The Noble Gases: How Their Electronegativity and Hardness

Feb 9, 2015 - ... Vrije Universiteit Brussel (Free University of Brussels-VUB), Pleinlaan 2, ... Combined with the ionization energies (in good agreem...
0 downloads 0 Views 2MB Size
Subscriber access provided by Columbia Univ Libraries

Article

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

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry A is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 32

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

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] *

 

1  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 2 of 32

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  

 

ACS Paragon Plus Environment

Page 3 of 32

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

The Journal of Physical Chemistry

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-­‐

3  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 4 of 32

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  

4  

 

ACS Paragon Plus Environment

Page 5 of 32

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

The Journal of Physical Chemistry

!

!

!

!

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  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 6 of 32

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  

6  

 

ACS Paragon Plus Environment

Page 7 of 32

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

The Journal of Physical Chemistry

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  

7  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 8 of 32

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  

8  

 

ACS Paragon Plus Environment

Page 9 of 32

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

The Journal of Physical Chemistry

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  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 10 of 32

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  

10  

 

ACS Paragon Plus Environment

Page 11 of 32

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

The Journal of Physical Chemistry

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  

11  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 12 of 32

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  

 

ACS Paragon Plus Environment

Page 13 of 32

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

The Journal of Physical Chemistry

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  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 14 of 32

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  

 

ACS Paragon Plus Environment

Page 15 of 32

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

The Journal of Physical Chemistry

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  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 16 of 32

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.    

 

16  

 

ACS Paragon Plus Environment

Page 17 of 32

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

The Journal of Physical Chemistry

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.  

17  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 18 of 32

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.  

         

18  

 

ACS Paragon Plus Environment

Page 19 of 32

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

The Journal of Physical Chemistry

  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.  

19  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 20 of 32

  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.  

20  

 

ACS Paragon Plus Environment

Page 21 of 32

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

The Journal of Physical Chemistry

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

21  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 22 of 32

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

 

22  

 

ACS Paragon Plus Environment

Page 23 of 32

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

The Journal of Physical Chemistry

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

23  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 24 of 32

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

24  

 

ACS Paragon Plus Environment

Page 25 of 32

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

The Journal of Physical Chemistry

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

 

 

25  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 26 of 32

References     1.   Christe,  K.  O.  Angew.  A  Renaissance  in  Noble  Gas  Chemistry.  Chem.  Int.  Ed.  2001,  40,   1419.     2.  

Bartlett,  N.  Xenon  Hexafluoroplatinate  (V)  Xe+    (PtF4)-­‐.  Proc.  Chem.  Soc.  1962,  218.  

  3.   Laszlo,  P.;  Schrobilgen,  G.  J.  One  or  Several  Pioneers?  The  Discovery  of  Noble-­‐Gas   Compounds.  Angew.  Chem.  Int  Ed.  1988,  27,  479-­‐489     4.   Huheey,  J.  E.;  Keiter,  E.  A.;  Keiter,  R.  L.  Inorganic  Chemistry:  Principles  of  Structure  and   Reactivity.  4th  ed.;  Harper  Collins  College:  New  York,  1993.     5.   Housecroft,  C.  E.;  SHarpe,  A.  G.  Inorganic  Chemistry,  2nd  ed.;  Pearson  Prentic  Hall:   England,  2005.     6.   Atkins,  P.;  Overton,  T.;  Rourke,  J.;  Weller,  M.;  Armstrong,  F.  Inorganic  Chemistry,  4th  ed.;   Oxford  University  Press:  Oxford,  2006.     7.     Pierrefixe,  S.C.H.A:  Poater,  J.;  Im.C.;  Bickelhaupt,  F.M.  Hypervalent  versus  Nonhypervalent   Carbons  in  Noble-­Gas  Complexes,  Chem.  Eur.J.,  2008,  14,  6901-­‐6911     8.   Pauling,  L.  The  Nature  of  the  Chemical  Bond,  3rd  ed.;  Cornell  University  Press:  Ithaca,   New  York,  1960.     9.   Frenking,  G.;  Shaik,  S.    Eds  The  Chemical  Bond:  Fundamental  Aspects  of  Chemical  Bonding,   Wiley:  New  York,  2014.     10.   De  Proft,  F.;  Ayers,  P.  W.;  Geerlings,  P.  The  Conceptual  DFT  Perspective  of  Bonding.  In   The  Chemical  Bond,  Fundamental  Aspects  of  Chemical  Bonding  Chapter  7;  Frenking,  G.,  Shaik,  S.,   Eds.;  Wiley:  New  York,  2014.     11.   Andersen,  T.  Atomic  Negative  Ions:  Structure,  Dynamics  and  Collisions  Phys.  Rep.  2004,   394,  157-­‐313    

26  

 

ACS Paragon Plus Environment

Page 27 of 32

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

The Journal of Physical Chemistry

12.   Bratsch,  S.  G.;  Lagowski,  J.  Predicted  Stabilities  of  Monatomic  Anions  in  Water  and  Liquid   Ammonia  at  298.15  K.  Polyhedron  1986,  5,  1763-­‐1770     13.  

Fung,  B.  The  Electronegativity  of  Noble  Gases.  J.  Phys.  Chem.  1965,  69,  596.  

  14.   Pauling,  L.  The  Nature  of  the  Chemical  Bond.  IV.  The  Energy  of  Single  Bonds  and  the   Relative  Electronegativity  of  Atoms.  J.  Am.  Chem.  Soc.  1932,  54,  3570-­‐3582     15.   Allred,  A.  L.    Electronegativity  Values  from  Thermochemical  Data.  J.  Inorg.  Nucl.  Chem.   1961,  17,  215-­‐221     16.   Mulliken,  R.S.;  Electronic  Structures  of  Polyatomic  Molecules  and  Valence.  V.  Molecules   RXn.    R.  S.  J.  Chem.  Phys.  1933,  1,  492-­‐503     17.  

Hohenberg,  P.;  Kohn,  W.  Inhomogeneous  Electron  Gas.  Phys.  Rev.  B  1964,  136,  864-­‐871  

  18.   Parr,  R.  G.;  Yang,  W.  Density  Functional  Theory  of  Atoms  and  Molecules;  Oxford  University   Press:  New  York,  1989.     19.  

Iczkowski,  R.  P.;  Margrave,  J.L  Electronegativity.  J.  Am.  Chem.  Soc.  1961,  83,  3547-­‐3551  

  20.   Parr,  R.  G.;  Donnelly,  R.  A.;  Levy,  M.  Palke,  W.  E.  Electronegativity:  The  Density  Functional   Viewpoint.  J.  Chem.  Phys.  1978,  68,  3801-­‐3807     21.   Simons,  J.;  Jordan,  K.  D.  Ab  initio  Electronic  Structure  of  Anions.  Chem.  Rev.  1987,  87,   535-­‐555     22.   Jordan,  K.  D.;  Voora,  V.  K.;  Simons,  J.  Negative  Electron  Affinities  from  Conventional   Electronic  Structure  Methods  Theor.  Chem.  Acc.  2014,  133,  1-­‐15.     23.   Parr,  R.  G.;  Pearson,  R.  G.  Absolute  Hardness:  Companion  Parameter  to  Absolute   Electronegativity    J.  Am.  Chem.  Soc.  1983,  105,  7512-­‐7516     24.  

Pearson,  R.  G.  Chemical  Hardness;  Wiley:  Weinheim,  1997.  

  27  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 28 of 32

25.   Allen,  L.  C.;  Huheey,  J.  C.    The  Definition  of  Electronegativity  and  the  Chemistry  of  the   Noble  Gases    J.  Inorg.  Nucl.  Chem.  1980,  42,  1523-­‐1524.     26.   Allred,  A.  L.;  Rochow,  E.  G.  A  Scale  of  Electronegativity  based  on  Electrostatic  Force  J.   Inorg.  Nucl.  Chem.  1958,  5,  264-­‐268     27.   Sanderson,  An  Interpretation  of  Bond  Lengths  and  a  Classification  of  Bonds  R.  T.  Science   1951,  114,  670-­‐672     28.   Sanderson,  R.  T.    Principles  of  Electronegativity  Part  I.  General  Nature    J.  Chem.  Ed.  1988,   65,  112-­‐118     29.  

Meek,  T.  L.  Electronegativities  of  the  Noble  Gases  J.  Chem.  Ed.  1995,  72,  17-­‐18  

  30.     Parr,  R.  G.;  Yang,  W.  Density-­‐Functional  Theory  of  the  Electronic  Structure  of  Molecules     Ann.  Rev.  Phys.  Chem.  1995,  56,  701-­‐728     31.       Geerlings,  P;  De  Proft  F.;  Langenaeker  W.,  Conceptual  Density  Functional  Theory   Chem.Rev.2003,  103,  1793-­‐1873     32.     Chermette,  H.Chemical  Reactivity  Indexes  in  Density  Functional  Theory    J.  Comput.  Chem.   1999,  20,  129-­‐154   33.     De  Proft,  F.;  Geerlings,  P.  Conceptual  and  Computational  DFT  in  the  Study  of  Aromaticity   Chem  Rev.  2001,  101,  1451-­‐1464     34.   Ayers,  P.  W.;  Anderson,  J.  S.  M.;  Bartolotti,  L.  J.  Perturbative  Perspectives  on  the  Chemical   Reaction  Prediction  Problem  Int.  J.  Quant.  Chem.  2005,  101,  520-­‐534     35.   Gazquez,  J.  L.  Perspectives  on  the  Density  Functional  Theory  of  Chemical  Reactivity  J.   Mex.  Chem.  Soc.  2008,  52,  3-­‐10     36.   Liu,  S.  B.  Conceptual  Density  Functional  Theory  and  some  Recent  Developments  Acta   Phys.  -­Chim.  Sin.  2009,  25,  590-­‐600     37.   Geerlings,  P.;  De  Proft,  F.  Conceptual  DFT:  the  Chemical  Relevance  of  Higher  Response   Functions  Phys.  Chem.  Chem.  Phys.  2008,  10,  3028-­‐3042   28  

 

ACS Paragon Plus Environment

Page 29 of 32

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

The Journal of Physical Chemistry

  38.   Giju,  K.  T.;  De  Proft,  F.;  Geerlings,  P.  Comprehensive  Study  of  Density  functional  Theory   Based  Properties  for  Group  14  Atoms  and  Functional  Groups,  −XY  3  (X  =  C,  Si,  Ge,  Sn,  Pb,   Element  114;  Y  =  CH  3  ,  H,  F,  Cl,  Br,  I,  At)    J.  Phys  Chem.  A  2005,  109,  2925-­‐2936     39.   Puiatti,  M.;  Mariano,  D.;  Vera,  A.;  Pierini,  B.  In  Search  for  an  Optimal  Methodology  to   Calculate  the  Valence  Electron  Affinities  of  Temporary  Anions     Phys.  Chem.  Chem.  Phys.  2009,  11,  9013-­‐9024     40.   Bartolotti,  L.  J.;  Gadre,  S.  R.;  Parr,  R.  G.  Electronegativities  of  the  Elements  from  Simple  Xα   Theory    J.  Am.  Chem.  Soc.  1980,  102,  2945-­‐2948     41.   Perdew,  J.  P.;  Parr,  R.  G.;  Levy,  M.;  Balduz,  J.  L.  Density-­‐Functional  Theory  for  Fractional   Particle  Number:  Derivative  Discontinuities  of  the  Energy  Phys.  Rev.  Lett  1982,  49,  1691-­‐1694     42.   Sablon,  N.;  De  Proft,  F.;  Geerlings,  P.;  Tozer,  D.  J.  On  the  Position  of  the  Potential  Wall  in   DFT  Temporary  Anion  Calculations  Phys.  Chem.  Chem.  Phys.  2007,  9,  5880-­‐5884     43.   Tozer,  D.  J.;  De  Proft  ,  F.  Computation  of  the  Hardness  and  the  Problem  of  Negative   Electron  Affinities  in  Density  Functional  Theory    J.  Phys.  Chem.  A  2005,  109,  8923-­‐8929     44.   De  Proft,  F.;  Sablon,  N.;  Tozer,  J.  D.;  Geerlings,  P.  Calculation  of  Negative  Electron  Affinity   and  Aqueous  Anion  Hardness  using  Kohn  Sham  HOMO  and  LUMO  Energies  Farad.  Discussions   2007,  135,  151-­‐159     45.   Becke,  A.  D.  Density-­‐functional  Exchange-­‐Energy  Approximation  with  Correct   Asymptotic  Behavior  Phys.  Rev.  A  1988,  38,  3098-­‐3100     46.   Lee,  C.;  Yang,  W.;  Parr,  R.  G.  Development  of  the  Colle-­‐Salvetti  Correlation-­‐Energy   Formula  into  a  Functional  of  the  Electron  Density    Phys.  Rev.  B  1988,  37,  785-­‐789     47.   Gaussian  09,  Revision  D.01,  Frisch,  M.  J.;  Trucks,  G.  W.;  Schlegel,  H.  B.;  Scuseria,  G.  E.;   Robb,  M.  A.;  Cheeseman,  J.  R.;  Scalmani,  G.;  Barone,  V.;  Mennucci,  B.;  Petersson,  G.  A.;  et  al.   Gaussian,  Inc.,  Wallingford  CT,  2009.     48.   Widmark,  P.  O.;  Persson,  B.  J.;  Roos,  B.  Density  Matrix  Averaged  Atomic  Natural  Orbital   (ANO)  Basis  Sets  for  Correlated  Molecular  Wave  Functions  Theor.  Chim.  Acta  1991,  79,  419-­‐432   29  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 30 of 32

  49.   Roos,  B.  O.;  Lindh,  R.;  Malmqvist,  P.;  Veryazov,  V.;  Widmark,  P.  O.  Main  Group  Atoms  and   Dimers  Studied  with  a  New  Relativistic  ANO  Basis  Set    J.  Phys.  Chem.  A  2004,  108,  2851-­‐2858     50.   Douglas,  M.;  Kroll,  N.  M.  Quantum  Electrodynamical  Corrections  to  the  Fine  Structure  of   Helium    Ann.  Phys.  1974,  82,  89-­‐155.     51.   Jansen,  G.;  Hess,  B.  A.  Revision  of  the  Douglas-­‐Kroll  Transformation    Phys.  Rev.  A  1989,   39,  6016-­‐6017     52.   Cancés,  E.;  Menuucci,  B.;  Tomasi,  J.  A  New  Integral  Equation  Formalism  for  the   Polarizable  Continuum  Model:  Theoretical  Background  and  Applications  to  Isotropic  and   Anisotropic  Dielectrics    J.  Chem.  Phys.  1997,  107,  3032-­‐3041     53.  

Lide,  D.  R.  CRC  Handbook  of  Chemistry  and  Physics,  62nd  ed.;  Boca  Raton,  1981.  

  54.     Ragavachari,  K;  Trucks,  G.W.;  Pople,  J.A.;  Head-­‐Gordon,  M,  A  Fifth  Order  Perturbation   Comparison  of  Electron  Correlation  Theories,  Chem.Phys.Lett.,  1989,  157,  479-­‐483     55.   Eliav,  E.;  Kaldor,  U.;  Ishikawa,  Y.;  Pyykko,  P.  Element  118:  The  First  Rare  Gas  with  an   Electron  Affinity  Phys.  Rev.  Lett.  1996,  77,  5350-­‐5352     56.   Weigend,  F;  Ahlrichs,  R.,  Balanced  Sets  of  Split  Value  Triple  Zeta  Valence  and  Quadruple   Zeta  Valence  Quality  for  H  to  Ru;  Phys.  Chem.  Chem.  Phys.  2005,  3297,  305-­‐330     57.  Halkier,  A.;  Helgaker,  T.;  Jorgensen,  P.;  Klopper,  W.;  Koch,  H.;  Olsen,  J.;  Wilson,  A.K.;  Basis  Set   Convengence  in  Correlated  Calculations  on  Ne,  N2  and  H2O,  Chem.Phys.  Lett.,  1998,  286,  243-­‐ 252     58.   Putz,  M.  V.;  Russo,  N.;  Sicilia,  E.  About  the  Mulliken  electronegativity  in  DFT    Theor.  Chem.   Acc.  2005,  114,  38-­‐45     59.   Slater,  J.  C.  The  Self  Consistent  Field  for  Molecules  and  Solid;  McGraw  Hill:  New  York,   1974.,  38-­‐45    

30  

 

ACS Paragon Plus Environment

Page 31 of 32

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

The Journal of Physical Chemistry

60.   Scerri,  E.R,  The  Periodic  Table:  its  Story  and  Significance,  Oxford  University  Press,  Oxford,   2007,  p280  and  references  therein     61.  Politzer,  P.;  Huheey,  J.  E.;  Murray,  J.  S.;  Grodzicki,  M.  Electronegativity  and  the  Concept  of   Charge  Capacity    J.  Mol.  Struct.  1992,  259,  99-­‐120     62.   Liao,  M.  S.;  Zhang,  Q.  E.  Chemical  Bonding  in  XeF2  ,  XeF4  ,  KrF2  ,  KrF4  ,  RnF2  ,  XeCl2  ,  and   XeBr2  :  From  the  Gas  Phase  to  the  Solid  State    J.  Phys.  Chem.  A  1998,  102,  10647-­‐10654     63.   Haiduke,  R.  L.  A.;  Filho,  H.  D.  P.  L.  M.;  da  Silva,  A.  B.  F.  A  Theoretical  Study  on  the  XeF2   Molecule  Chem.  Phys.,  2008,  348,  89-­‐96     64.   Cardenas,  C.;  Ayers,  P.;  De  Proft,  F.;  Tozer,  D.  J.;  Geerlings,  P.  Should  Negative  Electron   Affinities  be  used  for  Evaluating  the  Chemical  Hardness?    Phys.  Chem.  Chem.  Phys.  2011,  13,   2285-­‐2293     65.           Allen,  L.  C.  Electronegativity  is  the  Average  One-­‐Electron  Energy  of  the  Valence-­‐Shell   Electrons  in  Ground-­‐State  Free  Atoms    J.  Am.  Chem.  Soc.  1989,  111,  9003-­‐9014     66.  Murphy,  L.R.,  Meek,  T.L;  Allred,  A.L.;  Allen,  L.C.  Evaluation  and  Test  of  Pauling's   Electronegativity  Scale    J  Phys  Chem  A.  2000,  104,  5867-­‐5871      

 

 

 

     

 

31  

 

ACS Paragon Plus Environment

The Journal of Physical Chemistry

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

Page 32 of 32

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.    

32  

 

ACS Paragon Plus Environment