- Email: [email protected]
Interplay of direct and indirect coupling contributions in proton hyperfine splitting constants of alkyl radicals
-:
‘. ENTERPLAYOFDIR~~AND,I[NDIRECTCOUPL~GCONTR~~IONS .'~~NPR~TONH~~~INIE SPLIT~INGCONSTAN~S~FALKYLRADI~AL~
:
.,
:.
‘.
'.
.:
Y. ELIJNGER,A:l$ASSAT,R.SUBRA .., : .‘kafnxa~oire de Chimfe Urganique Phys@g du Centre d’Etuds Nucfeaires, _<8 - Grenoble, France
.’
,’
'1
.'
..
G.BERTHIER Lnborurofre de Chfmie Quantique,
.
13 rue Pierte et Marie Curie, Wis 5t?me, France
‘.
and’,
P.MILLIE La&war&e de Chimie, E.N.S., 24,tue Lhoywnd, Paris .%me, France
Reck&cd26 Jufy 1971 ,. An ah i&tio
catcufation’onthe CHs-&& radical swests that the spin-pokrization and spin&ocalization con-
_isibutions arc both equd.Iy impottznt nnd shouid be simuIianrortsly
hyperfine
mnridered
in the thcorctial
nrwlysis of proton
coupling constants oialkyfradicals.
The semi-empirical relationship i;(NB) = Bd + B2 c0s2e ,
(1)
suggested by McConnell [I] has frequently been us& in electron sp;k resonrnce spectroscopy to correlate pproton’hyperfiie splittings a(?I@ with the conformation of free radicals (e being the d&edral angle between th! p-orbitaf conning tee unpaired efectron and the C-C,-I-I@ plane)., In most of these studies 80 is assumed to be negligible relaiive to B2. However, in some ra+als it has been found that the term B, in eq. (1) is sight f2-51, This point has’bcen ten- ,’ tatively attribvted to a residual motion of +e ppio-, -. tons-in riiti,oalkane radical anions [6] and an inversion niotion,of t@ N-0 bond in n&oxides (73’. ... Fr,om a theoretical point $f.‘vjew,~there ha? been,;
calculation of hyperfme splittings of the ethyl radical, using a restricted open-shell formalism. The wavefunction has been computed by means of the IBMOL progrctm [9] _The closed and open-shell SCF equations have be’en solved following Roothaan’s method using a b&is set of gaussian orbitals containing 9 s and, 5 p type functions on carboq atoms ancl4 s functions on ~l~droge~ atoms:The molecular geometry has been adapted from ethane and’only the planar form of the paramagnetic centre has been examined. The htierftie splittings aH are the sum of two kontributions, .adirect ~~~b~tion ad Fomputed from the SCF wavefunct’ion $_and an indirect contribution Oi determined here by a fist-order +rtuibaii.&i treatment ttiking into .a&ou.nt spin-polarizatidn effe& [ 4 11.. This leads ia ‘.
‘cals, thii &$est:radi,cal
&wing
both Q’- and’@ctiu-‘,.
.with
”
:plings[8];. ” .,_ I-., .“) .;’ ‘_, :: ; :,.‘.,_ ..pd,:~.i~u(‘fI),~.‘.. We report here &+resuI&, of the first noriempu;lcaI .. : -, ;_ _ .. ..
,.
::
:‘. ,,,
;.:y : ,.,. ,:,,I : ;
I.‘, ... .,_ .._ 1.. (3) ,, ‘.; ,’ ..,_. :..: ._ ; ;-. : ._&‘:. ..i :.L .:’ /..’ ;_ _,‘. ., : .. ~+y,, ‘., ,, ,:;:, ..; ‘I ;‘yI,.,,..,. ,_~,~~,.‘,._: .,..,I. :“;, ,_,.:_. (,, ‘,I. _C’ ,.’ _’ -: :. .., ,.: ,. ,’ .. .. ,, ,. .~ -. ‘; I’ . . ._.. _‘;’ .:. ‘. . :. -’ .: _, .-.-: . ‘: 1 :::“. _ <:.:>.‘, i,. ‘1,’,_ ..:’ .;::_. -, ‘, .;.,,:,._ :_.:_, ..‘y : : :_., _. .‘;I .;.,; :,.,,: ,_ ,__.__, :,; .;., .,. ___. _,.; _ _:.: ,= .. .-‘..‘. ,, ,; ,_.. -:,’ ,-I ; _, .Y.. : :‘. ..,;: -.-:: _:,.,,,. ..l,.._,.‘ ‘... . ;I’ _:... ; .. ,.,.., /.,_,, . ;:. ., .’ . ,. ‘. .., .,, ..’ .::. ‘-,I .,, ,I .,., : ..’ ‘: ,. : 1,’ .. I. ,,_,..; .-.- ,. ,. ._. ‘_
1
Volum;
11, number
3
CHEMICAL
PHYSICS
c d
c (QV*~u’~u~d)OdO,)Q,.(rH) v+ EO -Q-v*
,’
(4)
where @dare doubly ocCupied orbitals, &,* virtual or- ._ bitals and 9, the orbital containing the unpaired electron. In order to be able to describe the.origin of hy; pen%e splittings in terms of localized interactions, we have determined equivalent lo&ed orbitals according to the procedure of Foster and Boys [ 121. Consequently, every term of the perturbation expansion may be related to a specific mono-excited state (d+v*). The main resuIts of the computation are f 13] : (i) The direct contribution to a-proton (Ha and Hb) splittings is zero. The direct contribution to &proton splittings (fig. 1) fits eq. (1) with B. = 0 and B2 = 19.20 Oe. (ii) As in the methyl radical [l l] ?, the indirect contribution to the a-couplings is negative. In confort Further details on hyperfiie splittings in alkyl radicals incIuding long range interactions will be published elsewhere 1131.
1971
a(Ha) =&lb) = -33.82 Oe and in conformaOe and a&b) = -34.04 Oe. = -33.60 tion II, Q(h) The indirect contribution to &proton splittings (fig. 1) fits eq. (1) with B, = -0.96 Oe and B, = 16.19 Oe. (iii) The calculated total hyperfiie splittings can be fitted to eq. (1) withBo = -0.96 Oe and B, = 35.39 Oe. This leads to an average value of 16.7 Oe for the freely rotating methyl group. (iv) The observed Q- and /$couplings are respectiveljr -22.38 Oe and 26.87 Oe [14]. Proton hyperfine splittings computed here are correct in sign but are slightly apart from the experimental values as in the ab initio calculations for methyl using SIater orbitals r151* (v) In all cases the dominant contribution to indirect couplings (90%) is the electron excitation from the bonding CH-orbital to the corresponding CH*antibonding orbital. (vi) In the absence of any vibronic effect, a P_ proton in the nodal plane of the 2p orbital containing the unpaired electron (cos8 = 0) would present a negative coupling due to spin poIa.rization. These results demonstrate that detocalization and spin polarization contribute almost equalIy to /?-hyperfiie splittings. This particukr point gives a better mation
pi = -2
15 October
LETTERS
I,
understanding
for the successful
development
of semi-
empirical methods in which orJy one of the two contributions is taken into account: if numerica agreement between observed and calculated hyperfme splittings is achieved by suitable parametrization, the cos2B variation is obtained independently of the actual nature of the coupling.
-lid
460
-60'
b’
Ongk
?H,
Ha Y&tH-320
Hb :
n120
:
I
6.0.
120.
160’
References [ 1 ] C. HeUer and H.M. hi&onnell, J. Chem. Phys. 32 (1960) 1535. [2] A. Hordield, JR. Mortonand D.H.Whiffen, hloL Phys. 5 (1962) 115. [3] D. Pooley and D.H. Whiffen,Tran+ Faraday Sot 5’; (1961) 1445. [S] E.W. Stone and A.H. hfaki, I. Chem. Phys. 37 (1962) 1326. 15] G. Cbpebt-Letourneux, H. Lernatcc, R. L-enk, M.A. hiare’cinl and A. l&sat, Bull. Sot. Chim. France (1968) 3963. [6] E.W. Stone and AH. Maki. 3. Chem. Phys. 37 (1962) 1326.
Fig. 1. 363
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CXEkICALPHY~ICS
.-.:
17(.1969) 2!?. MoLF’hya 1 (1958) 233;
m3;chemut, 4. chm. phyS..~9(1958) 43; “~‘Pi;..Lykos;f.Cfierit;Phys’ 32fl960)625; -‘.“:i _.’ -,’ ‘DH. Levy,Mdt$‘h~s.10 (1966) 233; ,.. ., D.~]tad&tsand M:Karpkis,J~ Chem. Phys. 44 (1966) ,[email protected]’ :,: :,;“, G.k ~etersson and A.D. Mc,Lachtan, J. Chem. Phys. 45 (1966)628. 1 i9J ‘A. Veihl, &~iD&d atid P:MiBi&, lBi&L UX! 36t%
’
:
:
LETTERS
_‘.
:
” _,
I5 oct&er.1971
[I.1 1 P. NW, 8. L&&d G. krthier, IntqI, J. _. ~‘Chem.,tobe&bLished.. J.N.,Fostei and.S.if;.Boii, Rev: pd. Ptiys. : .., ‘. 1740. 1x31 Y. EUinger, A; &sat; R. S&a, G. ~e&er ..MiilitS, to be published. [!4] R.W. Feswden and R.H. Sch&, J. Chem. ‘(1963) 2149: ., [ISI S.Y. Chang, ER. Davidson and G. Vinck,
Quantum 32 (1970) and P. ‘.,’ Phys. 39 J. k!hkm,
Phys:52 (1,970) 1740.
version, Laboratoire de Chin& de?EaAe Norma& Su., @&; ,‘, .’
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‘. ENTERPLAYOFDIR~~AND,I[NDIRECTCOUPL~GCONTR~~IONS .'~~NPR~TONH~~~INIE SPLIT~INGCONSTAN~S~FALKYLRADI~AL~
:
.,
:.
‘.
'.
.:
Y. ELIJNGER,A:l$ASSAT,R.SUBRA .., : .‘kafnxa~oire de Chimfe Urganique Phys@g du Centre d’Etuds Nucfeaires, _<8 - Grenoble, France
.’
,’
'1
.'
..
G.BERTHIER Lnborurofre de Chfmie Quantique,
.
13 rue Pierte et Marie Curie, Wis 5t?me, France
‘.
and’,
P.MILLIE La&war&e de Chimie, E.N.S., 24,tue Lhoywnd, Paris .%me, France
Reck&cd26 Jufy 1971 ,. An ah i&tio
catcufation’onthe CHs-&& radical swests that the spin-pokrization and spin&ocalization con-
_isibutions arc both equd.Iy impottznt nnd shouid be simuIianrortsly
hyperfine
mnridered
in the thcorctial
nrwlysis of proton
coupling constants oialkyfradicals.
The semi-empirical relationship i;(NB) = Bd + B2 c0s2e ,
(1)
suggested by McConnell [I] has frequently been us& in electron sp;k resonrnce spectroscopy to correlate pproton’hyperfiie splittings a(?I@ with the conformation of free radicals (e being the d&edral angle between th! p-orbitaf conning tee unpaired efectron and the C-C,-I-I@ plane)., In most of these studies 80 is assumed to be negligible relaiive to B2. However, in some ra+als it has been found that the term B, in eq. (1) is sight f2-51, This point has’bcen ten- ,’ tatively attribvted to a residual motion of +e ppio-, -. tons-in riiti,oalkane radical anions [6] and an inversion niotion,of t@ N-0 bond in n&oxides (73’. ... Fr,om a theoretical point $f.‘vjew,~there ha? been,;
calculation of hyperfme splittings of the ethyl radical, using a restricted open-shell formalism. The wavefunction has been computed by means of the IBMOL progrctm [9] _The closed and open-shell SCF equations have be’en solved following Roothaan’s method using a b&is set of gaussian orbitals containing 9 s and, 5 p type functions on carboq atoms ancl4 s functions on ~l~droge~ atoms:The molecular geometry has been adapted from ethane and’only the planar form of the paramagnetic centre has been examined. The htierftie splittings aH are the sum of two kontributions, .adirect ~~~b~tion ad Fomputed from the SCF wavefunct’ion $_and an indirect contribution Oi determined here by a fist-order +rtuibaii.&i treatment ttiking into .a&ou.nt spin-polarizatidn effe& [ 4 11.. This leads ia ‘.
‘cals, thii &$est:radi,cal
&wing
both Q’- and’@ctiu-‘,.
.with
”
:plings[8];. ” .,_ I-., .“) .;’ ‘_, :: ; :,.‘.,_ ..pd,:~.i~u(‘fI),~.‘.. We report here &+resuI&, of the first noriempu;lcaI .. : -, ;_ _ .. ..
,.
::
:‘. ,,,
;.:y : ,.,. ,:,,I : ;
I.‘, ... .,_ .._ 1.. (3) ,, ‘.; ,’ ..,_. :..: ._ ; ;-. : ._&‘:. ..i :.L .:’ /..’ ;_ _,‘. ., : .. ~+y,, ‘., ,, ,:;:, ..; ‘I ;‘yI,.,,..,. ,_~,~~,.‘,._: .,..,I. :“;, ,_,.:_. (,, ‘,I. _C’ ,.’ _’ -: :. .., ,.: ,. ,’ .. .. ,, ,. .~ -. ‘; I’ . . ._.. _‘;’ .:. ‘. . :. -’ .: _, .-.-: . ‘: 1 :::“. _ <:.:>.‘, i,. ‘1,’,_ ..:’ .;::_. -, ‘, .;.,,:,._ :_.:_, ..‘y : : :_., _. .‘;I .;.,; :,.,,: ,_ ,__.__, :,; .;., .,. ___. _,.; _ _:.: ,= .. .-‘..‘. ,, ,; ,_.. -:,’ ,-I ; _, .Y.. : :‘. ..,;: -.-:: _:,.,,,. ..l,.._,.‘ ‘... . ;I’ _:... ; .. ,.,.., /.,_,, . ;:. ., .’ . ,. ‘. .., .,, ..’ .::. ‘-,I .,, ,I .,., : ..’ ‘: ,. : 1,’ .. I. ,,_,..; .-.- ,. ,. ._. ‘_
1
Volum;
11, number
3
CHEMICAL
PHYSICS
c d
c (QV*~u’~u~d)OdO,)Q,.(rH) v+ EO -Q-v*
,’
(4)
where @dare doubly ocCupied orbitals, &,* virtual or- ._ bitals and 9, the orbital containing the unpaired electron. In order to be able to describe the.origin of hy; pen%e splittings in terms of localized interactions, we have determined equivalent lo&ed orbitals according to the procedure of Foster and Boys [ 121. Consequently, every term of the perturbation expansion may be related to a specific mono-excited state (d+v*). The main resuIts of the computation are f 13] : (i) The direct contribution to a-proton (Ha and Hb) splittings is zero. The direct contribution to &proton splittings (fig. 1) fits eq. (1) with B. = 0 and B2 = 19.20 Oe. (ii) As in the methyl radical [l l] ?, the indirect contribution to the a-couplings is negative. In confort Further details on hyperfiie splittings in alkyl radicals incIuding long range interactions will be published elsewhere 1131.
1971
a(Ha) =&lb) = -33.82 Oe and in conformaOe and a&b) = -34.04 Oe. = -33.60 tion II, Q(h) The indirect contribution to &proton splittings (fig. 1) fits eq. (1) with B, = -0.96 Oe and B, = 16.19 Oe. (iii) The calculated total hyperfiie splittings can be fitted to eq. (1) withBo = -0.96 Oe and B, = 35.39 Oe. This leads to an average value of 16.7 Oe for the freely rotating methyl group. (iv) The observed Q- and /$couplings are respectiveljr -22.38 Oe and 26.87 Oe [14]. Proton hyperfine splittings computed here are correct in sign but are slightly apart from the experimental values as in the ab initio calculations for methyl using SIater orbitals r151* (v) In all cases the dominant contribution to indirect couplings (90%) is the electron excitation from the bonding CH-orbital to the corresponding CH*antibonding orbital. (vi) In the absence of any vibronic effect, a P_ proton in the nodal plane of the 2p orbital containing the unpaired electron (cos8 = 0) would present a negative coupling due to spin poIa.rization. These results demonstrate that detocalization and spin polarization contribute almost equalIy to /?-hyperfiie splittings. This particukr point gives a better mation
pi = -2
15 October
LETTERS
I,
understanding
for the successful
development
of semi-
empirical methods in which orJy one of the two contributions is taken into account: if numerica agreement between observed and calculated hyperfme splittings is achieved by suitable parametrization, the cos2B variation is obtained independently of the actual nature of the coupling.
-lid
460
-60'
b’
Ongk
?H,
Ha Y&tH-320
Hb :
n120
:
I
6.0.
120.
160’
References [ 1 ] C. HeUer and H.M. hi&onnell, J. Chem. Phys. 32 (1960) 1535. [2] A. Hordield, JR. Mortonand D.H.Whiffen, hloL Phys. 5 (1962) 115. [3] D. Pooley and D.H. Whiffen,Tran+ Faraday Sot 5’; (1961) 1445. [S] E.W. Stone and A.H. hfaki, I. Chem. Phys. 37 (1962) 1326. 15] G. Cbpebt-Letourneux, H. Lernatcc, R. L-enk, M.A. hiare’cinl and A. l&sat, Bull. Sot. Chim. France (1968) 3963. [6] E.W. Stone and AH. Maki. 3. Chem. Phys. 37 (1962) 1326.
Fig. 1. 363
.Vc$i@
‘,
- ,’
ll,‘numb&
:
3
:
.‘.
thier, k&L Phyi (B].A$.k I+,ach&
::
”
,,
CXEkICALPHY~ICS
.-.:
17(.1969) 2!?. MoLF’hya 1 (1958) 233;
m3;chemut, 4. chm. phyS..~9(1958) 43; “~‘Pi;..Lykos;f.Cfierit;Phys’ 32fl960)625; -‘.“:i _.’ -,’ ‘DH. Levy,Mdt$‘h~s.10 (1966) 233; ,.. ., D.~]tad&tsand M:Karpkis,J~ Chem. Phys. 44 (1966) ,[email protected]’ :,: :,;“, G.k ~etersson and A.D. Mc,Lachtan, J. Chem. Phys. 45 (1966)628. 1 i9J ‘A. Veihl, &~iD&d atid P:MiBi&, lBi&L UX! 36t%
’
:
:
LETTERS
_‘.
:
” _,
I5 oct&er.1971
[I.1 1 P. NW, 8. L&&d G. krthier, IntqI, J. _. ~‘Chem.,tobe&bLished.. J.N.,Fostei and.S.if;.Boii, Rev: pd. Ptiys. : .., ‘. 1740. 1x31 Y. EUinger, A; &sat; R. S&a, G. ~e&er ..MiilitS, to be published. [!4] R.W. Feswden and R.H. Sch&, J. Chem. ‘(1963) 2149: ., [ISI S.Y. Chang, ER. Davidson and G. Vinck,
Quantum 32 (1970) and P. ‘.,’ Phys. 39 J. k!hkm,
Phys:52 (1,970) 1740.
version, Laboratoire de Chin& de?EaAe Norma& Su., @&; ,‘, .’
‘(
.,
:
:
_’ :.
._
: ;
..
.’
; : .:’
.’
.’
:
”
.
.’
‘.
:
: ..
..
“.
.’
..
_
.’ .
‘I-
‘.
::.;.
:
,,,
(.,’
.’
., .‘.,
.
.,
;
,_
: .:.,,:
:’ :.’
-’
.’
.._
j_’
)
%.
.,
L:
.~’