A Density Functional Theory and ab Initio Investigation of the

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A DFT and Ab Initio Investigation of the Oxidation Reaction of CO by IO Radicals Sarah Khanniche, Florent Louis, Laurent Cantrel, and Ivan Cernusak J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b00047 • Publication Date (Web): 23 Feb 2016 Downloaded from http://pubs.acs.org on February 29, 2016

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The Journal of Physical Chemistry

A DFT and ab Initio Investigation of the Oxidation Reaction of CO by IO Radicals Sarah Khanniche, †, ‡ Florent Louis, *, †, ‡ Laurent Cantrel, §, ‡ Ivan Černušák# †

Univ. Lille, CNRS, UMR 8522 - PC2A - PhysicoChimie des Processus de Combustion et de

l'Atmosphère, F-59000 Lille, France #

Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius

University in Bratislava, Mlynská dolina CH1, 84215 Bratislava, Slovakia §

Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PSN-RES, Cadarache, St Paul Lez

Durance, 13115, France ‡

Laboratoire de Recherche Commun IRSN-CNRS-Lille1 "Cinétique Chimique, Combustion,

Réactivité" (C3R), Cadarache, St Paul Lez Durance, 13115, France

ACS Paragon Plus Environment

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ABSTRACT. To get an insight into the possible reactivity between iodine oxides and CO, a first step was to study the thermochemical properties and kinetic parameters of the reaction between IO and CO using theoretical chemistry tools. All stationary points involved were optimized using the Becke's three-parameter hybrid exchange functional coupled with the Lee−Yang−Parr nonlocal correlation functional (B3LYP) and the Møller−Plesset second-order perturbation theory (MP2). Single-point energy calculations were performed using the coupled cluster theory with the iterative inclusion of singles and doubles and the perturbative estimation for triple excitations (CCSD(T)) and the aug-cc-pVnZ (n=T,Q, and 5) basis sets on geometries previously optimized at the aug-cc-pVTZ level. The energetics was then recalculated using the one component DK-CCSD(T) approach with the relativistic ANO basis sets. The spin-orbit coupling for the iodine containing species was calculated a posteriori using the restricted active space state interaction method in conjunction with the multi-configurational perturbation theory (CASPT2/RASSI) employing the complete active space (CASSCF) wave function as the reference. The CCSD(T) energies were also corrected for BSSE for molecular complexes and refined with the extrapolation to CBS limit while the DK-CCSD(T) values were refined with the extrapolation to FCI. The exploration of the potential energy surface revealed a twosteps mechanism with a trans and a cis pathway. The rate constants for the direct and complex mechanism were computed as a function of temperature (250−2500 K) using the canonical transition state theory. The three-parameter Arrhenius expressions obtained for the direct and indirect mechanism at the DK-CCSD(T)-cf level of theory is: 1.49 ×10-17 × T1.77 exp (-47.4 (kJ mol-1)/RT).


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1. Introduction Behavior of iodine in the reactor coolant system (RCS) as well as in the nuclear containment building of a pressurized water reactor during a severe accident has been a topic of several experimental programs and modeling studies.1-4 Indeed,

131

I is one of the most

important radiotoxic fission products that can migrate through the RCS, into the containment and further possibly leak into the environment. Iodine can exist in gaseous forms such as I2 and volatile organic iodides, produced from irradiated mixtures of paint solvents and iodine.5 Once released into the containment atmosphere, the gaseous species will be subject to radiolytic reactions, resulting in their conversion into iodine oxides.6-9 Particularly, the reaction of gaseous iodine with OH radicals, O, and H atoms, whose species are formed during the water radiolysis, produces a range of intermediates such as HOI, HI, and I atoms as well as iodine monoxide IO.10 The conversion of gaseous iodine to particulate species under the influence of irradiation is also thought to occur in the atmosphere above oceans11 where it plays a significant role in the depletion of ozone from the troposphere.12-14 Volatile iodine species such as I2, CH3I, or CH2I2 are produced by marine organisms including macroalgae and phytoplankton.15,16 Following their release, these iodine-bearing molecules are photolyzed under UV‐visible light and quickly release I atoms, which are subsequently oxidized by ozone to form iodine monoxide (IO).16-18 Atmospheric chemistry12,14,19 and containment chemistry20 is complex and challenging for iodine-containing species. Besides its implication in ozone depletion cycles, IO is known to play a key role in the formation of higher iodine oxides (IxOy), which have drawn particular attention in recent studies.21,22 IxOy are involved in new particles formation relevant to both


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atmospheric science23-25 and nuclear reactor accidents6,8,9. For these two reasons, the kinetics and mechanisms of reactions involving IO26 have been studied in a number of laboratories either from experimental measurements (IO + O3,27 IO + IO and IO + NO,28,29 IO + CHCl2CF2Cl and IO + HCOOH,30 IO + ClO,31 IO + HO2,32 IO + CH3SCH3,33 IO + CH3O2, IO + CF3O2, 27 IO + NO334 ) or from theoretical calculations (IO + HO2 and IO + CH3O2,35,36 IO + CH3I,37 IO + IO and IO + OIO22). In this paper, we will investigate the reaction mechanisms of IO radicals with carbon monoxide, which is a product of the incomplete combustion of carbon-containing materials. The reactivity of iodine with CO matters also from the nuclear point of view. Indeed, the significant loss of coolant, in the hypothetical case of a core melt accident, could lead to the formation of the corium at very high temperature (T > 2500 K). This fuel containing material could eventually melt through the reactor vessel and interacts with the concrete of the containment building. The so-called Molten Corium/Concrete Interaction (MCCI) result in the release of H2 and CO gases.38 Once released, CO could reduce the iodine oxides into molecular iodine according to the following reaction IO + CO → I + CO2

(R1)

Analog reactions of halogen monoxide XO (X = F and Cl) with CO were previously reported in the literature (Table 1). The reaction with FO radicals has been studied experimentally39-41 and theoretically42,43. In 1997, Su and Francisco highlighted the mechanism of the reaction by ab initio calculations.42 It was revealed that the first step corresponds to the addition of FO to CO. In case of a trans addition, a trans-FOCO intermediate40 was produced, which dissociated to F atom and CO2. As for the cis addition, it led directly to F and CO2. The FO+CO addition


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was found to be the rate limiting step and, in 2003, Louis et al.43 computed the temperature dependence of the rate constant over the 550 - 2500 K temperature range at the QCISD(T)/augcc-pVTZ//QCISD/6-311G(d) level of theory and derived a three-parameter Arrhenius expression (see Table 1).43 Kinetic investigations of the oxidation reaction of carbon monoxide by ClO radicals are scarce.43-45 The rate expression over the atmospheric temperature range (200 - 300 K) have been evaluated by Sander et al.45 on the basis of the experimental data of Clyne and Watson44 (Table 1). In 2003, Louis et al. reported the theoretical study of the CO + ClO reaction.43 Canonical TST was used to predict the rate constants at combustion temperatures (550 2500K). The calculations predict a very unstable cis conformer that dissociates into a more stable Cl + CO2 system as a result of the cleavage Cl-O bond of the trans-ClOCO radical. It was observed that over the same temperature range, the rate constant for the ClO + CO was close to the corresponding values for the reaction FO + CO. To the best of our knowledge, there are no literature data concerning the reaction of BrO radicals with CO. As regards with the IO + CO reaction, only one experimental kinetic study can be found in the literature. Recently, Larin et al.46 employed resonance fluorescence method to estimate the rate expression (in cm3 molecule-1 s-1) as follows: k (298 - 363 K) = (1.14 ± 0.06) × 10-14 exp ((612 ± 41)/T)

(1)

At 298 K, the rate constant was equal to 8.9 × 10-14 cm3 molecule-1 s-1. According to the authors, the IO + CO reaction possibly plays a significant role in the marine atmosphere. This is rather surprising as the reported values for the analog XO + CO (X = F and Cl) reactions are small and do not seem to impact on atmospheric chemistry (Table 1). For instance, the upper


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limits to the FO + CO and ClO + CO rate constants were reported to be 4 × 10-17 and 4.4 × 10-18 cm3 molecule-1 s-1 at 300 K, which is far lower than the value of Larin et al. (8.9 × 10-14 cm3 molecule-1 s-1). Table 1. Literature Rate Parameters for the XO + CO → X + CO2 Reactions (X = F, Cl, and I)

Reactant

A 3

Ea -1 -1

(cm molecule s )

k -1

(kJ mol )

FO + CO

3.37 × 10-14

method

ref

1.25 × 10-13

900 - 1400

experimenta

39

< 4 × 10-17

300

experimentb

41

< 5 × 10-16

550

experimentb

41

550 - 2500

theoryc

43

< 2.0 × 10-15

587

experimentd

44

< 4 × 10-18

200 - 300

review

45

-1 -1

(cm molecule s )

36.92

ClO + CO

IO + CO

T (K)

3

∼ 1.0 × 10-12

> 30.76

3.98 × 10-14

43.78

550 - 2500

theoryc

43

(1.14 ± 0.06) × 10-14

-5.09

298 - 363

experimente

46

298

experimente

46

8.9 × 10-14 a

thermal/mass spectrometry. b electron beam/electron spin resonance. c QCISD(T)/aug-ccpVTZ//QCISD/6-311G(d) level of theory. d electron beam/mass spectrometry. e resonance fluorescence

Given the potential impact of the title reaction in both atmospheric and nuclear chemistry, it is important to get a reliable quantitative picture of the title reaction. In this study, density functional theory (DFT) and high-level ab initio calculations were performed in order to calculate the reaction barrier for the oxidation reaction. The energetic was used together with TST calculations to compute rate constants in the temperature range of 250 – 2500 K. This


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methodology was employed previously to probe reactivity of iodine containing species and has yield predictions within chemical accuracy.47-52 This is the first time that the reaction of IO radicals with carbon monoxide is investigated using theoretical methods. This paper is organized as follow: Section 2 provides details on the computational methods used in this work. In Section 3, the results in terms of geometrics, energetics, and kinetics are presented and discussed. Implications of the title reaction for atmospheric and nuclear chemistry are highlighted in Section 4.

2. Computational Methods DFT and ab initio calculations were performed using the Gaussian09 software package.53 Reactants, transition states (TSs), molecular complexes on either the reactants' side or the products' side (MCR and MCP, respectively), and products were fully optimized with the Becke's three-parameter hybrid functional54 (B3LYP) and the Møller−Plesset second-order perturbation theory55 (MP2). For these calculations, the augmented correlation consistent polarized triple zeta56 (aug-cc-pVTZ) basis set for C and O atoms were employed. The iodine atom was described by the aug-cc-pVTZ-PP basis set of Peterson et al.,57 which incorporates a relativistic pseudopotential that largely accounts for scalar relativistic effects in iodine (this basis set will be written without the PP term throughout the paper). Vibrational frequencies and zero-point energies (ZPE) were determined at the same level of theory as geometries. The vibrational frequency scaling factors58 (0.963 and 0.952) scaling factors were used at the B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels of theory, respectively. To confirm the connection of the transition states with minima, the reaction path was followed using intrinsic


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reaction coordinate (IRC)59-61 calculations at the B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels as implemented by default in Gaussian09. For all stationary points, single-point energy calculations (SPC) were carried out at different high levels of theory using, in each case, the previously optimized geometries. Electronic energies were obtained by employing the single and double coupled cluster theory with inclusion of a perturbative estimation for triple excitation (CCSD(T))62-65 with the aug-ccpVnZ (n = T, Q, and 5) basis sets and the aug-cc-pVnZ (n = T, Q, and 5) basis sets of Peterson et al.57 for the iodine atom. Further, in order to estimate the basis set superposition error (BSSE), which results from the finite basis set approximation, the a posteriori Boys and Bernardi66 counterpoise (cp) scheme was applied to the loosely bound pre- and post-reactive complexes (MCR and MCP). To assess the complete basis set (CBS) limit, a two-fold scheme was adopted. The Hartree−Fock energies, EHF, were extrapolated for each species using the three-point exponential formula67,68 as follows: = − (n = 3, 4, 5)

(2)

As to correlation energy, Ecorr, the two-point extrapolation of Min et al.69 was applied =

× ×

(n= 5)

(3)

where and are the resulting CBS limit for EHF and Ecorr, respectively and n refers

to the cardinal number of the correlation consistent basis set (3 = aTZ, 4 = aQZ, and 5 = a5Z). Supplementary, SPCs were also conducted using the coupled cluster theory CCSD(T) in the basis of canonical orbitals as implemented in the Molcas7.9 program.70 In this way, the secondorder spin-free Douglas-Kroll-Hess Hamiltonian was applied to calculate scalar relativistic effects within the CCSD(T).71,72 In order to reduce the spin contamination that the CCSD procedure may bring into the final wave function, a simple spin-adaptation scheme was used,


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in which only the dominant DDVV part of T2 excitation amplitudes were adapted.73 The remaining T1 excitation amplitudes were left unadapted. The denominators used for the noniterative calculation of the triples contribution to the CCSD energy were produced from the diagonal Fock matrix elements. For open shell case, the triples procedure according to Watts et al.74 was chosen. This leads to the one-component spin-adapted approach DK-CCSD(T) based on the Restricted Open-shell Hartree-Fock reference (ROHF). For CO and CO2 molecules, Cholesky Decomposition75,76 based coupled cluster method for closed shell systems was used instead. The relativistic atomic natural orbital (ANO-RCC) basis sets of Roos77,78 were employed with valence (i) triple-ζ and (ii) quadruple-ζ contractions for C, O, and I atoms: C/O[4s3p2d1f] and I[7s6p4d2f1g] for (i) and C/O[5s4p3d2f1g] and I[8s7p5d3f2g] for (ii). The iodine 4d electrons are correlated. For the sake of completeness, the potential energies were extrapolated toward the full configuration interaction (FCI) limit using the continued fraction (cf) approximation as described by Goodson.79 It is important to take spin-orbit (SO) coupling into account for the reactivity of iodinecontaining species and radicals.80,81 The spin-orbit coupling was corrected a posteriori using the restricted active space state interaction method in conjunction with the multiconfigurational perturbation theory (CASPT2/RASSI) employing the complete active space (CASSCF) wave function as a reference. These calculations were also performed with the Molcas7.9 software.70 For iodine monoxide, the active space includes 11 valence electrons in 14 orbitals. Considering the remaining species from MCR to TSs on the reaction profile, the active space contains 19 valence electrons in 14 orbitals while it was reduced down to 15 active electrons in 13 orbitals for MCP. CASSCF/CASPT2 calculations were performed separately


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for doublet and quartet multiplicities. An inclusion of the SO effects for IO radical leads to the splitting of the ground state (2Πi) between 2Π3/2 and 2Π1/2 states of 2023 and 2062 cm-1 on B3LYP and Møller−Plesset geometries, respectively. Table 2 compares the SO splitting calculated in this work with previous theoretical studies and available experimental data. In 1972, Brown et al.82 estimated the SO splitting to be 2330 cm-1 from electron resonance spectra while in 1991, it was determined by Gilles et al.83 using photoelectron spectroscopy, the splitting was equal to 2091(40) cm-1. The theoretical values reported by Roszak84 (1683 cm-1) and Peterson57 (1772 cm-1) were obtained using pseudopotential-based SO calculations. Their results obtained using a basis set of triple-zeta quality were underestimated compared to the experimental value of Gilles et al.83 In the recent work of Šulková et al.,85 the all electron relativistic ANO basis sets was utilized contracted to the large and flexible sets. The estimated spin-orbit splitting (2144 cm-1) was in good agreement with the experimental value 2091(40) cm-1.83 In the present paper, the same methodology as highlighted in Šulková et al.

85

was

adopted. The main difference with our work lies in the choice of the active space. It included nine valence electrons in 12 orbitals while in our case (eleven active electrons in 14 orbitals), the electrons of the 5s iodine atomic orbital were also implicated. The values computed in this way were found to be in excellent agreement with the experiment.83 An even better estimation was obtained when the value was computed on the ab initio geometry.


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Table 2. Literature Spin-Orbit (SO) splitting (in cm-1) values of IO ground state

References

SO splitting (cm-1)

Notes

experiment

Brown et al.82

2330

electron resonance

experiment

Gilles et al.83

2091(40)

photoelectron spectroscopy

Theory

Roszak et al.84

1683

MRCI/pseudopotential

Theory

Peterson et al.57

1775

pseudopotential

Theory

Šulková et al.85

2144

CASPT2/RASSI

Theory

This work

2062a (2023b)

CASPT2/RASSI

values computed on MP2a and B3LYPb geometries

Rate Constant Calculations The rate constant of the reaction has been calculated following two different approaches as detailed in our previous studies.51,52 The direct mechanism considers the reaction from the reactants to the products (R1) and the formation of the pre-reactive complex (MCR) is disregarded. (R1)

IO + CO → TS → I + CO2

Canonical TST86-92 was applied to calculate the temperature dependence of the rate constant for the direct mechanism, kdirect, as follows: !"#$ % = Γ % ×

'( ) *

×+

+,- )

./ )+0/ )

× exp 4−

,- ./ 0/ '( )

5

(4)

where Γ(T) indicates the transmission coefficient used for the tunneling correction at temperature T, kB, and h are Boltzmann’s constant and Planck’s constant, respectively. QIO(T), QCO(T), and QTS(T) are the total partition functions of IO, CO, and the TS at the temperature T,


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respectively. EIO, ECO, and ETS are the total energies at 0 K including the zero-point energies and spin-orbit couplings. In the complex mechanism, the formation of MCR is considered according to the following two-step mechanism (R1a-R1c) adopted by Singleton and Cvetanovic93: '6

IO + CO 78 MCR

(R1a)

'9

MCR 78 IO + CO

(R1b)

':

MCR → TS

(R1c)

The formation/dissociation equilibrium of the pre-reactive complex is fast. The overall rate constant for the indirect mechanism, kindirect, can be written as: k !"#$ T = K ?,A T × k # T

(5)

where Ka,b (= ka / kb) is the equilibrium constant between the isolated reactants and the prereactive complex MCR and kc is the rate constant for the reaction from MCR to TS. Ka,b and kc were calculated using the following relations: B?,A % = +

+C0D ) ./ )+0/ )

# % = Γ % ×

'( ) *

× exp 4 +,- )

×+

C0D )

./ E 0/ C0D '( )

× exp 4−

5

,- C0D '( )

(6) 5

(7)

where QMCR(T) is the total partition function of the pre-reactive complex at the temperature T, respectively. EMCR is the total energy at 0 K including the zero-point energy and spin-orbit coupling. The tunneling corrections Γ(T) for kdirect and kc were calculated using a 1-D unsymmetrical Eckart potential barrier.94 Herein, Γ(T) is about 1.2 at 300 K showing that tunneling is small for the studied reaction.


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For IO species, the multiplicity of the 2Π3/2 and 2Π1/2 states and the corresponding energy gap of 2062 cm-1 and 2023 cm-1 on MP2 and B3LYP geometries respectively have been explicitly included in the computation of the electronic partition function. The GPOP program95 was used to extract information from Gaussian output files, to estimate the Eckart tunneling corrections, and to do the rate constant calculations over the temperature range of interest.

3. Results and Discussion The structures of all stationary points involved in the reaction title are presented in Figure 1 together with the principal geometric parameters computed with the DFT and ab initio methods. The corresponding optimized geometrical parameters and vibrational frequencies together with the ZPE and SO corrections are given in Tables 3 and 4.


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IO

MCR

TS1trans

CO

I

trans-IOCO

TS1cis

Page 14 of 44

CO2

MCP

TS2trans

TS2cis

Figure 1. Optimized structures at the B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ (values in parentheses) levels of theory for the reactants, products, and intermediate species. The bond lengths are in Angstroms.


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Table 3. Optimized geometry parametersa for intermediate species calculated at the B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels of theory

Parameter

MCR

TS1trans

TS1cis

trans IOCO

TS2trans

1.125

1.135

_

1.178

1.169

1.169

1.170

1.139

1.141

1.152

1.184

1.174

1.177

1.170

3.045

1.862

_

1.341

1.312

1.324

1.171

3.074

1.891

2.335

1.351

1.325

1.368

1.171

1.896

1.957

_

2.037

2.141

2.099

3.651

1.879

1.932

1.898

2.000

2.062

2.010

3.657

98.8

117.7

_

125.8

134.0

133.4

179.6

100.3

115.6

168.0

126.1

136.4

130.5

179.7

109.4

121.6

_

116.4

102.4

113.6

78.4

95.2

122.1

53.5

113.1

89.4

111.0

78.2

180.0

180.0

_

180.0

180.0

130.3

179.7

180.0

180.0

-0.2

180.0

180.0

95.6

-178.1

TS2cis

MCP

r(C-O1)

r(C-O2)

r(I-O2)

θ(O2CO1)

θ(IO2C)

φ(ΙΟ2CΟ1) a

Bond lengths in Angstroms, angles in degrees; First and second row correspond to the values at the B3LYP/aug-cc-pVTZ level and MP2/aug-cc-pVTZ levels of theory, respectively.

One can notice on Figure 1 and Table 3 that the I-O bond lengths and the IOC bond angles computed at the B3LYP level are overestimated compared to the post-HF method. For example the bond length is of 2.037 and 2.141 Å in trans-IOCO and TS2trans when using the Becke’s functional whereas it is of 2.000 and 2.062 Å in the corresponding structure with the MP2 approach. A similar trend is observed for IOC angle which is of 116.4 and 113.1° in the B3LYP and MP2 trans intermediate geometry, respectively. Conversely, the C-O bonds calculated using the DFT theory are predicted to be shorter than the values obtained with MP2.


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Indeed, it is of 1.341 and 1.351 Å in the trans-IOCO structure with the respective DFT and ab initio methods. As for I-O distance, it is worth pointing out that the bond length change, which is rather small in IO or MCR (∼0.02 Å), tends to increase as the I-O bond length becomes longer as the reaction proceeds from reactants to products as shown in Table 3. For instance, these values are 0.025, 0.037, and 0.079 Å in TS1trans, trans-IOCO, and TS2trans, respectively. As shown in Table 4, the SO corrections for all stationary points have a significant impact on the calculated potential energies. The calculated SO splitting for IO radical indicate a lowering of the ground state of ~ 14 kJ mol-1. The SO correction of -30.03 kJ mol-1 for I atom (Table 4) was taken from the theoretical work of Mečiarová et al. on the HI + CH3 reaction.49 For the remaining stationary points collected in Table 4, there are no literature data available. As expected from previous work,52 the SO corrections (SOC) for molecular complexes (MCR and MCP) are close to the ones obtained for either IO reactant or I product. The SOC values obtained with the Becke’s functional and MP2 parameters/coordinates are very consistent with each other. For instance, the computed values for IO reactant and TS1trans differ by only 0.2 kJ mol-1 between DFT and wave function methods and by 1 kJ mol-1 for MCR. The highest difference observed, 1.2 kJ mol-1, arises from TS2cis as the dihedral angle differs by 35° between B3LYP and ab initio geometries. The SOC values for trans-IOCO and for TS2trans are the same as their structures are very similar. Last, the corrections computed for the postreactive complex are within chemical accuracy (± 4 kJ mol-1) with the experimental value of iodine atom.49


16

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 4. Vibrational Frequencies, Zero-Point Energy (ZPE), and Spin-Orbit (SO) Corrections for Intermediate Species Calculated at the B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels of theory Species IO

MCR

TS1trans

TS1cis

trans-IOCO

TS2trans

TS2cis

MCP

I

Vibrational Frequencies (cm-1)a

ZPE (kJ mol-1)

SO (kJ mol-1)

674

3.9

-14.2

674

3.8

-14.4

32, 53, 64, 81, 676, 2210

18.0

-14.3

15, 50, 57, 105, 665, 2110

17.1

-15.9

419i, 81, 147, 264, 615, 2106

18.6

-5.7

545i, 75, 143, 250, 714, 2086

18.9

-5.5

_

_

711i, 157, 239, 404, 810, 2016

20.7

-12.9

179, 189, 392, 731, 1067, 1833

25.4

-6.2

183, 202, 444, 794, 1083, 1844

25.9

-6.7

818i, 118, 144, 657, 812, 1910

21.1

-6.3

817i, 116, 364, 683, 1121, 1898

23.8

-5.6

709i, 89, 115, 604, 787,1889

20.2

-7.2

276i, 164, 523, 658, 955, 1896

23.9

-6.0

8, 20, 669, 673, 1369, 2393

29.6

-33.4

11, 50, 649, 658, 1326, 2389

28.9

-32.2

_

_

_

_

_

-30.049

a

First row represents B3LYP/aug-cc-pVTZ calculations, and second row MP2/aug-cc-pVTZ calculations.


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The SO corrections as a function of C…O intermolecular distance between CO and IO in relevant species are depicted in Table 5. They are compared to the IO SO corrections. As already mentioned, the SOC values for MCR are similar to that of the iodine oxide. This indicates that the presence of CO at ~ 3 Å from IO in the pre-reactive complex does not affect the splitting of the radical. Below 3 Å, the carbon monoxide was found to quench the SO interaction in the corresponding species. Indeed, as the CO approaches IO, i.e. as C...O intermolecular distance decreases, when going from top to bottom in Table 3, the SO splitting diminishes. For instance, it is of -12.9 and -5.5 kJ mol-1 in TS1cis and TS1trans MP2 structures where the respective C…O distance is of ~ 2.3 Å and ~1.9 Å. Table 5. C…O intermolecular distances against SO Corrections for relevant Species Calculated at the B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels of theory.a Species

r(C…O2)

SO (kJ mol-1)

_

-14.2

_

-14.4

3.045

-14.3

3.074

-15.9

_

_

2.335

-12.9

1.862

-5.7

1.891

-5.5

IO

MCR

TS1cis

TS1trans a

First row represents B3LYP/aug-cc-pVTZ calculations, and second row MP2/aug-cc-pVTZ calculations.


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3.1. Reaction Mechanism and Geometries. The oxidation reaction of CO by IO radicals implies two successive elementary reactions: (i) IO + CO → trans-IOCO, which is characterized by a first transition structure TS1 with a trans and a cis geometry (TS1trans & TS1cis) and (ii) trans-IOCO → I + CO2, which involves a second transition state TS2 with two possible conformations (TS2trans and TS2cis). Indeed for the formation of the O-C bond between IO and CO, post-HF calculations predict a trans and a cis pathway, whereas, despite extensive searches, results at the DFT level have shown that it happens exclusively via a trans TS1 structure. In the trans channel (Figure 2.a), the I-O bond length was found to increase while the O…C distance keeps decreasing. Two torsions of 180° occur along the cis route (Figure 2.b), from MCR to TS1cis and from TS1cis to the trans intermediate. For the cleavage of the I-O bond, both DFT and ab initio calculations predict a trans and a cis pathway. In the trans pathway (Figure 3.a), the trans-IOCO intermediate undergoes an elongation of the I-O bond up to 2.141 Å in TS2trans followed by a 50° torsion of the dihedral angle. In the cis channel (Figure 3.b), the torsion of the trans intermediate occurs first while the I-O bond distance remains roughly of the same length 2.099 Å in TS2trans.


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Page 20 of 44

(a) Trans pathway

(b) Cis pathway

Figure 2. Schematic representation of the (a) trans and the (b) cis pathway for the addition of CO to IO.


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(a) Trans pathway

(b) Cis pathway

Figure 3. Schematic representation of the (a) trans and the (b) cis pathway for the breaking of I-O bond.


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Transition states TS1: TS1trans and TS1cis The first transition state (TS1) exhibits either a 180° IOCO torsional angle (TS1trans) at all levels of theory or a 0° torsional angle (TS1cis) at the MP2 level exclusively. The intermolecular O…C bond length in TS1trans was estimated to be 1.862 and 1.891 Å using the respective hybrid functional and wave function approaches. In the case of the cis TS1 structure optimized with the Møller−Plesset method, the O…C distance increased up to 2.335 Å.

TS2: TS2trans and TS2cis The second transition state (TS2) displays either a 180° IOCO torsional angle (TS2trans) at all levels of theory or a 130° and 95° IOCO angle (TS2cis) at the DFT and MP2 levels of theory, respectively. The I-O bond, which was computed to be 2.141 in TS2trans, is shortened down to 2.099 in TS2cis. Surprisingly, the dihedral angles shown in the TS2cis structures are not equal to 0° as in a classical cis conformer. To further investigate these very features, the rotational potential energy surface (RPES) for the IOCO radical was computed at both the B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ (see Figure 4). The RPES was obtained by performing a relaxed scan starting from the trans conformer (φ = 180°) where φ was varied by 15° intervals. Both methods predict a very unstable cis conformer that dissociates into the more stable system I + CO2 as a result of the cleavage of the I-O bond. As observed in Figure 4, the decomposition occurs at 135° and 90° at the respective B3LYP and MP2 levels of theory, that are in fair consistency with the dihedral angles in the corresponding transition structure TS2cis.


22

Energy relative to the trans conformer in kJ mol

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-1

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30

25

20

15

10

5 B3LYP/aug-cc-pVTZ MP2/aug-cc-pVTZ 0 0

45

90

135

180

225

270

315

360

φ in degrees

Figure 4. Rotational potential energy surface for the IOCO radical calculated at the B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels of theory.

Molecular complexes and trans-IOCO intermediate The IRC calculations have revealed that the minimum energy pathways connect both TS1trans and TS1cis to loosely bound van der Waals IO…CO reactant complex and to the trans-IOCO intermediate and that the TS2trans and TS2cis were also connected to the trans conformer and to loosely bound van der Waals I…CO2 product complex. The structure of the prereactive complex is similar to that of TS1trans with two characteristic differences: (i) the nascent O-C bond is much shorter in the transition state than in the MCR complex (1.862 Å in TS1trans compared to 3.045 Å in MCR), (ii) the I-O bond is longer in the transition state than in the reactant complex (1.957 Å in TS1trans compared to 1.896 Å in


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Page 24 of 44

MCR). The geometry of the trans-IOCO intermediate resemble that of TS2trans besides two main distinction: (i) the emerging new bond O-C is longer in the trans intermediate (1.341 Å) than in the second transition state (1.312 Å) (ii) the I-O bond is shorter in trans conformer (2.037 Å) than in TS2trans (2.141 Å). The MCP geometry is characterized by an I…O intermolecular distance of 3.651 Å and 3.657 Å in B3LYP and MP2 geometries, respectively. 3.2. Energetics. The predicted reaction enthalpies ∆rH0K and ∆rHo298K for four levels of theory are collected in Table 6 including ZPE and SOC corrections. The results obtained indicate that the reaction is highly exothermic. Overall, the values computed on the DFT and ab initio geometries are very consistent with each other, as they only differ by 1 kJ mol-1. ∆rH0K and ∆rHo298K exhibit similar trends detailed hereafter. The corresponding literature values are of (-299.4 ± 2.8) and (-301.3 ± 2.8) kJ mol-1, respectively on the basis of ∆fHo at 0 and 298 K for IO,57 CO,96 I,96 and CO2,96 whose values are listed in the JPL Publication Evaluation Number 1745. The reaction enthalpies calculated within the CCSD(T) approach using the Dunning’s basis sets are particularly in good agreement with their literature counterparts if the experimental uncertainties are taken into consideration. The values obtained at the CCSD(T)/CBS level are slightly higher than the literature values by ~ 2 to 4 kJ mol-1 on the corresponding B3LYP and MP2 geometries. A deviation of about 10 kJ mol-1 can be observed with the thermodynamic values evaluated at the CCSD(T) and DK-CCSD(T) levels. Even if the literature uncertainties are included, the enthalpies predicted with the relativistic coupled-cluster theory remain ~ 4 kJ mol-1 lower than the experimental data. Goodson’s extrapolations recipe to FCI increases slightly the exothermicity predicted at the DK-CCSD(T) levels by ~2 kJ mol-1.


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Table 6. Reaction enthalpies at 0 and 298 K calculated in kJ mol-1 on (a) B3LYP and (b) MP2 geometries at four levels of theory including ZPE and SO corrections.

(a) B3LYP/aug-cc-pVTZ geometry CCSD(T)/aug-cc-pV5Z CCSD(T)/CBS DK-CCSD(T)/ANO-RCC-VQZP DK-CCSD(T)-cf/ANO-RCC-VQZP (b) MP2/aug-cc-pVTZ geometry CCSD(T)/aug-cc-pV5Z CCSD(T)/CBS DK-CCSD(T)/ANO-RCC-VQZP DK-CCSD(T)-cf/ANO-RCC-VQZP Literature values

∆rH0K (kJ mol-1)

∆rHo298K (kJ mol-1)

-296.7 -296.8 -306.3 -308.6

-298.8 -298.9 -308.4 -310.7

-295.3 -295.2 -305.6 -308.0 -299.4 ± 2.8

-297.4 -297.2 -307.7 -310.1 -301.3 ± 2.8

Further, the literature value for iodine monoxide at 0 and 298 K can be reevaluated on the basis on our ∆rH0K and ∆rHo298K values computed at the DK-CCSD(T)-cf/ANO-RCCVQZP//MP2/aug-cc-pVTZ level of theory in conjunction with the reliable literature values for CO,96

I,96

and

CO296.

This

leads

to

∆fH0K

(IO)

=

135.8

kJ mol-1 and ∆fHo298K (IO) = 133.8 kJ mol-1 instead of 127.2 and 125.1 kJ mol-1,57 respectively. Tables 7 and 8 gather the enthalpies at 0 K of the stationary points relative to IO + CO at different levels of theory with different basis sets including ZPE, SOC, and BSSE corrections. The BSSE corrections were computed at the CCSD(T)/aug-cc-pV5Z on either B3LYP or MP2 optimized geometries. Their values are 1.0 and 1.7 kJ mol-1 for MCR and 1.6 and 2.6 kJ mol-1 for MCP, respectively. This is rather modest and below the required chemical accuracy threshold. For each species, the relative enthalpies at 0 K are consistent when using the same single-point energy level of theory on the different geometries. For instance, the computed energies E0 for TS1trans are 47.1 and 47.8 kJ mol-1 at the respective CCSDT/aug-cc-


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pV5Z//B3LYP/aug-cc-pVTZ and CCSDT/aug-cc-pV5Z//MP2/aug-cc-pVTZ levels of theory (Table 7) and 46.7 and 46.6 kJ mol-1 at the DK-CCSD(T)/ANO-RCC-VQZP//B3LYP/aug-ccpVTZ and DK-CCSD(T)/ANO-RCC-VQZP//MP2/aug-cc-pVTZ levels (Table 8). Indeed, the computed energies do not depend on the geometry optimization.48 The biggest difference between B3LYP and ab initio geometries arises from the TS2trans structure. It is of about 7 and 13 kJ mol-1 at the CCSD(T)/aug-cc-pVTZ and DK-CCSD(T)/ANO-RCC-VTZP levels of theory, respectively. The basis set in the CCSD(T) single-point energy calculation (Table 7) can affect slightly the SPC values, depending on the species considered. The molecular complexes and the TS1trans do not seem to be sensitive to the basis sets size. For TS1cis, increasing the basis sets from aug-cc-pVTZ to aug-cc-pVQZ and then from aug-cc-pVQZ to aug-cc-pV5Z changes the values by 4.0 and 2.4 kJ mol-1, respectively. For DK-CCSD(T) calculations (Table 8), when going from ANO-RCC-VTZP to ANO-RCC-VQZP, the values for MCR, TS1trans, and MCP changes only by 1.4, 0.5, and 1.6 kJ mol-1, respectively. For TS1cis and trans-IOCO, increasing the ANO basis sets from VTZP to VQZP leads to a respective deviation of about 3 and 4 kJ mol-1. The enthalpies computed at the CCSDT(T)/CBS level (Table 7) are very close to the ones obtained with the aug-cc-pV5Z basis sets while the DK-CCSD(T)-cf approach (Table 8) tends to destabilized slightly all stationary points involved in the reaction. Overall, the results obtained at all levels of theory converged and are consistent with each other.


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Table 7. Enthalpies at 0 K in kJ mol-1 relative to IO + CO calculated at the CCSD(T)/aug-ccpVnZ (n = T, Q, and 5) and CCSD(T)/CBS levels of theory including ZPE correction, spinorbit coupling and BSSE for the molecular complexes. geometry optimization level of theory B3LYP/aug-cc-pVTZ (MP2/aug-cc-pVTZ)

Species MCR TS1trans TS1cis trans-IOCO TS2trans TS2cis MCP

SPC* level of theory CCSD(T)/ CCSD(T)/ CCSD(T)/ aug-cc-pVTZ aug-cc-pVQZ aug-cc-pV5Z -3.8 (-5.3) -3.9 (-5.3) -3.8 (-5.2) 47.1 (48.3) 47.0 (47.7) 47.1 (47.8) _ (157.6) _ (153.6) _ (151.2) -18.5 (-18.3) -20.4 (-21.0) -20.7 (-21.6) -0.2 (7.6) -0.7 (3.9) -1.5 (1.6) -0.3 (1.5) -1.0 (-0.9) -1.3 (-1.5) -304.3 (-303.3) -304.6 (-303.1) -304.2 (-302.4) *Single-Point energy Calculation.

CCSD(T)/ CBS -3.7 (-5.3) 47.1 (47.8) _ (148.6) -21.3 (-22.3) -2.6 (-1.0) -1.8 (-2.2) -304.3 (-302.4)

Table 8. Enthalpies at 0 K in kJ mol-1 relative to IO + CO calculated at the DKCCSD(T)/ANO-RCC-VnZP (n =T and Q) and DK-CCSD(T)-cf/ANO-RCC-VQZP levels of theory including ZPE corrections and spin-orbit coupling. geometry optimization level of theory B3LYP/aug-cc-pVTZ (MP2/aug-cc-pVTZ) DK-CCSD(T)/ ANO-RCC-VTZP MCR -5.8 (-6.7) TS1trans 47.2 (47.1) TS1cis _ (154.7) trans-IOCO -20.1 (-20.5) TS2trans -1.6 (11.4) TS2cis -0.3 (0.2) MCP -313.6 (-313.2) *Single-Point-energy calculation. Species

SPC* level of theory DK-CCSD(T)/ ANO-RCC-VQZP -4.4 (-5.5) 46.7 (46.6) _ (151.8) -23.7 (-24.1) -4.8 (7.6) -4.0 (-3.4) -315.2 (-314.8)

DK-CCSD(T)-cf/ ANO-RCC-VQZP -0.9 (-2.1) 49.4 (49.5) _ (153.3) -21.0 (-21.2) -2.2 (9.9) -1.2 (-0.5) -311.4 (-311.0)


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Page 28 of 44

The relative enthalpies profiles at 0 K calculated at the CCSD(T)/CBS and DK-CCSD(T)cf/ANO-RCC-VQZP levels of theory on geometries obtained using the respective B3LYP/augcc-pVTZ and MP2/aug-cc-pVTZ methods are displayed in Figures 5 and 6. The formation of the prereactive complex MCR is predicted to lay between about 4-5 and 1-2 kJ mol-1 below reactants at the respective CCSD(T)/CBS and DK-CCSD(T)-cf levels. For the trans-IOCO intermediate to be formed, the reactants has to overcome a barrier corresponding to the transition structure TS1trans, which is approximately of 47 kJ mol-1 at the CCSD(T)/CBS level and of 49.5 kJ mol-1 using the DK-CCSD(T)-cf approach. The TS1cis species with a dihedral angle φ=0° is ~ 100 kJ mol-1 higher than TS1trans. The TS1cis vibrationally adiabatic barrier (E0) is very high as MCR has to undergo a rotation of the OI…CO angle of 180° to follow the cis pathway (Figure 2a). The trans-IOCO intermediate appears to be highly stabilized (~ -20 kJ mol-1 below reactants), if one compares to the trans-ClOCO conformer which was located 1.1 kJ mol-1 above ClO + CO.43 Unlike TS1, the trans and the cis barriers for the second step (corresponding to TS2trans and TS2cis) are predicted to be very close in energy. With DFT geometries, they differ from each other by only 0.8 to 1 kJ mol-1. This can be explained by the close values of the dihedral angles in TS2trans and TS2cis (φtrans = 180° and φcis = 130°). The gap increases slightly with the ab initio structures where φcis is of 95°. It is of 1.2 kJ mol-1 at the CCSD(T)/CBS level and it increases even more (~ 10 kJ mol-1) at the DK-CCSD(T)-cf/ANORCC-VQZP level. Interestingly, it was the TS2trans configuration which was slightly more stable than the corresponding trans geometry with the DFT method while with ab initio approach, TS2cis structure is predicted to lie below TS2trans. That means that in the latter case, the cis route has a ~ 1-10 kJ mol-1 lower energy than the trans path. Regardless the method, both trans and cis channels lead to a stable I…CO2 complex (MCP) that is much lower in


28

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energy than IO + CO. MCP is approximately 300 to 310 kJ mol-1 below reactants or, in other words, 3 to 7 kJ mol-1 more stable than I + CO2 product.

Figure 5. Reaction profiles at 0 K calculated at the CCSD(T)/CBS and DK-CCSD(T)-cf/ANORCC-VQZP (first row and second row, respectively) levels of theory on geometries obtained using the B3LYP/aug-cc-pVTZ methods.


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Page 30 of 44

Figure 6. Reaction profiles at 0 K calculated at the CCSD(T)/CBS and DK-CCSD(T)-cf/ANORCC-VQZP (first row and second row, respectively) levels of theory on MP2/aug-cc-pVTZ geometries.

3.3. Kinetic parameters calculations Rate constants Given the fact that the first transition structure TS1 presents the highest energy barrier, one can assume that the overall rate of the reaction is determined by the formation of the O-C bond. As


30

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the TS1cis is located approximately 150 kJ mol-1 above reactants, the trans channel with the formation of TS1trans at 47-49.5 kJ mol-1 appears to be the most favorable pathway. The calculations of the temperature dependence of rate constants have been performed at the CCSD(T)/CBS and DK-CCSD(T)-cf/ANO-RCC-VQZP levels of theory on B3LYP/aug-ccpVTZ and MP2/aug-cc-pVTZ geometries including ZPE, SOC, and BSSE corrections for the prereactive complex. Tables 9 and 10 list the values calculated with two approaches (direct and complex mechanisms) at six different temperatures (250, 300, 400, 1000, 1500, and 2500 K). Regardless the mechanism considered, the computed rate constants range from 10-23-10-22 to 10-21 cm3 molecule-1 s-1 for 250 K and 300 K. As the temperature rises, the rate constants increase from 10-19 cm3 molecule-1 at 400 K to 10-12 cm3 molecule-1 at 2500 K. Overall, the rate constants computed at all levels of theory on DFT and post-HF geometries are very consistent with each other. Some minor differences can be highlighted though: (i) The rate constants calculated at the CCSD(T)/CBS level on B3LYP and MP2 geometries are slightly higher than the ones computed with the corresponding DK-CCSD(T)-cf energies. Indeed, at 300 K, kCCSD(T)/CBS is of 5.38 and 4.13 × 10-21 cm3 molecule-1 s-1 with the B3LYP and MP2 methods respectively while the corresponding kDK-CCSD(T)-cf is of 2.10 × 10-21 cm3 molecule-1 s-1. This can be explained by the fact that the E0 for TS1trans obtained with the DKCCSD(T)-cf approach are slightly higher than the CCSD(T)/CBS E0 (49.4 and 47.1 kJ mol-1 respectively on DFT geometry). (ii) The values of k computed using the CCSD(T) energies with the CBS limit, are slightly smaller for the MP2 optimized geometries than for the B3LYP method. For instance, at 400 K, k is equal to 6.84 × 10-19 cm3 molecule-1 s-1 at the CCSD(T)/CBS//MP2/aug-cc-pVTZ level and 7.81 × 10-19 cm3 molecule-1 s-1 at the CCSD(T)/CBS//B3LYP/aug-cc-pVTZ level. Again, this is in good agreement with the TS1trans


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Page 32 of 44

computed vibrationally adiabatic barrier which is slightly smaller for the B3LYP geometry (47.1 kJ mol-1) than for the MP2 configuration (47.8 kJ mol-1) (iii) Finally, the rate constants obtained using the DK-CCSD(T)-cf energies with the relativistic ANO basis sets on the B3LYP and MP2 optimized geometries are predicted to be very close from each other which is not very surprising as the B3LYP and ab initio TS1trans are located at the same level on the PES (49.4 and 49.5 kJ mol-1, respectively). For example, at 1000 K, kDK-CCSD(T)-cf is of 1.05 × 10-14 and 1.02 × 10-14 cm3 molecule-1 s-1 with the DFT and post-HF methods. Regarding the DK-CCSD(T)-cf approach, the presence of the prereactive complex located at either 0.9 or 2.1 kJ mol-1 below reactant does not seem to have any significant impact on the predicted rate constants.

Table 9. Rate constants for the direct mechanism in cm3 molecule-1 s-1 calculated at six different temperatures on (a) B3LYP and (b) MP2 geometries at four levels of theory including ZPE correction and spin-orbit coupling. Temperature (K) (a) B3LYP/aug-cc-pVTZ geometry

250

300

400

1000

1500

2500

1.12 ×10-22 5.38 ×10-21 7.81 ×10-19 1.35 ×10-14 1.67 ×10-13

1.70 ×10-12

DK-CCSD(T)-cf/ANO-RCC-VQZP 3.62 ×10-23 2.10 ×10-21 3.86 ×10-19 1.02 ×10-14 1.38 ×10-13

1.52 ×10-12

CCSD(T)/CBS

(b) MP2/aug-cc-pVTZ geometry CCSD(T)/CBS

250

300

400

1000

1500

2500

8.07 ×10-23 4.13 ×10-21 6.84 ×10-19 1.29 ×10-14 1.65 ×10-13 1.72 ×10-12

DK-CCSD(T)-cf/ANO-RCC-VQZP 3.58 ×10-23 2.10 ×10-21 3.90 ×10-19 1.05 ×10-14 1.44 ×10-13 1.59 ×10-12


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Table 10. Rate constants for the complex mechanism in cm3 molecule-1 s-1 calculated at six different temperatures on (a) B3LYP and (b) MP2 geometries at four levels of theory including ZPE correction, spin-orbit coupling and BSSE for MCR. Temperature (K) (a) B3LYP/aug-cc-pVTZ geometry

250

300

400

1000

1500

2500

6.91 ×10-23 3.60 ×10-21 5.78 ×10-19 1.19 ×10-14 1.54 ×10-13

1.62 ×10-12


1.52 ×10-12

CCSD(T)/CBS

(b) MP2/aug-cc-pVTZ geometry

250

300

400

1000

1500

2500

3.51 ×10-23 2.06 ×10-21 3.85 ×10-19 1.05 ×10-14 1.44 ×10-13

1.58 ×10-12


1.59 ×10-12

CCSD(T)/CBS

Arrhenius Parameters. The modified three-parameter Arrhenius expressions k(T) = A × Tn exp(-Ea/RT), which makes explicit the temperature dependence of the pre-exponential factor A, fitted to the rate constants computed at different levels of theory over the temperature range 250-2500 K are reported in Table 11. As the values obtained for the four different levels of theory are, once again, very consistent with each other, we are confident in our predicted Arrhenius parameters.


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Table 11. Arrhenius parameters for the IO + CO reaction calculated over the temperature range 250-2500 K.

direct mechanism (complex mechanism) Aa

n

Ea b

CCSD(T)/CBS

1.47 ×10-17 (1.46 ×10-17)

1.77 (1.77)

44.9 (45.9)

DK-CCSD(T)-cf/ANO-RCC-VQZP

1.47 ×10-17 (1.47 ×10-17)

1.77 (1.77)

47.3 (47.3)

Aa

n

Ea b

CCSD(T)/CBS

1.49 ×10-17 (1.49 ×10-17)

1.77 (1.77)

45.7 (47.4)

DK-CCSD(T)-cf/ANO-RCC-VQZP

1.49 ×10-17 (1.49 ×10-17)

1.77 (1.77)

47.4 (47.4)

(a) B3LYP/aug-cc-pVTZ geometry

(b) MP2/aug-cc-pVTZ geometry

a b

in cm3 molecule-1 s-1 in kJ mol-1

The k(298 K) calculated value for the rate constant is 7 orders of magnitude below the measured value determined by Larin et al.46 (1.8 × 10-21 cm3 molecule-1 s-1 vs. 8.9 × 10-14 cm3 molecule-1 s-1). If we look at the temperature dependence of the rate constant, it can be noticed that, Larin et al.46 predict a negative activation energy (-5.09 kJ mol-1). Our computations show that the activation energy for reaction of IO with CO is 47.4 kJ mol-1. This result is consistent with activation energies reported for other XO + CO reactions (X = F, Cl) (Table 1). The calculated rate constants at atmospheric temperatures (T < 300 K) indicate that the IO + CO reaction could not play an important role in the atmospheric chemistry. At the temperature of the containment building (~ 400 K), the reaction rate is of the order of 10-19 cm3 molecule-1 s-1. In case of a core melt accident where the temperature is very high and can reach 1000 and 2500 K, k increases up to 10-14 - 10-12 cm3 molecule-1 s-1.


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In the light of our results, which are consistent with other analog reactions, we will apply our methodology to study the reactivity of CO with other iodine oxides such as OIO and I2O5 for which no experimental data is available.

4. Conclusions We have performed DFT and ab initio molecular orbital computations to get an insight into the mechanism, the thermodynamics, and the kinetics of the IO + CO reaction. The geometries of the stationary points were optimized at the B3LYP/aug-cc-pVTZ and MP2/aug-cc-pVTZ levels of theory. The energetics was computed at the CCSD(T)/aug-cc-pVnZ (n = T, Q, Z) levels and with the DK-CCSD(T) method in conjunction with the relativistic ANO basis sets with triple-ζ and quadruple-ζ contractions. Spin-orbit coupling for IO and all stationary points involved were computed. The CCSD(T) energies were also corrected for BSSE for molecular complexes and refined with the extrapolation to CBS limit while the DK-CCSD(T) values were refined with the extrapolation to FCI. The title reaction was predicted to occur through two elementary processes characterized by two transition structures (TS1 and TS2) that were connected by a trans-IOCO intermediate. The first step corresponds to the formation of the O-C bond and the second results in the cleavage of the I-O bond. Each step was predicted to occur through a trans and a cis pathway. In total, the reaction involved four TSs (TS1trans, TS1cis, TS2trans and TS2cis), a trans-IOCO intermediate, an IO…CO prereactive complex, and a I…CO2 postreactive structure. The IO + CO reaction is extremely exothermic and the energetics indicates that the addition of IO to CO is the rate-determining step. Predicted rate constants based on canonical TST


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including an asymmetrical Eckart tunneling correction was computed over the temperature range 250-2500 K assuming both direct and complex mechanisms. At the DK-CCSD(T)cf/ANO-RCC-pVQZ level on MP2 geometries, the rate constant based on a modified threeparameter Arrhenius expressions was estimated to be: (k in cm3 molecule s-1) k (T) = 1.49 ×10-17 × T1.77 exp (-47.4 (kJ mol-1)/RT) The geometries obtained with the DFT and post-HF methods were consistent with each other, indicating that one can rely on B3LYP optimized geometries. This is of particular interest for several heavy atoms-containing systems which would require excessive computational cost of calculations. The hybrid functional method can represent an alternative way to the perturbation theory to efficiently handle the geometric of such heavy systems. In a near future, the chemical speciation of iodine oxides in case of nuclear severe accident will be studied by thermodynamic and kinetic simulations.

AUTHOR INFORMATION Corresponding Author *[email protected] Notes The authors declare no competing financial interest.


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ACKNOWLEDGMENT Computer time for part of the theoretical calculations was kindly provided by the Centre de Ressources Informatiques (CRI) of the University of Lille1 and the Centre de Ressources Informatiques de Haute Normandie (CRIHAN). Part of the calculations were also performed at the Computing Centre of the Slovak Academy of Sciences using the supercomputing infrastructure acquired in project ITMS 26230120002 and 26210120002 (Slovak infrastructure for high-performance computing) supported by the Research & Development Operational Programme funded by the ERDF. This work was part of the MiRE project (Mitigation of outside releases in case of nuclear accident), which is funded by the French National Research Agency (ANR) through the PIA (Programme d'Investissement d'Avenir) under contract "ANR-11-RSNR-0013-01". We appreciate also the support from PIA managed by the ANR under grant agreement "ANR-11LABX-0005-01" called CaPPA (Chemical and Physical Properties of the Atmosphere), and, also supported by the Regional Council "Nord-Pas de Calais" and the "European Funds for Regional Economic Development". The authors thank also the Slovak Grant Agency VEGA (Grant 1/0092/14). This work was performed in the frame of the international collaboration agreement between IRSN, Comenius, Lille 1, and CNRS. References (1) Girault, N.; Fiche, C.; Bujan, A.; Dienstbier, J., Towards a better understanding of iodine chemistry in RCS of nuclear reactors. Nucl. Eng. Des. 2009, 239, 1162–1170. (2) Cantrel, L.; Louis, F.; Cousin, F., Advances in mechanistic understanding of iodine behaviour in PHEBUS-FP tests with the help of ab initio calculations. Ann. Nucl. Energy 2013, 61, 170–178. (3) Chevalier-Jabet, K.; Cousin, F.; Cantrel, L.; Séropian, C., Source term assessment with ASTEC and associated uncertainty analysis using SUNSET tool. Nucl. Eng. Des. 2014, 272, 207-218.


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A Density Functional Theory and ab Initio Investigation of the

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