6.U. Pittman, L. D. Kispert, and T. B. Patterson, Jr.
494
The correct form may be very nearly Lorentzian. However, we also asserted that in the soft sphere cases, characterized by the inner sphere cases, the Arrhenius form may reappear. Clearly, the form of the rate constant in an exact treatment is largely a function of the type of model representation of the system chosen. It is my hope that these few simple physical and mathematical arguments provided in this paper will serve to make understandable the underlying concepts common to
the growing and increasingly complicated general theory of these reactions. Acknowledgments. I should like to thank Professor A., G. Davies and Dr. Thirunamachandran for their hospitality and generosity in accomodating me during my stay in ‘London. I also acknowledge a number of stimulating conversations with Professor Allen Maccoll which had an indirect bearing on this work.
tudies.’ The Geometry of 1-Substituted Vinyl Radicals an
nrles U. Pittman, Jr.,* Lowell D. Kispert, and Thurman B. Patterson, Jr. Department of Chemstry, Un/vers/tyof Alabama, Tuscaloosa, Alabama 35486 (Recewed September 5, 79721 Pubhation costs asssted by The Unwerslty of Alabama
1,CAMO-SCF calculations, in the INDO approximation, have been performed on a series of l-substituted vinyl radicals, CH2=CX where X is F (4), OCH3 ( 5 ) , and BH2 (6). Also the cis- and trans-1,2-difluorovinyl radicals 7 and 8 were examined. When X is more electronegative than carbon, the bent (sp2) geometry is more stable than the linear (sp) geometry. However, the linear geometry is more stable when X is BH:!. The most stable geometries of both bent and linear 6 were those where the plane of the BH:! group was rotated out of the molecular plane (xz plane, with CZ-61 defined along the z axis) by 52 and W , respectively. In these out-of-plane geometries the x bonding from the “empty” boron p orbital to carbon was greatly reduced in both x and y planes. Barriers to inversion, u and T electron distributions, and the unpaired spin densities were studied. In the bent geometry of 4, 5, 7, and 8 the bulk of the unpaired spin density is in the px orbitals at both C-1 and the 1 substituent. The amount of spin density in the C - l px orbital increases sharply as the geometry approaches linearity. However, in 6 where BH2 is the substituent, the majority of the spin density is found in the py orbitals of 6 - 2 and boron in both linear and bent all-planar geometries. Rotation of the BH2 plane results in a marked increase in the C-1 px spin density. Calculations were also performed on both the 1-fluor0 and the 1,2-difluorovinyl cations 9 and 10- The linear geometry is strongly favored in both 9 and 10 where strong x x back-bonding from F-l to C-1 takes place. However, r X back-bonding is also found in the bent geometries. In both cases the CI-FI c bond is still strongly polarized toward fluorine. Unlike CH&H+, very little polarization of xy electron density at 6 - 2 toward C-1 takes place in 9 or 10. The instability of the bent geometry largely results from the necessity of promoting electron density from the 2s to the 2p orbital.
I~trod~ct~Qn Vinyl radicals are readily available from the thermal and photochemical decompositions of a,@-unsaturated peresters and diacyl peroxide^,"^ from radical additions to alkynes,“-” from the photolysis of vinyl iodides,lO and from electrochemical generation.ll Previous studies of vinyl radicals have been reviewed.12 Esr studies13-15of the unsubstituted ethylene radical ( I ) definitively supported a bent (sp2) structure in the condensed state with a low ( -2-3 kcal/rnol) barrier to i n ~ e r s i 0 n . lDetailed ~ molecular orbital calcuiatior1s,l6~~7 in which all angles and bond lengths were optimized, predicted the bent planar structure of 1 would be the most stable. A b initio calculations, using Gaussian-type basis sets,16 gave 0 = 130.8’. Many other theoretical calculations also favored the bent geometry for l m l S The Journal of Physical Chemistry, Vol. 77, No. 4 , 1973
1
The configurational stability of cis and trans l-substituted 1-alkenyl radicals, such as 2 and 3, have been stud(1) iNDO Theoretical Studies part IV. For papers 1-111 in this series see (a) L. D. Kispert, C. Engelman, C. Dyas, and C. U. Pittman, Jr., J. Amer. Chem. Soc., 93, 6948 (1971); (b) C. U. Pittman, Jr., C. Dyas. C. Engelman, and L. D. Kispert, J. Chem. Soc.. Faraday Trans. 2, 68, 345 (1972); ( c ) L. D. Kispert, C. U. Pittman, Jr., D. L. Allison, T. B. Patterson, Jr., C. W. Gilbert, Jr.. C. F. Hains, and J. Prather, J. Amer. Chem. Soc., 94, 5979 (1972). (2) J. A. Kamprneier and R. M. Fantazier, J. Amer. Chem. SOC., 88, 1959 (1966). (3) L. A . Singer and N. P. Kong, d. Amer. Chem. Soc., 88, 5213
(1966).
INDO Theoretical Studies
495
ied in solution by competition s t u d i e ~ . ~Kampmeier, ~J~ et al.,19 generated 2r and 3c by thermal decomposition of their corresponding terd-butyl cis- and trans-l-methoxypercrotonates in cumene. The radicals were quenched by hydrogen abstraction from cumene to give the cis- and ~ r a ~ ~ . . m e t h y l - ~ ~ p r o pethers e n y l with retention of stereochemistry. Thus, hydrogen abstraction was faster than the isomerization (21: 3c) of these radicals. Conversely, the isomerization of 1-alkylvinyl radicals (2a s 3a) is much faster than hydrogen transfer from cumene, and these two processes are competitive for 1-chlorovinyl radicals.12 While these experimental results actually reflect the ratio of the rate of hydrogen abstraction to the rate of isornerizatiom, it was suggested that the main effect is the rate of isornerization.l9 It was postulated that this rate depends on the nature of the 1 substituent and that the isomerization rate was a function of the electronegativity of the 1 substituent.19 However, it is quite possible that the rate of hydrogen abstraction is affected by the 1 substituent and by the nature of the radical's solvation. The character of the solvent sheI1 would depend, in part, on the 1 substituent, Thud, the argument that the rate of isomerization is greatly reduced as the electronegativity of the 1 substituent increases, while attractive, needs further
2,
3 a, X = CR,
b, X = C l C, X = OCH3
In this regard it is interesting that extended Hiickel molecular orbital cedculations have indicated the barrier to isomerization is greater for 1-hydroxy and 1-fluorovinyl radicals than for the 1-methylvinyl radical.20 It is well known that the IIIVDO technique includes repulsion integrals which permit a description of the unpaired spin density in s orbitals. Thus, in this paper we report molecular orbital calculations, in the END0 approximation, on the series of 1-substituted vinyl radicals where the 1 substituent is fluorine, mcithoxy, and BHz. The bent-planar (sp2) (4a-6a) and line,ar-planar (sp) (4b-6b) structures were compared in order to approximate the barrier to gas-phase isomeri.zation and, more import,antly, to illustrate the trend as the electmnegativity of the 1 substituent was varied. Calculations were also performed on the cis- and trans-1,2-difluorovinyl radicals 7 and 8 and the $arr:er to their interconversion.
b
1
4, X = F
5, X=OCHA 6 , X=BH,
7
8
The structures of the fluorine-substituted vinyl cations
CHzCF+ (9) and CHFCF+ (IO) were studied using the INDO technique, and they are also reported here. The parent cation in this series, CH&W+ was studied previously by two groups using ab initio16,21 and extended Huckel methods.22 It was shown to be planar with Czu symmetry. Thus, in contrast to CHzGH, a planar linear (sp) structure is favored for vinyl cation, CH&H+. The "empty" p orbital was stabilized through delocalization of electron density out of the 0 framework into this orbital.21 The thermodynamic stability of the vinyl cation, as determined by appearance and ionization potential studies,23324 lies between that of the methyl and ethyl cations. Vinyl cations have been generated in solution in an enormous number of s t ~ d i e s ,especially ~ ~ , ~ ~ via the solvolysis but their short lifeof vinyl trifluoromethanesulfonates,~~~~* times, have, to date, made direct spectroscopic observations impossible, even in strongly acidic media. This paucity of spectroscopic data prompted us to study the structure of 9 and 10.
Method The INDO program (CNINDO), CPE No. 141, was obtained from the Quantum Chemistry Program Exchange, Indiana University, and was modified for use on a Univac 1108. Structures were generated using the Gordon0. Simarnura, K. Tokumaru, and H. Yui, Tetrahedron Lett., 5141 (1966). P. G. Webb and J. A. Kamprneier, J. Amer. Chem. Soc.. 93, 3730 (1971). P. S. Skeli and R. G. Allen, J , Amer. Chem. SOC.,86, 1559 (1964). A. A. Oswald, K. Griesbaum, B. E. Hudson, Jr., and J. M. Bregrnan, J. Amer. Chem. SOC.,86,2877 (1964). J. A. Kampmeier and G . Chen, J. Amer. Chert. Soc.. 87, 2608 (1965). R. M. Kopchik and J. A. Kampmeier, J. Arner. Chem. Soc., 90, 6733 (1968). R. C. Neuman, Jr., and G. D. Holmes, J. Org. Chem., 33, 4317 (1968). A. I. Fry and M. A. Mitnick, J. Amer. Chem. Soc., 91, 6207 (1969). W. G. Bentrude, Annu. Rev. Phys. Chem.. '18, 300 (1967). R. W. Fessenden and R. H, Schuler, J. Chem. Phys., 39, 2147 (1963). E. Cochran, F. J. Adrian, and V. A. Bowers, J. Chem. Phys.. 40, 213 (1964). P. H. Kasai and E. B. Whipple, J. Arner. Chem. Soc., 89, 1033 (1967), W. A. Lathan, W. J. Hehre, and J. A. Popie, J. Amer. Chem. SOC., 93,608 (1971). P. Millie and G. Berthier, /nt. J. Quantum Chem., Symp., No. 2, 67 (1968). G. A. Peterson and A. D. McLachlan, J. Chem. Phys.. 45, 628 (1966); T. Yonezawa, H. Nakatsumi, 1. Kawamura, and H. Kato, Bull. Chem. SOC.Jap., 40, 2211 (1967); R. S. Drago and H. Peterson, Jr., J. Amer. Chem. Soc., 89, 5774. (1967); d. A. Pople, D. L. Beveridge, and P. A. Dobosh, J. Amer. Chem. Soc., 90, 4201 (1968); M. J. S. Dewar and M. Shansai, J. Arner, Chern. SOC.,91, 3654 (1969). M. S. Liu, S. Soloway, D. K. Wedergaerter, and J. A. Karnpmeier, J. Amer. Chem. SOC., 93, 3809 (1971); L. A. Singer and N. P. Kong, ibid.. 89, 5251 (1967). R. M. Kopchik, Ph.D. Thesis, University of Rochester, Rochester, N. Y., 1967: D. K. Wedegaertner, R. M. Kopchik, and 3. A . Kampmeier, J. Amer. Chem. Soc., 93, 6890 (1971). In this last reference, brief mention is made of a CNDO study showing the most stable form ofJhe 4-methoxyvinyl radical is bent and this is favored over the linear structure by 2.4 kcal/mol. R. Sustrnann, J. E. Williams, M. J. S. Dewar, L. C. Allen, and P. v. R. Schleyer, J. Amer. Chern. SOC.,91, 5350 (1969). R. H. Hoffmann, J. Chem. Phvs.. 40, 2480 (1964). A.Maccoil, Chem. Soc., Spec. Pub/., No. 16, 159 (1962) F. P. Lossing, "Mass Spectrometry," @. A. McDowell, Ed., McGraw-Hill, New York, N. Y., 1963, Chapter 11. For a review see H. 6. Richey, Jr., and J. M. Richey in "Carbonium Ions." Vol. 1 1 , G. A. Olah and P, v. R. Schleyer, Ed., Wiley-lnterscience, New York, M. Y., 1970, Chapter 21. M. Hanack, Accounts Chem. Res., 3,209 (1970). A. G. Martinez, M. Hanack, R. H. Surnmerville, P. v. R. Schleyer. and P. J. Starig, Angew. Chem., 82, 323 (1970). W. M. Jones and D. 13. Maness, J. Amer. Chem. Soc.. 91, 4314 (1969). The Journal of Physical Chemistry, Voi. 77, No. 4, !973
C. U. Pittrnan, L. D. Kispert, and T. B. Patterson, Jr.
496
TABLE I: Rehative Energies of the Optimized Linear and Bent Geometries of 1-Substituted Vinyl Radicals Radicals
7 substituent
At;
Most stable
kcal/mol
geometry
6.9 8.6 8.8 4.8 18.6 8.1
Bent Bent Bent Bent Linear Linear
s _ _ _ _ l I _ l I -
4a vs. 4b 7 vs. I-linear
F
vs. &linear 5a vs. 5b
F F OGH3
6a M. 6b
BI-iZ
Ga' vs. 6b'
en2
TABLE II: Calculated a Bond Orders of Vinyl Radicalsa K bond order
Radical
4a 4b Sa
5b 7
Bond
'r V
0.936 0.248 0.968 0.234 0.958 0.237 0.958 0.236 0.953 0.21 7 0.191 0.953 0.21 7 0.194 0.644 0.693 0.597 0.743 0.848 0.455 0.909 0.364 0.945 0.308
T X
0.332 0.289b 0.430 0.249 0.353 0.010 0.420 0.31 1 0.300 0.294b 0.150 0.316 O.30Zb 0.145= 0.424 0.31 3 0.41 1 0.432 0.392 0.569 0.383 0.41 3 0.415 0.507
plane. For all radicals and cations, the letters a and b were used to indicate a bent geometry and a linear geometry, respectively, at the 1-substituent position. In the case of X = BH2, primes were also added to indicate the additional presence of an out-of-plane geometry.
Results and Discussion 1-Substituted Vinyl Radicals. The calculated optimized geometries and total excess charge densities of both linear (lib and 5b) and bent (4a, 5a, 7, and 8) vinyl radicals are given in Figure 1. Figure 2 summarizes these data for four geometries (bent-planar (sa), linear-planar (6b), bentout-of-plane (6a'), and linear-out-of-plane (6b')) of vinyl radical 6. T h e major feature t o emerge is t h a t the bent geometries are more stable in 4, 5 , 7, and 8 where either F or OCH3 is t h e 1 substituent. Only when t h e 1 substituent is BHz does t h e linear geom.etry become more stable. The geometrical preference is expressed in Table I where the energy differences, AE, between bent and linear geometries are listed. These values of AE are also the barriers to isomerization for the radicals. I t is clear that t h e bent geometry is stabilized, relative to linear, when the l substituent is a n electronegative atom such as fluorine or oxygen. T h e more electropositive boron atom has t h e opposite effect. Thus, these INDO results strongly support Kampmeier'slQ postulate that the rate of isomerization is a function of the 1-substituent's electronegativity. Also the INDO results support the trend suggested by extended Hiickel calculations on vinyl radicals showing the barrier to isomerization is great,er for 1-OH and 1-F than for 1-
CH3." A second major feature immediately apparent is that i n
both the linear or bent geometries of radical 6, the plane defined by t h e BH2 substituent prefers to be rotated out of the molecular plane (by 45" in the linear, (Cub) geometry and 52" in the bent (6 = 160", geomelry), (6a)). This is a manifestation of the electronegativity difference between carbon and boron. The less electronegative boron may avoid accepting *-electron density donated from the carbon by undergoing partial rotation. The BW2 plane does not rotate a full 90" because this would bring the vacant "The z axis is defined dong the C2-C1 bond unless otherwise noted boron p orbital into conjugation with the px orbital on CThe z axis is defined along the CI-F, bond e The z axis is defined along 1.32 The relative energies of several optimized geometries tile C2-F2 bond Radical 6 where the piane of the BHa group IS rotated perpendicular to the rnoiecuiar plane defined by B, C-1, C-2, H-1, and H-2 of this radical are shown in Figure 3. T h e mmst stable geometry, 6b', is linear with the BHz plane rotated 45' t o I'ople model builder program, QCPE No. 135. Initial estithe molecular plane. Rotating 90" increases the energy mates of the structure of 1-substituted vinyl radicals and 14.6 kcal/mol while the maximum energy for the linear I-fluorovinyi cations were taken from available microwave geometry is the all-planar species 6b which is 24.7 kcal/ data of vinyl fluoridez9 and c~s-1,2-difluoroethylene.~~ mol less stable than 6b'. The all-planar-bent geometry, Then the C1 = C2 and CI-X bond lengths and the CZCIX 6a, is 43.3 kcal/mol less stable than 6 ' while rotating the bond angle were varied systematically for minimum3I RHz plane 52" (sa') sharply increases the stability to energy resulting in the minimized structures given in the within 8.1 kcal/mol of 6b'. results, The H1C2.CI2 and HC& angles and H-C2 lengths The energy difference between the trans- and cis-1,2for radicals 4, 5 , and 6 and for cation 9 were not optidifluorovinyl radicals (7 and 8) is negligible (cis is 0.2 mized but were assumed equal to those given for vinyl flukcal/mol more stable). The geometry at C-1, for both '7 ride.^^ Similarly che M1C2F2, FZCzC1, and HlCzCl anand 8, closely resembles that of 4a (6 = 136.7, 142.5, and gles and c 2 - P ~and &-H lengths for radicals 7 and 8 and 140" for 7 , 8 , and 4a, respectively), for cation 10 ware obtained from those given for cis-1,2a-Bond Orders of Vinyl Radicals (see Table II). In the d~fluoroethylene.~~ Sample calculations demonstrated 1-fluorovinyl radical (a), the CI-FI rY bond order is about that varying these angles and lengths had negligible ef(29) D. R. Lide, Jr., and D. Christensen, Spectrochim. Acia. 37, 665 fects on the results. (1961). Calculations were carried out for each optimized geom(30) V. W. Laurie, J. Chern. Phys., 34, 291 (1961). (31) J . A. Neider and R. Mead, Cornput. J., 7,308 (1964). etry in different coordinate systems to obtain the bond (32) The interaction of the occupied carbon orbitai with the empty boron order perpendicular and parallel to the bonds of interest. orbitai is not, in itself, destabilizing. Rather, this interaction reduces C-C K overlap and the net result is destabilizing, Unless otherwisr indicated, the xz plane is the molecular The Journal of Physical Chemktry, Vol. 77, No. 4, 1973
I NDO Theoretical Studies
497
+.036
-.166
U
x X bonding) is surprising. The same trends and magnitudes are found for C1-F1 A orders in both trans- and cis1,2-difluorovinyl radicals 7 and 8. The C2-F2 orders in 7 and 8 are of about the same magnitude as the C1-FI r y orders in 4a, 4b, 7,. and 8. However, the r x orders for CI-FI are greater than the rZ orders for c 2 - F ~when this comparison is made. In the 1-methoxyvinyl radical, the values of AA, (i.e., change in rYbond order) for the &-CI and C1-0 bonds is negligible going from bent 5a to linear 5b. Again, the bond lengths change little in this process. When the 1 substituent is BH2 (6), the C1-B A,, bond order is very large in both the bent-planar (6a) and linearplanar (6b) geometries (i.e., nY = 0.693 and 0.743, respectively). This effective "conjugation" greatly reduces the CZ-CI A , ~bond order (0.644 in 6a and 0.597 in 6b). B y rotating t h e BHz plane i n t h e bent or linear structures out of t h e plane, t h e C1-B rY bond order is sharply decreased (to 0.455 in 6a' and 0.364 in 6b'). Simultaneously t h e C Z - C ~.rYbond orders increase to 0.848 in 6a' and 0.909 in 6b'. For the linear geometry the A A . ~bond orders on rota6b') are -0.379 for C1-B and +0.312 for C2tion (6b C1. Rotating the BHz plane still further to 90" in the linear geometry results in a further decrease in the r y order of the CI-B bond and an increase in rYorder of the C2-C1 bond. However, the changes are now much smaller and are accompanied by an increase in the r x bond order for the C1-B bond. It is clear that t h e m i n i m u m energy for radical 6 is achieved w h e n t h e C1-Bl T bond orders are reduced to a m i n i m u m while achieving as m u c h c1-C~r2. bond order as possible. The less available boron is to accept electron density via A bonding at the expense of C-C A bonding, the more stable 6 becomes. Charge Distribution i n ]-Substituted Vinyl Radicals. The total charge densities on the vinyl radicals are summarized in Figures 1 and 2. Very little change in t h e total charge densities accompanies t h e geometry change f r o m bent to linear. This is true when the I substituent is F, OCH3, or BH2. Also there is a negligible change in total charge densities accompanying the trans to cis isomerization of 7 to 8. As expected the positive charge density at C-1 decreases in the series where t,he 1 substituent changes from F to OCHs to BH2. Examining the px, pU, and pz charge densities (see Table 111) shows that converting bent, radicals 4a, sa, or 6a to their linear forms 4b, 5b, or 6b causes only small changes in the px, pr, or pz charge densities. Isomeric radicals 7 and 8 also have charge distributions similar to each other. By defining the z axis along the C-F bonds in 4a, 7, and 8 a view of the D bond is obtained by comparing the carbon and fluorine pz densities. A t both C-l and C-2 t h e u bonds to fluorine are highly po1arizc.d touard fluorinc (i.e., 1 - q for p z i c - l ] = +0.273 and for pz,i.'-1 , = -0.474 in 4a). The magnitude of this polarization is about the same for the C1-F1 and the c 2 - F ~0 bonds. Apparently t h e radical center at C-1 does not seriously perturb t h e cr bond. The magnitude of the total charge densities a t C-1 (+0.131 in 7 and +0.132 in 8) and C-2 ($0.204 in 7 and +0.194 in 8) are due largely to the highly polarized D bond back donation from fluorine reducing with some r x and rITY the magnitude of the overall charge separation. In 7 and 8 the extent of r x and r y back donation from fluorine is slightly greater a t C - 1 than at C-2. T h i s accounts for the lower positive charge density a t C-1. There is a marked change i n total charge distribution i n 6 as t h e BH2 plane is rotated out o j the molecular planc
",,
y
i.018
H2
6
i.019
- ,030
-
0-C3 band 90' out-of-plene
h
HZ
t.021
H,
r,
- ,029 3
- .a02
H4
32 (C1-O-C,-II
define a p l a n e perpendicular t o t h e paper. )
- ,198
L
Z
2
. 15"
'1
1.013
- ,200
L
-.150
- ,145
+.aim
Figure 1. INDO optimized geometries and total charge of 1-substitutedviny! radicals 4a, 4b, 5a, 5b, 7, and 8.
densities
the same in both the bent (4a) and linear (4b) geometries (0.248 and 0.234, respectively). This is also true of r x bond orders (0.289 and 0.249). The magnitude of the rY and r x bond orders are about equal in both geometries of this radical. Since the C1-F1 bond length changes only slightly ( A / = 0.012 A between 4a and 4b), the decrease in the r x bond order going from bent to linear (where the C1 px orbital is now of the proper symmetry for maximizing
The Journal of Physical Chemistry, VoI. 77. No. 4, 7973
8
C. U. Pittman, L. D. Kispert, and T. t3. Patterson, Jr.
t.016
+.096
+ ,116
-.020
.-.092 Bent
t. 098
3% - Planar
6b Linear
-
Planar
- .064
~.046
n +
+.043
I.(
045
12
-.074
-. 047
+.044
+.037
Bent
-
Linear
out-of-plane
-
out- o f - Plane
Figure 2. INDO geometries and total charge densities of 1-BH2-substituted vinyl radicals.
also produces large changes in the C-1 px and B px charge densities and moderate changes in the C-2 py and B py orbitals. For example, the electron density in the (2-1 p+ orbital increases as the rotation of the BW:! plane takes 6a' and then decreases slightly on place going from 6a further rotation to 90" (see Table 111). Unpaired S p i n Distribution i n I-Substituted Vinyl Radicals. In t h e bent geometries of 4, 5, 7, and 8 t h e s orbital spin density is greater a t C-1 (and F-I f o r 4, 7, and 8) t h a n in t h e corresponding linear geometries. The amount of s orbital spin density a t (2-2, H-1, and H-2 increases going to the linear geometry. These changes, summarized in Table IV, result in the predicted hyperfine couplings shown there. However, the calculations predict a remarkable difference in the s orbital spin density when the, 1 substituent is BH:!. I n the bent-plunar (6a) and linearplanar (fib) geometries, m u c h larger s orbital spin densities are predicted a t C-2 and B. O n rotating the BN2 plane (6a 6a' and 6b 6b') t h e C-2 and B s orbital spin densities decrease while those on H-1, 19-2, 6-13, and N-4 increase. The predicted esr spectra of the bent- and linear-planar geometries differ only slightly, but the predicted spectra of bent and linear out-of-plane (6a' and 6b') differ markedly from each other as well as from 6a and 6b. Changes in the px, py, and pz orbital unpaired spin densities follow the same general pattern. When the 1 substituent is F or OCH;, t h e greatest spin density is found in t h e C-1 p x orbital f o r t h e bent geometries, and large spin densities are also found in the F or 0 p+ and the 6-1 pz orbitals. In the linear geometries the p+ spin density increases substantially. Again, it is when BH2 is the 1 substituent that entirely different spin distributions are calculated. I n both bent 6a and linear 6b planar structures, t h e largest spin densities are found in t h e C-2and B p y orbitals! For 6a and 6b the C-2 py spin densities are 0.604 and 0.658 while those for E3 p3. are 0.477 and 0.422, respectively. The sum of the unpaired p x , y ,slid unpaired spin density at C-1 is less than 0.1. 'This is in sharp con-
-
18.6
OOcut-of -plane
-+
Figure 3. Relative energies for several geometries of t h e 1BHZ-substituted binyl radical.
(by 52 and 45" in 6a' m d Bb', respectively) for both linear and bent forms. In both cases there is (1) a sharp reduction of electron density a t boron, (2) a parallel increase in electron density a t C-1, (3) a decrease in electron density at C-2, and (4) an increase a t H-1 and H-2. W-hen the M H 2 plane becomes perpendicular to the molecular plane, the electron densities a t boron and C-1 decrease while that a t C-2 increases slightly. Rotation of the BH2 plane The Journal of Physical Chowistry, Vol. 77, No. 4, 1973
-
99
INDO Theoretical Studies
TABLE I I I: Charge Densities and Unpaired Spin Densities in the pi, py, and pz Orbitals of Vinyl Radicalsa Charge density
Unpaired spin density
________-I
Radical atom l
l
_
_
PX ~
~
-
-
-
PY
Pz
Pr
0,068 -0.125 0.05% 0.073 -0.124 0.051 0.085 -0.142 1.38Id 0.190 -0.147 1 .383d -0.0084
0.273b 0.035 -0.474b 0.253 0.050 -0.426 0.115 0.031 1 .525d 0.191 0.048 1.315d 0.265*
0.453 (0.587b) -0.041 0.1 12 (0.076*) 0.758 - 0.07% - 0.06% 0.485 -0.049 0,145 0.725 -0.074 0.114 0.442
0.074 -0.079 0.005 0.052 - 0.055 0.003 0.057 -0.061 0.005 0.04% -0.052 0.004 0.075
0.155 (0.021b) 0.005 -0.016 (0,020*) 0.016 - 0.046 -0.028
- 0.0786
0.243c -0.4486 -0.4Ogc 0.270h
- 0.039
-0.074 0.005 - 0.006 0.072
r,.01% -0.012 0.003 0.727 (0.029*)
O.25!jc
- 0.042
-0.071 0.004
-0.017 -0.017 ( O . l l * ) 0.061 -0.016 -0.01 7 0.01 1 -0.017
PY
P2
-
0.175
4a
c-1
0.0506
c-2
0.063 0.0916 -0.090 0.075 0.076 0.081 0.080 1.654d -0.121 0.086 1.854d 0.18'1 (0.06gb) 0.196 0.0956 0.023c 0.165 (0.063b) 0.188 0.100b 0.024c 0.622 0.063 0.168 0.604 0.06'1 0.151 0.156 0.079 0.59qd 0.1 73 0.872 0.683d
F
c-1
4b
e-2 F
e-'I
5a
e-2
0 C" 1 c-2
5b
0 7
e-1
8
6-2 F-4 F.2 c-1 6-2 F- 1 F-2
6.4 6-2
6a
B C-1
61s
e-2 5
c-1
6a
c-2
B
e-1
6b
c-2 B
0.0474 0.0396 -0.014 -0.075 0.0478 0.0406 -0.139 -0.185 0.324 -0.140 -0.169 0.308 0.048 0.020 0.632a 0.047 0.046 - 0.612d
- C1.4496 - C.408r -C.077 c 010 0.196 -0.084 - 01.004 0.184 -C.049 - 0.008 C.793d - C ,054 -0.01%
Ci .82gd
0.101 0.026 0.49%(0.596b)
0.1 14 (0.0866) 0.066
- 0.005
-0.081 0.604 0.477 - 0.080 0.65% 0.422 -0.030
-0.001
0.01 7 0.011 -0.001
0.018 0.009 0.502 -0.042 0.049 0.422 -0.030 0.042
-0.11%
0.1 16 -0.076 0.253 0.156
0.114 -0,005 -0.012 0.01 5 - 0.043 -0.025 0.184
0.019 0.009
0.012 0.024 0.021 - 0.000 -'
- 0.015 -0.013
a Unless otherwise noted, the z axis is defined along the C2-C, boqd and the y axis perpendicular to the molecular plane (xz is tcle plane of vinyl group). *The z axis IS defined along the Cf-FI bond. The z axis IS defined along the 6 2 - F ~bond. Electron density g (not charge density)
trast to the bent and linear forms of 4, 5 , 7, and 8 where the py spin densities are very small. When either the bent or planar geometries of 6 have the BH2 plane rotated out of the molecular plane to 6a' or 6b', a large increase in the C-1 px spin density occurs (from -0.001 in 6a or 6b to 0.422 in 6a' or 0.502 in 6b'). This is accompanied by marked decreases in both the C-2 and El py spin densilies. The C-2 py spin density, for example, decreases from 0.604 and 0.658 in 6a and 6b to -0.118 and 0.253 rn 6a' and 6b'. respectively. Thus, partial E H , rotation is forcing unpaired spin density Sack into the @-I p r orbital Rotating the BH2 plane to 90", in the linear geometry, causes only a small further increase in the 6-1 px orbital (to 0.491) but a continued large decrease in C-2 and B py spin densities (to -0.033 and 1-0.005) is noted. With the BH2 plane perpendicular to the molecular plane, the vacant p orbital on boron lies paraliel to the x axis in the proper geometry for maximum C-B r 5 overlap. Thus, it is not surprising to see a sharp increase (from 0.042 to 0.329) in the boron px unpaired spin density relation of the BH2 plane from 45 (6bi') to 98".
Summarizing, Milaen the BH2 plane coincides with the
i e ly
x +.2@98
-9
+.0379
Fl
Figure 4. INDO optimized geometries and excesS charge densities on fluorovinyl cations 9 and 10.
molecular plane, the unpaired spin is Concentrated largely in the C-2 and B py orbitals, whether the geometry is bent or linear. Upon rotating the BHz plane 45" (52"), the radical is stabilized and the spin density in the C-1 px orbital increases sharply at the expense of the 6 - 2 and B py spin The Journal of Physical Chemistry, Vol. 77, No. 4, 1973
500
C. U.
Pittman. L. D. Kispert, arid T. B. Patterson, Jr.
TABLE IV: Calculated s Orbital Unapired Spin Densities and Esr Hyperfine Coupling Constants for Radicals
Radical aton-
-
s orbital spin density
Hyperfine coupling constant, G
Radical atom
s orbital spin density
__l___l-l
4a
4b
c-1 c-2 F H-1 H-2 c-1 c-2 F
n-i H-2
5a
c-1 C-2 c-3
0
5b
ti-1 H-2 H-3 n-4 H-5 C- ? C-2 c-3
0 H-7
3
H-2 H-3 H-4 H-5 c-1 c-2
F-1 F-2 H- 1
0.1 762 -0.0075 0.0039 0.1223 0.0375 0.0420 -0.353 -0.0013 -0.1518 --0.15 1 0 0.1392 0.0094 0.0004 0.0085 0.1370 0.0492 0.0006 0.001 9 0.0024 0.0385 -0.0331 0.0006 0.0044 0.1438 0.1429
-0.0006 -0.0007 --0.0006 0.1652 -0.0137 0.0030 0.001 7 0.1207
144.52 -6.18 176.54
bentplanar
c-2 F-1 F-2 H-1 C-1 C-2
linear planar
Hi H2 H3 H4 C-1 C-2
66.06 20.26 34.42 -28.95 56.98 81.96 81.51 114.14 -7.72 0.37 7.56 73.95 26.58 -3.00
-1.00 1.31 31.6 27.16 0.46 3.87 77.63 77.16 -0.30 -0.39 -0.33 135.52 -11.24 134.52 76.13 65.16
densities. Furl.her rotation to 90" returns a significant amount of unpaired spin to boron uia r Xoverlap. F'luorovinyl Cations. The bond angles, bond lengths, and total exces charge densities in vinyl cations 9 and 10 are shown in Ipigure 4. The calculated x bond orders are compiled in Table V aleng with the px, pLV,and pz charge densities. The most siriking feature o f cations 9 and 10 is their linPar (SI) at (,'I) structure. The preference for this linear geometry is large. For example, the energy of cation 9 increases by 2.0 Ircal/mol when the C1-F1 bond is bent 10" in the molecular plane (ie., 0 = 170"). Bending still further to H = 160, 143, and 120" increases the energy of 9 by 7 . 3 , 29.7, arid 70.0 kcal/mol, respectively. Although the energy of the bent geometry of cation 9 (0 = 120") is much greater than that of the linear geometry, the charge distribution was found to change only slightly. The .Ci-F x y bond order decreases by 0.02 and the Cl--Cz r y order increases by 0.0032 on decreasing 0 to 120". Significant hack r banding from fluorine to C-1 occurs in both 9 and 10. 1'h.k takes place between t h e fluorine and cnrbori p x orbitals. In spite of the large charge on C-1 in both 9 and 10, the n bond between C-1 and fluorine is still strongly polarized toward fluorine (1 - g for F1 p t orbital = -0.402). Unlike the unsubstituted cinyl cation, CHz=-CH+, studied b y Dewar, Allen, and Schleyer,21 separation of the charge for 9 into u and K contributions indicatw i ? e p l i t l l p polnrirution o f the C - 2 n electrons The Journal of P k p , c a ! Cheniistry, Vol 77, No. 4 , 1973
c-1
8
6a
B
6b
B Hi H2 H3 H4 Bent 6a' C-1 out-of- c - 2
plane
B
H-1 H-2 H-3 H-4 Linear 6b'C-1 out-of- c - 2
plane
B H-1 H-2 H-3 H-4
0.1 684 0.0084 0.0030 0.0047 0.0248 -0.01 15 0.0285 0.0208 -0.0226 -0.0218 -0.0155 -0.0157 -0.0112 0.031 2 0.01 76 -0.0249 -0.0241 -0.0129 -0.0130 0.0282 -0.0152 -0.0020 0.1085 0.0988 0.041 9 0.0183 0.0103 -0.0048 -0.0057 0.0514
0.0506 0.0790 0.0804
-
Hyperfine coupling constant, G 138.1 6.91 134.41 209.48 13.40 -9.47 23.53
0
- 12.21 -11.78 -8.35 -8.48 -9.16 25.57 0 13.43 -12.99 -6.96 -6.99 23.11 12.43
-
.-
0 58.59 53.36 22.61 9.88 8.44 -3.91
0 27.76 27.39 42.63 43.41
toward C-1 takes place (1 - q for p y = -0.360 for C-1 and -0.015 for C-2). The lack of charge transmission from C-2 to C-1 is also illustrated by the total charge densities. In vinyl cation 9 the charge at C-2 is -0,087 (4 - 4 ) . The same is true in 10 where the larger positive charge density a t C-2 (+0.241 = 4 - q ) results, largely, from the strongly polarized CZ -*F v bond and not from a strong interaction with C-1. There are two major sources of stabilization of the empty px orbital at C-1 in 9. The first is a hyperconjugative interaction of the C2-H1 and c 2 - H ~cr bonds with the vacant px orbital. This results in large plus charge densities at H-1 (+0.231) and H-2 (+0.230).33 Second, the availability of back x donation from px on fluorine supplies a substantial portion of the electron density found in the px orbital of C-1. This results in a large r X bond order between C1 and FI in both 9 (0.512) and 10 (0.592), respectively. Finally, it is instructive to compare the total charge densities (7 - q ) a t F-1 in ions 9 (-0.0006) and 10 (+0.0379) with that of vinyl fluoride (-0.182).3* This difference results from F 1 * C-1 r x back donation in cations 9 and 10. (33) In ethylene, the charge density on hydrogen is +0.015.See ref 34.
..-.
n 11A
(34) From INDO calculations cited in J. A. Pople and D. L. Beveridge, "Approximate Molecular Orbital Theory.~'McGraw-Hill, New York, N. Y.. 1970.
Intermolecular Attraction between Macroscopic Bodies
501
TABLE V: x Bonding Orders and Excess Charge Densities in pr, py, and pz Orbitals far 9 and 10 Cation Quantity
9
10
x Bond Orders
TyC1--C2 r)tC1-F1 T x C1--F1
0.9744 0.2220 0.5121
T y@2-F2
0.9478 0.192’1 0.5923 0.2338
Excess Charge Densities
c1
Pz
c2
Px
1-q
Py
Pz
R2
F1 2 - i P ; ‘ 2-qPY 1-C;p, F:, 2 - 17 Py 3 - (s(r)z) +dPZ))
4-0.5476 -0.0360 f0.2121 -0.01 27 -0.0152 f0.0277 +0.1800 +0.051 I -0.401 7
4-0.5886 -0.1414 +0.2136 +O. 1066 4-0.0462 +0.1135 4-0.2279 ,to. 0430 -0.405% +0.0522 -0.230%
The c1-F~bond distances in both 9 and 10 are substantially shorter than normal vinyl carbon-fluorine distances. For example, the C I - F ~distance in 10 of 1.2815 A is 0.055 A shorter than the c2-F~distance of 1.337 A found in 1,2-
difluoroethylene. This contraction is expected due to (1) the greater s character in the C-1 bonding orbital, ( 2 ) the reduced C-1 van der Waal radius which results from its high positive charge density, and (3) the increased x x bonding between C-1 and F-1. The latter effect is represented by the allenic resonance hybrid. It may be concluded that the linear geometry of the 1fluorovinyl cations results from the sp hybridization at C-1 which permits the bonding orbitals to utilize a maximum of s character. The “vacant” p orbital, as in the methyl cation, is a t a maximum distance from the nucleus. Conversion from linear (sp) to in-plane bent (sp2) geometry formally requires promotion of 1/3 of an electron from an s to a p orbital. There is no advantage gained by this promotion since the charge distribution and x bond orders do not change markedly upon bending. Thus, this promotion is unfavorable and the linear geometry prevails.
Acknowledgments. We wish to thank the Alabama Computer Center for making available an extensive amount of computer time and John Prather for some preliminary calculations on the fluoro substituents.
etermination of the lntermoleculair Forces of Attraction between Macroscopic Bodies for Separ,ations down to the Contact Point I . lBailey* and H. Daniels lnstitiite fur Physik und Chemie der Grenzflachen der Fraunhofer-Gesellschaft, 7000 Stuttgart 1, West Germany
(Rscewed M a y 22, 79721
An analysis of the forces of attraction between two sheets of mica forming a double cantilever beam system has been made. The intermolecular attraction acting in the gap near the bifurcation point causes the sheets to be drawn toward each other. Distributed loads which account for this additional deflection are discussed. Within the limits of accuracy of this experiment the intermolecular attraction between elementary areas may be described as the superposition of (i) the sum of ionic forces varying as the inverse square of the separation for very small separations and dying off exponentially and (ii) dispersion forces varying as the inverse cube of the separation for separations less than about 30 nm and as the inverse fourth power of the separation for larger separations. The results show that the energy of interaction is due primarily to the ionic structure of the crystal even when the patterns of positive and negative charge sites on the adjacent sheets do not match each other. The contribution of the dispersion forces to the cleavage energy is only about 8% of the total energy. At separations greater thaii 550 nm the attraction is almost entirely due to dispersion forces.
Introduction During the past decade great progress has been macle in our understanding of the processes occurring at surfaces
and interfaces. This has been stimulated partly by interest in neighboring fields such as investigations on colloid systems and adhesion between solids. Measurements of surface and interfacial energies, heats of wetting, contact The Journal of Physical Chemistry, Vol. 77, No. 4, 1973
