Thermochemistry of small iodine species

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Thermochemistry of small iodine species

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PHYSICA SCRIPTA

Phys. Scr. 88 (2013) 058304 (7pp)

doi:10.1088/0031-8949/88/05/058304

Thermochemistry of small iodine species ˇ K Sulkov´ a1,2,4 , J Federiˇc1 , F Louis3,4 , L Cantrel2,4 , L Demoviˇc1,5 and ˇ I Cernuˇ sa´ k1 1

Department of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Mlynsk´a dolina CH1, SK-84215 Bratislava, Slovakia 2 Institut de Radioprotection et de Sˆuret´e Nucl´eaire, PSN-RES, SAG, Centre de Cadarache, BP3, F-13115 Saint Paul Lez Durance Cedex, France 3 Physico Chimie des Processus de Combustion et de l’Atmosph`ere (PC2A) UMR 8522 CNRS/Lille 1, Universit´e Lille 1 Sciences et Technologies, Cit´e scientifique, Bˆat C11/C5, F-59655 Villeneuve d’Ascq Cedex, France 4 Laboratoire de Recherche Commun IRSN-CNRS-Lille1 ‘Cin´etique Chimique, Combustion, R´eactivit´e’ (C3 R), Centre de Cadarache, BP3, F-13115 Saint Paul Lez Durance Cedex, France 5 Computing Centre of the Slovak Academy of Sciences, D´ubravsk´a cesta 9, 845 35 Bratislava, Slovakia E-mail: [email protected]

Received 27 September 2013 Published 29 October 2013 Online at stacks.iop.org/PhysScr/88/058304 Abstract We present a systematic study of the thermochemistry for a set of iodine species relevant to atmospheric chemistry. The reactions include H, O and I atoms and H2 , OH, HI, I2 , iodine monoxide, hypoiodous acid (HOI) and H2 O species. The calculations presented were performed using completely renormalized coupled cluster theory including single, double and non-iterative triple substitutions in conjunction with the ANO-RCC basis sets developed for scalar relativistic calculations. The second-order spin-free Douglas–Kroll–Hess Hamiltonian was used to account for the scalar relativistic effects. The calculations also included spin–orbit corrections and semi-core correlation contributions. The resulting reaction enthalpies and Gibbs energies at 298 K have been compared with the experimental data. On the basis of a set ◦ of selected reactions we suggest an updated value for 1f H298 K of HOI based on the set of −1 isogyric reactions: −69.0 ± 3.7 kJ mol . PACS numbers: 31.15.am, 31.15.bw, 31.15.ve

ultra-fine nano-particles as a first step to cloud condensation nuclei [12–14]. HOI is supposed to be a temporary (night) reservoir product in one part of the ozone destruction cycle [15] that can later either undergo photolysis or can react with other atmospheric species (OH, HO2 ). Since HOI is a polar molecule, it is also prone to be removed from the troposphere by washout or rainout processes. Besides this, iodine-containing particles can be transported to the lower stratosphere, thereby making it possible for iodine to contribute to stratospheric ozone depletion as well [16]. There is still some uncertainty concerning the heat of formation of HOI, and this is one of the important molecules participating in iodine atmospheric chemistry. Berry et al performed a combined experimental and theoretical study ◦ of the reaction IO + CF3 I and reported 1f H298 K (HOI) = −1 −69.6 ± 5.4 kJ mol [17]. This value differs by about −1 ◦ 10 kJ mol−1 from the 1f H298 K (HOI) = −59.9 ± 6.9 kJ mol reported by Hassanzadeh and Irikura [18]. Furthermore, both

1. Introduction Iodine gas-phase chemistry has attracted the attention of both experimental and computational chemists for at least two reasons. First, iodine is one of the short-term high radioactive contaminants that can be released during an accidental break of a nuclear pressurized water-reactor (PWR) [1–4]. The potential harmfulness of 131 I arises from its ability to form volatile compounds that can escape the PWR containment [5]. In this context, it is important to know which products of possible chemical equilibria would be likely to be present in the primary circuit after the release of degraded fuel, as well as in the nuclear containment reactor itself. Second, atmospheric studies indicate the importance of iodine in the tropospheric ozone destruction [6–10]. Iodine monoxide (IO) can form ‘reservoir’ species: I2 O y (y = 2–5), IONO2 , and hypoiodous acid (HOI) [9, 11]. The formation of iodine oxides (I2 O y , y = 2–5) that can participate in the formation of 0031-8949/13/058304+07$33.00

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Phys. Scr. 88 (2013) 058304

of these values differ substantially from a previous theoretical determination by Glukhovtsev et al, which resulted in a value of −48.9 kJ mol−1 [19] and an estimate by Zhang et al of −42.7 kJ mol−1 [20]. Recently, Marshall applied the coupled cluster theory including single, double and non-iterative triple substitutions (CCSD(T)) in conjunction with the pseudopotential correlation consistent basis sets (aug-cc-pVTZ-PP and aug-cc-pVQZ-PP) to a series of bond-conserving reactions. In this type of calculation, the scalar relativistic effects are taken into account implicitly within the pseudopotential basis set. Extrapolating to the limit of the complete basis set (CBS), Marshall arrived −1 ◦ at 1f H298 [21]. Summarizing K (HOI) = −59.2 ± 5.4 kJ mol somewhat, it is fair to say that there is still quite substantial ◦ ‘dispersion’ in the 1f H298 K values for HOI published in the literature. In a series of our recent papers [22–25], we have successfully used CCSD(T) theory combined with the ANO-RCC family of relativistic all-electron basis sets [26] to calculate various thermodynamic and kinetic data related to iodine atmospheric chemistry. In these calculations, scalar relativistic effects are taken into account explicitly via the second-order spin-free Douglas–Kroll–Hess Hamiltonian [27–28]. The goal of this paper is to test the performance of the completely renormalized (CR)-CCSD(T) method in a training set of small molecules containing the heavy iodine atom, and then apply this approach to ◦ the determination of 1f H298 K (HOI) from a suitable set of chemical equilibria. So far, no published results have been presented in which the CR-CCSD(T) method is applied to iodine chemistry. This paper addresses this.

after bi-excitations (i.e. Tˆ = Tˆ1 + Tˆ2 ) leading to the so-called CCSD approximation. The corresponding CCSD equations are obtained by inserting 9CC into the Schr¨odinger equation projected by the reference function 80 and all available excitations. We note that the scaling behaviour of CCSD model is on the order of N 6 and the model including triple-excitations, CCSDT, is computationally rather demanding, scaling as N 8 (N is the number of basis functions). For this reason, there is an economical variant for the inclusion of the triple-excitations called CCSD(T). In CCSD(T), one calculates the triples contribution using the arguments borrowed from the perturbation theory and adds this contribution using all the information accumulated in the converged T1 and T2 CCSD amplitudes. Details of this so called ‘golden standard’ of computational chemistry can be found in [36–38]. Finally, we note that the method used in this paper—CR-CCSD(T)—is a variant of the CC approach, which is based on the method of moments of CC equations [39]. The key point in the completely renormalized CC method is the evaluation of the non-iterative correction that needs to be added to the conventional CCSD energy to recover the full configuration interaction result. For example, in the final energy expression for CCSD(T), the triples correction is rescaled by denominator h9| exp (T1 + T2 ) |8i that serves as a damping factor which damps large and unphysical values of perturbative triples in the case where non-dynamical electron correlation may become important [39–40]. The renormalized non-iterative corrections offer a promising way of extending the applicability of the standard corrections to a larger range of molecular geometries as documented by recent applications [41–43]. The influence of relativistic effects on chemical and physical properties of molecules becomes more important considering elements starting from the third row of the periodic table. Knowledge about these effects in the thermodynamics of related atoms and molecules is of vital importance for their chemical reactions. Relativistic effects are most important in the valence shells which can be strongly affected by kinematical relativistic effects (direct effects) and by spin–orbit (SO) coupling effects (indirect effects). The valence s and p orbitals are strongly affected by direct effects resulting in their energetic stabilization. The valence d and f electrons are energetically destabilized due to relativistic relaxation of other shells. This destabilization may lead, in turn, to an indirect stabilization of the next higher s and p shells with spatial extent similar to the d shell in question [44]. The atomic relativistic effects on excitation energies, ionization potentials and electron affinities have a direct influence on chemically relevant data, namely structure, electronic spectra and force constants of molecules. However, the rigorous relativistic theory developed originally by Dirac [45, 46] is computationally very demanding when applied to quantum chemistry problems because is describes electrons as particles with four complex numbers (four-component spinors). Douglas and Kroll [27] pointed out that this difficulty can be alleviated by a series of transformations, effectively leading to one-component (scalar) task that can be easily incorporated into existing quantum-chemistry codes and providing a very good estimate of the scalar relativistic contributions to various

2. Computational details We have employed a completely renormalized coupled cluster method—CR-CCSD(T) with the single and double excitations augmented with the non-iterative triple-excited contribution as developed by Piecuch et al [29–31] and implemented in the GAMESS-US package. This method presents a viable alternative for reactions where the multireference character (or non-dynamic correlation effects) in the reaction components may play a significant role [32], e.g. IO radical. Briefly, the original CC theory [33–35] relies on the exponential expansion of the wave function 9CC = exp (Tˆ ) 80 , where Tˆ is the excitation operator acting on a suitable reference state 80 (usually the single determinant Hartree–Fock wave function) and can be expressed using the Taylor expansion   9CC = 1 + Tˆ + Tˆ 2 /2+Tˆ 3 /3! + · · · 80 . The excitation operator comprises a sum of all possible excitation operators Tˆ = Tˆ1 + Tˆ2 + Tˆ3 + · · · . In practical applications it must truncated at a specific excitation level. A typical CC model is the one truncated 2

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molecular properties [47]. In this comment the second-order spin-free Douglas–Kroll–Hess Hamiltonian was applied in all calculations [27, 28] to account for the scalar relativistic effects. SO coupling effects are more significant for spectroscopic properties and energy separations of molecules containing heavy and very heavy atoms. The electronic structure of compound containing heavy atom is mostly characterized by a large number of electronic states. Near degeneracy between different electronic configurations and SO contaminations allow observations of electronic transitions that are forbidden in the non-relativistic picture (e.g. B 3 5u ← X 1 6g+ transition of I2 ). Various approaches can be pursued to compute SO effects [47]. All four-component methods are too expensive considering the computation time. The alternative way of how to deal with SO coupling is to use the less demanding two-component methods which are based on spin-free Hamiltonian and treat the SO coupling at the latest step. The inclusion of the SO correction is important also in studying the reactivity of iodine-containing species [23, 25, 48]. We have used the same SO corrections as calculated in our previous study [25], that was developed by Roos and Malmqvist [49]. This approach assumes that the strongest SO effects arise from the interaction of electronic states that are close in energy, and is based on the complete active space (CASSCF) wave functions as the basis states with energies improved by multiconfigurational perturbation theory (CASPT2). In the CASSCF step one selects the set of active orbitals and corresponding electrons (preferably all from the valence shells) and performs in this set-up a full configuration interaction calculation. As a rule, a series of the state-averaged CASSCF calculations is needed for a good resolution of the SO states. The SO coupling matrix elements are then calculated within the restricted active space/state interaction method (CASSCF/CASPT2/RASSI-SO) [50, 51] using a one-electron Fock-type SO Hamiltonian and represent a posteriori correction to spin-free states. For the IO radical (which was not reported in our previous paper [25]) the active space in CASSCF/ANO-RCC-large step comprised nine valence electrons in 12 orbitals. We have calculated 16 potential energy curves, eight of doublet and eight of quartet multiplicity. This was followed by CASPT2/ANO-RCC-large calculations with 23 correlated electrons [52]. The SO splitting obtained in this way is equal to 2144 cm−1 ; in excellent agreement with the experimental value 2091 cm−1 [53]. The other theoretical value reported by Peterson (1772 cm−1 ) from SO configuration interaction [54] using pseudo potentials is probably underestimated due to smaller aug-cc-pVTZ-PP basis set. For all species we have used the relativistic atomic Gaussian basis sets developed by Roos et al [26] that were derived from their predecessors of ANO family [55, 56]. This sets represent a contracted atomic orbital (AO) basis with contractions determined from relativistic atomic calculations, that is, they include the relativistic effects mentioned in previous paragraphs. In our case they were contracted to the large and flexible sets as follows: hydrogen (8s4p3d1f)/[6s4p3d1f], oxygen (14s9p4d3f2g)/[8s7p4d3f2g] and iodine (22s19p13d5f3g)/[10s9p8d5f3g], and are denoted as ANO-RCC-large. One of the advantages of the ANO-RCC

family of basis sets is that they were calibrated to accommodate the semi-core correlation effects that are important especially for iodine. CR-CCSD(T) equilibrium bond lengths (Re ), harmonic frequencies (ωe ), first anharmonicities (ωe xe ) and first coefficients of centrifugal distortion (αe ) for H2 , OH, HI, IO and I2 were determined by a sixth-order polynomial fit to at least 15 points of the potential energy curve using Dunham analysis [57]. To get the structures of HOI and H2 O including scalar relativistic effects, we optimized their geometries numerically at the DK-MP2/ANO-RCC-VQZP6 level using the MOLCAS suite [58] (including harmonic frequency check). Harmonic frequencies for HOI and H2 O were scaled by factor 0.9612 used also in our previous studies on iodine chemistry [23, 24]. These geometries were used in the final single-point energy CR-CCSD(T)/ANO-RCC-large calculations in GAMESS. We did not attempt to make any extrapolations to the CBS limit because it is not well defined within the ANO-RCC family. Nevertheless, our experience with its ‘large’ contraction of ANO-RCC indicates that the CC energies should be very close to the CBS limit [22, 24]. The thermodynamic quantities were evaluated at T = 298.15 K and p = 101 325 Pa within the rigid rotor/harmonic oscillator model, assuming ideal gas behaviour, with anharmonicity (ωe xe ) and centrifugal (αe ) corrections added for all diatomics using the EQUILI program [59]. The electronic energy levels and the corresponding degeneracy for O atom in the 3 P ground state (3 P0 , 3 P1 and 3 P2 states with 158.265 and 226.977 cm−1 splitting [60]), OH and IO radicals in their 2 5 ground state (2 53/2 and 2 51/2 with a 139.21 [61] and 2091 [53] cm−1 splitting for OH and IO, respectively) are included in the calculation of their electronic partition function. In the thermochemistry and in the subsequent evaluation of the standard enthalpy of formation at 298 K for HOI, we have considered the following set of chemical equilibria: (1) I + OH = HOI,

6

HI + OH = I + H2 O,

(2)

HI + HOI = I2 +H2 O,

(3)

IO + H = HOI,

(4)

IO + H = I + OH,

(5)

IO + H2 = HI + OH,

(6)

IO + HI = I2 + OH,

(7)

IO + HI = I + HOI,

(8)

I2 + H = I + HI,

(9)

Douglas–Kroll with the Moller–Plesset second-order perturbation theory using ANO-RCC quadruple-zeta contracted basis set.

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Table 4. Thermochemistry of small iodine speciesa (1r H and 1r G in kJ mol−1 , 1r S in kJ mol−1 K−1 , experimental data in italics taken from the COACH database [71]) with 1f H298 K (HOI) = −59.2 kJ mol−1 .

Table 1. Literature standard enthalpies of formation at 298 K (kJ mol−1 ). ◦ 1f H298 K

Species

Reference

H 217.999 ± 0.006 O(3 P) 249.17 ± 0.10 I(2 P3/2 ) 106.76 ± 0.04 OH 38.987 ± 1.21 HI 26.5 ± 0.10 IO 125.1 ± 2.5 I2 62.42 ± 0.08 H2 O −241.826 ± 0.042 Recently proposed value for: HOI −59.2 ± 3.3 . . .

[67] [67] [68] [67] [68] [69] [68] [67]

Reaction (1) I + OH = HOI

−193.5 −197.9 −205.3 (2) HI + OH = I + H2 O −194.4 −195.6 −200.8 (3) HI + HOI = I2 + H2 O −135.6 −134.8 −146.6 (4) IO + H = HOI −404.4 −409.1 −407.2 (5) IO + H = I + OH −210.8 −211.2 −201.9 (6) IO + H2 = HI + OH −72.6 −72.8 −64.3 (7) IO + HI = I2 + OH −52.9 −51.9 −54.6 (8) IO + HI = I + HOI −111.7 −112.7 −108.8 (9) I2 + H = I + HI −157.9 −159.4 −147.3 (10) I2 + O = I + IO −74.3 −75.4 −74.8 (11) I2 + OH = I + HOI −58.8 −60.9 −54.2 (12) HOI + H = IO + H2 −26.5 −25.5 −28.8 (13) HOI + O = IO + OH −15.5 −14.4 −20.6 (14) HOI + OH = IO + H2 O −82.7 −83.5 −91.9

[21]

Table 2. Spectroscopic constants for diatomics (experimental data from NIST webbook [70] are in italics). Parameter

H2

Re (Å)

0.7414 0.7414 ωe (cm−1 ) 4390.7 4401.2 ωe xe (cm−1 ) 123.2 121.3 αe (cm−1 ) 3.3 3.06

OH

HI

IOa

I2

0.9706 0.9697 3728.1 3737.8 86.9 84.9 0.8 0.72

1.6034 1.6092 2336.8 2309.0 38.2 39.6 0.2 0.17

1.8732 (1.8692) 1.8676 681.6 (696.1) 681.4 5.0 (4.5) 4.2 – 0.003

2.6606 2.6663 222.2 214.5 0.5 0.6 – 0.0001

IO data in parentheses refer to the 2 53/2 state calculated from the CASPT2/RASSI potential.

a

Table 3. DK-MP2/ANO-RCC-VQZP structural data obtained for H2 O and HOI. Experimental data are in italics. Parameter H2 O OH (Å) HOH (◦ )

Parameter HOI a

0.9596, 0.9572 104.21, 104.52a

ω (cm−1 ) 1635.9c , 1572.5d , 1595e

OH (Å) IO (Å) HOI (◦ ) ω (cm−1 )a

3836.9c , 3688.0d , 3657e 3963.9c , 3810.1d , 3756e

◦ ◦ ◦ 1r H0 K 1r H298 K 1r S298 K 1r G 298 K

−0.108 −0.110 −0.013 −0.021 −0.012 −0.012 −0.099 −0.100 0.014 0.010 0.018 0.020 −0.004 −0.002 −0.010 −0.011 0.018 0.012 0.001 −0.002 −0.008 −0.009 0.0002 0.001 0.007 0.007 0.010 −0.010

−165.8 −172.6 −191.7 −194.6 −131.0 −143.1 −379.5 −377.5 −215.4 −204.9 −78.2 −70.3 −50.7 −54.1 −109.7 −105.6 −164.7 −150.8 −75.6 −74.4 −58.5 −51.5 −25.5 −29.0 −16.5 −22.8 −80.5 −89.0

a

In the evaluation of experimental data the most recent −1 ◦ 1f H298 for HOI was taken from the review by K = −59.2 kJ mol Marshall [21].

b

0.9673, 0.9643 1.9784, 1.991b 103.96, 105.4b 605.6c , 582.1d , 575b 1102.3c , 1059.6d , 1068b 3785.1c , 3638.2d , 3626b

often exploits either isogyric or isodesmic reactions. In the former the number of electron pairs in reactants and products is conserved, while in the latter the number and types of bonds are conserved on the reactant and product sides. Let us, for example, consider HOI as a target species TS involved in the isogyric reaction i whose equation is:

a

Experiment [62]. Experiment [63]. c Unscaled frequencies. d Frequencies scaled by 0.9612. e Experiment [64]. b

TS + RS1,i = RS2,i + RS3,I ,

I2 + O = I + IO,

(10)

I2 + OH = 1I + HOI,

(11)

HOI + H = IO + H2 ,

(12)

HOI + O = IO + OH,

(13)

HOI + OH = IO + H2 O.

(14)

where RS1,i , RS2,i and RS3,i are reference species whose the enthalpies of formation are known in the literature. ◦ Then, 1f H298 K (TS)i, j is calculated using an algebraic sum of enthalpies of formation of the reference species RS involved in the isogyric/isodesmic reaction i and the enthalpy of ◦ reaction i at 298 K, 1r H298 K , i, evaluated with the calculation method as follows: ◦ ◦ ◦ 1f H298 K (TS) = − 1r H298 K,i − 1f H298 K (RS1 ) ◦ ◦ + 1f H298 K (RS2 ) + 1f H298 K (RS3 ).

3. Results and discussion Spectroscopic constants and geometry parameters of all molecular species are collected in tables 2 and 3. In table 4 we summarize the thermochemistry of small iodine species for the set of reactions (1)–(14); wherein, in the evaluation of −1 ◦ experimental data the most recent 1f H298 K = −59.2 kJ mol

The literature data for the standard enthalpies of formation at 298 K collected in table 1 were used in the final ◦ derivations of the 1f H298 K of HOI. In this derivation one 4

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Table 5. Standard enthalpies of formation at 298 K(kJ mol−1 ) of HOI derived from the selected reactions. ◦ ◦ 1f H298 K 11f H298 K Type

Reaction # (1) (3) (4) (8) (11) (12) (13) (14)

and non-relativistic), which is usually a rather lengthy calculation due to the basis set enormous size. In addition, such a calculation often suffers from linear dependencies in the basis set, making the comparison rather clumsy because after removing the linear dependencies one can get an unbalanced number of molecular orbitals for the components of the chemical equilibrium. Instead, we can refer to our related tests using smaller POL and POL-DK basis sets [65, 66], for reactions OH + CH2 I2 → H2 O + CHI2 and OH + CH2 I2 → HOI + CH2 I published previously [24]. The difference in CCSD(T) reaction energy was 3.8 kJ mol−1 in the former and 6.5 kJ mol−1 in the latter reaction. Clearly, for thermochemistry aiming at the chemical accuracy (±4 kJ mol−1 ) one cannot neglect scalar relativistic effects. In table 5, we present standard enthalpies of formation at 298 K of HOI derived from the selected reactions where the HOI is present. For the sake of comparison, we have also included the atomization process (HOI → H + O + I). −1 ◦ If we correct the 1f H298 K from table 5 (−48.1 kJ mol ) −1 to 0 K we arrive to −43.4 kJ mol which differs slightly from the atomic-process-based 1f H0◦K reported by Marshall, −50.5 kJ mol−1 (cf p 165 in [21]). The atomization process is computationally the most demanding task when aiming at the standard enthalpy of formation because it requires very accurate atomic energies and lacks any cancellation of possible errors that one can expect from the isogyric ◦ process. The 1f H298 K (HOI) derived from atomization is rather close to the value previously suggested by Glukhovtsev et al [19], obtained from a small basis set and pseudo-potential calculations and utilizing atomization processes. It is also close to the indirect estimate proposed by Zhang et al [20] based on the trends in the ratio of dissociation energies of HOI and IO. Considering the ways in which the ◦ 1f H298 K (HOI) was obtained in [19, 20] it is evident that these values suffer from a number of uncertainties that most ◦ probably lead to the underestimation of both 1f H298 K (HOI), thus disfavouring these data. The second value in table 5 refers to the non-isogyric process and also suffers from larger deviation, compared to the remaining subset, which ◦ delivered a quite consistent set of 1f H298 K ’s. If we now use for the evaluation of the standard enthalpy of formation ◦ reactions (3), (4), (8) and (11)–(14) we obtain 1f H298 K= −1 −68.8 kJ mol , and, restricting just to the isogyric set, −1 ◦ we get 1f H298 K = −69.0 kJ mol . Bearing in mind the ◦ possible sources of errors in terms of 11f H298 K , our final ◦ new estimate for 1f H298 K (HOI) is −69.0 ± 3.7 kJ mol−1 , which is in very good agreement with the value proposed previously by Berry et al (−69.6 ± 5.4 kJ mol−1 ) and differs from the recent Marshall value of −59.2 ± 3.3 kJ mol−1 . This difference (and similarly—the difference in SO splitting for IO mentioned in section 2) can be attributed to the use of a less flexible pseudo-potential basis set in the latter calculation. Our final comment concerns the −1 ◦ 1f H298 proposed by Hassanzadech K = −59.9 ± 6.9 kJ mol and Irikura [18] which is close to Marshall’s one. In our opinion, the disadvantage of their procedure lies in combining experimental geometries/frequencies, single-point CCSD(T) calculations with only moderate basis and neglecting the scalar relativistic effects. In addition, they adopted an indirect estimate of the SO correction for IO based on the calculation

Atomization I + OH = HOI HI + HOI = I2 + H2 O IO + H = HOI IO + HI = I + HOI I2 + OH = I + HOI HOI + H = IO + H2 HOI + O = IO + OH HOI + OH = IO + H2 O

−48.1 −52.8 −71.2 −66.0 −67.9 −67.5 −67.4 −70.7 −72.2

0.15 1.25 0.22 2.51 2.64 1.25 2.51 3.71 3.75

Isogyric Isogyric Isogyric Isogyric Isogyric

for HOI was taken from Marshall [21]. Finally, our updated set of standard enthalpies of formation at 298 K of HOI derived from selected reactions is in table 5. As one can see from table 2, the CR-CCSD(T)/ANO-RCC-large bond lengths and spectroscopic constants are in excellent agreement with experimental data. The differences between spin-free and SO-corrected Re , ωe and ωe xe for IO are marginal, so we have used the former set in thermochemistry. However, the shift in energy due to the SO coupling in IO is non-negligible and must be added to the total CR-CCSD(T) energy in thermochemistry. The same holds for the DK-MP2/ANO-RCC-VQZP geometry parameters for H2 O and HOI (table 3), they agree very well with the reference experimental data [62, 63]. Application of the scaling factor 0.9612 for frequencies of H2 O and HOI also provides very good agreement with the literature data in [63, 64]. The equilibria listed in table 4 have been chosen to be exothermic and are ordered according to the first reactant. Thus the processes (2) and (3) ‘belong’ to HI, processes (4)–(8) to IO, (9)–(11) to I2 and (12)–(14) to HOI. This complete set is, of course, redundant, because only (1), (3), (4), (8) and (11)–(14) can be utilized for the determination ◦ of 1f H298 K (HOI). While presenting an extended set of reactions, we can get better picture on the performance of the CR-CCSD(T) method applied to iodine chemistry. This larger set of reactions includes both the isogyric processes ((3), (8), (11), (12), (14)) and other reactions ((1), (10), (13)) where the number of electron pairs is not conserved. ◦ When we compare the theoretical 1r H298 K values with the experiment, our larger set yields standard deviation of 7.4 kJ mol−1 (with the correlation coefficient 0.9949). The subset selected for the subsequent evaluation of the ◦ 1f H298 K (HOI) yields even slightly better standard deviation of 5.9 kJ mol−1 (with the correlation coefficient 0.9905). The comparison of 1r G ◦298 K values yields similar standard deviations (5.6 and 4.2 kJ mol−1 , respectively). Thus, the CR-CCSD(T) method performs consistently and satisfactorily also for non-isogyric processes, at least for the larger set used in this work. The data in table 4 deserve one more comment. In principle, it is possible to also run non-relativistic calculation (without inclusion of the scalar relativistic contribution) to get the information on the importance of this correction. This would require to use uncontracted ANO-RCC basis set and two sets of energies (relativistic 5

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of 1 6 + IO− corrected by experimental electron affinity of IO. Most probably, these uncertainties may have a cumulative ◦ effect on the final 1f H298 K value reported in [18].

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4. Conclusions A series of iodine-containing species HI, I2 , IO, HOI and related chemical reactions of relevance to the atmosphere were investigated with the completely renormalized CC method including scalar relativistic effects within the second order Douglas–Kroll–Hess formalism, and with SO corrections added a posteriori. We have used the large ANO-RCC basis set in these calculations, which enables us to include the semi-core correlation effects as well. The DK-CR-CCSD(T) energies combined with the standard ◦ thermochemistry treatment yielded a set of 1r H298 K and ◦ 1r G 298 K values that is in good agreement with the experimental data derived from the COACH database. Finally, −1 ◦ an updated value for 1f H298 K (HOI) = −69.0 ± 3.7 kJ mol was derived, based on the set of isogyric reactions. To ◦ summarize, there are two sets of 1f H298 K (HOI) derived from ab initio quantum chemical calculations, one around −70 kJ mol−1 and the other around −60 kJ mol−1 . Although these values do not differ dramatically, the differences do exceed conventional chemical accuracy by approximately a factor of two; it would appear that the heat of formation of HOI is still an open problem.

Acknowledgments We appreciate the computer time provided by the Computing Centre of the SAS (ITMS 26230120002 and 26210120002), Slovak infrastructure for high-performance computing and by the project ‘Dobudovanie Centra excelentnosti met´od a procesov zelenej ch´emie (CEGreenII)’ (ITMS 26240120025), both supported by the Research & Development Operational Programme funded by the ERDF. This study was supported by the Research and Development Agency (projects APVV-0059-10 and LPP-0150-09). Florent Louis and Laurent Cantrel also thank the French ANR agency for support under contract no. ANR-11-LABX-0005 ‘Chemical and Physical Properties of the Atmosphere’ (CaPPA).

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