- Email: [email protected]
Thermochemical interpretation of ESCA chemical shifts using semi-empirical molecular orbital methods
.. Volume 13;number
4
CHEMI?.AL PHYSICS LEl-i-ERS
:‘
15 ‘hIarch
...
1671
:
.:
THERMOCHEMICAL INTERPRETATlON .OF‘ ESCA CHEMICAL SHIFTS USING SEMI-EMPIRICAL MOLiXULAR ORBITAi METHODS .D.C. FROiT, F.G. HERRING, C.A. MkO&LL
.-
and KS:WOOi..SEY
Deparrmenr of Chemistry, University-of Bri@t Columbia.. Vancouver S. &Wit Columbia, Canada Received
11 January
1972
The ESCA chemical shifts of carbon and nitrogen in a variety of chemical ekironments have been calculated from the energy difference (aE) between the pgent molecule and the isoelectronic nitrogen and oxygen containiiv&
Lotions using the hIINDO/I valence electron SCF MO method. For the case of carbon, a good correlation is obtained bchveen ti shifts are about one-third of rhe experimental values. The nitrogen experimental dats arc available to test the method in this case. The reasons
for this and the usefulness
of the approach
X-ray photoelectron spectroscopy is rapidly developing as a usefui technique for studying molecular electronic
structure
are discusxd.
photoelectron of eq. (1) h as zero kinetic energy, thus the core binding energy may be expressed as the energy difference between the molecule and the
[ 1, 21, and-as a means of testing
ab-initio molecular wavefunctions [3,4]. Several different approaches have been used to interpret the observed changes in core electron binding energies of particular atoms in different chemical environments, the $0 called ESCA chemical shift. These vary widely in their, degree of sophistication, from simple correla-
molecular ion. Jolly’s approach ass~~ncs that cores which have the i&me charge are chemically equivalent?, so that the M*’ icn may be represented by the ion of the element one higher in the periodic table than the atom involved in core ionisation. Thus, for example, the CHiC ion is represented by the NH: ion. In this case, how- _ ever, the ion will be-in its ground electronic state. Whilst the total electionic energy of these two species is not identical, the method-assumes that the e,nergy ofsubstitution,of equivalent cores is con&a& for all compounds of the element concerned. Thus the energy of.substitutidn of-the core Css+ by N5+ is assumed constant for carbon in all chemical environmr”nts. Hence the energy changes.of the following p&&es
tions’with the charge on the atom involved [3, 5,6], to direct calculation of the core electron binding ener-
.gies [3,4]. Recently, Jolly proposed an interesting method for estimating ESCA shifts using thermo-. dynamic data [7,8], and it is this method with which -we are concerned in the present communication. -.The core electron binding energy of a gaseous molecule M is the energy of the process
M-bM*+te,
and the chemical shift, although the calculated. shifts rhow better ‘absolute rgreement. but fewer
(1)
.’
are the saine;
wherp,‘* indicates that the sp&ies is an ion in which a dore,‘electron is_missing, and is not an ion in its ground electronic.gtate. The M*+ ion is, however, a species in wfiic’h &tronic relaxatidn has occurred-14, 91 , that is the .r&aining~.electrons of tee ion c&e adjusted
:.
&~tr~ni&y-to
ihe$crez&ed effective core:c@rge of :.th$ a:@* inyplveclin cork [email protected] ,.- ,. ,.; '. ,.
--::,; ... .:. _ .'_- .: :
:. . . :; :
I_ .y-
:-
;.
: :_,.., .. ,. :
._ '.
-_
T’By .core, tie mean.lhe -,.... ~.&ons. .
'. .._ _:
: .-
.. ;:
.:,
‘..
..,. :
.-
nucleus
an! ,jhs.remaining
'; '.._ : .1_ fr _,;._.,. .;: y_:,.l,_,_, __: --..: .Li ._. ;_ -:. ._. .; .. ,. :.I .-
.: ..'. ..-. -. ., : .. '. _;,_,'._ .I i. ~ '.,_ ..
,“;' 1.. .
:'.':. ':. -._ ,, ., .._ ._ .-',.' :
.
~. ,: ,~
c&eelec-
,. :
.. :.~,;":_~~:,~.;::~: .-,.
.; .,: &,' ', ~
:; .,
method
‘,~~‘$q%&~&Al j;ch.“transmut~tion“‘equations.
the dif‘f~.rc$ce in’&ergy of:the_ species .CHz+/NHqf and .. .CO,t[NOi @d:all ether is&electronic ion pairs should be.ih&lsatie..lhus
i&4i6tild.b& possidle
to expiess
the
&erg? of,&e @roce& in cq_ (I.) as the difference in ‘. -.tqta!-electronlc_cnergy.of the.parerit mo&le (M). .&tiie isoelectronic ion .of the element one higher iri ..thb p&riodic.table.(AE), plus the constant energy AcE : &r&smut&on
of M*.?. This of cou;se:is
.:..bicd&ge.nergy
ttierefore :~ .. BE.=AM;.
(BE),of the core electron, be.e%pressed as follows,’ ..
just the
which may
[T, lo] ,.and.a.meth&based
(4)
on the bond dissoci-
ation enerkes
of the Species obtained from electronegativity arguments [8] ; and correlated them with ‘the obseeed.ESCA shifts. Remarkably good agreement beiweenobserved atid calculated shifts was obtained :ii spite 0; ehe.relatiwely crude me*hods used for estimating k+: Tb test the method further, we have .used.i setii-empirical m&le&!ar orbital method for evaluating the energy differences (AfZ) between.the tidlectile and-isoelectronic ion of the element one hi&e.r in the peiiodictable. We have chosen to use Dewar’s MlNDO/l method [I I, i2] ,-since this.is -known tci give quite accvrate heats of formation for a variety of carbon, nitrogen and oxygen contai.ning compounds, in.tiost cases-accurate to within .2.5 kballmole (0.2 eV)ij-. This compares very favouryably with the a&age deviation between the caiculated anh’expeiim&tal values for A.& of k3 1 kcal/mole (I-!? +) fo,u?d by Jolly [8] , although it-must be ad‘rr+ted,..that:the exp&i.metital values &ay be unreliable .in‘s’ome cases.: Since ESCA shifts are usually measured :with an ac&&y.of,around iO.1 kV_at present, a?y i&pr&ement -in th8 &cur~cy of AE of this magnitude ‘ishighly &&able. Ai_yet; h&ever, the MIN.DO/I -.. -... ;_ .. I : t lkpe~i~e~&.val&
ITI& oft&
data
has bee.n gathered
fro_n~ .carbon
be rather inaccuiate.For
and nitrogen
containing compounds [ 1, 2, 5,6, 10, 131, and at the moment we are largely concerned with establishing .the validity of the approach. IV&have therefore simply calcu!ated the total electronic energy of the ground state molecule and isoelectronic ion of the element of one higher atomic .number within the MlNDO/l approximation scheme, and correlated the energy difference with the experimentally
.’
‘T’o‘test these a’guments, Jolly evaluated the energy $ffe&nces At? fqr molkcule/ion pairs such as CH&Hz, C02!“z etc., using both experimental -dais
tested in the case of ‘-mole&lar ions, and has.so &r only be& parameterised for H, C;N and O.atoms..:The latter is not too.problematic, howevei; since much of the presently available ESCA
has not been’thoroughly
shift of the 1s care electrons reference molecule. Tks method of evaluating 4E has the advantage method
ESCA
to some suitable
the ener,T
differences
over the bond dissociation
used by Jolly
bitrary assumptions
determined
relative
[S] in that.there
are no ar-.
involved, such as the dissociation
of ions so that the bonding electrons are shared equally by the atoms involved, or that covalent contributions to the bond energies are the same for molecule and.isoelectronic ion. The calculations w&re.carried out using the same geometry for the molecule and iscelectronic ion, and *is is necessary.since the lifetimes of core electron vacancies are expected to be short compared with vibrational relaxation times. Experimental thermod$namic data will of course correspond to the ion with a different geometry to. that of tlie molecule. Table I ljsts the calculated ESCA chemical shifts for .carbon and nitrogen in a variety of chemical environments evaluated in this manner, together with the experimental values. The experimental data were taken from refs. [2, 5, 10, lb], and for the presknt we have restricted ourselves to the gas phase. (Only urea..and ethylamine are solid state measurements.) Iye have d&e this iargely 30 avoid the effects of s.ample charging which occurs inthe solid state; and which may . lead to er&eous chemical shifts; atid because ESCA shifts &f ionic species iri the solid state- depend dn the lattice potentials which may not be kn&vnvej ac;-. curately. jt sho,uldIbe pointed out, howevkr, that this approach &in no way_estricted $I gaseous species, or indeed the ESCA.sp&ztrti of neutral mole&,& as has.already..-: been’indic&d by Jdlly [7]. i :: .,
Volume 13, number ;?
Experimental
-. .-Table-l’ I and calculated ESCA shifts for carbon and nizogen in gas phase
.Slolecule :
i. c*o 2_c*oz *CHzCH, *CHjC02 H CHjC*Q2H
‘CHJCH3 7. +CHd
calculated
‘. experimc&l
1.58 2.33 -0.78 0:45 1.38
5.2 6.8 -0.1 0.7 4.7
-0.14
LO.2
0 (dcf) al -1.38
8. *CHCH 9. *CHzO
10. *CHSOH 11. *CH$IHO 12. CH+Z*HO 13. *CH&H2NH2 14.0C*(NH1)7 15. HC’02H 16. (CH&C*O 17. (*CH&CO 18. .19. 20. 21. 32. 23. 24. .25. 26. 27. 28.
8
ESCA shift a) (in cV)
No
3. 4. .5. 6;
CHEMICAL PHYSICS LmERS . . . ..
0 (de0 n) 0.4
1.18 0.56
3.3 1.6
0.21 0.82 -0.53 1.38 1.56 1.23 -0.05
0.6 3.2 0.0 3.9 5.0 3.1 0.5
0 (det] a) -3.56 -2.66 0.04 1.27 -0.19 -4.00 -3.56 -4.18 1.11 1.72
N; CH3N*H2 *NH3 *NNO NN *0 HCN* (CH&N*H *NH2NH7 (CH&N’ *NO. *NOi
..
2
kre
5
6
7.
.‘a
versus calculated ESCA shiit for carbon. Nutiberirlg of points as given in table 1. The c&es and dotted lint refer to the corrected values of AE (set test).
0 (dell ai -4.8 -4.3 -1.3 2.6 -3.1 -5.0 -3.8 -5.2 0.4 2.5
also used for the isoelectronic
4
Fig. 1. Plot of experimental
a) Shifts for carbon are relative to methane, those for nitrogen to molecular nitrogen. * Denotes atom involved in core ioniution. The geometries of tie molecules studied were taken from ref. [ 2 I 1. The same. geometries
3
ions.
remarkably good straight line. Only acetylene falls significantly far from the line; and this may be accounted for by the known inadequacy of the I&NDO/l method iri predicting heats of formation of acetylenic compounds [ 1 l] _ Unforrunately the absolute agreeand-Cal&dated shifts rnent between the experimental is poor, the slope of the line of fig. 1 beirig 2.9 instead of unity as found by Jolly [i, 81; and as required by eq. (4). This discrepancy is readily explained however. @th.&& ttie .MINDO/I tiethod.givek accurate heats -. of formation of the.molecule, it has n9t beeh-properly-. ,. t@ted f&~mokctilfii [email protected] most di the cask c15ri- j .:
sidered here, the isoelectronic nitrogen molecular ion is unknown, so that no experimental data are available to test the accuracy of the heats of formation-of.the ions. Fortunately experimental data are available for three of the ions considered; namely, NH:, N$ and .: NO+. Comparison of the calculated heats of formation of these ions with the experimental values given in the literature [ 1.5, 161 shows the calculated values to be incorrec!. That of the NH: ion is 64.2 kcal tdo high, NO+ 20.8 kcal too high, and NO; 5 I .4-kcal too low. Correcting the calculated v&es of AE for the differences between the calculated and experimental v&es for the heats of formation of the molecule.and-isoelectronic ion in these three cases gives the new points indicated by the crosses in fig. 1. The dotted line drawn thiough them has a slope of unity; Although we can-. not .do likewise for the remainder of the points oti the ‘cor&.lation diagram, in view of the very accuiate re- ._ production-of the trend bf.the expetientgl E&A shifts,.we see no.reason-to suppose that the incorrect -’ sIope.is not due simply to the .failure’-of the.MINDb/ 1 -. ‘. method to give accurate heat&f fdimation for the.,. molecular ions. Sic& we do obtain an accura’telinear coGelation from 6ur c&dations, and the corrected tiaiues’of: A& wheie availqble do-give .a direci co&e- I ., ip&den&betwe&dE atid the:ESCA shift’as’in,: ,., ; :--.
CHEMICAL PHYSICS LETTERS
.,, ,So far relatively
(c.V)‘.. .: . .
ftiw ESCA tieastiremkts
have
..i.!:
been made of nitrogen Is binding eneigies in the ga& ‘I;.$ -phase. However, a few such measurements have be& ?: made, and. fig. 2 shows the correktion between their .‘j
...
..: t
‘.
.,,,
,..ShifL
I-..
:, !
: Es.@e &&al ‘.
15 March. 1972”::
.
:. . ...’
experimental ESCA shifts and‘those calculated from : i the difference in total energy of the molecule and iso-,,‘. electronic oxygen substitured cation. The correlation ‘ii is poorer in this ca&, and with only a few points on .:i.!
.‘.
1,‘; the graph it-is not obvious what line constitutes the .-; best fit to them. We have therefore chasen in this. case to draw in a line of unit slope. This fits the points‘.j
.. .’
,< moderately well. However, the fit can be improved :. considerably by correcting the calculated values for the true heats of formation of the molecule and mole&l ‘.:j uiar ion where available (~CN~~COi, N~~NO~~ NNO/NOSand NO’@:). These are indicated by the :’ : crosses in fig. 2. It may also be noted that the cal.:‘. culated heats of formation of N20 and NOi, two Cal&fared
mqlecular ions of the element ond higher in atomic nuniber. Also, since in general &e heats of formation of the.ground state m&e&les.are fairly accurately re-
,: points which deviate significantly froni the line, are. : considerably different from the experimentally ob-.. served vaIues (82.9 kcal too low for N20, and 84.0 kcal too low for NO,). The MINDOI 1 method gives quite good heats of formation for amines, heterg-1, aromatics and various alkyl.nitrites and nitrates, however f 12, 191, thus molecules such as HCN, N,O and ’ .-j NO, are not entirely typical of the accuracy o?: the method. Unfortunately, few other gas phase measure-- :. ments are available for nitrogen. However, the present ,-_ results,support those of’.Jolly et al. [IO], and indicate $ :I the method should be applicable to all first row ele: ments. 1: The conclusion ‘that an-expression of the type
.,.produced-by the MrNDO/l method, the calculated ions must vary “heats of formation of the isoelectronic ., in a,tiiQf?rti manner for the.linear correlation of. fig. 1 :.’tti o&r.-Thertis gdod reason fo suppose; therefore, ihat ~h~.~~~ND~~~;~ethod could be-modifjed to re-, 1 produce rhe he,@s. of formation of both mdetules and-
given in eq. (4) can be used for core election binding -‘? energieS throws light’on several interesting aspects qf ‘.‘: the na,ture of the core electron ionisation process, and. l suggests further use@1 applications of the ESCA tech- ;. nique: Since in the present calculations we-deal only. .:i wi~,electronic relaxation of the valence, &ctrons on .“I:
i&s si&ditaneously. The error iri the c&e of the ions ‘. would appear tt, be due to.the use of one centre int& ,’
-.:I core ionisation, the fact that a direct corrkspondknce ~~1 exists between. ihhe ESCA-shift and AE indicates that relaxation of the.iemai$ng iore elk’ctrcin must be con-:{: stant or ‘at !&ast very n&t&so;for first row elements -C. iegardless of chemical environment, This view is sup: :.!::i ii.: ported by recent calculations.by S@der who has given, a constant value.of -I 2 ;V for core electron .’ :‘.$jj relaGti’qn of all first’ row +m&t.s ,[ CS] . This iS also, .;?j in accdrd with the ‘Go& oE Schwartz [4] ,‘who indicat$$ that ;a.~nce.shell-ieorganisrttion is 5y:,far,ihe:_Go& -;:::‘+--” ... .. :.. ,
Shift fe.V) -d
-3
-2
-,
0
I
2
3
Fig. 2. Pkt of experimental versus calculated ESCA shifr.for -nitroSen. Numbering of points as given in table 1. The crosses
rrfer to rhc corrected $&ICS of AI5 (see test). .
‘Jolly’s case, & believe that the ESCA shift can be predicted
with gobd precision
from the energy
dif-
ference between pairs of molecules ‘and isoelectronic
: grals inappropriate ,.
to ionii: species; since we do not .. ..
::‘obseFe any dependentie’of the plbt in fig:1 on the - type_&f bonding’involv”“::Mqdification of the lhnlrNpO/i. n~et~od.~sing.a-~a~i~~l~ electronegativity::-proc~dure-forthe.one centre‘ iAtegrals,similar t&,,that,
Volume 13. number
4
important contiibutor to the ESCA cheinical shift, and that a highly accurate core description is not necessary for evaluating shifts. Indeed, in bur cati, the description of the core is the sitiplest possible’. Clearly therefore calculations such as these which do not expticitly treat core electrons can be very useful in understanding ESCA shifts. The procedure adopted here may in fact be considered as the semi~mpirical analogue of using ab-initio calculations to give the core binding energy’ from the energy difference between the molecule @I) and the core ionised ion (bl**) [4j . Cfearly this relationship between core binding energy shifts and the thermodynamic properties of the parent molecule and isoelectronic molecular ion should be useful for evaluating heats of formation of the species concerned from ESCA measurements. For example, ESCA studies of halogen compounds might be usefuUy employed to predict the stabilities of isoelectronic rare gas compounds. Aiso, &CA studies could. possibly be used to evaluate lattice energies and other solid state thermodynamic energies using this relationship. As noted earlier it should be.possible to use the correlation between ESCA shifts and A& to calibrate MIND0 type calculations to give the heats of formation of ionic species. This would be particularly useful in organic chemistry for the ~eoretical study of reaction mechanisms involving charged species e.g. carbonium ions. Finally, since the underlying reasons for the success of this approach are essentially the same as those of the mettiad involving calculation of the change in potential at the core due to the valence electrons [20], we see no reaspn why the present approach should not be applicable to elements beyond the &st row of the periodic table, as is the case for the potential mbdel. Oni of us (I.S.W.)
thanks
the.University
of British
support of a post-doctoral fellowship. We also thank the National Research .; CotinciI of Canada for’~nan~i~ support.
~,‘Columbia
15 March 1972
CHEMICAL PHYSICS ILEJXERS
for the financial
.’
..,
‘.
References
..
[I] K.Siegbahn.
C.Nordling. A.Fahlmart, R.Nordberg. K. Hamrin, J_H~dm~n, GJohansson, T.Bergmark, S.-E_ .. f&.&son, I.Ljndgr& and D.Lindberg. EXA-Atomic. molecular and solid state structure studied by means of electron spectroscopy (Almquist and Wiksells, Uppsala, ‘19671. [2] KSiegbahn, kordling, G.Johansson, J.Hedma& P.F. He&n, K.Hamrin, U.Gelius, T.Bergmark;, L.O.Wetme, R.h~anne and Y.Baer. ESCA applied to free molecules,’ ‘, (North-Holland.
Amsterdam,
1969).
(31 H Basch and L.C.Snyder. Chem. Phys. Letters 3 (1969) 333. [41 ~f.E.Schwnr&.Chrm. Phys. Letters 5 (197Oj 50. [ 51 U.Celius. P.F.Hcd&, J.Hedman, BILinderberg. R. Manne, R.N&dberg, C.NordIinp and K.Sicgbahn. Physica Script3 2 (1970) 70. [6] D.N.Hendric+n, JMHollandcr and W.L.Jolly. Inorg. Chem. 8 (1969) 2642. [71 W.LJolly and D.N.Hendrickson. J. Am. Chem. Sot. 92:. (LS70) lE6,: [8] W.L.JoBy, J. Am. Chem. Sot. 92(1970) 3260. -. I91 I.H.Hillier. V.R.Saunderi and hl.H.Wood. Chem. Phys. Letters 7 (1970) 323. [ 101 P.Finn, R.K.Pearson, J.hi.Holiander and W.L.Jolly. Inorg. Chem. 10 (1971) 378. (111 N.C.Baird and M.J.S.Dewar. J. Chem. Phys. 50 (1969) 1262. [I21 N.C.Eaird. XC.J.S.De&x and R.Sustmann, J. Chcm. Phys. 50 (1969) lf75. R.G.Aibridge, T’.Bergmark, U.Ericson, J. (L31 R.Nordberg, Hedman. CNordIing. K.Sicgbahn and B J.Lindbe:g, .’ Arkiv Kemi 28 (1968) ‘257. D.A.Shirley sod T.D.Thomas. [141 D.W.Davis, J.hf.Hollander, J..Chem. Phys. 52 (1970) 3295. Some thermodynamic aspects of inorganic 1151 D.A Johnson, chemistry (Cambridge Univ. Press, London, 1968). [I61 CI.F.Cordcs and N.R’.FBttcr. J. Phys. Chem. 62 (1958) 1340. ff71 R.D.Brown and ~t.L.He~fern~n., Australian J. Chem. 12 (1959) 319. L.C.Snyder, J. Chem:Phys. 55 (1971) 95. ” [IsI ” [I9? M.J.Dewar, ~f.Sbansb~ and S.D.WorIey, J. Am. Chem. Sot. 9 I( 1969) 3590.. Phys. Let&6 (1970) k311 ’ W-4 hl.E.Schwartz,~Chem. distances and co&guration iri ‘, 1211 Tables of interatomic molecules and ions, Special Public$ions Nos: il’and.‘LZ’, (The Che+al Society, London, 1958 and 196-S)..
._
4
CHEMI?.AL PHYSICS LEl-i-ERS
:‘
15 ‘hIarch
...
1671
:
.:
THERMOCHEMICAL INTERPRETATlON .OF‘ ESCA CHEMICAL SHIFTS USING SEMI-EMPIRICAL MOLiXULAR ORBITAi METHODS .D.C. FROiT, F.G. HERRING, C.A. MkO&LL
.-
and KS:WOOi..SEY
Deparrmenr of Chemistry, University-of Bri@t Columbia.. Vancouver S. &Wit Columbia, Canada Received
11 January
1972
The ESCA chemical shifts of carbon and nitrogen in a variety of chemical ekironments have been calculated from the energy difference (aE) between the pgent molecule and the isoelectronic nitrogen and oxygen containiiv&
Lotions using the hIINDO/I valence electron SCF MO method. For the case of carbon, a good correlation is obtained bchveen ti shifts are about one-third of rhe experimental values. The nitrogen experimental dats arc available to test the method in this case. The reasons
for this and the usefulness
of the approach
X-ray photoelectron spectroscopy is rapidly developing as a usefui technique for studying molecular electronic
structure
are discusxd.
photoelectron of eq. (1) h as zero kinetic energy, thus the core binding energy may be expressed as the energy difference between the molecule and the
[ 1, 21, and-as a means of testing
ab-initio molecular wavefunctions [3,4]. Several different approaches have been used to interpret the observed changes in core electron binding energies of particular atoms in different chemical environments, the $0 called ESCA chemical shift. These vary widely in their, degree of sophistication, from simple correla-
molecular ion. Jolly’s approach ass~~ncs that cores which have the i&me charge are chemically equivalent?, so that the M*’ icn may be represented by the ion of the element one higher in the periodic table than the atom involved in core ionisation. Thus, for example, the CHiC ion is represented by the NH: ion. In this case, how- _ ever, the ion will be-in its ground electronic state. Whilst the total electionic energy of these two species is not identical, the method-assumes that the e,nergy ofsubstitution,of equivalent cores is con&a& for all compounds of the element concerned. Thus the energy of.substitutidn of-the core Css+ by N5+ is assumed constant for carbon in all chemical environmr”nts. Hence the energy changes.of the following p&&es
tions’with the charge on the atom involved [3, 5,6], to direct calculation of the core electron binding ener-
.gies [3,4]. Recently, Jolly proposed an interesting method for estimating ESCA shifts using thermo-. dynamic data [7,8], and it is this method with which -we are concerned in the present communication. -.The core electron binding energy of a gaseous molecule M is the energy of the process
M-bM*+te,
and the chemical shift, although the calculated. shifts rhow better ‘absolute rgreement. but fewer
(1)
.’
are the saine;
wherp,‘* indicates that the sp&ies is an ion in which a dore,‘electron is_missing, and is not an ion in its ground electronic.gtate. The M*+ ion is, however, a species in wfiic’h &tronic relaxatidn has occurred-14, 91 , that is the .r&aining~.electrons of tee ion c&e adjusted
:.
&~tr~ni&y-to
ihe$crez&ed effective core:c@rge of :.th$ a:@* inyplveclin cork [email protected] ,.- ,. ,.; '. ,.
--::,; ... .:. _ .'_- .: :
:. . . :; :
I_ .y-
:-
;.
: :_,.., .. ,. :
._ '.
-_
T’By .core, tie mean.lhe -,.... ~.&ons. .
'. .._ _:
: .-
.. ;:
.:,
‘..
..,. :
.-
nucleus
an! ,jhs.remaining
'; '.._ : .1_ fr _,;._.,. .;: y_:,.l,_,_, __: --..: .Li ._. ;_ -:. ._. .; .. ,. :.I .-
.: ..'. ..-. -. ., : .. '. _;,_,'._ .I i. ~ '.,_ ..
,“;' 1.. .
:'.':. ':. -._ ,, ., .._ ._ .-',.' :
.
~. ,: ,~
c&eelec-
,. :
.. :.~,;":_~~:,~.;::~: .-,.
.; .,: &,' ', ~
:; .,
method
‘,~~‘$q%&~&Al j;ch.“transmut~tion“‘equations.
the dif‘f~.rc$ce in’&ergy of:the_ species .CHz+/NHqf and .. .CO,t[NOi @d:all ether is&electronic ion pairs should be.ih&lsatie..lhus
i&4i6tild.b& possidle
to expiess
the
&erg? of,&e @roce& in cq_ (I.) as the difference in ‘. -.tqta!-electronlc_cnergy.of the.parerit mo&le (M). .&tiie isoelectronic ion .of the element one higher iri ..thb p&riodic.table.(AE), plus the constant energy AcE : &r&smut&on
of M*.?. This of cou;se:is
.:..bicd&ge.nergy
ttierefore :~ .. BE.=AM;.
(BE),of the core electron, be.e%pressed as follows,’ ..
just the
which may
[T, lo] ,.and.a.meth&based
(4)
on the bond dissoci-
ation enerkes
of the Species obtained from electronegativity arguments [8] ; and correlated them with ‘the obseeed.ESCA shifts. Remarkably good agreement beiweenobserved atid calculated shifts was obtained :ii spite 0; ehe.relatiwely crude me*hods used for estimating k+: Tb test the method further, we have .used.i setii-empirical m&le&!ar orbital method for evaluating the energy differences (AfZ) between.the tidlectile and-isoelectronic ion of the element one hi&e.r in the peiiodictable. We have chosen to use Dewar’s MlNDO/l method [I I, i2] ,-since this.is -known tci give quite accvrate heats of formation for a variety of carbon, nitrogen and oxygen contai.ning compounds, in.tiost cases-accurate to within .2.5 kballmole (0.2 eV)ij-. This compares very favouryably with the a&age deviation between the caiculated anh’expeiim&tal values for A.& of k3 1 kcal/mole (I-!? +) fo,u?d by Jolly [8] , although it-must be ad‘rr+ted,..that:the exp&i.metital values &ay be unreliable .in‘s’ome cases.: Since ESCA shifts are usually measured :with an ac&&y.of,around iO.1 kV_at present, a?y i&pr&ement -in th8 &cur~cy of AE of this magnitude ‘ishighly &&able. Ai_yet; h&ever, the MIN.DO/I -.. -... ;_ .. I : t lkpe~i~e~&.val&
ITI& oft&
data
has bee.n gathered
fro_n~ .carbon
be rather inaccuiate.For
and nitrogen
containing compounds [ 1, 2, 5,6, 10, 131, and at the moment we are largely concerned with establishing .the validity of the approach. IV&have therefore simply calcu!ated the total electronic energy of the ground state molecule and isoelectronic ion of the element of one higher atomic .number within the MlNDO/l approximation scheme, and correlated the energy difference with the experimentally
.’
‘T’o‘test these a’guments, Jolly evaluated the energy $ffe&nces At? fqr molkcule/ion pairs such as CH&Hz, C02!“z etc., using both experimental -dais
tested in the case of ‘-mole&lar ions, and has.so &r only be& parameterised for H, C;N and O.atoms..:The latter is not too.problematic, howevei; since much of the presently available ESCA
has not been’thoroughly
shift of the 1s care electrons reference molecule. Tks method of evaluating 4E has the advantage method
ESCA
to some suitable
the ener,T
differences
over the bond dissociation
used by Jolly
bitrary assumptions
determined
relative
[S] in that.there
are no ar-.
involved, such as the dissociation
of ions so that the bonding electrons are shared equally by the atoms involved, or that covalent contributions to the bond energies are the same for molecule and.isoelectronic ion. The calculations w&re.carried out using the same geometry for the molecule and iscelectronic ion, and *is is necessary.since the lifetimes of core electron vacancies are expected to be short compared with vibrational relaxation times. Experimental thermod$namic data will of course correspond to the ion with a different geometry to. that of tlie molecule. Table I ljsts the calculated ESCA chemical shifts for .carbon and nitrogen in a variety of chemical environments evaluated in this manner, together with the experimental values. The experimental data were taken from refs. [2, 5, 10, lb], and for the presknt we have restricted ourselves to the gas phase. (Only urea..and ethylamine are solid state measurements.) Iye have d&e this iargely 30 avoid the effects of s.ample charging which occurs inthe solid state; and which may . lead to er&eous chemical shifts; atid because ESCA shifts &f ionic species iri the solid state- depend dn the lattice potentials which may not be kn&vnvej ac;-. curately. jt sho,uldIbe pointed out, howevkr, that this approach &in no way_estricted $I gaseous species, or indeed the ESCA.sp&ztrti of neutral mole&,& as has.already..-: been’indic&d by Jdlly [7]. i :: .,
Volume 13, number ;?
Experimental
-. .-Table-l’ I and calculated ESCA shifts for carbon and nizogen in gas phase
.Slolecule :
i. c*o 2_c*oz *CHzCH, *CHjC02 H CHjC*Q2H
‘CHJCH3 7. +CHd
calculated
‘. experimc&l
1.58 2.33 -0.78 0:45 1.38
5.2 6.8 -0.1 0.7 4.7
-0.14
LO.2
0 (dcf) al -1.38
8. *CHCH 9. *CHzO
10. *CHSOH 11. *CH$IHO 12. CH+Z*HO 13. *CH&H2NH2 14.0C*(NH1)7 15. HC’02H 16. (CH&C*O 17. (*CH&CO 18. .19. 20. 21. 32. 23. 24. .25. 26. 27. 28.
8
ESCA shift a) (in cV)
No
3. 4. .5. 6;
CHEMICAL PHYSICS LmERS . . . ..
0 (de0 n) 0.4
1.18 0.56
3.3 1.6
0.21 0.82 -0.53 1.38 1.56 1.23 -0.05
0.6 3.2 0.0 3.9 5.0 3.1 0.5
0 (det] a) -3.56 -2.66 0.04 1.27 -0.19 -4.00 -3.56 -4.18 1.11 1.72
N; CH3N*H2 *NH3 *NNO NN *0 HCN* (CH&N*H *NH2NH7 (CH&N’ *NO. *NOi
..
2
kre
5
6
7.
.‘a
versus calculated ESCA shiit for carbon. Nutiberirlg of points as given in table 1. The c&es and dotted lint refer to the corrected values of AE (set test).
0 (dell ai -4.8 -4.3 -1.3 2.6 -3.1 -5.0 -3.8 -5.2 0.4 2.5
also used for the isoelectronic
4
Fig. 1. Plot of experimental
a) Shifts for carbon are relative to methane, those for nitrogen to molecular nitrogen. * Denotes atom involved in core ioniution. The geometries of tie molecules studied were taken from ref. [ 2 I 1. The same. geometries
3
ions.
remarkably good straight line. Only acetylene falls significantly far from the line; and this may be accounted for by the known inadequacy of the I&NDO/l method iri predicting heats of formation of acetylenic compounds [ 1 l] _ Unforrunately the absolute agreeand-Cal&dated shifts rnent between the experimental is poor, the slope of the line of fig. 1 beirig 2.9 instead of unity as found by Jolly [i, 81; and as required by eq. (4). This discrepancy is readily explained however. @th.&& ttie .MINDO/I tiethod.givek accurate heats -. of formation of the.molecule, it has n9t beeh-properly-. ,. t@ted f&~mokctilfii [email protected] most di the cask c15ri- j .:
sidered here, the isoelectronic nitrogen molecular ion is unknown, so that no experimental data are available to test the accuracy of the heats of formation-of.the ions. Fortunately experimental data are available for three of the ions considered; namely, NH:, N$ and .: NO+. Comparison of the calculated heats of formation of these ions with the experimental values given in the literature [ 1.5, 161 shows the calculated values to be incorrec!. That of the NH: ion is 64.2 kcal tdo high, NO+ 20.8 kcal too high, and NO; 5 I .4-kcal too low. Correcting the calculated v&es of AE for the differences between the calculated and experimental v&es for the heats of formation of the molecule.and-isoelectronic ion in these three cases gives the new points indicated by the crosses in fig. 1. The dotted line drawn thiough them has a slope of unity; Although we can-. not .do likewise for the remainder of the points oti the ‘cor&.lation diagram, in view of the very accuiate re- ._ production-of the trend bf.the expetientgl E&A shifts,.we see no.reason-to suppose that the incorrect -’ sIope.is not due simply to the .failure’-of the.MINDb/ 1 -. ‘. method to give accurate heat&f fdimation for the.,. molecular ions. Sic& we do obtain an accura’telinear coGelation from 6ur c&dations, and the corrected tiaiues’of: A& wheie availqble do-give .a direci co&e- I ., ip&den&betwe&dE atid the:ESCA shift’as’in,: ,., ; :--.
CHEMICAL PHYSICS LETTERS
.,, ,So far relatively
(c.V)‘.. .: . .
ftiw ESCA tieastiremkts
have
..i.!:
been made of nitrogen Is binding eneigies in the ga& ‘I;.$ -phase. However, a few such measurements have be& ?: made, and. fig. 2 shows the correktion between their .‘j
...
..: t
‘.
.,,,
,..ShifL
I-..
:, !
: Es.@e &&al ‘.
15 March. 1972”::
.
:. . ...’
experimental ESCA shifts and‘those calculated from : i the difference in total energy of the molecule and iso-,,‘. electronic oxygen substitured cation. The correlation ‘ii is poorer in this ca&, and with only a few points on .:i.!
.‘.
1,‘; the graph it-is not obvious what line constitutes the .-; best fit to them. We have therefore chasen in this. case to draw in a line of unit slope. This fits the points‘.j
.. .’
,< moderately well. However, the fit can be improved :. considerably by correcting the calculated values for the true heats of formation of the molecule and mole&l ‘.:j uiar ion where available (~CN~~COi, N~~NO~~ NNO/NOSand NO’@:). These are indicated by the :’ : crosses in fig. 2. It may also be noted that the cal.:‘. culated heats of formation of N20 and NOi, two Cal&fared
mqlecular ions of the element ond higher in atomic nuniber. Also, since in general &e heats of formation of the.ground state m&e&les.are fairly accurately re-
,: points which deviate significantly froni the line, are. : considerably different from the experimentally ob-.. served vaIues (82.9 kcal too low for N20, and 84.0 kcal too low for NO,). The MINDOI 1 method gives quite good heats of formation for amines, heterg-1, aromatics and various alkyl.nitrites and nitrates, however f 12, 191, thus molecules such as HCN, N,O and ’ .-j NO, are not entirely typical of the accuracy o?: the method. Unfortunately, few other gas phase measure-- :. ments are available for nitrogen. However, the present ,-_ results,support those of’.Jolly et al. [IO], and indicate $ :I the method should be applicable to all first row ele: ments. 1: The conclusion ‘that an-expression of the type
.,.produced-by the MrNDO/l method, the calculated ions must vary “heats of formation of the isoelectronic ., in a,tiiQf?rti manner for the.linear correlation of. fig. 1 :.’tti o&r.-Thertis gdod reason fo suppose; therefore, ihat ~h~.~~~ND~~~;~ethod could be-modifjed to re-, 1 produce rhe he,@s. of formation of both mdetules and-
given in eq. (4) can be used for core election binding -‘? energieS throws light’on several interesting aspects qf ‘.‘: the na,ture of the core electron ionisation process, and. l suggests further use@1 applications of the ESCA tech- ;. nique: Since in the present calculations we-deal only. .:i wi~,electronic relaxation of the valence, &ctrons on .“I:
i&s si&ditaneously. The error iri the c&e of the ions ‘. would appear tt, be due to.the use of one centre int& ,’
-.:I core ionisation, the fact that a direct corrkspondknce ~~1 exists between. ihhe ESCA-shift and AE indicates that relaxation of the.iemai$ng iore elk’ctrcin must be con-:{: stant or ‘at !&ast very n&t&so;for first row elements -C. iegardless of chemical environment, This view is sup: :.!::i ii.: ported by recent calculations.by S@der who has given, a constant value.of -I 2 ;V for core electron .’ :‘.$jj relaGti’qn of all first’ row +m&t.s ,[ CS] . This iS also, .;?j in accdrd with the ‘Go& oE Schwartz [4] ,‘who indicat$$ that ;a.~nce.shell-ieorganisrttion is 5y:,far,ihe:_Go& -;:::‘+--” ... .. :.. ,
Shift fe.V) -d
-3
-2
-,
0
I
2
3
Fig. 2. Pkt of experimental versus calculated ESCA shifr.for -nitroSen. Numbering of points as given in table 1. The crosses
rrfer to rhc corrected $&ICS of AI5 (see test). .
‘Jolly’s case, & believe that the ESCA shift can be predicted
with gobd precision
from the energy
dif-
ference between pairs of molecules ‘and isoelectronic
: grals inappropriate ,.
to ionii: species; since we do not .. ..
::‘obseFe any dependentie’of the plbt in fig:1 on the - type_&f bonding’involv”“::Mqdification of the lhnlrNpO/i. n~et~od.~sing.a-~a~i~~l~ electronegativity::-proc~dure-forthe.one centre‘ iAtegrals,similar t&,,that,
Volume 13. number
4
important contiibutor to the ESCA cheinical shift, and that a highly accurate core description is not necessary for evaluating shifts. Indeed, in bur cati, the description of the core is the sitiplest possible’. Clearly therefore calculations such as these which do not expticitly treat core electrons can be very useful in understanding ESCA shifts. The procedure adopted here may in fact be considered as the semi~mpirical analogue of using ab-initio calculations to give the core binding energy’ from the energy difference between the molecule @I) and the core ionised ion (bl**) [4j . Cfearly this relationship between core binding energy shifts and the thermodynamic properties of the parent molecule and isoelectronic molecular ion should be useful for evaluating heats of formation of the species concerned from ESCA measurements. For example, ESCA studies of halogen compounds might be usefuUy employed to predict the stabilities of isoelectronic rare gas compounds. Aiso, &CA studies could. possibly be used to evaluate lattice energies and other solid state thermodynamic energies using this relationship. As noted earlier it should be.possible to use the correlation between ESCA shifts and A& to calibrate MIND0 type calculations to give the heats of formation of ionic species. This would be particularly useful in organic chemistry for the ~eoretical study of reaction mechanisms involving charged species e.g. carbonium ions. Finally, since the underlying reasons for the success of this approach are essentially the same as those of the mettiad involving calculation of the change in potential at the core due to the valence electrons [20], we see no reaspn why the present approach should not be applicable to elements beyond the &st row of the periodic table, as is the case for the potential mbdel. Oni of us (I.S.W.)
thanks
the.University
of British
support of a post-doctoral fellowship. We also thank the National Research .; CotinciI of Canada for’~nan~i~ support.
~,‘Columbia
15 March 1972
CHEMICAL PHYSICS ILEJXERS
for the financial
.’
..,
‘.
References
..
[I] K.Siegbahn.
C.Nordling. A.Fahlmart, R.Nordberg. K. Hamrin, J_H~dm~n, GJohansson, T.Bergmark, S.-E_ .. f&.&son, I.Ljndgr& and D.Lindberg. EXA-Atomic. molecular and solid state structure studied by means of electron spectroscopy (Almquist and Wiksells, Uppsala, ‘19671. [2] KSiegbahn, kordling, G.Johansson, J.Hedma& P.F. He&n, K.Hamrin, U.Gelius, T.Bergmark;, L.O.Wetme, R.h~anne and Y.Baer. ESCA applied to free molecules,’ ‘, (North-Holland.
Amsterdam,
1969).
(31 H Basch and L.C.Snyder. Chem. Phys. Letters 3 (1969) 333. [41 ~f.E.Schwnr&.Chrm. Phys. Letters 5 (197Oj 50. [ 51 U.Celius. P.F.Hcd&, J.Hedman, BILinderberg. R. Manne, R.N&dberg, C.NordIinp and K.Sicgbahn. Physica Script3 2 (1970) 70. [6] D.N.Hendric+n, JMHollandcr and W.L.Jolly. Inorg. Chem. 8 (1969) 2642. [71 W.LJolly and D.N.Hendrickson. J. Am. Chem. Sot. 92:. (LS70) lE6,: [8] W.L.JoBy, J. Am. Chem. Sot. 92(1970) 3260. -. I91 I.H.Hillier. V.R.Saunderi and hl.H.Wood. Chem. Phys. Letters 7 (1970) 323. [ 101 P.Finn, R.K.Pearson, J.hi.Holiander and W.L.Jolly. Inorg. Chem. 10 (1971) 378. (111 N.C.Baird and M.J.S.Dewar. J. Chem. Phys. 50 (1969) 1262. [I21 N.C.Eaird. XC.J.S.De&x and R.Sustmann, J. Chcm. Phys. 50 (1969) lf75. R.G.Aibridge, T’.Bergmark, U.Ericson, J. (L31 R.Nordberg, Hedman. CNordIing. K.Sicgbahn and B J.Lindbe:g, .’ Arkiv Kemi 28 (1968) ‘257. D.A.Shirley sod T.D.Thomas. [141 D.W.Davis, J.hf.Hollander, J..Chem. Phys. 52 (1970) 3295. Some thermodynamic aspects of inorganic 1151 D.A Johnson, chemistry (Cambridge Univ. Press, London, 1968). [I61 CI.F.Cordcs and N.R’.FBttcr. J. Phys. Chem. 62 (1958) 1340. ff71 R.D.Brown and ~t.L.He~fern~n., Australian J. Chem. 12 (1959) 319. L.C.Snyder, J. Chem:Phys. 55 (1971) 95. ” [IsI ” [I9? M.J.Dewar, ~f.Sbansb~ and S.D.WorIey, J. Am. Chem. Sot. 9 I( 1969) 3590.. Phys. Let&6 (1970) k311 ’ W-4 hl.E.Schwartz,~Chem. distances and co&guration iri ‘, 1211 Tables of interatomic molecules and ions, Special Public$ions Nos: il’and.‘LZ’, (The Che+al Society, London, 1958 and 196-S)..
._