Computational and Theoretical Chemistry 1046 (2014) 81–92

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Computational and Theoretical Chemistry

journal homepage: www.elsevier .com/locate /comptc

Thermodynamic stability of PFOS: M06-2X and B3LYP comparison

http://dx.doi.org/10.1016/j.comptc.2014.08.0032210-271X/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author.E-mail address: nmora@tru.ca (N. Mora-Diez).

Thomas Giroday a, M. Merced Montero-Campillo b, Nelaine Mora-Diez a,⇑a Thompson Rivers University, Department of Chemistry, Kamloops, BC V2C 0C8, Canadab Universidad Autónoma de Madrid, Departamento de Química, Cantoblanco, 28049 Madrid, Spain

a r t i c l e i n f o

Article history:Received 10 June 2014Received in revised form 3 August 2014Accepted 3 August 2014Available online 11 August 2014

Keywords:PFOSThermodynamic stability of acids andanionsM06-2XB3LYP

a b s t r a c t

The thermodynamic stability in the gas phase, water and octanol of the neutral and anionic forms of the89 PFOS isomers is studied at the M06-2X/6-311++G(d,p) level of theory using the SMD solvation model.The structure–stability relationship is explored and compared to previous B3LYP calculations. This studyaims to improve the thermodynamic data for these compounds using a functional that is expected toovercome known deficiencies of the B3LYP functional when considering medium-range electron correla-tion effects. The M06-2X results place emphasis on the substitution patterns at the head and tail ends ofthe molecule as a factor in stability, while substitution patterns on the middle carbons tend to decreasestability. Analysis of the electron density revealed a subtle balance between weak interactions in theseperfluorinated compounds. M06-2X ranks highly-substituted isomers as more stable than B3LYP did,and ranks linear isomers quite low in relative stability compared to B3LYP. It has been shown that thedifference in stability for these compounds is mostly enthalpic, with small entropy changes betweenthe two functionals for most compounds.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Perfluorooctane sulfonic (PFOS) compounds are created duringthe manufacturing processes of telomerisation and electrochemi-cal fluorination [1]. PFOS are extremely persistent in the environ-ment, and present toxicity risks when accumulated in humanbodies [2]. Since these compounds possess both a sulfonic groupand several strong carbon–fluorine bonds, they are soluble inwater, are not easily absorbed by organic matter, and are not vol-atile. These properties make these compounds very nonbiodegrad-able. Although 89 isomers exist, the most common isomer presentin solution is the linear isomer, in some cases comprising up to 88%of the PFOS material in the sample [2]. Several studies have tried tofind an explanation for this finding which seems to be independentof the thermodynamic stability of these compounds [3–7]. Some ofthese studies have focused only on the least branched isomers(labelled 83–89 in the nomenclature system proposed by Rayneet al. [6], which is also used in this work).

With the exception of a few studies on PFOS and their deriva-tives PFOSAmide and PFASAmide [3–9], little theoretical researchhas been performed on these compounds. To the best of our knowl-edge, the complete series of 89 PFOS has been studied by Rayneet al. using the semi empirical method PM6 in the gas phase

(focusing on the neutral forms) [7], and by our group (focusingon the neutral and anionic forms) at the B3LYP/6-311 + G(d,p) levelof theory in the gas phase, water and octanol (with solvent effectstaken into account by means of the polarizable continuum model(PCM)) [3]. Knowledge of physicochemical data for these com-pounds (e.g., various acid dissociation constants and partition coef-ficients) could be used to better understand their origin, chemicaltransformation, and environmental distribution and transport innature. Very little experimental data exist for PFOS, which high-lights the importance of theoretical work on this topic.

There is experimental [10,11] and theoretical [3,6,7] evidencefor the helical shape of the linear isomer (PFOS 89), which is wellreproduced at the M06-2X, B3LYP and PM6 levels of theory. Basicorganic chemistry concepts tell us that within isomers, the morebranched a hydrocarbon, the more thermodynamically stable it is[12]. Some DFT studies also confirm this finding, making use ofthe M06-2X functional [13]. This result was not observed withPFOS when using the B3LYP functional or the PM6 semi-empiricalmethod. The B3LYP study showed that the thermodynamic stabil-ity of each isomer is independent of the type of species (neutral oranionic) considered and the medium (gas phase, aqueous and oct-anol solutions) [3].

After having performed our previous PFOS study [3], we becameaware of problems associated with the B3LYP functional regardingits inability to properly reproduce the thermodynamic stabilitywithin a series of organic isomers [14–18]. Since accurate

82 T. Giroday et al. / Computational and Theoretical Chemistry 1046 (2014) 81–92

thermodynamic values are required for a correct understanding ofthe relative thermodynamic stability of PFOS, and good standardGibbs free energies of formation are required to calculate accurateacid dissociation constants in different media and various partitioncoefficients for these compounds (which is work currently in prep-aration), the work previously done by our group [3] should be per-formed with a better functional. Previous studies have indicatedthat the M06-2X functional can properly describe the thermody-namic stability within a series of chain isomers [13,19,20], hence,this was the functional chosen for this work. Preliminary resultsshow that the M06-2X calculations are in closer agreement withthe available experimental data (pKa in water and octanol–waterpartition coefficient for the linear isomer, PFOS 89) than theB3LYP calculations. The DFT comparison of thermodynamic stabil-ities reported in this study is also of interest from a methodologicalpoint of view. Furthermore, it will be relevant to further investigatein a follow up study if the PFOS thermodynamic stability differ-ences found between these two functionals lead to significant dif-ferences in the calculation of the previously mentioned physicochemical quantities and their trends among the series of isomers.

2. Computational details

The Gaussian09 software package [21] was used to optimizeand properly characterize the equilibrium geometries of the 89PFOS in their neutral and anionic forms. Calculations were per-formed using the M06-2X [19] functional and the 6-311++G(d,p)basis set. As previously indicated, the nomenclature system sug-gested by Rayne et al. [6] was used in this work. In this system(see Table S1 of the Supporting Information (SI) section), isomersare ranked from most substituted (PFOS 1) to least substituted(PFOS 89).

While B3LYP fails to properly reproduce heats of reaction andbond energies in large (4 or more carbons) molecules due to defi-ciencies in the description of dispersion forces [14,19c] and haseven greater problems when describing mid-range electron corre-lation in both nonhalogenated and halogenated alkane chains (1.5–2.5 Å) [14–18] the M06 set of meta-hybrid functionals include anempirical fitting of their parameters that allows an increasedresponse to dispersion forces. M06-2X was chosen for its increasedaccuracy with main group atom energies and reaction kinetics, aswell as for its ability to describe these medium-range electron cor-relations and van der Waals interactions much more effectivelythan B3LYP [19,20].

Given the experimental and theoretical evidence for the helicalshape of the linear and most abundant PFOS, PFOS 89 [7,22–24]which is well reproduced with the B3LYP (and M06-2X) functional,the remaining isomers were initially obtained (and further opti-mized and characterized using the B3LYP functional) by makingsubstitutions on the helical optimized gas-phase framework ofPFOS 89 [3]. This was the practical approach followed to performglobal optimizations of each of the 89 neutral and anionic isomersin the three media considered. The optimized B3LYP/6-311 + G(d,p) gas-phase geometries [3] were used as starting pointfor the M06-2X gas-phase optimizations. Calculations in water andoctanol were performed using the SMD method on both geometryoptimizations and frequency calculations. Since the same proce-dure is followed for the entire set of isomers with both functionals,we expect the stability comparison to be meaningful, even thoughwe cannot claim we are working with the global minimum geom-etries of these compounds.

The topology of the electron density was analyzed by means ofthe widely used Atoms in Molecules (AIM) Bader’s theory, in whichthe molecular graphs contain first-order saddle points (bondcritical points, BCPs) associated with bond paths [25]. BCP density

values are related to the strength and nature of the interactionbetween two given nuclei. The NCIPLOT program allows the char-acterization of non-covalent interactions [26]. These weak interac-tions are accompanied by low-density and reduced gradient valuesthat can be located by using gradient isosurfaces containingregions of real space. The sign of the second eigenvalue of the elec-tron-density Hessian helps to distinguish if the non-covalent inter-actions are of a bonding (k2 < 0) or non-bonding (k2 > 0) nature.Usually, in 3D NCI representations, a blue–green–red colour codeis used in the isosurfaces. Blue colour denotes strong attractivenon-covalent interactions, whereas red colour denotes strongrepulsive non-covalent interactions. In 2D NCI plots, the reduceddensity gradient (RDG) is represented versus the product[sign(k2) * q]. The density q provides information about thestrength of the interaction, and the sign of k2 indicates the natureof the interaction (bonding or non-bonding).

3. Results and discussion

The results of the calculations are presented in order of stabilityin Table 1, listing the neutral isomers and their relative Gibbs freeenergies of formation (G) (in kJ/mol at 298.15 K) for both M06-2Xand B3LYP [3] calculations in each of the three media considered:the gas phase, aqueous and octanol solutions. Similar results forthe anionic PFOS are presented in Table 2. The same M06-2X datalisted following the naming label (i.e., from PFOS 1 to PFOS 89),together with the B3LYP and PM6 [7] data, appear in Tables S2and S3 of the SI section. The first part of the discussion focusseson the M06-2X results, while the second part compares theseresults with the B3LYP data reported in Ref. [3].

3.1. Discussion of the M06-2X results

Solvation increases the thermodynamic stability relative to thegas phase for neutral and anionic PFOS. As expected, anions aremore stabilized due to solvation in more polar solutions, but neu-tral PFOS are calculated to have lower G values in octanol thanwater. The average G differences for the acids in gas–octanol,gas–water and octanol–water are 19.3, 8.7 and �10.6 kJ/mol,respectively, while for the anions these values are 172.1, 184.6and 12.4 kJ/mol. The differences in the calculated G values for theneutral PFOS between each pair of media considered (gas–octanol,gas–water and octanol–water) are listed in Table S4, together withsimilar data for the anions. The three sets of values for neutral andanionic PFOS are also plotted in Figs. S1 and S2.

The relative stability of neutral PFOS is not affected by the med-ium (gas phase, aqueous or octanol solutions). The relative G valuesfor a given type of PFOS in several pairs of media are plotted inFigs. S3 and S4 (for the neutrals) and S6, S7 (for the anions). Thedifferences in relative G values between pairs of media are shownin Figs. S5 (neutrals) and S8 (anions). Small differences (with meanabsolute deviations between 1.2 and 2.2 kJ/mol) can be observedbetween the relative G values of the neutrals in each of the pairsof media considered (see Table S2 and Figs. S3–S5), which leadsto similar stability orders. The relative G values of the neutrals inevery pair of media correlate very well with R2 values 0.991(gas–octanol), 0.988 (gas–water) and 0.997 (octanol–water). Theresults of the linear correlations are reported in Table S5. Similarsmall relative G differences and good linear correlation (withR2 = 0.992) are also obtained for the anions in octanol and water(see Table S5 and Fig. S7). However, as expected, larger discrepan-cies (and poor correlations) are obtained for the anions when com-paring gas–octanol and gas–water relative G values since thethermodynamic stability of changed species is more stronglyaffected by solvation (see Table S3 and Figs. S6–S8). The relative

Table 1Stability order of neutral PFOS in the gas phase, octanol and water calculated at the M06-2X/6-311++G(d,p) (this work) and B3LYP/6-311+G(d,p) (Ref. [3]) levels of theory.a

Stability order Gas Octanol Water

M06-2X B3LYP M06-2X B3LYP M06-2X B3LYP

1 54 0.0 68 0.0 48 0.0 82 0.0 48 0.0 82 0.02 48 2.3 82 1.6 54 4.8 68 1.1 54 1.5 68 0.23 68 6.2 54 3.1 68 6.7 48 4.4 68 5.0 48 4.74 82 12.1 48 5.2 25 10.7 54 4.5 25 6.3 54 5.45 25 12.6 83 14.7 82 12.2 83 13.5 82 9.4 89 12.96 47 21.1 89 16.5 47 19.9 89 14.2 47 17.2 83 13.17 32 28.6 88 17.9 32 29.6 88 15.7 73 28.6 88 15.48 59 34.6 72 20.2 73 32.8 72 19.1 32 28.9 72 18.79 14 34.8 73 26.2 59 32.9 73 25.1 59 30.3 31 25.1

10 73 34.9 31 26.6 14 36.4 31 26.0 56 32.3 73 25.511 56 35.5 32 27.8 80 36.5 87 26.7 80 33.5 87 26.412 17 38.9 71 28.4 56 36.8 71 27.0 77 34.9 71 26.513 72 39.8 87 28.6 72 37.3 85 27.1 14 35.5 86 26.814 80 40.1 62 28.7 77 38.0 86 27.7 72 36.4 85 27.015 77 41.3 85 29.0 17 38.2 32 28.3 17 36.8 80 28.216 83 42.3 86 30.0 83 39.3 80 28.7 83 38.5 32 28.617 31 43.2 80 30.1 31 41.0 62 29.4 35 38.5 35 28.818 29 44.6 47 30.5 35 42.2 77 29.8 31 39.2 62 28.919 71 45.0 35 30.7 71 42.6 47 30.0 71 40.2 77 29.020 11 46.0 77 31.4 11 44.0 35 30.5 11 40.4 47 29.321 46 46.8 76 33.3 29 44.6 76 31.7 34 42.1 76 31.722 35 47.7 84 33.9 88 45.7 84 33.6 61 43.4 84 33.723 88 48.7 70 34.9 52 46.8 64 34.8 29 43.5 64 33.924 52 49.0 25 35.7 34 46.9 25 35.2 52 44.2 25 35.225 34 49.6 64 36.2 75 47.5 59 36.0 46 45.2 59 35.726 49 49.7 59 37.3 46 47.6 70 36.6 88 45.3 70 36.227 24 49.9 34 37.9 49 47.8 79 36.8 76 45.6 34 36.528 70 50.4 79 38.8 76 48.8 34 37.9 49 45.8 79 38.229 61 51.6 75 39.6 61 50.0 75 38.6 24 47.9 75 38.330 75 52.5 63 44.2 70 51.0 63 42.5 75 48.0 63 41.931 76 53.2 29 44.6 24 51.2 17 45.0 70 48.4 56 44.332 53 55.5 56 44.7 89 53.6 56 46.4 62 51.9 17 45.333 62 55.6 17 45.4 85 56.5 29 46.6 89 52.6 40 45.734 89 58.2 40 45.4 62 56.6 40 46.9 40 52.9 81 46.035 37 58.9 11 46.1 87 56.8 81 47.1 60 53.6 29 46.336 13 59.2 14 47.8 37 57.6 65 48.7 85 54.1 65 48.237 85 59.2 81 48.6 40 58.2 11 48.8 37 54.2 11 48.838 87 59.5 69 50.0 69 58.3 69 50.3 87 54.3 67 50.239 40 59.6 65 50.1 86 58.3 67 50.8 86 54.5 66 50.640 6 59.6 53 51.6 64 58.7 66 51.3 79 55.9 69 51.041 79 60.3 66 52.5 60 58.9 52 52.0 53 56.3 52 52.642 69 60.5 67 53.1 79 59.0 14 52.3 69 57.0 14 53.243 86 61.4 52 54.2 6 59.5 53 53.3 84 57.4 53 55.144 64 61.7 37 56.8 53 60.3 37 56.4 6 58.0 39 56.145 4 62.1 39 58.1 84 60.5 39 57.0 81 58.8 37 56.846 51 62.5 33 58.3 13 61.9 33 58.9 64 59.2 61 57.247 1 62.6 30 58.9 33 62.1 61 58.9 51 59.3 30 58.248 60 63.1 61 59.9 81 62.3 30 59.1 9 61.2 33 58.349 84 63.1 51 60.7 51 62.4 51 60.6 30 61.5 51 60.150 9 63.4 46 62.6 9 62.9 78 63.7 4 61.6 78 63.051 81 63.8 6 63.0 30 63.4 46 64.2 55 61.8 46 64.552 33 64.8 44 64.8 4 63.6 6 64.4 13 61.8 44 65.153 55 65.3 78 65.2 1 65.1 44 65.6 33 62.1 6 65.454 15 65.5 49 67.0 63 66.2 49 66.7 1 62.8 74 65.755 30 66.3 74 68.3 55 66.6 74 66.9 63 63.6 49 67.156 63 68.5 36 72.0 39 67.6 36 71.6 39 64.5 36 71.057 23 71.6 60 73.7 15 67.8 60 72.1 57 65.0 60 71.658 39 71.7 43 74.8 57 68.1 42 73.0 15 65.8 42 72.659 57 72.2 42 74.9 74 71.7 43 73.1 42 68.5 43 72.960 74 74.7 24 79.5 44 72.5 45 78.7 74 69.0 55 82.561 44 75.6 45 79.7 23 73.4 24 82.5 23 70.3 45 83.262 42 76.4 55 82.7 42 73.9 55 82.6 65 70.9 24 83.463 5 77.3 5 83.2 36 74.1 5 83.9 78 71.3 5 84.364 78 77.6 15 83.3 16 74.2 38 85.3 44 71.5 38 84.465 10 78.0 13 83.7 65 74.6 16 86.8 36 72.3 9 86.866 65 78.0 9 85.1 78 74.9 13 86.9 16 73.4 13 88.567 16 78.0 38 86.8 5 75.1 15 87.1 5 73.6 10 89.268 36 78.3 16 87.4 66 75.9 9 87.3 67 73.8 16 90.069 66 80.4 10 89.0 67 77.2 57 89.8 66 75.4 15 90.270 67 80.7 4 90.1 10 78.2 10 89.9 10 76.9 57 90.371 45 82.8 57 90.3 45 78.8 4 93.4 45 77.8 4 93.972 18 83.8 8 93.0 43 81.5 8 94.5 43 78.0 8 94.573 43 85.7 7 100.1 2 87.5 7 101.7 28 82.6 7 102.3

(continued on next page)

T. Giroday et al. / Computational and Theoretical Chemistry 1046 (2014) 81–92 83

Table 1 (continued)

Stability order Gas Octanol Water

M06-2X B3LYP M06-2X B3LYP M06-2X B3LYP

74 2 87.4 1 102.5 18 88.1 41 103.0 18 85.2 41 102.575 28 88.0 41 104.6 28 88.7 1 105.5 2 85.3 1 108.076 8 90.2 2 107.4 38 90.4 2 109.0 38 87.0 2 109.977 12 96.4 12 108.9 8 90.9 12 110.3 8 87.3 12 111.978 38 97.3 18 109.2 26 94.0 18 112.1 26 92.0 23 121.179 26 97.8 23 116.6 12 97.3 58 119.4 12 93.5 18 121.3b

80 19 97.9 58 120.0 27 97.7 23 119.5 27 93.8 27 122.081 27 98.6 28 121.1 19 98.3 28 121.7 19 95.7 50 122.282 7 101.2 27 122.7 7 102.9 27 123.2 7 100.4 58 122.683 3 105.8 22 123.1 3 108.1 22 124.6 41 103.3 28 123.284 21 107.5 20 123.2 41 108.8 20 124.7 22 106.7 20 123.885 22 110.7 50 124.9 22 110.7 50 126.5 21 106.8 22 125.386 41 115.3 19 126.8 21 111.0 26 129.7 3 107.7 26 130.887 58 119.3 26 128.0 58 115.6 19 131.0 58 111.2 19 131.088 20 119.4 21 129.6 20 117.4 21 132.7 20 117.1 21 133.989 50 123.9 3 139.6 50 122.1 3 139.6 50 118.5 3 137.2

a PFOS labels shown in bold, relative G values (in kJ/mol at 298.15 K) shown in italics.b Estimated from a single-point calculation in water (see Ref. [3]).

84 T. Giroday et al. / Computational and Theoretical Chemistry 1046 (2014) 81–92

G values for the anions in the gas phase, relative to the values inoctanol and water, tend to be greater from PFOS 38 to 89.

Figs. S9–S12 display the M06-2X relative G values between neu-tral and anionic PFOS for the same medium. In general, the relativeG values of anionic PFOS tend to be larger than the values of theneutral PFOS regardless of the medium considered. The greatestdifferences can be found for the least branched isomers (PFOS57–89, but also for PFOS 12 and 41). Exceptions to this generalobservation in at least two of the media considered are PFOS 2 to6, 9, 13, 18, 20, 23, 25, 29, 32, 44, 47, 48 and 50, most of whichare among the most branched isomers. There is no significant lin-ear correlation between the calculated G values of neutral andanionic PFOS for a given medium (see Table S5).

3.1.1. Stability order and structureThe ten most stable neutral PFOS in the gas phase are predicted

to be 54 > 48 > 68 > 82 > 25 > 47 > 32 > 59 > 14 > 73 (73 has a rela-tive G of 34.9 kJ/mol). Fig. 1 displays the optimized structures ofthe nine most stable, with their relative G values. A patternobserved for this group is the substitution at the carbon atombeside the head group and/or at the tail end of the molecule, butno substitution in any other position (except for 47 and 59). Itappears that trifluoromethyl (TFM) substitutions at the tail helpincrease thermodynamic stability. Deviations from the optimizedhelical structure of PFOS 89 are difficult to spot in the highlysubstituted isomers (54, 48, 59, 14), but in the others, hints ofthe helical structure can be seen. Few changes were noticed whenanalyzing the most stable neutral isomers in octanol and water.

The ten least stable neutral PFOS in the gas phase are50 < 20 < 58 < 41 < 22 < 21 < 3 < 7 < 27 < 19 (50 has a relative G of123.9 kJ/mol). The optimized structures of the first nine with theirrelative G values are shown in Fig. 2. These isomers are highlysubstituted; three of them (20, 3 and 27) have substituents in allthe available main-chain positions. The major trend noticeableamongst these compounds is the substitution at the middle carbonatoms of the main chain, i.e. carbon atoms that are not at the tail ornext to the head group, even if there is also substitution next to thehead group and/or at the tail. In regard to the helical structurefound abundantly in the most stable isomers, the least stable iso-mers consistently show little to no resemblance to the helicalstructure. Few changes to these observations were noted whenanalyzing the least stable neutral isomers in octanol and water.

There are no major differences when the most stable anions andneutrals in the three media considered are compared. The ten moststable anions in the gas phase are 48 > 25 > 68 > 54 > 47 > 32 > 14 >

29 > 82 > 11 (11 has a relative G of 40.8 kJ/mol). The ten least stableanions in the gas phase are 58 < 41 < 50 < 22 < 21 < 12< 38 < 43 < 7 < 67 (58 has a relative G of 140.8 kJ/mol). Slightvariations can be observed for the anions when comparing thegas-phase results to those in octanol and water. The results inthe two solvents considered are very similar.

3.1.2. Non-covalent interaction (NCI) analysisAs mentioned in the introduction, it is common knowledge that

branched alkanes are more stable than linear alkanes. Many papersin the literature have been devoted to analyzing the origin of thisfact, called branching effect. As expected, not all DFT methods aresuitable to study it. GGA functionals do not behave properly dueto the gradient term, unless they are specifically parameterizedto avoid this problem and take into account medium range elec-tron correlation, as in the case of the M06-2X functional. Severalauthors have pointed out that the branching effect is governedby attractive interactions. The protobranching model, first formu-lated in 2007 [27], was used very recently by McKee and Schleyerfocusing on 1,3-alkyl-alkyl interactions [28]. They concluded thatthe 1,3-alkyl-alkyl electron correlation effects (which are not theonly force behind the branching effect) are attractive. Similar tothe 1,3-alkyl-alkyl interactions, the 1,5-H-H interactions in hydro-carbons have been identified as weakly attractive by Johnsonet al.’s NCI analysis [26]. However, repulsive interactions werefound near the C–C bonds instead. In the case of PFOS, instead ofhydrogen there are fluorine atoms, but only some of them caninteract depending on their relative position. Fluorine–fluorineinteractions can be characterized through Atoms in Molecules(AIM) procedures when a small amount of electron density isfound in the Bond Critical Path (BCP) between two fluorine atoms.What do AIM and NCI tell us about PFOS?

We decided to study and compare two of the PFOS isomers, 54(the most stable one) and 89 (the linear isomer), by analyzing theirtopologies through Bader’s AIM and Johnson’s NCI procedures. Theresults obtained are depicted in Figs. 3 and 4. Fig. 3 shows themolecular graphs of isomers 54 and 89. To state a reference, C–Cbonds have density values around 0.25 on their BCPs, whereasthe BCP values of the C–F bonds are around 0.27. For simplicity,only the F–F interactions are shown. In isomer 89, only one BCPis found (q = 0.012). However, an extended network of weak F–Finteractions is present in isomer 54, with values ranging from0.005 to 0.018. These weak interactions are 1,5 (q = 0.013–0.014),1,6 (q = 0.013–0.018) and even 1,8 F–F (q = 0.005) interactions.This last value is very significant as it shows that two fluorine

Table 2Stability order of anionic PFOS in the gas phase, octanol and water calculated at the M06-2X/6-311++G(d,p) (this work) and B3LYP/6-311+G(d,p) (Ref. [3]) levels of theory.a

Stability order Gas Octanol Water

M06-2X B3LYP M06-2X B3LYP M06-2X B3LYP

1 48 0.0 68 0.0 48 0.0 68 0.0 48 0.0 68 0.02 25 4.9 48 1.5 68 5.9 48 2.1 25 6.4 48 1.83 68 7.6 32 20.8 25 8.6 54 13.7 68 7.0 54 13.44 54 18.0 54 21.8 54 11.7 82 15.5 54 7.9 82 14.05 47 18.5 25 24.0 47 18.1 83 24.5 47 17.0 83 24.26 32 24.1 47 24.7 82 24.4 32 25.5 82 19.6 32 26.07 14 27.3 82 33.3 32 25.9 47 27.2 32 28.2 47 26.58 29 28.2 29 34.2 29 36.7 25 29.4 14 37.0 72 27.39 82 39.0 83 34.6 14 37.1 72 30.7 29 37.2 89 28.5

10 11 40.8 31 37.7 17 45.1 89 31.2 56 40.6 88 30.011 17 41.6 62 39.4 56 45.7 88 33.5 59 42.4 25 32.612 9 43.8 72 39.8 72 46.0 62 35.9 73 43.8 62 33.113 13 46.7 14 41.0 11 46.3 31 36.0 80 44.6 31 33.414 46 47.9 35 42.9 31 47.1 35 39.0 31 45.1 71 35.815 6 48.3 64 46.6 73 48.1 71 39.3 77 45.1 35 36.716 31 49.3 89 47.8 59 48.5 29 39.8 72 45.4 86 38.717 56 49.7 71 48.5 83 49.5 64 41.3 17 45.7 64 39.118 24 49.7 88 49.3 35 50.4 87 42.2 11 46.8 80 40.619 4 54.6 11 49.6 80 50.7 85 43.0 83 47.7 87 40.820 35 54.8 46 50.2 77 51.0 73 43.3 71 49.1 85 41.621 72 56.4 34 50.5 71 51.9 86 43.9 35 49.7 29 42.622 34 56.6 73 52.7 34 52.2 80 45.0 34 50.6 73 43.023 73 57.6 6 53.4 24 54.0 70 47.0 24 52.2 70 43.524 83 58.9 17 53.9 46 54.7 84 47.0 52 52.9 34 44.425 1 59.2 70 55.5 6 55.3 34 47.1 46 53.9 77 45.826 23 60.8 85 59.5 88 55.9 14 47.8 88 54.3 76 46.727 71 60.9 87 60.1 9 56.1 77 48.0 70 56.4 84 46.728 59 62.3 84 61.6 52 57.9 76 49.5 6 57.2 79 48.529 49 63.0 86 61.6 70 59.0 11 51.8 9 57.9 59 50.130 62 63.2 44 62.4 13 59.2 79 53.3 61 58.2 14 50.431 52 65.1 77 62.5 62 59.2 75 55.2 49 58.3 11 51.432 15 66.0 80 62.5 49 60.3 59 55.3 75 58.5 75 52.733 18 66.8 56 62.6 75 61.9 17 55.9 62 58.6 40 53.634 5 67.0 76 62.7 4 62.4 56 56.4 76 59.8 17 54.735 80 67.3 69 63.7 76 64.1 46 57.0 53 61.9 56 56.036 77 67.4 40 64.7 69 64.5 40 57.6 69 62.1 69 56.437 2 67.9 30 67.1 61 65.0 69 59.2 13 62.4 30 56.838 44 68.4 75 67.7 53 65.5 6 59.9 4 62.7 63 56.839 70 69.1 33 67.9 64 65.8 44 62.4 40 63.3 53 59.540 69 69.8 9 68.2 40 67.3 63 62.6 64 63.9 46 59.941 33 70.0 59 68.2 86 68.1 81 62.9 79 64.2 44 61.042 30 70.1 79 69.3 89 68.1 53 63.4 85 64.5 81 61.143 51 71.4 53 69.5 1 68.3 52 65.7 89 64.7 65 61.544 64 72.6 13 71.5 85 68.3 65 66.9 87 64.7 6 61.845 53 73.1 52 71.9 87 68.4 67 67.2 51 66.2 66 61.846 75 74.0 51 73.6 23 68.5 66 67.3 86 66.4 52 62.347 88 74.9 24 73.7 44 68.6 33 67.7 5 66.5 67 62.348 37 75.6 63 73.8 51 68.8 30 68.4 60 67.8 51 66.149 40 76.1 65 79.5 5 69.1 51 69.3 23 67.9 33 66.850 76 76.4 37 80.1 79 69.3 39 73.3 37 67.9 39 69.951 10 79.1 81 80.2 33 69.7 37 74.6 55 68.1 61 71.152 3 79.6 39 81.6 37 70.8 9 76.0 1 68.6 37 71.253 55 80.0 49 82.2 15 71.0 61 77.2 44 68.8 78 75.754 16 80.6 36 82.9 30 72.5 24 78.5 81 69.7 49 78.255 61 81.4 66 83.0 55 72.8 49 79.7 33 70.4 45 78.656 36 82.2 67 84.8 81 73.0 13 80.6 30 70.8 9 79.257 85 83.5 5 87.2 84 73.4 78 81.4 15 71.5 36 80.358 89 84.9 15 87.2 60 74.2 36 81.5 84 72.1 74 82.859 39 85.2 4 87.9 18 77.1 45 83.2 63 73.2 24 82.960 79 85.6 2 89.3 39 78.0 74 84.0 57 76.2 13 83.461 87 85.9 1 90.3 63 78.2 43 88.9 39 77.2 43 84.662 84 86.4 45 91.5 2 79.8 5 89.3 36 78.4 60 84.863 60 87.5 61 92.2 36 81.6 60 90.6 18 78.7 42 87.064 86 87.7 10 93.3 57 81.7 15 91.3 42 81.1 5 89.565 81 90.2 74 95.0 16 82.8 42 91.6 2 81.7 55 90.366 63 93.5 18 95.2 10 84.0 4 93.1 74 81.8 38 91.067 57 93.7 16 96.0 42 84.8 55 93.7 16 82.0 15 92.068 45 94.4 78 96.8 74 86.4 38 95.8 78 82.9 4 93.869 27 96.4 55 101.1 65 87.5 10 96.2 67 83.5 10 96.070 19 96.7 23 102.1 78 87.7 16 97.2 10 83.5 16 96.471 74 97.0 43 102.7 45 89.8 2 99.4 65 83.6 57 101.672 42 98.3 60 103.7 66 90.2 1 101.7 45 84.9 2 102.973 28 99.7 42 104.8 67 90.3 18 102.5 66 84.9 8 103.1

(continued on next page)

T. Giroday et al. / Computational and Theoretical Chemistry 1046 (2014) 81–92 85

Table 2 (continued)

Stability order Gas Octanol Water

M06-2X B3LYP M06-2X B3LYP M06-2X B3LYP

74 8 100.0 38 106.6 3 92.6 8 105.6 28 90.0 18 104.475 65 101.5 7 109.2 28 93.8 57 106.1 43 91.6 1 105.276 20 102.7 8 109.4 43 96.0 7 109.5 8 93.3 7 107.177 78 104.2 3 113.7 8 98.5 23 111.1 3 94.3 23 114.478 66 106.5 57 115.3 19 98.8 41 120.7 38 96.6 41 116.279 26 106.6 20 118.4 38 98.9 20 122.2 19 98.1 20 122.580 67 107.8 27 128.0 27 101.7 3 124.5 27 100.0 12 123.681 7 109.2 41 130.3 26 105.1 12 126.8 26 102.1 3 128.682 43 109.3 19 131.7 12 108.8 27 129.1 12 105.2 27 129.483 38 110.5 12 131.9 20 110.0 28 131.4 7 106.7 50 129.584 12 114.3 50 133.4 7 110.4 19 132.8 21 109.4 28 130.485 21 116.4 28 136.0 21 112.4 50 132.8b 20 112.7 19 131.986 22 122.0 26 139.3 22 118.0 22 136.7 22 114.1 58 134.087 50 123.3 22 140.8 50 120.0 58 138.0 50 116.3 26 138.488 41 136.0 21 145.7 41 124.9 26 139.6 41 120.2 22 138.789 58 140.8 58 147.0 58 130.2 21 140.7 58 126.0 21 139.1

a PFOS labels shown in bold, relative G values (in kJ/mol at 298.15 K) shown in italics.b Estimated from a single-point calculation in octanol (see Ref. [3]).

Fig. 1. Most stable gas-phase neutral isomers with their relative G values in kJ/mol at 298.15 K (M06-2X results; all main-chain carbons are perfluorinated but depicted assimple carbons for simplicity).

86 T. Giroday et al. / Computational and Theoretical Chemistry 1046 (2014) 81–92

T. Giroday et al. / Computational and Theoretical Chemistry 1046 (2014) 81–92 87

atoms in the head and the tail of the molecule are connectedthrough a very weak bonding interaction.

The NCI results are summarized in Fig. 4. Both 2D and 3D repre-sentations for isomers 54 and 89 are shown. As the sign of k2 reveals(see Computational Details), there is a delicate equilibrium betweenvery weak (near zero, significantly less than hydrogen bonds values)attractive and repulsive interactions in the F–F network of thesemolecules. Darker green regions indicate van der Waals attractionsbetween F atoms, while lighter green regions evidence repulsive

Fig. 2. Least stable gas-phase neutral isomers with their relative G values in kJ/mol at 2simple carbons for simplicity).

C–F interactions. These two kinds of very weak interactions are bal-anced in 89, whereas the F–F attractive van der Waals interactionsare slightly stronger than the C–F repulsions in 54. This combinationof very weak attractive and repulsive interactions due to the pres-ence of fluorine atoms shows that the relative disposition of covalentbonds in linear and branched isomers are not the only determinantsof the relative stability among the PFOS isomers. In other words, asJohnson et al. expressed, ‘‘(the NCI) approach reveals the underlyingchemistry that complements the covalent structure’’ [26].

98.15 K (M06-2X results; all main-chain carbons are perfluorinated but depicted as

Fig. 3. Molecular graphs of isomers 54 and 89 from the AIM analysis. Bond critical points of weak F–F interactions are marked with green dots along with their density values.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Above: 3D NCI gradient isosurfaces colored on a blue–green–red scale (�0.03 to 0.03 au) according to values of sign(k2) q; below: 2D NCI plots: reduced densitygradient versus the electronic density multiplied by the sign of the second Hessian eigenvalue. (For interpretation of the references to colour in this figure legend, the reader isreferred to the web version of this article.)

88 T. Giroday et al. / Computational and Theoretical Chemistry 1046 (2014) 81–92

3.2. Comparison of the M06-2X and B3LYP results

The relative G values calculated with M06-2X (SMD) and B3LYP(PCM) are listed in Table 2 in the three media considered. Differencesbetween these values for each solvent and type of isomer are shown

in Table S6. The PM6 results [7] for the neutrals in the gas phase arealso compared with the M06-2X results reported in this paper. Thevalues of Table S6 appear plotted in Figs. 5 and 6 in each of the threemedia for the neutral and anionic PFOS, respectively. Additionalcomparisons using bar graphs are shown in Figs. S13–S17.

-90.0

-70.0

-50.0

-30.0

-10.0

10.0

30.0

50.0

70.0

90.0

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89

G d

iffer

ence

s (k

J/m

ol)

Neutral PFOS

gas

octanol

water

gas - PM6

Fig. 5. Relative G differences (M06-2X and B3LYP) between isomers of neutral PFOS in three media, shown along with PM6 data for comparison.

-90.0

-70.0

-50.0

-30.0

-10.0

10.0

30.0

50.0

70.0

90.0

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89

G d

iffe

ren

ces

(kJ/

mo

l)

Anionic PFOS

gas

octanol

water

Fig. 6. Relative G differences (M06-2X and B3LYP) between isomers of anionic PFOS in three media.

T. Giroday et al. / Computational and Theoretical Chemistry 1046 (2014) 81–92 89

By studying Figs. 5 and 6, the first observation that can be madeis that when comparing the M06-2X and B3LYP data, the differ-ences observed are basically the same regardless of the mediumconsidered and the type of PFOS (neutral or anionic). More evi-dence of this comes from inspecting the average deviations listed

at the bottom of Table S6; these values oscillate between 14.4and 15.8 kJ/mol. Hence, for simplicity, the following discussion willfocus on the neutral PFOS in the gas phase. Furthermore, three dis-tinct regions can be observed and will be discussed below (seeFigs. 3 and 4, as well as Table S6).

90 T. Giroday et al. / Computational and Theoretical Chemistry 1046 (2014) 81–92

For PFOS 1–28, the most substituted isomers (highly branched)with a main-chain of up to four carbon atoms, the M06-2X relativeG values are all lower than predicted by B3LYP (with the exceptionof PFOS 7; see Table S2). Hence, these compounds are predicted tobe more stable relative to the other PFOS with M06-2X than withB3LYP. However, they are not the most stable overall, with eithermethod. In fact, only 7 (4) of these PFOS rank among the 44 moststable, while the remaining 21 (24) rank among the 45 least stablePFOS with M06-2X (B3LYP). For PFOS 29–61 we find two sub-groups with differences that almost cancel each other out. PFOS29–45 are ranked slightly less stable by M06-2X (with higher rel-ative G values) than by B3LYP. A reciprocal effect is observed forPFOS 46–61, i.e. they are ranked slightly more stable (with lowerrelative G values) in M06-2X than B3LYP. Finally, a large differenceis observed for the less substituted isomers, PFOS 62–89. These iso-mers are ranked much less stable by M06-2X (with higher relativeG values) than by B3LYP, suggesting that the most linear isomersare not as stable compared to other isomers, as previously pre-dicted [3]. Of these 28 PFOS isomers, 20 (26) rank among the 44most stable with M06-2X (B3LYP). According to M06-2X, the mostlinear isomers (83–89) are much less stable relative to the otherPFOS than previously predicted by B3LYP. Their predicted orderof stability (from 83 to 89; B3LYP: 5th, 22nd, 15th, 16th, 13th,7th, 6th) changes greatly with M06-2X (from 83 to 89: 16th,

49th, 37th, 43th, 38th, 23th, 34th).When comparing gas phase M06-2X data to gas phase PM6

data, the results vary wildly with few patterns or trends save forthe less branched isomers 70–89, for which the M06-2X relativeG values are all lower than predicted by PM6.

The B3LYP study reported that there is some relationshipbetween relative stability and the degree of deviation from thehelical conformation of the main chain due to CF3 substitution incertain positions [3]. Even though it is not possible to find a simplepattern to relate branching and the degree of helical distortion, themost stable isomers were not found to be significantly distorted

Fig. 7. M06-2X and B3LYP relative entropie

from the helical conformation of PFOS 89. In the present studyusing the M06-2X functional, as previously discussed, the moststable isomers are found to have substitutions on the carbon nextto the head group and/or at the tail end of the molecule, while forthe least stable isomers there is substitution on the middle carbonsof the main chain, even if there is also substitution next to the headgroup and/or at the tail. Four isomers rank among the ten most sta-ble with both functionals (54, 48, 68 and 82), which happen to bethe four most stable isomers. Moreover, eight of the ten least stableisomers are predicted by both functionals as well (19, 27, 3, 21, 22,58, 20 and 50).

The M06-2X (SMD) and B3LYP (PCM) calculations both predicttrends of relative thermodynamic stability that are independentof the medium considered and of the type of PFOS (neutral oranionic).

3.2.1. Enthalpy and entropy contributions to the Gibbs free energiesSeveral figures have been added to help rationalize the enthalpy

(H) and entropy (S) contributions to the calculated Gibbs free ener-gies at the two levels of theory considered, focusing on the group ofneutral PFOS in the gas phase. Fig. 7 displays the calculated M06-2X and B3LYP relative entropies at 298.15 K (Fig. S18 displaysthe calculated M06-2X and B3LYP absolute values). Plots of theM06-2X and B3LYP relative G, H and S values are shown inFigs. S19 and S20, respectively, of the SI section. Furthermore,Fig. 8, displays the relative G, H and S differences (M06-2X andB3LYP) for this group of compounds.

An interesting observation is that the overall trend observed(with three distinct regions) for the differences (MO6-2X andB3LYP) in relative G values for the neutral and anionic PFOS in eachof the three media considered, is repeated when looking at the (rel-ative and absolute) entropies of the neutral PFOS in the gas phaseusing both functionals (see Figs. 7 and S18). The relative S values(see Fig. 7) are also quantitatively similar for both functionals,

s of the neutral PFOS in the gas phase.

Fig. 8. Relative G, H and S differences (M06-2X and B3LYP) between isomers of neutral PFOS in the gas phase.

T. Giroday et al. / Computational and Theoretical Chemistry 1046 (2014) 81–92 91

showing greater differences (with higher M06-2X relative values)for the least branched isomers (PFOS 62–89).

Given that the relative G and H values with each functional (seeFigs. S19 and S20) follow a very similar general pattern as well, itcan be concluded that the differences in stability for these com-pounds is mostly enthalpic, with small entropy changes betweenthe two functionals for most compounds. The plots of the relativeG, H and S differences (MO6-2X and B3LYP) shown in Fig. 8, con-firm the previous observation: the graphs for G and H are almostidentical, with more (but still very small) variations for the least-branched isomers.

4. Conclusions

The thermodynamic stability results for the 89 PFOS isomersusing the M06-2X functional have been discussed in detail andcompared to the previously reported B3LYP results [3]. For themost substituted PFOS (1–28), the M06-2X relative G values areall lower than predicted by B3LYP, while for the least substitutedisomers (PFOS 62–89) the opposite situation is observed. Hence,PFOS 83–89, which were predicted to be among the most stableisomers with B3LYP, are no longer so when considering the M06-2X calculations. It has been shown that the difference in stabilityfor these compounds is mostly enthalpic, with small entropychanges between the two functionals for most compounds. Fewdifferences were found in the relative stabilities of the neutraland anionic PFOS in any of the three media considered (the gasphase, aqueous and octanol solutions) using both functionals. Fur-thermore, as shown by the AIM and NCI analyses, when relatingstructure and thermodynamic stability in PFOS, the non-covalentinteractions between –CF3 groups are as important as the covalentstructure. Hence, regular thermodynamic stability patterns foundin aliphatic hydrocarbons seem to no longer strictly apply whenconsidering a different family of aliphatic isomers such as PFOS.

Work currently in process that deals with the calculation of var-ious acid dissociation constants and partition coefficients of PFOS

will reveal if the differences found when comparing the thermody-namic stability of these compounds using the M06-2X and B3LYPfunctionals affect the calculated trends of these physicochemicalproperties in a significant manner.

Acknowledgments

The authors would like to thank the Natural Sciences andEngineering Research Council of Canada (NSERC) and ThompsonRivers University (CUEF U-REAP program) for financial support.Thanks are also due to Information Technology Services at TRU.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.comptc.2014.08.003.

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