The Noble Gases: How Their Electronegativity and Hardness

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The Noble Gases: How Their Electronegativity and Hardness Determines Their Chemistry Jonathan Furtado, Frank De Proft, and Paul Geerlings J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp5098876 • Publication Date (Web): 09 Feb 2015 Downloaded from http://pubs.acs.org on February 16, 2015

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The Journal of Physical Chemistry

The Noble Gases: how their Electronegativity and Hardness determines their Chemistry Jonathan Furtado1, Frank De Proft2 and Paul Geerlings* 2 1

Quantum Chemistry and Physical Chemistry Section, Department of Chemistry,

Katholieke Universiteit Leuven Celestijnenlaan 200f 3000 Leuven, 2 General Chemistry Group (ALGC), Faculty of Sciences and Bio-engineering Sciences, Vrije Universiteit Brussel (Free University of Brussels-VUB) Pleinlaan 2 1050 Brussels, Belgium

Corresponding author. Tel: 003226293314 Fax: 003226293317 E-‐mailaddress: [email protected] *

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ABSTRACT The establishment of an internally consistent scale of noble gas electronegativities is a long standing problem. In the present study the problem is attacked via the Mulliken definition, which in recent years gained widespread use to its natural appearance in the context of conceptual Density Functional Theory. Basic ingredients of this scale are the electron affinity and the ionisation potential. Whereas the latter can be computed routinely, the instability of the anion makes the judicious choice of computational technique for evaluating Electron Affinities much more tricky. We opted for Puiatti’s approach extrapolating the energy of high ! solvent stabilised anions to the ! = 1 (gas phase) case. The results give negative electron affinity values, monotonically increasing (except for Helium which is an outlier in most of the story) to almost zero at eka-‐Radon in agreement with high level calculations. The stability of the B3LYP results is succesfully tested both via improving the level of theory (CCSD(T)) and expanding the Basis Set. Combined with the ionisation energies (in good agreement with experiment), an electronegativity scale is obtained displaying (1) a monotonic decrease of ! when going down the periodic table (2) top values not for the noble gases but for the halogens, as opposed to most (extrapolation) procedures of existing scales, invariably placing the noble gases on top (3) noble gases having electronegativities close to the chalcogens. In the accompanying hardness scale (hardly, if ever, discussed in the literature) the noble gases turn out to be by far the farthest the hardest elements, again with a continuous decrease with increasing Z. Combining ! value of the halogens and the noble gases the Ngδ+F δ-‐ bond polarity emerging from ab initio calculations naturally emerges. In conclusion the chemistry of the noble gases is for a large part determined by their extreme hardness, equivalent to a high resistance to changes in its electronic population coupled to their high

electronegativity. 2


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1. Introduction The “accomplished fact” that noble gases were “not only noble but also inert” 1 stood the test of time for many decades until Bartlett in 1962 synthesized the first noble gas compound XePtF6 2A multitude of studies were published later on leading to the synthesis and characterization of many Xenon, Radon and Krypton compounds. 3 Nowadays every inorganic chemistry textbook (for example 4, 5, 6) contains a chapter on the “Group 18 elements” with typical ingredients such as occurrence and physical properties of the noble gases but also the description of the synthesis and structure of some selected Xenon, Krypton and Radon compounds (in descending order of frequency). An overall characteristic of these compounds is that the fluoride-‐ and oxo-‐ compounds are dominating be it that in recent years also compounds with bonds to nitrogen, carbon and metals have been prepared. When discussing structure, reactivity, stability… of compounds it has become commonplace in modern chemistry to relate them to a (large) extent to their charge distributions as reflected in the polarity and polarizability of bonds and the associated energetics .In this context properties of a compound also those containing noble gas-‐ atoms7 like the Ionisation Energy, the Electron Affinity, are of fundamental importance to get insight in the how and why of the chemical bond and chemical bonding. 6, 8, 9, 10 While a property like the Ionisation Energy, I, is experimentally known for the noble gases and is discussed for its periodicity in the aforementioned textbooks, much less known e.g. for its counterpart the Electron Affinity, A, for the simple, well known reason that these Electron Affinities are said to be negative ,indicating that the anion of a noble gas atom, even in its ground state, is at a higher energy than the neutral atom and unstable to electron loss. Some values were proposed based on Electron Transmission Spectroscopy (ETS) corresponding however to atomic excited states11, other values were obtained by extrapolation, such as those by Bratsch and Lagowski12 and Fung13 , in the former case by a quadratic extrapolation of iso-‐

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electronic sequences , in the latter case by quadratic interpolation in the Energy (E) vs. number of electrons (N) curve (vide infra). As a fundamental property to describe the polarity of bonds, the electronegativity has undergone an almost similar fate for the noble gases. Being not experimentally accessible, it has been coupled, in a variety of ways, to measurable quantities in the context of various models. The most famous approach is of course Pauling’s endeavour 8,14 leading to a scale (later on refined by Allred15) based on an ingenious combination of thermodynamics and quantum mechanics. It’s most influential counterpart is the Mulliken Scale16, developed in the same period of early applications of quantum mechanics in chemistry. , the mid -‐1930’s, directly relating the electronegativity to the average of the Ionisation Energy and the Electron Affinity discussed above. This scale has gained increasing importance in the last decades due to its direct link to and foundation in Density Functional Theory 17,18 where it pops up in the Izcowski Margrave formula19 as (minus ) the first derivative of the energy with respect the number of electrons at constant external potential, i.e. minus the electron chemical potential20, µ. It bears the advantage to be computable as in the Ionisation Energy and the Electron Affinity can be accurately obtained with present day computational techniques. However, and thus the aforementioned ”problem “persists, the A value for noble gas atoms is negative, hampering the numerical evaluation of the Electron Affinity of noble gases (for reviews on the determination of negative Electron Affinities see [21], [22]). This problem also pervades in the calculation of the “companion parameters” hardness, η, and softness, S23 which in the same Iczkowski Margrave type approximation of the E=E(N) curve are

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!

!

!

!

given as (! − !) and respectively. Their use is preponderant when applying e.g. Pearson’s HSAB principle. 24 Whereas to the best of our knowledge no hardness/softness values were published on noble gases before, several extensions of existing scales (not only Pauling’s and Mulliken’s) to the noble gases have been published. Allen and Huheey25 evaluated the electronegativities of the noble gases by applying extrapolation procedures to the Allred-‐Rochow 26, Mulliken, Pauling and Sanderson27, 28 scales. These values were later on revised by Meek 29 who concluded that, when comparing the electronegativities of the noble gases with those of their neighbours in the periodic table, in the four cases considered, the noble gases had higher electronegativities than the corresponding (i.e. belonging to the same row in the Periodic Table) halogens, and that the magnitude of the difference decreases when going down in the Periodic Table. Similar results were obtained by Fung13 manipulating existing scales to account for the noble gas behaviour. In view of their fundamental role in Conceptual DFT 30à37,and in modern organic and inorganic chemistry in globo, we envisaged a relatively simple computational approach for obtaining trustworthy χ and η values by a similar method, allowing direct comparisons, and use of these values preferable in an absolute but certainly in a relative context to discuss bonds and bonding involving noble gas atoms. A comparable study was performed in our group on the Group 14 atoms C, Si, Ge, Sn, Pb, Uuq … also extended to their functional groups.38 This calls for a systematic, simple treatment of the problem of the negative A’s to be used in conjunction with the cases of positive A’s and I. This approach will be based on stabilizing anions in solvents with high dielectric constant, ε, and extrapolating a series of results to the ε=1 case as presented by Puiatti et al39 on a series of organic compounds obviously not involving 5



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noble gas atoms. To the best of our knowledge this is the first systematic, non-‐empirical study on Electron Affinities of noble gases, the only exception being an approximate simple Xα theory approach by Bartolotti, Gadre and Parr40 not mentioned by Meek, but whose results will be included in our discussion. 2. Theoretical Background and Computational Details As stated above the basic quantities envisaged, electronegativity, !, and hardness,!, are defined in a conceptual DFT context as (minus) the first and the second derivatives of the energy E vs. the number of electron N and constant external potential v (i.e. the potential felt by the electrons due to the nucleus)

!!

! = −

!! !

! =

!! !

!

! !! ! !

(1)

Note that in some texts the factor ½ is dropped.30b Traditionally, a quadratic E vs. N was assumed, leading in a finite difference approach to 16, 30, 31

! =

!!! !

! =

!!! !

(2)

with I and A being the first vertical Ionisation Energy and Electron Affinity respectively. It was later on proven that the exact E vs. N curve is a sequence of straight lines with a derivative discontinuity at the integers. The slope in the region (N0-‐1,N0) (N0 denoting the number of

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electrons for the neutral systems) is I ,the one in the region(N0,N0+1) is A.41 It is clearly seen that ! in definition (2) is the average of these slopes and ! , its difference. The pre-‐eminent hurdle on the path to determining ! and ! of noble gases then remains the calculation of the electron affinity due to the instability of the ground state anion. Several possibilities to circumvent the problems with unstable or temporary anions exist and were used in our group ranging from the use of an external wall potential42,to estimating A via the hardness and use of Koopman’s theorem43,44 and exploiting the stabilization by a polar solvent. 33

The latter option was chosen in the present work in view of its straightforward applicability to anions where the extra electron is in a highly diffuse orbital as is the case in the noble gases. In that case the diffuse cloud can be stabilised by placing the system in a solvent: the higher its dielectric constant, the larger the stabilisation effect. Puiatti et al. have shown that the electron affinity can then be obtained as,

A = lim !→! ! ! where ∆!

! !

! !

(3)

is the energy difference (anion-‐netural) for a given !. The electron affinity in

vacuum is thus associated to the ΔE value extrapolated to ! = 1. The electron affinities and ionisation potentials for all the nobles gases were calculated as a function of ! at the B3LYP45,46 level of theory using the computational chemistry package, Gaussian 09.47 The rather large atomic natural orbital-‐ relativistic correlation consistent (ANO-‐ RCC) basis set48,49 was employed for reasons that are twofold: first, an accurate description of electron affinities requires diffuse functions and second, for elements at the bottom of a group

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in the periodic table, relativistic effects become pronounced and cannot be ignored. The latter is implemented in G09 via a Douglas-‐Kroll-‐Hess 2nd order scalar relativistic calculation.50,51 For solvent effects, the IEFPCM methodology52 was adopted with ε varying from 78.39(water) to 1.43(Argon)( or 1 ! from 0.012 to 0.70 ) affording a fair extrapolation to ε=1 (1/ε=1.0). The list of solvents was the same as used by Puiatti et al., but the dielectric constants differ in the more recent version of G09 we have opted for. Once the corresponding A's were obtained, they were fitted via linear regression against the inverse of the dielectric constant and the absolute correlation coefficient was seen to be practically unity. In addition, to analyse the trends in the periodic table and to show the validity of this method to the noble gas atoms, the same procedure was applied to group VI and group VII atoms.

3. Results and Discussion To start with, the electron affinities of the noble gases were calculated using the ΔE vs (1/ε) extrapolation method with the series of solvents mentioned in § 2. In Figure 1 we give the plot for Krypton where an almost perfect linear relationship is found between ΔE and 1/ε ; it should be noticed that for highly polar solvents (ε>7.6) the ΔE values are positive, for lower ε they become negative leading to an extrapolated value of -‐1.76 eV. for ε=1. Note that the extrapolation can be done safely, the slopes for the regions with positive and negative ΔE’s being equal. This situation was also encountered by Puiatti et al.39 As rechecked by us, e.g. in the case of acetone, part of the ΔE vs (1/ε) curve has positive ΔE values until ε>2.5 , but then passes to negative values without changing slope , leading to a trustworthy extrapolation to ε=1 and an electron affinity of (-‐1.46 eV). A similar situation is found for Xenon, the 1/ ε value at which ΔE changes sign being 0.02 leading to an A value of -‐2.41 eV. For the

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lighter noble gases (Ne shown in fig. 2) the whole ΔE region for 1/ε varying between 0 and ∞ is now negative. The curve is perfectly linear so that on the basis of the Kr case we consider the extrapolation also in this type of cases to be adequate. In this way a A value of -‐4.88 eV. is obtained for Neon. In the case of Ionisation Energies, the same extrapolation scheme, tested for reasons of internal consistency, gave again perfect linear relationships with extrapolation results in perfect agreement with the gasphase energy difference between cation and neutral species. The gas phase values turn out to be in good agreement with experiment, the largest deviation being 0.9 eV for Radon.53 In order to scrutinize the reliability of these values we first recomputed the A values at a much higher level of theory, CCSD(T)54 with the same basis (ANORCC), among others as it is known that B3LYP sometimes leads to overbinding of the excess electron. 22 The results are included in Table 1, together with those for the Ionization Energy, all value being obtained in the ε à 1 extrapolation As can be seen the overall trend both for the Ionisation Energies and Electron Affinities is reproduced. It is particularly comforting and reassuring that the difficult-‐to-‐obtain Electron Affinities do not suffer from a dramatic overbinding effect at B3LYP level: all CCSD(T) values are more negative than their B3LYP counterparts, but the average deviation is only 0.19 eV, with no sequence being inverted. The consequence is that the μ and η values will also be close and without inverted sequence (vide infra). For the remaining of the discussion the more easily accessible B3LYP values will be used throughout. Concentrating again on the B3LYP values, the I and A values collected in Table 1 and Figures 3 and 4 firstly display the well-‐known decrease of the Ionisation Energy when going down in the Periodic Table. Combined with Tables 2 and 3 the increasing trend in I when passing in a given row from group 16 via 17 and 18 is retrieved. 4, 5, 6 The electron affinities are all negative, as 9



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expected, but show a regular, increasing trend starting from Ne, the value for He being an outlier (vide infra). Note that for Rn a value of about -‐1 eV. is obtained and that extrapolation of the curve to element 118(eka-‐Radon; Uuo) yields a value of about 0 eV; this finding is qualitative agreement with the high level relativistic calculations by Eliav et al.55, predicting Element 118 to be the first rare gas with an electron affinity, i.e. a positive A, the value being 0.056 eV with an error bound of 0.01 eV(the non-‐relativistic calculations led to a negative A value). Overall the A values show a much greater variability than those estimated by Bratsch and Lagowski be it that their sequence: (He:-‐0.5, Ne: -‐1.2, Ar: -‐1.0, Kr: -‐1.0, Xe: -‐0.8, Rn: -‐0.7) displays the same overall characteristics as our sequence. In Figure 5 an overview is given via the A vs (1/ε) curve which noble gases can be expected to have positive (or come close to having) A values for high dielectric constants (Rn, Xe, Kr). Note again the outlier behavior of He. Combining the I and A values into electronegativities, one obtains (Table 1, Figure 6) values between 11 and 5 eV when passing from He to Rn. In order to test the stability of the electron affinity values for extension of the basis set, which in case of negative A values, tend to discard the extra electron away from the atom, we carried out some test calculations with large basis sets (Ahlrich’s Def2-‐TZVP and Def2-‐QZVP bases56) combined in Helgaker’s two point formula with n=4 for approximating the Complete Basis Set Limit57. The results, at CCSD(T) level, are quite close to those in Table 1: for electronegativity: 10.66(He), 8.05 (Ne), 5.96 (Ar), 5.51 (Xe), 5.79 (Rn) and for hardness 13.53 (He), 13.13 (Ne), 9.44 (Ar), 6.64 (Xe) and 5.63 (Rn). (The results for Kr were absolute outliers probably to an unknown issue in the basis). Except for this spurious result the values show the correct order of magnitude and sequence. They illustrate that the tendency of a larger basis with more diffuse functions of destabilizing the anion, and giving “a way out” to the extra electron is still compensated by the continuum embedding. Combining the results with the stability upon increasing the level of theory (CCSD(T) vs DFT-‐B3LYP mentioned above) these observations

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justify the model we are adopting by extrapolating “embedded” values for A, even when they are negative, to the ε = 1 limit. The results are “stable” in order of magnitude and sequence giving trustworthiness to the chemistry derived from them. Returning now first to the discussion of the electronegativities and sticking to the original B3LYP values, Table 1 shows that the He case is again an outlier; for the other noble gases a range of 8.5-‐5.5 eV. is obtained, placing the noble gases lower than the halogens (10.5-‐7 eV) and slightly above the chalcogens. The comparison with Meek’s compilation and revision29 and Fung’s work13 shows two differences: the halogens show the highest electronegativity and a lower value for He than Ne is obtained. The comparison halogens-‐noble gases should be regarded in the context of the physical meaning/construction of the Mulliken electronegativity.16 It considers two situations that can occur when noble gas atoms become involved in a chemical bond and charge transfer occurs: electron loss which results in a sharp increase of the electronic energy due to its high I, and electron gain which also results in an increasing energy due to the large, negative affinity. The overall result is a lower electronegativity than the halogens. The uniform decrease starting from Ne on the other hand is present in all scales. Looking at eqn. (2) it is clear that the electronegativity values are dominated by I as is their trend; the negative A values however increase without changing their ordering and bring them finally about 2 eV lower than the corresponding halogens. These results are in qualitative agreement with Parr’s results obtained from Xα theory40, one of the forerunners of modern DFT and by Putz58 who used an alternative formulation in the framework of DFT. Indeed using Slater’s spin non-‐ polarized X transition state method59 Parr et al. obtained values which were all negative and showed the same trend as in Figure 5, the absolute values being situated between -‐1.63(Ne) and -‐1.08(Xe); the electronegativities show exactly the same trend as in Figure 6 and invariably lie lower than their halogen counterparts . The He position as outlier both in I and ! is reminiscent of the discussion on the position of H and He in the Periodic table which regained interest in

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recent years (see for example [60] for an excellent overview). Turning now to the hardness values the minus sign in front of A in eqn (2) results in extremely hard noble gases, way above the halogens. He and Ne are similar (~13.5 eV) (again counter-‐intuitive but in agreement with the aforementioned outlier position of He) and then a continuous decrease when going down the periodic table is observed, ending with a 7 eV value of Rn (cf.figure 7). These values are between 3(Rn) and 6(Ne) eV higher than the corresponding halogens, leading to the hardest “column” in the Periodic Table. Combined with the previous considerations about the interplay between I and A for ! and ! we come to the conclusion that, at first sight, noble gases would be ready to be involved in a covalent bond because of their moderately high electronegativity (comparable with the chalcogens). However due to their extreme chemical hardness only the slightest gain or loss of electrons results in a considerable destabilisation. This nicely corresponds to Pearson’s argument24 that the hardness of the atom X is in the definition(1) half of the energy change of the transmutation reaction: 2X à X+ + X-‐ again showing combined events of electron uptake and electron release. Comparing the moderate to high electronegativities with the extreme hardness of the noble gases we come to the conclusion that the chemistry of the noble gases is governed by their hardness. The fundamental difference between electronegativity and hardness is often formulated in a way that electronegativity measures the initial tendency of an atom to attract electrons (when involved in a bond) whereas the hardness measures the ability to accommodate the incoming charge, a property related to charge capacity.61 How to explain that bonding involving the heavy noble gases can be found with such boundary conditions for χ and η ? Looking at Xe, Figure 7 indicates that its hardness is comparable with that of Fluorine, the hardest atom except the light noble gases, but F has a higher electronegativity leading to Xe-‐F compunds in which the polarity can be expected to be Xeδ+F δ-‐ 12


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which also results for example from DFT calculations on XeF2 and XeF4 by Liao and Zhang62 with Mulliken charges of +1.00 and +2.00 for Xe and by a more in depth study by Haidukee et al. leading to a Bader QTAIM charge of 1.232 on Xe in XeF2.63 Both studies, different in basic methodology and in the charge analysis thus clearly yield a Xeδ+F δ-‐ polarity, favouring a scale with lower electronegativities for the noble gases as compared to the halogens. Our repetition of this exercise on XeF2 using the ANO-‐RCC basis set at B3LYP level, incorporating relativistic effects, yields a Bader Charge of + 1.18 on Xe. All this gives supplementary confidence in our scale as the electronegativity sequences in Meek’s compilation invariably put the noble gases on top of the halogens. A final comment on the particular issue of the negative A’s should be given. In the Conceptual DFT community there has been some debate concerning the use of negative A values in the evaluation of DFT reactivity descriptors such as electronegativity and hardness (for an extensive analysis by some of the present authors see. An alternative for negative A’s is to put them equal to zero; the in depth discussion in58 leads to an, albeit prudent conclusion, that eqn (2) with A as it comes out of any calculation is in favour. We nevertheless discuss the possibility that all negative A’s would be put equal to 0 in the present study. The electronegativities would be equal to the hardness and the ionisation potential, indicating that everything is determined by the Ionisation Energy only. Aspects of polarizability, inherently present in hardness31 do not come to the forefront for distinguishing ! and !. This description would be in our vision less balanced. On top of that it would be strange that elements which show the highest electronegativities would never be involved in a chemical bond. The polarity in the above mentioned XeF4 compound also contradicts his hypothesis. It should be noted that Allen touched upon a similar problem65,66 some years ago when discussing his electronegativity scale, based on average one-‐electron energy values of the valence shell 13



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electrons, with the noble gases at maximal value in a given row .For him this trend is a logical illustration that noble gases hold these electrons too tight to permit chemical bonding. He insists on the two sided character of their electronegativity: the high values for their role in holding electrons, zero values for attracting electrons. In the Mulliken language this means A=0, leading to very high ! values, higher than those of the halogens with the disadvantages discussed before. On the other hand higher values for holding electrons correspond to higher hardness. 4.Conclusions A systematic approach has been presented to evaluate the Electron Affinity, electronegativities and hardness of the group 18 elements; the fundamental problem of the instability of the anions is circumvented by Puiatti’s strategy to extrapolate the energy of high ε solvent stabilised anions to ε=1. Negative Electron Affinities were found for all noble gases, be it that an extrapolation of the series to eka-‐Radon leads to a value close to 0, possibly positive, in agreement with high level calculations in the literature. In combination with the Ionisation Energies, calculated along the same way, an internally consistent electronegativity scale has been presented on the basis of the Mulliken definition which (re)gained widespread interest in view of its natural appearance in Conceptual Density Functional Theory. The stability of the B3LYP results is succesfully tested both via improving the level of theory (CCSD(T)) and expanding the Basis Set. With respect to the halogens and the chalcogens, the noble gases display a high but not the highest electronegativities (the privilege of the halogens) comparable to the chalcogens, as opposed to nearly all results from attempting to extrapolate existing electronegativity scales to the noble gases, as compiled by Meek. The hardness scale, to the best of our knowledge, evaluated for the first time at high level, clearly shows that the noble gases are, by far, the hardest elements. The 14


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combination of high electronegativity and extremely high hardness is the key to understand the chemistry of the noble gases. Their position in the electronegativity sequence, below the halogens, offers a rationale to interpret the polarity of noble gas halogen or oxygen bonds. All in all the new scale gives an internally consistent conceptual DFT based picture of the “why” of the chemical inertness of noble gases (extremely high hardness) and the “when ” when it can be overruled(lower hardness values for the high Z-‐elements) and the polarity of the resulting noble gas –halogen or -‐ oxygen bonds. 5. Acknowledgements This work was conducted as part of the Erasmus Mundus Master in Theoretical Chemistry and Computational Modelling in the KU Leuven.and J.F. would like to thank Prof. Arnout Ceulemans (KUL) for the opportunity as well as for helpful discussions. The internship of JF at the VUB is highly appreciated as is the help of Dr. Balazs Pinter for insight and advice. P.G. and F.dP. thank the FWO, Flanders and the VUB for continuous support to their group, in particular the VUB for a Strategic Research Program conveyed to ALGC, started up at January 1, 2013. 15



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x Element

Ionisation Energy

Electron Affinity

Electronegativity

Hardness

Helium

24.94 (24.56)

-‐2.70 (-‐2.99)

11.12 (10.79)

13.82 (13.78)

Neon

21.69 (21.51)

-‐4.88 (-‐5.25)

8.41 (8.13)

13.29 (13.38)

Argon

15.77 (15.72)

-‐3.14 (-‐3.34)

6.31 (6.19)

9.45 (9.53)

Krypton

14.13 (14.14)

-‐2.41 (-‐2.59)

5.86 (5.78)

8.26 (8.37)

Xenon

12.44 (12.46)

-‐1.76 (-‐1.86)

5.34 (5.30)

7.10 (7.16)

Radon

11.74 (11.52)

-‐1.27 (-‐1.31)

5.23 (5.10)

6.50 (6.42)

Table 1 Ionisation energy, electron affinity, electronegativity and chemical hardness calculated at B3LYP/ANO-RCC level for group VIII elements. All values are in eV. (CCSD(T) values with the same basis set, and also obstained with ! à 1 Extrapolation Scheme are included for comparision.

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Element

Ionisation Energy

Electron Affinity

Electronegativity

Hardness

Oxygen

14.13

1.64

7.89

6.25

Sulphur

10.54

2.16

6.35

4.19

Selenium

9.82

2.12

5.97

3.86

Tellurium

8.92

2.11

5.52

3.41

Polonium

8.52

2.01

5.27

3.26

Table 2 Ionisation energy, electron affinity, electronegativity and chemical hardness calculated at B3LYP/ANO-RCC level for group VI elements. All values are in eV.

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Element

Ionisation Energy

Electron Affinity

Electronegativity

Hardness

Fluorine

17.71

3.50

10.61

7.10

Chlorine

13.04

3.64

8.34

4.70

Bromine

11.91

3.49

7.78

4.21

Iodine

10.65

3.30

6.97

3.68

Astatine

10.11

3.13

6.62

3.49

Table 3 Ionisation energy, electron affinity, electronegativity and chemical hardness calculated at B3LYP/ANO-RCC level for group VII elements. All values are in eV.

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Figure 1 The electron affinity of Krypton as calculated from equation (3) in different solvents plotted as a function of the inverse dielectric constant in eV at B3LYP/ANO-RCC.

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Figure 2 The electron affinity of Neon as calculated from equation (3) in different solvents plotted as a function of the inverse dielectric constant in eV at B3LYP/ANO-RCC.

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Figure 3 Ionisation Energies of groups VI,VII and VIII. All values are in eV

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Figure 4 Electron affinities of groups VI,VII and VIII. All values are in eV

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Figure 5 The electron affinity of the noble gases as calculated from equation (3) as a function of the inverse dielectric constant in eV

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Figure 6 Electronegativities of groups VI,VII and VIII. All values are in eV.

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Figure 7 Absolute hardness of groups VI,VII and VIII. All values are in eV

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TOC graphic

Estimates of the electronegativities and chemical hardness of the noble gas atoms are provided, based on computations of their ionization energy and (negative) electron affinity. The noble gas atoms show an important elektronegativity, be it less than the halogens, but they prove to be considerably harder than the corresponding halogens. The electron affinities of the noble gas in general become less negative when going down in the Periodic Table, which is illustrated in the graphic with the decreasing magnitude of the electron clouds in the anion.

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The Noble Gases: How Their Electronegativity and Hardness

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