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A new index for estimating the relative stability of carbonium ions
Journal of Molecular Structure (Theochem), 119 (1985) 379-382 EIsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands
Short communication
A NEW INDEX FOR ESTIMATING CARBONIUM IONS
CA1 JINFENG
THE RELATIVE
STABILITY
OF
and CA1 WENZHENG
Department of Chemistry, South China Normal University, (People’s Republic of China)
Guangzhou
(Received 2 April 1984)
ABSTRACT A new index, BEZ~, is suggested for estimating the relative stability of carbonium ions. To confii the validity of the new index, more than 100 different carbonium ions L_-_ __l_..l_L__l L__ --&L--I r-+-_,l..“:^-” UK= ^“^ 1.1 :.. guuu ,.,,A auLvvUl=Ur . ..“..............+ .&CL nave L__“eel, CaKulaLeu uy LL^ Ult: nlWlT\T\ l”,lYU” I‘ItXu”U. ~“‘,~,UD,“IID “&till recognized facts.
Many traditional concepts [l] have been used to explain the stability of carbonium ions. These include inductive effect, charge distribution, conjugation effect, hyperconjugation effect, negative hyperconjugation effect, etc.; all of these lack a quantitative dimension and involve arbitrary decisions in their application. Thus in most cases it is difficult to account for the relative stability of carbonium ions; for instance, how to ascertain which one of the following csrbonium ions is the most stable: CHz=CH-CH+-CF3, (CHs)&H+ and
This type of problem cannot be solved with traditional concepts. It is therefore necessary to find a quantitative dimension for estimating the relative stability of carbonium ions. From a study of fundamental principles and MO calculations of quantum organic chemistry, we suggest a new index ZEZ,, equivalent to the sum of the resonance integral contribution energy of the active center C+ with all other atoms in a carbonium ion, to estimate the relative stability of .carbonium ions. This suggestion is based on two theoretical aspects: (a) The resonance integral contribution energy Ezs is closely related to the interaction of two atoms. It is the chief characteristic of covalent bonds [ 21. We have
0166-1280/85/$03.30
0 1985 Eisevier Science Publishers B.V.
where P,,” and HPy are the density matrix element and resonance integral which correspond to the atomic orbit&, p and Y. (b) The carbon atom C’ is the most active center in a carbonium ion, its relationships with other atoms must therefore be correlated to the stability of the carbonium ions. Therefore, we suggest index L?Z,, R for estimating the relative stability of the carbonium ions. As an example the stabilities of CH& and CH,CHl will L,. ,,...1,..1,+-rl Ut:I;~Gu.lIIWU. For CH:,
3H,. ,C;-H1 4H
ZE& = EFI + EF3 + ET4 = -0.4437
- 0.4437 - 0.4437
= -1.3311 H3 H? and for CH,CH& Hq- C2- C: l&H 5
6
XE;B=Ez+Ez+E;+E;+Eg+E: = -0.5299
+ 0.0059 + 0.0008 + 0.0008 - 0.4447 - 0.4445
= -1.4116 In this work, the relative stabilities of more than 100 carbonium ions (including primary, secondary and tertiary carbonium ions) have been calculated by the MNDO method. For illustration a number of examples are given below: Comparison of primary carbonium ions Example 1. CH,CHi and its fluorine derivative Relative stability: CH$H2+ > CF,CH: W&
-1.4116
-1.3750
Index ZEza represents the inductive effect correctly. Example 2. Relative stability: CH3CH2CH2+ < CH,=CH-CH=CH-CH:
=EB
-1.4101
-1.5220
Index XE& shows that the conjugation’effect
stabilizes the carbonium ion.
381
Example Relative stability: 2
CH~CH~CH~CH$
<
-1.5204
-1.4092
=%B
cn$
Index ZE:, corresponds to the conjugation effect of the benzene ring. Example 4. Relative stability: CH&H=CH+ZH: -1.5147
=:s
c* < 0 o-1.5204
Index ZEtB indicates that the stabilization effect of CH,CH=CH’- is less than that of
A 0-
Comparison of the relative stability of secondary carbonium ions Example 5. Relative stability: CHBCH%HJ > CFBCH%HB > CFJCH%FB -1.4831
=%B
-1.4082
-1.4569
Index ZE& indicates that the more F atoms in the e-position, the greater t.hhp mwdiv~ “IA., “‘V”....m._
hvnprconillsntion --J r______,-b--‘____
effect _--__ 1 and -_-
the _--_
kc, the _-_LL ----
stabifitv. --------d
-
Example 6. Relative stability: CH3CH+CH&H3 < CH3CH+CH=CH2 -1.4810
=ZB
-1.5763
< CH2=CHCH+CH=CHZ -1.6613 ZEEB shows that the more conjugation functional groups, the greater the stability. Example 7. O\CH
Relative stability:
Wh3
Ho -1.4746
O$H
CH$H+CH3
-=
HO
CHkHzCH3
-1.5843
In spite of the complication of these carbonium ions, index XEzB normally indicates that the direct connection of the benzene ring to C+ has a larger stabilizing effect than the indirect connection of the benzene ring.
382
Comparison of tertiary carbonium ions Example 8. Relative stability: (CH&C*> -1.5470
=%
(CF&C+ -1.4322
I;Ezx shows that the negative hyperconjugation effect of an F substituent makaa -...*I””
thhp oarhnninm _I” vu-VVIIAUIII
inn rlnctahln -“Ia UIIYVUVIb.
Comparison of different para-substituents of the benezene ring Example 9. Relative stability :
cng +C$
=2,
-1.5249
-1.5187
’
CH@C@
-1.5212
>
H-@C”:
>
-1.5204
-1.5148
Despite the slight effect of different functional groups at the pam-position, ZE&, can still be used to estimate the relative stability of the carbonium ions. CONCLUSIONS
From all the above examples and calculated results, we may conclude that the relative stability of carbonium ions increases while ZE& decreases. However, the relative stability decreases while ZEzB increases. This conclusion is in good agreement with the facts. Therefore, we consider that ZEF, is a good index for estimating the reiative stabiiities of carbonium ions. Use of ZEzx is particularly advantageous when a carbonium ion is simultaneously affected by several complicated substituent groups. Notes: (a) Here the MNDO program used here has already been applied in some papers published in J. Mol. Struct., Theochem. (b) The geometries of the models were chosen from Pople and Gordon’s standard geometry [ 31. REFERENCES 1 Q. Y. Jiang, Chem. Abstr., 97 (1982) 197531f; C. C. Chen, Chem. Abstr., 94 (1981) 156120r; F. A. Liu, Chem. Abstr., 94 (1931) 156121s; K. Okamoto, Chem. Abstr., 92 (1979) 197245n. 2 H. Fisher and H. Kolhnar, Theor. Chim. Acta, 16 (1970) 163. 3 J. A. Pople and M. S. Gordon, J. Am. Chem. Sot., 89 (1967) 4253.
Short communication
A NEW INDEX FOR ESTIMATING CARBONIUM IONS
CA1 JINFENG
THE RELATIVE
STABILITY
OF
and CA1 WENZHENG
Department of Chemistry, South China Normal University, (People’s Republic of China)
Guangzhou
(Received 2 April 1984)
ABSTRACT A new index, BEZ~, is suggested for estimating the relative stability of carbonium ions. To confii the validity of the new index, more than 100 different carbonium ions L_-_ __l_..l_L__l L__ --&L--I r-+-_,l..“:^-” UK= ^“^ 1.1 :.. guuu ,.,,A auLvvUl=Ur . ..“..............+ .&CL nave L__“eel, CaKulaLeu uy LL^ Ult: nlWlT\T\ l”,lYU” I‘ItXu”U. ~“‘,~,UD,“IID “&till recognized facts.
Many traditional concepts [l] have been used to explain the stability of carbonium ions. These include inductive effect, charge distribution, conjugation effect, hyperconjugation effect, negative hyperconjugation effect, etc.; all of these lack a quantitative dimension and involve arbitrary decisions in their application. Thus in most cases it is difficult to account for the relative stability of carbonium ions; for instance, how to ascertain which one of the following csrbonium ions is the most stable: CHz=CH-CH+-CF3, (CHs)&H+ and
This type of problem cannot be solved with traditional concepts. It is therefore necessary to find a quantitative dimension for estimating the relative stability of carbonium ions. From a study of fundamental principles and MO calculations of quantum organic chemistry, we suggest a new index ZEZ,, equivalent to the sum of the resonance integral contribution energy of the active center C+ with all other atoms in a carbonium ion, to estimate the relative stability of .carbonium ions. This suggestion is based on two theoretical aspects: (a) The resonance integral contribution energy Ezs is closely related to the interaction of two atoms. It is the chief characteristic of covalent bonds [ 21. We have
0166-1280/85/$03.30
0 1985 Eisevier Science Publishers B.V.
where P,,” and HPy are the density matrix element and resonance integral which correspond to the atomic orbit&, p and Y. (b) The carbon atom C’ is the most active center in a carbonium ion, its relationships with other atoms must therefore be correlated to the stability of the carbonium ions. Therefore, we suggest index L?Z,, R for estimating the relative stability of the carbonium ions. As an example the stabilities of CH& and CH,CHl will L,. ,,...1,..1,+-rl Ut:I;~Gu.lIIWU. For CH:,
3H,. ,C;-H1 4H
ZE& = EFI + EF3 + ET4 = -0.4437
- 0.4437 - 0.4437
= -1.3311 H3 H? and for CH,CH& Hq- C2- C: l&H 5
6
XE;B=Ez+Ez+E;+E;+Eg+E: = -0.5299
+ 0.0059 + 0.0008 + 0.0008 - 0.4447 - 0.4445
= -1.4116 In this work, the relative stabilities of more than 100 carbonium ions (including primary, secondary and tertiary carbonium ions) have been calculated by the MNDO method. For illustration a number of examples are given below: Comparison of primary carbonium ions Example 1. CH,CHi and its fluorine derivative Relative stability: CH$H2+ > CF,CH: W&
-1.4116
-1.3750
Index ZEza represents the inductive effect correctly. Example 2. Relative stability: CH3CH2CH2+ < CH,=CH-CH=CH-CH:
=EB
-1.4101
-1.5220
Index XE& shows that the conjugation’effect
stabilizes the carbonium ion.
381
Example Relative stability: 2
CH~CH~CH~CH$
<
-1.5204
-1.4092
=%B
cn$
Index ZE:, corresponds to the conjugation effect of the benzene ring. Example 4. Relative stability: CH&H=CH+ZH: -1.5147
=:s
c* < 0 o-1.5204
Index ZEtB indicates that the stabilization effect of CH,CH=CH’- is less than that of
A 0-
Comparison of the relative stability of secondary carbonium ions Example 5. Relative stability: CHBCH%HJ > CFBCH%HB > CFJCH%FB -1.4831
=%B
-1.4082
-1.4569
Index ZE& indicates that the more F atoms in the e-position, the greater t.hhp mwdiv~ “IA., “‘V”....m._
hvnprconillsntion --J r______,-b--‘____
effect _--__ 1 and -_-
the _--_
kc, the _-_LL ----
stabifitv. --------d
-
Example 6. Relative stability: CH3CH+CH&H3 < CH3CH+CH=CH2 -1.4810
=ZB
-1.5763
< CH2=CHCH+CH=CHZ -1.6613 ZEEB shows that the more conjugation functional groups, the greater the stability. Example 7. O\CH
Relative stability:
Wh3
Ho -1.4746
O$H
CH$H+CH3
-=
HO
CHkHzCH3
-1.5843
In spite of the complication of these carbonium ions, index XEzB normally indicates that the direct connection of the benzene ring to C+ has a larger stabilizing effect than the indirect connection of the benzene ring.
382
Comparison of tertiary carbonium ions Example 8. Relative stability: (CH&C*> -1.5470
=%
(CF&C+ -1.4322
I;Ezx shows that the negative hyperconjugation effect of an F substituent makaa -...*I””
thhp oarhnninm _I” vu-VVIIAUIII
inn rlnctahln -“Ia UIIYVUVIb.
Comparison of different para-substituents of the benezene ring Example 9. Relative stability :
cng +C$
=2,
-1.5249
-1.5187
’
CH@C@
-1.5212
>
H-@C”:
>
-1.5204
-1.5148
Despite the slight effect of different functional groups at the pam-position, ZE&, can still be used to estimate the relative stability of the carbonium ions. CONCLUSIONS
From all the above examples and calculated results, we may conclude that the relative stability of carbonium ions increases while ZE& decreases. However, the relative stability decreases while ZEzB increases. This conclusion is in good agreement with the facts. Therefore, we consider that ZEF, is a good index for estimating the reiative stabiiities of carbonium ions. Use of ZEzx is particularly advantageous when a carbonium ion is simultaneously affected by several complicated substituent groups. Notes: (a) Here the MNDO program used here has already been applied in some papers published in J. Mol. Struct., Theochem. (b) The geometries of the models were chosen from Pople and Gordon’s standard geometry [ 31. REFERENCES 1 Q. Y. Jiang, Chem. Abstr., 97 (1982) 197531f; C. C. Chen, Chem. Abstr., 94 (1981) 156120r; F. A. Liu, Chem. Abstr., 94 (1931) 156121s; K. Okamoto, Chem. Abstr., 92 (1979) 197245n. 2 H. Fisher and H. Kolhnar, Theor. Chim. Acta, 16 (1970) 163. 3 J. A. Pople and M. S. Gordon, J. Am. Chem. Sot., 89 (1967) 4253.