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Dipole moment calculations in molecules with charged atoms (zwitterionic forms) — mesomeric moments
Journal of Molecular Structure, 318 (1994) 211-216 0022-2860/94/$07.00 0 1994 - Elsevier Science B.V.All rights reserved
211
Dipole moment calculations in molecules with charged atoms (zwitterionic forms) - mesomeric moments S. Dari, E. Beneteau, H. Hucteau, A. ProutiQe* Laboratoire de Spectrochimie, Facultt! des Sciences et des Techniques, UniversitP de Nantes, 2. rue de la Houssiniire, 44072 Nantes Cedex 03, France
(Received 23 July 1993) Abstract A practical method of dipole moment calculation of molecules with charged atoms is presented. The method is a combination of the classical bond moments additivity method and of electrostatic calculations taking into account interactions between charges and polarizable atoms. The method is tested successfully on simple zwitterionic species and then applied to molecules with mesomeric forms. The conjugation effects are well represented by the method which gives reasonable values for the corresponding mesomeric moments and complementary information on the percentages of the mesomeric forms.
Introduction Dipolmetry is the preferred electro-optic method with regard to its practical applications in the field of stereochemistry of the liquid state. The experiments, mainly dielectric constant measurements, are simple and their interpretation through the additivity model is generally easy. In this model, the calculated molecular dipole moment G, the sum of the bond moments ci, is compared to the experimental one. This method is empirical but its efficiency has been largely proved, particularly by the work of the Exner [1,2] and Lumbroso [3] groups. At present, exact quantum chemical and even semi-empirical methods are less practical and less suitable for the usual applications in dipolmetry. The bond moment additivity method gives accurate results when deviations AGi caused by changes in the surroundings of the bonds are negligible. Three reasons may be given in Ahis case. First, the electrostatic interactive field E is * Corresponding
author.
SSDZ 0022-2860(93)07894-3
due to low partial charge q in relatiolto the electronic charge e. Second, the two fields E corresponding to the charges +q and -q of the bonded atoms induce compensating deviations in the far surroundings. Third, in the nearby surroundings the mutual interaction between the bonded atoms is already taken into account by the bond moment value itself. It should be noted that in such molecules, atomic charges qi are fictitious ones corresponding to a bond moment value pi = qil (I being the bond length); in fact all atoms are neutral. The limits of the bond moment additivity occur if one of the three previous conditions fails. For instance, in zwitterioqs or in molecules with strong conjugation, the simple additivity must be corrected by considering the effects of real charges (q = *e) located on several (generally two) atoms. For zwitterions, G calculations noted in the literature ay simplest and correspond to the basic definition ql (I is the distance between the two charges) without any interaction correction or bond moments addition [4]. Quantum chemical methods are also used but the values they give are too approximate
212
S. llari et ai./J. Md
for a precise analysis [S]. The case_of ion pairs is well treated because in addition to ql , the moments induced by the charges on the polarizable ions are considered [6] and, moreover, no (covalent) bond moments exist. For molecules with strong conjugation effects, leading to mesomeric forms with charged atoms, Exner and co-workers [7-IS] and Lumbroso and co-workers [I 6,171 introduce an additional vector, the mesomeric moment &i. This vector, obtained by the difference between experimental and calculated F values in some reference molecules, leads to reasonable results but cannot give precise information about the related mesomeric forms. For some time the main object of our research group has been to bring improvements in the applications of electro-optic methods which unfortunately have been hindered by discrepancies and theoretical problems, especially in liquids. Recently, we were interested in a dipolmetric study which included the use of mesomeric moments [18]. More recently we used with success electrostatic interaction calculations to evaluate polarizability changes due to salvation phenomena [19]. In this work we intend to apply such interaction calculations combined with the additivity model in order to determine a suitable ; calculation method in molecules with charged atoms. In the following sections the calculation method is detailed, then tested on zwitterions and finally applied to mesomeric forms.
Stnrct. 318 (1994) 211-216
This bond model is coherent because dipole moments are related to asymmetrical electronic repartitions along the bonds and it is realistic because deviations from simple additivity are minor (see Introduction). (2) The simple electrostatic calculations, used with success in ion pairs [6], for the additional moments c(q) and ~{q/~) are due to the real charges +q and -q on A and B atoms, r+spectively. FromAhe basic moment definition, I being the vector AB (in the chemical notation):
&I) = G+ and the moments induced by the charges fq on all atoms of the molecule
+
---V
-t
wh3e Ej(-4) = qBXj/4reo(BXj)3 and Ej(+q) = qAXj/4rEo(AXj)3 are the electrostatic fields due to -q and +q on the atom Xj and oj is the polarizability of atom X1. This atomic model is coherent because charges are located on atoms and the atomic polarizability scheme is known to give realistic interaction results [20]. The combination of these two methods leads for the calculated molecular moment to
iLdc= im+iad + i-&d4
Dipole moment calculations
In practical calculations, we assumed oj = Go (the mean value) and used the formula (p in D, distances in A and CEiin A3):
General method
Ccalc
= C
G+i Co) + 4.8063 i
Our method is a simple combination of two well proven methods. (1) The additivity of covalent bond moments zi(0), from the work of Exner and Lumbroso (see related references). For a molecule without charged atoms,
G(O) =C i
Gi(O)
x
+ x&j i
[BZj/(BXj)3 - A%j/(AXj)31 I
(1) It should be noted that in the case of more than two charged atoms, a more general formula can be obtained easily by similar additional terms relating to other charged atoms.
213
S. Dari et al/J. Mol. Struct. 318 (1994) 211-216
Table 1 EI~tro-optic parameters used in ~~euiations (a) Bond and group moments pi (D) (1,2,7-151 H-C,3 C-N H-C,1 0 0.3 0.45 C=N 1.80
c=o 2.50
c-o
c-s
c-a
0.74
0.90
1.60
N-O 0.40
C=S 2.16
C-NO* 4.00
C-Br 1.57
m,/(Ar/C=S) 0.45
N=O 2.00
(b) Atom mean polarizabilities 51 (A3) [21] H
C
0.408
1.027
=o 0.659
Details
00.752
CAr
fN
1.322
1.088 S 3.063
-NC
0.537 S3.83
of calculation parameters
Electra-optic and geometrical parameters used in our calculations are given in Tables 1 and 2. The 2, vectors given in Table l(a) are mesomeric moments used in the last section. They are related to the conjugation between Ar and C=X (X = 0 or S). Calculated p values are in many cases very sensitive to aj values. Rigorous calculations must take into account pola~zability anisotropies, which is not actually feasible with accuracy. Nevertheless, we refined our assumed dj, values by two realistic modifications. For charged atoms we adopted values similar to
1.40 c1 2.317
.;;
‘N’ /
y>
0.692
1.68
Br 3.465
_N+<
-ol.
0.831
Li+ 0.03
0.602
Br5.02
those observed in ions. ti(N+) is deduced from the corresponding (Y(N) value through the ratio &(N+)/a(N) = 0.494 observed in NH: and NH3 [21]. 6(0-) and c%(S) are deduced from $0) and d(S) through the mean ratio 6(X-)/6(X) = 1.25 observedforx = F,Cl,BrandI[2l](seeTable l(b)). Then, because the molecular CE value must be constant, we reported differences 6(N)&(N’) = +S and &(A) - &(A-) = -6 (A = 0 or S) on bonded atoms (with an equal part for each single bond in the case of +I?). In fact, results obtained without these corrections are always qualitatively consistent and even quantitatively suitable in some cases which shows
Table 2 Geometrical
parameters
used in calculations
[1,2,22,23]
(a) Bond angles’ (deg)
*
(b) Bond lengthsb (in A) C-H CA,-H 1.10 1.08
c-c
CAr -CAr
CA,-c
1.54
1.40
1.50
c-s 1.82
N=O 1.22
c,-Cl 1.70
CA,--Br 1.85
N-O 1.36
C-N 1.47
a For Me, Et, Ar and Ar-X we adopted “ideal” values (109.46 or 120“). b For the Li+Br- distance we used the sum of van der Waals radii: 0.59 + 1.96 = 2.55 A.
C=N 1.34
c-o 1.43
S. Dari et al./J. Mol. Struct. 318 (1994) 211-216
214
Table 3 Dipole rnorne~~ along the x axis (in D) of molecules with localized charges fe
P(O)
CL(q)
PWff)
PC&
Pexp WI
Li+Br- + x / 0-W)
12.26
-3.13
8.53
8.65
R=Me
1.83
3.06
-1.58
3.31
3.15
R-N+
R = Et
1.83
3.06
-1.51
3.38
3.25
1.83
3.06
-0.35
4.24
4.05
1.27
6.53
-2.96
4.84
4.81
+ x
\o -(OS) Me3N+-O-+ x
that our & modifications reasonable method.
R = Ar
are improvements
of a
Test of the method on zwitterionic forms
In Table 3 calculated z values are compared to experimental ones for three nitro compounds and for trimethylamine oxide, and the results for LiBr are given as an example of an ion pair. In our calculations we consider zwitterions N+-O- which implies that conjugation between NOz (or NO) and R (= Me, Et or Ar) is negligible. This ass~ption is consistent because in the more doubtful case, ArNO*, observation of solution data showed that conjugation was close to zero 1151. Moreover, in Ar-NO*, crystal ab initio calculations lead to a large prevalence of the zwitterionic form N+-Ov51. The comparison between pcalc and P,,~ clearly shows the consistency of the method. In the case of nitro compounds, the slight systematic difference clcalc> Pexp could be easily explained by a deviation of our geometrical parameters from the real geometry in solution. The use of the observed crystal geometry [25] in Ar-NO2 gave us similar data (pcaic = 4.3 D). On the contrary, good agreement is obtained by using an ON0 angle value of 134” [23] instead of 124” [22]. In addition, details of Table 3 indicate the relative importance of each term p(O), p(q) and p(q/cr) and thus the necessity of taking into account the covalent bond moments ~(0) and the inductive moments p(q/a) together with the main term p(q).
App~cation to mol~les
with two mesomeric forms
We applied our method to the following mesomeric forms of N-dimethylamides (x=0) and N-dimethylthioamides (X=S) Me,N-
RR -
Me,N+-Cc
C+
X
R
_
X
(1) uncharged form
(2) zwitterionic form
The results are presented in Table 4. The corresponding calculated values $(I) and G(2) are compared to the ex~~mental one, Gexr,. In this case a strong conjugation occurs (pexp >> p( 1)) and the experimental value can be interpreted by a statistical averaging of the two limit forms as follows: lOOi&
=Pl
im
+IG(4
(2)
where p1 and p2 are the related percentages of forms (1) and (2). From z(l), G(2) and c,, values we deduced pI and p2 through Eq. (2) as indicated below in the case of Me2NCHO: (l~~~~p)2 = IPI /-b(l)
fP2&W2
+ IPl CLyU) + P2&m2
The x axis is along the NC direction and the y axis is perpendicular in the N-C=0 plane. Then from p2 = 100 - pI and from the calculated components (in D) p,(l) = 1.76, ~~(1) = 2.04, ~~(2) = 5.58 and ~~(2) = 2.71, we
215
Mol. Struct. 318 f1994) 211-216
S. Duri et d/J.
Table 4 Dipole moments ()I), percentages of mesomeric forms (pt and pz) and mesomeric moments m’ (m and the angle LYbetween N”c and G) for molecules with two mesomeric forms
<,”
Me2N-
X
ia)
P(2)
(D)
(D) t&c
X
R
N-C+
0
H Ar Ar-Me Ar-Cl Ar-Br Ar-NOi
2.69 2.80 2.98 2.47 2.48 3.60
6.21 4.47 4.73 4.68 4.64 16.50
H Ar Ar-Me Ar-Cl Ar-Br Ar-NO2 b
2.37 2.57 2.75 2.21 2.21 3.47
10.05 8.65 8.69 8.35 8.31 22.08
S
X
&3X,
PI
P2
m (W/a
@W
This work
Exner [9,10]
Lumbroso
1.41/o 1.41/o I.4110 1.4110 1.41/o
1.70/56 1.70156 1.70156 1.70156 1.70156
2.46118
3.2156
[3,17]
‘X3.81 3.84 3.96 3.76 3.75 5.14 4.74 4.95 (S.OZy (4.72)a (4.83)& 5.88
66 36 41 42 41 88
34 64 59 58 59 12
1.3219.9 1.32J8.6 1.3218.6 1.31/8.4 1.3018.2 1.59j4.1
69 60 61 59 57 85
31 40 39 41 43 15
2.45125 2.4913 1 2.44132 2.54132 2.65132 2.97123
2.46118
a Assumed values (from G( 1) and the mean m’ value of Exner [lo]). b In the case of R : Ar-N02, four charged atoms are considered (N+, X- and N+, O- for the Nor, group) which explains the strong ~(2) values. If the zwitterionic form of NO2 is not considered, incoherent results are obtained: ~(2) < p,r_
obtain pi2 - 3.075pi + 1.594 = 0 with p’ = p/100. Finally, the unique realistic values are p1 = 66 and p2 = 34. The p1 and p2 values thus calculated are presented in Table 4. Then, values for the mesomeric moment 2, according to the definition of Exner or Lumbroso, m’ = 1Zexp- Z(l) =
PLm
+P;iQ)
-&I)
are deduced and compared to the mean values of Exner and Lumbroso in the last columns of Table 4. Examination of Table 4 shows that our m values are close to those of Exner which proves the consistency of the method because the Exner values are the mean of real (experimental) values. The main difference concerns the vector direction (only 8” in the more reliable case of N-dimethylbenzoamides); our vector direction is in fact intermediate between those of Exner and Lumbroso. The explanation of the slight o deviation could be the use of the mesomeric moments 2, in our F(2) calculations (see Table l(a)). In fact, this con-
jugation effect corresponds to the participation of other zwitterionic forms (with other charges located along Ar-C=X) and a rigorous calculation, not actually practicable, must take those forms into account. In spite of this systematic error, reasonable data are observed because 2, concerns a low conjugation effect. As indicated below Table 4, such calculations are practicable in nitro derivatives because we considered a whole zwitterionic form for the NO2 group. An interesting point in this study is the mutual confirmation between our method and that of Exner. In our method the main hypothesis is the interpretation with two limit moment vectors. In Exner’s, the hypothesis is to adopt an identical mesomeric moment in all derivatives. An additional independent proof could be provided by the knowledge of zext, components (along the x and y axes, see the above calculation details), by means of microwave studies in the gas phase for instance.
S. Dari et al.}J. Mol. Struct. 318 (1994) 211-216
216
Conclusion By means of a simple and practical combined model we have succeeded in obtaining reasonable values for the dipole moments of zwitterionic molecular forms and realistic values for the mesomerit vectors G. Our calculation method has the advantage of determining precisely the statistical ~r~entages of the two limit forms, obtaining 4 directly for each studied molecule (which allows, for instance, comparison of the conjugation effect in various compounds) and. finally of supplying a realistic understanding of the mesomeric moment based upon simple electrostatic explanations. Applications to more complex molecules are in progress in our laboratory; initial results obtained on dimethyl p-nitrophenylamidines are in agreement with different theoretical calculations performed by other authors [26]. Acknowl~gement The authors thank Professor 0. Exner for his helpful and important comments. References 0. Exner, Dipole moments in organic chemistry, Georg Thieme, Stuttgart, 1975. 0. Exner, in S. Patai, (Ed.), The Chemistry of Functional Groups, Supplement A. The Chemistry of Double-Bonded Functional Groups, Wiley, London, 1977, p. 1. H. Lumbroso and G. Pifferi, Bull. Sot. Chim. Fr., (1969) 3401. A.D. Buckingham, Aust. J. Chem., 6 (1953) 93. K.T. Potts, P.M. Murphy, M.R. Deluca and W.R. Kuehnling, J. Org. Chem., 53 (1988) 2898.
6 E.S. Rittner, J. Chem. Phys., 19 (1951) 1030. 7 0. Exner and J.P.F.N. Engberts, Collect. Czech. Chem. Commun., 44 (1979) 3378. 8 0. Exner, Collect. Czech. Chem. Commun., 46 (1981) 1002. 9 0. Exner and Z. Papouskova, Collect. Czech. Chem. Commun., 45 (1980) 2410. 10 0. Exner and K. Waisser, Collect. Czech. Chem. Commun., 47 (1982) 828. 11 0. Exner, M. Budesinsky, D. Hnyk, V. Vsetecka and E.D. Raczynska, J. Mol. Struct., 178 (1988) 147. 12 0. Exner and N. Motekov, Collect. Czech. Chem. Commun., 47 (1982) 814. 13 0. Exner and A. Bapcum, Collect. Czech. Chem. Commun., 47 (1982) 29. 14 0. Exner, R. Fruttero and A. Gasco, Struct. Chem., 1 (1990) 417. 15 0. Exner, U. Folli, S. Marcaccioli and P. Vivarelli, J. Chem. Sot., Perkin Trans. 2, (1983) 757. 16 H. Lumbroso and D.M. Bertin, J. Mol. Struct., 239 (1990) 235. 17 C. Pigenet and H. Lumbroso, Bull. Sot. Chim. Fr., 10 (1972) 3743. 18 C. Cellerin, A. Abouelfida, J.P. Pradtre, A. Proutiere, J.C. Raze, M. Bouzid and 0. Exner, J. Mol. Struct., 265 (1992) 215. 19 M.N. Camus, E. Megnassan, A. Proutiere and M. Chabanel, J. Mol. Struct., 295 (1993) 155. 20 J. Applequist, J.R. Carl and K.K. Fung, J. Am. Chem. Sot., 94 (1972) 2952. 21 S.S. Batsanov, Refractometry and Chemical Structure, Consultants Bureau: New York, 1961, and references cited therein. and R.A. Ford, The Chemist’s 22 A.J. Gordon Companion, Wiley-Interscience, New York, 1972. 23 R.C. Weast (ed.), Handbook of Chemistry and Physics, 69th edn., CRC Press, Boca Raton, Florida, 1980. 24 Al. McLeilan, Tables of Experimental Dipole Moments, Rahara Enterprises, El Cerrito, 1974. and T.M. 25 R. Boese, D. Bllser, M. Nussbaumer Krygowski, Struct. Chem., 3 (1992) 363. 26 R. Anulewicz, T.M. Krygowski, E.D. Raczynska and C. Laurence, J. Phys. Org. Chem., 4 (1991) 331.
211
Dipole moment calculations in molecules with charged atoms (zwitterionic forms) - mesomeric moments S. Dari, E. Beneteau, H. Hucteau, A. ProutiQe* Laboratoire de Spectrochimie, Facultt! des Sciences et des Techniques, UniversitP de Nantes, 2. rue de la Houssiniire, 44072 Nantes Cedex 03, France
(Received 23 July 1993) Abstract A practical method of dipole moment calculation of molecules with charged atoms is presented. The method is a combination of the classical bond moments additivity method and of electrostatic calculations taking into account interactions between charges and polarizable atoms. The method is tested successfully on simple zwitterionic species and then applied to molecules with mesomeric forms. The conjugation effects are well represented by the method which gives reasonable values for the corresponding mesomeric moments and complementary information on the percentages of the mesomeric forms.
Introduction Dipolmetry is the preferred electro-optic method with regard to its practical applications in the field of stereochemistry of the liquid state. The experiments, mainly dielectric constant measurements, are simple and their interpretation through the additivity model is generally easy. In this model, the calculated molecular dipole moment G, the sum of the bond moments ci, is compared to the experimental one. This method is empirical but its efficiency has been largely proved, particularly by the work of the Exner [1,2] and Lumbroso [3] groups. At present, exact quantum chemical and even semi-empirical methods are less practical and less suitable for the usual applications in dipolmetry. The bond moment additivity method gives accurate results when deviations AGi caused by changes in the surroundings of the bonds are negligible. Three reasons may be given in Ahis case. First, the electrostatic interactive field E is * Corresponding
author.
SSDZ 0022-2860(93)07894-3
due to low partial charge q in relatiolto the electronic charge e. Second, the two fields E corresponding to the charges +q and -q of the bonded atoms induce compensating deviations in the far surroundings. Third, in the nearby surroundings the mutual interaction between the bonded atoms is already taken into account by the bond moment value itself. It should be noted that in such molecules, atomic charges qi are fictitious ones corresponding to a bond moment value pi = qil (I being the bond length); in fact all atoms are neutral. The limits of the bond moment additivity occur if one of the three previous conditions fails. For instance, in zwitterioqs or in molecules with strong conjugation, the simple additivity must be corrected by considering the effects of real charges (q = *e) located on several (generally two) atoms. For zwitterions, G calculations noted in the literature ay simplest and correspond to the basic definition ql (I is the distance between the two charges) without any interaction correction or bond moments addition [4]. Quantum chemical methods are also used but the values they give are too approximate
212
S. llari et ai./J. Md
for a precise analysis [S]. The case_of ion pairs is well treated because in addition to ql , the moments induced by the charges on the polarizable ions are considered [6] and, moreover, no (covalent) bond moments exist. For molecules with strong conjugation effects, leading to mesomeric forms with charged atoms, Exner and co-workers [7-IS] and Lumbroso and co-workers [I 6,171 introduce an additional vector, the mesomeric moment &i. This vector, obtained by the difference between experimental and calculated F values in some reference molecules, leads to reasonable results but cannot give precise information about the related mesomeric forms. For some time the main object of our research group has been to bring improvements in the applications of electro-optic methods which unfortunately have been hindered by discrepancies and theoretical problems, especially in liquids. Recently, we were interested in a dipolmetric study which included the use of mesomeric moments [18]. More recently we used with success electrostatic interaction calculations to evaluate polarizability changes due to salvation phenomena [19]. In this work we intend to apply such interaction calculations combined with the additivity model in order to determine a suitable ; calculation method in molecules with charged atoms. In the following sections the calculation method is detailed, then tested on zwitterions and finally applied to mesomeric forms.
Stnrct. 318 (1994) 211-216
This bond model is coherent because dipole moments are related to asymmetrical electronic repartitions along the bonds and it is realistic because deviations from simple additivity are minor (see Introduction). (2) The simple electrostatic calculations, used with success in ion pairs [6], for the additional moments c(q) and ~{q/~) are due to the real charges +q and -q on A and B atoms, r+spectively. FromAhe basic moment definition, I being the vector AB (in the chemical notation):
&I) = G+ and the moments induced by the charges fq on all atoms of the molecule
+
---V
-t
wh3e Ej(-4) = qBXj/4reo(BXj)3 and Ej(+q) = qAXj/4rEo(AXj)3 are the electrostatic fields due to -q and +q on the atom Xj and oj is the polarizability of atom X1. This atomic model is coherent because charges are located on atoms and the atomic polarizability scheme is known to give realistic interaction results [20]. The combination of these two methods leads for the calculated molecular moment to
iLdc= im+iad + i-&d4
Dipole moment calculations
In practical calculations, we assumed oj = Go (the mean value) and used the formula (p in D, distances in A and CEiin A3):
General method
Ccalc
= C
G+i Co) + 4.8063 i
Our method is a simple combination of two well proven methods. (1) The additivity of covalent bond moments zi(0), from the work of Exner and Lumbroso (see related references). For a molecule without charged atoms,
G(O) =C i
Gi(O)
x
+ x&j i
[BZj/(BXj)3 - A%j/(AXj)31 I
(1) It should be noted that in the case of more than two charged atoms, a more general formula can be obtained easily by similar additional terms relating to other charged atoms.
213
S. Dari et al/J. Mol. Struct. 318 (1994) 211-216
Table 1 EI~tro-optic parameters used in ~~euiations (a) Bond and group moments pi (D) (1,2,7-151 H-C,3 C-N H-C,1 0 0.3 0.45 C=N 1.80
c=o 2.50
c-o
c-s
c-a
0.74
0.90
1.60
N-O 0.40
C=S 2.16
C-NO* 4.00
C-Br 1.57
m,/(Ar/C=S) 0.45
N=O 2.00
(b) Atom mean polarizabilities 51 (A3) [21] H
C
0.408
1.027
=o 0.659
Details
00.752
CAr
fN
1.322
1.088 S 3.063
-NC
0.537 S3.83
of calculation parameters
Electra-optic and geometrical parameters used in our calculations are given in Tables 1 and 2. The 2, vectors given in Table l(a) are mesomeric moments used in the last section. They are related to the conjugation between Ar and C=X (X = 0 or S). Calculated p values are in many cases very sensitive to aj values. Rigorous calculations must take into account pola~zability anisotropies, which is not actually feasible with accuracy. Nevertheless, we refined our assumed dj, values by two realistic modifications. For charged atoms we adopted values similar to
1.40 c1 2.317
.;;
‘N’ /
y>
0.692
1.68
Br 3.465
_N+<
-ol.
0.831
Li+ 0.03
0.602
Br5.02
those observed in ions. ti(N+) is deduced from the corresponding (Y(N) value through the ratio &(N+)/a(N) = 0.494 observed in NH: and NH3 [21]. 6(0-) and c%(S) are deduced from $0) and d(S) through the mean ratio 6(X-)/6(X) = 1.25 observedforx = F,Cl,BrandI[2l](seeTable l(b)). Then, because the molecular CE value must be constant, we reported differences 6(N)&(N’) = +S and &(A) - &(A-) = -6 (A = 0 or S) on bonded atoms (with an equal part for each single bond in the case of +I?). In fact, results obtained without these corrections are always qualitatively consistent and even quantitatively suitable in some cases which shows
Table 2 Geometrical
parameters
used in calculations
[1,2,22,23]
(a) Bond angles’ (deg)
*
(b) Bond lengthsb (in A) C-H CA,-H 1.10 1.08
c-c
CAr -CAr
CA,-c
1.54
1.40
1.50
c-s 1.82
N=O 1.22
c,-Cl 1.70
CA,--Br 1.85
N-O 1.36
C-N 1.47
a For Me, Et, Ar and Ar-X we adopted “ideal” values (109.46 or 120“). b For the Li+Br- distance we used the sum of van der Waals radii: 0.59 + 1.96 = 2.55 A.
C=N 1.34
c-o 1.43
S. Dari et al./J. Mol. Struct. 318 (1994) 211-216
214
Table 3 Dipole rnorne~~ along the x axis (in D) of molecules with localized charges fe
P(O)
CL(q)
PWff)
PC&
Pexp WI
Li+Br- + x / 0-W)
12.26
-3.13
8.53
8.65
R=Me
1.83
3.06
-1.58
3.31
3.15
R-N+
R = Et
1.83
3.06
-1.51
3.38
3.25
1.83
3.06
-0.35
4.24
4.05
1.27
6.53
-2.96
4.84
4.81
+ x
\o -(OS) Me3N+-O-+ x
that our & modifications reasonable method.
R = Ar
are improvements
of a
Test of the method on zwitterionic forms
In Table 3 calculated z values are compared to experimental ones for three nitro compounds and for trimethylamine oxide, and the results for LiBr are given as an example of an ion pair. In our calculations we consider zwitterions N+-O- which implies that conjugation between NOz (or NO) and R (= Me, Et or Ar) is negligible. This ass~ption is consistent because in the more doubtful case, ArNO*, observation of solution data showed that conjugation was close to zero 1151. Moreover, in Ar-NO*, crystal ab initio calculations lead to a large prevalence of the zwitterionic form N+-Ov51. The comparison between pcalc and P,,~ clearly shows the consistency of the method. In the case of nitro compounds, the slight systematic difference clcalc> Pexp could be easily explained by a deviation of our geometrical parameters from the real geometry in solution. The use of the observed crystal geometry [25] in Ar-NO2 gave us similar data (pcaic = 4.3 D). On the contrary, good agreement is obtained by using an ON0 angle value of 134” [23] instead of 124” [22]. In addition, details of Table 3 indicate the relative importance of each term p(O), p(q) and p(q/cr) and thus the necessity of taking into account the covalent bond moments ~(0) and the inductive moments p(q/a) together with the main term p(q).
App~cation to mol~les
with two mesomeric forms
We applied our method to the following mesomeric forms of N-dimethylamides (x=0) and N-dimethylthioamides (X=S) Me,N-
RR -
Me,N+-Cc
C+
X
R
_
X
(1) uncharged form
(2) zwitterionic form
The results are presented in Table 4. The corresponding calculated values $(I) and G(2) are compared to the ex~~mental one, Gexr,. In this case a strong conjugation occurs (pexp >> p( 1)) and the experimental value can be interpreted by a statistical averaging of the two limit forms as follows: lOOi&
=Pl
im
+IG(4
(2)
where p1 and p2 are the related percentages of forms (1) and (2). From z(l), G(2) and c,, values we deduced pI and p2 through Eq. (2) as indicated below in the case of Me2NCHO: (l~~~~p)2 = IPI /-b(l)
fP2&W2
+ IPl CLyU) + P2&m2
The x axis is along the NC direction and the y axis is perpendicular in the N-C=0 plane. Then from p2 = 100 - pI and from the calculated components (in D) p,(l) = 1.76, ~~(1) = 2.04, ~~(2) = 5.58 and ~~(2) = 2.71, we
215
Mol. Struct. 318 f1994) 211-216
S. Duri et d/J.
Table 4 Dipole moments ()I), percentages of mesomeric forms (pt and pz) and mesomeric moments m’ (m and the angle LYbetween N”c and G) for molecules with two mesomeric forms
<,”
Me2N-
X
ia)
P(2)
(D)
(D) t&c
X
R
N-C+
0
H Ar Ar-Me Ar-Cl Ar-Br Ar-NOi
2.69 2.80 2.98 2.47 2.48 3.60
6.21 4.47 4.73 4.68 4.64 16.50
H Ar Ar-Me Ar-Cl Ar-Br Ar-NO2 b
2.37 2.57 2.75 2.21 2.21 3.47
10.05 8.65 8.69 8.35 8.31 22.08
S
X
&3X,
PI
P2
m (W/a
@W
This work
Exner [9,10]
Lumbroso
1.41/o 1.41/o I.4110 1.4110 1.41/o
1.70/56 1.70156 1.70156 1.70156 1.70156
2.46118
3.2156
[3,17]
‘X3.81 3.84 3.96 3.76 3.75 5.14 4.74 4.95 (S.OZy (4.72)a (4.83)& 5.88
66 36 41 42 41 88
34 64 59 58 59 12
1.3219.9 1.32J8.6 1.3218.6 1.31/8.4 1.3018.2 1.59j4.1
69 60 61 59 57 85
31 40 39 41 43 15
2.45125 2.4913 1 2.44132 2.54132 2.65132 2.97123
2.46118
a Assumed values (from G( 1) and the mean m’ value of Exner [lo]). b In the case of R : Ar-N02, four charged atoms are considered (N+, X- and N+, O- for the Nor, group) which explains the strong ~(2) values. If the zwitterionic form of NO2 is not considered, incoherent results are obtained: ~(2) < p,r_
obtain pi2 - 3.075pi + 1.594 = 0 with p’ = p/100. Finally, the unique realistic values are p1 = 66 and p2 = 34. The p1 and p2 values thus calculated are presented in Table 4. Then, values for the mesomeric moment 2, according to the definition of Exner or Lumbroso, m’ = 1Zexp- Z(l) =
PLm
+P;iQ)
-&I)
are deduced and compared to the mean values of Exner and Lumbroso in the last columns of Table 4. Examination of Table 4 shows that our m values are close to those of Exner which proves the consistency of the method because the Exner values are the mean of real (experimental) values. The main difference concerns the vector direction (only 8” in the more reliable case of N-dimethylbenzoamides); our vector direction is in fact intermediate between those of Exner and Lumbroso. The explanation of the slight o deviation could be the use of the mesomeric moments 2, in our F(2) calculations (see Table l(a)). In fact, this con-
jugation effect corresponds to the participation of other zwitterionic forms (with other charges located along Ar-C=X) and a rigorous calculation, not actually practicable, must take those forms into account. In spite of this systematic error, reasonable data are observed because 2, concerns a low conjugation effect. As indicated below Table 4, such calculations are practicable in nitro derivatives because we considered a whole zwitterionic form for the NO2 group. An interesting point in this study is the mutual confirmation between our method and that of Exner. In our method the main hypothesis is the interpretation with two limit moment vectors. In Exner’s, the hypothesis is to adopt an identical mesomeric moment in all derivatives. An additional independent proof could be provided by the knowledge of zext, components (along the x and y axes, see the above calculation details), by means of microwave studies in the gas phase for instance.
S. Dari et al.}J. Mol. Struct. 318 (1994) 211-216
216
Conclusion By means of a simple and practical combined model we have succeeded in obtaining reasonable values for the dipole moments of zwitterionic molecular forms and realistic values for the mesomerit vectors G. Our calculation method has the advantage of determining precisely the statistical ~r~entages of the two limit forms, obtaining 4 directly for each studied molecule (which allows, for instance, comparison of the conjugation effect in various compounds) and. finally of supplying a realistic understanding of the mesomeric moment based upon simple electrostatic explanations. Applications to more complex molecules are in progress in our laboratory; initial results obtained on dimethyl p-nitrophenylamidines are in agreement with different theoretical calculations performed by other authors [26]. Acknowl~gement The authors thank Professor 0. Exner for his helpful and important comments. References 0. Exner, Dipole moments in organic chemistry, Georg Thieme, Stuttgart, 1975. 0. Exner, in S. Patai, (Ed.), The Chemistry of Functional Groups, Supplement A. The Chemistry of Double-Bonded Functional Groups, Wiley, London, 1977, p. 1. H. Lumbroso and G. Pifferi, Bull. Sot. Chim. Fr., (1969) 3401. A.D. Buckingham, Aust. J. Chem., 6 (1953) 93. K.T. Potts, P.M. Murphy, M.R. Deluca and W.R. Kuehnling, J. Org. Chem., 53 (1988) 2898.
6 E.S. Rittner, J. Chem. Phys., 19 (1951) 1030. 7 0. Exner and J.P.F.N. Engberts, Collect. Czech. Chem. Commun., 44 (1979) 3378. 8 0. Exner, Collect. Czech. Chem. Commun., 46 (1981) 1002. 9 0. Exner and Z. Papouskova, Collect. Czech. Chem. Commun., 45 (1980) 2410. 10 0. Exner and K. Waisser, Collect. Czech. Chem. Commun., 47 (1982) 828. 11 0. Exner, M. Budesinsky, D. Hnyk, V. Vsetecka and E.D. Raczynska, J. Mol. Struct., 178 (1988) 147. 12 0. Exner and N. Motekov, Collect. Czech. Chem. Commun., 47 (1982) 814. 13 0. Exner and A. Bapcum, Collect. Czech. Chem. Commun., 47 (1982) 29. 14 0. Exner, R. Fruttero and A. Gasco, Struct. Chem., 1 (1990) 417. 15 0. Exner, U. Folli, S. Marcaccioli and P. Vivarelli, J. Chem. Sot., Perkin Trans. 2, (1983) 757. 16 H. Lumbroso and D.M. Bertin, J. Mol. Struct., 239 (1990) 235. 17 C. Pigenet and H. Lumbroso, Bull. Sot. Chim. Fr., 10 (1972) 3743. 18 C. Cellerin, A. Abouelfida, J.P. Pradtre, A. Proutiere, J.C. Raze, M. Bouzid and 0. Exner, J. Mol. Struct., 265 (1992) 215. 19 M.N. Camus, E. Megnassan, A. Proutiere and M. Chabanel, J. Mol. Struct., 295 (1993) 155. 20 J. Applequist, J.R. Carl and K.K. Fung, J. Am. Chem. Sot., 94 (1972) 2952. 21 S.S. Batsanov, Refractometry and Chemical Structure, Consultants Bureau: New York, 1961, and references cited therein. and R.A. Ford, The Chemist’s 22 A.J. Gordon Companion, Wiley-Interscience, New York, 1972. 23 R.C. Weast (ed.), Handbook of Chemistry and Physics, 69th edn., CRC Press, Boca Raton, Florida, 1980. 24 Al. McLeilan, Tables of Experimental Dipole Moments, Rahara Enterprises, El Cerrito, 1974. and T.M. 25 R. Boese, D. Bllser, M. Nussbaumer Krygowski, Struct. Chem., 3 (1992) 363. 26 R. Anulewicz, T.M. Krygowski, E.D. Raczynska and C. Laurence, J. Phys. Org. Chem., 4 (1991) 331.