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A study of the mechanism of the substituent effect in substituted benzenes by the group function method
Journal of Molecular Structure,
39 (1977) 139-144 OElsevier Scientific Publishing Company, Amsterdam
- Printed in The Netherlands
A STUDY OF THE MECHANISM OF THE SUBSTITUENT SUBSTITUTED BENZENES BY THE GROUP FUNCTION
JOZEF
-0
and VILIAM
Polymer
Institute
KLIMO
of the Slovak Academy
(Received 29 November
EFFECT IN METHOD
of Sciences,
809 34 Bratislaua (Czechoslovakia)
1976)
ABSTRACT The group function method in the INDO approximation is used for studying the substituen effect in three substituted benzenes. For NH,, OH and F substituents the n-inductive, u-inductive, and resonance effects are calculated. INTRODUCTION Although the most general parameter characterizing substituents is the Hammet u constant, deeper insight into the mechanism of their effect is still a matter of investigation. Several such mechanisms have been discussed [ 1] ; however it is not easy to examine the individual effects separately. Since there is no standard nomenclature for substituent effect, in the present paper we use, in accord with Dewar [ 51, the following classification for the individual effects of substituents: (i) n-inductive effect (I) - substituent forms a polar u-bond to the adjacent conjugated carbon atom thus affecting the n-electron density of a molecule; (ii) o-inductive effect - as in (i); the changes in the u-system are followed; (iii) ekctromeric (resonance) effect (E) of substituents with n-electrons able td interact with electrons of the conjugated system. Kang et al. [!& 31 employed a theory of molecular orbit& to point out that the o-constants correlate with simple indices of the MO theory. Here they used the idea of separating a u-constant into two independent components: field (F) and resonance (R) components in terms of the relation u = OR + bF [4,5]. They obtained a good correlation between u constants and r-electron density by a proper choice of representation of these components for various substituents. Clark and Emsley [6] studied sub&ituted benzenes by the PPP method. These authors calculated n-inductive and resonanceeffecta’by appropriate modification of the valelice state ionization potentials.- The compared the results of the calculations with ‘H and ‘% chemical shifts at the position pam to the substituents, kit&the transition energies and oscillator strengths. In the
140
present paper, we inve_stigatethe effect of benzene substituents on the change of the 5~-and u-electron densities in the individual positions separately for all the effects mentioned ((i)-(iii)). We use the group function method, in which the R- and o-systems are solved separately in terms of the method derived by McWeeny [7] in the INDO approximation. METHOD OF CALCULATION
AND PARAMETERS
Molecules with weakly interacting groups of electrons can be solved by the generalized group function method used by McWeeny [7], who also used the method for studying heterocyclic compounds [S]. He divided the systems investigated into 7r-and o-electron parts, the total wavefunction being written as a product of the respective group functions ti =MA
[@,@,I
(1)
where A is the antisymmetrizer and M the normalizing coefficient. $J, and 9, are the antisymmetric functions describing IV, u-electrons and lV, Ir-electrons, respectively. The total energy E = Ef!,, +F=E=+E&
=En+E=+E-
(2)
where
where hgff(i) = h(i) + J”(i) -P(i), h(i) being the one-electron and g(ij) two-electron parts of the Hamiltonian and E” is calculated from both d, and Hamiltonian h(i) for electron in field of “bare” nuclei. Similar relations are valid for the rr-system. For studying substituent effects in benzene, the NH2, OH and F substituents are used. The effect of u- and n-electrons of substituents on changes in n- or u-electron densities in benzene is followed. In the first place we calculate 9, and @, of benzene (A) and then $I,“” and #zB (B), where XB is the respective substituted benzene. To solve the influence of a substituent without x-electrons on & of benzene the calculation is adapted so that the n-electrons of the substituent are omitted from the n-system and included in the core Hamiltonian (C). Thus the possibility arises of determining the changes in R- and u-electron densities of benzene according to the individual effect (( i)-(iii)) (see above). The INDO ,method is used [ 91. Interatomic distances: r,, = 1.4 A, r-H = 1.08 A, r,, = 1.36 A (phenol), r-H = 0.96 A (phenol), rc__F= 1.33 A, r-N = 1.40 A (aminobenzene), ~N-H = 1.01 A, valence angles 120”. We assume that all the systems considered are planar*. *It followsfrom the experiment thataminobenzeneis not planar[lo].
RESULTS
AND DISCUSSliON
Kahitaky and Topsom [l] classifiedthe possiblemechanismsof the substituenteffect on electron densitiesof the P and u-systems,respectwely, into 7 types, 4 of which can be determinedby our calculation. (1) Tbe changeof the electron density in the n-system of benzeneresulting from the n-inductiveeffect. (Calculation(C) for &,-changewith respect to benzene.) (2) The change of electron densitiesin the n-system of benzene resulting from the resonanceeffect. (The resultsof calculation(C) are subtracted from the resultsof (B) for $J,_) (3) The changeof electron densitiesin the u-system of benzene resulting from the u-inductiveeffect. (Calculation(C) for @,-change with respectto benzene.) (4) The changeof electron densitiesin the u-system of benzeneresulting from the interactionwith the substituentn-electrons.(Results of calculation (C) are subtractedfrom the resultsof calculationfB) for rp,.) In these effects, both the direct interactionof the substituentelectrons with II- and o-electronsof benzene and the indirect interaction of these electronsby U-R and n-u pol~ations, respectively,are included. In calculation(C), n-electronsare included in the core H~~toni~ and therefore the resultsrepresentthe n-inductiveeffect. Table 1 presents quantitativeexpressionof this effect as givenby the INDO method. No uniform scheme can be determinedfor its descriptionbecausein all three casesdifferent resultsare obtainedcaused by the el~ctronegativi~ of substituents. The resonanceeffect shows at all positionsa descendingtendency from the NH2substituentthroughOH to fluorine,whichis in line with 0: constantsf I It causesan increasein the election density compared to benzene in the orthoandparu-positionsand a decreasein the me&-position. This is the effect most frequentlystudiedin the chemistryof unsaturatedcompounds and the resultsobtained do not go beyond the assumedlimit. The a-inductiveeffect and the effect of n-electronsof substituentson the u-systemsare listed in Table 2, The o-inductiveeffect decreaseswith djstaneeas has been assumedin ref. 1; the only exception is the para-position wherethe decreaseis not in accord with the scheme S+‘&5-(o) S&6’ (m) 6666- (p). The valuesat the pam-positionsdiffer only slightly from the valuesat meta-positions. The effect of s-electrons of substituentson a-electrondensitiesis largest in ortho-positions.It is negligiblein the me&z-position.A relativelyhigh value is m the hum-positionwhich is In agreementwith the resonanceeffect. Discussionabout the mentionedeffects should be continued. It would be ~ter&jng not only to look at the n-inductiveeffect as a whole but also to differentiatethe part causedby polarizationof the o-frameworkand the rest of the effect. Smilarly in ref. 1 the resonanceeffect was divided into
0.02757 -0,085Ol 0.06492
4 6 6,
0.02414 -0,07020 0,062Ol
-0.06361 -0,04117 0.02341
(B)
I
2
0I 43
0.02400 -0.08027 0.06113
0.00367 -0.00474 0.00379
i-e
-0.08024 -0.06601 0.02400
-0.00474 -0.00146 0.00367
cavorting to this scheme
(D)
(C)
OH
-caieuIation of the whole ~u~t~tu~d system, L(C)- without effect of the n.electrons of substituent. (D!- effect of n-electrons of substituent ((ID) = (B) - (C)).
annotation
I1 b(S3)
-0.08601 -0,06747 0.02%7
(B)
NH,
1 z,
Position (D)
0.00602 -1).00572 -0.00166
(C)
-0.04361 -0,00029 -0.02454 0.01996 0.00467 0.00682
(B)
F
0.01996 0.00467 0,01912 -0.06448 -0.04861 -0.06030 0,06089 -0.01469 0.06356
-0.00216 -0.06145 0.00382 0.00069 -0.04176 0.01969
(C)
Changes in n-electron densities in benzene ~sulting from substitutiona~b
TABLE 1
0,01629 -0.04831 0,lOMl
-0.04832 -0.03036 0.01629
(D)
143 TABLE
2
Changes in u-electron Position
densities
in benzene
NH,
resulting
from substitutiona
OH
F
09
CD)
(B)
(C)
(D)
(B)
u-3
1 :
0.0109 -0.0006 0.0157
-CL0139 -aooo7 -0.ooo2
a0248 -a0004 a0164
4 5 6
-0.0006 -0.0109 0.0664
-a0002 -0.0139 0.0868
60004 0.0246 -0.0004
-a004 0.0023 0.009 a0036 -0.0116 0.1567
-a0214 a0028 -O.O028 a0031 -0.0302 0.1466
a0174 -0.0005 Q0118 aooo5 a0187 0.0091
-a0217 0.0063 a0021 0.0063 -0.0317 0.2321
-a0354 0.0062 -0.0061 o.oo62 -0.0354 0.2182
‘Denotations
(D) 0.0137 a0001 a0082 0.0001 0.0137 00139
(B), (C), (D) as in Table 1.
more contributions. Here only summary effects can be given. The resonance effect agrees well not only with the theories available so far but also with the results of NMR spectroscopy. The respective ok constants at the parapositions and ‘H changes in chemical shifts with respect to benzene (Table 3) correspond best to this change in the n-electron density as a result of substitution. The u-inductive effect diminishes with distance as has been assumed but the sign alternation occurs (except for aniline) which has been predicted by Katritzky and Topsom [1] for the systems studied by us. Quantum-chemical methods have advantages of not being confined only to monosubstituted compounds studied and enabling a better insight into the mechanism of the substituent effect. As soon as we succeed in reducing substi-
TABLE
3
Changes in n-electron densities in substituted henzenes, ub constants and respective changes of the chemical
shifts
Suhstituents
AqR 0
NH*
m
P 0
(0) OH ;“m)
P 0
F
with respect
m P
a
-0.080 0.024 -0.056
to benzene
(p.p.m.)
ohb
A.Q~ c
AoH
0.057
-0.085 0.027 -0.057
0.587-0.755 0.135-0.25 0.553-0.65
-0.064
0.55-0.72
-0.061 -0.064 0.019
0.023
0.12-0.208
0.019
-6.042 -0.048 0.015 -0.030
0.641
-0.041
0.44-0.48
0.034
-0.049 0.020 -9.024
0.308-0.537 0.022-0.079 0.217-0.289
Whsngks of rr-ekctr& densities &aulting from the resonance effect. bTaken from ref. 1. =Total change of nelectron densities resulting from substitution.
[l)
144
tution constants to quantum-chemical indices, as seen, e.g., from Table 3, the study of the substitution effect will be much easier and also possible for more complicated polysubstituted compounds. REFERENCES 1 2 3 4 5 6 7 8
9 10
A. R Katritzky and R. D. Topsom, J. Chem. E&c., 48 (1971) 427. S. Kangand D. L. Beoeridge, Theor. Chim. Acta, 22 (1971) 312. S. Kang and M. I-L cho, Int. J. Quantum Chem. Symp., 7 (1973) 319. M. J. S. Dewar, Hy~~onjuga~on, Ronald Press, New York, 1962. M. J. S. Dewar, The Molecular Orbital Theory of Organic Chemistry, McGraw-Hill, New York, 1969. D. T. Clark and J. W. Emsley, Mol. Phys.. 12 (1967) 365. R. McWeeny, F&v. Mod. Phys., 32 (1960) 335. R McWeeny, in E. D. Bergman and 3. PuBman (Bds.), Quantum Aspects of Heterocyclic Compounds in Chemistry and Biochemistry, Vol. II, The Jerusalem Symposia on Quantum Chemistry and Biochemistry, 3erusalem, 1970, p. 65. J. A.. Pople and D. L. Beveridge. Approximate MoIecdar Orbital Theory, McGraw-Hill, New York, 1970. D. G. Lister and J. K. Tyler. J. Chem. Sot. Chem. Commun.. (1966) 152.
39 (1977) 139-144 OElsevier Scientific Publishing Company, Amsterdam
- Printed in The Netherlands
A STUDY OF THE MECHANISM OF THE SUBSTITUENT SUBSTITUTED BENZENES BY THE GROUP FUNCTION
JOZEF
-0
and VILIAM
Polymer
Institute
KLIMO
of the Slovak Academy
(Received 29 November
EFFECT IN METHOD
of Sciences,
809 34 Bratislaua (Czechoslovakia)
1976)
ABSTRACT The group function method in the INDO approximation is used for studying the substituen effect in three substituted benzenes. For NH,, OH and F substituents the n-inductive, u-inductive, and resonance effects are calculated. INTRODUCTION Although the most general parameter characterizing substituents is the Hammet u constant, deeper insight into the mechanism of their effect is still a matter of investigation. Several such mechanisms have been discussed [ 1] ; however it is not easy to examine the individual effects separately. Since there is no standard nomenclature for substituent effect, in the present paper we use, in accord with Dewar [ 51, the following classification for the individual effects of substituents: (i) n-inductive effect (I) - substituent forms a polar u-bond to the adjacent conjugated carbon atom thus affecting the n-electron density of a molecule; (ii) o-inductive effect - as in (i); the changes in the u-system are followed; (iii) ekctromeric (resonance) effect (E) of substituents with n-electrons able td interact with electrons of the conjugated system. Kang et al. [!& 31 employed a theory of molecular orbit& to point out that the o-constants correlate with simple indices of the MO theory. Here they used the idea of separating a u-constant into two independent components: field (F) and resonance (R) components in terms of the relation u = OR + bF [4,5]. They obtained a good correlation between u constants and r-electron density by a proper choice of representation of these components for various substituents. Clark and Emsley [6] studied sub&ituted benzenes by the PPP method. These authors calculated n-inductive and resonanceeffecta’by appropriate modification of the valelice state ionization potentials.- The compared the results of the calculations with ‘H and ‘% chemical shifts at the position pam to the substituents, kit&the transition energies and oscillator strengths. In the
140
present paper, we inve_stigatethe effect of benzene substituents on the change of the 5~-and u-electron densities in the individual positions separately for all the effects mentioned ((i)-(iii)). We use the group function method, in which the R- and o-systems are solved separately in terms of the method derived by McWeeny [7] in the INDO approximation. METHOD OF CALCULATION
AND PARAMETERS
Molecules with weakly interacting groups of electrons can be solved by the generalized group function method used by McWeeny [7], who also used the method for studying heterocyclic compounds [S]. He divided the systems investigated into 7r-and o-electron parts, the total wavefunction being written as a product of the respective group functions ti =MA
[@,@,I
(1)
where A is the antisymmetrizer and M the normalizing coefficient. $J, and 9, are the antisymmetric functions describing IV, u-electrons and lV, Ir-electrons, respectively. The total energy E = Ef!,, +F=E=+E&
=En+E=+E-
(2)
where
where hgff(i) = h(i) + J”(i) -P(i), h(i) being the one-electron and g(ij) two-electron parts of the Hamiltonian and E” is calculated from both d, and Hamiltonian h(i) for electron in field of “bare” nuclei. Similar relations are valid for the rr-system. For studying substituent effects in benzene, the NH2, OH and F substituents are used. The effect of u- and n-electrons of substituents on changes in n- or u-electron densities in benzene is followed. In the first place we calculate 9, and @, of benzene (A) and then $I,“” and #zB (B), where XB is the respective substituted benzene. To solve the influence of a substituent without x-electrons on & of benzene the calculation is adapted so that the n-electrons of the substituent are omitted from the n-system and included in the core Hamiltonian (C). Thus the possibility arises of determining the changes in R- and u-electron densities of benzene according to the individual effect (( i)-(iii)) (see above). The INDO ,method is used [ 91. Interatomic distances: r,, = 1.4 A, r-H = 1.08 A, r,, = 1.36 A (phenol), r-H = 0.96 A (phenol), rc__F= 1.33 A, r-N = 1.40 A (aminobenzene), ~N-H = 1.01 A, valence angles 120”. We assume that all the systems considered are planar*. *It followsfrom the experiment thataminobenzeneis not planar[lo].
RESULTS
AND DISCUSSliON
Kahitaky and Topsom [l] classifiedthe possiblemechanismsof the substituenteffect on electron densitiesof the P and u-systems,respectwely, into 7 types, 4 of which can be determinedby our calculation. (1) Tbe changeof the electron density in the n-system of benzeneresulting from the n-inductiveeffect. (Calculation(C) for &,-changewith respect to benzene.) (2) The change of electron densitiesin the n-system of benzene resulting from the resonanceeffect. (The resultsof calculation(C) are subtracted from the resultsof (B) for $J,_) (3) The changeof electron densitiesin the u-system of benzene resulting from the u-inductiveeffect. (Calculation(C) for @,-change with respectto benzene.) (4) The changeof electron densitiesin the u-system of benzeneresulting from the interactionwith the substituentn-electrons.(Results of calculation (C) are subtractedfrom the resultsof calculationfB) for rp,.) In these effects, both the direct interactionof the substituentelectrons with II- and o-electronsof benzene and the indirect interaction of these electronsby U-R and n-u pol~ations, respectively,are included. In calculation(C), n-electronsare included in the core H~~toni~ and therefore the resultsrepresentthe n-inductiveeffect. Table 1 presents quantitativeexpressionof this effect as givenby the INDO method. No uniform scheme can be determinedfor its descriptionbecausein all three casesdifferent resultsare obtainedcaused by the el~ctronegativi~ of substituents. The resonanceeffect shows at all positionsa descendingtendency from the NH2substituentthroughOH to fluorine,whichis in line with 0: constantsf I It causesan increasein the election density compared to benzene in the orthoandparu-positionsand a decreasein the me&-position. This is the effect most frequentlystudiedin the chemistryof unsaturatedcompounds and the resultsobtained do not go beyond the assumedlimit. The a-inductiveeffect and the effect of n-electronsof substituentson the u-systemsare listed in Table 2, The o-inductiveeffect decreaseswith djstaneeas has been assumedin ref. 1; the only exception is the para-position wherethe decreaseis not in accord with the scheme S+‘&5-(o) S&6’ (m) 6666- (p). The valuesat the pam-positionsdiffer only slightly from the valuesat meta-positions. The effect of s-electrons of substituentson a-electrondensitiesis largest in ortho-positions.It is negligiblein the me&z-position.A relativelyhigh value is m the hum-positionwhich is In agreementwith the resonanceeffect. Discussionabout the mentionedeffects should be continued. It would be ~ter&jng not only to look at the n-inductiveeffect as a whole but also to differentiatethe part causedby polarizationof the o-frameworkand the rest of the effect. Smilarly in ref. 1 the resonanceeffect was divided into
0.02757 -0,085Ol 0.06492
4 6 6,
0.02414 -0,07020 0,062Ol
-0.06361 -0,04117 0.02341
(B)
I
2
0I 43
0.02400 -0.08027 0.06113
0.00367 -0.00474 0.00379
i-e
-0.08024 -0.06601 0.02400
-0.00474 -0.00146 0.00367
cavorting to this scheme
(D)
(C)
OH
-caieuIation of the whole ~u~t~tu~d system, L(C)- without effect of the n.electrons of substituent. (D!- effect of n-electrons of substituent ((ID) = (B) - (C)).
annotation
I1 b(S3)
-0.08601 -0,06747 0.02%7
(B)
NH,
1 z,
Position (D)
0.00602 -1).00572 -0.00166
(C)
-0.04361 -0,00029 -0.02454 0.01996 0.00467 0.00682
(B)
F
0.01996 0.00467 0,01912 -0.06448 -0.04861 -0.06030 0,06089 -0.01469 0.06356
-0.00216 -0.06145 0.00382 0.00069 -0.04176 0.01969
(C)
Changes in n-electron densities in benzene ~sulting from substitutiona~b
TABLE 1
0,01629 -0.04831 0,lOMl
-0.04832 -0.03036 0.01629
(D)
143 TABLE
2
Changes in u-electron Position
densities
in benzene
NH,
resulting
from substitutiona
OH
F
09
CD)
(B)
(C)
(D)
(B)
u-3
1 :
0.0109 -0.0006 0.0157
-CL0139 -aooo7 -0.ooo2
a0248 -a0004 a0164
4 5 6
-0.0006 -0.0109 0.0664
-a0002 -0.0139 0.0868
60004 0.0246 -0.0004
-a004 0.0023 0.009 a0036 -0.0116 0.1567
-a0214 a0028 -O.O028 a0031 -0.0302 0.1466
a0174 -0.0005 Q0118 aooo5 a0187 0.0091
-a0217 0.0063 a0021 0.0063 -0.0317 0.2321
-a0354 0.0062 -0.0061 o.oo62 -0.0354 0.2182
‘Denotations
(D) 0.0137 a0001 a0082 0.0001 0.0137 00139
(B), (C), (D) as in Table 1.
more contributions. Here only summary effects can be given. The resonance effect agrees well not only with the theories available so far but also with the results of NMR spectroscopy. The respective ok constants at the parapositions and ‘H changes in chemical shifts with respect to benzene (Table 3) correspond best to this change in the n-electron density as a result of substitution. The u-inductive effect diminishes with distance as has been assumed but the sign alternation occurs (except for aniline) which has been predicted by Katritzky and Topsom [1] for the systems studied by us. Quantum-chemical methods have advantages of not being confined only to monosubstituted compounds studied and enabling a better insight into the mechanism of the substituent effect. As soon as we succeed in reducing substi-
TABLE
3
Changes in n-electron densities in substituted henzenes, ub constants and respective changes of the chemical
shifts
Suhstituents
AqR 0
NH*
m
P 0
(0) OH ;“m)
P 0
F
with respect
m P
a
-0.080 0.024 -0.056
to benzene
(p.p.m.)
ohb
A.Q~ c
AoH
0.057
-0.085 0.027 -0.057
0.587-0.755 0.135-0.25 0.553-0.65
-0.064
0.55-0.72
-0.061 -0.064 0.019
0.023
0.12-0.208
0.019
-6.042 -0.048 0.015 -0.030
0.641
-0.041
0.44-0.48
0.034
-0.049 0.020 -9.024
0.308-0.537 0.022-0.079 0.217-0.289
Whsngks of rr-ekctr& densities &aulting from the resonance effect. bTaken from ref. 1. =Total change of nelectron densities resulting from substitution.
[l)
144
tution constants to quantum-chemical indices, as seen, e.g., from Table 3, the study of the substitution effect will be much easier and also possible for more complicated polysubstituted compounds. REFERENCES 1 2 3 4 5 6 7 8
9 10
A. R Katritzky and R. D. Topsom, J. Chem. E&c., 48 (1971) 427. S. Kangand D. L. Beoeridge, Theor. Chim. Acta, 22 (1971) 312. S. Kang and M. I-L cho, Int. J. Quantum Chem. Symp., 7 (1973) 319. M. J. S. Dewar, Hy~~onjuga~on, Ronald Press, New York, 1962. M. J. S. Dewar, The Molecular Orbital Theory of Organic Chemistry, McGraw-Hill, New York, 1969. D. T. Clark and J. W. Emsley, Mol. Phys.. 12 (1967) 365. R. McWeeny, F&v. Mod. Phys., 32 (1960) 335. R McWeeny, in E. D. Bergman and 3. PuBman (Bds.), Quantum Aspects of Heterocyclic Compounds in Chemistry and Biochemistry, Vol. II, The Jerusalem Symposia on Quantum Chemistry and Biochemistry, 3erusalem, 1970, p. 65. J. A.. Pople and D. L. Beveridge. Approximate MoIecdar Orbital Theory, McGraw-Hill, New York, 1970. D. G. Lister and J. K. Tyler. J. Chem. Sot. Chem. Commun.. (1966) 152.