Density Functional Study of Sulfur (SF6) and its Hydrogen Derivatives Jacek Piechota, Marta Kinga Bruska

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Jacek Piechota, Marta Kinga Bruska. Density Functional Study of (SF6) and its Hydrogen Derivatives. Molecular Simulation, Taylor & Francis, 2008, 34 (10-15), pp.1041-1050. ￿10.1080/08927020802258708￿. ￿hal-00515048￿

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For Peer Review Only Density Functional Study of Sulfur Hexafluoride (SF6) and its Hydrogen Derivatives

Journal: Molecular Simulation/Journal of Experimental Nanoscience

Manuscript ID: GMOS-2008-0043.R1

Journal: Molecular Simulation

Date Submitted by the 15-May-2008 Author:

Complete List of Authors: Piechota, Jacek; University of Warsaw, ICMM Bruska, Marta; Jagiellonian University, Department of Chemistry

Keywords: sulfur hexafluoride, greenhouse gases, density functional theory

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1 2 "Catchline" (i.e. wording at head of first page only) Journal Name in Full 3 Vol. X, No. X, Month 200X, 000–000 4 (PLEASE LEAVE THESE VOLUME/ 5 6 ISSUE DETAILS TO BE ASSIGNED BY 7 JOURNALS PRODUCTION AT 8 A LATER STAGE) 9 10 11 12 The Authors 13 14 (DO NOT INCLUDE THIS AT FIRST SUBMISSION FOR 15 BLIND REVIEW, BUT DO INCUDE IT WHEN PREPARING 16 For Peer THE FINALLYReview ACCEPTED Only MANUSCRIPT FOR SUBM.) 17 Molecular Simulation 18 19 RESEARCH NOTE 20 21 22 Density Functional Study of Sulfur Hexafluoride (SF 6) and its Hydrogen Derivatives. 23 24 25 26 Abstract 27 28 29 Density functional study has been performed for group of compounds derived from sulfur 30 hexafluoride (SF 6) by consecutively substituting with hydrogen. SF 6 is widely used as the 31 insulating gas in the electrical industry and is recognized as one of the greenhouse gases with 32 33 extraordinary global warming potential. The aim of the present study is to look for potential 34 industrial alternatives to SF 6 as well as to examine mechanisms that can contribute to its faster 35 atmospheric decay. The ground state geometries, binding energies, vibrational spectra, charge 36 distributions, dipole moments, as well as thermodynamic properties for the series of the SF 6-nHn 37 (n=0…6) have been obtained and discussed. For comparison, computational results for 38 39 the SCl 6 have also been included in the present study. 40 41 Keywords : sulfur hexafluoride; greenhouse gases; density functional theory; 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 "Catchline" (i.e. wording at head of first page only) Journal Name in Full 3 Vol. X, No. X, Month 200X, 000–000 4 5 6 7 8 9 10 11 12 13 M. K. Bruska, J. Piechota 14 15 16 For Peer Review Only 17 Molecular Simulation 18 19 20 RESEARCH NOTE 21 22 23 Density Functional Study of Sulfur Hexafluoride (SF 6) and its Hydrogen Derivatives. 24 25 26 27 28 a b* 29 MARTA KINGA BRUSKA AND JACEK PIECHOTA 30 a Department of Chemistry, Jagiellonian University, ul. R. Ingardena 3,30-060 Kraków, Poland 31 b Interdisciplinary Centre for Materials Modelling, University of Warsaw, ul. Pawinskiego 5a, 02-106 Warszawa, Poland 32 33 34 35 36 Abstract 37 38 39 Density functional study has been performed for group of compounds derived from sulfur 40 hexafluoride (SF ) by consecutively substituting fluorine with hydrogen. SF is widely used as the 41 6 6 42 insulating gas in the electrical industry and is recognized as one of the greenhouse gases with 43 extraordinary global warming potential. The aim of the present study is to look for potential 44 industrial alternatives to SF 6 as well as to examine mechanisms that can contribute to its faster 45 atmospheric decay. The ground state geometries, binding energies, vibrational spectra, charge 46 distributions, dipole moments, as well as thermodynamic properties for the series of the SF H 47 6-n n 48 (n=0…6) molecules have been obtained and discussed. For comparison, computational results for 49 the SCl 6 molecule have also been included in the present study. 50 51 Keywords : sulfur hexafluoride; greenhouse gases; density functional theory; 52 53 54 55 56 57 58 59 60 ______* Email: [email protected] - 2 -

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1 2 1. Introduction 3 4 Interest in the sulfur hexafluoride (SF ) system stems both from practical and theoretical 5 6 6 considerations. It is one of the most popular (next to air) insulating gases, with a breakdown 7 strength of about 3 times that of air. It has a number of technologically important properties: it is 8 not flammable and non-toxic; at normal temperatures, it is also non-corrosive, and is fairly inert. 9 That is why SF 6 is commonly used in industry as a gaseous dielectric and as a plasma etching gas in 10 applications such as: circuit breakers, gas-insulated busbar systems, and also for large scale 11 12 scientific applications such as tandem particle accelerators. Other areas of application of SF 6 13 include the magnesium industry to protect molten magnesium from oxidation and potentially 14 violent burning, and semiconductor manufacturing to create circuitry patterns on silicon wafers. 15 Also, SF 6 is a candidate refrigerant to replace the chlorofluorocarbons (CFC's) which are damaging 16 For Peer Review Only the ozone layer. For an extensive review of SF 6 technical applications see, for example, [1] and 17 publications therein. 18 19 On the theoretical side, SF 6 has become a classic molecule for the study of electron 20 attachment at ultralow electron energies. The attachment of low energy electrons to SF 6 results in 21 — — formation of a metastable negative by the process: SF 6 + e → SF 6 [2-5]. An understanding of 22 the thermal electron attachment properties and temperature behaviour of rate constant for SF is, in 23 6 24 turn, of importance in the design of gaseous insulators and diffuse discharge switchers. 25 Furthermore, SF 6 has a unique, octahedral symmetry structure, which provides good 26 example of shape resonance phenomena. The infrared active modes of octahedral molecules are of 27 F1u symmetry and ν3 as well as ν4 bands are allowed in absorption [6]. In particular, the region of 28 the ν fundamental near 950 cm -1 has very strong absorption. The bond dissociation energy of SF 29 3 6 30 (to SF 5 + F) is 3.82 eV, but photodissociation is not observed until the photon energy exceeds ~10 31 eV [4]. 32 However, at the same time SF 6 is the most potent greenhouse gas that has been evaluated by 33 the Intergovernmental Panel on Climate Change (IPCC), with a global warming potential (GWP) of 34 22,800 times that of CO 2 when compared over a 100 year period [7]. Two main factors contributing 35 to this extraordinary high value of GWP is strong radiative forcing (0.52 Wm -2ppb-1) and very long 36 37 atmospheric lifetime (3200 years) [8]. In the stratosphere, the highest energy solar photons have an 38 energy of ~6 eV, so it is very unlikely that SF 6 will be photodissociated there. Therefore, although 39 the concentration of SF 6 is still relatively low in the Earth's atmosphere (5.21 ppt) [8], it is one of 40 the greenhouse gases that the Kyoto Protocol seeks to control [9], as even small amounts of SF 6 41 emissions can constitute a significant carbon-equivalent emission tonnage. 42 Apart from destroying ozone layer greenhouse gases that can absorb infrared radiation in the 43 -1 44 so-called “atmospheric window” between the wavelengths of 800 - 1400 cm are of great concern 45 because they are able to trap radiation that would have otherwise been emitted into space — most of 46 the radiation emitted by the earth's surface at wavelengths within in the atmospheric window would 47 have passed through the Earth's atmosphere without heating it. 48 Recently, another compound with extremely strong radiative forcing (of 0.59 Wm -2ppb -1), 49 50 identified as trifluoromethyl sulfur pentafluoride (SF 5CF 3), has been detected in the atmosphere 51 [10,11]. It is supposed that SF 5CF 3 originates as a breakdown product of SF 6 formed by high- 52 voltage discharges in electric industry equipment [10]. Atmospheric lifetime of SF 5CF 3 (~800 53 years) is lower than that of SF 6, but its value of GWP (~17,700) is one of the highest of all other 54 greenhouse gases [7]. 55 56 It is worth noting, however, that the greenhouse gases with the greatest GWP values are the 57 fully fluorinated compounds (FFC’s): CF 4, C 2F6, C 3F8, c-C4F8, SF 6, NF 3 and CHF 3, that are widely 58 used by the semiconductor industry [12]. As for now there is no significant mechanism for their 59 destruction in the natural circulation of the Earth's atmosphere — as a result their atmospheric 60 lifetimes are estimated to be up to 50,000 years for CF 4 [7]. In case of CFC’s a wide variety of alternative compounds has been investigated with the aim - 3 -

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1 2 of protecting the ozone layer and reducing the global warming. The basic concept in the process of 3 development of alternative CFC’s is the introduction of a hydrogen atom into the CFC molecule to 4 reduce its atmospheric lifetime without detrimenting its properties. In this way, several 5 6 hydrochlorofluorocarbons (HCFC’s) and hydrofluorocarbons (HFC’s) have already been developed 7 and have found practical use. The introduction of hydrogen atoms into the molecule raises the 8 compound’s reactivity towards OH radicals as the reactivity with OH radicals is related to the 9 stability of the molecule in the troposphere [13]. 10 Motivated by this fact we have studied the series of the SF H (n=0…6) molecules where 11 6-n n 12 the fluorine atoms of SF 6 were consecutively replaced with the hydrogen atoms. The aim of the 13 study is to look for potential industrial alternatives to SF 6 as well as to examine mechanisms that 14 can contribute to its faster atmospheric decay. SCl 6 has been also taken into consideration to 15 compare our results with a heavier analogue of the SF 6 molecule. To our best knowledge this is the 16 For Peer Review Only first report on the properties of the SF 6-nHn series of compounds. 17 The present study is based on density functional theory (DFT) [14,15]. This approach has 18 19 over the past decade emerged as a tangible and versatile computational method with applications in 20 many subfields of chemistry. The DFT-based methods can provide bond energies, structures and 21 other electronic properies of high accuracy. The method has previously been applied to similar 22 studies on diatomic 3 d monoxides [16,17]. 23 The rest of the paper is organized as follows. Computational details are reported in Section 24 25 2. In Section 3 the ground state geometries, bonding energies, vibrational spectra, charge 26 distributions partitioned by Hirshfeld method, dipole moments, as well as thermodynamic 27 properties are presented and analyzed. In Section 4 the main points of this work are summarized 28 and perspectives for future research are outlined. 29 30 31 2. Computational details 32 33 As mentioned in the introduction, the computational method used for the purpose of the present 34 study is based on DFT as implemented in the DMol 3 code [18,19] available as part of the Materials 35 Studio 4.0 software environment [20]. For an extensive review of the DMol 3 description and its 36 features we refer the reader to [18,19] and references therein. We present here only a summary of 37 3 38 the input parameters set up in the DMol package in order to get stable and accurate results, as 39 compared to experiment and other calculations. 3 40 DMol uses numerical functions on an atom-centered grid as its atomic basis. For the 41 purpose of the present study the DNP basis set was used for all atoms. The DNP basis set uses 42 double-numerical quality basis set with polarization functions. This means that for each occupied 43 44 atomic orbital one numerical function is generated and a second set of this functions is given for 45 valence atomic orbitals. It also generates polarization d-functions on all non-hydrogen atoms and 46 polarization p-function on all hydrogen atoms. The DNP basis sets are comparable in quality to 47 Gaussian 6-31G** basis sets. 48 The quality of the integration grid that controls the selection of mesh points for the 49 numerical integration procedure used in the evaluation of the matrix elements was chosen to be 50 3 51 FINE. The electron density in DMol is expanded in terms of multipolar partial densities (auxiliary 52 density) used to specify the maximum angular momentum Lmax of the multipolar fitting functions 53 that specify the analytical form of the charge density and the Coulombic potential. This parameter 54 was set to be OCTUPOLE which corresponds to Lmax of 3. 55 The local density approximation (LDA) can be used to predict the structures and relative 56 57 energies of covalent and ionic systems quite accurately. However, usually bond energies are 58 overestimated while vibrational frequencies are underestimated than those obtained within other 59 methods and experimental data. These problems with the LDA method can be corrected to large 60 extent by using the so-called gradient-corrected (or nonlocal) functionals. However, extensive test calculation with local and non-local functionals yielded that in the case of SF 6 it is the LDA method

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1 2 with Perdew-Wang functional (PWC) that yield the results closer to available experimental data. 3 We have therefore adopted this approach in all calculations performed for the purpose of the present 4 study. 5 6 Vibrational spectra and Hessians were computed by finite differences of analytic first 7 derivatives. This means that each atom in the system was displaced in each Cartesian direction. The 8 results of Hessian evaluation have been used to compute thermodynamic properties of the 9 molecules. Point group symmetry was used to reduce the total number of displacements. The 10 vibrational analysis was performed at the final geometry. Hirshfeld partitioned charges were 11 12 defined relative to the deformation density. Finally, the convergence criteria were established to be 13 FINE both for the SCF density convergence (the density convergence threshold for SCF) and for 14 the optimization energy convergence (the threshold for energy convergence during geometry 15 optimization). The numerical values for these thresholds were 10 -6 Ha and 10 -5 Ha, respectively. 16 For Peer Review Only 17 3. Results and discussion 18 19 20 3.1 Geometry optimization 21 22 The accuracy of the data obtained in the course of the present study can be compared only in the 23 case of the reference SF molecule. There have been quite a number of electronic properties 24 6 25 calculations for this system, and the predicted properties vary remarkably depending upon the 26 methodology of the computation (see Ref. 31 for the discussion). Therefore we decided to compare 27 results yielded by our calculation with theoretical studies founded on DFT [21-22] that are available 28 for the SF 6 molecule. The first and the most extensive work (however, without calculated 29 vibrational frequencies) came from Tang and Callaway [21] who performed calculations for SF 6 in 30 the local spin density (LSD) approximation. Delley [22] studied static deformations and vibrations 31 32 of SF 6 with an applied strong static electric field; basic molecular properties in the absence of 33 external electrostatic fields in local as well as gradient corrected approximations to DFT were 34 obtained. To our knowledge these are all numerical studies of the electronic structure of the SF 6 35 molecule based on DFT methodology. Molecular properties of SF 6 are collected in Table 1. 36 It can be seen from Table 1 that our results obtained for the SF molecule are in good 37 6 agreement with those presented in Ref. 21 and Ref. 22. The maximum deviation of calculated 38 -1 39 frequencies is at 49 cm , that is less than 10% in comparison with experimental values. The LDA 40 PWC approximation thus gives a fairly accurate description of the energy surface near the 41 equilibrium conformation. Surprisingly enough, the gradient corrected functionals perform 42 significantly worse for this molecule, except for the binding energy. 43 44 The equilibrium structures as obtained from optimization of geometry of all studied 45 molecules in their ground states are shown in Figure 1. The structures were optimized in imposed 46 symmetry, relevant to each molecule (see the labels under the figure labels). The highest symmetry 47 point group O h is adopted by the SF 6 molecule, as well as by the SH 6 and SCl 6 ones. With the 48 substitution of fluorine atoms by the hydrogen ones the symmetry is lowered, but symmetries of the 49 SF H (n=1…5) molecules are consistent with the correlation table of the O group. For molecules 50 6-n n h 51 SF 6-nHn (n=2,3,4) two possible nonequivalent conformations exist: the first one, denoted further as 52 (a), in which one of the hydrogen atoms is perpendicular to other hydrogen atom(s), and the second 53 one, denoted as (b), in which all hydrogen atoms are in the same plane. Subsequent DMol 3 54 computations of other properties were performed at these final geometries. The point group 55 symmetries were imposed on each molecule in order to reduce the computational time whenever 56 57 possible. 58 Closer examination of structural data obtained shows that geometry of the SF 6-nHn (n=1…6) 59 molecules resembles that of the SF 6 parent one. Due to large amount of data collected detailed 60 values of bond lengths and angles are available from the authors. For the purpose of the present study only principal trends are summarized. The relevant H-S-F angles are very close to 90 o or

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1 o 2 180 , respectively. The most deformed structure is that of SF 2H4 (a) with low, C2v symmetry. The 3 deviation from 180 o is about 10 o. The molecular distances between sulfur and fluorine atoms 4 increase as the fluorine atoms are substituted by the hydrogen ones, and hydrogen-sulfur distances 5 6 are smaller than the fluorine-sulfur ones. These trends are illustrated in Figure 2a and 2b. It is worth 7 to mention that in the case of SCl 6 the chlorine-sulfur distance is significantly larger and equals to 8 2.1461 Å. Trend in binding energy for the SF 6-nHn (n=0…6) series and SCl 6 is illustrated in Figure 9 3. 10 The SF molecule has the highest binding energy as compared to the SF H (n=1…6) 11 6 6-n n 12 series. Interestingly enough, the SCl 6 and SH 6 molecules have similar values of binding energies. 13 These results are listed in Table 2. Since the SF 6, SH 6 and SCl 6 molecules have octahedral 14 symmetry, as well as the SF 4H2 (b) and SF 2H4 (b) have tetragonal symmetry, there are no static 15 dipole moments in their case. The values of dipole moments obtained for the molecules under study 16 are listed in TableFor 3, and its analysisPeer is postponed Review to Section 3.3. Only 17 Closer examination of single particle eigenvalues (depicted in Figure 4) yields that with 18 19 increasing number of the H atoms in the SF 6-nHn system the number of eigenstates is gradually 20 diminishing, as there are less electrons. Symmetries of the orbitals are changing according to 21 symmetries of the given SF 6-nHn system (in order to keep the Figure 4 as readable as possible we 22 decided to label eigenstates only for SF 6 and SH 6 molecules). Because of the same molecular 23 symmetry of the SF and SH molecules molecular orbitals have the same symmetry in their case. 24 6 6 25 However, there are fewer electrons in SH 6 than in SF 6, so only 6 first single particle eigenstates in 3 26 energetically lowest states with symmetries A 1g, T 1u i E g are occupied. 27 28 3.2 Optical properties 29 30 Normal modes and their frequencies for all the SF 6-nHn (n=0…6) molecules are shown in Figure 5, 31 while explicit values, supplemented with data obtained for SCl , are listed in Tables 4 and 5. In 32 6 33 Table 6 square of first derivatives of molecular dipole moments wrt infrared active normal modes 34 are shown. Calculated absorption spectra are collected in Figure 6. 35 The infrared absorption spectrum of SF 6 is composed of two bands. Only ν3 and ν4 modes 36 with F 1u symmetry satisfy dipole selection rules and are allowed in absorption. Their maxima are 37 located at 567.2 and 938.06 cm -1 with intensity respectively 22.17 and 390.19 km/mol. Both of 38 these normal modes are triple degenerate and correspond to the change of bond lengths and bond 39 40 angles. 41 The frequencies of vibrations are expected to increase as hydrogen atoms are substituted for 42 fluorine ones. This effect can be attributed to the extension of reduced masses of these molecules, as 43 well as the decrease of intermolecular interactions (see the Figure 2a and 2b and Table 2): binding 44 energies are decreasing and bond lengths are increasing. As a consequence, with increasing n in 45 46 SF 6-nHn (n=0…6) spectra are shifted into higher energies. Variations in mass distribution and 47 molecular geometries cause also alterations in symmetries of normal modes. The intensity of 48 absorption for the fundamental vibrational transitions is given by: 49 50 −1 51 A= Bnw ⋅h⋅νnw ⋅c ⋅ NA, 52 53 where A is the integral coefficient of absorption (measure of absorption in band), ν is the 54 nw 55 frequency of transition between n and w levels, and B nw is the Einstein coefficient for induced 56 emission, which can be expressed as: 57 8π 3 58 2 Bnw = 2 ⋅ µnw , 59 3h 60 in which nw is the transition moment for n and w levels. For the fundamental transitions, this - 6 -

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1 2 quantity is proportional to square of first derivatives of molecular dipole moments wrt infrared 3 active normal modes. As it is shown in Table 6, these values are increasing with the increasing rate 4 of replacement of fluorine by hydrogen. 5 6 Molecules SCl 6 and SH 6 are again quite similar to SF 6. As they adopt Oh point group 7 symmetry, the infrared spectra are analogous to this of SF 6. The difference is in the frequencies of 8 normal modes and intensities of their absorption. SCl 6, as a heavier molecule, has lower vibrational 9 transition intensity as well as lower frequencies of normal modes. In contrast to this, SH 6 has a 10 much higher vibrational transition intensity and higher frequencies of normal modes. This means 11 12 that SH 6 absorbs even more radiation than SF 6, but in for higher frequencies. SH 6 has also nearly 13 two times lower binding energy than SF 6 and, as such, is less stable. -1 14 It is also worth to mention that strongest absorption band of SF 6 at ~940 cm is located in 15 the atmospheric window mentioned in Section 1, and no other molecule studied here has so strong 16 For Peer Review Only absorption band in this frequency region as SF 6 has. 17 18 19 3.3 Charge distribution and dipole moments 20 21 Charge partitioning as obtained from Hirshfeld method for all the SF6-nHn (n=0…6) molecules and 22 the SCl 6 one is listed in Table 7. These values are normalized to single atoms, so one should bear in 23 mind that for given n in SF 6-nHn qS = (6-n)•qF + n•qH. Hirshfeld analysis for SF 6 indicates positive 24 charge on the sulfur atom and small negative charges on the fluorine atoms. Negative charges on 25 the fluorine atoms increase while positive charge on the sulfur atom decreases as fluorine atoms are 26 27 gradually substituted with the hydrogen atoms. Although not included here, the results of Mulliken 28 analysis are consistent with the results of Hirshfeld one. 29 The dipole moment of a molecule is determined by the charges and the induced dipoles on 30 the constituent atoms. Because of symmetric charge distribution, there are no static dipole moments 31 in molecules: SF , SF H (b), SF H (b), SH and SCl . The SF H has almost two times smaller 32 6 4 2 2 4 6 6 5 33 magnitude of dipole moment than SFH 5, although charges on constituent atoms are larger in SF 5H 34 than in SFH 5, and both molecules have the same symmetry. One can assume that for SFH 5 the 35 charge and induced dipole contributions have the same polarity that account for its large dipole 36 moment, in contrast to SF 5H. In case of the SF 3H3 (a) and (b) molecules the large difference in 37 dipole moments is caused by different symmetry of charge distribution. 38 39 40 3.4 Thermodynamical properties 41 42 Basic thermodynamic properties such as total entropy, vibrational entropy, free energy, heat 43 capacity and zero point vibrational energy have been also calculated for the SF 6-nHn (n=0…6) and 44 SCl 6 molecules. The results are presented in Table 8 and Figures 7 to 12. Values of heat capacity 45 decrease with molecular mass reduction. As the heat capacity is defined as the amount of heat 46 required to change the temperature of a substance by one degree, larger molecules will need more 47 48 heat than smaller ones. This suggest that insulating properties of SCl 6 are the best of all the 49 molecules studied here, in particular better than these of SF 6. The industrial usage of SF 6 instead of 50 SCl 6 is due to greater stability of SF 6 than SCl 6 (bonding energy for SF 6 is twice higher than that 51 for SCl 6). Total and vibrational entropy decreases as fluorine atoms are substituted with hydrogen 52 ones. On the other hand the free energy and zero point vibrational entropy show opposite tendency. 53 54 This behaviour is in good relation to changes in molecular mass of studied compounds. 55 56 4. Conclusions 57 58 In the present study the series of the SF 6-nHn (n=0…6) molecules have been examined for the first 59 time. Molecular constants such as equilibrium bond distances, binding energies, vibrational 60 frequencies, charge distributions partitioned by Hirshfeld method, dipole moments, as well as thermodynamic properties have been determined and analyzed. - 7 -

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1 2 The results of IR spectra simulations confirm that it is fluorine atoms that play crucial role in 3 greenhouse effect of SF 6. For other molecules with octahedral symmetry, such as SH 6 and SCl 6, 4 their absorption bands are outside the atmospheric window. On the other hand, for the SF H 5 6-n n 6 (n=1…5) molecules with lower symmetries, there are more absorptions bands with reduced 7 intensities as compared to SF 6. 8 Because of inherent approximations in DFT, computational methods based on this approach 9 are not expected to yield very accurate values of molecular constants, as wavefunction based ab 10 initio methods do. Rather, due to their efficiency and robustness DFT-based methods constitute 11 12 valuable tool in predicting general trends across a wide range of compounds. Therefore, the present 13 study can be regarded as the first step toward more detailed examination of the series of SF 6-nHn 14 (n=0…6) molecules. Further research can cover following areas: 15 (1) formation of metastable negative ; 16 (2) reaction pathsFor with OH Peer radicals; Review Only 17 (3) investigation of excited states. 18 19 These topics are outside the scope of the present study, but the need for further ab initio 20 calculations for these systems is therefore obvious. 21 22 23 Acknowledgements 24 25 The authors are indebted to Dr. Paweł M. Masiak, Institute of Physics, Polish Academy of Sciences, 26 27 for many valuable discussions, and to Dr. Carsten Menke, Accelrys, Inc., for his technical 3 28 assistance with the DMol code. 29 30 References 31 32 [1] IEE Colloquium on An Update in SF6 and Vacuum Switchgear at Distribution Levels 33 (Digest No.1996/185), IEE, London, 1996 34 35 [2] A. Chutjian, A. Garscadden, J.M. Wadehra, Electron attachment to molecules at low 36 electron energies , Phys. Rep. 264 (1996), p. 393 37 38 [3] R. Morrow, Theory of electrical corona in SF 6, Nucl. Instr. and Meth. in Phys. Res. A 382 39 (1996), p. 57 40 41 [4] L.G. Christophorou, J.K. Olthoff, Electron interactions with SF 6, J. Phys. Chem. Ref. Data 42 29 (2000), p. 267 43 44 [5] P.-T. Howe, A. Kortyna, M. Darrach, A. Chutjian, Low-energy electron attachment to SF 6 at 45 sub-meV resolution using a tunable laser photoelectron method , Phys. Rev. A 64 (2001), 46 042706 47 48 [6] K. Kim, R.S. McDowell, W.T. King, Integrated infrared intensities and transition moments 49 in SF6 , J. Chem. Phys. 73 (1980), p. 36 50 51 [7] IPCC Working Group 1 (WG1), Changes in Atmospheric Constituents and in Radiative 52 Forcing , in 2007 IPCC Fourth Assessment Report (AR4) . Available at 53 http://ipcc-wg1.ucar.edu/wg1/wg1-report.html. 54 55 [8] Wen-Tien Tsai, The decomposition products of sulfur hexafluoride (SF6): Reviews of 56 environmental and health risk analysis , Journal of Fluorine Chemistry 128 (2007), p. 1345 57 58 [9] Kyoto Protocol to the United Nations Framework Convention on Climate Change . Available 59 at: http://unfccc.int/resource/docs/convkp/kpeng.pdf 60 [10] W.T. Sturges, T.J. Wallington, M.D. Hurley, K.P. Shine, K. Sihra, A. Engel, D.E. Oram, S.A. Penkett, R. Mulvaney, C.A.M. Brenninkmeijer, A Potent Greenhouse Gas Identified in - 8 -

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1 2 the Atmosphere: SF5CF3 , Science 289 (2000), p. 611 3 4 [11] P. Masiak, A.L. Sobolewski, Theoretical study of the photophysics of SF5CF3 , Chem. Phys. 5 313 (2005), p. 169 6 7 [12] PFC, HFC, SF 6 Emissions from Semiconductor Manufacturing , in Good Practice Guidance 8 and Uncertainty Management in National Greenhouse Gas Inventories , p. 3.69. Available 9 at: http://www.ipcc-nggip.iges.or.jp/public/gp/english/ 10 11 [13] A. Sekiya, M. Yamabe, K. Tokuhashi, Y. Hibino, R. Imasu, H. Okamoto, Evaluation and 12 selection of CFC alternatives in Fluorine and the Environment: Atmospheric Chemistry, 13 Emissions & Lithosphere (Advances in Fluorine Science, Vol. 1) A. Tressaud, ed., Elsevier 14 Science, 2006 15 16 [14] P. Hohenberg,For W. Kohn, Peer Inhomogeneous Review Electron Gas , Phys. Only Rev. 136 (1964), p. B864. 17 18 [15] W. Kohn, L. J. Sham, Self-Consistent Equations Including Exchange and Correlation 19 Effects , Phys. Rev. 140 (1965), p. A1133. 20 21 [16] J. Piechota, M. Suffczynski, Electronic structure of the CoO molecule , Phys. Rev. A 48 22 (1993), p. 2679 23 [17] J. Piechota, M. Suffczynski, Density functional study of the diatomic first row transition 24 25 metal oxides , Z. Phys. Chem. 200 (1997), p. 39 26 [18] B. Delley, An all-electron numerical method for solving the local density functional for 27 28 polyatomic molecules , J. Chem. Phys. 92 (1990), p. 508 29 [19] B. Delley, From molecules to solids with the DMol3 approach , J. Chem. Phys. 113 (2000), 30 p. 7756 31 32 [20] Information available at: http://www.accelrys.com/products/mstudio/ 33 34 [21] R. Tang, J. Callaway, Electronic structure of SF 6, J. Chem. Phys. 84 (1986), p. 6854 35 [22] B. Delley, Vibrations and dissociation of molecules in strong electric fields:N , NaCl, H O 36 2 2 37 and SF 6, J. Mol. Struct. (Theochem) 434 (1998), p. 229 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2 List of Figures 3 4 Figure 1. Equilibrium geometries of the SF 6-nHn (n=0…6) series and SCl 6 in their ground states: a. SF 6, O h symmetry; b. 5 SF 5H, C 4v symmetry; c. SF 4H2 (a), C 2v symmetry; d. SF 4H2 (b), D 4h symmetry; e. SF 3H3 (a), C 3v symmetry; f. SF 3H3 (b), 6 C2v symmetry; g. SF 2H4 (a), C 2v symmetry; h. SF 2H4 (b), D 4h symmetry; i. SFH 5, C 4v symmetry; j. SH 6, O h symmetry; 7 k. SCl 6, O h symmetry. 8 9 Figure 2. Interatomic distances in the SF 6-nHn (n=0…6) series and SCl 6 a. fluorine-sulfur distances; b. hydrogen-sulfur 10 distances. 11 12 Figure 3. Binding energies for the SF 6-nHn (n=0…6) series and SCl 6 13 14 Figure 4. Single particle eigenvalues for the SF 6-nHn (n=0…6) series. For readability only eigenstates for SF 6 and SH 6 15 molecules are labelled. 16 For Peer Review Only 17 Figure 5. Normal modes (7-21) and their frequencies for the SF6-nHn (n=0…6) series. 18 19 Figure 6. Calculated absorption spectra for the SF 6-nHn (n=0…6) molecules and SCl 6 in their ground states: a. SF 6, O h 20 symmetry; b. SF 5H, C 4v symmetry; c. SF 4H2 (a), C 2v symmetry; d. SF 4H2 (b), D 4h symmetry; e. SF 3H3 (a), C 3v 21 symmetry; f. SF 3H3 (b), C 2v symmetry; g. SF 2H4 (a), C 2v symmetry; h. SF 2H4 (b), D 4h symmetry; i. SFH 5, C 4v symmetry; 22 j. SH 6, O h symmetry; k. SCl 6, O h symmetry. 23 24 Figure 7. Total entropy for the SF 6-nHn (n=0…6) molecules and SCl 6. 25 26 Figure 8. Entropy as a function of temperature for the SF 6-nHn (n=0…6) molecules and SCl 6. 27 28 Figure 9. Vibrational entropy for the SF 6-nHn (n=0…6) molecules and SCl 6. 29 30 Figure 10. Zero Point Vibrational Energy (ZPVE) for the SF 6-nHn (n=0…6) molecules and SCl 6. 31 32 Figure 11. Free energy for the SF 6-nHn (n=0…6) molecules and SCl 6. 33 34 Figure 12. Heat capacity for the SF 6-nHn (n=0…6) molecules and SCl 6. 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

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1 2 List of Tables 3 4 Table 1. Experimental and calculated properties of the SF 6 molecule. 5 6 Table 2. Binding energy in [eV] and [J]. 7 8 Table 3. Magnitudes of dipole moments vectors [Debye] and [C·m] . 9 10 Table 4. Frequencies of normal modes in [cm -1]. 11 12 Table 5. Intensities of normal modes in [km·mol -1]. 13 14 Table 6. Square of first derivatives of molecular dipole moments wrt infrared active normal modes in [a.u.]. 15 16 Table 7. Charges partitionedFor by Hirshfeld Peer method. Review Only 17 18 Table 8. Thermodynamic properties. 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

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1 2 3 Table 1. Experimental and calculated properties of the SF 6 molecule. 4 d Parameter Unit Present Ref. 31 Ref. 32 Experiment 5 a 6 Binding energy eV 26.81 25.06 26.12 22.06 (20.12) b 7 d(S—F) Å 1.587 1.584 1.588 1.564 -1 c 8 ν1 A 1g cm 723.5 — 718 772.269 9 -1 c ν 2 E g cm 625.5 — 622 641.608 10 -1 c ν 3 F1u cm 938.1 — 931 947.289 11 -1 c 12 ν 4 F1u cm 567.2 — 562 614.589 -1 c 13 ν 5 F2g cm 477.9 — 476 523.449 14 -1 c ν 6 F2u cm 315.7 — 312 348.428 15 a SF 6 → S + 6F 16 b Table 8 in Ref. 4. p. 280For Peer Review Only 17 c Table 7 in Ref. 4, p. 280 18 d PWC calculation 19 20 Table 2. Binding energy in [eV] and [J]. 21 22 Molecule Symmetry Binding energy 23 [eV ] [J] 24 -18 25 SF 6 Oh 26.810 4.295·10 -18 26 SF 5H C4v 25.663 4.112·10 27 -18 28 SF 4H2 (a) C2v 24.090 3.860·10 -18 29 SF 4H2 (b) D4h 24.508 3.927·10 30 SF H (a) C 22.381 3.586·10 -18 31 3 3 3v -18 32 SF 3H3 (b) C2v 22.565 3.615·10 33 SF H (a) C 20.670 3.316·10 -18 34 2 4 2v -18 35 SF 2H4 (b) D4h 20.058 3.214·10 36 SFH C 18.165 2.910·10 -18 37 5 4v -18 38 SH 6 Oh 15.230 2.440·10 39 -18 SCl 6 Oh 14.372 2.303·10 40 41 42 Table 3. Magnitudes of dipole moments vectors in [Debye] and [C·m]. 43 Molecule Symmetry Dipole magnitude 44 45 [Debye] [C·m] 46 SF O 0.080 0.267·10 -30 47 6 h -30 48 SF 5H C4v 1.752 5.844·10 49 -30 SF 4H2a C2v 2.659 8.871·10 50 -30 51 SF 4H2b D4h 0.001 0.003·10 52 -30 SF 3H3a C3v 3.634 12.122·10 53 -30 54 SF 3H3b C2v 2.151 7.175·10 -30 55 SF 2H4a C2v 3.392 11.314·10 56 SF H b D 0.067 0.223·10 -30 57 2 4 4h -30 58 SFH 5 C4v 2.610 8.706·10 59 SH O 0.039 0.131·10 -30 60 6 h -30 SCl 6 Oh 0.042 0.141·10

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1 2 6 6

3 0 0 0 0 0 0 0 0 0 1.3 1.3 1.3 SCl SCl 4 139.7 139.7 139.7 205.7 205.7 205.7 230.7 230.7 230.7 253.9 263.2 263.2 400.1 400.1 400.1 116.7 116.7 116.7 5 6 7 8 6 6

9 0 0 0 0 0 0 0 0 0 SH SH 49.6 49.6 49.6 678.2 678.2 678.2 10 1319.5 1319.5 1319.5 1322.8 1322.8 1322.8 1329.3 1329.3 1329.3 1909.2 1909.2 2014.5 2014.5 2014.5 2173.2 11 12 13 5 14 5 0 0 0 0 2.4 2.4 6.9 6.9 168 30.2 32.2 32.2 99.5 357.3 357.3 15 630.4 787.3 787.3 16 1112.5 For1220.5 1264.9 1264.9 1405.5 Peer1405.5 1553.4 2070.1 2198.5 2198.5 2277.0 Review2438.2 Only 17 18 b SFH b SFH 4 19 4 H H 0 0 0 0 0 0 0 2 20 2 20.5 20.5 11.7 40.3 40.3 361.6 284.2 284.2 430.8 430.8 611.7 837.5 937.2 21 1119.8 1119.8 1299.7 1423.6 1423.6 1651.4 2174.4 2293.1 2293.1 2354.9 22 23 a SF 24 a SF 4 4 H 25 H 0 5 1 0 2 2 0.3 4.5 4.6 27.2 12.6 12.8 58.5 44.3 82.1 171.2 186.8 26 337.7 634.1 675.0 774.9 890.6 956.3 1213.5 1228.2 1338.8 1352.8 1402.4 2451.8 2484.5 2501.8 2505.1 27 28 29 b SF b SF 3 30 3 H H 0 3 3 0.8 3.8 0.1 9.1 1.1 2.6

31 26.7 13.1 33.1 33.5 24.1 17.6 191.5 389.1 346.9 375.9 422.0 607.4 698.4 844.9 941.8 32 1134.9 1159.4 1262.4 1280.3 1449.0 2523.6 2540.9 2592.0 33 34 13 - - a SF 35 a SF 3 3 H H 0 3 36 3 0.9 0.9 4.5 5.6 1.7 1.7 20.7 20.7 40.6 26.4 26.4 156.1 156.1 188.3 367.2 367.2 486.3 690.7 690.7 786.5 866.8

37 1098.6 1098.6 1347.1 1361.3 1361.3 2575.2 2575.5 2575.5 38 39 40 b SF b SF 2 41 2 H H 0 0 0 0 0 0 0 4 4 5.1 5.1 0.5 0.5 90.3 0.05

42 417.7 417.7 276.2 380.1 380.1 418.7 584.6 642.6 649.4 860.2 860.2 43 1195.5 1195.5 1253.2 1253.2 2649.1 2725.0 44 45 a SF a SF 2 2 46 ]. -1 H H 0 0 4 47 4 1.5 7.9 3.4 8.4 0.3 1.7 ]. 10.2 25.9 15.1 13.6 168.8 192.2 395.6 325.8 348.2 399.4 464.4 530.6 620.0 718.4 809.6 875.7 -1 48 1086.8 1169.1 1263.1 1391.9 2621.4 2636.2 49 50 51 H SF 52 H SF 5 5 0 0 0 1.3 1.3 8.7 8.7 0.1 0.1 0.2

53 19.1 14.9 SF SF 296.3 346.2 346.2 449.0 515.3 515.3 572.6 606.5 659.2 832.1 902.6 902.6 189.4 407.7 407.7 54 1241.0 1241.0 2707.1 55 56 57 6 6

58 0 0 0 0 0 0 0 0 0 22.2 22.2 22.2 390.2 390.2 390.2 59 315.6 315.6 315.6 477.7 477.7 477.7 567.0 567.0 567.0 625.0 625.0 722.9 937.4 937.4 937.4 60 7 8 9 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 10 11 12 13 14 15 16 17 18 19 20 21 Mode SF Mode SF Table 5.of Intensities normal modes[km·mol in Table4. Frequencies of normal [cm in modes

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1 2 3 4 6 0 0 0 0 0 0 0 0 0 SCl

5 0.001 0.001 0.001 0.119 0.119 0.119 6 7 8

9 6 0 0 0 0 0 0 0 0 0

10 SH 0.05 0.05 0.05 0.69 0.69 0.69 11 12 13 14 5

15 0 0 0 0 0.1 0.17 0.03 16 0.003 0.003 For0.007 0.007 Peer0.033 0.033 0.364 0.364 Review Only 17 18 19 b SFH 20 4 H 0 0 0 0 0 0 0 2

21 0.29 0.29 0.021 0.021 0.369 0.012 0.041 0.041 22 23 24 a SF

25 4 H 0 0 0 26 2 0.06 27 0.175 0.191 0.005 0.028 0.013 0.013 0.001 0.005 0.005 0.045 0.084

28 [a.u.]. 29 30 b SF 3

31 H 0 0 3

32 0.001 0.004 0.027 0.014 0.195 0.397 0.034 0.009 0.001 0.003 0.031 0.028 0.018 33 34 14 - - 35 a SF

36 3 H 0 37 3 38 0.001 0.001 0.005 0.159 0.159 0.192 0.021 0.021 0.006 0.002 0.002 0.041 0.027 0.027 39 40

41 b SF 2 H

42 0 0 0 0 0 0 0 0 0 0 4

43 0.005 0.005 0.092 0.427 0.427 44 45 46 dipole infraredwrt moments active normal in modes a SF 47 2 H 0 0 0 0 0 0 4

48 0.2 0.4 0.01 0.01 0.01 0.17 0.03 0.02 0.01 49 50 51 52 H SF

53 5 0 0 0 0 0 0 SF 54 0.001 0.001 0.009 0.009 0.019 0.015 0.193 0.416 0.416 55 56 57

58 6 0 0 0 0 0 0 0 0 0 0.4 0.4 0.4 59 SF 0.02 0.02 0.02 60

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Table6. Square derivatives of first of moleculars Mode

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1 2 3 Table 7. Charges partitioned by Hirshfeld method. 4 5 Molecule Symmetry Charges 6 7 S F H/Cl

8 9 SF 6 Oh 0.5801 -0.0967 - 10 SF 5H C4v 0.5013 -0.1148 0.0729 11

12 SF 4H2a C2v 0.4224 -0.1333 0.0553

13 14 SF 4H2b D4h 0.4249 -0.1419 0.0714 15 SF H a C 0.3396 -0.1591 0.0459 16 3 3 3vFor Peer Review Only

17 SF 3H3b C2v 0.3459 -0.1643 0.0490 18

19 SF 2H4a C2v 0.2613 -0.2078 0.0386 20 SF H b D 0.2776 -0.1619 0.0116 21 2 4 4h

22 SFH 5 C4v 0.1917 -0.2248 0.0066 23

24 SH 6 Oh 0.1361 - -0.0227 25 SCl O 0.3411 - -0.0568 26 6 h 27 28 29 30 31 Table 8. Thermodynamic properties. 32 Molecule Symmetry Total entropy Vibrational ZPVE Free energy Heat capacity 33 [cal·mol -1· K-1] entropy [kcal·mol -1] [kcal·mol -1] [cal·mol -1· K-1] 34 [cal·mol -1·K-1] 35 36 SF 6 Oh 77.235 9.128 12.682 -18.776 24.175 37 SF 5H C4v 74.798 7.662 17.349 -18.355 21.553 38 39 SF 4H2a C2v 71.896 5.977 21.816 -17.829 18.883

40 SF 4H2b D4h 72.350 6.239 21.906 -17.928 18.933 41 42 SF 3H3a C3v 68.412 4.780 26.870 -17.165 16.156

43 SF 3H3b C2v 68.879 4.337 25.992 -17.262 16.249 44 SF H a C 65.210 2.576 29.664 -16.462 13.770 45 2 4 2v 46 SF 2H4b D4h 64.384 2.624 29.165 -16.259 13.735 47 SFH C 60.170 1.800 32.541 -15.331 11.263 48 5 4v 49 SH 6 Oh 54.932 0.231 34.238 -13.948 9.253 50 SCl 6 Oh 101.464 28.160 5.302 -23.158 34.214 51 a 52 Zero Point Vibrational Energy. 53 54 55 56 57 58 59 60

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1 "Catchline" (i.e. wording at head of first page only) Journal Name in Full 2 Vol. X, No. X, Month 200X, 000–000 3 4 5 6 7 8 9 10 M. K. Bruska, J. Piechota 11 12 13 14 Molecular Simulation 15 RESEARCH NOTE 16 For Peer Review Only 17 18 Density Functional Study of Sulfur Hexafluoride (SF6) and its Hydrogen Derivatives. 19 20 21 22 a b* 23 MARTA KINGA BRUSKA AND JACEK PIECHOTA 24 a Department of Chemistry, Jagiellonian University, ul. R. Ingardena 3,30-060 Kraków, Poland 25 b Interdisciplinary Centre for Materials Modelling, University of Warsaw, ul. Pawinskiego 5a, 02-106 Warszawa, Poland 26 27 28 29 Abstract 30 31 Density functional study has been performed for a group of compounds derived from sulfur 32 hexafluoride (SF 6) by consecutively substituting fluorine with hydrogen. SF 6 is widely used as the 33 insulating gas in the electrical industry and is recognized as one of the greenhouse gases with 34 extraordinary global warming potential. The aim of the present study is to look for potential 35 industrial alternatives to SF 6 as well as to examine mechanisms that can contribute to its faster 36 atmospheric decay. The ground state geometries, binding energies, vibrational spectra, charge 37 distributions, dipole moments, as well as thermodynamic properties for the series of the SF 6-nHn 38 (n=0…6) molecules have been obtained and discussed. For comparison, computational results for 39 the SCl 6 molecule have also been included in the present study. 40 41 Keywords : sulfur hexafluoride; greenhouse gases; density functional theory; 42 43 44 45 46 47 48 49 ______* Email: [email protected] 50 51 - 1 - 52 53 54 55 56 57 58 59 60

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1 1. Introduction 2 3 Interest in the sulfur hexafluoride (SF 6) system stems both from practical and theoretical 4 considerations. It is one of the most popular (next to air) insulating gases, with a breakdown 5 strength of about 3 times that of air. It has a number of technologically important properties: it is 6 not flammable and non-toxic; at normal temperatures, it is also non-corrosive, and is fairly inert. 7 That is why SF 6 is commonly used in industry as a gaseous dielectric and as a plasma etching gas in 8 applications such as: circuit breakers, gas-insulated busbar systems, and also for large scale 9 scientific applications such as tandem particle accelerators. Other areas of application of SF 6 10 include the magnesium industry to protect molten magnesium from oxidation and potentially 11 violent burning, and semiconductor manufacturing to create circuitry patterns on silicon wafers. 12 Also, SF 6 is a candidate refrigerant to replace the chlorofluorocarbons (CFC's) which are damaging 13 the ozone layer. For an extensive review of SF 6 technical applications see, for example, [1] and 14 publications therein. Formatted: 15 Because of its unique structure, unusual spectroscopy, and applied interest, the SF 6 molecule Justified has been a subject of much interest both experimentally and theoretically. Photoelectron [2-4], 16 For Peer Review Only valence-shell [5-7], and inner-shell [8-11] photoionization and valence-shell [12] and inner-shell 17 [13-16] electron energy-loss experimental measurements have been performed. The unique, 18 octahedral symmetry structure of SF provides good example of shape resonance phenomena. The 19 6 infrared active modes of octahedral molecules are of F1u symmetry and ν3 as well as ν4 bands are 20 -1 allowed in absorption [17]. In particular, the region of the ν3 fundamental near 950 cm has very 21 strong absorption. The bond dissociation energy of SF 6 (to SF 5 + F) is 3.82 eV, but 22 photodissociation is not observed until the photon energy exceeds ~10 eV [18]. 23 On the theoretical side, SF 6 has become a classic molecule for the study of electron 24 attachment at ultralow electron energies. The attachment of low energy electrons to SF 6 results in — — 25 Deleted : 2 formation of a metastable negative ion by the process: SF 6 + e → SF 6 [18 -21 ]. An understanding 26 Deleted : of the thermal electron attachment properties and temperature behaviour of rate constant for SF 6 is, in 5 27 turn, of importance in the design of gaseous insulators and diffuse discharge switchers. 28 Deleted : However, at the same time SF 6 is the most potent greenhouse gas that has been evaluated by Furthermore, SF 6 has a 29 unique, octahedral symmetry structure, the Intergovernmental Panel on Climate Change (IPCC), with a global warming potential (GWP) of which provides good example of shape 30 22,800 times that of CO 2 when compared over a 100 year period [22 ]. Two main factors resonance phenomena. The infrared 31 contributing to this extraordinary high value of GWP is strong radiative forcing (0.52 Wm -2ppb -1) active modes of octahedral molecules are of F1u symmetry and ν3 as well as ν4 32 and very long atmospheric lifetime ( 800-3200 years) [ 22-26 ]. In the stratosphere, the highest energy bands are allowed in absorption [6]. In 33 particular, the region of the ν3 solar photons have an energy of ~6 eV, so it is very unlikely that SF 6 will be photodissociated there. fundamental near 950 cm -1 has very 34 Therefore, although the concentration of SF 6 is still relatively low in the Earth's atmosphere (5.21 strong absorption. The bond dissociation energy of SF 6 (to SF 5 + F) is 3.82 eV, but 35 ppt) [26 ], it is one of the greenhouse gases that the Kyoto Protocol seeks to control [ 27 ], as even photodissociation is not observed until 36 small amounts of SF 6 emissions can constitute a significant carbon-equivalent emission tonnage. the photon energy exceeds ~10 eV [4].¶ 37 Apart from destroying ozone layer , greenhouse gases that can absorb infrared radiation in Formatted: Indent: First line: 38 the so-called “atmospheric window” between the wavelengths of 800 - 1400 cm -1 are of great 35.45 pt 39 concern because they are able to trap radiation that would have otherwise been emitted into space . Deleted : 7 40 In other words, without greenhouse gases most of the radiation emitted by the earth's surface at Deleted : 8 41 wavelengths within in the atmospheric window would have passed through the Earth's atmosphere Deleted : 8 42 without heating it. Deleted : 9 -2 -1 43 Recently, another compound with extremely strong radiative forcing (of 0.59 Wm ppb ), Deleted : — 44 identified as trifluoromethyl sulfur pentafluoride (SF 5CF 3), has been detected in the atmosphere 45 [28 ,29 ]. It is supposed that SF 5CF 3 originates as a breakdown product of SF 6 formed by high- Deleted : 10 46 voltage discharges in electric industry equipment [28 ]. Atmospheric lifetime of SF 5CF 3 (~800 Deleted : 11 47 years) is lower than that of SF 6, but its value of GWP (~17,700) is one of the highest of all other Deleted : 10 greenhouse gases [ 22]. 48 Deleted : 7 It is worth noting, however, that the greenhouse gases with the greatest GWP values are the 49 fully fluorinated compounds (FFC’s): CF 4, C 2F6, C 3F8, c-C4F8, SF 6, NF 3 and CHF 3, that are widely 50 Deleted : 12 51 - 2 - 52 53 54 55 56 57 58 59 60

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1 used by the semiconductor industry [ 30 ]. As for now there is no significant mechanism for their Deleted : 12 2 destruction in the natural circulation of the Earth's atmosphere — as a result their atmospheric 3 lifetimes are estimated to be up to 50,000 years for CF 4 [22 ]. Deleted : 7 4 In case of CFC’s a wide variety of alternative compounds has been investigated with the aim 5 of protecting the ozone layer and reducing the global warming. The basic concept in the process of 6 development of alternative CFC’s is the introduction of a hydrogen atom into the CFC molecule to 7 reduce its atmospheric lifetime without detrimenting its properties. In this way, several 8 hydrochlorofluorocarbons (HCFC’s) and hydrofluorocarbons (HFC’s) have already been developed 9 and have found practical use. The introduction of hydrogen atoms into the molecule raises the 10 compound’s reactivity towards OH radicals as the reactivity with OH radicals is related to the 11 stability of the molecule in the troposphere [ 31]. Deleted : 3 12 Motivated by this fact we have studied the series of the SF 6-nHn (n=0…6) molecules where 13 the fluorine atoms of SF 6 were consecutively replaced with the hydrogen atoms. The aim of the 14 study is to look for potential industrial alternatives to SF 6 as well as to examine mechanisms that 15 can contribute to its faster atmospheric decay. SCl6 has been also taken into consideration to compare our results with a heavier analogue of the SF molecule. To our best knowledge this is the 16 For Peer 6 Review Only first report on the properties of the SF H series of compounds. 17 6-n n The present study is based on density functional theory (DFT) [ 32 ,33 ]. This approach has Deleted : 14 18 over the past decade emerged as a tangible and versatile computational method with applications in Deleted : 15 19 many subfields of chemistry. The DFT-based methods can provide bond energies, structures and 20 other electronic properies of high accuracy. The method has previously been applied to similar 21 studies on diatomic 3 d transition metal monoxides [ 34 ,35 ]. Deleted : 16 22 The rest of the paper is organized as follows. Computational details are reported in Section Deleted : 17 23 2. In Section 3 the ground state geometries, bonding energies, vibrational spectra, charge 24 distributions partitioned by Hirshfeld method, dipole moments, as well as thermodynamic 25 properties are presented and analyzed. In Section 4 the main points of this work are summarized 26 and perspectives for future research are outlined. 27 28 2. Computational details 29 30 As mentioned in the introduction, the computational method used for the purpose of the present 3 31 study is based on DFT as implemented in the DMol code [36 ,37 ] available as part of the Materials Deleted : 18 3 32 Studio 4.0 software environment [ 38 ]. For an extensive review of the DMol description and its Deleted : 19 33 features we refer the reader to [ 36 ,37 ] and references therein. We present here only a summary of Deleted : 20 3 34 the input parameters set up in the DMol package in order to get stable and accurate results, as Deleted : 18 35 compared to experiment and other calculations. Deleted : 3 19 36 DMol uses numerical functions on an atom-centered grid as its atomic basis. For the 37 purpose of the present study the DNP basis set was used for all atoms. The DNP basis set uses 38 double-numerical quality basis set with polarization functions. This means that for each occupied 39 atomic orbital one numerical function is generated and a second set of this functions is given for 40 valence atomic orbitals. It also generates polarization d-functions on all non-hydrogen atoms and 41 polarization p-function on all hydrogen atoms. The DNP basis sets are comparable in quality to 42 Gaussian 6-31G** basis sets. The quality of the integration grid that controls the selection of mesh points for the 43 numerical integration procedure used in the evaluation of the matrix elements was chosen to be 44 FINE. The electron density in DMol 3 is expanded in terms of multipolar partial densities (auxiliary 45 density) used to specify the maximum angular momentum Lmax of the multipolar fitting functions 46 that specify the analytical form of the charge density and the Coulombic potential. This parameter 47 was set to be OCTUPOLE which corresponds to Lmax of 3. 48 The local density approximation (LDA) can be used to predict the structures and relative 49 energies of covalent and ionic systems quite accurately. However, usually bond energies are 50 51 - 3 - 52 53 54 55 56 57 58 59 60

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1 overestimated while vibrational frequencies are underestimated than those obtained within other 2 methods and experimental data. These problems with the LDA method can be corrected to large 3 extent by using the so-called gradient-corrected (or nonlocal) functionals. However, extensive test 4 calculations with local and non-local functionals yielded that in the case of SF 6 it is the LDA 5 method with Perdew-Wang functional (PWC) that yield the results closer to available experimental 6 data. We have therefore adopted this approach in all calculations performed for the purpose of the 7 present study. 8 Vibrational spectra and Hessians were computed by finite differences of analytic first 9 derivatives. This means that each atom in the system was displaced in each Cartesian direction. The 10 results of Hessian evaluation have been used to compute thermodynamic properties of the 11 molecules. Point group symmetry was used to reduce the total number of displacements. The 12 vibrational analysis was performed at the final geometry. Hirshfeld partitioned charges were 13 defined relative to the deformation density. Finally, the convergence criteria were established to be 14 FINE both for the SCF density convergence (the density convergence threshold for SCF) and for 15 the optimization energy convergence (the threshold for energy convergence during geometry optimization). The numerical values for these thresholds were 10 -6 Ha and 10 -5 Ha, respectively. 16 For Peer Review Only

17 3. Results and discussion 18

19 3.1 Geometry optimization 20 21 The accuracy of the data obtained in the course of the present study can be compared only in the 22 case of the reference SF 6 molecule. There have been quite a number of electronic properties 23 calculations for this system, and the predicted properties vary remarkably depending upon the 24 methodology of the computation (see Ref. 39 for the discussion). Therefore we decided to compare Deleted : 31 25 results yielded by our calculation with theoretical studies founded on DFT [ 39,40 ] that are available Deleted : 21-22 26 for the SF 6 molecule. The first and the most extensive work (however, without calculated 27 vibrational frequencies) came from Tang and Callaway [ 39 ] who performed calculations for SF 6 in Deleted : 21 28 the local spin density (LSD) approximation. Delley [ 40 ] studied static deformations and vibrations Deleted : 22 29 of SF 6 with an applied strong static electric field; basic molecular properties in the absence of 30 external electrostatic fields in local as well as gradient corrected approximations to DFT were 31 obtained. To our knowledge these are all numerical studies of the electronic structure of the SF 6 32 molecule based on the DFT methodology. Molecular properties of SF 6 are collected in Table 1. 33 It can be seen from Table 1 that our results obtained for the SF 6 molecule are in good 34 agreement with those presented in Ref. 39 and Ref. 40 . The maximum deviation of calculated Deleted : 21 -1 35 frequencies is at 49 cm , that is less than 10% in comparison with experimental values. The LDA Deleted : 22 36 PWC approximation thus gives a fairly accurate description of the energy surface near the 37 equilibrium conformation. Surprisingly enough, the gradient corrected functionals perform 38 significantly worse for this molecule, except for the binding energy. 39 The equilibrium structures as obtained from optimization of geometry of all studied 40 molecules in their ground states are shown in Figure 1. The structures were optimized in imposed 41 symmetry, relevant to each molecule (see the labels under the figure labels), in order to reduce the 42 computational time whenever possible. The highest symmetry point group O h is adopted by the SF 6 molecule, as well as by the SH and SCl ones. With the substitution of fluorine atoms with the 43 6 6 hydrogen ones the symmetry is lowered, but symmetries of the SF H (n=1…5) molecules are 44 6-n n consistent with the correlation table of the Oh group. For molecules SF 6-nHn (n=2,3,4) two possible 45 nonequivalent conformations exist: the first one, denoted further as (a), in which one of the 46 hydrogen atoms is perpendicular to other hydrogen atom(s), and the second one, denoted as (b), in 47 which all hydrogen atoms are in the same plane. Subsequent DMol 3 computations of other 48 properties were performed at these final geometries. 49 Closer examination of structural data obtained shows that geometry of the SF 6-nHn (n=1…6) 50 51 - 4 - 52 53 54 55 56 57 58 59 60

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1 molecules resembles that of the SF 6 parent one. Due to large amount of data collected detailed 2 values of bond lengths and angles are available from the authors [41]. For the purpose of the present 3 study only principal trends are summarized. The relevant H-S-F angles are very close to 90 o or o 4 180 , respectively. The most deformed structure is that of SF 2H4 (a) with low, C2v symmetry. The 5 deviation from 180 o is about 10 o. The molecular distances between sulfur and fluorine atoms 6 increase as the fluorine atoms are substituted by the hydrogen ones, and hydrogen-sulfur distances 7 are smaller than the fluorine-sulfur ones. These trends are illustrated in Figure 2a and 2b. It is worth 8 to mention that in the case of SCl 6 the chlorine-sulfur distance is significantly larger and equals to 9 2.1461 Å. Deleted : Trend in binding energy for the SF 6-nHn (n=0…6) series and SCl 6 is 10 The results obtained for binding energies for the SF 6-nHn (n=0…6) series and SCl 6 are listed illustrated in Figure 3. 11 in Table 2. The SF 6 molecule has the highest binding energy as compared to the SF 6-nHn (n=1…6) series. Interestingly enough, the SCl 6 and SH 6 molecules have similar values of binding energies. Deleted : These results are listed in 12 Table 2 13 Since the SF 6, SH 6 and SCl 6 molecules have octahedral symmetry, as well as the SF 4H2 (b) and 14 SF 2H4 (b) have tetragonal symmetry, there are no static dipole moments in their case. The values of 15 dipole moments obtained for the molecules under study are listed in Table 3, and its analysis is postponed to Section 3.3. 16 For Peer Review Only Closer examination of single particle eigenvalues (depicted in Figure 3) yields that with Deleted : 4 17 increasing number of the H atoms in the SF H system the number of eigenstates is gradually 18 6-n n diminishing, as there are less electrons. Symmetries of the orbitals are changing according to 19 symmetries of the given SF H system (in order to keep the Figure 3 as readable as possible we Deleted : 4 20 6-n n decided to label eigenstates only for SF 6 and SH 6 molecules). Because of the same molecular 21 symmetry of the SF 6 and SH 6 molecules molecular orbitals have the same symmetry in their case. 22 However, there are fewer electrons in SH 6 than in SF 6, so only 6 first single particle eigenstates in 3 23 energetically lowest states with symmetries A 1g, T 1u and E g are occupied. Deleted : i 24 25 3.2 Optical properties 26 27 Explicit values of the frequencies and intensities of the normal modes for all the SF 6-nHn (n=0…6) Deleted : N 28 molecules are listed in Tables 4 and 5, respectively, supplemented with data obtained for SCl 6. In Deleted : and their frequencies 29 Table 6 square of first derivatives of molecular dipole moments wrt infrared active normal modes Deleted : shown in Figure 5, while 30 are shown. explicit values, Deleted : 31 The infrared absorption spectrum of SF 6 is composed of two bands. Only ν3 and ν4 modes , with F 1u symmetry satisfy dipole selection rules and are allowed in absorption. Their maxima are Deleted : are listed in Tables 4 and 5. 32 -1 33 located at 567.2 and 938.06 cm with intensity respectively 22.17 and 390.19 km/mol. Both of Deleted : Calculated absorption spectra are collected in Figure 6. 34 these normal modes are triple degenerate and correspond to the change of bond lengths and bond angles. 35 The frequencies of vibrations are expected to increase as hydrogen atoms are substituted for 36 fluorine ones. This effect can be attributed to the extension of reduced masses of these molecules, as 37 well as the decrease of intermolecular interactions (see Figure 2a and 2b, as well as Table 2): 38 binding energies are decreasing and bond lengths are increasing. As a consequence, with increasing 39 n in SF 6-nHn (n=0…6) spectra are shifted into higher energies. Variations in mass distribution and 40 molecular geometries cause also alterations in symmetries of normal modes. The intensity of 41 absorption for the fundamental vibrational transitions is given by: 42 43 −1 44 A= Bnw ⋅h⋅νnw ⋅c ⋅ NA , 45 46 where A is the integral coefficient of absorption (measure of absorption in band), νnw is the 47 frequency of transition between n and w levels, and B nw is the Einstein coefficient for induced 48 emission, which can be expressed as: 49 50 51 - 5 - 52 53 54 55 56 57 58 59 60

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1 3 8π 2 2 Bnw = 2 ⋅ nw , 3 3h 4 in which is the transition moment for n and w levels. For the fundamental transitions, this 5 nw quantity is proportional to square of first derivatives of molecular dipole moments wrt infrared 6 active normal modes. As it is shown in Table 6, these values are increasing with the increasing rate 7 of replacement of fluorine by hydrogen. 8 Molecules SCl 6 and SH 6 are again quite similar to SF 6. As they adopt Oh point group 9 symmetry, the infrared spectra are analogous to this of SF . The difference is in the frequencies of 10 6 normal modes and intensities of their absorption. SCl 6, as a heavier molecule, has lower vibrational 11 transition intensity as well as lower frequencies of normal modes. In contrast to this, SH 6 has a 12 much higher vibrational transition intensity and higher frequencies of normal modes. This means 13 that SH 6 absorbs even more radiation than SF 6, but in the range of higher frequencies. SH 6 has also Deleted : for 14 nearly two times lower binding energy than SF 6 and, as such, is less stable. -1 15 It is also worth to mention that strongest absorption band of SF 6 at ~940 cm is located in Formatted: Justified 16 the atmospheric windowFor mentioned inPeer Section 1, and noReview other molecule studied hereOnly has so strong 17 absorption band in this frequency region as SF 6 has. 18 19 3.3 Charge distribution and dipole moments 20 21 Charge partitioning as obtained from Hirshfeld method for all the SF 6-nHn (n=0…6) molecules and 22 the SCl 6 one is listed in Table 7. These values are normalized to single atoms, so one should bear in 23 mind that for given n in SF 6-nHn qS = (6-n)•qF + n•qH. Hirshfeld analysis for SF 6 indicates positive 24 charge on the sulfur atom and small negative charges on the fluorine atoms. Negative charges on the fluorine atoms increase while positive charge on the sulfur atom decreases as fluorine atoms are 25 gradually substituted with the hydrogen atoms. Although not included here, the results of Mulliken 26 analysis are consistent with the results of Hirshfeld one. 27 The dipole moment of a molecule is determined by the charges and the induced dipoles on 28 the constituent atoms. Because of symmetric charge distribution, there are no static dipole moments 29 in molecules: SF 6, SF 4H2 (b), SF 2H4 (b), SH 6 and SCl 6. The SF 5H has almost two times smaller 30 magnitude of dipole moment than SFH 5, although charges on constituent atoms are larger in SF 5H 31 than in SFH 5, and both molecules have the same symmetry. One can assume that for SFH 5 the 32 charge and induced dipole contributions have the same polarity that account for its large dipole 33 moment, in contrast to SF 5H. In case of the SF 3H3 (a) and (b) molecules the large difference in 34 dipole moments is caused by different symmetry of charge distribution. 35 36 3.4 Thermodynamical properties 37 38 Basic thermodynamic properties such as total entropy, vibrational entropy, free energy, heat 39 capacity and zero point vibrational energy have been also calculated for the SF 6-nHn (n=0…6) and 40 SCl 6 molecules. The results are presented in Table 8 . Additionally, entropy as a function of Formatted: Font: (Default) Times temperature for all the molecules studied here is depicted in Figure 4. Values of heat capacity New Roman, Complex Script Font: 41 Times New Roman decrease with molecular mass reduction. As the heat capacity is defined as the amount of heat 42 Formatted: Font: 12 pt, Complex 43 required to change the temperature of a substance by one degree, larger molecules will need more Script Font: 12 pt heat than smaller ones. This suggest that insulating properties of SCl are the best of all the 44 6 Deleted : and molecules studied here, in particular better than these of SF . The industrial usage of SF instead of 45 6 6 Formatted: Font: (Default) Times SCl is due to greater stability of SF than SCl (bonding energy for SF is twice higher than that 46 6 6 6 6 New Roman, Complex Script Font: for SCl ). Total and vibrational entropy decreases as fluorine atoms are substituted with hydrogen Times New Roman 47 6 ones. On the other hand the free energy and zero point vibrational entropy show opposite tendency. Deleted : s 48 This behaviour is in good relation to changes in molecular mass of studied compounds. Deleted : 7 to 12 49 50 51 - 6 - 52 53 54 55 56 57 58 59 60

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1 4. Conclusions 2 3 In the present study the series of the SF 6-nHn (n=0…6) molecules have been examined for the first 4 time. Molecular constants such as equilibrium bond distances, binding energies, vibrational 5 frequencies, charge distributions partitioned by Hirshfeld method, dipole moments, as well as 6 thermodynamic properties have been determined and analyzed. 7 The results of IR spectra simulations confirm that it is fluorine atoms that play crucial role in 8 greenhouse effect of SF 6. For other molecules with octahedral symmetry, such as SH 6 and SCl 6, 9 their absorption bands are outside the atmospheric window. On the other hand, for the SF 6-nHn 10 (n=1…5) molecules with lower symmetries, there are more absorptions bands with reduced 11 intensities as compared to SF 6. Because of inherent approximations in DFT, computational methods based on this approach 12 are not expected to yield very accurate values of molecular constants, as wavefunction based ab 13 initio methods do. Rather, due to their efficiency and robustness DFT-based methods constitute 14 valuable tool in predicting general trends across a wide range of compounds. Therefore, the present 15 study can be regarded as the first step toward more detailed examination of the series of SF H 16 For Peer Review Only6-n n (n=0…6) molecules. Further research can cover following areas: Formatted: Indent: Before: 0 pt, 17 (1) formation of metastable negative ions; Hanging: 35.45 pt, Space After: 6 pt 18 (2) reaction paths with OH radicals; Formatted: Font: Italic, Complex Script Font: Italic 19 (3) investigation of excited states. 20 Formatted: Font: Italic, Complex These topics are outside the scope of the present study, but the need for further ab initio Script Font: Italic 21 calculations for these systems is therefore obvious. Formatted: Font: Italic, Complex 22 Script Font: Italic, Subscript 23 Formatted: Font: Italic, Complex 24 Acknowledgements Script Font: Italic 25 Formatted: Font: Italic, Complex 26 The authors are indebted to Dr. Paweł M. Masiak, Institute of Physics, Polish Academy of Sciences, Script Font: Italic, Subscript 27 for many valuable discussions, and to Dr. Carsten Menke, Accelrys, Inc., for his technical Formatted: Font: Italic, Complex 3 Script Font: Italic 28 assistance with the DMol code. Formatted: 29 Font: Italic, Complex References Script Font: Italic, Subscript 30 Formatted: Font: Italic, Complex 31 [1] IEE Colloquium on An Update in SF6 and Vacuum Switchgear at Distribution Levels Script Font: Italic 32 (Digest No.1996/185), IEE, London, 1996 Formatted: Font: Italic, Complex 33 Script Font: Italic 34 [2] D. C. Frost, C. A. McDowell, J. S. Sandhu, D. A. Vroom, Photoelectron spectrum of sulfur Formatted: Font: Italic, Complex Script Font: Italic 35 hexafluoride at 584 Å, J. Chem. Phys. 46 (1967), p. 2008 Formatted: Font: Italic, Complex 36 [3] B. M. Addison Jones, K. H. Tan, G. M. Bancroft, F. Cerrina, A comparison of shape Script Font: Italic, Subscript 37 resonant behavior in the inner-shell photoabsorption and valence-level photoelectron Formatted: Font: Italic, Complex 38 spectra of sulfur hexafluoride, sulfur chloride fluoride and hexafluoride (SF 6, Script Font: Italic 39 SF 5Cl and SeF6), Chem. Phys. Lett. 129 (1986), p. 468 Formatted: Font: Italic, Complex Script Font: Italic, Subscript 40 [4] B. M. Addison Jones, K. H. Tan, B. W. Yates, J. N. Cutler, G. M. Bancroft, J. S. Tse, 41 Formatted: Font: Italic, Complex A comparison of valence level photoelectron cross sections for SF 6, SeF 6 and “F 6” from 21 Script Font: Italic 42 eV to 100 eV photon energy , J. Electron Spectrosc. Relat. Phenon. 48 (1989), p. 155 Formatted: Font: Italic, Complex 43 Script Font: Italic, Subscript 44 [5] V. H. Dibeler, J. A. Walker, Photoionization efficiency curve for SF6 in the wavelength region 1050 to 600 Å, J. Chem. Phys. 44 (1966), p. 4405 Formatted: Font: Italic, Complex 45 Script Font: Italic 46 [6] R. N. Compton, R. H. Huebner, P. W. Reinhardt, L. G. Christophroou, Threshold electron Formatted: Font: Italic, Complex 47 impact excitation of atoms and molecules: detection of triplet and temporary negative ion Script Font: Italic 48 states , J. Chem. Phys. 48 (1968), p. 901 Formatted: Font: Italic, Complex Script Font: Italic 49 [7] D. M. P. Holland, D. A. Shaw, A. Hopkirk, M. A. MacDonald, S. M. McSweeney, A study Formatted: Font: Italic, Complex 50 Script Font: Italic 51 - 7 - 52 53 54 55 56 57 58 59 60

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1 of the absolute photoabsorption cross section and the photoionization quantum efficiency of 2 sulfur hexafluoride from the ionization threshold to 420 Å, J. Phys. B 25 (1992), p. 4823 3 [8] T. A. Ferret, D. W. Lindle, P. A. Heimann, M. N. Piancastelli, P. H. Kobrin, H. G. Kerkhoff, 4 U. Becker, W. D. Brewer, D. A. Shirley, Shape-resonant and many-electron effects in the S Formatted: Font: Italic, Complex 5 2p photoionization of sulfur hexafluoride , J. Chem. Phys. 89 (1988), p. 4726 Script Font: Italic 6 7 [9] R. E. LaVilla, Sulfur K and L and fluorine K x-ray emission and absorption spectra of Formatted: Font: Italic, Complex Script Font: Italic 8 gaseous sulfur hexafluroide , J. Chem. Phys. 57 (1972), p. 899 9 [10] D. Blechschmidt, R. Haensel, E. E. Koch, U. Nielsen, T. Sagawa, Optical spectra of gaseous Formatted: Font: Italic, Complex 10 and solid sulfur hexafluoride in the extreme ultraviolet and soft x-ray region , Chem. Phys. Script Font: Italic 11 Lett. 14 (1972), p. 33 12 [11] J. L. Dehmer, Evidence of effective potential barriers in the x-ray absorption spectra of Formatted: Font: Italic, Complex 13 molecules , J. Chem. Phys. 56 (1972), p. 4496 Script Font: Italic 14 15 [12] T. Sakae, S. Sumiyoshi, E. Murakami, Y. Matsumoto, K. Ishibashi, A. Katase, Scattering of Formatted: Font: Italic, Complex Script Font: Italic 16 electrons by methane,For carbon tetrafluoridePeer and sulfReviewur hexafluoride in the 75-700Only eV range , 17 J. Phys. B 22 (1989), p. 1385 18 [13] A. P. Hitchcock, C. E. Brion, M. J. Van der Wiel, Ionic fragmentation of sulfur hexafluoride Formatted: Font: Italic, Complex 19 ionized in the sulfur 2p shell , J. Phys. B 11 (1978), p. 3245 Script Font: Italic 20 [14] A. P. Hitchcock, C. E. Brion, Inner shell excitation of sulfur hexafluoride by 2.5 keV Formatted: Font: Italic, Complex 21 electron impact , Chem. Phys. 33 (1978), p. 55 Script Font: Italic 22 23 [15] K. H. Sze, C. E. Brion, Inner-shell and valence-shell electronic excitation of sulfur Formatted: Font: Italic, Complex Script Font: Italic 24 hexafluoride, , and hexafluoride by high energy electron 25 impact: an investigation of potential barrier effects , Chem. Phys. 140 (1990), p. 439 26 [16] J. F. Ying, C. P. Mathers, K. T. Leung, Momentum-transfer dependence of sulfur 2p Formatted: Indent: Before: 0 pt, 27 excitations in sulfur hexafluoride by angle-resolved electron-energy-loss spectroscopy , Hanging: 35.45 pt 28 Phys. Rev. A 47 (1993), p. R5 Formatted: Font: Italic, Complex Script Font: Italic 29 [17] K. Kim, R.S. McDowell, W.T. King, Integrated infrared intensities and transition moments 30 in SF6 , J. Chem. Phys. 73 (1980), p. 36 31 32 [18] L.G. Christophorou, J.K. Olthoff, Electron interactions with SF 6, J. Phys. Chem. Ref. Data 33 29 (2000), p. 267 Deleted : 34 [19 ] A. Chutjian, A. Garscadden, J.M. Wadehra, Electron attachment to molecules at low ¶ 35 electron energies , Phys. Rep. 264 (1996), p. 393 Deleted : 2 Deleted : 3 36 [20 ] R. Morrow, Theory of electrical corona in SF , Nucl. Instr. and Meth. in Phys. Res. A 382 37 6 Deleted : [4] L.G. Christophorou, J.K. (1996), p. 57 Olthoff, Electron interactions with SF 6, 38 J. Phys. Chem. Ref. Data 29 (2000), p. 39 [21 ] P.-T. Howe, A. Kortyna, M. Darrach, A. Chutjian, Low-energy electron attachment to SF 6 at 267 ¶ 40 sub-meV resolution using a tunable laser photoelectron method , Phys. Rev. A 64 (2001), Deleted : 5 41 042706 Deleted : [6] K. Kim, R.S. McDowell, W.T. King, Integrated infrared intensities 42 [22 ] IPCC Working Group 1 (WG1), Changes in Atmospheric Constituents and in Radiative and transition moments in SF6 , J. Chem. 43 Forcing , in 2007 IPCC Fourth Assessment Report (AR4) . Available at Phys. 73 (1980), p. 36¶ 44 http://ipcc-wg1.ucar.edu/wg1/wg1-report.html Deleted : 7 Deleted : 45 [23] Ko, M., N. Sze, W.-C. Wang, G. Shia, A. Goldman, F. Murcray, D. Murcray, C. Rinsland, . 46 Formatted: Indent: Before: 0 pt, Atmospheric Sulfur Hexafluoride: Sources, Sinks and Greenhouse Warming , J. Geophys. Hanging: 35.45 pt, Space After: 6 47 Res. 98(D6) (1993), p. 10499 48 Formatted: Font: Italic, Complex Script Font: Italic 49 [24] Morris, R., T. Miller, A. Viggiano, J. Paulson, S. Solomon, G. Reid, Effects of electron and ion reactions on atmospheric lifetimes of fully fluorinated compounds , J. Geophys. Res. Formatted: Font: Italic, Complex 50 Script Font: Italic 51 - 8 - 52 53 54 55 56 57 58 59 60

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1 100(D1) (1995), p. 1287 2 [25] Geller, L., J. Elkins, J. Lobert, A. Clarke, D. Hurst, J. Butler, R. Myers, Tropospheric SF 6: Formatted: Font: Italic, Complex 3 Observed Latitudinal Distribution and Trends, Derived Emissions and Interhemispheric Script Font: Italic 4 Exchange Time , Geophys. Res. Lett., 24 (1997), p. 675 Formatted: Font: Italic, Complex 5 Script Font: Italic, Subscript 6 [26 ] Wen-Tien Tsai, The decomposition products of sulfur hexafluoride (SF6): Reviews of Formatted: Font: Italic, Complex 7 environmental and health risk analysis , Journal of Fluorine Chemistry 128 (2007), p. 1345 Script Font: Italic Deleted : 8 [27 ] Kyoto Protocol to the United Nations Framework Convention on Climate Change . Available ¶ 9 Formatted: Indent: Before: 0 pt, at: http://unfccc.int/resource/docs/convkp/kpeng.pdf Hanging: 35.45 pt 10 [28 ] W.T. Sturges, T.J. Wallington, M.D. Hurley, K.P. Shine, K. Sihra, A. Engel, D.E. Oram, Deleted : 8 11 S.A. Penkett, R. Mulvaney, C.A.M. Brenninkmeijer, A Potent Greenhouse Gas Identified in Deleted : 12 9 the Atmosphere: SF5CF3 , Science 289 (2000), p. 611 Deleted : 13 10 14 [29 ] P. Masiak, A.L. Sobolewski, Theoretical study of the photophysics of SF5CF3 , Chem. Phys. Deleted : 11 15 313 (2005), p. 169 16 For Peer Review Only Deleted : 12 [30 ] PFC, HFC, SF 6 Emissions from Semiconductor Manufacturing , in Good Practice Guidance 17 and Uncertainty Management in National Greenhouse Gas Inventories , p. 3.69. Available 18 at: http://www.ipcc-nggip.iges.or.jp/public/gp/english/ 19 [31] A. Sekiya, M. Yamabe, K. Tokuhashi, Y. Hibino, R. Imasu, H. Okamoto, Evaluation and Deleted : 1 20 selection of CFC alternatives in Fluorine and the Environment: Atmospheric Chemistry, 21 Emissions & Lithosphere (Advances in Fluorine Science, Vol. 1) A. Tressaud, ed., Elsevier 22 Science, 2006 23 Deleted : 14 24 [32 ] P. Hohenberg, W. Kohn, Inhomogeneous Electron Gas , Phys. Rev. 136 (1964), p. B864. 25 [33 ] W. Kohn, L. J. Sham, Self-Consistent Equations Including Exchange and Correlation Deleted : 15 26 Effects , Phys. Rev. 140 (1965), p. A1133 27 [34 ] J. Piechota, M. Suffczynski, Electronic structure of the CoO molecule , Phys. Rev. A 48 Deleted : 16 28 (1993), p. 2679 29 30 [35 ] J. Piechota, M. Suffczynski, Density functional study of the diatomic first row transition Deleted : 17 31 metal oxides , Z. Phys. Chem. 200 (1997), p. 39 32 [36 ] B. Delley, An all-electron numerical method for solving the local density functional for Deleted : 18 33 polyatomic molecules , J. Chem. Phys. 92 (1990), p. 508 34 [37 ] B. Delley, From molecules to solids with the DMol3 approach , J. Chem. Phys. 113 (2000), Deleted : 19 35 p. 7756 36 Deleted : 20 37 [38 ] Information available at: http://www.accelrys.com/products/mstudio/ Deleted : 21 38 [39 ] R. Tang, J. Callaway, Electronic structure of SF 6, J. Chem. Phys. 84 (1986), p. 6854 39 Deleted : 40 [40 ] B. Delley, Vibrations and dissociation of molecules in strong electric fields:N 2, NaCl, H 2O 22 and SF , J. Mol. Struct. (Theochem) 434 (1998), p. 229 41 6 42 [41] Information available at: http://www.icm.edu.pl/~jp/SF6_bonds_angles.pdf 43 44 45 46 47 48 49 50 51 - 9 - 52 53 54 55 56 57 58 59 60

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1 List of Figures 2 3 Figure 1. Equilibrium geometries of the SF 6-nHn (n=0…6) series and SCl 6 in their ground states: a. SF 6, O h symmetry; b. 4 SF 5H, C 4v symmetry; c. SF 4H2 (a), C 2v symmetry; d. SF 4H2 (b), D 4h symmetry; e. SF 3H3 (a), C 3v symmetry; f. SF 3H3 (b), C2v symmetry; g. SF 2H4 (a), C 2v symmetry; h. SF 2H4 (b), D 4h symmetry; i. SFH 5, C 4v symmetry; j. SH 6, O h symmetry; 5 k. SCl 6, O h symmetry. 6 7 Figure 2. Interatomic distances in the SF 6-nHn (n=0…6) series and SCl 6 a. fluorine-sulfur distances; b. hydrogen-sulfur distances. 8 9 Figure 3. Single particle eigenvalues for the SF 6-nHn (n=0…6) series. For readability only eigenstates for SF 6 and SH 6 Deleted : Figure 3. Binding energies for 10 molecules are labelled. the SF 6-nHn (n=0…6) series and SCl 6¶ 11 ¶ Deleted : 12 Figure 4. Entropy as a function of temperature for the SF 6-nHn (n=0…6) molecules and SCl 6. 4 Deleted : Figure 5. Normal modes (7- 13 21) and their frequencies for the SF6-nHn 14 (n=0…6) series.¶ ¶ 15 Figure 6. Calculated absorption spectra 16 For Peer Review Only for the SF 6-nHn (n=0…6) molecules and SCl 6 in their ground states: a. SF 6, O h 17 symmetry; b. SF 5H, C 4v symmetry; c. 18 SF 4H2 (a), C 2v symmetry; d. SF 4H2 (b), D4h symmetry; e. SF 3H3 (a), C 3v 19 symmetry; f. SF 3H3 (b), C 2v symmetry; g. 20 SF 2H4 (a), C 2v symmetry; h. SF 2H4 (b), D4h symmetry; i. SFH 5, C 4v symmetry; j. 21 SH 6, O h symmetry; k. SCl 6, O h symmetry.¶ 22 ¶ Figure 7. Total entropy for the SF 6-nHn 23 (n=0…6) molecules and SCl 6.¶ 24 ¶ 25 Deleted : 8 26 Deleted : Figure 9. Vibrational entropy for the SF 6-nHn (n=0…6) molecules and 27 SCl 6.¶ ¶ 28 Figure 10. Zero Point Vibrational Energy 29 (ZPVE) for the SF 6-nHn (n=0…6) molecules and SCl 6.¶ 30 ¶ 31 Figure 11. Free energy for the SF 6-nHn (n=0…6) molecules and SCl 6.¶ 32 ¶ 33 Figure 12. Heat capacity for the SF 6-nHn (n=0…6) molecules and SCl .¶ 34 6 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 - 10 - 52 53 54 55 56 57 58 59 60

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1 List of Tables 2 3 Table 1. Experimental and calculated properties of the SF 6 molecule.

4 Table 2. Binding energy in [eV] and [J]. 5 6 Table 3. Magnitudes of dipole moments vectors [Debye] and [C·m] . 7 -1 8 Table 4. Frequencies of normal modes in [cm ].

9 Table 5. Intensities of normal modes in [km·mol -1]. 10 11 Table 6. Square of first derivatives of molecular dipole moments wrt infrared active normal modes in [a.u.]. 12 Table 7. Charges partitioned by Hirshfeld method. 13 14 Table 8. Thermodynamic properties. 15 16 For Peer Review Only 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 - 11 - 52 53 54 55 56 57 58 59 60

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1 2 Table 1. Experimental and calculated properties of the SF 6 molecule. d 3 Parameter Unit Present Ref. 3 9 Ref. 40 Experiment Deleted : 1 a 4 Binding energy eV 26.81 25.06 26.12 22.06 (20.12) Deleted : 32 5 d(S—F) Å 1.587 1.584 1.588 1.564 b -1 c 6 ν1 A 1g cm 723.5 — 718 772.269 -1 c 7 ν 2 E g cm 625.5 — 622 641.608 -1 c 8 ν 3 F1u cm 938.1 — 931 947.289 -1 c 9 ν 4 F1u cm 567.2 — 562 614.589 -1 c 10 ν 5 F2g cm 477.9 — 476 523.449 -1 c 11 ν 6 F2u cm 315.7 — 312 348.428 a SF 6 → S + 6F 12 b Table 8 in Ref. 18 . p. 280 Deleted : 4 13 c Table 7 in Ref. 18 , p. 280 Deleted : 14 d PWC calculation 4 15 16 Table 2. Binding energy in [eV]For and [J]. Peer Review Only 17 Molecule Symmetry Binding energy 18 [eV ] [J] 19 SF O 26.810 4.295·10 -18 20 6 h -18 21 SF 5H C4v 25.663 4.112·10 -18 22 SF 4H2 (a) C2v 24.090 3.860·10 -18 23 SF 4H2 ( b) D4h 24.508 3.927·10 24 -18 SF 3H3 (a) C3v 22.381 3.586·10 25 -18 SF 3H3 (b) C2v 22.565 3.615·10 26 -18 27 SF 2H4 (a) C2v 20.670 3.316·10 -18 28 SF 2H4 (b) D4h 20.058 3.214·10 -18 29 SFH 5 C4v 18.165 2.910·10 -18 30 SH 6 Oh 15.230 2.440·10 31 SCl O 14. 372 2.303·10 -18 32 6 h

33 34 Table 3. Magnitudes of dipole moments vectors in [Debye] and [C·m]. 35 Molecule Symmetry Dipole magnitude 36 [Debye] [C·m] -30 37 SF 6 Oh 0.080 0.267 ·10 38 -30 SF 5H C4v 1.752 5.844 ·10 39 SF H a C 2.659 8.871 ·10 -30 40 4 2 2v -30 41 SF 4H2b D4h 0.001 0.003 ·10 -30 42 SF 3H3a C3v 3.634 12.122·10 -30 43 SF 3H3b C2v 2.151 7.175·10 44 -30 SF 2H4a C2v 3.392 11.314·10 45 -30 SF 2H4b D4h 0.067 0.223 ·10 46 -30 47 SFH 5 C4v 2.610 8.706 ·10 -30 48 SH 6 Oh 0.039 0.131 ·10 -30 49 SCl 6 Oh 0.042 0.141·10 50 51 - 12 - 52 53 54 55 56 57 58 59 60

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1 Table 4. Frequencies of normal modes in [cm -1]. 2 3 Mode SF 6 SF 5H SF 4H2a SF 4H2b SF 3H3a SF 3H3b SF 2H4a SF 2H4b SFH 5 SH 6 SCl 6 4 7 315.6 296.3 325.8 276.2 367.2 346.9 337.7 430.8 630.4 1319.5 139.7 5 8 315.6 346.2 348.2 380.1 367.2 375.9 634.1 430.8 787.3 1319.5 139.7 6 9 315.6 346.2 399.4 380.1 486.3 422.0 675.0 611.7 787.3 1319.5 139.7 7 10 477.7 449.0 464.4 418.7 690.7 607.4 774.9 837.5 1112.5 1322.8 205.7 11 477.7 515.3 530.6 584.6 690.7 698.4 890.6 937.2 1220.5 1322.8 205.7 8 12 477.7 515.3 620.0 642.6 786.5 844.9 956.3 1119.8 1264.9 1322.8 205.7 9 13 567.0 572.6 718.4 649.4 866.8 941.8 1213.5 1119.8 1264.9 1329.3 230.7 10 14 567.0 606.5 For809.6 860.2Peer 1098.6 1134.9Review 1228.2 1299.7 Only1405.5 1329.3 230.7 11 15 567.0 659.2 875.7 860.2 1098.6 1159.4 1338.8 1423.6 1405.5 1329.3 230.7 12 16 625.0 832.1 1086.8 1195.5 1347.1 1262.4 1352.8 1423.6 1553.4 1909.2 253.9 17 625.0 902.6 1169.1 1195.5 1361.3 1280.3 1402.4 1651.4 2070.1 1909.2 263.2 13 18 722.9 902.6 1263.1 1253.2 1361.3 1449.0 2451.8 2174.4 2198.5 2014.5 263.2 14 19 937.4 1241.0 1391.9 1253.2 2575.2 2523.6 2484.5 2293.1 2198.5 2014.5 400.1 15 20 937.4 1241.0 2621.4 2649.1 2575.5 2540.9 2501.8 2293.1 2277.0 2014.5 400.1 16 21 937.4 2707.1 2636.2 2725.0 2575.5 2592.0 2505.1 2354.9 2438.2 2173.2 400.1 17 18 Table 5. Intensities of normal modes in [km·mol -1]. 19 20 Mode SF 6 SF 5H SF 4H2a SF 4H2b SF 3H3a SF 3H3b SF 2H4a SF 2H4b SFH 5 SH 6 SCl 6 21 7 0 0 1.5 0 0.9 0.8 0.3 20.5 168 0 0 22 8 0 1.3 0 5.1 0.9 3.8 171.2 20.5 2.4 0 0 23 9 0 1.3 7.9 5.1 4.5 26.7 186.8 0 2.4 0 0 10 0 0 3.4 0 156.1 13.1 0 361.6 0 0 0 24 11 0 8.7 8.4 0 156.1 191.5 5 0 30.2 0 0 25 12 0 8.7 10.2 90.3 188.3 389.1 27.2 0 6.9 0 0 26 13 22.2 19.1 168.8 0 0 33.1 12.6 0 6.9 49.6 1.3 27 14 22.2 0 192.2 417.7 20.7 0.1 12.8 11.7 32.2 49.6 1.3 28 15 22.2 14.9 395.6 417.7 20.7 0 1 40.3 32.2 49.6 1.3 29 16 0 189.4 25.9 0 5.6 9.1 4.5 40.3 0 0 0 17 0 407.7 0 0 1.7 1.1 0 0 0 0 0 30 18 0 407.7 0.3 0.5 1.7 2.6 4.6 0 357.3 678.2 0 31 19 390.2 0.1 1.7 0.5 40.6 33.5 58.5 284.2 357.3 678.2 116.7 32 20 390.2 0.1 15.1 0 26.4 24.1 44.3 284.2 0 678.2 116.7 33 21 390.2 0.2 13.6 0.05 26.4 17.6 82.1 0 99.5 0 116.7 34 35 36 - 13 - 37 38 39 40 41 42 43 44 45 http://mc.manuscriptcentral.com/tandf/jenmol 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page 29 of 30

1 2 Table 6. Square of first derivatives of moleculars dipole moments wrt infrared active normal modes in [a.u.]. 3 4 Mode SF 6 SF 5H SF 4H2a SF 4H2b SF 3H3a SF 3H3b SF 2H4a SF 2H4b SFH 5 SH 6 SCl 6 5 7 0 0 0 0 0.001 0.001 0 0.021 0.17 0 0 6 8 0 0.001 0 0.005 0.001 0.004 0.175 0.021 0.003 0 0 7 9 0 0.001 0.01 0.005 0.005 0.027 0.191 0 0.003 0 0 8 10 0 0 0 0 0.159 0.014 0 0.369 0 0 0 11 0 0.009 0.01 0 0.159 0.195 0.005 0 0.03 0 0 9 12 0 0.009 0.01 0.092 0.192 0.397 0.028 0 0.007 0 0 10 13 0.02 0.019 For0.17 0 Peer0 0.034Review 0.013 0 Only0.007 0.05 0.001 11 14 0.02 0 0.2 0.427 0.021 0 0.013 0.012 0.033 0.05 0.001 12 15 0.02 0.015 0.4 0.427 0.021 0 0.001 0.041 0.033 0.05 0.001 13 16 0 0.193 0.03 0 0.006 0.009 0.005 0.041 0 0 0 14 17 0 0.416 0 0 0.002 0.001 0 0 0 0 0 18 0 0.416 0 0 0.002 0.003 0.005 0 0.364 0.69 0 15 19 0.4 0 0 0 0.041 0.031 0.06 0.29 0.364 0.69 0.119 16 20 0.4 0 0.02 0 0.027 0.028 0.045 0.29 0 0.69 0.119 17 21 0.4 0 0.01 0 0.027 0.018 0.084 0 0.1 0 0.119 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 - 14 - 37 38 39 40 41 42 43 44 45 http://mc.manuscriptcentral.com/tandf/jenmol 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page 30 of 30

1 2 Table 7. Charges partitioned by Hirshfeld method. 3 4 Molecule Symmetry Charges 5 S F H/Cl 6 SF 6 Oh 0.5801 -0.0967 - 7

8 SF 5H C4v 0.5013 -0.1148 0.0729

9 SF 4H2a C2v 0.4224 -0.1333 0.0553 10 SF H b D 0.4249 -0.1419 0.0714 11 4 2 4h

12 SF 3H3a C3v 0.3396 -0.1591 0.0459 13 SF 3H3b C2v 0.3459 -0.1643 0.0490

14 15 SF 2H4a C2v 0.2613 -0.2078 0.0386

16 SF 2H4b D4h For0.2776 -0.1619Peer 0.0116 Review Only 17 SFH C 0.1917 -0.2248 0.0066 18 5 4v

19 SH 6 Oh 0.1361 - -0.0227

20 SCl 6 Oh 0.3411 - -0.0568 21

22

23

24 Table 8. Thermodynamic properties. 25 26 Molecule Symmetry Total entropy Vibrational ZPVE Free energy Heat capacity [cal·mol -1· K-1] entropy [kcal·mol -1] [kcal·mol -1] [cal·mol -1· K-1] 27 [cal·mol -1·K-1] 28 SF O 77.235 9.128 12.682 -18.776 24.175 29 6 h 30 SF 5H C4v 74.798 7.662 17.349 -18.355 21.553 31 SF 4H2a C2v 71.896 5.977 21.816 -17.829 18.883

32 SF 4H2b D4h 72.350 6.239 21.906 -17.928 18.933 33 SF 3H3a C3v 68.412 4.780 26.870 -17.165 16.156 34 SF H b C 68.879 4.337 25.992 -17.262 16.249 35 3 3 2v 36 SF 2H4a C2v 65.210 2.576 29.664 -16.462 13.770 37 SF 2H4b D4h 64.384 2.624 29.165 -16.259 13.735

38 SFH 5 C4v 60.170 1.800 32.541 -15.331 11.263

39 SH 6 Oh 54.932 0.231 34.238 -13.948 9.253 40 SCl O 101.464 28.160 5.302 -23.158 34.214 41 6 h aZero Point Vibrational Energy. 42 43 44 45 46 47 48 49 50 51 - 15 - 52 53 54 55 56 57 58 59 60

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