predicting the electric strength of proposed sf6 replacement gases ...

OE8-01 

PREDICTING THE ELECTRIC STRENGTH OF PROPOSED SF6 

REPLACEMENT GASES BY MEANS OF DENSITY FUNCTIONAL 

THEORY 

M. Rabie 1* and C. M. Franck 1 

1 Power Systems and High Voltage Laboratories, ETH Zurich, 8092 Zurich, Switzerland 

*Email: 

Abstract: We computationally estimate the electric strength (ES) and the boiling point 

(T B ) of 2611 carbonyl compounds. Namely we systematically analyze the groups of 

hydrofluoro-ketones, -aldehydes and acyl fluorides as well as perfluoro-ketones and – 

aldehydes. The elemental composition is restricted to solely hydrogen, fluorine, a single 

oxygen atom and 3 to 5 carbon atoms. Our method is based on the strong correlations 

between the ES of electronegative gases and certain predictors [1]. Predictors are simple 

functions of molecular properties, which are calculated ab-initio by means of density 

functional theory (DFT). We use the same method to estimate T B of the gas samples [1]. 

Recently certain C 5 - and C 6 -perfluoroketones were proposed as dielectric insulation 

medium in electrical power system equipment [2-4]. We compare our calculated values of 

the ES and T B of these compounds with other carbonyl compounds. We detect influence 

of the chemical structure on the ES and T B of a species and we identify other hydro- and 

per-fluoro carbonyl compounds of similar or even better insulation properties. 

1 INTRODUCTION 

Considerable effort has been undertaken to find 

gases and gas mixtures that are appropriate for 

insulating high voltages in electrical power system 

equipment [5-8]. Sulfur hexafluoride (SF 6 ), which is 

widely used in gas insulated switchgears, has a 

high value of the electric strength (ES) compared 

to other compounds with similar boiling point (T B ). 

Initially, without pre-selection the number of 

potential SF 6 replacement candidates is very high 

due to the diversity of chemical structures. 

However, characteristics sought in SF 6 

replacement gases, in addition to high ES, typically 

include chemical stability, low toxicity, short 

atmospheric lifetime and boiling point ranges that 

are suitable for high voltage applications. Thus, 

compounds that cannot achieve these criteria may 

be excluded from the list of promising SF 6 

substitutes. 

A systematic search for new insulation gases 

without excluding possible candidates is desirable. 

In principle, the ES of a gas can be determined by 

breakdown experiments [9] or by kinetic modeling 

of the breakdown process on the basis of 

microscopic electron-molecule cross sections [10]. 

These methods are time and resource intensive 

and thus can be applied to a narrow selection of 

gases only. However, in a previous work it was 

shown that the ES strongly correlates with certain 

predictors which are simple functions of certain 

molecular properties [1]. These molecular 

properties are calculated by means of Density 

Functional Theory (DFT). Thus, the ES of new 

molecules can be predicted by computational 

methods alone before testing their electric and 

chemical behavior in experiments. 

Recently certain C 5 - and C 6 -perfluoro-ketones 

were proposed as dielectric insulation medium in 

electrical power system equipment [2-4]. These 

examples are specific substructures of a large 

class of carbonyl compounds with thousands of 

different structures. We are particularly interested 

in the dependency of the ES on the respective 

molecular structure. Therefore, in this work all 

different structures of carbonyl compounds will be 

analyzed. We estimate computationally the ES and 

the boiling point T B of 2611 chemically valid 

molecules that contain 3 to 5 C-atoms, an arbitrary 

number of hydrogen and fluorine atoms and a 

single carbonyl group (C=O). These compounds 

are namely: hydrofluoro-ketones, -aldehydes and 

as well as perfluoro-ketones and -aldehydes. 

The present paper is structured as followed: 

Section 2 describes our method for the complete 

structure generation of the desired chemical 

classes and the subsequent geometry optimization 

of the molecule and the calculation of its properties 

by means of DFT. Further we present our method 

for estimating the ES by means of strong 

correlations between the ES and certain molecular 

properties. In Section 3 we present the results of 

our calculations for 2611 different chemical 

structures. The huge amount of data produced by 

our calculations is discussed in Section 4. Further, 

we discuss individual compounds that show 

extraordinary good characteristics for the usage as 

insulation gases. Finally, we conclude with the 

benefit of our results for future insulation gases in 

high voltage electrical power system. 

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2 METHODS 

2.1 Structure Generation 

We use the Open Structure Generator OMG [11], 

which generates for a given elemental composition 

C x H y F z O all chemically valid molecules. The 

number of C-atoms x, H-atoms y and F-atoms z 

are arbitrary integers which provide chemically 

valid molecular formulas. The number of possible 

isomers for one elemental composition growth 

dramatically with increasing x as well as the 

computation time for the subsequent DFTcalculation 

of the single molecule. Therefore, we 

restrict our calculations to the class of carbonyl 

compounds with x = {3, 4, 5}. This initial list of 

molecules generated by OMG contains carbonyl 

compounds, alcohols, ethers and other chemical 

groups. We select from this list the subset of 

molecules that contain the carbonyl group, using 

the Open Babel-toolbox [12]. This subset we split 

into three groups: ketones, aldehydes and acyl 

fluorides. The latter are aldehydes where the 

hydrogen atom at the carbonyl group is substituted 

by a fluor atom. 

The molecular structure of each generated 

molecule is saved as a tmole-file created by the 

Open Babel-toolbox. This file contains the entire 

structure information of the molecule as spatial 

three-dimensional coordinates of the atoms. 

2.2 Density Functional Calculations 

We calculate molecular properties for isolated gas 

molecules whose structure has been optimized in 

the electronic ground state. Vibrational and 

temperature corrections have been neglected. 

These Kohn-Sham DFT calculations were 

performed with the Turbomole program package 

[13] employing the BP86 density functional [14, 15] 

in combination with density fitting techniques. 

Ahlrichs' polarized valence triple-zeta basis def- 

TZVP [16] was applied in the calculations of ε i 

a 

while the larger def2-QZVPP basis set [17] was 

used for the calculation of α and µ. We perform the 

DFT calculation for the neutral and the positively 

charged molecules to calculate ε i a . We evaluate 

energy differences between potential curves of 

neutral molecule and cation, neglecting the 

discrete structure of the vibrational energy levels. 

The quantities α and µ are calculated for the 

geometry-optimized neutral molecule. 

2.2 Correlation Method 

Within a multiple regression analysis it was shown 

that there are clear correlations between the ES or 

T B of an electronegative gas and certain predictors, 

which are simple functions of selected DFTcalculated 

molecular properties [1]. The carbonyl 

compounds which are investigated in this work are 

polar molecules. For polar gases the ES and T B 

are functions of the DFT-calculated molecular 

properties: 

electric dipole moment µ 

 

 

 

average static electronic polarizability α 

adiabatic ionization energy ε i 

a 

electron number N e 

molecular mass m. 

We calculate the ES of polar molecules by the 

linear regression 

 

 

Er 

x1 x2 p0 p1x 1 

p2x2 

, , (1) 

with the predictors x 1 = µ 0.3 N e 

1.3 

, x 2 = α 0.6 ε i a2.8 and 

the coefficients are (p 0 , p 1 , p 2 ) = (- 1.05, 3.8×10 -3 , 

5.6×10 -4 ). Here, E r is the ES relative to SF 6 . The 

standard deviation of the calculated values of the 

ES with respect to the measured values is σ = 0.35 

. 

The boiling point T B is estimated by 

B 

T y , y q q y q y , (2) 

1 2 0 1 1 2 2 

with the predictors y 1 = α 0.23 µ 0.04 , y 2 = ε i 

a 0.07 m 0.01 

and the coefficients (p 0 , p 1, p 2 ) = (3.37, 0.27, -2.83) 

×10 3 . The calculated values of T B have a standard 

deviation of σ = 28 K. 

3 RESULTS 

3.1 C3/C4/C5-Carbonyl compounds 

Following Section 2, we estimated the ES and T B 

of overall 2611 carbonyl compounds. The structure 

generation with OMG yields 4826 species. The 

subsequent DFT-structure optimizations of the 

neutral as well as the positively charged molecules 

converge for 2611 structures. The stability of the 

cation is necessary to calculate the ionization 

energy ε i a of the neutral molecule, as described in 

Section 2.2. 

Figure 1(a) shows the results of our analysis for 

the 48 converged C 3 -compounds, which are 

subdivided into 17 ketones, 18 aldehydes and 13 

acyl fluorides. The 365 structures of the C 4 - 

compounds consist of 138 ketones, 117 aldehydes 

and 110 acyl fluorides. The results are displayed in 

Figure 1(b). The 2198 structures of C 5 - carbonyl 

compounds are 923 ketones, 685 aldehydes and 

590 acyl fluorides, and their values of E r and T B are 

shown in Figure 1(c). The standard deviation σ of 

our calculated values of E r and T B is given in 

Section 2.2. 

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Table 1 gives the mean values of E r and T B for the 

three groups of ketones, aldehydes and acyl 

aldehydes. Here, is calculated as an average 

over all E r of the compounds of one group, e.g. the 

17 ketones. 

The influence of the number of F-atoms z on the 

ES of a molecular gas is illustrated in Figure 2. 

Here, we calculate the mean values and 

of C 5 -hydrofluoro carbonyl compounds with 

elemental composition C 5 H y F z O, where the mean 

values are taken over an ensemble of molecules 

with fixed z and arbitrary y. We choose z from 0 to 

9 F-atoms. For perfluoro-carbonyl compounds the 

number of F-atoms is z = 10 and the number of 

different isomers resulting from our analysis is n = 

0 for 

Table 1: Mean values of Electric strength , 

boiling point and number of F-atoms of 

different groups. The mean values are taken over n 

molecules. 

group 

[rel. SF 6] 

 

[K] 

 

C 3-Ketones 0.39 319 2.00 17 

C 3-Aldehydes 0.56 320 1.89 18 

C 3-Acyl Fluorides 0.98 293 3.15 13 

C 4-Ketones 0.69 352 2.58 138 

C 4-Aldehydes 0.77 345 2.39 117 


C 5-Ketones 0.94 375 3.30 923 

C 5-Aldehydes 1.00 370 2.91 685 


SF 6 1 209 [18] 6 1 

n 

the group of aldehydes, n = 1 for the group of acyl 

aldehydes and n = 2 for the group of ketones. 

Thus, mean values are not meaningful in this case. 

It can be clearly seen from Figure 2 that for all 

three groups increases whereas 

decreases as z increases. 

Figure 3 (a) displays again the data points of 

Figure 1, but divided into the three classes of C 3 -, 

C 4 - and C 5 - carbonyl compounds. Thus, the 

influence of the number of C-atoms on the ES and 

T B can be seen more clearly. 

Figure 1: Predicted electric strength E r relative to 

SF 6 vs predicted boiling point T B for 2611 carbonyl 

compounds containing (a) 3, (b) 4 and (c) 5 C- 

atoms. The data set contains 48 C 3 -, 365 C 4 - and 

2198 C 5 - carbonyl compounds, and it is split into 

ketones, aldehydes and acyl fluorides (triangles). 

The star indicates the measured values of E r and 

T B of SF 6 [18]. 

Figure 2: Mean values of E r vs mean values of T B 

for hydrofluoro-carbonyl compounds containing 5 

C-atoms and 0 to 9 F-atoms (for the definition of 

“mean value” see text). The solid lines connect the 

data points of molecules with arbitrary number of 

H-atoms but different number of F-atoms to guide 

the eye. The number of F-atoms increases from 

right to left. 

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3.2 Molecules of high ES and low T B 

In this section we give detailed results for selected 

molecules that might be interesting candidate 

gases due to their relatively high values of E r and 

low values of T B . In general, these are the 

molecules in the upper left corner of Figure 3(a). 

The data points in the inset are plotted in Figure 

3(b). The selected C 3 -compounds are enumerated 

with increasing T B from (1) to (4), the C 4 - 

compounds from (5) to (7) and the C 5 -compounds 

from (8) to (12). The values of E r and T B for these 

structures are given in Table 2. We also compare 

the data of these molecules with values of the 

boiling point T B L predicted by other methods [20]. 

The molecules (1) and (2) are perfluorocompounds, 

whereas (3) and (4) are hydrofluorocompounds 

with 1 and 2 H-atoms, respectively. 

The DFT-optimization with Turbomole of the C 4 - 

compounds results in no stable geometry for 

compounds with z = 8, although OMG generates 3 

isomers for C 4 F 8 O. Thus, the best results for E r 

and T B are given by the hydrofluoro-compounds (5) 

to (6). The compounds with the highest value of E r 

are generally the C 5 -perfluoro-compounds and C 5 - 

hydrofluoro-compounds with only one or two H- 

atoms. The values of E r and T B for the ketones (9) 

and (11) explicitly mentioned in [2] as well as the 

perfluoro-aldehyde (8) and the acyl fluorides (10) 

and (12) are listed in Table 2. 

In addition to the C 5 -carbonyl compounds we 

estimated the electric strength for the perfluoro(2- 

methyl-3-pentanone)-compound C 6 F 12 O, proposed 

in [2-4]. Its boiling point is 322 K and due to 

photolysis in sunlight within approximately 5 days it 

has very low global warming and ozone depletion 

potential [2]. Our calculated values for this gas are 

E r = 2.44 and T B = 314 K. 

Table 2: Values of E r [rel. SF 6 ], T B [K] and T B L [K] 

[20] for selected compounds. 

Nr SMILES E r T B T B 

L 

C 3 –compounds 

(1) FC(=O)C(C(F)(F)F)(F)F 1.34 255 280 

(2) O=C(C(F)(F)F)C(F)(F)F 1.03 262 280 

(3) FC(C(C(=O)F)(F)F)F 1.11 263 288 

(4) FC(=O)CC(F)(F)F 1.31 278 302 


(5) FC(=O)C(C(C(F)(F)F)F)(F)F 1.63 270 317 

(6) FC(C(C(F)(F)F)(C(=O)F)F)F 1.82 277 

(7) FCC(C(F)(F)F)(C(=O)F)F 1.91 295 


(8) FC(=O)C(C(F)(F)F)(C(F)(F)F)C(F)(F)F 2.77 283 303 

(9) O=C(C(C(F)(F)F)(C(F)(F)F)F)C(F)(F)F 1.93 293 310 

(10) FC(C(C(C(F)(F)F)(F)F)(C(=O)F)F)F 2.28 296 

(11) O=C(C(C(C(F)(F)F)(F)F)(F)F)C(F)(F)F 2.01 302 322 

(12) FC(=O)C(C(C(F)(F)F)C(F)(F)F)(F)F 2.67 304 

Figure 3: (a) Predicted electric strength E r relative 

to SF 6 vs predicted boiling point T B for 2611 

molecules. The complete list of molecules is split 

into carbonyl compounds containing 3 (triangles), 4 

(circles) and 5 carbon atoms (dots). (b) Inset of 

Figure 3(a) with all molecules with values in the 

Interval T B = [230, 320] and E r = [0.9, 2.9]. The 

compounds (1) to (12) are listed in Table 2, 3 and 

4. The compound C 6 F 12 O from [2-4] is indicated by 

the cross. 

Figure 4: From left to right: 2D-structures of 

molecules Nr (1) to (4) of Table 2, taken from 

PubChem [19]. In this representation hydrogen 

atoms are not indicated with symbols. 

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Figure 4: From left to right: 2D-structures of 

molecules (8), (9) and (11) from Table 2, taken 

from PubChem [19]. 

4 DISCUSSION 

Our analysis estimates the ES and T B of a large 

number of molecules. However, not for all possible 

OMG-generated structures the DFT-optimization 

converges to a stable geometry. This may have a 

computational or a physical reason: Either the 

OMG-generated geometry is not accurate and 

therefore the structure optimization of the molecule 

exceeds the computation-time, or a stable cation 

state does not exist and it dissociates during the 

structure optimization into smaller fractions. Then 

the calculation of ε a 

i and thus the ES is not 

possible. However, the sample of calculated data 

is sufficient and it is reasonable to assume that the 

ES and T B will not significantly change for notincluded 

molecules. 

We clearly observe certain trends for the ES and 

T B . The values of these quantities strongly vary 

with the elemental composition and the molecular 

structure, as illustrated in Figure 1, 2 and 3. The 

dependency of the ES on the chemical group 

becomes clear from Table 1: the mean values of 

the ES of the ketones are always smaller than the 

ones of the aldehydes. We do not observe this 

effect due to increasing number of F-atoms , 

since of the aldehydes is even smaller than 

of the ketones. The group of acyl fluorides 

always shows both highest values of E r and lowest 

values of T B . We note that is larger for the acyl 

fluorides than for both the aldehydes and the 

ketones due the forbidden elemental composition 

C x H 2x O for the acyl-fluorides. 

In general, increasing number of C-atoms in a 

molecule increases the rate of elastic collisions, 

and thus the ES, as shown in Figure 3(a). The 

increased value of T B for larger molecules is the 

result of increasing van der Waals interaction. As 

illustrated in Figure 2, for increasing number of F- 

atoms z the ES increases due to the higher rate of 

electron attachment. Further, we find a surprisingly 

strong decrease of T B as z increases. We believe 

that strongly fluorized molecules suffer from 

decreasing hydrogen bond attraction. 

The selected molecules of Section 3.2 show good 

characteristics for insulation gases. On the one 

hand the C 3 - acyl fluorides (1) to (3) and the 

ketone (2) show values of the ES only slightly 

larger than SF 6 and low values of T B compared to 

the C 4 and C 5 -compounds. On the other hand the 

C 5 -compounds show the highest values of the ES, 

but slightly larger values of T B . Indeed, the ketones 

(9) and (11) from [2] show desirable properties. 

However, there seems to be another ideal 

candidate for electrical insulation, the perfluoroaldehyde 

(8). Its value of the ES clearly exceeds 

the one of all other molecules with similar T B . 

5 CONCLUSION 

Within a systematic procedure we calculated the 

electric strength and the boiling point of more than 

2000 hydrofloro- and perfluoro- carbonyl 

compounds in a computational efficient way. 

Strong influence of the chemical structure and the 

elemental composition on these gas quantities was 

measured. Moreover, interesting candidates with 

predicted values of the electric strength higher than 

SF 6 were identified. Other important characteristics 

of SF 6 replacement gases as chemical stability, 

toxicity and atmospheric lifetime were not within 

the scope of this paper but might be analyzed in 

combination with chemical databases in future. A 

quantitative investigation of the electric strength 

should follow for the top-candidates, e.g. by Swarm 

parameter measurements and the derivation of the 

critical electric field strength [21]. 

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