- Email: [email protected]
HMO perturbational considerations of correlations between chemical shifts and some theoretical indices of reactivity
Tetrahedron Letters No.47, pp. 4109-4112, 1970.
Pergamon Press.
Printed in Great Britain.
RMOPERTURBATICNAL CONSIDERATI~S OF CORRELATIONSRETUEIW CHm1CALSzIIFTs ARD SCME TREORETICALINDIClBOPBEICTIVITY J.Kuthan Department of organic Chemiatq, Inatltuteof Chamicel Technology,Prague 6, Czechoalovakla T.M.Kzygowakl Inatituta of PundamentelProblema of dhemiatry, The Unlvareltj,Wareerr
22, Poland
(Received in UK 21 May 1970; accepted for publication 10 September 1970)
Recently, the oorreletlonabetween chemical ahifte In proton RNR spectra, t r,
anb acme theoreticalindicee of reactivitjr were obtained (l-4) for acne
conjugatedhydrooarbone.In the caee of benzenoidhydrocarbonathla idea la of particular interaet beceuae of the Couleon-Ruahbrooketheorem (5) which etatae that qr= 1 for all r positionawhen celculatiouaare made by uae of HMO or SCF-PPP methode (61. Then the linear relation between t, end qr (7-g) ie not fulfilled. The aim of this paper ie to eubatentietethe correlationsbetween : 1) the chemical shift8 t, end free valence, Fr, and 2) the chemlcel shifts t, and the atom-atom self-polarIsabIlIty W.r,r. All the considerationaare made In the simple RMO verelon of the perturbation theory. Let ua eeaume the magnetic field acting on a molecule ae a perturbation; then the pi-electronenergy of the molecule change8 because of ahangea In the Coulomb Integrals,a,+
a: + der, and the reaonmce Integrala,bra-)
bZa + dbra (10,ll).Thus in the RMO theolegone can find the,ahange In pl-electron due to this perturbationIn the following fora 1 (1)
43.09
4110
No.47
where the components kind6
of integrale.
a 8110~of partial around
In the other
at&c
e.g.
center
AEPi
to the general
( AEpi) I?* 9,dar+
*rr,r(dar)2+***+
Neglecting
of a suitable
series
positione I
(for
of the po8ltlone
1
other
atoma of a given
AEPi ra
s
(2)
of the perturbation
terms in (3)
s d+
veluee
one obtaine
2 > 8
+
can be regarded
of compounde.
theory
see
conotanta.
Therefore
constant
-
(14)
‘LQ1. definition
(4)
for
hydrocarbone
B & of free
Within
a given
*
the energy (AEPi),. Ho, then It
field nuclear
cal
magnetic
six
1. Ae
magnetic
field
-arising
Ii, = orrHo,
the chemical
shift
actually ehould
dipole,
a8 : (5)
prs valence
BSF,
F,
-
where ae
be proportional p,
-xp,, 6
N_
C
(6)
5 t,
=
q
correlatione
%*
ring current
ie the
screening -
of
to the energy
( AEPi) r”P
e*g*
between the value6
form of the empirical
+
expressee the influence
from pi electron
ie defined
a proportionality
+
“qr
clam
da,= A and dbrs= B, where
a ( OEPI) r
could
angular and non-angu-
might be rewritten
+
:
characteristic8
the cyclic
(1311, respectively. eq.(4)
approximately
dbra
Pr,
and compoundr one can aaeume that
the Coulson
magnetic
within
(3)
a8 structural
For instance
approximately
definition
(AEPQ c
a general
with
perturbatione
8
*
da, and dbrI
have the dar and dbrI
euppose
with local
ae
2~Predbre+~~re,rs(dbre)2+***
the second-order
where the values
priate
can be defined
can write
( A@),
If
bond6 r-6
relation8hipe
one
one get8
connected
+
r
HYO method (12))
Including
(nEPi)r
of the two
:
According
A and B are
~ZVJIIthe perturbation
hand the value
bonded via
( AEpi) rm
lar
arise
AEgk
and
pi-electrononergier being
the r-th
molecule,
AEFi
(AEPilr between
( see (15)
*
and t,. t,
of the appro-
where Hr ie
conetant
ctandard
external
the lo-
Section
(15)
and
one can ale0 Ualng
eq.(6)
and the reactivity
No.47
4111
indices qr and Fr
can be
obtained :
tr(ppm) =
a qr +
b Fr
+
c
(7)
which has been found for nonalternanthgdrocarboneand iona (2). For the benzenoid hydrocarbon8 qr = 1 (5,6) and one get8 t,(ppm) =
b F,
+
c'
(8)
which is In a good agreementwith the correlationfound ( correlationcoefficient r = 0.970 ) (1). On the other hand, if the reeonance terma In the perturbationlxpaneion (3) are not taken into cormideration,one gets the #imp10 relation I
provided the dbrs values are not significantor are aesumed to m
linearly
with the atomic terms. Thus applying an assumptioneimilar to that made In eq.(6), one can obtain the linear relation, t,(ppm) = a,, 9Krr ,
+
conet.
(10)
which give8 a good correlationcoefficient,r = 0.977 (1). The originalmethod8 for chemical-shiftcalculationsbased on HMO theory were proposed by Pople (10) and YcWeelly (11). Our procedure could be coneidered as an extreme simplificationof the LLcWeenytheory which leada to the following expressionfor the proton screening conetent (15) : r) ra,8tu,rr,r8,rt, u
(11)
where fl and f2 are algebraic functions of ar8a and distance parameters8rs, stu and rr,r8,rt,ru,reap* Separating the first term in eq.(ll) into the dlfferent term8 for r = 8
oy
and r # s
one arrives at eq.(12) :
=
+
qr f;
>
b P,,
fl
(12)
l-P8
which appears to be equivalentto eqs.(5) and (7) provided the functionsfl and f; are approximatelyconstant for a given kind of position and only the neighbouring e-terms are taken into consideration.
Analogous
4112
No.47
aerumptionstaking the second term in eq.(ll) tion8hipeof the kind
(10) or (91,
into
amount
give
rise
to rela-
respectively.
REFERENCES
1.
J.Kuthan, Coll.C8echoelov.Chem.Camm., 2, 1222 (1968).
2.
J.Kuthan, Z.DonnerovAand V.SkBla, E,
3.
J.Kuthan, ibid., 35, 714 (1970).
4.
K.D.Bartleand D.W.Jone8,J.Phys.Chea.,72, 293 (1969).
5.
C.A.Couleonand G.R.Rwshbrooke,Proc.CslPbridge Phil.Soc., 36, 1931 (19401.
6.
A.Brickstockand J.A.Pople,Trane.Ferad.Soc.,50, 901 (1954).
7.
1.C.Smit.h and W.G.Schneider,Can.J.Chem.,3, 1158 (1958).
8.
G.Fraenkel,R.A.Carter,A.McLachlanend J.H.RichaFds,J.Am.Chem.Soc.,-i 82,
32, 2398 (1969).
5846 (1960). 9.
R.Spieseckeand W.G.Schneider,TetrahedronLetters, 1961, 468.
10. J.A.Pople,Yol.Phyi.,L,,175 (1958). Yol.Phys.,1, 311 (1958). 11. R.NcWeeray, I 12. E.Heilbronnerand H.Bock, Da8 HMC-ModellUral 8eine Anuendung, und
Grundlagen
Hmdhabung, Verlag-Ch8mi8,Weinheim, 1968.
13. R.H.Hartin,Tetrahedron,22, 897 (19641. 14. C.A.Coulson,Disc.Farad.Soc.,2, 9 (1947). 15. J.D.Yemory,Qumtm Inc., New York,
Theory of Uagnetio Re8onanceParametere,YoGrav-Hill
St.Louie,San Franoisca,London, Sydney, 1968.
Pergamon Press.
Printed in Great Britain.
RMOPERTURBATICNAL CONSIDERATI~S OF CORRELATIONSRETUEIW CHm1CALSzIIFTs ARD SCME TREORETICALINDIClBOPBEICTIVITY J.Kuthan Department of organic Chemiatq, Inatltuteof Chamicel Technology,Prague 6, Czechoalovakla T.M.Kzygowakl Inatituta of PundamentelProblema of dhemiatry, The Unlvareltj,Wareerr
22, Poland
(Received in UK 21 May 1970; accepted for publication 10 September 1970)
Recently, the oorreletlonabetween chemical ahifte In proton RNR spectra, t r,
anb acme theoreticalindicee of reactivitjr were obtained (l-4) for acne
conjugatedhydrooarbone.In the caee of benzenoidhydrocarbonathla idea la of particular interaet beceuae of the Couleon-Ruahbrooketheorem (5) which etatae that qr= 1 for all r positionawhen celculatiouaare made by uae of HMO or SCF-PPP methode (61. Then the linear relation between t, end qr (7-g) ie not fulfilled. The aim of this paper ie to eubatentietethe correlationsbetween : 1) the chemical shift8 t, end free valence, Fr, and 2) the chemlcel shifts t, and the atom-atom self-polarIsabIlIty W.r,r. All the considerationaare made In the simple RMO verelon of the perturbation theory. Let ua eeaume the magnetic field acting on a molecule ae a perturbation; then the pi-electronenergy of the molecule change8 because of ahangea In the Coulomb Integrals,a,+
a: + der, and the reaonmce Integrala,bra-)
bZa + dbra (10,ll).Thus in the RMO theolegone can find the,ahange In pl-electron due to this perturbationIn the following fora 1 (1)
43.09
4110
No.47
where the components kind6
of integrale.
a 8110~of partial around
In the other
at&c
e.g.
center
AEPi
to the general
( AEpi) I?* 9,dar+
*rr,r(dar)2+***+
Neglecting
of a suitable
series
positione I
(for
of the po8ltlone
1
other
atoma of a given
AEPi ra
s
(2)
of the perturbation
terms in (3)
s d+
veluee
one obtaine
2 > 8
+
can be regarded
of compounde.
theory
see
conotanta.
Therefore
constant
-
(14)
‘LQ1. definition
(4)
for
hydrocarbone
B & of free
Within
a given
*
the energy (AEPi),. Ho, then It
field nuclear
cal
magnetic
six
1. Ae
magnetic
field
-arising
Ii, = orrHo,
the chemical
shift
actually ehould
dipole,
a8 : (5)
prs valence
BSF,
F,
-
where ae
be proportional p,
-xp,, 6
N_
C
(6)
5 t,
=
q
correlatione
%*
ring current
ie the
screening -
of
to the energy
( AEPi) r”P
e*g*
between the value6
form of the empirical
+
expressee the influence
from pi electron
ie defined
a proportionality
+
“qr
clam
da,= A and dbrs= B, where
a ( OEPI) r
could
angular and non-angu-
might be rewritten
+
:
characteristic8
the cyclic
(1311, respectively. eq.(4)
approximately
dbra
Pr,
and compoundr one can aaeume that
the Coulson
magnetic
within
(3)
a8 structural
For instance
approximately
definition
(AEPQ c
a general
with
perturbatione
8
*
da, and dbrI
have the dar and dbrI
euppose
with local
ae
2~Predbre+~~re,rs(dbre)2+***
the second-order
where the values
priate
can be defined
can write
( A@),
If
bond6 r-6
relation8hipe
one
one get8
connected
+
r
HYO method (12))
Including
(nEPi)r
of the two
:
According
A and B are
~ZVJIIthe perturbation
hand the value
bonded via
( AEpi) rm
lar
arise
AEgk
and
pi-electrononergier being
the r-th
molecule,
AEFi
(AEPilr between
( see (15)
*
and t,. t,
of the appro-
where Hr ie
conetant
ctandard
external
the lo-
Section
(15)
and
one can ale0 Ualng
eq.(6)
and the reactivity
No.47
4111
indices qr and Fr
can be
obtained :
tr(ppm) =
a qr +
b Fr
+
c
(7)
which has been found for nonalternanthgdrocarboneand iona (2). For the benzenoid hydrocarbon8 qr = 1 (5,6) and one get8 t,(ppm) =
b F,
+
c'
(8)
which is In a good agreementwith the correlationfound ( correlationcoefficient r = 0.970 ) (1). On the other hand, if the reeonance terma In the perturbationlxpaneion (3) are not taken into cormideration,one gets the #imp10 relation I
provided the dbrs values are not significantor are aesumed to m
linearly
with the atomic terms. Thus applying an assumptioneimilar to that made In eq.(6), one can obtain the linear relation, t,(ppm) = a,, 9Krr ,
+
conet.
(10)
which give8 a good correlationcoefficient,r = 0.977 (1). The originalmethod8 for chemical-shiftcalculationsbased on HMO theory were proposed by Pople (10) and YcWeelly (11). Our procedure could be coneidered as an extreme simplificationof the LLcWeenytheory which leada to the following expressionfor the proton screening conetent (15) : r) ra,8tu,rr,r8,rt, u
(11)
where fl and f2 are algebraic functions of ar8a and distance parameters8rs, stu and rr,r8,rt,ru,reap* Separating the first term in eq.(ll) into the dlfferent term8 for r = 8
oy
and r # s
one arrives at eq.(12) :
=
+
qr f;
>
b P,,
fl
(12)
l-P8
which appears to be equivalentto eqs.(5) and (7) provided the functionsfl and f; are approximatelyconstant for a given kind of position and only the neighbouring e-terms are taken into consideration.
Analogous
4112
No.47
aerumptionstaking the second term in eq.(ll) tion8hipeof the kind
(10) or (91,
into
amount
give
rise
to rela-
respectively.
REFERENCES
1.
J.Kuthan, Coll.C8echoelov.Chem.Camm., 2, 1222 (1968).
2.
J.Kuthan, Z.DonnerovAand V.SkBla, E,
3.
J.Kuthan, ibid., 35, 714 (1970).
4.
K.D.Bartleand D.W.Jone8,J.Phys.Chea.,72, 293 (1969).
5.
C.A.Couleonand G.R.Rwshbrooke,Proc.CslPbridge Phil.Soc., 36, 1931 (19401.
6.
A.Brickstockand J.A.Pople,Trane.Ferad.Soc.,50, 901 (1954).
7.
1.C.Smit.h and W.G.Schneider,Can.J.Chem.,3, 1158 (1958).
8.
G.Fraenkel,R.A.Carter,A.McLachlanend J.H.RichaFds,J.Am.Chem.Soc.,-i 82,
32, 2398 (1969).
5846 (1960). 9.
R.Spieseckeand W.G.Schneider,TetrahedronLetters, 1961, 468.
10. J.A.Pople,Yol.Phyi.,L,,175 (1958). Yol.Phys.,1, 311 (1958). 11. R.NcWeeray, I 12. E.Heilbronnerand H.Bock, Da8 HMC-ModellUral 8eine Anuendung, und
Grundlagen
Hmdhabung, Verlag-Ch8mi8,Weinheim, 1968.
13. R.H.Hartin,Tetrahedron,22, 897 (19641. 14. C.A.Coulson,Disc.Farad.Soc.,2, 9 (1947). 15. J.D.Yemory,Qumtm Inc., New York,
Theory of Uagnetio Re8onanceParametere,YoGrav-Hill
St.Louie,San Franoisca,London, Sydney, 1968.