2440
Y. Ellinger, R. Subra,
G.Berthier, and J. Tomasi
Theoretical Treatment of Electrophilic Reactivity in Nitroxides and Ketyl Radicals through ab-Initio Molecular Electrostatic Potentials Y. Ellinger," R. Subra, G. Berthler, and J. Tomasi Laboratoire de Chimie Organique Physique, Departement de Recherche Fondamentale du Centre d'Etudes Nucleaires de Grenoble, F. 3804 1 Grenobie-Cedex, France, and Laboratorio di Chimica Quantistica ed Energetica Molecolare, I, 56 100, Pisa, ltalia (Received May 30, 1975) Publication costs assisted by CEA, Grenoble
Isopotential-energy maps of electrostatic molecular potentials have been drawn for nitroxide (H2NO), iminoxy (HZCNO), and ketyl (HzCO-) radicals. Electrophilic attack is clearly favored a t the oxygen lone pairs in the case of H2N0, but at the nitrogen lone pair in HzCNO, suggesting different protonation approaches in the two types of nitroxides.
Introduction
From the V(F) function, we have calculated, point by point, the value of the electrostatic interaction energy W ( i ) = It is now a well-established fact that electrostatic molecq V ( i ) between an external point charge q and the molecuular potentials have proved to be highly successful for inlar charge distribution. The results are presented here in vestigating molecular reactivity in ionic-type reactions, the form of maps of W ( i ) for selected planes, taken q as especially in the case of protonation of closed-shell moleunit positive charge. The starting point of our calculations c u l e ~ . Most ~ - ~ probable sites of attack and reactions paths is the ab initio wave functions determined in our previous can be safely predicted, giving a way to compare different ~ ~ r using k the ~ ~spin-restricted ' ~ ~ formalism of Rooreaction sites in a series of related molecules. thaan.lOJ1 The basis set consists of (7s,3p/3s) gaussianThe electrostatic potential gives a first-order approximatype orbitals12 contracted to (3s,2p/ls). tion of the interaction energy between a unit point charge, 1. The HzNO Radical. It is now known that the nitroxide a proton, for example, and the charge distribution of the functional group does not possess a well-defined intrinsic molecule; variation of the molecular geometry and reargeometry but may exist in a planar13 or a pyramidal form.14 rangement of the electronic cloud when the proton apFor that reason we have considered several values of the proaches are not considered. The effects of these possible torsion angle a made by the NO bond and the HNH plane. factors have been investigated in detail several times, using Electrostatic interaction energies are reported here for cy = the supermolecule model which takes into account the two O', Le., the planar geometry, for a = 20°,an average experiinteracting species as a unique en tit^.^^^^ It has been shown mental value. The other structural parameters (NO = 1.34 that exchange polarization effects, charge transfer, and 8; NH = 1.02 A; HNH = 123') have been obtained pregeometrical optimization do not change the overall reactivv i o u ~ l yby~ ~a complete optimization of the molecular geity pattern obtained from the electrostatic model. The poometry. Isopotential-energy maps drawn in the symmetry larization effect has been found to reinforce the electrostatplane of the molecule (C, for any a ) and in the perpendicuic factor, the charge transfer term being unable to reverse lar section containing the NO bond are given in Figures 1 it.5 A recent perturbation treatment of protonation enerand 2 for a = 0 and 20°, respectively. gies in competitive reactions corroborates the validity of In the symmetry plane containing the unpaired 7r electhe first-order electrostatic approximation.6 tron (or pseudo T if a # 0), the potential curves show a In this paper we present an approach to protonation wide attractive region surrounding the NO bond with two problems in open-shell molecules. We have considered the minima located a t the nitrogen and oxygen atoms, respecfirst members of the nitroxide (HzNO), ketyl (HzCO-), and tively, while the NHz region appears strongly repulsive. iminoxy (HzCNO) series which have proved p r e v i o u ~ l y ~ - ~The depth of the minimum above the nitrogen atom into be highly representative of the respective functional creases from -17.9 ( a = 0') to -34.5 (cy = 20') and reaches groups for the molecular geometries as well as for the evo-56.7 kcal/mol for a hypothetical torsion of a = 60'. This lution of hyperfine splittings with conformation changes in can be correlated with an increasing s character of the nithe different series. trogen hybrid entering into the open-shell MO. The miniElectrostatic Molecular Potential of Simple Free Radicals The electrostatic potential V(F) arising from the electronic and nuclear charge distribution of a molecule a t every point in its neighboring space is given by
where p ( F 1 ) is the first-order density function. The first term clearly gives the potential arising from the nuclei. The Journal of Physical Chemistry, Vol. 79, No. 22, 1975
mum appearing near the oxygen atom is more exactly identified on the diagram drawn for the perpendicular plane. In fact, this plane contains two minima located in the direction of the two oxygen lone pairs. The two attractive wells a t the oxygen atom are deeper than the nitrogen one, and remarkably unaffected when varying a within the experimental limits of torsion of the radical center. 2. The HzCNO Radical. We have considered the most stable conformation previously determined by optimization of all the geometrical pararnetemgbThe calculated equilibrium bond lengths are 1.082, 1.26, and 1.33 A for the CH,
2441
Theoretical Treatment of Electrophilic Reactivity
N
0
1
b
60
N
0
N
0
'-y-20Y
Figure 2. lsoenergy curves for the interaction of bent HlNO (a =
20') with a proton (kcaVmole):(a) symmetry plane: (b) perpendicu-
lar section containing the NO bond.
Figure 1. lsoenergy curves for the interaction of planar H2NO with a proton (kcaVmole): (a) symmetry plane; (b) perpendicular section containing the NO bond.
CN, and NO bonds, respectively. The CNO angle is found to be equal to 122O. An angle of 119.5' is obtained between the two CH bonds, the methylenic group being tilted by 4 O toward the trans position with respect to the NO bond. The isopotential curves drawn in the molecular plane containing the unpaired a electron are given in Figure 3. The potential presents an oblong attractive depression on the less crowded side of the NO bond, the remainder of the molecule being surrounded by a repulsive area. A deep minimum (-53.7 kcal/mol) appears near the nitrogen, corresponding to the direction intuitively attributed to the lone pair. A secondary minimum can be seen a t the extremity of the NO bond. In fact, a detailed investigation of the per-
pendicular sections shows two equal minima (-35.0 kcal/ mol) above and below the molecular plane and confirms that the deepest attractive well is located a t the nitrogen atom. 3. The H2CO- Radical. The structure of this radical ion being unknown, we have considered its equilibrium conformation determined by an optimization of all the geometrical parameter^.^^ Bond lengths of 1.09 and 1.33 A are obtained for the CH bonds and CO bond, respectively. The system is found to be nonplanar with an out-of-plane angle of 24' and an HCH angle of 117.5'. As for HzNO, isopotential-energy maps have been drawn in the symmetry plane and in the perpendicular plane containing the CO bond.15 They indicate that the radical is entirely inside an attractive sphere as a consequence of the negative charge of the molecule. The most attractive position is found to be located at the oxygen. It appears as a hemispherical shell with two minima (-249.4 kcal/mole) in the direction of the The Journal of Physical Chemistry, Vol. 79, No. 22, 1975
Y. Ellinger, R. Subra, G. Berthier, and J. Tomasi
2442 /
I
/
60
20\
I
Figure 3. lsoenergy curves for the interaction of H2CNO with a pro(kcel/mole):molecular plane.
ton
oxygen lone pairs. The electrostatic potential computed for a postulated planar radical leads to the same conclusions ( V ( i )minimum = -249.3 kcal/mol).
The observed decrease in g factor was attributed to the fact that the contribution of the open shell to the electronic population of oxygen decreases and the n--A* transition energy increases.lgb From a qualitative point of view, one may parallel the remarkable constancy of the electrostatic interaction energy and the small range of the pK, (viz -5.5 f 1) found by Malatesta and Ingold20 for protonated nitroxides of very different geometries. Given this similarity, it seems rather unlikely that entropy effects for any of the radicals differ very much from that of the other members of the series. However, we cannot exclude the possibility of a compensation between the effects of molecular deformation of the radical site and the concommitant variation of the entropy term. Finally it is perhaps necessary to emphasize again that the electrostatic potential method gives a valuable approximation of the protonation process and this with a considerable saving in computer time as compared to any optimization calculation on the supermolecule.
Acknowledgment. The authors are particularly grateful to Dr. R. Bonaccorsi for her help in performing the calculations. Thanks are also due to a referee for improvements in the form of the manuscript.
References and Notes Discussion Following the established criteria for protonation-site predictions, the most favorable reaction center would be the oxygen atom in the nitroxide and ketyl groups, while nitrogen attack would be favored in iminoxy radicals. When analyzing the localized description of the SCF wave function of the molecules (in the present case Boys exclusive orbitals16 calculated in the frame of the +-A separation) the exact location of the minimum potential is found in a good approximation to be in the direction of the lone pair of the heteroatoms. This confirms the correspondence already mentioned2b between electrostatic potentials and descriptive concepts of theoretical chemistry such as hybridization. The validity of the electrostatic predictions can be checked independently by the results of a very recent ab initio calculation of the hydroxymethyl radical CHpOH (the supermolecule corresponding to the interaction of H&O- with Hf).17 The equilibrium geometry obtained after optimization of bond lengths and bond angles (Figure 1 of ref 17) corresponds very well to the present results. These complementary calculations confirm the ability of the electrostatic potential method for investigating the protonation processes in open-shell systems as well as in ordinary closed-shell molecules. However it should be clear that the electrostatic description which gives valuable ideas on the preferential site of protonation a t least during the first steps of the approach of reactants would lead to erroneous conclusions if rearrangements or prototropic migrations follow the formation of the primary adduct. The fact that the preferential site found in complexing the nitroxide group with a positive charge is the oxygen atom corroborates the interpretations of the ESR experiments on the interaction between these type of radicals and Lewis acid@ or proton-donor m~lecules.'~ Attaching a proton to one of its lone pairs makes the oxygen more attractive to the ?r bonding electrons and pushes the antibonding unpaired -A* electron toward the nitrogen atom as a consequence of which the nitrogen hyperfine splitting a N increases. The Journal of Physical Chemistry, VoI. 79, No. 22, 1975
Address correspondence to this author at Centre dEtudes Nuclealres de Grenoble. (a) R. Bonaccorsi, E. Scrocco, and J. Tomasi, J. Chem. Phys., 52, 5270 (1970); (b) Theor. Chim. Acta, 21, 17 (1971); (c) G. Berthier, R. Bonaccorsi, E. Scrocco, and J. Tomasi, ibM., 26, 101 (1972); (d) R. Bonaccorsl, A. Pullman, E. Scrocco, and J. Tomasi, ibM., 24, 51 (1972); (e) R. Bonaccorsi. A. Pullman, E. Scrocco, and J. Tomasi, Chem. Phys. Lett., 12, 622 (1972); (f) C. Petrongolo and J. Tomasi, ibM., 20, 201 (1973); (g) C. Giessner-Prettre and A. Pullman, Theor. Chim. Acta, 33, 91 (1974); (h) J. Bertran, E. Silla, R. Carbo, and M. Martin, Chem. Phys. Lett., 31, 267 (1975). Solvation processes have also been investigated through electrostatic potentials; see for instance (a) R. Bonaccorsi, C. Petrongolo, E. Scrocco, and J. Tomasi, Theor. Chim. Acta, 20, 331 (1971); (b) G. Aiagona. R. Clmiraglia, E. Scrocco, and J. Tomasi, ibid., 25, 103 (1972); (c) G. Alagona, A. Pullman, E. Scrocco, and J. Tomasi, Int. J. Peptide Res., 5, 251 (1973). For more details, a general survey on molecular electrostatic potentials can be found in E. Scrocco and J. Tomasi, Fortschr. Chem. Forsch., 42, 95, (1973). A. Pullman, Chem. Phys. Lett., 20, 29 (1973). R. J. Bartlett and H. Weinstein, Chem. Phys. Lett., 30, 441 (1975). For HgNO, see for instance (a) J. Douady, Y. Ellinger, A. Rassat, R. Subra, and G. Berthier, Mol. Phys., 17, 217 (1969); (b)A. W. Salotto and L. Burnelle, J. Chem. Phys.. 53, 333 (1970); (c) Y. Ellinger, R. Subra, A. Rassat, J. Douady, and G. Berthier. J. Am. Chem. Soc., 97, 476 (1975). For HpCO- see for instance ref 7c and G. R. Underwood, Mol. Phys.. 22, 729 (1971). For H&NO see for instance (a) G. Berthier. H. Lemaire, A. Rassat, and A. Velllard, Theor. Chim. Acta, 3, 213 (1965); (b) Y. Ellinger, Thesis, Grenoble, 1973. C. C. J. Roothaan, Rev. Mod. Phys., 32, 179 (1960). A. Veillard, D. J. David, and P. Millie, IBMOL CDC 3600 Version, Laboratoire de Chimie de I'Ecole Normale Superieure, Paris, 1967. E. Clementi, J. M. Andre, M. CI. Andre, D. Klint. and D. Hahn, Acta Phys. Acad. Sci. Hung., 27, 493 (1969). (a) R. P. Shibaeva and L. 0. Atovmian, Zh. Strukt. Khim., 13, 887 (1972); (b) B.Andersen and P. Andersen, Acta Chem. Scand., 20, 2728 (1966); (c) B. Chion, A. Capiomont. and J. Lajzerowicz-Bonneteau, Acta CrystaIIogr., Sect. 6, 28, 618 (1972); (d) J. W. Turley and F. P. Boer, bid., 28, 1641 (1972); (e) G. Kruger and J. Boeyens, ibid., 28, 668 (1970). (a) J. Lajzerowlcz-Bonneteau, Acta CrystaIIogr., Sect. 6, 24, 196 (1968); (b) D. Bordeaux, A. Capiomont, and J. Lajzerowicz-Bonneteau, C. R. Acad. Sci.. in press; (c) D. Hawley, G. Ferguson, and J. M. Robertson, J. Chem. Soc. 6, 1255 (1968); (d) A. Capiomont, Acta CrystalIogr. Sect. S, 29, 1720 (1973); (e) A. Capiomont, B. Chion, and J. Lajzerowicz-Bonneteau, ibM., 27, 322 (1971); (f) A. Capiomont and J. Lajzerowlcz-Bonneteau, ibid., 28, 2298 (1972); (g) G. Glldewell. D. W. Rankin, A. G. Robiette, G. M. Sheldrick, and S. M. Williamson, J. Chem. Soc. A, 478 (1971). The maps have not been reported here in order to save space but they are available on request from the authors.' S. F. Boys In "Quantum Theory of Atoms, Molecule and the Solid
Alkynyl
Cations
2443
State”, P. 0. Lowdin. Ed., Academic Press, New York, N.Y.. 1966, p 253. (17) T. K. Ha, Chem. Phys. Lett., 30,379 (1975). (18) (a) E. M. Hoffman and T. E. Eames, J. Am. Chem. SOC., 91, 2169 (1969); (b) T. E. Earnes and E. M. Hoffman, ibid., 91, 5168 (1969); (c) E. M. Hoffman and T. B. Eames, ibid., 93, 3141 (1971); (d) A. H. Cohen
and E. M. Hoffman, inorg. Chem., 13, 1484 (1974); (e) C. Hambly and J. B. Raynor, J. Chem. SOC.,Dalton Trans., 604 (1974). (19) (a) H. Lemaire and A. Rassat, J. Chim. Phys., 61, 1580 (1964); (b) T. Kawamura, S. Matsunami, and T. Yonezawa, Bull. Chem. SOC.Jpn., 40, 11 11 (1987), see also P. J. Zandstra, J. Chem. Phys., 41, 3655 (1964). (20) V. Malatesta and K. U. Ingold, J. Am. Chem. Soc.. 95,6404 (1973).
Charge Distribution and Structure of Alkynyl Cations. An INDO Study C. U. Pittman, Jr.,* 0. Wilemon, J. E. Fojtasek, and L. D. Kispert‘ Department of Chemistry, The University of Alabama, University, Alabama 35486 (Received June 5, 1975) Publication costs assisted by the University of Alabama
Geometry-optimized INDO calculations were performed on a series of alkynyl cations, R1RzC+-C=CR3. The geometries, charge densities, ?r-bond orders, and *-orbital electron densities are discussed in terms of RzC=C=C+R. the relative contributions of the alkynyl and allenic resonance hybrids: RzC+-C=CR The allenic hybrid makes a larger contribution when R1, Rz, R3 = H than when R1, Rz,R3 = CH3. The allenic hybrid makes its largest contribution when R1, Rz = H and RS = phenyl. When R1 and/or R2 are fluorine, the contribution by the allenic hybrid is reduced. These results are compared to recent 13C NMR chemical shift observations.
-
Proton and I3C NMR spectroscopy has been used extensively to probe the structure and charge distribution in carbo ~ a t i o n s . l -Recently, ~ Olah et al. reported the I3C4and IH5 NMR spectra of a series of alkynyl cations, I, and, on
I
I1
the basis of the 13C NMR chemical shifts, concluded that the positive charge is extensively delocalized (Le., the mesomeric allenyl cations, 11, contribute extensively to the ions’ structure). In particular, both the a and y carbons were significantly deshielded where R1 = RP = R3 = CH3. Here, Olah predicted the contributions of I and I1 to be in about a 2:l ratio and the charge at C, should be about twice that a t Cy.* The allenic forms, 11, and vinyl cations have proved to be elusive to observe under stable conditions in Thus, it might be expected that the vinyl character of alkynyl cations would be stabilized less than their corresponding allylic cations. Indeed, the solvolysis rate of 3-chloropropyne was a factor of 100 less than 3-ch1oropropene.l However, Taft et al.9 found the relative stabilization energies of CHz=CH2CHz+ and CH=CHCHz+ vs. CH3+ were -2.35 and -2.40 eV, respectively, in the gas phase. Since we had already performed geometry-optimized theoretical studies, in the INDO approximation, on substituted allylic cations,1° extension of these studies to alkynyl cations was performed to probe their charge distributions.
Results Calculations were performed on the alkynyl cation series Ia-g. Geometry optimization was carried out by the “brute
Rl
>C+ -C=C-RJ R? Ri RL RJ I a H H H b CHj CH, CHI c H H Ph d H H F e H F F f F F F g CHI CHI F force” method as described p r e v i o ~ s l y . ~All ~ - ~ bond ~ lengths and angles were fully optimized except for the C-H lengths and angles of the methyl groups and the phenyl ring of IC.The ring geometry in ICwas partially optimized. Calculations employed the CNINDO program, QCPE number 141. The optimized geometries are shown in Figure 1. In all cases the molecular plane was the xy plane. Thus, the pz orbitals were those perpendicular to the molecular plane. The x axis was defined along line formed by the linear C,-Cp-C, system. The favored C,C&, geometry was linear in all cases. An examination of the calculated bond lengths, charge densities, rz-bond orders, and T -and o-electron distributions in Ia-g provided a picture of both the electron distribution and (qualitatively) the magnitude of the contribution of hybrid 11. In every case, the C,-Co length was substantially greater than the Cp-Cy length. The C,-Cp lengths varied from 1.325 (IC)to 1.372 A (If) while the C r C , lengths varied from 1.220 (Ig) to 1.270 8, (IC).The C,-Co lengths decreased in the order If > Ig = Ib > Ie > Ia > Id > IC. Thus, progressive methyl and a-fluorine substitution seems to favor a larger contribution of hybrid I. These groups stabilize the cation and thereby reduce the contribution by I1 needed. The Journal of Physicai Chemistry, Vol. 79,
No. 22, 1975
