature of the bond-ing for ReO+ and ReO2 + is discussed and analyzed primarily using theoretical calculations at the B3LYP/def2-TZVPPD level of theory. The ground state of ReO+ is identified as either 5 or 3, with the latter favored once estimates of spin-orbit splitting are included. Bond energies for ground state ReO+ are calculated at this level as well as BP86 and CCSD(T,full) levels using several different basis sets. BP86 theoretical bond energies are higher than the experimental value, whereas B3LYP and CCSD(T,full) values are lower, although estimated spin-orbit corrections increase the latter close to experiment. Potential energy surfaces for the reaction of Re+ with O2 are also calculated at the B3LYP/def2-TZVPPD level of theory and reveal that ground state Re+ (7S) inserts into O2 by form-ing a Re+(O2) (5A) complex which can then couple with additional surfaces to form ground state ReO2 + (3B1). Several explanations for the unusual dual endothermic features are explored, with no unambiguous explanation being evident. As such, this heavy metal system provides a very interest-ing experimental phenomenon of both adiabatic and nonadiabatic behavior. © 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4818642] I. INTRODUCTION Periodic trends in reactivity and thermochemistry are readily studied in the gas phase where the obligations of closed shell structures and solvation are removed. Thus, the gas phase is an ideal venue for determining the energetics of bond-making and bond-breaking processes at a molecu-lar level. One particularly important set of molecules for such studies are transition metal oxides, which can act as models of important oxidation catalysts. The characteristics of such transition metal oxides have been reviewed by Schröder and Schwarz,1, 2 who also summarize what is known about the thermodynamics of these species, information that is critical to understanding, evaluating, and predicting their reactivity. Although the thermochemistry for most transition metal ox-ides is well established, this is not true for many of the third row transition metal oxides and their cations. In the present work, we seek to remedy this situation for the particular case of ReO+. There are few studies of the gas phase oxides of rhenium. For neutral ReO, the 1969 compilation of Brewer and Rosen-blatt notes that ReO "has never been observed"3 and Ped-ley and Marshall4 discount the lone experimental measure-ment at that time from Farber et al. (which suggested D(ReO) = 8.2 eV),5 choosing an estimated bond energy of 6.45 ± 0.87 eV instead. Battles, Gundersen, and Edwards used high temperature mass spectrometry (HTMS) to investi-gate the vapor above combinations of Re(s) + ReO2(s) and ReO2(s) + ReO3(s).6 They found the main gas-phase com-ponent to be Re2O7 with small amounts of ReO3. From Re2O7(g), an appearance energy for ReO2 + of ∼20 eV was determined. Similarly, Skinner and Searcy used HTMS to study vapors over Re2O7(s) + ReO3(s), Re2O7(s) + ZnO(s), and Re2O7(s) + MgO(s), thereby determining the heat of for-mation of ReO3(g) and lower limits to those for Re2O6(g), ReO2(g), and ReO(g).7 Appearance energies for ReO3 +, ReO2 +, and ReO+ from ReO3(g) were measured as 12.5 ± 0.4, 14.4 ± 1.0, and ∼18 eV, respectively. Bondybey and co-workers used ion cyclotron resonance mass spectrome-try (ICR-MS) to examine several gas-phase rhenium oxide cations, ReOn + where n = 2-6 and 8.8 In a subsequent study by this group, they performed collision-induced dissociation (CID) studies on all these species, reporting bond energies in most cases, along with density functional calculations of these species in their ground electronic states.9 At present, this study provides the most accurate thermochemistry for ReO2 + and ReO+, with bond energies for O atom loss of 7.4 ± 2.25 and 5.0 ± 1.35 eV, respectively. Finally, in in-ductively coupled plasma/selected ion flow tube (ICP/SIFT) experiments by Bohme and co-workers, Re+ was found to re-act slowly with O2 to form ReO2 + by three-body association, with subsequent additions of oxygen yielding ReOn + where n = 3-6.10 The failure to observe reaction (1) at thermal 0021-9606/2013/139(8)/084305/13/$30.00 139, 084305-1 © 2013 AIP Publishing LLC This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.97.11.184 On: Wed, 16 Jul 2014 13:14:00 084305-2 P. B. Armentrout J. Chem. Phys. 139, 084305 (2013) energies suggests that D(Re+-O) < D(O2) = 5.1 eV, Re+ + O2 → ReO+ + O, (1) as also concluded by Beyer et al.9 Bohme and co-workers also found that Re+ reacts with NO to form ReOn + where n = 1 - 4, which they attributed to sequential termolecular reactions forming N2O as the neutral product,11 although this interpre-tation has been questioned for other metals.12 Clearly, the thermochemistry of the rhenium oxide cations is not known very well. The present study is designed to provide more quantitative information about ReO+ by ex-amining the kinetic energy dependence of reaction (1) using guided ion beam tandem mass spectrometry (GIBMS). This work reveals the energetics, kinetics, and dynamics of the in-teraction of the rhenium metal cation with O2. In previous studies in our laboratory, GIBMS has been used to systemati-cally study the kinetic energy dependent reactions of O2 with atomic cations of the first-row,13-21 second-row,15, 16, 22-27 and third-row transitionmetals16, 28-33 and main group metals.34-36 In many cases, analyses of the cross sections for the analogues of reaction (1) have enabled determination of the BDEs of the metal oxide cation, MO+. The present work extends these studies to include the metal ion Re+, and as such, is part of an ongoing effort in our laboratory to understand the periodic trends in the BDEs of metal oxides. As will be seen below, the kinetic energy dependent cross section for reaction (1) is unusual, exhibiting two endothermic features, which parallels similar behavior recently observed for the neighboring ele-ment, Os+ reacting with O2.33 The reasons behind this behav-ior are explored in terms of spin-conservation and adiabatic versus nonadiabatic behavior. II. EXPERIMENTAL AND THEORETICAL A. General experimental The guided ion beam tandem mass spectrometer on which these experiments were performed has been described in detail previously.37, 38 Briefly, atomic rhenium ions are gen-erated in a direct current discharge flow tube (DC/FT) source described below, extracted from the source, accelerated, and focused into a magnetic sector momentum analyzer for mass selection of primary ions. The mass-selected ions are deceler-ated to a desired kinetic energy and focused into an octopole ion beam guide that uses radio-frequency (rf) electric fields to trap the ions in the radial direction and ensure complete col-lection of reactant and product ions.39, 40 The octopole passes through a static gas cell with an effective length of 8.26 cm that contains the reaction partner (here, O2) at a low pressure (less than ∼0.3 mTorr) so that multiple ion-molecule colli-sions are improbable. The unreacted parent and product ions are confined radially in the guide until they drift to the end of the octopole where they are extracted, focused, and passed through a quadrupole mass filter for mass analysis of prod-ucts. Ions are subsequently detected with a secondary electron scintillation ion detector41 using standard pulse counting tech-niques. Reaction cross sections are calculated from product ion intensities relative to reactant ion intensities after correct-ing for background signals.42 Uncertainties in absolute cross sections are estimated to be ±20%. The kinetic energy of the ions is varied in the labo-ratory frame by scanning the dc bias on the octopole rods with respect to the potential of the ion source region. Lab-oratory (Lab) ion energies are converted to energies in the center-of-mass frame (CM) by using the formula ECM = Elab × m/(m + M), where m and M are the neutral and ionic reac-tant masses, respectively. Two effects broaden the cross sec-tion data: the kinetic energy distribution of the reactant ion and the thermal motion of the neutral reactant gas (Doppler broadening).43 The absolute zero and the full width at half maximum (FWHM) of the kinetic energy distribution of the reactant ions are determined using the octopole beam guide as a retarding potential analyzer, as described previously.42 The distributions of ion energies, which are independent of energy, are nearly Gaussian and have a typical FWHM of 0.4-0.5 eV (Lab) in these studies. Uncertainties in the absolute zero of the energy scale are ±0.1 eV (Lab) and ±0.014 eV (CM). B. Ion source Re+ ions are produced in a dc-discharge/flow tube (DC/FT) ion source,38 consisting of a cathode held at a high negative voltage (0.7-1.5 kV) over which a flow of approx-imately 90% He and 10% Ar passes at a total pressure of 0.3-0.5 Torr and ambient temperature. The dc-discharge ion-izes Ar and then accelerates these ions into the cathode, which is a rhenium cylinder attached to an iron holder. As the ions are swept down the meter-long flow tube, they undergo ∼105 thermalizing collisions with He and Ar. As demonstrated earlier,44, 45 trace amounts (<0.1%) of low-lying excited states are observed to survive these flow conditions, but these are easily removed by introducing CH4 to the flow tube about 15 cm downstream of the discharge zone at a pressure of ∼100 mTorr.With the addition of this cooling gas, the DC/FT source produces Re+ ions in the ground state, as demonstrated in previous studies of Re+ with H2, HD, and D2 and with CH4 and CD4.44, 45 When compared to a surface ionization source, the DC/FT source has been found to generate Sc+,46 Fe+,47 Co+,48 Ni+,49 Ru+,50 Rh+,50 and Pd+50 ions with an average electronic temperature of 700 ± 400 K, and Y+, Zr+, Nb+, and Mo+ ions with an average electronic temperature of 300 ± 100 K.51 In the case of Re+, even an elevated electronic temperature products a pure beam of 7S3 (6s15d5) ground state because excited states are too high in energy to be pop-ulated. The 5D first excited state has an energy of 1.827 eV (average over all spin-orbit levels) with the 5S (6s15d5) sec-ond excited state at 2.135 eV.52 C. Data analysis Cross sections of endothermic reactions are modeled us-ing Eq. (2),53-56 σ (E) = σ0gi (E + Ei − E0)n /E, (2) where σ0 is an energy-independent scaling factor, E is the relative kinetic energy of the reactants, n is an adjustable This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.97.11.184 On: Wed, 16 Jul 2014 13:14:00 084305-3 P. B. Armentrout J. Chem. Phys. 139, 084305 (2013) parameter that characterizes the energy dependence of the process,53 and E0 is the 0 K threshold for reaction of elec-tronic, vibrational, and rotational ground state reactants. The model involves an explicit sum of the contributions of individ-ual ro-vibrational states of the room temperature O2 reactant (ν = 1580 cm−1, B = 1.4456 cm−1),57 denoted by i, having energies Ei and populations gi. As noted above, contributions from excited electronic states of Re+ are zero. Before compar-ison with the experimental data, Eq. (2) is convoluted with the kinetic energy distributions of the reactant ions and neutrals at 300 K.42 The σ0, n, and E0 parameters are then optimized using a nonlinear least-squares analysis to give the best repro-duction of the data. Error limits for E0 are calculated from the range of threshold values for different data sets over a range of acceptable n values combined with the absolute uncertainty in the kinetic energy scale. D. Theoretical calculations Most quantum chemistry calculations reported here were computed using the B3LYP hybrid density functional method and performed with the GAUSSIAN 09 suite of programs.58 The B3LYP method is based on the hybrid gradient-corrected exchange functional proposed by Becke59 combined with the gradient-corrected correlation functional of Lee, Yang, and Parr.60 We also used the BP86 density functional,61 along with coupled cluster with single, double, and perturbative triple excitations (CCSD(T,full)).62-65 The BP86 functional is cho-sen specifically because it was found to perform well for a variety of transition metal complexes66 and has been found to yield reasonable upper limits on the thermochemistry of organometallic species in previous work, where B3LYP gives reasonable lower limits.67 The def2-TZVPPD basis set was used for oxygen in most calculations and gives good results for the thermochemistry of O2 with an O-O bond energy cal-culated using B3LYP as 5.25 eV, compared to the experimen-tal value of 5.115 eV, Table I.68 BP86 yields a high value (near 6.1 eV) and even the CCSD(T,full) approach is off somewhat with a bond energy of 4.88 eV. Increasing the size of the ba-sis set to def2-QZVPPD or use of aug-cc-pVxZ basis sets (x = T, Q, 5) leads to excellent agreement for CCSD(T,full) with bond energies of 5.03-5.11 eV, whereas these basis sets affect the results for the two DFT approaches very little, Table I. For rhenium, several basis sets were used, all using rel-ativistic effective core potentials (ECPs) that are small core (60 electrons) such that the 5s, 5p, 5d, and 6s orbitals are ex-plicitly considered. The def2-TZVPPD and def2-QZVPPD69 use ECPs developed by Andrea et al.70 We also utilized the energy-consistent pseudopotentials and correlation consistent basis sets developed by Figgen et al. (aug-cc-pVxZ-PP where x = T, Q, and 5)71 along with comparable basis sets on oxy-gen. For both types of basis sets, the triple and quadruple zeta include f and g type polarization functions on Re, and the quintuple zeta adds h and i functions as well. (The def2 and aug-cc-pVxZ-PP basis sets were obtained from the basis set exchange of the Environmental and Molecular Sciences Lab-oratory, EMSL.72, 73) In all cases, the thermochemistry calcu-lated and cited here for ReO+ and ReO2 + is corrected for zero TABLE I. Bond energy of O2 (3 −) and 7S→5D excitation energy for the atomic rhenium ion (eV) calculated at several levels of theory. State Basis set B3LYP BP86 CCSD(T,full) Expt. D0(O2, 3g −) def2-TZVPPD 5.25 6.06 4.88 5.115 def2-QZVPPD 5.27 6.07 5.04 aug-cc-pVTZ 5.24 6.05 5.03 aug-cc-pVQZ 5.28 6.08 5.07 aug-cc-pV5Z 5.28 6.08 5.11 CBSa 5.15 7S→5D(5d6) def2-TZVPP 2.125 2.319 2.476 1.827b def2-QZVPP 2.128 2.320 2.454 aug-cc-pVTZ 2.145 2.335 2.468 aug-cc-pVQZ 2.145 2.335 2.468 aug-cc-pV5Z 2.158 2.344 2.408 CBSa 2.299 7S→5D(6s25d4) def2-TZVPP 2.595 2.793 2.764 1.827b def2-QZVPP 2.582 2.779 2.746 aug-cc-pVTZ 2.576 2.781 2.740 aug-cc-pVQZ 2.576 2.781 2.740 aug-cc-pV5Z 2.571 2.777 2.755 CBSa 2.784 aComplete basis set limit. bStatistically weighted mean of spin-orbit levels. point energy effects, after scaling the frequencies by 0.989.74 For those systems where the aug-cc-pVxZ basis sets were used, we also performed a complete basis set extrapolation us-ing two-point (Q,5) protocols for both the Hartree-Fock total energy and the CCSD(T) correlation energy, as recommended by Halkier et al.75, 76 One means of testing the validity of the theoretical re-sults is to compare calculated excitation energies of the various states of Re+ to experimentally measured values, Table I. Experimentally, the 5D first excited state has an en-ergy of 1.827 eV (average over all spin-orbit levels) above the 7S(6s15d5) ground state with the 5S(6s15d5) second ex-cited state at 2.135 eV.52 (Although Moore identifies the 5D state as having a 6s25d4 configuration, more recent evalu-ations indicate mixed character of these five J levels (0-4) including 6s25d4, 6s15d5, and 5d6.77) The present calcula-tions properly identified the ground state as the 7S in all cases and find that the 5D(5d6) state lies ∼2.14 (B3LYP), ∼2.33 (BP86), and ∼2.44 (CCSD(T,full)) eV above the 7S ground state, whereas excitation to the 5D(6s25d4) state re-quires ∼2.58, ∼2.78, and ∼2.75 eV, respectively (where it was ensured that these states had no spin-contamination), Table I. Lower lying quintet states could also be calculated but these were invariably spin contaminated, s(s + 1) = 6.98 instead of 6. The present results are comparable to previous theoretical results, e.g., Ohanessian et al. calculate that the 5D(5d6) and 5D(6s25d4) states lie 2.64 and 2.94 eV above the 7S ground state;78 Dai and Balasubramanian calculated an ex-cited 5G(6s15d5) state lying at 2.687 eV;79 and Holthausen et al.80 find a ground state of 5D(5d6) using the B3LYP and BHLYP functionals, with the 7S state lying 0.26 and 0.10 eV higher in energy, whereas their QCISD and QCISD(T) cal-culations provided the correct ordering with quintet excita-tion energies of 1.11 and 1.09 eV, respectively. Excitation This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.97.11.184 On: Wed, 16 Jul 2014 13:14:00 084305-4 P. B. Armentrout J. Chem. Phys. 139, 084305 (2013) energies for triplet and singlet states of Re+ have not been experimentally identified largely because of the extensive spin-orbit coupling for this heavy metal. III. RESULTS A. Reaction of Re+ with O2 Figure 1 shows cross sections for the reaction of Re+ with O2 at a pressure of 0.29 mTorr yielding ReO+ and ReO2 + as a function of kinetic energy. The ReO+ cross section exhibits two features. The first feature has an apparent threshold near 0 eV, reaches a maximum near 1 eV and then plateaus. The second feature has an apparent threshold near 1.5 eV, reaches a maximum near 5 eV, and then starts to decline because the ReO+ product ion can dissociate further in reaction (3), Re+ + O2 → ReO+ + O → Re+ + O + O, (3) which has a thermodynamic threshold of 5.115 eV = D0(O2). Notably the endothermicity of reaction (1) observed here agrees with the conclusions of Beyer et al.9 and the failure to observe reaction (1) at room temperature by Bohme and co-workers.10 Our cross sections for reaction (1) at near ther-mal energy (0.05 eV) can be converted to a rate coefficient at 300 K of (5 ± 2) × 10−13 cm3 molecule−1 s−1, three orders of magnitude smaller than the collision limit and small enough to agree with the failure to observe this process in the previous study. Figure 1 also shows the cross section for the formation of ReO2 +. The magnitude of this cross section was found to depend linearly on O2 pressure, such that it disappears when extrapolated to zero pressure. Thus, this product is formed in the sequential reaction (4), ReO+ + O2 → ReO2 + + O, (4) or by a termolecular association process.We exclude the latter process because Koyanagi et al. find the termolecular process FIG. 1. Cross sections for the reaction of Re+ (7S) with O2 at a pressure of 0.29 mTorr as a function of kinetic energy in the center-of-mass frame (lower axis) and laboratory frame (upper axis). Formation of ReO+ (circles), ReO2 + (triangles), and their total (line) are indicated. The arrow shows the O2 bond energy at 5.115 eV. FIG. 2. Estimated cross section for reaction (4) determined as described in the text as a function of kinetic energy in the center-of-mass (lower axis) and laboratory (upper axis) frames. The arrow indicates the O2 bond energy at 5.115 eV. The line shows the Langevin-Gioumousis-Stevenson collision cross section, Eq. (5). in He at 0.35 Torr has an apparent bimolecular rate constant of only 1.1 × 10−12 cm3 s−1,10 such that the termolecular process with an O2 pressure that is three orders of magnitude smaller would not be observed. More insight into ReO2 + pro-duction can therefore be obtained by interpreting the raw data as if the ReO+ species is the reactant and the intensities are again converted to an absolute cross section. Figure 2 shows the data taken at P(O2) = 0.29 mTorr interpreted in this fash-ion. Data taken at P(O2) = 0.19, 0.15, and 0.10 mTorr are quantitatively similar in magnitude and energy dependence. It should be realized that this interpretation is not precisely correct in that the kinetic energy of the ReO+ product is no longer accurately reflected by the energy axis shown (that of the Re+ + O2 reactants). Nevertheless, the ReO2 + cross section obtained falls off uniformly with energy below 2 eV, with an energy dependence and magnitude below 0.3 eV that matches that expected for ion-neutral collisions according to the Langevin-Gioumousis-Stevenson (LGS) model,81 Eq. (5), σLGS=πe(α/2πε0E)1/2, (5) where e is the charge on the electron, α is the polarizability volume of the neutral reactant molecule (1.57 Å3 for O2),82 and ε0 is the permittivity of vacuum. Thus, reaction (4) ap-pears to occur at the collision limit with no barrier. The cross section for reaction (4) shown in Figure 2 also exhibits a high energy feature starting about 2 eV. Although it is possible that this corresponds to formation of an ex-cited state of ReO2 +, it is also plausible that this simply fol-lows from the second feature in the primary ReO+ product cross section. This latter possibility recognizes the fact that the ReO+ products formed at threshold in this second feature have little kinetic energy and hence should react efficiently in an exothermic process. This is again a reflection that the energy scale shown may not be accurate. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.97.11.184 On: Wed, 16 Jul 2014 13:14:00 084305-5 P. B. Armentrout J. Chem. Phys. 139, 084305 (2013) B. Analysis of the ReO+ product cross section The first endothermic feature in the ReO+ product cross section presumably corresponds to the formation of ground state ReO+ in reaction (1). This process has an apparent threshold near 0 eV and then plateaus starting around 1 eV before the rise of the second endothermic feature near 1.5 eV. Because the only neutral product that can accompany ReO+ is atomic O, the second feature is plausibly assigned to the formation of electronically excited products. The energy dif-ference between the two features is smaller than the lowest excitation of the O neutral product, which requires 1.97 eV to form the 1D state.68 Therefore, we tentatively assign the second cross section feature to the formation of electronically excited ReO+, an assumption explored further below. In the low energy region, the total cross section of mul-tiple data sets for the endothermic reaction (1) were analyzed in detail using Eq. (2) as described above, with optimum val-ues of the fitting parameters listed in Table II. A representa-tive model is shown in Figure 3. Because the rotational, vi-brational, translational, and electronic energy distributions of the reactants are explicitly included in the modeling, the E0 thresholds determined using Eq. (2) correspond to 0 K. From the thresholds measured, the ReO+ BDE at 0 K can be calcu-lated using Eq. (6), D0(Re+−O) = D0(O−O) − E0. (6) This equation assumes that there are no activation barriers in excess of the endothermicity of reaction (1), an assump-tion that is often true for ion-molecule reactions because of the long-range attractive forces.42, 55 This assumption is also confirmed by the theoretical calculations of the potential en-ergy surfaces for this reaction (see below). Thus, from the threshold of 0.29 ± 0.05 eV, Eq. (6) indicates that D0(ReO+) = 4.82 ± 0.05 eV. Our bond energy is in good agreement with the much less precise value of 5.0 ± 1.35 eV determined using CID by Beyer et al.9 When combined with the estimated value for D(ReO) of 6.45 ± 0.87 eV4 and the ionization energy of Re, IE(Re) = 7.83352 eV,83 the estimated value for IE(ReO) is 9.46 ± 0.87 eV. This value is comparable to the IEs of other nearby third-row transition metal oxides, 9.1-10.1 eV.1 If the models of the low energy feature are extended to higher energies and subtracted from the data, the remain-ing high energy feature can then be analyzed independently. The high energy feature can be accurately reproduced using Eq. (2) with E0 = 1.64 ± 0.28 eV, Table II. The difference in the threshold energies is 1.35 ± 0.28 eV. Modeling of the data above 5 eV includes consideration of the decline in the cross section associated with reaction (3). A statistical model for this process includes two parameters: the energy onset for reaction (3), ED, and a parameter p that controls the shape TABLE II. Parameters of Eq. (2) used to model reaction (1).a σ0 n E0 (eV) 5.5 ± 0.6 0.8 ± 0.2 0.29 ± 0.05 2.4 ± 0.9 1.5 ± 0.3 1.64 ± 0.28 aUncertainties are two standard deviations. FIG. 3. Zero-pressure extrapolated cross sections for reaction (1) as a func-tion of kinetic energy in the center-of-mass frame (lower axis) and laboratory frame (upper axis) on both linear (part a) and log (part b) scales. The best fits to the data using Eq. (2) with parameters of Table II are shown as dashed lines. The solid lines show the sum of these models convoluted over the ki-netic and internal energy distributions of the reactant neutral and ion. The arrows show the O2 bond energy at 5.115 eV. of the cross section in this region.34 Here, the data are accu-rately reproduced when ED is held to D0(O2) = 5.115 eV, and p = 1. Figure 3 shows that the low-energy feature, the high-energy feature, and the decline in the cross section at high energies are reproduced nicely by these models. Similar re-productions are found for all data sets. C. Theoretical results for ReO+ B3LYP/def2-TZVPPD calculations performed here in-dicate that the ground state of ReO+ is 5 with a bond length of 1.679 Å and a valence electron configuration of 1σ21π41δ22σ12π1. In this designation of the molecular or-bitals (mos), the Re (5s, 5p), and O (1s, 2s) core electrons are This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.97.11.184 On: Wed, 16 Jul 2014 13:14:00 084305-6 P. B. Armentrout J. Chem. Phys. 139, 084305 (2013) TABLE III. Bond lengths, energies, and vibrational frequencies calculated at various levels of theory for ReO+ (5), ReO+ (3), and ReO+ (1 +). State Level Basis set r(Re-O) (Å) E (Eh) ωe (cm−1) D0/Erel (eV)a D0/Erel (eV)a incl. spin-orbit 5 B3LYP def2-TZVPPD 1.679 −153.174976 1015 4.42 0.125 def2-QZVPPD 1.678 −153.180051 1014 4.43 0.129 aug-cc-pV5Z 1.671 −153.482727 1022 4.52 0.141 BP86 def2-TZVPPD 1.687 −153.279784 1003 5.23 0.100 def2-QZVPPD 1.686 −153.285250 1001 5.25 0.101 aug-cc-pV5Z 1.679 −153.583863 1008 5.32 0.112 CCSD(T) def2-TZVPPD 1.687 −152.773144 3.97 0.003 def2-QZVPPD 1.682 −152.857127 4.10 0.035 aug-cc-pV5Z 1.671 −153.252703 4.27 0.111 CBSb −153.339197 4.27 0.164 3 B3LYP def2-TZVPPD 1.613 −153.174098 1157 0.033 4.70 def2-QZVPPD 1.612 −153.179297 1155 0.029 4.72 aug-cc-pV5Z 1.605 −153.482428 1164 0.017 4.82 BP86 def2-TZVPPD 1.622 −153.277949 1126 0.058 5.49 def2-QZVPPD 1.622 −153.283439 1124 0.057 5.51 aug-cc-pV5Z 1.615 −153.582445 1132 0.046 5.59 CCSD(T) def2-TZVPPD 1.611 −152.767753 0.155 4.13 def2-QZVPPD 1.607 −152.852940 0.123 4.29 aug-cc-pV5Z 1.600 −153.251314 0.047 4.54 CBSb −153.339753 −0.006 4.59 1 + B3LYP def2-TZVPPD 1.607 −153.133104 1175 1.149 1.432 def2-QZVPPD 1.606 −153.138432 1173 1.142 1.429 aug-cc-pV5Z 1.600 −153.440360 1179 1.163 1.462 BP86 def2-TZVPPD 1.617 −153.231763 1139 1.315 1.573 def2-QZVPPD 1.616 −153.237356 1137 1.312 1.571 aug-cc-pV5Z 1.609 −153.535252 1143 1.331 1.601 CCSD(T) def2-TZVPPD 1.625 −152.740066 0.910 1.071 def2-QZVPPD 1.620 −152.825302 0.876 1.069 aug-cc-pV5Z 1.610 −153.223430 0.806 1.075 CBSb −153.312854 0.727 1.049 aBond energy to Re+(7S)+O(3P) (roman) or relative energy compared to ground state (italics). Values include corrections for zero point energies (ZPE). CCSD(T,full) values use B3LYP frequencies. bComplete basis set limit. not included, the 1σ and 1π are the Re-O bonding mos, with 2π and 3σ being the antibonding counterparts. The 1δ is pure Re(5d) nonbonding and the 2σ is mostly Re(6s) nonbonding. Given these identifications, the 5 state has six electrons in bonding mos and one in an antibonding mo for a bond order of 2.5. In addition to the 5 state, there is also a low-lying 3 state that involves moving an electron from the 2π antibond-ing orbital to the 1δ nonbonding orbital (1σ21π41δ32σ1), such that it has a bond order of 3 and a shorter bond, 1.613 Å. This triplet state was identified as the ground state in the-oretical work by Beyer et al., although it is not apparent whether other spin states were explored.9 They obtained a bond length of 1.62 Å at the B3LYP/LanL2DZ/D95(d) level of theory. Yao et al.84 examined the 5d metal oxides and their singly charged states using nine different density function-als, the Stuttgart/Dresden effective core potential and basis sets (SDD) on the metals,70 and the 6-311+G(d) basis set on oxygen. They assigned the ground state of ReO+ as 3 − (1σ21π41δ22σ2) with unidentified singlet states lying 0.22 (0.68) eV and unidentified quintet states lying 1.08 (0.37) eV higher in energy at the B3LYP (BLYP) levels. Recently, Brites et al.85 performed very high level calculations, multireference configuration interaction (MRCI) using the aug-cc-pV5Z-PP basis set and fully relativistic pseudo potential on Re from Figgen et al.71 They identified the 3 as the ground state with 3 − and 1 + states lying 0.52 and 0.94 eV higher in energy, but do not appear to have considered a 5 state. In our work, the excitation energy of the 3 state is only 0.03 eV at the B3LYP/def2-TZVPP level, such that there is obviously some question as to the true identity of the ground state. To test this, we calculated the 5-3 excitation energy at several different levels of theory using several different basis sets (in-cluding def2-QZVPPD, the aug-cc-pVxZ-PP basis sets where x = T, Q, and 5, and their complete basis set (CBS) extrap-olation) with the results compiled in Table III (results for x = T and Q are not listed as these are very similar to those for x = 5). For B3LYP, BP86, and CCSD(T,full) approaches, the 5 remained the ground state for all basis set sizes with ex-citation energies to the 3 of 0.01-0.16 eV, although at the CBS limit the 3 lies 0.006 eV below the 5. Complicating the ground state assignment is the spin-orbit splitting of these two states. To explore this issue further, we assume that Eso = A MS with A being the spin-orbit splitting constant, is the orbital angular momentum quan-tum number, and MS is the spin quantum number associated This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.97.11.184 On: Wed, 16 Jul 2014 13:14:00 084305-7 P. B. Armentrout J. Chem. Phys. 139, 084305 (2013) with a particular = + MS level.86 Eso can also be as-signed as equal to ai i•si where i•si is the dot product of the orbital angular momentum and the spin of electron i and ai is the spin-orbit parameter for electron i, which we take as ap-proximately equal to ζ 5d(Re), the atomic spin-orbit constant for the 5d electrons of atomic Re.86 For the 5(δ2σ1π1) state, these expressions lead to Eso ( = 3) = 2 A(5) = ζ 5d(Re)/2, such that A(5) is approximately ζ 5d(Re)/4 ∼ 2545 cm−1/4 = 636 cm−1. Ignoring any interactions with other states, this places the 5−1 level at 2 × A = 1272.5 cm−1 (0.158 eV) below the unperturbed 5 state. For the 3 state, the spin-orbit splitting constant, A(3) should equal ζ 5d(Re)/2 = 1272.5 cm−1 such that the 33 level should lie 2 × A(3) = 2545 cm−1 (0.316 eV) below the unperturbed state, the 32 level should lie at the unperturbed state energy, and 31 should be 2545 cm−1 above the unperturbed state (5090 cm−1 above 33). This approach is nicely validated by spectroscopy on the isoelectronic ReN molecule, where the splitting be-tween the three 3 levels has been measured as 1810 ± 140 and 3080 ± 140 cm-1, for a splitting of 4990 ± 140 cm−1 between the 33 and 31 levels.87 (Here the energy of the 32 is pushed down by interaction with the 12 state arising from the same configuration.) In addition, spin-orbit calcula-tions for ReO+(3) performed at the CASSCF/cc-pV5Z-PP level by Brites et al.85 find A(3) = 1323.4 cm−1, in good agreement with the 1272.5 cm−1 estimate here. Thus, includ-ing these estimated spin-orbit corrections, the 5−1 → 33 excitation energy should be lowered by 0.158 eV. These es-timated spin-orbit corrections mean that the 3 becomes the likely ground state for all calculations and basis sets used, Table III, with the excitation to the 5−1 state ranging from 0.003 to 0.164 eV. The 0 K bond energy of the 5 state calculated at the B3LYP/def2-TZVPPD level of theory is 4.42 eV, somewhat below the 4.82 ± 0.05 eV experimental value determined above. Use of different basis sets and theoretical approaches (BP86 and CCSD(T,full)) were also explored, with results compiled in Table III. The aug-cc-pVxZ basis sets increase the BDE by about 0.1 eV. The BP86 approach yields BDEs greater than the B3LYP results by ∼0.8 eV, whereas the CCSD(T,full) calculations have lower BDEs by 0.25-0.45 eV, with smaller differences for larger basis sets. One possible ex-planation for discrepancies between experiment and theory is spin-orbit interactions, which are not explicitly included in the present calculations but were estimated above. Experimental and theoretical bond energies are calculated with respect to the Re+ (7S) state, which has no spin-orbit splitting. As dis-cussed above, the 3 and 5states of ReO+ should have first-order spin-orbit splitting that decrease the energies of the = 3 and −1 levels of these states, such that corrected the-oretical BDEs for these states should be increased by 0.32 and 0.16 eV, respectively, as indicated in Table III. Now the BDEs for the 33 ground state level increase to 4.7-4.8 eV at the B3LYP level, remain 0.8 eV higher for BP86 calcula-tions, and range from 4.1 to 4.6 eV at the CCSD(T,full) level. With this correction, all levels of theory now suggest that the bond energy measured experimentally is that of the 3 state, with BDEs calculated at the B3LYP level being in ex-cellent agreement with experiment, whereas the CCSD(T,full) values are somewhat low and the BP86 values are high, Table III. Additional singlet, triplet, quintet, and septet excited states of ReO+ were also located at the B3LYP and CCSD(T,full) levels using the def2-TZVPPD basis set with results listed in Table IV. B3LYP and CCSD(T,full) results are generally similar both in bond lengths and excitation en-ergies. Other states of ReO+ located have excitation energies of 0.43-3.51 eV above the 5. These excitation energies are in reasonable agreement with the few states previously cal-culated by Yao et al.84 and Brites et al.85 It can be seen that states identified as having bond orders of 3 have bond lengths of ∼1.61 Å. For states having bond orders of 2.5, the bond lengths increase to ∼1.67 Å, whereas the states with bond orders of 2 increase to ∼1.73 Å. Two states with bond or-ders of 1.5 have longer bonds, 1.87 and 1.93 Å. Examina-tion of the vibrational frequencies find that they also track TABLE IV. Electronic configurations, bond orders, bond lengths, energies, and vibrational frequencies calculated at the B3LYP(CCSD(T,full))/def2-TZVPPD level for ReO+.a State Configuration Bond order r(Re-O) (Å) E (Eh) ωe (cm−1)b Erel (eV)c 5 1σ21π41δ22σ12π1 2.5 1.679/1.687 −153.174976 1004 0.00/0.00 3 1σ21π41δ32σ1 3 1.613/1.611 −153.174098 1144 0.03/0.16 3 − 1σ21π41δ22σ2 3 1.622/1.619 −153.159477 1116 0.43/0.49 3/ 1σ21π41δ32π1 2.5 1.671/1.686 −153.148081 1044 0.73/0.73 1 + 1σ21π41δ4 3 1.607/1.625 −153.133104 1162 1.15/0.91 1 1σ21π41δ22σ2 3 1.618/1.631 −153.123106 1138 1.42/1.24 1/ 1σ21π41δ32π1 2.5 1.666/1.666 −153.119138 1045 1.52/1.72 5 + 1σ21π41δ22π2 2 1.728/1.725 −153.115318 939 1.62/1.86 3H 1σ21π41δ22σ12π1 2.5 1.670/d −153.110840 1048 1.75/d 7 1σ21π31δ22σ12π2 1.5 1.934/1.935 −153.093766 681 2.19/2.19 5 1σ21π41δ12σ12π2 2 1.740/1.739 −153.086048 918 2.41/2.65 7 + 1σ11π41δ22σ12π2 1.5 1.869/1.864 −153.046109 725 3.49/3.51 aB3LYP and CCSD(T,full). bVibrational frequency scaled by 0.989. cRelative energies including corrections for zero point energies (ZPE) scaled by 0.989. CCSD(T,full) values use B3LYP frequencies. dCollapses to the 3/ state at the CCSD(T,full) level. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.97.11.184 On: Wed, 16 Jul 2014 13:14:00 084305-8 P. B. Armentrout J. Chem. Phys. 139, 084305 (2013) reasonably well with the bond order, ∼1140 cm−1 for 3, ∼1030 cm−1 for 2.5, ∼930 cm−1 for 2, and ∼700 cm−1 for 1.5. Finally, although the present calculations should provide useful guidelines for the presence of excited states, they are limited to single configurations and therefore do not address the true multiconfiguration character of these states. D. Analysis of the ReO2 + product cross section As discussed above, the ReO2 + product is formed in the secondary reaction (4). This process appears to be barrier-less, as shown in Figure 2. Thus, these results indicate that D0(ORe+-O) > D0(O-O) = 5.115 eV. This agrees with the 7.4 ± 2.25 eV value obtained from CID experiments by Beyer et al.9 E. Theoretical results for ReO2 + The bonding in metal dioxides has been described pre-viously by Kretzschmar et al. (although they use x as the symmetry axis with the molecule in the xz plane, such that b1 (out-of-plane) and b2 (in-plane) designations are switched compared with the nomenclature adopted here).88 Here, we utilize conventions recommended previously,89 in which the molecule has C2v symmetry along the z-axis with the molecule lying in the yz plane. Core electrons on Re (5s, 5p) and O (1s, 2s) are not included in these mos. The 1a1 orbital is bonding and formed from the 5dy 2 orbital of Re and the 2pz of each oxygen atom, thus forming in-plane Re- O π bonds. There are two doubly occupied, σ-bonding mos (1b2 and 2a1) resulting from interaction of the Re(5dyz) and Re(5dx2-z2) orbitals with in-phase and out-of-phase combina-tions of the O(2py) orbitals on each oxygen atom. The 1a2 and 1b1 mos are doubly occupied out-of-plane π-like mos, which involve the Re(5dxy) and Re(5dxz) orbitals combined with out-of-phase and in-phase combinations of the O(2px) orbitals, respectively. The 2b2 mo, which is mostly nonbond-ing in character, is formed from an out-of-phase combination of O(2pz) orbitals. The 3a1 orbital, also largely nonbonding, is a 6s-5dx2 hybrid along with a little O(2py) character. Higher lying mos include 2b1, 4a1, 2a2, 3b2, and 5a1, which are an-tibonding versions of the 1b1, 2a1, 1a2, 1b2, and 1a1 bonding mos, respectively. In previous theoretical work on ReO2 +, Beyer et al. lo-cated a ground state 3B1, with a 5B2 state having a Re+(O2) geometry lying 3.55 eV higher in energy.9 (They identify these states as 3B2 and 5B1, respectively, apparently using the same designations as Kretzschmar et al.) For ReO2 +, our calculations also find a 3B1 ground state with equal Re- O bond lengths of 1.669 Å and a bond angle of 112.0◦, geometrical parameters that match those of Beyer et al.,9 Table V. The valence electronic configuration of this state is 1a1 21b2 21a2 22a1 21b1 22b2 23a1 12b1 1. From this configuration, the 3B1 state has ten electrons in bonding and 1 electron in an antibonding mo such that each ReO bond has a bond order of 2.25. This is reasonable when one compares the 1.669 Å bond length with those listed for the ReO+ species having bond or-ders of 2.5, Table IV. Further, this bond order characterization is commensurate with the bond energy. At the B3LYP/def2- TZVPPD level of theory, the 3B1 state is calculated to lie TABLE V. Bond lengths (Å), bond angles (◦), and energies calculated at the B3LYP/def2-TZVPPD level for ReO2 +.a State Configuration r(Re-O) OReO r(O-O) ReOO E (Eh) ZPE(Eh ) Erel (eV) 3B1 1a1 21b2 21a2 22a1 21b1 22b2 23a1 12b1 1 1.669 112.0 −228.489618 0.005569 0.00 1.67 112.3 0.005557 0.00 1A1 1a1 21b2 21a2 22a1 21b1 22b2 23a1 2 1.659 107.4 −228.486059 0.005654 0.10 3A1 1a1 21b2 21a2 22a1 21b1 22b2 23a1 14a1 1 1.680 115.6 −228.454431 0.005344 0.95 3A2 1a1 21b2 21a2 22a1 21b1 22b2 23a1 12a2 1 1.687 97.4 −228.435543 0.005751 1.48 1A1 1a1 21b2 21a2 22a1 21b1 22b2 22b1 2 1.680 122.7 −228.430936 0.005407 1.59 5A(A2) 1a1 21b2 21a2 22a1 21b1 22b2 13a1 12b1 14a1 1 1.660, 1.849 135.2 −228.407763 0.004200 2.19 1A2 b 1a1 21b2 21a2 22a1 21b1 22b2 13a1 12b1 14a1 1 1.727 137.6 −228.389553 0.002515 2.64 5A1 1a1 21b2 21a2 22a1 21b1 22b2 13a1 12b1 12a2 1 1.754 93.1 −228.384939 0.003448 2.79 3B2 1a1 21b2 21a2 22a1 21b1 22b2 13a1 24a1 1 1.729 110.1 −228.371307 0.002864 3.15 5B1 1a1 21b2 21a2 22a1 21b1 22b2 13a1 12a2 14a1 1 1.771 84.4 −228.360760 0.005584 3.51 1B2 1a1 21b2 21a2 22a1 21b1 22b2 13a1 24a1 1 1.719 122.2 −228.354523 0.003185 3.61 5B2 1a1 21b2 21a2 22a1 21b1 23a1 12b1 12a2 14a1 1 1.870 45.2 1.439 67.4 −228.350264 0.005109 3.78 1.88 1.43 0.005066 3.55 5A(B1) 1a1 21b2 21a2 22a1 11b1 22b2 23a1 12b1 14a1 1 1.897, 2.638 27.0 1.282 110.6 −228.324636 0.004132 4.45 3B1 1a1 21b2 21a2 22a1 21b1 23a1 22b1 14a1 1 1.916 40.7 1.332 69.7 −228.315369 0.004587 4.72 7A(B1) 1a1 21b2 21a2 12a1 11b1 22b2 23a1 12b1 12a2 14a1 1 1.956, 2.396 33.2 1.312 92.2 −228.315023 0.004465 4.72 1A(A1) 1a1 21b2 21a2 22a1 21b1 23a1 24a1 2 1.845, 1.850 45.8 1.439 66.9 −228.314751 0.004930 4.74 9 − 1σ21π42σ12π21δ23σ13π2 2.949, 4.152 0.0 1.203 180.0 −228.308621 0.004029 4.88 7A2 1a1 21b2 21a2 12a1 21b1 22b2 13a1 12b1 12a2 14a1 1 1.890 65.2 −228.299343 0.003714 5.13 7A(B1) 1a1 21b2 21a2 22a1 21b1 12b2 13a1 12b1 12a2 14a1 1 1.687, 2.451 143.1 −228.297371 0.002970 5.16 7B1 1a1 21b2 21a2 22a1 21b1 12b2 13a1 12b1 12a2 14a1 1 1.898 127.5 −228.294647 0.003224 5.24 7A1 1a1 21b2 21a2 12a1 21b1 12b2 23a1 12b1 12a2 14a1 1 1.924 127.5 −228.286502 0.003573 5.47 aValues in italics are from Beyer et al.9 bHas an imaginary asymmetric stretch (604 cm−1) and collapses to the 1A1 state. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.97.11.184 On: Wed, 16 Jul 2014 13:14:00 084305-9 P. B. Armentrout J. Chem. Phys. 139, 084305 (2013) 5.00 eV below the Re+(7S) + O2 reactant asymptote and to have a D0(ORe+-O) BDE of 5.83 eV. This theoretical value compares favorably to the experimental limit of >5.12 eV (measured here) and the CID value of 7.4 ± 2.25 eV of Beyer et al.9 Table V lists the geometries and energies of various stable states of rhenium dioxide cations, OReO+, calculated at the B3LYP/def2-TZVPPD level of theory. The first excited state of ReO2 + is calculated to be a 1A1 state lying 0.10 eV above the ground state, having Re+-O bond lengths of 1.659 Å, and a OReO angle of 107.4◦. This state is formed by moving an electron from the 2b1 to the 3a1 orbital, such that the ReO bonds have a bond order of 2.5, consistent with the slightly shorter bond length. Other excited states with C2v symmetry were located with excitation energies of 0.95-5.47 eV above the ground state, bond lengths of 1.68-1.92 Å, and bond an-gles of 40.7◦-127.5◦. Two states are found to break C2v sym-metry by extending one of the Re-O bonds. The 5A and 7A states, which would have 5A2 and 7B1 designations if the bond lengths were equal, have one short Re-O bond similar to those of the ReO+ diatomic, and one much longer bond, 1.85 and 2.45 Å, respectively. Two of the C2v states, 5B2 and 3B1, are better character-ized as adducts of Re+ with O2. These are typified by small OReO bond angles (<45◦), short OO bond distances (1.33 and 1.44 Å compared to free O2 at 1.204 Å), and larger Re- O bond lengths (1.87 and 1.92 Å) than the dioxides. The lowest of these, the 5B2 state, was previously located by Beyer et al., with similar bond lengths and excitation energy,9 Table V. Three additional adduct states have Cs symmetry with unequal Re-O bond lengths.We also located a state hav-ing nonet spin, which corresponds to high spin coupling of the Re+(7S) + O2(3g −) reactants. This species is linear with a very long Re-O bond, 2.948 Å, such that the O2 bond is nearly unperturbed, 1.203 Å. This species presumably has a purely electrostatic bond and is only 0.11 eV below the reactants. F. Potential energy surfaces for Re+ + O2 on the way to forming ReO+ + O Calculated potential energy surfaces for the interaction of Re+ with O2 (3g −) are shown in Figures 4(a) and 4(b). They are separated into surfaces having A and A symmetry as only curves within these groups will strongly interact un-der experimental conditions for this triatomic system, which necessarily has a plane of symmetry. In most cases, species have C2v symmetry throughout. In the interaction between Re+ (7S,A1,A) with O2 (3g −,B1,A), the first step is forma-tion of an association complex intermediate, Re+(O2) (5A) on the A surfaces, which has an energy 0.54 eV below the Re+ (7S) + O2 (3g −) asymptote. This intermediate has ReO bond lengths of 1.897 Å, an OO bond length of 1.282 Å, and bond angles of OReO = 27.0◦ and ReOO = 110.6◦. As the OReO bond angle gets larger, the potential energy surfaces evolve into the more strongly bound rhenium dioxide cationic species, with the 1A1 and 3B1 states being the lowest in en-ergy on the A and A surfaces, respectively. Note that singlet and triplet states of ReO2 + cannot be formed in spin-allowed processes from the ground state Re+ (7S) + O2 (3g −) re-actants and therefore can only be accessed by a curve cross-ing with one of the quintet or septet surfaces. Importantly, all of the ReO2 + surfaces except those of the high-spin septets have minima that lie below the ReO+ + O product asymp-tote, calculated to be 0.83 eV (0.55 eV including estimated FIG. 4. B3LYP/def2-TZVPPD calculations of the potential energy surfaces for the interaction of Re+ with O2 in C2v symmetry as a function of the O-Re+-O bond angle in degrees. The surfaces are separated into A (a) and A (b) symmetry with singlet, triplet, quintet, and septet states indicated by black, red, blue, and green lines, respectively. Species having C2v symmetry are shown by full lines and those with Cs symmetry are dashed lines. Horizontal lines indicate the experimental energy zero, corresponding to the Re+ (7S) + O2 (3g −) reactants at 0.0 eV, and Re+(5D) reactant at 2.125 eV, along with dashed lines showing the two experimental energy thresholds determined for formation of ReO+ + O products, 0.29 and 1.64 eV above the reactants. Circles indicate avoided crossings in C2v (filled) and Cs (open) symmetry. This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.97.11.184 On: Wed, 16 Jul 2014 13:14:00 084305-10 P. B. Armentrout J. Chem. Phys. 139, 084305 (2013) spin-orbit energies) above the Re+ + O2 asymptote at this level of theory (0.29 ± 0.05 eV experimentally). Using the CCSD(T,full)/def2-QZVPPD(aug-cc-pV5Z) approaches, the calculated endothermicity is 0.94 (0.84) eV, which shifts to 0.75 (0.57) eV after including estimated spin-orbit energies. Notably, the A surfaces cannot be accessed from ground state reactants within the Born-Oppenheimer approximation. Low-energy pathways leading to the ReO2 + intermediates are available on the A surfaces, but even here there appears to be a surface crossing point that lies above the energy of the reactants, namely that between the small-angle 3B1 and 5B1 surfaces. This crossing occurs near OReO = 54◦ at an en-ergy calculated to be 0.42 eV above ground state reactants. It was verified that both surfaces have very similar geometries at this point, with ReO bond lengths of 1.84 Å, such that the sur-faces actually do intersect at this point. Importantly, this en-ergy remains below that calculated for ground state products, 0.83 eV, and conceivably could lie lower as a result of spin-orbit coupling associated with the Re+(5D) + O2(3g −) reac-tants that couple to form the 3B1 surface. Given these obser-vations, the energy of this surface crossing seam should not influence the threshold observed for product formation. Formation of ReO+ (3) + O (3P) products should be able to evolve in spin-allowed pathways from several of the singlet, triplet, and quintet ReO2 + species and ReO+ (5) + O (3P) can be formed from triplet, quintet, and septet in-termediates. Indeed, explicit calculations of the surfaces for ORe+-O bond cleavage from the lowest ReO2 + states of sin-glet, triplet, and quintet spin show no reverse activation bar-riers, with the latter two states correlating with dissociation to ReO+ (3) + O(3P). These dissociation pathways require breaking C2v symmetry such that they are not conveniently shown in Figures 4(a) and 4(b). Thus, the experimentally mea-sured threshold should correspond to the asymptotic limit for formation of ReO+ + O, thereby yielding accurate thermo-chemistry for ReO+. IV. DISCUSSION The behavior observed for reaction (1), Figures 1 and 3, is unusual in that two endothermic features are observed. Although it is energetically possible to form excited states in most ion-molecule reactions at elevated kinetic energies, it is unusual for individual product states to give rise to dis-tinct features in GIB experiments, although such behavior has been observed in several previous studies, as discussed below. Clearly, the routes to the two products in question must differ in some fundamental way. Several plausible explanations are discussed here, although it will be seen that none appear to be definitive in the present case. (1) One potential explanation for the two features is the presence of excited states of Re+. We discount this pos-sibility because no evidence for such excited states is ob-served in other systems, reactions with H2 and CH4.44, 45 Further, addition of a quenching gas (CH4) to the source region yielded no change in the cross sections observed. (2) The high energy feature could correspond to formation of ground state O (3P) at low energies and O (1D) at high energies. However, the excitation energy of 1.35 ± 0.28 eV measured here is well below the 1.97 eV as-sociated with this excitation.68 (3) In previous work, two endothermic features were ob-served in the cross section for formation of VS+ from reaction of V+ with CS2 90 and attributed to reactions (7) and (8). V+(5D) + CS2 1 + g → VS+(3 −) + CS(1 +), (7) → VS+(5) + CS(1 +). (8) Here formation of the VS+ (3 −) ground state is spin forbidden and formation of VS+ (5) is spin-allowed. This distinction can explain why the latter process is easily observed as a distinct feature in the cross section even though it is much more endothermic than the for-mer process. Therefore, the two features observed here for reaction (1) are plausibly assigned to an overall spin-forbidden reaction at low energy and an overall spin-allowed process at high energies, thus forming two dif-ferent electronic states of the ReO+ product ion. Belying this explanation is the fact that both reactions (9) and (10) are spin-allowed, Re+(7S) + O2(3 − g ) → ReO+(3) + O(3P), (9) → ReO+(5) + O(3P), (10) such that formation of ground state products (no matter what their identity) from ground state reactants is spin-allowed. Indeed, formation of any ReO+ product state except singlets is spin-allowed, as septet, quintet, and triplet states of ReO+ along with O(3P) can be formed via quintet intermediates. Furthermore, it seems unlikely that spin is a very good quantum number for this heavy element system. Nevertheless, we can pursue this idea further by comparing the experimental excitation energy of 1.35 ± 0.28 eV with the theoretical excitation energies in Table IV. In this energy range, there is both a 1 + state at 1.15 eV and a 5 + state at 1.62 eV, although these values change to 1.43 and 1.91 eV, respectively, when approximate spin-orbit corrections are made (and higher energy fine structure levels of the 3/ state also move within the experimental energy band). (At the CCSD(T,full)/def2-QZVPPD level(CBS) levels of theory, the 1 + state excitation energy is 0.88 (0.73) eV, 1.07 (1.05) eV after spin-orbit corrections, Table III.) As the lowest lying singlet in Table IV, the for-mer state is unique. Notably, reaction (11) is truly spin-forbidden and therefore requires coupling between quin-tet and triplet surfaces: Re+(7S) + O2(3 − g ) → ReO+(1 +) + O(3P). (11) Thus, this singlet state is plausibly assigned to the high energy feature observed experimentally; however, it This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.97.11.184 On: Wed, 16 Jul 2014 13:14:00 084305-11 P. B. Armentrout J. Chem. Phys. 139, 084305 (2013) remains unclear why formation of this state should lead to a unique experimental signature, and especially why a spin-forbidden reaction would be favored at high kinetic energies. (4) Another reaction for which two endothermic fea-tures were observed is S+ (4S) + H2 → SH+ (3 −) + H (2S).91 Here, the higher energy feature could be explained as a spin-allowed reaction along a quartet surface exhibiting a barrier, whereas the lower en-ergy feature requires changing to the doublet surface associated with the ground state of the H2S+ (2B1) intermediate. If the Re+ + O2 behaved similarly, then reaction at low collision energies could form the ground state ReO2 + (3B1) intermediate or perhaps the low-lying ReO2 + (1A1), which are technically spin-forbidden pro-cesses from ground state reactants. These intermediates could then dissociate to form either ReO+ (3) or ReO+ (5) + O(3P). However, these same products could also be formed from quintet states of ReO2 + that can be formed from ground state reactants in spin-allowed processes. Furthermore, this scenario does not provide a clear explanation for the origins of the higher energy cross section feature. (5) An intriguing possibility focuses on the character of the surfaces in the entrance channel, which is effectively shown in Figures 4(a) and 4(b) at small OReO bond angles. For ground state reactants, only 5A, 7A, and 9A surfaces evolve from ground state reactants with the low-spin 5A being the most attractive and 9A be-ing largely repulsive. As shown in Figure 4(b), this 5A surface crosses surfaces of other spin leading to sta-ble ReO2 + intermediates including the 3B1 ground state. Along these surfaces, there is potentially a small barrier to form ReO2 + (3B1) in excess of the reactant energy where the small angle 3B1 and 5B1 surfaces cross. There should be no barriers for dissociation to ReO+ + O in excess of the product asymptotic energy. Thus, at low kinetic energies, the reactants pass slowly through the crossing regions, allowing the electrons to adjust to dif-ferent configurations along the reaction coordinate. Un-der such conditions, spin inversion can be efficient, and adiabatic behavior is expected. However, all of these sur-faces exhibit avoided crossings with surfaces evolving from higher energy reactant states, such that as the nu-clear motion speeds up at elevated collision energies, the reactants pass more quickly through the crossing regions, the electrons have less time to adapt, and the Born-Oppenheimer approximation begins to fail. Thus, as the kinetic energy of the reactants increases, it be-comes increasingly likely that the reactants will behave diabatically during the collision event and remain on the surface associated with the electron configuration of the ground state reactants. This could lead to a higher barrier to the reaction, observed experimentally as the second cross section feature. Intriguingly, the surfaces of A symmetry (which can-not be accessed adiabatically from ground state reactants) are qualitatively different in the entrance channel. Here, no low-energy pathways are found because they can only evolve from Re+(5D) + O2(3g −) or higher energy reactants. Coupling of the A and A surfaces can occur at elevated kinetic en-ergies by electronic-rotational (Coriolis) coupling, as previ-ously observed for reactions of state-specific rare gas cations (Ar+, Kr+, and Xe+) with H2, D2, and HD in the vicinity of 1-2 eV relative kinetic energies.42, 92, 93 Coriolis coupling oc-curs when high rotational velocities of the collision plane of the reactants cause the electrons to "lag" out of the plane. Thus, one possibility is that the low energy behavior observed experimentally corresponds to adiabatic reactions along the A surfaces, and the high energy feature observed experimen-tally is associated with reactions along the A surfaces with possible contributions from diabatic pathways on A. In evaluating these various possibilities, it is important to note that the related Os+ + O2 → OsO+ + O reaction also exhibited two distinct endothermic features,33 presum-ably for the same intrinsic reasons. In addition, the Ir+ + O2 →IrO+ + O reaction shows similar behavior, although more subtly.94 There too, specific considerations of the five expla-nations above were applied with similar unsatisfying results. In all three systems, the observed experimental behavior ap-pears most likely to be associated with adiabatic behavior at low energies followed by some sort of nonadiabatic behavior at higher energies. It seems odd that such behavior is observed for these heavy metal systems where spin is no longer likely to be a very good quantum number, whereas lighter congeners do not exhibit such dual thresholds.19, 22, 95 Assuming that spin need not be conserved, the singlet, triplet, quintet, and septet surfaces shown in Figures 4(a) and 4(b) should couple effi-ciently, such that reaction (1) is controlled by effects in the entrance channel with explanation 5 above providing the most plausible path for the Re+, Os+, and Ir+ systems. V. CONCLUSION The kinetic-energy dependence of the Re+ + O2 reaction is examined using guided ion beam tandem mass spectrom-etry. The cross section for ReO+ formation exhibits distinct endothermic features with thresholds measured to be 0.29 ± 0.05 and 1.64 ± 0.28 eV. The former threshold yields a bond energy for ReO+ of 4.82 ± 0.05 eV, which agrees well with previous imprecise experimental values. Forma-tion of ReO2 + was also observed in an exothermic secondary process, leading to thermochemistry in agreement with the literature. Detailed quantum mechanical calculations are performed for ReO+ and ReO2 + species. The nature of the bonding is analyzed at the B3LYP, BP86, and CCSD(T,full) levels of theory. Basis sets for the metal include def2-QZVPPD, def2- TZVPPD, aug-cc-pVxZ-PP (x = T, Q, 5) and small core rel-ativistic effective core potentials with def2 and aug-cc-pVxZ basis sets used for oxygen. Reasonable agreement between theoretical and experimental bond energies is found for most levels of theory, with B3LYP and CCSD(T,full) being on the low side and BP86 being on the high side. The calculated ground state of ReO+ is either 5 or 3, although addi-tional consideration of spin-orbit effects suggests that the 3 is the probable ground state. Potential energy surfaces for the This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 155.97.11.184 On: Wed, 16 Jul 2014 13:14:00 084305-12 P. B. Armentrout J. Chem. Phys. 139, 084305 (2013) interaction of Re+ with O2 are also calculated at the B3LYP/def2-TZVPPD level of theory. These surfaces demon-strate that Re+ inserts into O2 to form ground state ReO2 + via a curve crossing model and that ground state ReO+ can be formed with no barriers in excess of endothermicity, consis-tent with the experimental results. 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