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Structure of Some Alkynylcarbenium Ions
(12) See: (a) W. A. Lathan, L. A. Curtiss, W. J. Hehre, J. B. Lisle, and J. A. Pople, Prog. Phys. Org. Chem., 11, 175 (1974); (b) J. A . Popie in “Modern Theoretical Chemistry”, Vol. 4, H. F. Schaefer, Ed., Plenum Press, New York, 1977, p 1. (13) STO-3G and 4-31G force constants for water and ammonia required for the calculation of vibrational frequencies have been reported: H. B. Schlegel and S. Wolfe, J. Chem. Phys., 63, 3632 (1975). (14) The performance of the STO-3G and 4-31G basis sets with regard to the calculation of hydrogenation energies has previously been discussed: W. J. Hehre, R. Ditchfieid, L. Radon, and J. A . Pople, J. Am. Chem. SOC.,92, 4796 (1970). (15) A number of comparisons of relative isomer energies at the STO-3G// STO-3G and 4-31G//STO-3G levels have appeared in the literature: (a) L.
Radom, W. J. Hehre,and J. A. Pople, J. Am. Chem. Soc., 93, 5339(1971): (b) W. A . Lathan, L. Radom, P. C. Hariharan, W. J. Hehre, and J. A. Pople, Fortschr. Chem. forsch., 40, 1 (1973). (16) We propose a nomenclature A//B to indicate calculations which have been performed at level A using a geometry which is optimum for level B. Thus 3-21G//STO-3G indicates a 3-21G level calculation using an optimum STO-3G geometry. (17) Limited assessment of the STO-3G and 4-31G basis sets with regard to the calculation of dipole moments has previously been published: ref 2a and 15a and (a) W. J. Hehre and J. A. Pople, J. Am. Chem. SOC.,92,2191 (1970); (b) ibid., 97, 6941 (1975). (18) J. S. Binkley, J. A. Pople, M. S. Gordon, and W. J. Hehre, unpublished results.
A Theoretical Study of the Structure and Charge Distribution of Some Alkynylcarbenium Ions M. Dorado, 0. M6, and M. Yhiiez* Contribution f r o m the Departainento de Qulmica Fjsica J Qujmica Cucintira. Centro Coordinado C S I C - C A M , Facultad de Ciencias C-XIV, Unicersidad Autbnoma, Cantoblanco. Madrid, 34, Spain. Receiced February 28, I 9 7 9
Abstract: We have carried out STO-3G minimal basis set “ab initio” calculations to determine t h e structure and charge distribution, using the YSP population analysis, of the propargyl cation and some of its mono-, di-, and trisubstituted derivatives. Our results indicate that progressive N substitution favors a greater participation of mesomeric form XYC,,+ -Cd=C,Z, while y substitution increases the contribution of form XYC,=C,j=C,+ - Z. The relative stability of the different derivatives is also discussed.
I. Introduction Alkynylcarbenium ions were directly observed first by Richey, Philips, and Rennick’ in 1965. Ever since, the number of experimental and theoretical studies on these (and related) cations has been considerable.* This interest is justified because alkynyl cations are directly related to and can be a convenient model3 for vinyl cations, which are, in turn, intermediates in solvolyses of vinyl halide^,^-^ vinyl triflate~,’.~ and the electrophilic addition to alkynes9 Alkynyl cations can exist in the two mesomeric forms presented in Figure 1 . Since the paper of Richey et al.’ was published, a considerable experimental effort was devoted to studying the inhcrent stabilities, structure,lO.iI and charge distribution3 of these cations. This last aspect constitutes one of the most recent and interesting applications of I3C magnetic resonance spectroscopy, since it has been proved“ that chemical shifts reflect the charge densities on carbons of similar hybridization and subs t i t ution. All these experimental s t u d i e ~ I~indicate , ~ ~ , ~that mesomeric form I I is an important contributor to the stability of these cations. However, little can be said on how substituents might change the relative importance of these mesomeric forms, because only tertiary ions are stable, and this makes observation of electronic changes a t C,,, C,d,or C, i m p ~ s s i b l eHow.~ ever. theoretical work can yield valuable information on this problem. The first members of this family, propargyl cation and its possible isomers, have been already studied at the “ab initio” level, using different basis sets.” However, no effort was devoted to evaluate the structure and charge distribution of alkynyl cations, with the only exception being the semiempirical calculations of Pittman et al.I4 I n this paper we present an “ab initio” study of some alkynylcarbenium ions. We will center our discussion on the rel0002-7863/80/ I SO?-0947$Ol .OO/O
ative stability of mesomeric forms I and I I and on the influence of the substituents on the stability of either form, in each particular case. We will calculate the charge distribution using the YSP population a n a l y ~ i s ,which ’~ has been proved very reliablelh to evaluate charge densities in neutral and charged systems. YSP population analysis is a density-partitioning technique based on the representation of the electron density p ( r ) by an expansion in terms of spherical atomic density basis functions which do not present the limitations of the Mulliken population analysis, in the sense that the charge distributions obtained do not depend on the details of the basis set used in spanning the molecular wave function. 11. Calculations
We have carried out a geometry optimization of these mono-, di-, and trisubstituted propargyl cation derivatives (IIIa-I), presented in Figure 2, using a STO-3G minimal basis set.17 In the optimization process for IIIb-f, the following restrictions were adopted: the methyl group was kept unchanged, assuming local C3L.symmetry with C H bond lengths equal to I . I O A and HCH bond angles equal to 109.47’. For 1111cation, the NH2 group was also kept unchanged and in the same plane of the molecule, assuming local Clc symmetry with N H bond length equal to 1 .O8, and the N H N bond angle equal to 1 2 0 O . I n all cases (IIla-I) we have taken the C,-C&, skeleton as linear. With these restrictions, all the remaining parameters were optimized, until changes in the total energy were less than au for variations of f0.005 8, in the bond lengths and 0.1 O in the bond angles. 111. Monosubstituted DerivatiFes
We present in Table I the optimized geometry of propargyl C 1980 Anieric‘in Chemical Societl
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Journal of the American Chemical Society
/ 102:3 1 January 30, 1980
Table 1. Geometrical Parameters for Propargyl Cation and Its Monosubstituted Derivatives in the Conformation of Minimal Energy llla
lllb
1.360 1.214 1.109 1.109 1.091
1.348 1.222 1.106 1.106 I .484
Bond Lengths 1.380 1.204 1.1 10 1.515 1.070
121.1 121.1 117.8
121.4 121.4 117.2
Bond Angles (deg) 1 17.6 124.0 118.4
. I 13.563 92
-152.179 40
Y
';.-ccs-c8-
2
X/
-
Illc
lllg
Illh
IIII
1.351 1.237 1.107 1.107 1.280
1.397 1.198 1.120 1.292 1.089
1.319 1.242 1.099 1.099 1.294
121.2 121.2 117.6
121.8
121.6 116.6
121.3 121.3 117.4
--21 1.022 75
-2 I 1.037 48
-'167.955 02
(A)
Energies ( a u ) -152.175 10
+
y\ C X/
F
cp-CaZ 1258
*9L
I
II
Figure 1. Mesomeric forms of alkynylcarbenium ions. V
+69
111
X
Y
a
H
H
b
H
c
H
d
H CH3 CH3 H H H F F H
H CH3 C H3 C H3 C H3 H F F F F
e f
9 h I
j k I
H
Z H CH3
H CH3 H CH3 F H F H F NH2
Figure 2. Alkynyl cations included in this study.
cationi3and its F- and CH3-monosubstituted derivatives. The inclusion of 1111cation in this table will be justified later. It is clear, from values in Table I, that a substitution (IIIc,h) considerably increases the C,-C@ bond length and shortens the Cp-C, bond relative to the parent cation (IIIa), indicating that this substitution favors a considerable contribution of form I. On the contrary, y substitution (IIIb,g) yields shorter C,-Ca and larger Cp-Cy bonds than those in the parent cation, which is evidence that y substitution increases the participation (see Figure 1) of form 11. It is also evident that a different mechanism must be involved i n these effects, since the substituents are of a very different nature. To study this aspect of the problem, we have evaluated the charge distribution of these cations, using the YSP population ana1y~is.l~ The results obtained are presented in Figure 3. Fluorine substitution at C, increases considerably the charge on this carbon, stabilizing a structure with more participation of form I (see Figure I ) . Obviously, y substitution has the same effect on the y-carbon atom, increasing the contribution of form 11.
t96
..,.,
Fi'gure 3. Charge distribution ( electron) of propargjl cation and its monosubstituted derivatives. obtained using YSP population analysis and a STO-3G basis set.
When the substituent is a methyl group there is no substantial increase of the charge on the substituted carbon atom (see Figure 3). As it has been shownI8 that hyperconjugation is particularly intense in ionic species, u e will analyze the a-electron density on these cations. Mulliken electron charge densities in the pL orbitals (perpendicular to the molecular plane) are given in Table 1I for I l k - c species. We can observe that methyl cy substitution produces a decrease of the a charge density at C,, and an increase a t C3 and C,, favoring a greater participation of form I, uhile the opposite effect is observed when substitution takes place a t the y carbon, favoring the participation of mesomeric form 11. In general, our results show that, if Y (see Figure 1) is a substituent that either withdraws cr electrons from C,, or donates ir charge into the 2pCo orbital, participation of form I is favored. When substituent Z (see Figure 1 ) presents the same behavior, a greater participation of form I 1 occurs. These effects are more intense in the case of fluorine substitution, because fluorine not only withdraws cr electrons from C,,, but also donates K charge into the 2 p C orbital ~ to a considerable extent. It is also interesting to note that the a-substituted fluorine derivative (IIlh) is more stable than the y-substituted one (IIIg). When the substituent is a methyl group the situation Table 11. Electron Density in the p) Orbital of I l l a , I l l b . and I l l c Alkynyl Cations
C,, Cd C,
IIla
lllb
Illc
0.409 1.129 0.462
0.472 1.126 0.456
0 391 1.135 0.544
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Strirctrire of S o m e Alkynylcarbenium Ions
Table Ill. Geometrical Parameters for Di- and Trisubstituted Propargyl Cation Derivatives in the Conformation of Minimal Energy Illd
Ille
cy-2
1.365 1.212 1.107 1.516 1.485
I .395 1.197 1.524 1.524 1.084
Bond Lengths (A) 1.381 1.204 1.525 1.525 1.486
CJC,"X C&,Y XC
