A Priori Theoretical Model for Discovery of Environmentally

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A Priori Theoretical Model for Discovery of Environmentally Sustainable Perfluorinated Compounds Xiaojuan Yu, Hua Hou, and Baoshan Wang J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b00606 • Publication Date (Web): 21 Mar 2018 Downloaded from http://pubs.acs.org on March 24, 2018

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The Journal of Physical Chemistry

A Priori Theoretical Model for Discovery of Environmentally Sustainable Perfluorinated Compounds

Xiaojuan Yu, Hua Hou, Baoshan Wang*

College of Chemistry and Molecular Sciences, Wuhan University, Wuhan, 430072, People's Republic of China

*Corresponding author. E-mail: [email protected]

ACS Paragon Plus Environment

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

Abstract

Since SF6 is the most potent greenhouse gas, the search for a viable alternative is taking on great urgency for several decades but without success. The demanding combination of performance, safety, and environmental properties for the new chemistry superior to SF6 was thought to be nearly impossible to achieve. In contrast to the commonly used mixtures with two or three individual gases, a hybrid model has been proposed to create the new perfluorinated compounds with multiple unsaturated chemical bonds by means of full or partial integration of the parent molecules. Unique combination of a series of paradoxical properties that is high in dielectric strength and stability, low in boiling point, and significantly lower in global warming potential is achieved for the first time. The present a priori theoretical predictions shed new lights on the rational molecular design of the perfluorinated compounds and will greatly inspire experimental synthesis and field tests on the new chemistry for dielectric use.


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1. Introduction Sulfur hexafluoride (SF6) is one of the most extensively studied polyatomic molecular gases because of its fundamental importance in chemistry, physics, and industry. Recently, SF6 has been identified as a reactive fluorination reagent catalyzed by organometallic compounds in organic synthesis,1,2 although SF6 is well-known because of its extremely chemical inertness and high dielectric strength for insulation in the transmission and distribution of electrical energy.3,4 Meanwhile, SF6 is the most potent greenhouse gas due to its extremely long atmospheric lifetime 3200 years and efficient absorption of infrared radiation at wavelengths near 10.5 µm.5-7 Consequently, SF6 has the largest global warming potential (GWP), which is 23500 times greater than that of the naturally occurring greenhouse gases (e.g., CO2). More seriously, the contribution of SF6 to global warming is expected to be cumulative and virtually permanent because all of the SF6 gases will be eventually released into the atmosphere by the electric power industry without disposal or recoverable methods that actually destroy it. It has been observed that the amount of SF6 in the atmosphere is increasing at a rate of 9% per year from barely measurable quantities two decades ago to current level near 7.3 ppq.8 In view of the massive applications of SF6 in electrical industry, seeking the alternatives has been taken on greater and greater urgency since 1980s.9,10 Unfortunately, to design the alternative gases, the unique combination and balance of a series of paradoxical properties (e.g., high dielectric strength, low boiling point, low GWP) required in dielectric applications is extremely challenging. After decades of research, a large amount of efforts to search for the



gases superior to SF6 has been unsuccessful to date. Only synthetic air and SF6/N2 gas mixtures have been employed as alternatives to pure SF6 by means of trial-and-error.11 Perfluorocarbon compounds including c-C4F8, CF3I, C5F10O, C6F12O, and C4F7N were evaluated as well.12-15 Although all these gases have high dielectric strength and low GWP, the boiling points are too high to be used for gaseous insulation. Currently, mixing with buffer gases (N2 or CO2) is the only option by means of trial-and-error screening. However, operating gas mixtures in electric equipments has many perceived disadvantages, for example, elusive optimal mixing ratio, more difficult gas supply and recovery procedures, concentration controls, challenge of handling leaks and disposal. Therefore, while much effort to search for the gases superior to SF6 has been undertaking, the current strategy to discover alternatives hits both experimental and theoretical bottlenecks.

To identify the environmentally sustainable replacement gas for SF6, a new


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physical model on the basis of ab initio theoretical chemistry is highly desirable. SF6 itself is a famous hypervalent molecule with an octahedral geometry consisting of six equivalent S-F bonds formed by the sp3d2 hybridization scheme. A group of novel dielectric molecules superior to SF6 have been constructed theoretically by means of 'hybrids' for the first time in this work (see Scheme 1), which is in distinct contrast to the commonly used binary or ternary mixtures. On the basis of the high-level ab initio quantum chemistry calculations, it has been demonstrated that the present a priori identification of green perfluorinated compounds sheds new lights on the molecular design of the alternatives for SF6.

2. Computational Methods Geometries of the molecules involved in this work were fully optimized using the density functional theory at the M06-2X/Aug-cc-pVTZ+d level.16,17 Further optimizations with the larger basis set (e.g., M06-2X/Aug-cc-pVQZ+d) or with the higher-level electron correlations (e.g., MP2/aug-cc-pVTZ+d for all species and CCSD/aug-cc-pVTZ+d for the selected species)18,19 were carried to confirm that the geometrical parameters have been well converged (Figure S1). Anharmonic vibrational

frequencies

and

IR

spectra

were

calculated

at

the

M06-2X/aug-cc-pVTZ+d level by a second-order perturbation approach20 to verify that the optimized structures correspond to the stable minima with all real frequencies. The UV absorption spectra were simulated using the nuclear ensemble approach as implemented in the Newton-X program.21,22 The initial geometry distribution was



generated by a Wigner distribution in the ground vibrational state of the ground electric state. The transition energies and moments were computed using the time-dependent TD-M06-2X/aug-cc-pVTZ+d method.23 The GWP data were calculated using the integrated IR absorption cross sections, radiative efficiencies, and atmospheric lifetimes, which have been detailed elsewhere.24,25 Briefly, radiative forcing per unit concentration change or radiative efficiency (RE) was calculated using the simplified model by Pinnock et al.,24 250

RE = ∑10σ i ( vi ) Fi ( vi ) i =1

where σi is the absorption cross section in cm2molecule-1 averaged over a 10 cm-1 interval around the wavernumber νi, and Fi(νi) is the instantaneous, cloudy sky, radiative forcing per unit cross section in W m-2 (cm2molecule-1cm-1)-1 for a 0 to 1 ppbv increase in absorber. The values for Fi(νi) as a function of wavenumber were determined by Pinnock et al. using their narrow-band radiative transfer model taking into account infrared absorption and emission by carbon dioxide, water vapor and ozone, methane, nitrous oxide and clouds, for global-average conditions, in the wavenumber range 0 to 2500 cm-1. The potential energy profiles for the oxidation reactions of dielectric gas molecules by OH radicals in atmosphere were calculated by optimizing the key transition states at the M06-2X/aug-cc-pVTZ+d level. Vibrational frequencies were computed at the same level of theory to check the nature of the stationary point and to obtain zero-point energy correction. Each transition state has one and only one imaginary frequency. The barrier heights were calculated at the ROCBS-Q26 level on


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the basis of the M06-2X/aug-cc-pVTZ+d optimized geometries. The rate coefficients (kOH) were calculated using the multichannel transition state/RRKM theory with the rigid-rotor harmonic-oscillator (RRHO) approximation at the energy/angular momentum resolved level by solving the master equations numerically in the presence of 760 Torr of N2.27 Note that a few reactions, for instance, SF4CF2+OH and SF3CF+OH, are barrierless. The minimum energy paths for the addition of OH to S or C sites of the unsaturated bonds were obtained by partial optimization of the reaction coordinates at the M06-2X/aug-cc-pVTZ+d level and the rate coefficients were estimated using the flexible transition state theory.28 The calculation of atmospheric lifetimes is complicated because there are many loss mechanisms.25 For simplicity, we confined ourselves to a summary of three major atmospheric loss processes for the molecules of concern, which include chemical reaction with OH radicals(τOH) and photolysis(τphoto), as well as uptake by the oceans (τocean). The chemical lifetime of a gas is determined by the rate coefficient kOH at 275 K and the mean global tropospheric OH concentration (1×10-6 molecule/cm3): τOH = kOH-1[OH]-1 The lifetime due to photochemical destruction is related to the photodissociation coefficient or frequency of photodissociation J: τphoto = J-1, J = ∫ Φ(λ )σ (λ ) F (λ )d λ where σ(λ) is the UV absorption cross section (base e) of the compound in units of cm2molecule-1 and F(λ) is the solar actinic flux (photons cm-2s-1), and the integration was carried out over the wavelength range of 290 - 400 nm.29 Quantum yield Φ(λ)



was assumed to be unity under all conditions for simplicity. Because the atmospheric lifetime is highly insensitive to the oceanic hydrolysis lifetime, a rough estimate of the uptake of a gas was obtained by the rate limiting step of the transfer velocity across the air-sea boundary layer, viz.:30, 31

where Z is a scale height of the troposphere of ~ 7000 m, ν is the oceanic transfer velocity ~3.7 m/d, focean = 0.71 is the fraction of Earth's surface area covered by ocean, and H represents the volume ratio Henry's Law coefficient.32 The total lifetime τ is given by:

τ = (1/ τ OH + 1/ τ photo + 1/ τ ocean ) . −1

It should be noted that there are often significant uncertainties associated with atmospheric lifetimes because of its complexity.25 Given the spatial and temporal variability of reaction partners and photolysis and the potential for chemical feedbacks, it is necessary to use atmospheric models to accurately determine lifetimes, which is beyond the scope of the present study. Enthalpies of formation, electron affinities, and ionization potentials of the hybrid molecules were calculated using the Gaussian-4 composite method,33 of which the accuracy has been well established. Electronegativity, and hardness were calculated using the frontier orbital energies of HOMO and LUMO.34 Molecular surface was defined to be the envelope contour of electronic density ρ(r) = 0.001au,35 which encompasses more than 96% of the total electronic charge. The electrostatic potential

Vs(r) on the molecular surface was created around the molecule by the numerical grids


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and then various statistical variables were computed to predict dielectric strength and boiling point using the structure-activity relationship (SAR) in terms of a general interaction properties function.36 The relative dielectric strength (Er) with respect to SF6 and boiling points (Tb in K) of the gas molecules were calculated using the SAR model developed recently by the authors, viz.:37

where As is the total surface area of the molecule. The parameters σtot2 (statistical variance), Π (average deviation), and ν (degree of balance) are a group of statistically-defined quantities that characterize molecular surface electrostatic potentials, and the parameters α, χ, η correspond to molecular polarizability, absolute electronegativity and hardness, respectively. All the SAR parameters were calculated at the M06-2X/6-31+G(d) level of theory. The ab initio calculations involved in this work were carried out with the Gaussian09 programs38 and the Molpro suite of programs.39

3. Results and Discussion Two types of hybrid schemes, namely, integrated and fractional chimeras, can be realized according to the specific molecular structures of the parent gases to be used for construction. For instance, in comparison with the 50%SF6 + 50%N2 gaseous mixture, the hybridization between SF6 and N2 can occur in two manners: first, the N2 molecule is integrated as a whole into one of the S-F bonds of SF6, forming SF5N2F;



second, half SF6 and half N2 structures are combined together to generate SF3N, or SF4NF by two-third SF6 with half N2. A series of hybrid molecules have been predicted accordingly (Figure 1), making use of SF6, C2F4, C2F2, NF3, c-C4F8, CF4, C2F6, SO2, and CO2 as the parents. All new molecular structures involve the unsaturated chemical bonds. For example, the S≡C triple bond exists in SF3CF (1/2SF6 + 1/2C2F2), consisting of 67%C2p and 33%(0.62S3p + 0.37S3d) with the bond order 2.37. Similar bonding mechanism occurs in the S=C double bond of SF4CF2. Neither fully fluorinated S=C nor S≡C molecules have been ever known in the laboratory. However, before the synthesis of these novel compounds is called on, the following three questions should be answered unambiguously: Are the compounds environmentally friendly, namely, with low GWP? Is the dielectric strength comparable to or higher than SF6, and simultaneously the boiling temperature is low? Are they thermally stable enough to exist under ambient condition?

3.1 GWP Assessments It is worth noting that the unsaturated bonds in the hybrid structures are very helpful to reduce GWP. Using the theoretical anharmonic IR spectra (Figure 2), the radiative efficiencies for the hybrid molecules were calculated to be in the range 0.2~0.4 (RE, Table 1) with the largest value of 0.68 for SF5N2F, which are comparable to those of SF6 (0.52) and perfluorocarbons (0.1~0.5). Apparently, all the hybrid molecules absorb IR energy in the window at 8-12 µm which is largely transparent in


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the natural atmosphere. However, the high reactivity toward the atmospheric radicals (e.g., hydroxyl, OH) allows them to be removed rapidly from the atmosphere. The barriers for the addition routes of the OH radical to the S≡N, S=N, S≡C, S=C, C=N, and -C-N=N-C bonds are fairly low, i.e., in the range 0-3 kcal/mol (Table S1) and the rate coefficients at ambient condition are in the 10-15~10-12 cm3molecule-1s-1 orders of magnitude. The lifetimes were estimated to be at most 30 year in view of the typical atmospheric concentration of OH radicals (106~107 cm-3).40 Therefore, the GWP for these hybrid molecules are in the range 0-2000, which is considerably lower than that of SF6 or perfluorocarbons. However, three molecules including SF5NNF, CF3SO2F, and CF3OC(O)F, need further assessment. The addition of OH to the N=N double bond of SF5NNF involves a barrier of 9.1 kcal/mol, which is so high that its atmospheric depletion by OH radical is unimportant. On the other hand, it was found that SF5NNF has a broad and relatively strong UV absorption in 250~350nm with the cross-sections in 10-19 ~10-18 cm2 orders of magnitude (Figure 3). Moreover, the absorption becomes much stronger in the VUV region. Therefore, the excited molecule formed after VUV and UV radiation could be photodissociated directly or more reactive to OH radicals. As a result, the atmospheric lifetime of SF5NNF could be reduced significantly to a few days or weeks, leading to the negligible GWP. In contrast, neither CF3SO2F nor CF3OC(O)F has observable UV absorption above 250 nm (Figure 3). In view of the significant barriers for the reactions of CF3SO2F+OH and CF3OC(O)F+OH (Table S1), it is conceivable that the dominant removal process for CF3SO2F and



CF3OC(O)F should be the heterogeneous hydrolysis in the upper mixed layer of basic water where they are transported by diffusion. It has been shown experimentally that the hydrolysis of sulfuryl fluoride in basic ocean water occurs in minutes to hours and thus the transfer velocity across the air-sea boundary layer is the rate limiting step.30,31 The atmospheric lifetimes for CF3SO2F and CF3OC(O)F were estimated roughly to be 40 years and 15 years, resulting in the GWP of 3678 and 1739, respectively, which are much lower than that of SF6.

3.2 Dielectric and Boiling Point Assessments Dielectric performance of the hybrid molecules can outperform SF6 significantly, Dielectric strength (Er) relative to SF6 and boiling point (Tb) are listed in Table 1. It is very encouraging that the dielectric strength of the hybrid molecules is generally higher than or at least comparable to that of SF6, as determined by the unique molecular electrostatic potential surface (Figure 4). The dielectric strength is proportional to the surface area As, the total variance σtot2, the index parameter ν of electrostatic balance of the positive and negative regions, polarizability α, and electronegativity χ. While all the hybrid molecules have the similar As and αχ with their parents (Table S2), the perfect balance of the positive and negative electrostatic surface in SF6, c-C4F8, CF4, C2F6, etc., is destroyed completely by hybrid integration. Therefore, the quantity of νσtot2 becomes significantly larger than the zero value of the parents. For example, the value of νσtot2 of SF3N is 20.1, which promotes the dielectric strength by a factor of roughly 1.1. However, the internal charge separation


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of the molecule or local polarity, as measured by the parameter Π, may cause dramatic loss of the dielectric strength. Fortunately, such a negative effect appears to be well compensated by the enhanced molecule's capacity for noncovalent attractive interactions due to νσtot2. For instance, the dielectric strength of SF3N is improved by 35% and 355% with respect to the parental molecules SF6 and N2, respectively. On the other hand, boiling points of the hybrid molecules have increased as well in comparison with those of the parents because of the generally larger Π and the lower molecular hardness. However, most of them (e.g., SF3N, SF4NF, CF2NCF3, CF3SO2F, CF3OC(O)F) have boiling points being fairly below -10°C, which can still meet the requirements for electric applications.

3.3 Thermal Stability Assessments Thermal stability of the hybrid molecules has been enhanced considerably, as shown by the greatly negative enthalpies of formation at standard state, ∆Hf,298.15, and relatively high electron affinities and ionization potentials (Table 2). At first sight, the species with multiple bonds seems to be less stable in view of the values of ∆Hf,298.15. For example, the SF3N molecule involves the S≡N triple bond and its ∆Hf,298.15 is -83.3 kcal/mol, which is considerably higher than that of SF6 (-291.7 kcal/mol). However, ab initio calculations confirmed that the thermal unimolecular decomposition or isomerization of SF3N is negligible even at extremely high temperatures (e.g., ~3000 K whenever partial discharge or arc occurs) because the significant barriers (e.g., > 70 kcal/mol) have to be surmounted for all the possible



reaction routes (Figure S2). Evidently, the hybrid dielectric molecules shed new light on the most difficult combination of properties of the compound that is high in dielectric strength and stability and at the same time much lower in GWP. Reliability of the rational design and theoretical predictions could be assessed by the good agreement between experimental and theoretical boiling points available for a few species (Table 1). As for the dielectric strength, only trifluoromethanesulfonyl fluoride (CF3SO2F) has been measured experimentally to be 1.41,9 which is in excellent agreement with the present theoretical estimate, 1.33. Finally, it is worth emphasizing that the present hybrid design should not be limited to the integrated and fractional schemes between two molecules. Multiple and mixed hybrid constructions are interesting enough to warrant evaluation and even better performance could be achieved specifically. For instance, up to six N2 or CO2 molecules can be integrated into SF6 to form S(NNF)6 or S(COOF)6 with the dielectric strength being 3.9 and 5.4 times higher than that of SF6. Ternary fractional chimera by SF6, N2, and CF4 gives (CF3)SF2N molecule, of which the dielectric strength is improved to 2.0 in comparison with the value of 1.35 for the binary hybrid between SF6 and N2. In addition, the right balance of properties to function as a SF6 alternative could be tuned elaborately by means of substitution using various groups such as -CF3, -NF2, and -CN.

4. Concluding Remarks


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In summary, a new hybrid model to identify the environmentally sustainable dielectric gases to replace SF6 has been proposed successfully for the first time, in contrast to the conventional physical mixing of two or three individual gases. Both dielectric performance and thermodynamic stability of the hybrid molecules have been carried forward or even improved significantly from the parent molecules. Meanwhile, the atmospheric lifetimes are shortened considerably due to the enhanced reactivity toward chemical or photolytic degradations, and thus all the hybrid molecules are environmentally friendly compounds with considerably less greenhouse emissions than SF6. Except for a few molecules in the CAS-registered reference databases, i.e., SF3N, SF4NF, CF3SO2F, CF3OCOF, CF2NCF3, the other fully fluorinated compounds involving the multiple hybrid bonds such as S=C and S≡C are experimentally unknown yet. None of them has been considered as the potential gaseous dielectric before. Selective synthesis of these novel perfluoro-compounds in laboratory and testing their dielectric, safety, and environmental properties should be worthwhile.

ASSOCIATED CONTENT Supporting Information Geometrical parameters optimized at various levels of theory, electrostatic potential parameters used in the structure-activity relationship to predict dielectric strengths and boiling points, geometries of the transition states, barrier heights, Cartesian coordinates, and vibrational frequencies for the reactions of the hybrid



molecules with OH radicals, energetic profile for the unimolecular decomposition / isomerization of SF3N. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author Email: [email protected]

Notes The authors declare no competing financial interests.

ACKNOWLEDGMENTS This work was supported by the National Key Research and Development Program of China (No. 2017YFB0902500) and by the National Natural Science Foundation of China (No. 21573165).

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Page 22 of 29

Table 1. Physical chemistry and environmental properties of the hybrid molecules. a Er

Tb /°C

RE/Wm-2ppbv-1

τ / years

GWP

SF5N2F

1.37

-7

0.68

1

10

SF6+N2

SF3N

1.35

-30(-27)

0.30

5

916

SF6+N2

SF4NF

1.07

-17 (-14)

0.47

0.13

9

SF6+C2F4

SF4CF2

0.83

-4

0.35

0.001

0

SF6+C2F2

SF3CF

1.02

4

0.31

0.006

1

c-C4F8+N2

c-C4F8N2

2.21

44

0.21

0.01

1

c-C4F8+N2

c-C3F5N

1.42

-8

0.22

16

1602

CF4+N2

CF2NF

0.93

-60

0.07

0.7

26

C2F6+N2

CF2NCF3

1.07

-30 (-33)

0.21

20

2091

CF4+SO2

CF3SO2F

1.45

-28 (-22)

0.23

40

3678

CF4+CO2

CF3OC(O)F

2.01

-37 (-36)

0.23

15

1739

Parent

Hybrid

Molecules

Molecules

SF6+N2

a

Er: relative dielectric strength with respect to SF6. Tb: boiling point. The experimental data are listed in the parenthesis. RE: radiative efficiency. τ: total atmospheric lifetime. GWP: 100-year time horizon global warming potentials relative to CO2.


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Table 2. Enthalpies of formation (∆Hf,298.15, in kcal/mol), electron affinities (EA, in eV) and ionization potentials (IP, in eV) of the hybrid molecules at the Gaussian-4 level of theory. ∆Hf,298.15

EA

IP

SF5N2F

-193.8

0.95

11.7

SF3N

-83.3

1.79

11.7

SF4NF

-141.7

2.01

10.8

SF4CF2

-216.4

1.48

9.7

SF3CF

-70.6

0.67

10.6

c-C4F8N2

-332.5

2.38

10.0

c-C3F5N

-199.8

0.90

11.4

CF2NF

-79.7

0.19

11.7

CF2NCF3

-240.7

0.78

11.8

CF3SO2F

-273.3

0.65

12.6

CF3OC(O)F

-297.0

0.53

12.2

Molecules



Figure Captions

Figure 1. Optimized geometrical parameters for various hybrid molecules at the M06-2X/aug-cc-pVTZ+d level of theory. Bond distances are in Ångstroms. The data in parenthesis are the Wiberg bond orders.

Figure 2. Anharmonic infrared spectra of the hybrid molecules calculated at the M06-2X/aug-cc-pVTZ+d level of theory in comparison with that of SF6. The experimental spectrum of SF6 is shown as dashed line for comparison.

Figure 3. Theoretical UV absorption spectra for SF5N2F, CF3SO2F, and CF3OC(O)F. The grey area shows the standard errors of the absorption coefficients (σ) obtained from fifty nuclear ensembles.

Figure 4. Electrostatic potential surfaces of the hybrid molecules mapping to the total electron density surface with an isovalue ρ = 0.001au. The color scale indicates the potentials ranging from -0.04 au (red) to +0.04 (blue).


Page 24 of 29

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Figure 1. Optimized geometrical parameters for various hybrid molecules at the M06-2X/aug-cc-pVTZ+d level of theory. Bond distances are in Ångstroms. The data in parenthesis are the Wiberg bond orders.



Figure 2. Anharmonic infrared spectra of the hybrid molecules calculated at the M06-2X/aug-cc-pVTZ+d level of theory in comparison with that of SF6. The experimental spectrum of SF6 is shown as dashed line for comparison.


Page 26 of 29

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Figure 3. Theoretical UV absorption spectra for SF5N2F, CF3SO2F, and CF3OC(O)F. The grey area shows the standard errors of the absorption coefficients (σ) obtained from fifty nuclear ensembles.



Figure 4. Electrostatic potential surfaces of the hybrid molecules mapping to the total electron density surface with an isovalue ρ = 0.001au. The color scale indicates the potentials ranging from -0.04 au (red) to +0.04 (blue).


Page 28 of 29

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