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On some features of electron density distributions in unsaturated hydrocarbons
113
Journal of Molecular Structure (Theochem), 284 (1993) 113-122 0166-1280/93/%06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved
On some features of electron density distributions unsaturated hydrocarbons
in
Natalia A. Ogorodnikova A.N. Nesmeyanov Institute of Organo-Element Compounds, Russian Academy of Sciences, 2% Vavilov Str., Moscow 117813, Russian Federation (Received 9 July 1992; in final form 28 October 1992) Abstract A comparative analysis of electron density distributions derived from ab initio MO calculations was carried out for substituted ethylenes, substituted benzenes, Csubstituted styrenes, 4-substituted P,&difluorostyrenes, and ions of ally1 and trimethylenemethyl types. Changes in the atomic effective charges due to substitution or due to a direct variation in the number of electrons within a system were considered. Linear relationships were found between the rr and d components of the charge changes on an unsaturated carbon atom of a carbon chain. The regression coefficients proved to be negative. The regularities were found to be invariant with respect to both the level of ab initio calculation (3G, 4-3lG, 6-3lG, 6-3lG** and 6-31 l++G**) and the definition of the atomic charge (Bader’s criterion or the Mulliken approach). Data from ab initio MO calculations reported in the literature were used.
Introduction
Taft was the first to find out (CND0/2 [l]; ab initio, STO-3G [2]) that the r and g components of the atomic charges on the para-carbons of monosubstituted benzenes are linearly correlated. This feature of the charge density distributions of monosubstituted benzenes is invariant with respect to the level of ab initio calculation. Indeed, if one considers the changes in the para-carbon atom charges resulting from substitution, it appears that there are no statistically significant distinctions between the x/a regression lines (I), (2) and (3) (here and after, see Table 1) for the changes in the para-carbon atom charges in XCsHs in relation to benzene evaluated using the 3G [2], 4-31G [4] and 6-31G [5] basis sets, respectively (the atomic charges were obtained from the Mulliken populations [l 11). Moreover, these empirical regressions prove to be different evaluations of one and the same theoretical straight line. The regression line
for the total number of the observations for the para-carbon atom charges (3G, 4-31G and 631G) is the following: AqFPara = -0.55Aq,cPra + 0.003 N = 42; r = 0.994; S = 0.003
(4)
where AqfPra and AqzPra are the changes in the 7r and cr components of the para-carbon atom charges in XC6H5 in comparison with those in benzene [12]. Thus the charge appearing on the para-carbon atom in a monosubstituted benzene molecule as a result of a substitution divides into the r and LTcomponents in one and the same ratio [13], no matter what level of ab initio calculation (3G, 4-31G or 6-31G) is used. It can be seen that the sign of the regression coefficients in Eq. (1) t (4) is negative, i.e. the increase (decrease) in the 0 charge on an atom corresponds to the decrease (increase) in the x charge on that atom.
Aq::” = -0.58Aq:B
Aq?
Aq:O = -0.38AqFfl + 0.0006
(7)’
(8)’
Aq?
AqF-
(9)B
(lO)b-f
- 0.001
+ 0.0003
+ 0.0002
= -0.56Aq$‘“=’
= -0.75Aqp
= -0.79Aq(P
+ 0.0002
3G, 4-31G, 6-31G; Muhiken
3G; Mulhken
3G; Mu&ken
,&Carbon regression (for X see of XC6HS
X = NH2, OH, Me, H, F,
atoms of CHaCHX (for X see (5)) and of 4-XC&I&HCH2 regression (6)); pars-carbon atoms (for X see regressions (I), (2) and (3))
4-XC&I&HCF2: CFs, CN, NO,
4-XC6H4CHCH2: X = NH2 pl, NH2 py, OH, Me, H, F, CHO, CF,, CN, NO*
0.98
0.999
8 69
0.986
0.994
10
8
0.9995
0.982
10
19
CHzCHX: X = NH* pl, NH2 py, OMe, OH, F, Me, H, CHCH2, CCH, CN, CFs, CHO @is), CHO (trans), COMe (cis), COMe (trans), COCN, COCFs, NO, Nor
4-31G; Mulliken
(6)’
- 0.012
0.994
42
XC6HS: for X see regressions (l), (2) and (3)
3G, 4-31G, 6-31G; Mulliken
A,$@ = -0.54Aq:O
+ 0.003
(5Y
= -0.55Aqzp=
Aq?-
(4)b_d
0.995
19
XC6HS: X = O-, COO-, NH2, OH, Me, F, H, CHCHa, CHNH, CCH, CCF, CN, NC, CHO, CFO, COOH, NO, Nor, NH;
0.999
0.999
6-31G; Mulliken
+ 0.005
Aq:(4) = -0.55Aq;(4)
(3)d
12
r
13
+ 0.001
Aq:‘(4) = -0.53Aqzt4’
cv
XC6Hs: X = NH2 pl, NH2 py, OH, F, Me, H, CH*F, CFs, CN, CHO, NOz, NH;
N
XC6HS: X = NH2 pl, NH1 py, OMe, OH, F, Me, H, CHCHr, CCH, CN, NO, Nor, CHO
3G; Mulliken
Aq$(4) = -0.56Aq2c4)+ 0.~11
(1)”
Compounds
4-31G; Muhiken
Basis set; charge definition
Regression No.
q = bq’ + a
Table 1 Parameters of the regression equationsa q = ba + a
0.01
0.0002
0.0009
0.0006
0.0003
0.013
0.003
0.0038
0.001
0.001
S
q: = -0.81q:
(13)’
- 0.17
+ 0.11
+ 0.001
6-31 l++G**// 6-31G***, Bader
6-31G+**I Bader
3G; M&liken 0.03 1 0.096
0.97 0.96
7 15
CHrCHX: X = CHCHr, CO, NH2 (see text) Ions of ally1 and methallyl types and I-propyl anion (see Fig. 5)
0.002
0.99
43
Meta- and para-carbon atoms of XC6H5 (for X see regression (1)); C2 and C3 atoms of 4-XC&I.,CHCH~ (for X see regression (6))
a In the equations given, data from ab initio MO calculations reported in the literature were used. The present statistical analysis dealt with the regression equations in which the values of the regression coefficients and the free members, as well as the average values of the charges, the standard deviations (2, jj and A’) and the SSD, = (xi - n)2 values contained two more significant figures than in the table. For the correlations of the regression coefficients and the regression lines, standard statistical procedures were used [3]. The accepted confidence level is 5%; when the confidence level is otherwise, it is mentioned in the text. b The charge changes in relation to benzene from the data given in Ref. 2. ‘The charge changes in relation to benzene according to the data given in Ref. 4. d The charge changes in relation to benzene from the data given in Ref. 5. e Tbe charge changes in relation to ethylene according to the data given in Ref. 4. f Tbe charge changes in relation to styrene according to the data given in Ref. 6. g The charge changes in relation to /!?,&difluorostyrene according to the data given in Ref. 7. h The values of the charges were calculated [ 171using the data given in Ref. 8. i The values of the charges were calculated [17] using the data given in Refs. 9 and 10; see Fig. 5.
qy = -1.4qy
Aqzamm= -0.56Aq:-“
(12)h
(1 I)bpf
116
N.A. OgorodnikovajJ.
Mol. Struct. (Theochem)
284 (1993) 113-122
unsaturated hydrocarbons is invariant with respect to both the level of ab initio calculation used and the definition of the atomic charge applied. Results and discussion
x
-0.58
f6)
36,
i??Z.dC’hcn
-ai’9
(7)
3G,
iX!u~Lhm
- 0.75
(9)
3%
ZnldCC~Auz
Fig. 1, The relationships between the T and u components of the atomic charges derived from ab initio MO calculations. The coefficient, the number of the regression, the basis set level, and the definition of the atomic charge are given. For X and references, see Table 1.
In the present paper I show that a linear ratio between the r and CTcomponents of the charge changes on a carbon atom upon changes in the electron density distribution within a molecule, the regression coefficient being negative, is also characteristic of other unsaturated hydrocarbons. This feature of the electron density distributions of
The present study was concerned with the changes in the A and (Tcomponents of the carbon atom charges resulting from in particular a substitution in ethylene, styrene and /3,@difluorostyrene. The data on the carbon atom charges derived from ab initio calculations using the 4-31G (substituted ethylenes [4]) and 3G @-substituted styrenes [6] and /?,P-difluorostyrenes [7’j) basis sets were obtained from the literature (the atomic charges were taken from the Mulliken populations). It was found that the linear relationships, with the negative sign of the regression coefficients, were actually fulfilled between the changes in the x and u charges on the carbon atoms in these systems (see Table 1 and Fig. 1). Relation (5) is given for the pcarbon atom in substituted ethylenes (Fig. 2). Relations (6) and (8) are given for P-carbon atoms in styrenes and ,f3$-difluorostyrenes. Relations (7) and (9) correspond to a-carbon atoms in styrenes and P@difluorostyrenes, respectively. It should be emphasized that, despite the distinctions between the molecules and the basis set levels, not only the sign but also the value of the regression coefficients for the b-carbon atoms (even position) in substituted ethylenes (Eq. (5)) and styrenes (Eq. (6)), on the one hand, and for the a-carbon atoms (odd position) in substituted styrenes (Eq. (7)) and ,@difluorostyrenes (Eq. (9)), on the other hand, are equal. Indeed the regression coefficients (5) (4-31G) and (6) (3G) for the /?-carbon atoms do not differ significantly even at the 10% confidence level, and the free members of both regression lines are smaller than their standard deviations. Furthermore, there are no statistically significant differences between the regression lines for a-carbon atoms (7) and (9) (all 3G). The angle coefficients of these regressions do not differ significantly even at the 20% confidence level. Moreover, there are no statistically significant
117
N.A. Ugoro~~ovu~~. Mol. Stmct. fTkeoeke~~ 284 (1993) 113-122
Fig. 2. The correlation Q between the changesin the ?rand u com~nen~ of the charges (41on the @carbon atom in substitu~ ethylenes CH&HX in relation to ethylene. For X see the figure.
distinctions between the n/o regression lines for any of the even positions, i.e. the p-carbon atoms of ethylenes ((5), 4-31G), the p-carbon atoms of styrenes ((6), 3G), and the pars-carbon atoms of benzenes ((4), combined for the 3G, 4-31G and 631G levels). The regression line for the total number of observations (3G, 4-31G and 6-31G) for the
even positions is: AqFevan = -0.56Aa~cvcn - 0.001 (10) N = 69; r = 0.98; S = 0.01 where Aqfeven and Aq:““” are the changes in the even carbon atom charges in the substituted
118
N.A. OgorodnikovalJ. Mol. Struct. (Theochem) 284 (1993) 113-122
-0.03
-0.02
Fig. 3. The correlations between the R and u components of the charges [7] on the a-carbon atoms (0) (7) and P-carbon atoms (0) (6) of esubstituted ,!3#difluorostyrenes (4-XC6H&HCF2) in relation to those of P&difluorostyrene. For X, see the figure.
with those of compounds in comparison unsubstituted ones. Thus not only the paracarbon atom charge changes but also the charge changes on all the even carbon atoms of the unsaturated carbon chains, as a result of a substitution, divide into the x and LTcomponents in one and the same ratio [13] independently of the level of ab initio calculation (3G, 4-31G or 6-31G) used. However, a direct substitution at the carbon atom under consideration changes its properties. Thus the regression coefficients for the P-carbon atoms in styrene and P&difluorostyrene (Eqs. (6) and (X), respectively; all 3G) differ significantly, even at the 0.1% confidence level. There are also significant (even at the 0.1% con-
fidence level) differences between the regression coefficients for cv and P-carbon atoms in both styrene (Eqs. (6) and (7)) and ,Q-difluorostyrene (Eqs. (8) and (9)) (all 3G) (Fig. 3, for instance). Thus the known greater sensitivity to substitution of the even atoms of the conjugated chains in comparison with the odd atoms is accompanied by a significant difference between their r/a regression coefficients [ 141. It has also been shown [15] that the regression lines (3G) for the ortho-, meta- and para-carbon atoms of the benzene ring of monosubstituted benzenes and of 4-substituted styrenes do not differ significantly. The regression line for the total number of observations for the ring carbon atoms of monosubstituted benzenes and 4-sub-
119
N.A. OgorodnikovalJ. Mol. Struct. (Theochem) 284 (1993) 113-122
stituted styrenes was found to be [15]: AqFarom = -0.56Aq;Wom + 0.001 (10) N = 43; I = 0.99; S = 0.002 where AqFarom and AqFarom are the changes in the 7r and 0 components of the ring carbon atom charges of XC6Hs or XC6H,CHCH2 in comparison with those of benzene or styrene, respectively (see Ref. 12, for example). It can be seen that there is virtually no difference between regression lines (10) and (11). Thus the net charges occurring on the ortho-, meta- and para-carbon atoms in the benzene ring (3G) due to substitution divide into the r and c components in nearly the same ratio [13] as do the charges on the even carbon atoms of the conjugated carbon chains (3G, 4-31G and 631G). The linear r/a relationships with negatively signed regression coefficients hold true not only for different levels of ab initio calculation but also for different definitions of the atomic charge. Bader’s quantum topology Thus, using approach [16], electron populations for atoms can be obtained by integrating the function of the electron density within a certain volume around the atom. By means of this approach, the 7r and total electron populations for the atoms in butadiene, acrolein and vinylamine have been calculated (6-31G** [8]), depending on the molecular conformation (the rotation about the simple C-C or C-N bonds). Using the data in Ref. 8, it was found that the linear relation (12) with the negatively signed regression coefficient is actually fulfilled between the 7~and 0 charges (see Ref. 17) of the carbon atom of the CH2 group for the three conformations of butadiene (cis, trans, and an orthogonal arrangement of the two planar vinyl groups), two conformations of acrolein (cis and trans) and two conformations of vinylamine (planar, and an orthogonal arrangement of the planar vinyl and amino groups). The same feature is also characteristic of the terminal carbon atom of ions of ally1 and trimethylenemethyl types. References 9 and 10 give
the results of ab initio calculations on a series of such ions and the I-propyl anion with the use of 6-3 11++G* * wavefunctions calculated at 6-3 1G* geometries. The electron populations (n. and total) for atoms were obtained using Bader’s approach [16]. Making use of the data from Refs. 9 and 10, it was found that the linear relationship (13) (Fig. 4) with a negatively signed regression coefficient is also valid between the r and (Tcomponents [17] of the charge on the carbon atom in the terminal CH2 group of these ions (Fig. 5). It is worth mentioning that, according to the above examples, the origin of the changes of the atomic charges may also be a direct change in the number of electrons within a system. Indeed, the total change in the charge amounts to four electrons when passing from the methallyl dication to the trimethylenemethyl dianion. Thus the regularities found (i.e. the linear relationships with negatively signed regression coefficients) between the w and 0 components of the charge changes on unsaturated carbon atoms of carbon chains, are valid for both different levels of ab initio calculation (3G, 4-31G, 6-31G, 631G** and 6-31 l++G**) and different definitions of the atomic charge (Bader’s criterion and the Mulliken approach). Conclusion In the present study a comparative analysis was made of electron density distributions derived from ab initio MO calculations on substituted ethylenes, substituted benzenes, 4-substituted styrenes, 4-substituted /?,/I-difluorostyrenes, and ions of ally1 and trimethylenemethyl types. Changes in the effective atomic charges due to modification of the electron density distribution within a molecule were considered. Modifications of electron density distributions can result from both substitution and a direct variation in the number of electrons within a system. Linear relationships were found between the x and ff components of the charge changes on unsaturated carbon atoms of carbon chains. The regression coefficients were found to be negative.
120
N.A. Ogorodnikova/J. Mol. Struct. (Theochem) 284 (1993) 113-122
fec7 6 -3ff++.6**
-0.6
Fig. 4. The correlation (12) between the x and u components [17]of the charges (Refs. 9 and 10) on the carbon atoms in the terminal CH2 group of the ally1and methallylions and of the I-propyl anion. The numberingof the points corresponds to the numbering in Fig. 5. These regularities were found to be invariant with respect to both the level of ab initio calculation (3G, 4-31G, 6-31G, 6-31G** and 6-311++G**) and the definition of the atomic charge (Bader’s criterion or the Mulliken approach). Significant differences were found between the regression coefficients for the even and odd atoms of the conjugated carbon chains. The known greater sensitivity of the even atoms in comparison with odd ones to substitution is thus accompanied by a significant difference in the ratios between the 7~and 0 components of their atomic charges. The
net charges on the ortho-, meta- and para-carbon atoms of the benzene ring due to substitution (3G) divide into the r and m components in nearly the same ratio as for the charges on the even carbons of the conjugated carbon chains (3G, 4-31G and 631G). The character of the influence of the substituent also reverses when passing from even to odd positions of the conjugated chains (see Fig. 3, for instance). The origin of both the negative sign of the coefficients in the correlations between the x and 0 components of the atomic charges, and the
N.A. OgorodnikovalJ. Mol. Struct. (Theo&m)
284 (1993) 113-122
121
t~~mttAytenrmethy& &an yon , pt. fl - 0.523 cw, d
%
mrthattyt &catioh, pt. c,y2
9 G
+ 0.706 - 0.613
i
+ O./T9
r9.97
w
acrtalde&de
enoCate , PC.
19, f7
cu,
mrtAattyt ration,
Sym.
H
b
C% -tH attlyt
7+
0.465 - 0.460
Hd
cs27
H
Qcefatddyde
CnO&te + O.lbO -0.441
7
G H
anion,
sym _
ry
ra 373 G+o.IPp
H
r+o,37
H
.cfO,
ace&ztdeAyde
H
anion, H
enofate, 270’
n
sot. TS w-0.407 d - 0.003 CfO,4J
H H ’ -3-
cro,
ace tone
enofa te
H
T+ 0./9& G -0.4J3 t fO,57
d PH3
f21
anion
cr - 0.356 d .+ 0.186
H
L9,
methat yt onion. Spl. ; H T-CR408 -CH
li7
7+0.2/2 d - 0.415
+H
at'tyt
90 -
,
f3I
+0.233 f9.63
H
mcthattyt anion, *of. Lf
51-a39/ I$ to.210 T9.71
n
f
-p.zopyC
If ,& x
‘T - 0.360
d
~a201 c: -0.470
-co./91 tS6l
ani on
HH
i:u
-rY H
rro,
f5 I
Fig. 5. The Aand 0 componentsof the chargeson the carbon atoms in the terminalCH2group of the ally1and methallylions and of the I-propyl anion. Calculations(see Ref. 17)weredone usingthe data from Refs. 9 and 10.The first figurewithin the square brackets is a reference number, and the second one is the number of the point in Fig. 4. reversal of the substituent influence in passing from even to odd positions of the conjugated carbon chains seems to lie in the electron interaction. A new method was used in the present study and in two previous ones [l&18]. The study of the correlations between the x and u components of
the atomic charges in combination cations of statistical theoretical enables one to compare quantitatively ences derived from various levels of culations and thereby to find regularities inherent in them. These
with appliapproaches the dependab initio calout general observations
122
N.A. Ogorodnikova/J. Mol. Strut. (Theo&em) 284 (1993) 113-122
lead to a better understanding of some features of the electron structure of unsaturated compounds.
Acknowledgements The author wishes to thank Drs. Nina P. Gambaryan and Ivan V. Stankevich for valuable discussion and assistance, and also to express his gratitude to Professor Charles W. Bock, Drs. Mendel Trachtman and Philip George for making available to him the results of their calculations.
References R.T.C. Brownlee and R.W. Taft, J. Am. Chem. Sot., 92 (1970) 7007. W.J. Hehre, R.W. Taft and R.D. Topsom, Prog. Phys. Org. Chem., 12 (1976) 159. A. Hald, Statistical Theory with Engineering Applications, New York, 1952 (Russian translation, Izd. Inostr. Lit., Moscow, 1956). S. Marriott and R.D. Topsom, J. Mol. Struct. (Theothem), 106 (1984) 277. C.W. Bock, M. Trachtman and P. George, personal communication, 1991. W.F. Reynolds, P.G. Mezey and G.K. Hamer, Can. J. Chem., 55 (1977) 522.
7 W.F. Reynolds, V.G. Gibb and N. Plavac, Can. J. Chem., 58 (1980) 839. 8 K.B. Wiberg, R.E. Rosenberg and P.R. Rablen, J. Am. Chem. Sot., 113 (1991) 2890. 9 K.B. Wiberg, J. Am. Chem. Sot., 112 (1990) 4177. 10 K.B. W&erg, C.M. Breneman and T.J. LePage, J. Am. Chem. Sot., 112 (1990) 61. 11 R.S. Mulliken, J. Chem. Phys., 23 (1955) 1833, 1841, 2338,2343. 12 Aq$ and Aq: are expressed in terms of the differences of the effective charges Aq: = qF(C,HsX) - qF(C6Hs); Aq: = q:(CsHsX) - q:(CsHti). 13 With an accuracy of e, where 1e15 S, S being the standard deviation. 14 In a forthcoming paper (now in preparation), it will be shown that there are statistically significant differences between the n/a regression coefficients for the even and odd positions of conjugated carbon chains, using data from 6-31 l++G**//6-3lG* calculations (with atomic populations in the framework of Bader’s approach) as well. 15 N.A. Ogorodnikova and B.A. Kvasov, Izv. RAN, Ser. Chim., (1992) 1345 (in Russian). 16 R.F.W. Bader, Act. Chem. Res., 18 (1985) 9. 17 Here there are absolute charges, i.e. the atomic charges in relation to the neutral atoms in the corresponding hybridization. They are determined as follows: qn = 1 - n,; q. = q1 - qn; qt = 6 - n,; n,, n,, rr and the total electron populations of the atoms were taken from Refs. 8-10. 18 N.A. Ogorodnikova, J. Mol. Struct. (Theochem), 279 (1993) 71.
Journal of Molecular Structure (Theochem), 284 (1993) 113-122 0166-1280/93/%06.00 0 1993 - Elsevier Science Publishers B.V. All rights reserved
On some features of electron density distributions unsaturated hydrocarbons
in
Natalia A. Ogorodnikova A.N. Nesmeyanov Institute of Organo-Element Compounds, Russian Academy of Sciences, 2% Vavilov Str., Moscow 117813, Russian Federation (Received 9 July 1992; in final form 28 October 1992) Abstract A comparative analysis of electron density distributions derived from ab initio MO calculations was carried out for substituted ethylenes, substituted benzenes, Csubstituted styrenes, 4-substituted P,&difluorostyrenes, and ions of ally1 and trimethylenemethyl types. Changes in the atomic effective charges due to substitution or due to a direct variation in the number of electrons within a system were considered. Linear relationships were found between the rr and d components of the charge changes on an unsaturated carbon atom of a carbon chain. The regression coefficients proved to be negative. The regularities were found to be invariant with respect to both the level of ab initio calculation (3G, 4-3lG, 6-3lG, 6-3lG** and 6-31 l++G**) and the definition of the atomic charge (Bader’s criterion or the Mulliken approach). Data from ab initio MO calculations reported in the literature were used.
Introduction
Taft was the first to find out (CND0/2 [l]; ab initio, STO-3G [2]) that the r and g components of the atomic charges on the para-carbons of monosubstituted benzenes are linearly correlated. This feature of the charge density distributions of monosubstituted benzenes is invariant with respect to the level of ab initio calculation. Indeed, if one considers the changes in the para-carbon atom charges resulting from substitution, it appears that there are no statistically significant distinctions between the x/a regression lines (I), (2) and (3) (here and after, see Table 1) for the changes in the para-carbon atom charges in XCsHs in relation to benzene evaluated using the 3G [2], 4-31G [4] and 6-31G [5] basis sets, respectively (the atomic charges were obtained from the Mulliken populations [l 11). Moreover, these empirical regressions prove to be different evaluations of one and the same theoretical straight line. The regression line
for the total number of the observations for the para-carbon atom charges (3G, 4-31G and 631G) is the following: AqFPara = -0.55Aq,cPra + 0.003 N = 42; r = 0.994; S = 0.003
(4)
where AqfPra and AqzPra are the changes in the 7r and cr components of the para-carbon atom charges in XC6H5 in comparison with those in benzene [12]. Thus the charge appearing on the para-carbon atom in a monosubstituted benzene molecule as a result of a substitution divides into the r and LTcomponents in one and the same ratio [13], no matter what level of ab initio calculation (3G, 4-31G or 6-31G) is used. It can be seen that the sign of the regression coefficients in Eq. (1) t (4) is negative, i.e. the increase (decrease) in the 0 charge on an atom corresponds to the decrease (increase) in the x charge on that atom.
Aq::” = -0.58Aq:B
Aq?
Aq:O = -0.38AqFfl + 0.0006
(7)’
(8)’
Aq?
AqF-
(9)B
(lO)b-f
- 0.001
+ 0.0003
+ 0.0002
= -0.56Aq$‘“=’
= -0.75Aqp
= -0.79Aq(P
+ 0.0002
3G, 4-31G, 6-31G; Muhiken
3G; Mulhken
3G; Mu&ken
,&Carbon regression (for X see of XC6HS
X = NH2, OH, Me, H, F,
atoms of CHaCHX (for X see (5)) and of 4-XC&I&HCH2 regression (6)); pars-carbon atoms (for X see regressions (I), (2) and (3))
4-XC&I&HCF2: CFs, CN, NO,
4-XC6H4CHCH2: X = NH2 pl, NH2 py, OH, Me, H, F, CHO, CF,, CN, NO*
0.98
0.999
8 69
0.986
0.994
10
8
0.9995
0.982
10
19
CHzCHX: X = NH* pl, NH2 py, OMe, OH, F, Me, H, CHCH2, CCH, CN, CFs, CHO @is), CHO (trans), COMe (cis), COMe (trans), COCN, COCFs, NO, Nor
4-31G; Mulliken
(6)’
- 0.012
0.994
42
XC6HS: for X see regressions (l), (2) and (3)
3G, 4-31G, 6-31G; Mulliken
A,$@ = -0.54Aq:O
+ 0.003
(5Y
= -0.55Aqzp=
Aq?-
(4)b_d
0.995
19
XC6HS: X = O-, COO-, NH2, OH, Me, F, H, CHCHa, CHNH, CCH, CCF, CN, NC, CHO, CFO, COOH, NO, Nor, NH;
0.999
0.999
6-31G; Mulliken
+ 0.005
Aq:(4) = -0.55Aq;(4)
(3)d
12
r
13
+ 0.001
Aq:‘(4) = -0.53Aqzt4’
cv
XC6Hs: X = NH2 pl, NH2 py, OH, F, Me, H, CH*F, CFs, CN, CHO, NOz, NH;
N
XC6HS: X = NH2 pl, NH1 py, OMe, OH, F, Me, H, CHCHr, CCH, CN, NO, Nor, CHO
3G; Mulliken
Aq$(4) = -0.56Aq2c4)+ 0.~11
(1)”
Compounds
4-31G; Muhiken
Basis set; charge definition
Regression No.
q = bq’ + a
Table 1 Parameters of the regression equationsa q = ba + a
0.01
0.0002
0.0009
0.0006
0.0003
0.013
0.003
0.0038
0.001
0.001
S
q: = -0.81q:
(13)’
- 0.17
+ 0.11
+ 0.001
6-31 l++G**// 6-31G***, Bader
6-31G+**I Bader
3G; M&liken 0.03 1 0.096
0.97 0.96
7 15
CHrCHX: X = CHCHr, CO, NH2 (see text) Ions of ally1 and methallyl types and I-propyl anion (see Fig. 5)
0.002
0.99
43
Meta- and para-carbon atoms of XC6H5 (for X see regression (1)); C2 and C3 atoms of 4-XC&I.,CHCH~ (for X see regression (6))
a In the equations given, data from ab initio MO calculations reported in the literature were used. The present statistical analysis dealt with the regression equations in which the values of the regression coefficients and the free members, as well as the average values of the charges, the standard deviations (2, jj and A’) and the SSD, = (xi - n)2 values contained two more significant figures than in the table. For the correlations of the regression coefficients and the regression lines, standard statistical procedures were used [3]. The accepted confidence level is 5%; when the confidence level is otherwise, it is mentioned in the text. b The charge changes in relation to benzene from the data given in Ref. 2. ‘The charge changes in relation to benzene according to the data given in Ref. 4. d The charge changes in relation to benzene from the data given in Ref. 5. e Tbe charge changes in relation to ethylene according to the data given in Ref. 4. f Tbe charge changes in relation to styrene according to the data given in Ref. 6. g The charge changes in relation to /!?,&difluorostyrene according to the data given in Ref. 7. h The values of the charges were calculated [ 171using the data given in Ref. 8. i The values of the charges were calculated [17] using the data given in Refs. 9 and 10; see Fig. 5.
qy = -1.4qy
Aqzamm= -0.56Aq:-“
(12)h
(1 I)bpf
116
N.A. OgorodnikovajJ.
Mol. Struct. (Theochem)
284 (1993) 113-122
unsaturated hydrocarbons is invariant with respect to both the level of ab initio calculation used and the definition of the atomic charge applied. Results and discussion
x
-0.58
f6)
36,
i??Z.dC’hcn
-ai’9
(7)
3G,
iX!u~Lhm
- 0.75
(9)
3%
ZnldCC~Auz
Fig. 1, The relationships between the T and u components of the atomic charges derived from ab initio MO calculations. The coefficient, the number of the regression, the basis set level, and the definition of the atomic charge are given. For X and references, see Table 1.
In the present paper I show that a linear ratio between the r and CTcomponents of the charge changes on a carbon atom upon changes in the electron density distribution within a molecule, the regression coefficient being negative, is also characteristic of other unsaturated hydrocarbons. This feature of the electron density distributions of
The present study was concerned with the changes in the A and (Tcomponents of the carbon atom charges resulting from in particular a substitution in ethylene, styrene and /3,@difluorostyrene. The data on the carbon atom charges derived from ab initio calculations using the 4-31G (substituted ethylenes [4]) and 3G @-substituted styrenes [6] and /?,P-difluorostyrenes [7’j) basis sets were obtained from the literature (the atomic charges were taken from the Mulliken populations). It was found that the linear relationships, with the negative sign of the regression coefficients, were actually fulfilled between the changes in the x and u charges on the carbon atoms in these systems (see Table 1 and Fig. 1). Relation (5) is given for the pcarbon atom in substituted ethylenes (Fig. 2). Relations (6) and (8) are given for P-carbon atoms in styrenes and ,f3$-difluorostyrenes. Relations (7) and (9) correspond to a-carbon atoms in styrenes and P@difluorostyrenes, respectively. It should be emphasized that, despite the distinctions between the molecules and the basis set levels, not only the sign but also the value of the regression coefficients for the b-carbon atoms (even position) in substituted ethylenes (Eq. (5)) and styrenes (Eq. (6)), on the one hand, and for the a-carbon atoms (odd position) in substituted styrenes (Eq. (7)) and ,@difluorostyrenes (Eq. (9)), on the other hand, are equal. Indeed the regression coefficients (5) (4-31G) and (6) (3G) for the /?-carbon atoms do not differ significantly even at the 10% confidence level, and the free members of both regression lines are smaller than their standard deviations. Furthermore, there are no statistically significant differences between the regression lines for a-carbon atoms (7) and (9) (all 3G). The angle coefficients of these regressions do not differ significantly even at the 20% confidence level. Moreover, there are no statistically significant
117
N.A. Ugoro~~ovu~~. Mol. Stmct. fTkeoeke~~ 284 (1993) 113-122
Fig. 2. The correlation Q between the changesin the ?rand u com~nen~ of the charges (41on the @carbon atom in substitu~ ethylenes CH&HX in relation to ethylene. For X see the figure.
distinctions between the n/o regression lines for any of the even positions, i.e. the p-carbon atoms of ethylenes ((5), 4-31G), the p-carbon atoms of styrenes ((6), 3G), and the pars-carbon atoms of benzenes ((4), combined for the 3G, 4-31G and 631G levels). The regression line for the total number of observations (3G, 4-31G and 6-31G) for the
even positions is: AqFevan = -0.56Aa~cvcn - 0.001 (10) N = 69; r = 0.98; S = 0.01 where Aqfeven and Aq:““” are the changes in the even carbon atom charges in the substituted
118
N.A. OgorodnikovalJ. Mol. Struct. (Theochem) 284 (1993) 113-122
-0.03
-0.02
Fig. 3. The correlations between the R and u components of the charges [7] on the a-carbon atoms (0) (7) and P-carbon atoms (0) (6) of esubstituted ,!3#difluorostyrenes (4-XC6H&HCF2) in relation to those of P&difluorostyrene. For X, see the figure.
with those of compounds in comparison unsubstituted ones. Thus not only the paracarbon atom charge changes but also the charge changes on all the even carbon atoms of the unsaturated carbon chains, as a result of a substitution, divide into the x and LTcomponents in one and the same ratio [13] independently of the level of ab initio calculation (3G, 4-31G or 6-31G) used. However, a direct substitution at the carbon atom under consideration changes its properties. Thus the regression coefficients for the P-carbon atoms in styrene and P&difluorostyrene (Eqs. (6) and (X), respectively; all 3G) differ significantly, even at the 0.1% confidence level. There are also significant (even at the 0.1% con-
fidence level) differences between the regression coefficients for cv and P-carbon atoms in both styrene (Eqs. (6) and (7)) and ,Q-difluorostyrene (Eqs. (8) and (9)) (all 3G) (Fig. 3, for instance). Thus the known greater sensitivity to substitution of the even atoms of the conjugated chains in comparison with the odd atoms is accompanied by a significant difference between their r/a regression coefficients [ 141. It has also been shown [15] that the regression lines (3G) for the ortho-, meta- and para-carbon atoms of the benzene ring of monosubstituted benzenes and of 4-substituted styrenes do not differ significantly. The regression line for the total number of observations for the ring carbon atoms of monosubstituted benzenes and 4-sub-
119
N.A. OgorodnikovalJ. Mol. Struct. (Theochem) 284 (1993) 113-122
stituted styrenes was found to be [15]: AqFarom = -0.56Aq;Wom + 0.001 (10) N = 43; I = 0.99; S = 0.002 where AqFarom and AqFarom are the changes in the 7r and 0 components of the ring carbon atom charges of XC6Hs or XC6H,CHCH2 in comparison with those of benzene or styrene, respectively (see Ref. 12, for example). It can be seen that there is virtually no difference between regression lines (10) and (11). Thus the net charges occurring on the ortho-, meta- and para-carbon atoms in the benzene ring (3G) due to substitution divide into the r and c components in nearly the same ratio [13] as do the charges on the even carbon atoms of the conjugated carbon chains (3G, 4-31G and 631G). The linear r/a relationships with negatively signed regression coefficients hold true not only for different levels of ab initio calculation but also for different definitions of the atomic charge. Bader’s quantum topology Thus, using approach [16], electron populations for atoms can be obtained by integrating the function of the electron density within a certain volume around the atom. By means of this approach, the 7r and total electron populations for the atoms in butadiene, acrolein and vinylamine have been calculated (6-31G** [8]), depending on the molecular conformation (the rotation about the simple C-C or C-N bonds). Using the data in Ref. 8, it was found that the linear relation (12) with the negatively signed regression coefficient is actually fulfilled between the 7~and 0 charges (see Ref. 17) of the carbon atom of the CH2 group for the three conformations of butadiene (cis, trans, and an orthogonal arrangement of the two planar vinyl groups), two conformations of acrolein (cis and trans) and two conformations of vinylamine (planar, and an orthogonal arrangement of the planar vinyl and amino groups). The same feature is also characteristic of the terminal carbon atom of ions of ally1 and trimethylenemethyl types. References 9 and 10 give
the results of ab initio calculations on a series of such ions and the I-propyl anion with the use of 6-3 11++G* * wavefunctions calculated at 6-3 1G* geometries. The electron populations (n. and total) for atoms were obtained using Bader’s approach [16]. Making use of the data from Refs. 9 and 10, it was found that the linear relationship (13) (Fig. 4) with a negatively signed regression coefficient is also valid between the r and (Tcomponents [17] of the charge on the carbon atom in the terminal CH2 group of these ions (Fig. 5). It is worth mentioning that, according to the above examples, the origin of the changes of the atomic charges may also be a direct change in the number of electrons within a system. Indeed, the total change in the charge amounts to four electrons when passing from the methallyl dication to the trimethylenemethyl dianion. Thus the regularities found (i.e. the linear relationships with negatively signed regression coefficients) between the w and 0 components of the charge changes on unsaturated carbon atoms of carbon chains, are valid for both different levels of ab initio calculation (3G, 4-31G, 6-31G, 631G** and 6-31 l++G**) and different definitions of the atomic charge (Bader’s criterion and the Mulliken approach). Conclusion In the present study a comparative analysis was made of electron density distributions derived from ab initio MO calculations on substituted ethylenes, substituted benzenes, 4-substituted styrenes, 4-substituted /?,/I-difluorostyrenes, and ions of ally1 and trimethylenemethyl types. Changes in the effective atomic charges due to modification of the electron density distribution within a molecule were considered. Modifications of electron density distributions can result from both substitution and a direct variation in the number of electrons within a system. Linear relationships were found between the x and ff components of the charge changes on unsaturated carbon atoms of carbon chains. The regression coefficients were found to be negative.
120
N.A. Ogorodnikova/J. Mol. Struct. (Theochem) 284 (1993) 113-122
fec7 6 -3ff++.6**
-0.6
Fig. 4. The correlation (12) between the x and u components [17]of the charges (Refs. 9 and 10) on the carbon atoms in the terminal CH2 group of the ally1and methallylions and of the I-propyl anion. The numberingof the points corresponds to the numbering in Fig. 5. These regularities were found to be invariant with respect to both the level of ab initio calculation (3G, 4-31G, 6-31G, 6-31G** and 6-311++G**) and the definition of the atomic charge (Bader’s criterion or the Mulliken approach). Significant differences were found between the regression coefficients for the even and odd atoms of the conjugated carbon chains. The known greater sensitivity of the even atoms in comparison with odd ones to substitution is thus accompanied by a significant difference in the ratios between the 7~and 0 components of their atomic charges. The
net charges on the ortho-, meta- and para-carbon atoms of the benzene ring due to substitution (3G) divide into the r and m components in nearly the same ratio as for the charges on the even carbons of the conjugated carbon chains (3G, 4-31G and 631G). The character of the influence of the substituent also reverses when passing from even to odd positions of the conjugated chains (see Fig. 3, for instance). The origin of both the negative sign of the coefficients in the correlations between the x and 0 components of the atomic charges, and the
N.A. OgorodnikovalJ. Mol. Struct. (Theo&m)
284 (1993) 113-122
121
t~~mttAytenrmethy& &an yon , pt. fl - 0.523 cw, d
%
mrthattyt &catioh, pt. c,y2
9 G
+ 0.706 - 0.613
i
+ O./T9
r9.97
w
acrtalde&de
enoCate , PC.
19, f7
cu,
mrtAattyt ration,
Sym.
H
b
C% -tH attlyt
7+
0.465 - 0.460
Hd
cs27
H
Qcefatddyde
CnO&te + O.lbO -0.441
7
G H
anion,
sym _
ry
ra 373 G+o.IPp
H
r+o,37
H
.cfO,
ace&ztdeAyde
H
anion, H
enofate, 270’
n
sot. TS w-0.407 d - 0.003 CfO,4J
H H ’ -3-
cro,
ace tone
enofa te
H
T+ 0./9& G -0.4J3 t fO,57
d PH3
f21
anion
cr - 0.356 d .+ 0.186
H
L9,
methat yt onion. Spl. ; H T-CR408 -CH
li7
7+0.2/2 d - 0.415
+H
at'tyt
90 -
,
f3I
+0.233 f9.63
H
mcthattyt anion, *of. Lf
51-a39/ I$ to.210 T9.71
n
f
-p.zopyC
If ,& x
‘T - 0.360
d
~a201 c: -0.470
-co./91 tS6l
ani on
HH
i:u
-rY H
rro,
f5 I
Fig. 5. The Aand 0 componentsof the chargeson the carbon atoms in the terminalCH2group of the ally1and methallylions and of the I-propyl anion. Calculations(see Ref. 17)weredone usingthe data from Refs. 9 and 10.The first figurewithin the square brackets is a reference number, and the second one is the number of the point in Fig. 4. reversal of the substituent influence in passing from even to odd positions of the conjugated carbon chains seems to lie in the electron interaction. A new method was used in the present study and in two previous ones [l&18]. The study of the correlations between the x and u components of
the atomic charges in combination cations of statistical theoretical enables one to compare quantitatively ences derived from various levels of culations and thereby to find regularities inherent in them. These
with appliapproaches the dependab initio calout general observations
122
N.A. Ogorodnikova/J. Mol. Strut. (Theo&em) 284 (1993) 113-122
lead to a better understanding of some features of the electron structure of unsaturated compounds.
Acknowledgements The author wishes to thank Drs. Nina P. Gambaryan and Ivan V. Stankevich for valuable discussion and assistance, and also to express his gratitude to Professor Charles W. Bock, Drs. Mendel Trachtman and Philip George for making available to him the results of their calculations.
References R.T.C. Brownlee and R.W. Taft, J. Am. Chem. Sot., 92 (1970) 7007. W.J. Hehre, R.W. Taft and R.D. Topsom, Prog. Phys. Org. Chem., 12 (1976) 159. A. Hald, Statistical Theory with Engineering Applications, New York, 1952 (Russian translation, Izd. Inostr. Lit., Moscow, 1956). S. Marriott and R.D. Topsom, J. Mol. Struct. (Theothem), 106 (1984) 277. C.W. Bock, M. Trachtman and P. George, personal communication, 1991. W.F. Reynolds, P.G. Mezey and G.K. Hamer, Can. J. Chem., 55 (1977) 522.
7 W.F. Reynolds, V.G. Gibb and N. Plavac, Can. J. Chem., 58 (1980) 839. 8 K.B. Wiberg, R.E. Rosenberg and P.R. Rablen, J. Am. Chem. Sot., 113 (1991) 2890. 9 K.B. Wiberg, J. Am. Chem. Sot., 112 (1990) 4177. 10 K.B. W&erg, C.M. Breneman and T.J. LePage, J. Am. Chem. Sot., 112 (1990) 61. 11 R.S. Mulliken, J. Chem. Phys., 23 (1955) 1833, 1841, 2338,2343. 12 Aq$ and Aq: are expressed in terms of the differences of the effective charges Aq: = qF(C,HsX) - qF(C6Hs); Aq: = q:(CsHsX) - q:(CsHti). 13 With an accuracy of e, where 1e15 S, S being the standard deviation. 14 In a forthcoming paper (now in preparation), it will be shown that there are statistically significant differences between the n/a regression coefficients for the even and odd positions of conjugated carbon chains, using data from 6-31 l++G**//6-3lG* calculations (with atomic populations in the framework of Bader’s approach) as well. 15 N.A. Ogorodnikova and B.A. Kvasov, Izv. RAN, Ser. Chim., (1992) 1345 (in Russian). 16 R.F.W. Bader, Act. Chem. Res., 18 (1985) 9. 17 Here there are absolute charges, i.e. the atomic charges in relation to the neutral atoms in the corresponding hybridization. They are determined as follows: qn = 1 - n,; q. = q1 - qn; qt = 6 - n,; n,, n,, rr and the total electron populations of the atoms were taken from Refs. 8-10. 18 N.A. Ogorodnikova, J. Mol. Struct. (Theochem), 279 (1993) 71.