Gas-Phase Reactivity of Cesium-Containing Species by Quantum

Article pubs.acs.org/JPCA

Gas-Phase Reactivity of Cesium-Containing Species by Quantum Chemistry Katarína Šulková,*,†,# Laurent Cantrel,*,†,§ and Florent Louis‡,§ †

Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSN-RES, SAG, LETR, St Paul Lez Durance 13115, France PhysicoChimie des Processus de Combustion et de l’Atmosphère (PC2A), UMR CNRS 8522, Université Lille 1 Sciences et Technologies, 59655 Villeneuve d’Ascq Cedex, France § Laboratoire de Recherche Commun IRSN-CNRS-Lille1 “Cinétique Chimique, Combustion, Réactivité” (C3R), Centre de Cadarache, BP3, St Paul Lez Durance 13115, France ‡

S Supporting Information *

ABSTRACT: Thermodynamics and kinetics of cesium species reactions have been studied by using high-level quantum chemical tools. A systematic theoretical study has been done to find suitable methodology for calculation of reliable thermodynamic properties, allowing us to determine bimolecular rate constants with appropriate kinetic theories of gas-phase reactions. Four different reactions have been studied in this work: CsO + H2 = CsOH + H (R1), Cs + HI = CsI + H (R2), CsI + H2O = CsOH + HI (R3), and CsI + OH = CsOH + I (R4). All reactions involve steam, hydrogen, and iodine in addition of cesium. Most of the reactions are fast and (R3) and (R4) proceed even without energetic barrier. In terms of chemical reactivity in the reactor coolant system (RCS) in the case of severe accident, it can be expected that there will be no kinetic limitations for main cesium species (CsOH and CsI) transported along the RCS. Cs chemical speciation inside the RCS should be governed by the thermodynamics.

1. INTRODUCTION This paper is the sixth of a series1−5 devoted to a better understanding of the chemical speciation along the transport of fission products in the reactor coolant system (RCS) to estimate the source term in the case of a nuclear power plant accident. Iodine and cesium are of high importance for health consequences in the case of outside releases. For iodine transport along the RCS, iodine/steam/hydrogen network modeling has been improved by implementing kinetics3 in severe accident software like ASTEC.6 For cesium, after revising the thermodynamic data4 of the main Cs species, which could be formed in the RCS, we can wonder if cesium compound formation could be subject to kinetic limitation. Only few works dealt with kinetics of cesium reaction. In Wren’s report7 devoted to the Cs−I−O−H mechanism, some cesium rate constants were estimated by a rough method due to the lack of available experimental data. From their simulations, the cesium species reach thermochemical equilibrium in less than 0.1 s at 1000 K for relevant CANDU (CANada Deuterium Uranium) reactor conditions. Cronenberg and Osetek8 confirmed later, in using the same kinetics as Wren, that the Cs−I−O−H kinetic system is fast enough to reach equilibrium for the relevant PWR (pressurized water reactor) whereas Burón and Fernandez9 have concluded that the assumption of chemical equilibrium could be inaccurate to predict cesium− iodine species distribution under severe accident conditions in using other rate constant evaluations. Nevertheless, Wren pointed out that the rate constants for bimolecules are highly © XXXX American Chemical Society

uncertain and need to be refined. Considerable experimental efforts are required to measure the rate constants of the elementary reactions (not readily available). The most suitable alternative is to use theoretical tools to determine bimolecular rate constants with appropriate kinetic theories. The main objective of this work is to determine the kinetics of the cesium reactions with theoretical methods. It presents the results of a systematic theoretical study of the reactivity of four elemental reactions containing iodine and cesium species leading to the two main Cs-containing species in the RCS (CsOH and CsI): CsO + H 2 ↔ CsOH + H

(R1)

Cs + HI ↔ CsI + H

(R2)

CsI + H 2O ↔ CsOH + HI

(R3)

CsI + OH ↔ CsOH + I

(R4)

On the basis of the methodology from our previous paper,4 we performed quantum chemistry calculations to compute the energetics of gas-phase reactions (vibrationally adiabatic barriers and reaction enthalpies). In addition, equilibrium geometries, harmonic frequencies, and overall energy profiles of these reactions have been investigated because until now there Received: June 10, 2015 Revised: August 3, 2015

A

DOI: 10.1021/acs.jpca.5b05548 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

determinant reference wave function was negligible for all species involved, showing that the wave function was not contaminated by states with higher multiplicities. The pseudopotential calculations usually result in good agreement with the all-electron basis set calculations. Due to a limited choice of basis sets for cesium, we decided to compare our results with the all-electron CCSD(T) calculations using the MOLCAS7.8 program package34 with the similar methodology as used in our previous paper.35 Three types of relativistic contraction of the ANO-RCC primitive set for H(8s4p3d1f), O(14s9p4d3f2g), Cs(26s22p15d4f2g), and I(22s19p13d5f3g) have been used: ANO-RCC-VTZP, ANO-RCC-VQZP, and ANO-RCC-LARGE.36 To minimize the possible basis set superposition error (BSSE), we have applied the modification of the Boys−Bernardi37,38 counterpoise (cp) correction as proposed by Xantheas.39 In contrast to the standard Boys− Bernardi correction; this modification includes also the geometry relaxation when going from the subsystems to the supersystem. The cp correction is applicable to weakly interacting molecular complexes (MCR, MCP) but not to TSs, where it can lead to discontinuous potential surfaces.40 Therefore, we will use only cp correction for molecular complexes later in the discussion. To investigate the convergence of CC energy sequences toward the full configuration-interaction (FCI) limit, we used the extrapolation procedure proposed by Goodson, continuedfraction approximation (cf),41 in the energetics of all studied reactions. The approximant for a coupled-cluster sequence is constructed as follows:

have been no such theoretical works dealing with these reactions. Another goal of the present work is to find a suitable methodology for calculation of reliable thermodynamic properties of reactions containing cesium species.

2. METHODOLOGY AND COMPUTATIONAL DETAILS 2.1. Methodology for Optimization. The stationary points on each reaction profile (reactants, molecular complexes, transition states, and products) were determined using the second-order Møller−Plesset perturbation theory (MP2)10,11 and four DFT functionals; two hybrid-GGAs (B3LYP12,13 MPW1K14) and two hybrid meta-GGAs (M06-2X,15,16 M06HF17). In the geometry optimizations we have used Dunning’s triple-ζ correlation consistent basis sets cc-pVTZ and aug-ccpVTZ for light atoms18 and the Stuttgart scalar relativistic effective core potentials (RECP) on iodine (ECP28MDF)19 and cesium (ECP46MDF)20 atoms associated with the corresponding valence basis sets ((aug)-cc-pVTZ-PP on iodine and ECP46MDF on cesium). All geometry optimizations and vibrational frequencies calculations were performed with the GAUSSIAN09 program package.21 Vibrational frequencies were multiplied by an appropriate scaling factor.22 To check that the specific transition state (TS) connects the different local minima (molecular complex of reactant (MCR) and molecular complex of product (MCP)), we performed intrinsic reaction coordinate analyses (IRC)23,24 at the MP2/cc-pVTZ and MP2/aug-cc-pVTZ levels of theory. The stability of the wave function was systematically checked using the algorithm25,26 implemented in GAUSSIAN09 software. 2.2. Methodology for Energetics. To obtain the reliable energetic information, single-point energy calculations at all previously optimized stationary points were performed using the coupled cluster theory including single, double, and noniterative triple substitutions, CCSD(T).27,28 Two basis set series were used, both employing RECPs on iodine and cesium atoms, Dunning’s aug-cc-pVnZ-PP (n = T, Q, 5) basis and the def2-nZVP basis set.18 Their all-electron counterparts were used for light atoms. When the Dunning series of correlation consistent basis sets is used, the calculated CCSD(T) energies are usually extrapolated to the complete basis set limit (CBS) using two relations, one of Halkier et al.29 E(n) = E(Halkier) + An−3

ECCcf =

1−

δ2 / δ1 1 − δ3 / δ 2

(3)

where δ1 = ESCF, δ2 = ECCSD − ESCF, and δ3 = ECCSD(T) − ECCSD. This method works quite well even for stretched bonds, typical for TS, and is applicable for molecules with smooth convergence in CCSD.35 In our case, however, only the results calculated with the ANO-RCC basis set can be properly extrapolated. On the basis of the formula for cf correction (eq 3), in which we take the ratio of SCF energy in the numerator and the correlation contributions in denominator, it is evident that the denominator becomes artificially large when RECPs are used in comparison with all-electron basis sets. In RECPs a large portion of SCF energy is replaced by the potential and, therefore, the ratio of the correlation energy contributions and the SCF energy δ2/δ1 in the Goodson’s formula becomes much larger than in the all-electron basis set. The resulting cf correction is thus artificially overestimated and worsens the overall energetics. Therefore, this extrapolation technique is not suitable when other than all-electron basis sets are used. 2.3. Methodology for Spin−Orbit Coupling (SOC). Spin−orbit coupling plays an important role in the reactivity of heavy atoms like iodine and cesium.42−45,35,46,47 To estimate the effect of SO correction to the ground state of atoms and molecules, we used the restricted active space state interaction method (CASSCF/CASPT2/RASSI-SO,48 shortly CASPT2/ RASSI-SO) in conjunction with the second-order multiconfigurational perturbation theory (CASPT2), employing the complete active space (CASSCF) wave function as a reference. Atomic mean field integrals (AMFI) were used to decrease the computational effort with a negligible loss of accuracy. All calculations reported have been done using the MOLCAS7.8 package. SOC effects were included as an a

(1)

with the cardinal number n = 3 (aVTZ), 4 (aVQZ), 5 (aV5Z) and corresponding to the CCSD(T)/aug-cc-pVnZ (n = T, Q, 5) level of theory (two-parameter extrapolation), and second of Peterson et al.30 2

E(n) = E(Peterson) + A−(n − 1) + B−(n − 1)

δ1

(2)

with n = 3, 4, and 5 (three-parameter extrapolation). In our case, however, due to the lack of such basis set series for the cesium atom, we employed the same basis set (ECP46MDF) on cesium in all calculations. That means its correlation energy is not systematically improved in contrast to other atoms. This inconsistency prevents us from using the extrapolation techniques reliably, and therefore, we decided to omit the extrapolated values from the discussion. The reliability of the single reference CCSD wave function with respect to possible multireference character was checked by means of the T1 diagnostic31,32 together with inspection of the largest amplitude (LA) at all the stationary points.33 Spin contamination arising from the use of unrestricted single B


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The Journal of Physical Chemistry A posteriori correction (using one-electron Fock-type spin−orbit Hamiltonian to approximate the SOC operator). The relativistic ANO-RCC primitive sets were contracted to H[6s4p3d1f], O[8s7p4d3f2g], Cs[12s10p8d4f2g], and I[10s9p8d5f3g],36 which correspond to the ANO-RCCLARGE contraction. An inclusion of SO effects in the case of OH (2Πi) radical leads to splitting of the ground state and lowering the energy by −0.831 kJ mol−1. The calculated correction is in good agreement with our previous work35 and other theoretical works49,50 (−0.833 kJ mol−1) and also with the literature value from the NIST-JANAF thermochemical database51 (−0.836 kJ mol−1). The calculated SO correction for iodine (2P3/2) is −30.3 kJ mol−1, which is close to the value −27.8 kJ mol−1 from Roos et al.48 and in excellent agreement with the experiment of −30.3 kJ mol−1.51 For the remaining species, the SO coupling between the ground state and the excited states is almost quenched, due to the large energy separation between them. In such cases we consider the energy shift due to the second-order spin−orbit effect. The calculated value of the spin−orbit correction for HI (1Σ+) is −2.3 kJ mol−1, which is in excellent agreement with the value of Feller et al.52 (−2.1 kJ mol−1). Special attention was given to SO coupling of molecules CsI (1Σ+) and CsO (2Σ+). Molecular structure and thermodynamic properties including spin−orbit correction for both molecules have been studied recently by Badawi et al.4 In this paper, the SO correction for CsI (−20.19 kJ mol−1) has been taken from the work of Berkowitz et al.53 and the value for molecule CsO (−1.2 kJ mol−1) from the work of Hirota.54 These values, however, do not correspond to the spin−orbit splitting of the ground states of CsI and CsO molecules but refer to the splitting of the ground state of CsI+ and excited state of CsO. To support our claim, we performed calculations of the SO corrections. There are only two theoretical works55,56 studying ground and low-lying excited states of cesium iodide. A large energy separation between the ground X1Σ+ and the lowest excited state 3Π is observed, which clearly indicates that no spin−orbit coupling affects the ground state. In our work inclusion of SO effects leads to lowering of the energy of the Ω ground state X0+ (−0.07 kJ mol−1 or 6 cm−1) due to the splitting of the degenerated excited states 1,3Π. A similar study was performed by Alekseyev et al.,57 where the ground state of sodium iodide is weakly influenced by SO interaction and its energy is lowered by 20−30 cm−1. Cesium monoxide has been the subject of numerous studies within the series of alkali metal monoxides.58−61 Lee et al.58 predicted that effects of spin−orbit coupling on the 2Σ+−2Π separation will decrease as the metal gets heavier within the series. In our work, we have investigated the interaction between the 2Σ+ and 2Π states of CsO and calculated the spin−orbit correction of the Ω ground state X1/ 2 to be −0.01 kJ mol−1. This value is negligibly small, and we can summarize that the SO effect does not influence the ground state of the CsO radical. Considering previous facts, in the present work we will use our calculated SO correction for molecules CsI (−0.07 kJ mol−1) and CsO (−0.01 kJ mol−1). The SO effects of TSs and molecular complexes have been calculated using the same methodology as for reactants and products discussed above. On the basis of the Hammond’s postulate,62 the structure of the transition state depends on the exothermicity/endothermicity of the studied reaction. Exothermic reaction is characterized by the transition state with a structure similar to reactants (reactant-like), whereas in the case

of endothermic reaction the transition state is more productlike. The SO splitting obeys the same rule.35 Reactions R1 and R2 are exothermic; therefore, the transition states are expected to be reactant-like and the SO effect should be comparable with those of reactants. It is best visible on reaction R2, where the SO correction of TS2 has been calculated to be −1.42 kJ mol−1 whereas the SO correction of the reactant HI is −2.26 kJ mol−1 and of the MCR2 is −1.97 kJ mol−1. On the product side, the SO correction of MCP2 has been calculated to be −0.48 kJ mol−1, which is comparable to that of the product molecule CsI (−0.07 kJ mol−1). Calculated spin−orbit corrections to the potential energies of all stationary points are gathered in Table S5 of the Supporting Information. 2.4. Methodology for the Kinetics. The rate constants for reactions R1 and R2 have been calculated using the canonical transition state theory63−65 employing two different methods. The first one is based on an elemental reaction occurring in a one-step mechanism (direct mechanism) whereas the second one (complex mechanism) corresponds to a two-step mechanism involving a fast pre-equilibrium between the reactants (R) and the prereactive complex (first step) followed by an abstraction leading to the postreactive complex and products (P) (second step). The description of our methodology has been already fully detailed in our previous paper.35 The GPOP program66 was used to extract information from Gaussian output files, to calculate the Eckart tunneling corrections, and to do the rate constant calculations over the temperature range of interest.

3. RESULTS AND DISCUSSION To maintain readability, detailed information and discussion regarding the structural parameters and vibrational frequencies calculated for all reactants, TSs, molecular complexes, and products at different levels of theory, and Cartesian coordinates for TSs and molecular complexes are presented in the Supporting Information. 3.1. Reaction CsO + H2 ↔ CsOH + H. The potential energy profile for the CsO + H2 ↔ CsOH + H exothermic reaction (−48.7 kJ mol−1) calculated at the CCSD(T)/aug-ccpV5Z//MP2/aug-cc-pVTZ level is shown in Figure 1. The electronic binding energies for molecular complexes, barriers,

Figure 1. Potential energy profile for the CsO + H2 ↔ CsOH + H reaction calculated at the CCSD(T)/aug-cc-pV5Z//MP2/aug-ccpVTZ level of theory with (black line) and without (red line) ZPE and SO corrections. C


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Table 1. Energy Contributions to Enthalpies at 0 and 298 K Including Spin−Orbit Corrections (kJ mol−1) Calculated at CCSD(T)/aug-cc-pVnZ//MP2/aug-cc-pVTZ, CCSD(T)/def2-nZVPPD//MP2/aug-cc-pVTZ and CCSD(T)/ANO-RCC// MP2/aug-cc-pVTZ Levels of Theory (Continued-Fraction Estimates in Parentheses in Italic) CsO + H2 → CsOH + H (R1) forward

reverse

equilibrium

CsO + H2 → MCR1

CsO+ H2 → TS1

CsOH + H → MCP1

CsOH + H → TS1

CsO + H2 = CsOH + H

ΔH0K

ΔH‡0K

ΔH0K

ΔH‡0K

ΔrH0K

aug-cc-pVnZ CCSD(T)/TZ CCSD(T)/QZ CCSD(T)/5Z ZPE correction SO correction CCSD(T)/TZtotala CCSD(T)/QZtotala CCSD(T)/5Ztotala CCSD(T)/5Ztotala at 298 K

−9.43 −9.43 −9.41 +7.32 +0.00 −2.11 −2.11 −2.09

12.62 11.22 11.39 −2.52 +0.01 10.11 8.71 8.88

CCSD(T)/TZVPPD CCSD(T)/QZVPPD ZPE correction SO correction CCSD(T)/TZVPPDtotala CCSD(T)/QZVPPDtotala CCSD(T)/QZVPPDtotala at 298 K

−9.30 −9.51 +7.32 +0.00 −1.98 −2.19

8.57 10.62 −2.52 +0.01 6.06 8.11

−0.85 −0.91 −0.98 +0.25 +0.00 −0.60 −0.66 −0.73

60.32 62.22 62.66 −3.21 +0.00 57.11 59.01 59.45

−47.70 −51.00 −51.27 +0.69 +0.01 −47.00 −50.30 −50.57 −51.20 (−0.63)b

−0.89 −0.91 +0.25 +0.00 −0.64 −0.66

61.44 62.49 −3.21 +0.00 58.22 59.27

−52.87 −51.87 +0.69 +0.01 −52.17 −51.17 −51.80 (−0.63)b

−1.46 −1.50 −0.87 +0.25 +0.00 +0.10 −1.22 (−0.01) −1.26 (−0.01) −0.53 (−0.01)

60.70 61.42 61.43 −3.21 +0.00

−51.49 −51.23 −48.46 +0.69 +0.01

57.42 (−0.07) 58.13 (−0.08) 58.12 (−0.09)

−51.05 −50.81 −48.02 −48.65

def2-nZVPPD

ANO-RCC CCSD(T)/VTZP CCSD(T)/VQZP CCSD(T)/LARGE ZPE correction SO correction cp correction/LARGE CCSD(T)/VTZPtotala CCSD(T)/VQZPtotala CCSD(T)/LARGEtotala CCSD(T)/LARGEtotala at 298 K a

−11.22 −11.37 −8.99 +7.32 +0.00 +0.76 −3.87 (+0.04) −3.99 (+0.06) −0.82 (+0.10)

9.21 10.20 12.97 −2.52 +0.01 6.37 (−0.33) 7.32 (−0.36) 10.10 (−0.36)

(−0.26) (−0.29) (−0.26) (−0.63)b

Total CCSD(T) value with the sum of individual corrections. bThermal corrections to enthalpies at 298 K (ddH in kJ mol−1)

and overall reaction enthalpies ΔrH at 0 and 298 K calculated at different levels of theory are collected in Tables 1 and 2. The influence of the geometry optimization level on energetics is rather small in the case of the overall reaction enthalpies, where differences are within the 1 kJ mol−1 range. The largest difference is seen for MCR1 in M06-HF and M06-2X geometries. These are differing by as much as ∼7 kJ mol−1 from that calculated in MP2, B3LYP, and MPW1K geometries, due to the significant difference in the geometry of MCR1. On the basis of these results and the experience from our previous papers,1−4 the MP2 geometries will be used in further discussion of energetics. The convergence with the basis set size was evaluated in three series of basis sets, aug-cc-pVnZ, def2-nZVPPD, and ANO-RCC. By the comparison of results calculated in allelectron and pseudopotential basis sets, we are able to evaluate also the error associated with the pseudopotential approach. A smooth convergence is observed in aug-cc-pVnZ series. The def2-nZVPPD and ANO-RCC series converge in another direction, ANO-RCC converging more slowly. The results calculated in the all-electron and pseudopotential basis agree fairly well, varying by about 2 kJ mol−1.

The SO corrections to the electronic energies are negligibly small to discuss any influence on the reaction pathway. Conversely ZPE corrections tend to destabilize the molecular complexes and stabilize the activation barriers from both the forward and reverse sides (Figure 1). The destabilization range is markedly higher for MCR1 (from 4.60 kJ mol−1 at the B3LYP level to 11.10 kJ mol−1 at the M06-2X level), than for MCP1 (from 0.23 kJ mol−1 at M06-HF to 0.86 kJ mol−1 at M06-2X). The stabilization effects for transition state TS1 range from −1.20 kJ mol−1 (forward activation barrier at B3LYP level) to −7.60 kJ mol−1 (reverse activation barrier at M06-HF level). The Goodson continued-fraction approximation has been used to investigate the convergence of CC energies toward FCI. When looking at the results calculated with ANO-RCC basis set (Table 1), we find the effect of cf correction is close to zero, slightly destabilizing the molecular complex from the reactant side and stabilizing the overall reaction enthalpy. The small contribution of the cf correction indicates a good convergence of the correlation treatment already at the CCSD(T) level. The compensation of the BSSE (cp correction in Table 1) including geometry relaxation is only modest, indicating that the ANORCC basis set is quite close to saturation. The activation D


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Table 2. Energy Contributions to Enthalpies at 0 and 298 K Including Spin−Orbit Corrections (kJ mol−1) Calculated at CCSD(T)/aug-cc-pV5Z//methoda/aug-cc-pVTZ Level of Theory (Thermal Corrections to Enthalpies at 298 K (ddH in kJ mol−1) in parentheses) CsO + H2 → CsOH + H (R1) forward

a

reverse

equilibrium

CsO + H2 → MCR1

CsO + H2 → TS1

CsOH + H → MCP1

CsOH + H → TS1

CsO + H2 = CsOH + H

ΔH0K

ΔH‡0K

ΔH0K

ΔH‡0K

ΔrH0K

CCSD(T)/5Z ZPE correction CCSD(T)/5Ztotalb CCSD(T)/5Ztotalb at 298 K

−6.71 +9.90 3.19

M06-HF Geometry 12.31 −0.80 −7.17 +0.23 5.15 −0.57

62.80 −7.60 55.20

−50.49 +0.43 −50.05 −50.66 (−0.61)


−6.63 +11.10 4.47

M06-2X Geometry 11.25 −0.24 −1.85 +0.86 9.41 0.62

62.56 −3.16 59.40

−51.31 +1.31 −49.99 −50.61 (−0.62)


−6.99 +4.60 −2.39

B3LYP Geometry 10.52 −1.20 9.33

−1.03 +0.76 −0.27

61.79 −1.86 59.93

−51.27 +0.66 −50.60 −51.06 (−0.46)


−9.30 +7.19 −2.11

MPW1K Geometry 11.19 −0.52 −3.45 +0.55 7.75 0.03

62.16 −4.80 57.36

−50.98 +1.35 −49.62 −50.10 (−0.48)

M06-HF, M06-2X, B3LYP, MPW1K. bTotal CCSD(T) value with the sum of individual corrections.

calculated in MP2 geometry is depicted in Figure 2. The electronic binding energies for molecular complexes, barriers,

enthalpies at 0 K for the forward and reverse reaction range between 5.2−10.1 kJ mol−1 (forward side) and 55.2−59.9 kJ mol−1 (reverse side) depending on the level of theory. Our best estimates of ΔrH°298K are −48.7 and −51.2 kJ mol−1 calculated in ANO-RCC and aug-cc-pV5Z basis sets, respectively. The calculated reaction enthalpies were compared to those evaluated from the literature standard enthalpies of formation of the species of interest (Table S6 of the Supporting Information). Using the NIST-JANAF51 values, the corresponding ΔrH°298K literature value is −104.2 ± 54.5 kJ mol−1. When the NIST-JANAF values with Cordfunke and Konings67 values are used for CsO and CsOH, the ΔrH°298K calculated literature value is −77.2 ± 13.0 kJ mol−1. Because of the scattered literature values of the standard enthalpy of formation for CsO and CsOH with large uncertainties it is hard to judge the agreement with our results. To our best knowledge there are no theoretical works studying thermodynamic properties for this reaction. Only Badawi et al.4 derived average standard enthalpies of formation for CsO and CsOH species (+18.2 and −252.6 kJ mol−1 at 298 K) from the calculated reaction enthalpies and evaluated (literature) enthalpies for the reference species using one isogyric reaction. Applying Badawi et al. values (together with our calculated SO corrections) instead those of Cordfunke and Konings, we obtain ΔrH°298K = −52.8 kJ mol−1, which is closer to our values of reaction enthalpies. 3.2. Reaction Cs + HI ↔ CsI + H. In this reaction, the TS2 structure was not located on the PES by M06-2X, B3LYP, and MPW1K functionals. Only the MP2 level of theory and M06HF functional (100% of Hartree−Fock exchange) were able to locate the transition state. The potential energy profile for the Cs + HI ↔ CsI + H exothermic reaction (−31.9 kJ mol−1)

Figure 2. Potential energy profile for the Cs + HI ↔ CsI + H reaction calculated at the CCSD(T)/aug-cc-pV5Z//MP2/aug-cc-pVTZ level of theory with (black line) and without (red line) ZPE and SO corrections.

and overall reaction enthalpies ΔrH at 0 and 298 K calculated at these two levels of theory are collected in Table 3. The effect of the geometry optimization level employing either the MP2 or M06-HF method on energetics is negligibly small when looking at the overall reaction enthalpies (0.23 kJ mol−1) and the differences for the remaining stationary points on the reaction coordinate do not exceed 3 kJ mol−1. When looking at the results, we can notice significant discrepancy (∼10 kJ mol −1) between all-electron and E


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Table 3. Energy Contributions to Enthalpies at 0 and 298 K Including Spin−Orbit Corrections (kJ mol−1) Calculated at Different Levels of Theory (Continued-Fraction Estimates in Parentheses in Italic) Cs + HI → CsI + H (R2) forward

CCSD(T)/TZ CCSD(T)/QZ CCSD(T)/5Z ZPE correction SO correction CCSD(T)/TZtotala CCSD(T)/QZtotala CCSD(T)/5Ztotala CCSD(T)/5Ztotala at 298 K CCSD(T)/5Z ZPE correction SO correction CCSD(T)/5Ztotala CCSD(T)/5Ztotala at 298 K CCSD(T)/TZVPPD CCSD(T)/QZVPPD ZPE correction SO correction CCSD(T)/TZVPPDtotala CCSD(T)/QZVPPDtotala CCSD(T)/QZVPPDtotala at 298 K CCSD(T)/VTZP CCSD(T)/VQZP CCSD(T)/LARGE ZPE correction SO correction cp correction/LARGE CCSD(T)/VTZPtotala CCSD(T)/VQZPtotala CCSD(T)/LARGEtotala CCSD(T)/LARGEtotala at 298 K a

reverse

equilibrium

Cs + HI → MCR2

Cs + HI → TS2

CsI + H → MCP2

CsI + H → TS2

Cs + HI = CsI + H

ΔH0K

ΔH‡0K

ΔH0K

ΔH‡0K

ΔrH0K

CCSD(T)/aug-cc-pVnZ//MP2/aug-cc-pVTZ (n = T, Q, 5) −4.74 −1.40 −30.04 −5.06 −1.77 −30.78 −4.83 −0.76 −31.09 +0.44 −10.45 +6.20 +0.29 +0.84 −0.41 −4.01 −11.01 −24.25 −4.33 −11.38 −24.99 −4.10 −10.37 −25.30

9.28 10.25 10.74 +2.71 −1.35 10.64 11.61 12.10

−10.68 −12.02 −11.49 −13.16 +2.19 −21.65 −22.99 −22.46 −20.61 (−1.85)b

CCSD(T)/aug-cc-pVnZ//M06-HF/aug-cc-pVTZ (n = T, Q, 5) −3.56 −2.88 −28.78 +0.66 −9.76 +6.43 +0.29 +0.84 −0.41 −2.61 −11.80 −22.76

7.59 +4.65 −1.35 10.89

−10.47 −14.41 +2.19 −22.69 −20.89 (−1.80)b

CCSD(T)/def2-nZVPPD//MP2/aug-cc-pVTZ (n = T, Q) −3.07 5.00 −27.26 −4.28 −0.62 −27.62 +0.44 −10.45 +6.20 +0.29 +0.84 −0.41 −2.34 −4.61 −21.47 −3.55 −10.23 −21.83

4.74 12.82 +2.71 −1.35 6.10 14.18

0.25 −13.44 −13.16 +2.19 −10.72 −24.41 −22.56 (−1.85)b

3.99 15.20 21.34 +2.71 −1.35

0.56 −15.34 −22.66 −13.16 +2.19

5.14 (−0.20) 16.40 (−0.16) 22.55 (−0.15)

−10.32 −26.34 −33.70 −31.85

CCSD(T)/ANO-RCC//MP2/aug-cc-pVTZ −3.76 4.54 −27.31 −4.40 −0.14 −27.61 −3.67 −1.32 −25.29 +0.44 −10.45 +6.20 +0.29 +0.84 −0.41 +0.88 +2.24 −3.04 (−0.01) −5.17 (−0.11) −21.75 (−0.23) −3.71 (−0.03) −9.94 (−0.19) −22.09 (−0.28) −2.08 (−0.03) −11.14 (−0.21) −17.54 (−0.28)

(+0.09) (−0.03) (−0.07) (−1.85)b

Total CCSD(T) value with the sum of individual corrections. bThermal corrections to enthalpies at 298 K (ddH in kJ mol−1)

The addition of ZPE and spin−orbit corrections tends to destabilize the molecular complexes and the activation barrier from the reverse side, and to stabilize the activation barrier from the forward side (Figure 2). The destabilization ranges from 0.73 kJ mol−1 (MCR2 complex formation in MP2 geometry) to 6.02 kJ mol−1 (MCP2 complex formation in M06-HF geometry). The stabilization effects for the forward activation barrier −9.61 kJ mol−1 have been calculated in MP2 geometry, and −8.92 kJ mol−1 in M06-HF geometry. The effect of ZPE to the overall reaction enthalpy has a destabilization character in contrast to a stabilization character of SO effects. Goodson extrapolations to FCI (ANO-RCC basis) tend to slightly stabilize molecular complexes and transition states from the forward and reverse side. The effect of cf corrections to the overall (equilibrium) enthalpy is close to zero. The compensation of the BSSE (cp correction in Table 3) is below the required chemical accuracy threshold 4 kJ mol−1. It indicates that ANO-RCC basis set is close to saturation. The

pseudopotential calculations. In aug-cc-pVnZ series we observe convergence, which is not systematic. This can be attributed to the use of RECPs on both cesium and iodine atoms, when only the hydrogen atom is represented by all-electron basis. Moreover, the basis on cesium is not increasing systematically with the cardinal number, as it is in the case of I and H atoms. The limited choice of basis sets for cesium is thus a main obstacle in accurate predictions of small cesium-containing species. The def2-nZVPPD and ANO-RCC converge a bit slowly, yet systematically, to the correct result in comparison with experiment. There is an evident agreement in the convergence trends of the def2-nZVPPD and ANO-RCC series, but a larger basis than def2-QZVPPD would be needed for better comparison. Unfortunately, such a basis set for cesium is not available at the moment. Overall, ANO-RCCLARGE results are not fully converged yet but seem to approach best to the experimental value. F


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Table 4. Energy Contributions to Overall Reaction Enthalpies at 0 K Including Spin−Orbit Corrections (kJ mol−1) Calculated at CCSD(T)/aug-cc-pV5Z//methoda/aug-cc-pVTZ, CCSD(T)/def2-nZVPPD//MP2/aug-cc-pVTZ, and CCSD(T)/ANORCC//MP2/aug-cc-pVTZ Levels of Theory and the Conversion of Overall Reaction Enthalpies to 298 K (Last Row) (Continued-Fraction Estimates in Parentheses in Italic) CsI + H2O → CsOH + HI (R3) aug-cc-pVnZ CCSD(T)/TZ CCSD(T)/QZ CCSD(T)/5Z ZPE correction SO correction CCSD(T)/TZtotalb CCSD(T)/QZtotalb CCSD(T)/5Ztotalb CCSD(T)/5Ztotalb at 298 K

MP2

M06-HF

M06-2X

B3LYP

170.32 169.73 167.40 −11.94 −2.19 156.20 155.61 153.27 152.99

169.94 169.26 166.86 −10.55 −2.19 157.20 156.52 154.12 153.76

170.40 169.97 167.93 −11.74 −2.19 156.47 156.04 154.00 153.71

170.34 170.12 168.29 −12.98 −2.19 155.17 154.95 153.12 153.00

def2-nZVPPD MP2

a

CCSD(T)/TZVPPD CCSD(T)/QZVPPD

165.40 178.05

ZPE correction SO correction CCSD(T)/TZVPPDtotalb CCSD(T)/QZVPPDtotalb

−11.94 −2.19 151.27 163.92

CCSD(T)/QZVPPDtotalb at 298 K

163.64

MPW1K 170.31 169.89 167.76 −13.20 −2.19 154.92 154.50 152.37 152.21 ANO-RCC MP2

CCSD(T)/VTZP CCSD(T)/VQZP CCSD(T)/LARGE ZPE correction SO correction CCSD(T)/VTZPtotalb CCSD(T)/VQZPtotalb CCSD(T)/LARGEtotalb CCSD(T)/LARGEtotalb at 298 K

164.64 173.05 177.14 −11.94 −2.19 152.57 (+2.05) 161.32 (+2.40) 165.47 (+2.45) 165.19

MP2, M06-HF, M06-2X, B3LYP, MPW1K. bTotal CCSD(T) value with the sum of individual corrections.

means that all electron treatment is the most reliable methodology for cesium containing systems. 3.3. Reactions CsI + H2O ↔ CsOH + HI and CsI + OH ↔ CsOH + I. The results of these two reactions will be discussed together because no transition states have been located on the PES. Reactions that proceed without the need of exceeding activation energy belong to the reactions with no barrier in the potential energy surface between reactants and products and usually play important roles in combustion processes, in the atmosphere, and interstellar space.70 In such cases, the classical TST fails, but we are able to provide reaction enthalpies together with the considerations of the effects of all individual corrections.

activation enthalpies calculated at 0 K for the forward and reverse reaction are presented in Table 3. The results for ΔH‡0K from the forward side (∼−11 kJ mol−1) has shown that the reaction should be dictated by entropy changes. The Gibbs free energy of activation ΔG‡ has been calculated 7.1 kJ/mol at 298 K at the CCSD(T)/ANO-RCC-LARGE//MP2/aug-cc-pVTZ level of theory, showing the applicability of the TST formula. The reverse activation enthalpies have been calculated from 10.9 to 22.6 kJ mol−1 depending on the level of theory used. The reaction enthalpies have been compared with the experimental values evaluated using the literature standard enthalpies of formation from Table S6 of the Supporting Information. Our best calculated ΔrH°298K is −31.9 kJ mol−1 in the ANO-RCC basis set. Using the NIST-JANAF51 values in combination with Cordfunke and Konings CsI data,67 the corresponding ΔrH°298K literature values are −40.7 ± 3.4 or −39.2 ± 3.4 kJ mol−1. When using the value for CsI molecule from Roki et al.,68 we obtain similar ΔrH°298K literature values −39.7 ± 3.1 or −38.2 ± 3.1 kJ mol−1, respectively. And finally using the NIST-JANAF values with the value for CsI from Glushko et al.,69 we obtain ΔrH°298K literature values −38.7 ± 4.3 and −37.2 ± 4.3 kJ mol−1. There are no theoretical works studying thermodynamic properties of this reaction; only Badawi et al.4 derived average standard enthalpy of formation for CsI molecule (−136.0 kJ mol−1 at 298 K). As in the first reaction, we used this value for CsI molecule together with those from NIST-JANAF and calculated the reaction enthalpies ΔrH°298K −22.4 ± 1.3 and −20.9 ± 1.3 kJ mol−1. These values are close to our calculated ΔrH°298K with aug-cc-pVnZ and def2-nZVPPD basis sets. With the ANO-RCC results we are close to the experiment (considering the uncertainties) which

CsI + H 2O ↔ CsOH + HI

The overall reaction enthalpies ΔrH at 0 and 289 K calculated at different levels of theory are collected in Table 4. The reaction is strongly endothermic (165.2 kJ mol−1). As in the previous reaction (R2), we observe discrepancies (∼10 kJ mol−1 ) between all-electron basis and pseudopotential calculation. The calculation with the aug-cc-pVnZ series converges in the opposite direction compared to those performed with the def2-nZVPPD and ANO-RCC series. In the def2-nZVPPD and ANO-RCC series, we observed relatively slow convergence but in the direction toward experiment. The contribution of ZPE and spin−orbit corrections to the reaction enthalpies is negative; this effect oscillates between 14 and 15 kJ mol−1. The spin−orbit correction value to the overall enthalpy has been calculated to be −2.2 kJ mol−1. The cf correction contribution to the overall reaction enthalpies is positive when looking at the results with ANO-RCC basis set (∼2.4 kJ mol−1). G


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Table 5. Energy Contributions to Overall Reaction Enthalpies at 0 K Including Spin−Orbit Corrections (kJ mol−1) Calculated at CCSD(T)/aug-cc-pV5Z//methoda/aug-cc-pVTZ, CCSD(T)/def2-nZVPPD//MP2/aug-cc-pVTZ, and CCSD(T)/ANORCC//MP2/aug-cc-pVTZ Levels of Theory and the Conversion of Overall Reaction Enthalpies to 298 K (Last Row) (Continued-Fraction Estimates in Parentheses in Italic) CsI + OH → CsOH + I (R4) aug-cc-pVnZ CCSD(T)/TZ CCSD(T)/QZ CCSD(T)/5Z ZPE correction SO correction CCSD(T)/TZtotalb CCSD(T)/QZtotalb CCSD(T)/5Ztotalb CCSD(T)/5Ztotalb at 298 K

MP2

M06-HF

M06-2X

B3LYP

−10.20 −5.97 −5.22 +6.16 −29.40 −33.43 −29.21 −28.46 −29.97

−10.10 −6.07 −5.34 +6.95 −29.40 −32.55 −28.52 −27.79 −29.38

−9.92 −5.91 −5.24 +6.82 −29.40 −32.49 −28.49 −27.82 −29.34

−10.22 −6.17 −5.51 +6.24 −29.40 −33.37 −29.33 −28.67 −30.02

def2-nZVPPD MP2

a

CCSD(T)/TZVPPD CCSD(T)/QZVPPD

−15.84 −4.48

ZPE correction SO correction CCSD(T)/TZVPPDtotalb CCSD(T)/QZVPPDtotalb

+6.16 −29.40 −39.08 −27.72

CCSD(T)/QZVPPDtotalb at 298 K

−29.23

MPW1K −9.69 −5.70 −5.05 +6.30 −29.40 −32.79 −28.80 −28.15 −29.55 ANO-RCC MP2

CCSD(T)/VTZP CCSD(T)/VQZP CCSD(T)/LARGE ZPE correction SO correction CCSD(T)/VTZPtotalb CCSD(T)/VQZPtotalb CCSD(T)/LARGEtotalb CCSD(T)/LARGEtotalb at 298 K

−13.91 −11.19 −8.43 +6.16 −29.40 −36.03 (+1.12) −33.08 (+1.35) −30.28 (+1.39) −31.79

MP2, M06-HF, M06-2X, B3LYP, MPW1K. bTotal CCSD(T) value with the sum of individual corrections.

contribution to the overall reaction enthalpy is oscillating around 1.3 kJ mol−1. Our calculated ΔrH°298K (−31.8 kJ mol−1 with ANO-RCC, −30.0 kJ mol−1 with aug-cc-pV5Z, and −29.2 kJ mol−1 with def2-QZVPPD basis) have been compared with the literature values obtained from the standard enthalpies of formation of the species of interest (Table S6 of the Supporting Information). When using the NIST51,22 values in combination with Cordfunke and Konings CsI value,67 we find the corresponding ΔrH°298K literature value to be −35.7 ± 14.9 kJ mol−1. Since the uncertainty for the CsOH molecule is quite large from the NIST database, we used the Cordfunke and Konings value also for the CsOH molecule and obtained the value −33.3 ± 5.3 kJ mol−1. When using NIST values for I and OH, Gurvich et al.71 for CsOH, and Glushko et al.69 for CsI molecules, we obtained −34.3 ± 8.2 kJ mol−1. When using the combination of the NIST values with Cordfunke and Konings (CsOH) and Roki et al.68 (CsI), we evaluated the reaction enthalpy to be −34.3 ± 5.0 kJ mol−1. Our calculated results agree well with experiment, considering the experimental uncertainties. 3.4. Rate Constants for CsO + H2 ↔ CsOH + H and Cs + HI ↔ CsI + H. The calculations of the rate constant over the temperature range 250−2500 K have been performed at the CCSD(T)/ANO-RCC-Large//MP2/aug-cc-pVTZ level of theory including all necessary corrections (ZPE, SO, cf, cp) using both direct and complex mechanisms as discussed in section 2. Their evolutions as a function of the temperature are plotted in Figure 3. The values calculated at three different temperatures (750, 1000, and 1500 K) are listed in Table 6. Rate constants calculated using the one-step mechanism are close to these calculated with the complex mechanism.

The reaction enthalpies have been also calculated using the literature standard enthalpies of formation of the species of interest (Table S6 of the Supporting Information). Using the NIST-JANAF51 values in combination with Cordfunke and Konings67 for the CsI molecule, the corresponding ΔrH°298K literature value is 163.1 ± 15.0 kJ mol−1. When using the NISTJANAF values in combination with Cordfunke and Konings for CsI and CsOH molecules, we obtain 165.5 ± 5.4 kJ mol−1. When using the NIST-JANAF values with Roki et al.68 (CsI molecule) and Cordfunke and Konings (CsOH molecule), we obtain the value 164.5 ± 4.9 kJ mol−1. With the remaining experimental values, we obtained similar results. Compared with our calculated ΔrH°298K (165.2 kJ mol−1 with ANO-RCCLARGE basis and 163.6 kJ mol−1 with def2-QZVPPD basis), the results are in very good agreement with the experimental values. CsI + OH ↔ CsOH + I

The reaction enthalpies ΔrH at 0 and 298 K are collected in Table 5. Comparison of all electron and pseudopotential basis sets shows good agreement for this exothermic reaction (−31.8 kJ mol−1). The effect of ZPE corrections to the overall reaction enthalpies is positive whereas the effect of spin−orbit corrections is strongly negative. As shown in Table 5, there is a dominant contribution of SO correction (−29.4 kJ mol−1) to the overall ΔrH coming from the SO effect of iodine atom (−30.3 kJ mol−1). Without inclusion of SO correction we would never approach the experimental ΔrH value. This proves the fact that it is necessary to investigate the effect of spin− orbit coupling when dealing with heavy atoms. The addition of the cf correction behaves similarly as in reaction R3. Its H


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estimated the activation energy of reaction R2 by using the semiempirical rule developed by Otozai.72 As shown in Table 6, our calculated values are larger than those found in the literature, showing that this reaction proceeds very fast. Reactions R3 and R4 are barrierless, so we can consider they are fast and limited by the diffusion.

4. CONCLUSIONS The gas-phase reactivity of four elemental reactions containing cesium and iodine species has been studied using ab initio and DFT methods. The stationary points on each reaction profile were optimized using the MP2 method and four DFT functionals (M06-HF, M06-2X, B3LYP, MPW1K). Singlepoint calculations have been performed using the CCSD(T) level with three series of basis sets: aug-cc-pVnZ (n = T, Q and 5), def2-nZVPPD (n = T, Q) with RECPs for both iodine and cesium atoms; and all-electron ANO-RCC with three types of contractions (T, Q, and LARGE) with all necessary corrections (ZPE, SO, cf) to obtain the suitable methodology. The rate constant calculations over the temperature range 250−2500 K have been performed at the CCSD(T)/ANO-RCC-LARGE// MP2/aug-cc-pVTZ level of theory and fitted with a modified three-parameter Arrhenius expression. From a general point of view, these cesium reactions are fast and kinetic limitations should be restricted; thermochemical equilibrium should provide good speciation for a cesium−iodine−steam−hydrogen mixture but it has to be confirmed by experiment. In details, conclusions from the results should be revealed as following: (i) Pseudopotential basis sets must be used with caution for small diatomic systems containing cesium and the results should be verified by all-electron calculations. A limited choice of large basis sets for cesium brings restriction in accurate predictions of small cesium containing species. With RECPs, there is no systematically increasing basis set for cesium causing convergence problems in aug-ccpVnZ series. In def2 series, there is no larger basis than def2-QZVPPD, which makes it difficult to follow the convergence trends. The all-electron ANO-RCC series seems to be well balanced and large enough for studied systems, but their use is limited by the size of the system. Because of these limitations, discrepancies between the all-electron basis and pseudopotential calculation have been observed. (ii) Only the results obtained from all-electron calculations can be properly extrapolated to the full configuration interaction limit using the Goodson’s extrapolation formula. The cf correction is artificially overestimated when RECPs are used and worsens the overall energies. (iii) SO effects are very important when dealing with heavy elements iodine and cesium. The most important

Figure 3. Temperature dependence of the rate constants of reactions R1 and R2 calculated with the two different methods (direct and complex mechanisms).

The modified three-parameter Arrhenius expressions k(T) = BTn exp(−Ea/RT) fitted to the rate constants for reactions R1 and R2 computed over the temperature range 250−2500 K are direct mechanism k (in cm3 molecule−1 s−1) = 2.02 × 10−20T 2.89 exp(260/T ) (R1) −1 −1

3

k (in cm molecule

−14 1.56

s ) = 1.55 × 10

T

exp(1440/T ) (R2)

complex mechanism k (in cm3 molecule−1 s−1) = 1.33 × 10−20T 2.94 exp(240/T ) (R1)

k (in cm3 molecule−1 s−1) = 1.55 × 10−14T1.56 exp(1335/T ) (R2)

As can be seen from the above equations, the slopes of the predicted Arrhenius plots for both reactions show a nonArrhenius behavior over the studied temperature range. This phenomenon is much more marked for the reaction of the Cs atom with the HI molecule (R2). In the literature, to our knowledge, there are no experimental data available concerning rate constants for reactions R1 and R2. For reaction R2 the rate constants calculated in this work can be compared with some rough estimation performed earlier.7,9 Burón and Fernández

Table 6. Rate Constantsa (cm3 molecule−1 s−1) Calculated at the CCSD(T)/ANO-RCC-LARGE//MP2/aug-cc-pVTZ Level of Theory Including All Corrections (ZPE, SO, cf, cp) at 750, 1000, and 1500 K for the Reactions CsO + H2 → CsOH + H (R1) and Cs + HI → CsI + H (R2) (Comparison with Available Literature Data) k (750 K)

reaction R1 R2

a

5.8 2.8 8.8 9.2

× × × ×

10−12 (5.2 × 10−12) 10−9 (3.2 × 10−9) 10−12 10−11

k (1000 K) 1.2 2.8 2.0 2.7

× × × ×

k (1500 K)

10−11 (1.1 × 10−11) 10−9 (3.1 × 10−9) 10−11 10−10

3.6 3.4 5.1 9.5

× × × ×

10−11 (3.4 × 10−11) 10−9 (3.6 × 10−9) 10−11 10−10

ref this work this work Wren7 Burón and Fernandez9

Values calculated with the complex mechanism are in parentheses. I


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The Journal of Physical Chemistry A contribution of the SO effect (−29.4 kJ mol−1) to the overall ΔrH has been observed in the last reaction CsI + OH ↔ CsOH + I (R4). The spin−orbit effect of the iodine atom (−30.3 kJ mol−1) at the product side lowers the overall enthalpy significantly. Without the inclusion of SO correction in this reaction we would never approach the experimental ΔrH value. (iv) The reaction CsO + H2 ↔ CsOH + H (R1) was calculated to be exothermic characterized by relatively small forward activation enthalpies (10.1 and 8.9 kJ mol−1 with ANO-RCC and aug-cc-pV5Z basis sets, respectively). Our best estimates of the overall reaction enthalpy ΔrH°298K are −48.7 kJ and −51.2 kJ mol−1 with the ANO-RCC and aug-cc-pV5Z basis sets, respectively. (v) The reaction Cs + HI ↔ CsI + H (R2) was calculated to be exothermic (ΔrH°298K −31.9 kJ mol−1 in ANO-RCC basis). The activation enthalpy from the reactant side (∼−11 kJ mol−1) shows that the reaction should be dictated by entropy changes. The Gibbs free energy of activation is calculated 7.1 kJ mol−1. (vi) The reaction CsI + H2O ↔ CsOH + HI (R3) is endothermic (ΔrH°298K = 165.2 kJ mol−1 with the ANORCC-LARGE basis set) whereas the reaction CsI + OH ↔ CsOH + I (R4) is exothermic (ΔrH°298K = −31.8 kJ mol−1 with the ANO-RCC-LARGE basis set). Both reactions proceed without the transition state. (vii) Rate constants calculated using the direct mechanism are close to these calculated with the complex mechanism. The calculated values for reaction R2 are larger when compared with available literature data showing that the reaction goes very fast. The barrierless reactions R3 and R4 are considered to be fast and limited by the diffusion. Experimental tests are planned to study the reactivity between cesium and iodine in steam atmosphere along a thermal gradient tube. The thermodynamics and kinetics calculations will be performed and compared to experimental measurements.

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*Laurent Cantrel. E-mail: [email protected]. Fax: (33)320436977. Present Address #

Advanced Technologies Research Institute, Faculty of Materials Science and Technology, Slovak University of Technology in Bratislava, Hajdóczyho 1, 917 24 Trnava, Slovakia

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank for the support provided by the Slovak Grant Agency VEGA (contracts 1/0770/13 and 1/0465/15). Computer time for part of the theoretical calculations was kindly provided by the Centre de Ressources Informatiques de Haute Normandie (CRIHAN) and the Centre de Ressources Informatiques (CRI) of the University of Lille1. This work was part of the CaPPA project (Chemical and Physical Properties of the Atmosphere), which is funded by the French National Research Agency (ANR) through the PIA (Programme d’Investissement d’Avenir) under contract “ANR-11-LABX-0005-01″ and by the Regional Council “ Nord-Pas de Calais ≫ and the “European Funds for Regional Economic Development (FEDER). The authors thank also S. Souvi (IRSN, St Paul Lez Durance, France) for fruitful discussions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b05548. Optimized geometry parameters for reactants and products at different levels of theory (Table S1), calculated unscaled vibrational frequencies for reactants and products at different levels of theory (Table S2), optimized Cartesian coordinates for transition states and molecular complexes at different levels of theory (Table S3), calculated unscaled vibrational frequencies for transition states and molecular complexes at different levels of theory (Table S4), spin-orbit corrections (Table S5), enthalpies (Table S6), discussions of geometries and vibrational frequencies, optimized structural parameters for TSs and molecular complexes calculated at different levels of theory and corresponding imaginary harmonic vibrational frequencies for reactions R1 and R2 (Tables S7 and S8), scaling factors (Table S9). (PDF)

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REFERENCES

(1) Canneaux, S.; Xerri, B.; Louis, F.; Cantrel, L. Theoretical Study of the Gas-Phase Reactions of Iodine Atoms (2P3/2) with H2, H2O, HI, and OH. J. Phys. Chem. A 2010, 114 (34), 9270−9288. (2) Hammaecher, C.; Canneaux, S.; Louis, F.; Cantrel, L. A Theoretical Study of the H-Abstraction Reactions from HOI by Moist Air Radiolytic Products (H, OH, and O (3P)) and Iodine Atoms (2P3/2). J. Phys. Chem. A 2011, 115 (24), 6664−6674. (3) Xerri, B.; Canneaux, S.; Louis, F.; Trincal, J.; Cousin, F.; Badawi, M.; Cantrel, L. Ab Initio Calculations and Iodine Kinetic Modeling in the Reactor Coolant System of a Pressurized Water Reactor in Case of Severe Nuclear Accident. Comput. Theor. Chem. 2012, 990, 194−208. (4) Badawi, M.; Xerri, B.; Canneaux, S.; Cantrel, L.; Louis, F. Molecular Structures and Thermodynamic Properties of 12 Gaseous Cesium-containing Species of Nuclear Safety Interest: Cs2, CsH, CsO, Cs2O, CsX, and Cs2X2 (X = OH, Cl, Br, and I). J. Nucl. Mater. 2012, 420 (1−3), 452−462. (5) Grégoire, A. C.; Kalilainen, J.; Cousin, F.; Mutelle, H.; Cantrel, L.; Auvinen, A.; Haste, T.; Sobanska, S. Studies on the Role of Molybdenum on Iodine Transport in the RCS in Nuclear Severe Accident Conditions. Ann. Nucl. Energy 2015, 78, 117−129. (6) Cousin, F.; Kissane, M. P.; Girault, N. Modelling of Fissionproduct Transport in the Reactor Coolant System. Ann. Nucl. Energy 2013, 61, 135−142. (7) Wren, D. J. Kinetics of Iodine and Cesium Reactions in the Candu Reactor Primary Heat Transport System Under Accident Conditions. AECL Report 7781 Atomic Energy of Canada Ltd., 1983. (8) Cronenberg, A. W.; Osetek, D. J. Reaction Kinetics of Iodine and Cesium in Steam/Hydrogen Mixtures. Nuclear Technology 1988, 81 (3), 347−359. (9) Burón, M.; Fernández, S. Final report EUR3751-88-12, Cátedra de Tecnologia Nuclear, Madrid, 1990. (10) Møller, C.; Plesset, M. S. Note on an Approximation Treatment for Many-Electron Systems. Phys. Rev. 1934, 46, 618−622. (11) Bartlett, R. J.; Stanton, J. F. Applications of Post-Hartree-Fock Methods: A Tutorial. In Reviews in Computational Chemistry; John Wiley & Sons, Inc.: New York, 2007; pp 65−169. (12) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic-Behavior. Phys. Rev. A: At., Mol., Opt. Phys. 1988, 38 (6), 3098−3100.

AUTHOR INFORMATION

Corresponding Authors

*Katarı ́na Šulková. E-mail: [email protected]. Tel: +421 906 068 735. J


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The Journal of Physical Chemistry A (13) Lee, C. T.; Yang, W. T.; Parr, R. G. Development of the ColleSalvetti Correlation-Energy Formula into a Functional of the ElectronDensity. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37 (2), 785− 789. (14) Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. Adiabatic Connection for Kinetics. J. Phys. Chem. A 2000, 104 (21), 4811−4815. (15) Zhao, Y.; Truhlar, D. G. A New Local Density Functional for Main-Group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions. J. Chem. Phys. 2006, 125 (19), 194101. (16) Zhao, Y.; Truhlar, D. G. The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06 Functionals and 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. (17) Zhao, Y.; Truhlar, D. G. Density Functional for Spectroscopy: No Long-Range Self-Interaction Error, Good Performance for Rydberg and Charge-Transfer States, and Better Performance on Average than B3LYP for Ground States. J. Phys. Chem. A 2006, 110 (49), 13126−13130. (18) Dunning, T. H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron Through Neon and Hydrogen. J. Chem. Phys. 1989, 90 (2), 1007−1023. (19) Peterson, K. A.; Shepler, B. C.; Figgen, D.; Stoll, H. On the Spectroscopic and Thermochemical Properties of ClO, BrO, IO, and Their Anions. J. Phys. Chem. A 2006, 110 (51), 13877−13883. (20) Lim, I. S.; Schwerdtfeger, P.; Metz, B.; Stoll, H. All-Electron and Relativistic Pseudopotential Studies for the Group 1 Element Polarizabilities from K to Element 119. J. Chem. Phys. 2005, 122 (10), 104103. (21) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; et al. Gaussian 09, Revision B.01; Gaussian, Inc.: Wallingford, CT, 2009. (22) Johnson, R. D., III. Computational Chemistry Comparison and Benchmark Database; StandardReference Database Number 101, Release 16a; NIST: Gaithersburg, MD, August 2013. (23) Gonzalez, C.; Schlegel, H. B. An Improved Algorithm for Reaction Path Following. J. Chem. Phys. 1989, 90 (4), 2154−2161. (24) Gonzalez, C.; Schlegel, H. B. Reaction Path Following in MassWeighted Internal Coordinates. J. Phys. Chem. 1990, 94 (14), 5523− 5527. (25) Seeger, R.; Pople, J. A. Self-consistent Molecular Orbital Methods. XVIII. Constraints and Stability in Hartree−Fock theory. J. Chem. Phys. 1977, 66 (7), 3045−3050. (26) Bauernschmitt, R.; Ahlrichs, R. Stability Analysis for Solutions of the Closed Shell Kohn−Sham Equation. J. Chem. Phys. 1996, 104 (22), 9047−9052. (27) Purvis, G. D.; Bartlett, R. J. A Full Coupled-Cluster Singles and Doubles Model: The Inclusion of Disconnected Triples. J. Chem. Phys. 1982, 76, 1910. (28) Pople, J. A.; Head-Gordon, M.; Raghavachari, K. Quadratic Configuration Interaction. A General Technique for Determining Electron Correlation Energies. J. Chem. Phys. 1987, 87 (10), 5968− 5975. (29) Halkier, A.; Helgaker, T.; Jørgensen, P.; Klopper, W.; Koch, H.; Olsen, J.; Wilson, A. K. Basis-Set Convergence in Correlated Calculations on Ne, N2, and H2O. Chem. Phys. Lett. 1998, 286 (3− 4), 243−252. (30) Peterson, K. A.; Woon, D. E.; Dunning, T. H., Jr. Benchmark Calculations with Correlated Molecular Wave Functions. IV. The Classical Barrier Height of the H+H2– > H2+H Reaction. J. Chem. Phys. 1994, 100 (10), 7410−7415. (31) Lee, T. J.; Taylor, P. R. A Diagnostic for Determining the Quality of Single-Reference Electron Correlation Methods. Int. J. Quantum Chem. 1989, 36 (S23), 199−207. (32) Rienstra-Kiracofe, J. C.; Allen, W. D.; Schaefer, H. F. The C2H5+O2 Reaction Mechanism: High-Level Ab Initio Characterizations. J. Phys. Chem. A 2000, 104 (44), 9823−9840.

(33) Zhang, Y.; Zhang, W.; Zhang, T. L.; Tian, W. X.; Wang, W. L. A Computational Study on the Reaction Mechanism of C2H5S with HO2. Comput. Theor. Chem. 2012, 994, 65−72. (34) Aquilante, F.; Vico, L. D.; Ferre, N.; Ghigo, G.; Malmqvist, P. A.; Neogrady, P.; et al. Software News and Update MOLCAS 7: The Next Generation. J. Comput. Chem. 2010, 31 (1), 224−247. (35) Šulková, K.; Šulka, M.; Louis, F.; Neogrády, P. Atmospheric Reactivity of CH2ICl with OH Radicals: High-Level OVOS CCSD(T) Calculations for the X-Abstraction Pathways (X = H, Cl, or I). J. Phys. Chem. A 2013, 117 (4), 771−782. (36) Roos, B. O.; Lindh, R.; Malmqvist, P.; Veryazov, V.; Widmark, P. Main Group Atoms and Dimers Studied with a New Relativistic ANO Basis Set. J. Phys. Chem. A 2004, 108 (15), 2851−2858. (37) Boys, S. F.; Bernardi, F. The Calculation of Small Molecular Interactions by the Differences of Separate Total Energies. Some Procedures with Reduced Errors. Mol. Phys. 1970, 19 (4), 553−566. (38) Chalasinski, G.; Szczesniak, M. M. Origins of Structure and Energetics of van der Waals Clusters from ab Initio Calculations. Chem. Rev. 1994, 94 (7), 1723−1765. (39) Xantheas, S. S. On the Importance of the Fragment Relaxation Energy Terms in the Estimation of the Basis Set Superposition Error Correction to the Intermolecular Interaction Energy. J. Chem. Phys. 1996, 104 (21), 8821−8824. (40) Lendvay, G.; Mayer, I. Some Difficulties in Computing BSSEcorrected Potential Surfaces of Chemical Reactions. Chem. Phys. Lett. 1998, 297 (5−6), 365−373. (41) Goodson, D. Z. Extrapolating the Coupled-cluster Sequence Toward the Full Configuration-interaction Limit. J. Chem. Phys. 2002, 116, 6948−6956. (42) Jasper, A. W.; Klippenstein, S. J.; Harding, L. B. The Effect of Spin−Orbit Splitting on the Association Kinetics of Barrierless Halogen Atom−Hydrocarbon Radical Reactions. J. Phys. Chem. A 2010, 114 (18), 5759−5768. (43) Mečiarová, K.; Cantrel, L.; Č ernušaḱ , I. Thermodynamic Data of Iodine Reactions Calculated by Quantum Chemistry. Training Set of Molecules. Collect. Czech. Chem. Commun. 2008, 73, 1340−1356. (44) Louis, F.; Č ernuša ḱ , I.; Canneaux, S.; Mečiarová, K. Atmospheric Reactivity of CH3I and CH2I2 with OH Radicals: A Comparative Study of the H- versus I-Abstraction. Comput. Theor. Chem. 2011, 965 (2−3), 275−284. (45) Šulka, M.; Šulková, K.; Louis, F.; Neogrády, P.; Č ernušaḱ , I. A Theoretical Study of the X-Abstraction Reactions (X = H, Br, or I) from CH2IBr by OH Radicals: Implications for Atmospheric Chemistry. Z. Phys. Chem. 2013, 227, 1337−1359. (46) Šulková, K.; Federič, J.; Louis, F.; Cantrel, L.; Demovič, L.; Č ernušaḱ , I. Thermochemistry of Small Iodine Species. Phys. Scr. 2013, 88 (5), 058304. (47) Mečiarová, K.; Šulka, M.; Canneaux, S.; Louis, F.; Č ernušaḱ , I. A Theoretical Study of the Kinetics of the Forward and Reverse Reactions HI+CH3 = I+CH4. Chem. Phys. Lett. 2011, 517 (4−6), 149− 154. (48) Roos, B. O.; Malmqvist, P. Relativistic Quantum Chemistry: The Multiconfigurational Approach. Phys. Chem. Chem. Phys. 2004, 6 (11), 2919−2927. (49) Huber, K. P.; Herzberg, G. Molecular Spectra And Molecular Structure. IV. Constants of Diatomic Molecules; Van Nostrand Reinhold: New York, 1979. (50) Hess, B. A.; Buenker, R. J.; Marian, C. M.; Peyerimhoff, S. D. Investigation of Electron Correlation on the Theoretical Prediction of Zero-Field Splittings of 2Π Molecular States. Chem. Phys. Lett. 1982, 89 (6), 459−462. (51) Chase, M. W. NIST-JANAF Thermochemical Tables.Journal of Physical and Chemical Reference Data, Monograph (9), 1998. (52) Feller, D.; Peterson, K. A.; de Jong, W. A.; Dixon, D. A. Performance of Coupled Cluster Theory in Thermochemical Calculations of Small Halogenated Compounds. J. Chem. Phys. 2003, 118, 3510−3522. (53) Berkowitz, J.; Dehmer, J. L.; Walker, T. E. H. PES of Hightemperature Vapors. IV. The Cesium Halides. Effect of Spin-orbit K


Article

The Journal of Physical Chemistry A Interaction on the Photoelectron and Mass Spectra of the Alkali Halides. J. Chem. Phys. 1973, 59 (7), 3645−3653. (54) Hirota, E. Recent Progress in High-Resolution Spectroscopic Studies on Transient Molecules. Bull. Chem. Soc. Jpn. 1995, 68 (1), 1− 16. (55) Kurosaki, Y.; Matsuoka, L.; Yokoyama, K.; Yokoyama, A. Ab Initio Study on the Ground and Low-lying Excited States of Cesium Iodide (CsI). J. Chem. Phys. 2008, 128 (2), 024301. (56) Kurosaki, Y.; Yokoyama, K. Ab Initio Study on the Low-lying Potential Energy Curves of the Diatomic Cesium Iodide Cation (CsI+). Comput. Theor. Chem. 2012, 999, 239−245. (57) Alekseyev, A. B.; Buenker, R. J.; Liebermann, H.-P.; Hirsch, G. Spin-orbit Configuration Interaction Study of the Potential Energy Curves and Radiative Lifetimes of the Low-lying States of Bismuth Hydride. J. Chem. Phys. 1994, 100 (4), 2989−3001. (58) Lee, E. P. F.; Lozeille, J.; Soldan, P.; Daire, S. E.; Dyke, J. M.; Wright, T. G. An Ab Initio Study of RbO, CsO and FrO (X2Σ+; A2Π) and their cations (X3Σ−; A3Π). Phys. Chem. Chem. Phys. 2001, 3, 4863−4869. (59) Langhoff, S. R.; Bauschlicher, C. W.; Partridge, H. Theoretical Study of the Diatomic Alkali and Alkaline-earth Oxides. J. Chem. Phys. 1986, 84 (8), 4474−4480. (60) Buenker, R. J.; Liebermann, H.-P. Configuration Interaction Calculations of Potential Curves and Annihilation Rates for Positronic Complexes of Alkali Monoxides. J. Chem. Phys. 2009, 131 (11), 114107. (61) Yamada, C.; Hirota, E. The Microwave Spectrum of the Cesium Monoxide CsO Radical. J. Chem. Phys. 1999, 111 (21), 9587−9592. (62) Hammond, G. S. A Correlation of Reaction Rates. J. Am. Chem. Soc. 1955, 77 (2), 334−338. (63) Eyring, H. The Activated Complex in Chemical Reactions. J. Chem. Phys. 1935, 3 (2), 107−115. (64) Johnston, H. S. Gas Phase Reaction Rate Theory; Ronald: New York, 1966; p 372. (65) Laidler, K. J. Theories of Chemical Reaction Rates; McGraw-Hill: New York, 1969. (66) Miyoshi, A. GPOP software; revision 2013.07.15m4, 2014. (67) Cordfunke, E. H. P.; Konings, R. J. M. Thermochemical Data for Reactor Materials and Fission Products; Elsevier: Amsterdam, 1990. (68) Roki, F.-Z.; Ohnet, M.-N.; Fillet, S.; Chatillon, C.; Nuta, I. Critical Assessment of Thermodynamic Properties of CsI Solid, Liquid and Gas Phases. J. Chem. Thermodyn. 2014, 70, 46−72. (69) Glushko, V. P.; Gurvich, L. V.; Bergman, G. A.; Veitz, I. V.; Medvedev, V. A.; Khachkuruzov, G. A.; Jungman, V. S. Thermodynamic Properties of Pure Substances; Nauka: Moscow (Russia), 1982; Vol. IV. (70) Guthrie, J. P.; Pitchko, V. Reactions of Carbocations with Water and Azide Ion: Calculation of Rate Constants from Equilibrium Constants and Distortion Energies Using No Barrier Theory. J. Phys. Org. Chem. 2004, 17 (6−7), 548−559. (71) Gurvich, L. V.; Bergman, G. A.; Gorokov, L. N.; Iorish, V. S.; Leonidov, V. Y.; Yungman, V. S. Thermodynamic Properties of Alkali Metal Hydroxides. Part II. Potassium, Rubidium, and Cesium Hydroxides. J. Phys. Chem. Ref. Data 1997, 26, 1031−1110. (72) Kume, S.; Otozai, K. Research on Activation Energy. II. Some Applications of the Empirical Rule. Bull. Chem. Soc. Jpn. 1951, 24 (6), 257−261.

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Gas-Phase Reactivity of Cesium-Containing Species by Quantum

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