Bond length changes resulting from halogen substitution of oxirane

Carol A. Deakyne, Joseph P. Cravero, and William S. Hobson. J. Phys. Chem. , 1984, 88 (24), pp 5975–5981. DOI: 10.1021/j150668a046. Publication Date...
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J . Phys. Chem. 1984,88, 5975-5981 does not depend on whether or not factor group splitting is observed; all that is required is the correct identification of spectral activity. However, the approach is likely to be more useful the weaker any factor group effects. In the limit of zero factor group splitting, it reduces to an oriented gassite group analysis. If factor group splittings are larger than site group effects, then ambiguity may well arise. Fortunately, this is not likely to be a common

5975

situation because site splitting is normally the larger. Acknowledgment. This research project has been supported by the Royal Society under its European Science Exchange Programme through a bursary to L.-J.N., who also has received f i x ~ ~ isupport al by the British Chmcil. Registry No. Ammonium sulfate, 7783-20-2.

Bond Length Changes Resulting from Halogen Substitution of Oxirane Carol A. Deakyne,* Joseph P. Cravero, and William S. Hobson Department of Chemistry, College of the Holy Cross, Worcester, Massachusetts 01610 (Received: May 3, 1984; In Final Form: July 19, 1984)

Fluorine substituents have been shown to alter the ring bond lengths in oxirane. Orbital compositions, overlap populations, charge distributions, orbital energy splitting diagrams, and charge density difference plots obtained from ab initio wave functions are investigated to determine the origin of the observed substituent effect. This approach enables us to rationalize the experimentally determined geometry of cis-1,2-difluorooxiraneand to predict bond length changes for trans-l,2-difluorooxirane and tetrafluorooxirane and the relative stabilities of cis- and trans- 1,2-difluorooxirane. The geometry changes are accounted for by interactions between the fluorine and occupied ring orbitals. The differences in fluorine substituent effects on oxirane and cyclopropane and the applicability of the approach to chlorinated oxiranes are discussed.

I. Introduction Substituent effects on the geometries of three-membered ring compounds have been widely studied in recent In (1) Pwhan, J. M.; Baldwin, J. E.; Rygare, W. H. J. Am. Chem. Soc. 1969, 91, 1896-1898. (2) Perretta, A. T.;Laurie, V. W. J. Chem. Phys. 1975, 62, 2469-2473. (3) Gillies, C. W. J. Mol. Spectrosc. 1976, 59, 482-492. (4) Flygare, W. H.; Narath, A.; Gwinn, W. D. J. Chem. Phys. 1962,36, 200-208. (5) Cole, K. C.; Gilson, F. R. J. Mol. Struct. 1975, 28, 385-390. (6) Jones, W. J.; Stoicheff, B. P. Can. J . Phys. 1964, 42, 2259-2263. (7) Ramaprasad, K. R.; Laurie, V. W.; Craig, N. C. J. Chem. Phys. 1976, 64,4832-4835. (8) Stigliani, W. M.; Laurie, V. W.; Li, J. C. J . Chem. Phys. 1975, 62, 1890-1892. (9) Hedberg, L.; Hedberg, K.; Boggs, J. E. J. Chem. Phys. 1982, 77, 2996-3002. (10) Deakyne, C. A,; Allen, L. C.; Craig, N. C. J. Am. Chem. SOC.1977, 99,3895-3903. Deakyne, C. A.; Allen, L. C.; Laurie, V. W. Ibid. 1977,99, 1343-1349. (11) Skancke, A.; Boggs, J. E. J . Am. Chem. SOC.1979,101,4063-4067. (12) Fitzpatrick, N. J.; Fanning, M. 0.J . Mol. Struct. 1975,25, 197-204; 1976, 33, 257-63. (13) Hoffmann, R. Tetrahedron Lett. 1970,2907-2909. Hoffmann, R.; Stohrer, W.-D. J . Am. Chem. SOC.1971.93, 6941-6948. (14) Hoffmann, R. J . Am. Chem. SOC.1968, 90, 1475-1485. Stohrer, W.-D.; Hoffmann, R. Angew. Chem. 1972, 11, 825-826. (15) Hoffmann, R.; Fujimoto, H.; Swenson, J. R.; Wan, C.-C. J. Am. Chem. SOC.1973, 95, 7644-7650. (16) Rohmer, M.-M.; Roos, B. J . Am. Chem. SOC.1975,97,2025-2030. (17) Delker, G. L.; Wang, Y.; Stucky, G. D.; Lambert, R. L., Jr.; Haas, C. K.;Seyferth, D. J. Am. Chem. SOC.1976, 98, 1779-1784. (18) Hirose, C. Bull. Chem. SOC.Jpn. 1974, 47, 1311-1318. (19) Gillies, C. W. J . Mol. Spectrosc. 1978, 71, 85-100. (20) Creswell, R. A.; Schwendeman, R. H. J . Mol. Spectrosc. 1977,64, 295-301. Creswell, R.A,; Manor, P. J.; Assink, R. A.; Schwendeman, R. H. Ibid. 1977, 64, 365-375. (21) Politzer, P.; Trefonas, P., 111; Politzer, I. R.; Elfman, B. Ann. N.Y. Acad. Sci. 1981,367,478-490. Politzer, P., personal communication (STO-

3G results).

(22) Politzer, P.; Daiker, K. C.; Estes, V. M.; Baughman, M. Int. J . Quantum Chem., Quantum Biol. Symp. 1978, 5, 291-299. (23) CatalHn, J.; YHfiez, M. J . Am. Chem. SOC.1978, 100, 1398-1401. (24) Hopkinson, A. C.; Lien, M. H.; Csizmadia, I. G.; Yates, K. Theor. Chim. Acta 1978, 47, 97-109.

particular, a number of e~perimentall-~ and theoreticalg-14 investigations of substituted cyclopropanes have provided information on the effect of electronegative substituents on the cyclopropane ring. In contrast, the effect of electronegative substitution on the oxirane ring has not been well studied. In fact, only structures of several chlorinated oxiranes2’derived from ab initio calculations and a microwave structure of cis- 1,2-difl~orooxirane~~ have been reported. Gillieslg results for the latter molecule indicate that cis-l,2-difluoro substitution of oxirane shortens all of the ring bonds. In order to elucidate the origin of these fluorine substituent effects and to ascertain geometry changes for some related systems, the following four molecules have been considered in detail and wave functions have been calculated for each: oxirane (I), cis1,2-difluorooxirane (11), trans- 1,2-difluorooxirane (111), and tetrafluorooxirane (IV).

I

I1

1x1 IV While it is possible to determine bond length changes and relative energies for these molecules via a global optimization of their structures, it was desired to develop another method that is both economical and applicable to these and larger molecules, where global optimization is not feasible. Consequently, the approach adopted in this paper is to utilize oxirane as the reference molecule and to retain its geometry in the other three molecules. The ring bond length modifications brought about by fluorination of oxirane and the groups of symmetry orbitals responsible for (25) Hinchliffe, A. Adu. Mol. Relaxation Interact. Processes 1981, 20, 71-76, 77-80.

0022-365418412088-5975.$01.50/00 1984 American Chemical Society

The Journal of Physical Chemistry, Vol. 88, No. 24, 1984

5976

the observed changes are determined via charge density difference plots. The charge density difference maps detail the charge transfers and accompanying forces (defined by the HellmannFeynman theorem) acting on the ring nuclei as a result of substitution for hydrogen. The plots are employed in lieu of more standard analysis techniques since overlap population changes are and orbital energy unreliable for strained rings10~1z~16~z1~z3~z6~z7 splitting diagrams and orbital composition changes are too complex to yield overall changes in geometry for heavily substituted systems. However, once the geometry modifications and relevant groups of symmetry orbitals are known, these techniques are used to locate the controlling orbitals and to predict relative changes along the series of molecules. In an earlier paper,1° we found charge density difference plots useful in rationalizing and predicting bond length changes due to fluorination of cyclopropane. Difference maps have also been used by other researchers for many years. For example, they have been employed by Bader et a1.z8to probe charge redistributions upon molecule formation, by Desmeules and Allenz9 to examine charge redistributions upon hydrogen bond formation, by Eisenstein and Hirshfeld30 to study substituent effects on the charge density in the formyl group, and by Morokuma31 to investigate the various terms in his hydrogen bond energy decomposition scheme. In this article, the experimentally determined geometry of cis-1,2-difluorooxirane (11) is rationalized, bond length changes for trans-l,2-difluorooxirane(111) and tetrafluorooxirane (IV) and the relative stabilities of I1 and I11 are predicted, an explanation for the differences in fluorine substituent effects on oxirane and cyclopropane is suggested, the relative filling of an unoccupied C-0-C antibonding oxirane orbital in the substituted oxiranes is investigated, and the applicability of our approach to chlorinated oxiranes is considered.

Deakyne et al. TABLE I: Values of Contours for Difference Plots ( e / ( a ~ ) ~ ) no. density no. density no. density -9 -1.00000 -2 -0.00032 4 0.00316 -8 -0.31620 -1 -0.00010 5 0.01000 -7 -6

-5 -4 -3

-0.10000 -0.03162 -0.01000

-0.00316 -0.00100

0

0.00000

1

0.00010

6 7

0.03162 0.10000

2 3

0.00032 0.00100

8

9

0.31620 1.00000

functions. It follows then that the STO-3G s,p basis set is sufficient for our purposes. Many other theoretical studies of oxirane have been carried o ~ t . ~ ~ , ~These ~ , include ~ ~ - calibrations ~ ~ , ~ ~ of- recently ~ ~ developed m e t h o d ~ , ~investigations l-~~ of the ionization e n e r g i e ~ ~and ~-~~ optical activity48of oxirane, and studies of selected ring-opening and fragmentation reactionsz2,24,25,4~51 it undergoes. Some of these calculation^^^*^*^^ utilized the STO-3G basis set, but all were done at geometries somewhat different from ours. In addition, overlap populations, charge distributions, and most of the orbital energies and molecular orbital (MO) coefficients relevant to our study were not reported. W e can find no theoretical investigations in the literature on cis-1,2-difluorooxirane, trans- 1,2-difluorooxirane, or tetrafluorooxirane. Geometry Choice. For all four molecules, the bond angles and bond lengths utilized in these calculations are derived from experimentally determined structures. C-C, C-0,and C-H bond respectively) and C-0-C and lengths (1.47, 1.43, and 1.08 %., H-C-H bond angles (62.0 and 117', respectively) are those for I.'* C-F bond distances (1.35 A) and H-C-F bond angles (1 11') are the values for II.19 F-C-F bond angles (108') are those obtained for 1,l -difluorocyclopropane.Z The procedure of retaining the ring geometry of I in the other three compounds was suggested by Hoffmann et al.15 With this 11. Computational Details choice of geometries, the charge redistributions that occur in the substituted molecules reflect whether the substituents weaken or Wave functions for all four molecules were obtained by ab initio strengthen the ring bonds. Furthermore, the ring atoms must be SCF-MO calculations using the minimal STO-3G s,p basis set3233 superimposed in the charge density difference plots to make a of the GAUSSIAN 70 series of programs.34 All calculations were comparison of the bonding regions of the reference and substituted done on a VAX 111780 computer. molecules possible. Although g e o m e t r i e ~ force , ~ ~ constant^,^^ and electric dipole Charge Density Difference Plots. Changes in overlap popumoments3z of oxygen- and fluorine-containing molecules are relationsSz are widely used to predict changes in bond lengths. produced fairly inaccurately at the STO-3G level, their relative However, for strained ring systems this procedure can be misvalues along a series of substituted molecules are reproduced leading, since there is frequently a discrepancy between calculated satisfactorily. Thus, computed trends in charge distributions are overlap population changes and reported bond length reliable despite underestimated electric dipole moments3z and This disagreement is consistent with the exaggerated back-bonding and charge a l t e r n a t i ~ n . ~ ~ , ~ ~ , ~ ~changes.10~12~16~z1~23~z6~27 observation of Bader et alaz8that bonding depends not only on Rohmer and Roos16 and Hariharan and P ~ p l have e ~ ~shown the amount of charge in a bond but also on whether it is conthat in order to completely and correctly describe the electronic centrated or diffuse and on whether it is directed along the bond structure in three-membered rings, it is necessary to include poaxis or away from it. Problems arise with bonding interpretations larization functions in the basis set. However, Rohmer and R d 6 and Deakyne et al.1° have found that substituent effects on three-membered rings can be correctly represented without d (38) Lathan, W. A,; Radom, L.; Hariharan, P. C.; Hehre, W. J.; Pople, (26) Lehn, J. M.; Wipff, G. Theor. Chim. Acta 1973,28,223-233; Chem. Phys. Lett. 1972, 15, 450-454. (27) Newton, M. D.; Schulman, J. M. J. Am. Chem. SOC.1972, 94,

-

-.

761-711 . . ..

(28) Bader, R. F. W.; Henneker, W. H.; Cade, P. E. J . Chem. Phys. 1967, 46, 3341-3363. Bader, R. F. W.; Keaveny, I.; Cade, P. E. Ibid. 1967, 47, 3381-3402. (29) Desmeules, P. J.; Allen, L. C. J. Chem. Phys. 1980,72,4731-4748. (30) Eisenstein, M.; Hirshfeld, F. L. J. Comput. Chem. 1983, 4, 15-22. (31) Yamabe, S.; Morokuma, K. J. Am. Chem. Soc. 1975,97,4458-4465. (32) Hehre, W. J.; Pople, J. A. J. Am. Chem. SOC.1970,92,2191-2197. (33) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J. Chem. Phys. 1969, 51, 2657-2664. Hehre, W. J.; Ditchfield, R.; Stewart, R. F.; Pople, J. A. Ibid. 1970,52,2769-2774. (34) Hehre, W. J.; Lathan, W. A.; Ditchfield, R.; Newton, M. D.; Pople,

J. A. "Quantum Chemistry Program Exchange"; University of Indiana: Bloomington, IN, 1973; Program No. 236. The GAUSSIAN 70 series of programs was modified for use on the VAX 11/780 computer. (35) Newton, M. D.; Lathan, W. A,; Hehre, W. J.; Pople, J. A. J. Chem. Phvs. 1970.52. 4064-4072. 736) Pople, J. A.; Gordon, M. J. Am. Chem. SOC.1967, 89, 4253-4261. Radom, L.; Hehre, W. J.; Pople, J. A. Ibid. 1972, 94, 2371-2381. (37) Hariharan, P. C.; Pople, J A. Chem. Phys. Lett. 1972, 16, 217-219.

J. A. Top. Curr. Chem. 1973, 40, 1-45. (39) Clark, D. T. Theor. Chim. Acta 1969, 15, 225-234. (40) Von Niessen, W.; Cederbaum, L. S.; Kraemer, W. P. Theor. Chim. Acta 1977344, 85-93. (41) Schaefer, L.; Van Alsenoy, C.; Scarsdale, J. N. THEOCHEM 1982, 3, 349-364. (42) Talaty, E. R.; Simons, G. Theor. Chim. Acta 1978, 48, 331-335. (43) Skancke, P. N.; Fogarasi, G.; Boggs, J. E. J . Mol. Srruct. 1980,62, 259-273. (44) Lischka, H.; Koehler, H. J. Chem. Phys. Lett. 1979, 63, 326-331. (45) Bouma, W. J.; Radom, L.; Rodwell, W. R. Theor. Chim. Acta 1980, 56, 149-155. (46) Mollere, P. D.; Houk, K. N. J . Am. Chem. Soc. 1977,99,3226-3233. McAlduff, E. J.; Houk, K.N. Can. J . Chem. 1977, 55, 318-332. (47) Basch, H.; Robin, M. B.; Kuebler, N. A.; Baker, C.; Turner, D. W. J. Chem. Phys. 1969, 51, 52-66. (48) Rauk, A. J . Am. Chem. SOC.1981, 103, 1023-1030. (49) Alagona, G.; Scrocco, E.; Tomasi, J. Theor. Chim. Acta 1979, 51, 11-35. Bonaccorsi, R.; Scrocco, E.; Tomasi, J. J. Chem. Phys. 1970, 52, 5270-5284. (50) Hayes, E. F. J. Chem. Phys. 1969, 51, 4787-4790. (51) Bigot, B.; Sevin, A.; Devaquet, A. J. Am. Chem. Soc. 1979, 101, 1095-1100. 1101-1106. (52) Mulliken, R. S . J . Chem. Phys. 1955, 23, 1833-1840, 1841-1846, 2338-2342, 2343-2346.

Bond Length Changes in Halogen-Substituted Oxirane

ss

SA

ss

SA

The Journal of Physical Chemistry, Vol. 88, No. 24, 1984 5911 TABLE I 1 Bond Overlap Populations molecule

C-0

c-c

0.203 0.194 0.193 0.181

0.283 0.266 0.267 0.247

C-F

C-H ~~

A 2

I

7

I1 I11 IV

13

10

19

Figure 1. Molecular orbital diagrams for fluoro substitution of oxirane. The orbitals are classified according to the reflections in the plane of the molecule and perpendicular to it (SS, SA, SS, SA).54 Related orbitals of a given type are shown vertically under the symmetry heading.

based on population analysis because this method does not take the disposition of the charge into account.28 (See ref 10 for a more complete analysis of this problem.) Thus, we have obtained charge density difference plots to aid us in our consideration of substituent effects on oxirane. Charge density difference maps employ a sum over many orbitals and display both the amount and the disposition of the charge in a bond. Consequently, they are a useful tool for resolving the net effect of substituent-induced charge redistributions on the geometries of strained rings. This technique has been used previously to ascertain and elucidate bond length changes brought about by fluorination of cyclopropane.10 Three sets of charge density difference maps were generated from the oxirane (I) and tetrafluorooxirane (IV) wave functions via a program developed by W. L. J ~ r g e n s e n . The ~ ~ three sets of maps represent charge density differences in the plane containing the ring nuclei (Le., Y = 0.0) and in planes 0.1 and 0.7 A above the molecular plane. Each set includes separate plots for the orbitals of SS symmetry,54S A symmetry,54A S and AA symmetry54(except for the Y = 0.0 plane), and the sum of all MOs. The plots were computed by using I as the reference molecule and subtracting its valence MOs from the corresponding MOs of I V . I is compared to I V rather than 11, whose geometry has been determined experimentally, for the following reasons. First, the symmetry of oxirane is retained in tetrafluorooxirane but not in 1,2-difl~orooxirane.~~ Analysis of the plots is more straightforward when the molecules being studied have the same symmetry. Second, it will be shown below (section I11 A, B) that once the source and outcome of the substituent effects in any one (53) The original program written at Princeton University has been modified for use on the VAX 11/780 computer. (54) The molecular orbitals for molecules I and IV have been classified with respect to two symmetry planes. The first symbol represents the symmetry of the MO with respect to reflection in the plane of the molecule, Le., whether it is symmetric (S) or antisymmetric (A). The second symbol represents the orbital symmetry with respect to reflection in the plane perpendicular to the molecular plane passing through 0 and bisecting the C-C bond. The overall symmetry of these molecules leads to four different sets of orbital symmetries, SS, SA, AS, and AA. The overall symmetry of molecules I1 and 111 is lower than that of molecules I and IV. The only plane of symmetry for I1 is the plane perpendicular to the plane of the ring passing through 0 and bisecting the C-C bond. 111 has no planes of symmetry; it has a C, axis of symmetry in the plane of the ring which passes through 0 and bisects the C-C bond. Thus, the molecular orbitals in these compounds are classified as simply symmetric (S) or antisymmetric (A) with respect to reflection in this plane or rotation about this axis. However, despite the lower symmetry of molecules I1 and 111, it is still possible to correlate the MOs of these molecules with those of molecules I and IV, since the composition of the MOs has only changed slightly.

0.385 0.373 0.373

0.221 0.221 0.214

of these molecules have been identified, they are germane to the others as well. As a result of our geometry choice (see above), these contour maps reflect only those charge redistributions and attendant forces brought about by substitution. The maps show that the substituent-parent molecule interaction produces significant charge redistributions primarily in the molecular plane since all three sets of plots are essentially equivalent. Thus, only the maps representing the charge density differences in the Y = 0.0 plane have been included in this paper. A logarithmic contour scale was used in the plots. The contour values are listed in Table I. In accordance with the standard convention, solid lines denote regions of increase and dashed lines regions of decrease. 111. Results and Analysis of Results

A . Charge Distributions. Atomic charges from population analysisSZare given below for molecules I-IV. The diagrams show

,o, - 0 204

/

\-0,0480

,0\-0.213

/ \ 0.153 -0.127

0.0751

I1

I

0 -0.217

/\

0.353

- 0.123

- 0 131

1x1

IV

that for all three substituted systems the oxygen is more negative and the carbons and hydrogens are more positive than these atoms are in I. Substitution of four hydrogens causes the oxygen to gain 0.013e and the carbons to lose 0.401e. Replacing only two hydrogens causes the oxygen to gain 0.009e (11) or 0.008e (111) and the carbons to lose 0.201e (11) or 0.199e (111). Hence, fluorination of oxirane is producing a charge alternation e f f e ~ twith ~ ~ the ,~~ charge changes on I V at least 1'/2 times larger than those on I1 and 111. Comparing only I1 and I11 reveals that the charges on the hydrogens and fluorines in these molecules vary more than the charges on the oxygens and carbons. Overall, the cis isomer has a slightly more delocalized charge distribution since the fluorines are less negative and the hydrogens are less positive in I1 than in 111. Skancke and Boggs" also find more delocalized charges in the cis form of 1,2-difluorocyclopropane. B. Orbital Compositions, Orbital Energy Correlation Diagrams, and Overlap Populations. Figure l is a schematic representation of the changes in orbital composition generated by fluorination. Only those valence orbitals of oxirane most affected by the substituents (in terms of changes in overlap between the contributing atomic orbitals) have been included in the figure. For the substituted molecules the MOs pictured are the symmetry-allowed bonding and antibonding combinations of substituent orbitals mixed with oxirane orbitals. One relevant combination is formed from M 0 2 (SS symmetry54)and from M 0 3 (SA symmetry;54the other combination is essentially nonbonding with respect t o the ring bonds) of oxirane; two each are formed from M 0 5 (SS symmetry54)and M 0 7 (SA symmetrys4). Comparing molecules 11,111, and I V to I, it is apparent that replacing two or four hydrogens produces the same pattern of atomic orbital (AO) coefficient changes. Furthermore, with the exception of M 0 5 , the coefficient changes are essentially identical for I1 and 111.

5978 The Journal of Physical Chemistry, Vol. 88, No. 24, 1984

Deakyne et al.

-0.40-

-0.50-0.60-

-0.10-0.80-

t

E

(a.u.1 -1.00-1.10-

-1.20-1.30-1.40-

-1.50-

- l.60-c1s FLUOf

!-DIXIRANE

I

OXIRANE

TRAN FLUOR

2-0‘-

.IRAN€

Figure 2. Orbital energy correlation diagrams for cis (left) and trans (right) difluoro addition to oxirane.

Figure 2 is an orbital energy correlation diagram for I, 11, and 111. IV has not been included in the diagrain to reduce its complexity. The figure shows which oxirane orbitals are affected by difluoro substitution and their relative stabilities. It is evident that the changes in orbital energies are very similar for I1 and I11 compared to the case of I. The biggest difference is in the amount of splitting between the orbitals of the fluorine-substituted molecules and MO5 of oxirane. The C-0 and C-C overlap populations (Table 11) for 11,111, and I V are all smaller than they are for I. The values for I1 and I11 are essentially equal and about midway between the values for I and IV. The analogous trends in the changes in overlap populations, orbital compositions, charge distributions, and orbital energies described above for 11, 111, and I V compared to the case of I indicate that difluoro and tetrafluoro substitution of oxirane modify its molecular properties in the same direction but not to the same extent. This inlplies that any conclusions drawn about the origin and consequences of the substituent effects in any of the molecules 11-IV are pertinent to the others. However, the fluorine-induced geometry changes for I1 and I11 will be similar to each other but smaller than those induced for IV. Although the orbital energy splitting diagram (Figure 2), orbital composition changes (Figure l), and overlap population changes (Table 11) predict the relative changes along the series of molecules, they are of limited use in predicting whether the ring bonds will lengthen or shorten. Examination of the changes in orbital composition yields conflicting conclusions regarding the effect of substitution on the ring bond lengths. Figure 2 shows that all four relevant oxirane orbitals are stabilized overall upon fluorination, and therefore, it does not enable us to distinguish between them. Bonding interpretations based on overlap populations are not reliable for the reasons mentioned above. Therefore, charge density difference plots have been obtained to determine the substituent-induced geometry changes. C. Charge Density Difference Plots. The set of plots subtracting the valence MOs of oxirane from those of tetrafluorooxirane in the plane containing the ring nuclei is -presented in Figure 3. Neither the hydrogen atoms nor the fluorine atoms

Figure 3. Charge density difference plots (A) substracting the SS symmetry valence orbitals of oxirane from the SS symmetry valence orbitals of tetrafluorooxirane, (B) subtracting the SA symmetry valence orbitals of oxirane from the SA symmetry valence orbitals of tetrafluorooxirane, and (C) subtracting the sum of all the oxirane valence MOs from the sum of all the tetrafluorooxirane valence MOs. The plots represent charge density differences in the Y = 0.0 plane, Le., the plane containing the ring nuclei. A logarithmic contour scale was used. Solid lines delineate regions of increase; dashed lines delineate regions of decrease.

have been included in the figure because they are not in the Y = 0.0 plane. The difference maps are interpreted by dividing up the substituent-induced charge redistributions into regions of charge loss and gain around the nuclei and then analyzing the charge changes in terms of the resultant force acting on each atom. This method of analysis is based on the Hellmann-Feynman theoremss which relates the electronic charge distributions to forces exerted on the nuclei. In addition, the method uses information intuitively provided from chemical experience in selecting the regions. The concepts involved in assigning the forces are as follows:28 (1) Charge increase in the region between the nuclei increases screening of the nuclear charges and creates an attractive ( 5 5 ) Feynman, R. P. Phys. Rev. 1939, 56, 340-343. Hellmann, H. “Einfuhrung in die Quantenchemie”; Franz Deuticke: Leipzig, 1937; p 285 ff.

Bond Length Changes in Halogen-Substituted Oxirane force which draws the nuclei together. (2) Charge lost between the nuclei and built up on the backside of the nuclei deshields the nuclear charges and pulls the nuclei apart. (3) Charge transferred into the region along the internuclear axis is most effective in shortening the bond. (4) A diffuse charge transfer above and below the bond into an s or p orbital is relatively ineffective in shortening the bond. Analyses based on the Hellmann-Feynman theorem have also been used by Debs6 and Nakatsuj?’ to predict molecular geometries. D. cis-l,2-Difuorooxirane and Tetrafuorooxirane. Figure 3C and schematic V give the total charge density redistribution

n

V

in oxirane caused by tetrafluoro substitution. There is a charge loss between the carbons and the fluorines which pushes the carbons away from the fluorines toward the opposite C-0 bond, and there is a charge gain between the carbons that draws them toward each other. The net effect is a displacement of the carbons toward the center of the ring. Charge is gained both in front and in back of the oxygen. However, the charge buildup in front of the oxygen is more effective in moving this atom because it is greater, more contracted, and more polarized than the diffuse symmetrical charge increase behind the oxygen?8 Since the charge density in front of the oxygen is polarized toward the carbons, the oxygen shifts downward toward the C-C bond. Figure 3A and schematic VI demonstrate that the charge

+ )&,

,-. \ *.

-.’

VI

changes around the oxygen result primarily from the charge redistributions in the S S symmetry orbitals,54though in Figure 3C the latter have been modified somewhat by the charge gain on the oxygen in the SA symmetry orbitals54 (Figure 3B and schematic VII). The forces moving the carbons are a combination

K-.,

1I --1 I

‘.-I

VI1

of the forces arising from the S A symmetry orbitals which pull the carbons toward the center of the ring and those arising from the SS symmetry orbitals which draw the carbons together below the internuclear axis, although the former forces dominate (Figure 3C). Overall, these rearrangements of the oxygen and carbons lead to a shortening of all three ring bonds. This conclusion is completely consistent with the experimental results for 118 and II,l9 since the changes in charge distributions (part A), overlap populations (Table 11), and orbital diagrams (Figure 1) for I1 and IV (compared to those for I) indicate that fluorine substitution of two or four hydrogens induces geometry changes in the oxirane ring in the same direction. However, the changes induced by four flourines are approximately twice as large as those induced by two, suggesting the following geometry for IV in the absence of steric effects.

IV ~

~~~

(56) Deb, B. M. J. Am. Chem. SOC.1974, 96, 2030-2044. (57) Nakatsuji, H. J. Am. Chern. Sor. 1973, 95, 345-354, 354-361.

The Journal of Physical Chemistry, Vol. 88, No. 24, 1984 5979 The charge density difference plots manifest the group of symmetry orbitals responsible for the observed geometry modifications; the orbital diagrams reveal the dominant orbital within the pertinent group. The orbital compositions (Figure 1) show that fluorine-oxirane interaction leads to C-0 bond shortening as a result of (1) the decrease in antibonding overlap between the oxygen and carbons in M 0 2 (SS symmetry) and (2) the increase in bonding overlap between these atoms in M 0 3 (SA symmetry). The C-C bond shortens due to (1) the fluorine-induced charge redistributions in M 0 2 (SS symmetry) which direct the bonding charge density closer to the internuclear axis and (2) the charge redistributions in M 0 7 (SA symmetry) which decrease the antibonding character of this bond. E. cis-l,2-Dijluorooxirane and trans-l,2-Dijluorooxirane. The orbital energy splittings (Figure 2), overlap populations (Table 11), charge distributions (part A), and orbital compositions (Figure 1) indicate that I1 and 111 will have similar but not identical energies and geometries. Examination of the orbitals depicted in Figure 1 shows that the interactions between the fluorines and SA symmetry orbitalss4 of oxirane generate a larger decrease in the C-C antibonding overlap in trans- 1,2-difluorooxirane than in cis-l,2-difluorooxirane. The fluorine interactions with the SS symmetry orbitalss4 of oxirane decrease the C-C bonding overlap more in the cis form than in the trans form, particularly in M 0 5 of oxirane. Both charge redistributions will strengthen the C-C bond in the trans isomer compared to that in the cis isomer, implying that trans- 1,2-difluorooxirane will have a shorter C-C bond than cis-l,2-difluorooxirane.However, the differences in charge density on the carbons in the A symmetry orbitalss4 of I1 and I11 and in the S symmetry orbitalss4of I1 and I11 will have opposing effects on their C-0 bond strengths. Furthermore, for both sets of orbitals, any charge losses (gains) on the carbons in one isomer compared to that in the other tend to be balanced by charge gains (losses) on the oxygen. This leads to the conclusion that the C - 0 bond lengths will not differ much in I1 and 111. Our results also suggest that trans- 1,2-difluorooxirane will be more stable than cis-l,2-difluorooxirane.Figure 2 shows that the fluorine-AS symmetry orbitals4 interactions are more stabilizing for the cis isomer, whereas the fluorine-SA symmetry orbital interactions are more stabilizing for the trans isomer. In net, the relative stabilizing effects of these two interactions nearly cancel each other. Thus, the discriminating feature of Figure 2 is the interaction between the fluorines and M 0 5 of oxirane, since the other fluorine-SS symmetry orbital interactions are equally stabilizing for I1 and 111. The F-M05 interaction produces two new orbitals and is destabilizing because the new antibonding orbital is more antibonding than the new bonding orbital is bonding. cis-1,2-Difluorooxirane (11) will be less stable than trans-l,2-difluorooxirane(111) since the bonding orbital produced from the interaction is less stable for the cis isomer than for the trans isomer (-0.6400 vs. -0.669 1 au). The larger coefficient changes for the ring atoms (Figure 1) and the larger magnitudes of the pertinent fluorine coefficients (see ref 58 for details) for the cis form in the relevant orbitals indicate that there is a more effective interaction between the fluorines and M 0 5 for this form. This causes a bigger decrease in bonding charge density in the oxirane ring of I1 and destabilizes it more than 111. Our conclusion on the origin of the lower stability of the cis isomer of 1,2-difluorooxirane is similar but not equivalent to Bingham’s conclusion on the origin of the “cis effect”.s9 Bingham has used simple and compelling arguments to organize and explain a number of experimental results. On the surface his arguments seem to apply to this case as well, since they would predict that trans-1,2-difluorooxiraneis more stable than cis-l,2-difluoroxirane (58) For M 0 7 the magnitudes of the fluorine orbital coefficients for the cis isomer are F 2s. 0.251; F 2px, 0.0893; F 2py, 0.418; and F 2p,, 0.0232; for the trans isomer they are F 25, 0.119; F 2px, 0.162; F 2py,0.306; F 2p,, 0.0245. For M012, the magnitudes for the cis isomer are F 2s, 0.0196; F 2p,, 0.435; F 2py, 0.219; F 2p,, 0.394; for the trans isomer they are F 2s, 0.0101; F 2p,, 0.330; F 2py, 0.433; and F 2p,, 0.255. (59) Bingham, R. C. J . Am. Chem. SOC.1976, 98,535-540.

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The Journal of Physical Chemistry, Vol. 88, No. 24, 198 4

due to a greater destabilization of the cis form via the F-M05 interaction. However, while the general concept does apply, the detailed analysis of our data indicates that there is not complete agreement between Bingham's proposal and our results. According to Bingham's proposal,59the explanation for the lower stability of the cis isomer would be a greater destabilization of the antibonding orbital produced from the F-M05 interaction for this isomer, whereas our results suggest that the explanation lies in the smaller stabilization of the corresponding bonding orbital for the cis form. The above conclusions on the geometries and energies of I1 and I11 concur with the results obtained by Skancke and Boggs" for cis- and trans-l,2-difluorocyclopropaneand with the experimentally determined relative energies of the substituted cyclopropanes.60 Skancke and Boggs" have calculated optimum geometries for cis- and trans- 1,2-difluorocyclopropaneat the 4-21 basis set leve161and find (1) the CI-C2 bond length is shorter in the trans form, (2) the C3-C1,2 bond lengths are essentially the same for both, and (3) the trans isomer is more stable, in agreement with experimental observation.60 Although these researchers infer that the lower stability of the cis isomer is due to the unfavorable delocalization proposed by Bingham,sg their results are also consistent with our explanation. The evidence Skancke and Boggsl' cite to support their conclusion is the longer CI-C2 bond length and the larger delocalization of the charges of the cis isomer. They did not analyze the orbital energy splittings or the orbital compositions of the two 1,2-difluorocyclopropaneforms. Since similar C1-C2 bond length differences and charge distributions are observed for the 1,2-difluorooxiranes and the 1,2difluorocyclopropanes, it is feasible that the explanation for the relative stabilities of the cis and trans isomers is the same for both systems. F. 1,2-Dijluorocyclopropane,1,1,2,2-Tetrafluorocyclopropane, 1,2-Difluorooxirane, and Tetrafluorooxirane. The effect of 1,2-difluoro and 1,1,2,2,-tetrafluoro substitution on the ring bond lengths of cyclopropane was examined in an earlier paper.1° The results indicate that fluorination of cyclopropane does not generate the same bond length changes in all of the ring bonds as does fluorination of oxirane. The schematics obtained from the charge density difference plots comparing 1,1,2,2-tetrafluorocyclopropane to cyclopropaneI0 are the following.

VI11

IX

X

Schematic X represents the total charge density redistribution in cyclopropane induced by tetrafluoro substitution, VI11 the charge rearrangements in the SS symmetry orbitals, and IX the charge shifts in the SA symmetry orbitals. Schematic X shows that the CI-C2 bond lengths will be shorter and the C3-Cl,2 bond lengths will essentially not change upon substitution of cyclopropane, in contrast to the shortening of all the ring bonds upon substitution of oxirane (schematic V). The greater electronegativity of the oxygen in tetrafluorooxirane compared to that of the CH2 group in 1,1,2,2-tetrafluorocyclopropane enables the oxygen to compete more effectively with the CF2 groups for the electron density. Thus, the oxygen in IV is more negative by 0.013e than the oxygen in I (part A), whereas the CH, group in 1,1,2,2-tetrafluorocyclopropaneis more positive by 0.015e than the CH2 groups in cyclopropane.1° The charge loss in the CH2 group arises from a loss of 0.032e on each of the hydrogens: the charge density is transferred from the hydrogens to C3 and the fluorines.I0 The charge buildup between the hy(60) Craig, N. C.; Chao, T.N. H.; Cuellar, E.; Hendriksen, D. E.; Koepke, J. W. J . Phys. Chem. 1975, 79, 2270-2282. (61) Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E. J . Am. Chem. SOC. 1979, 101, 2550-2560. (62) Agopovich, J. W.; Alexander, J.; Gillies, C. W.; Raw, T.T.J . Am. Chem. SOC.1984, 106, 2250-2254; in press.

Deakyne et al. drogens and C3 in the SS symmetry orbitals (schematic VIII) combined with the charge loss on C3 in the SA symmetry orbitals (schematic IX) of cyclopropane (to which the hydrogens on C3 do not contribute) pull C3 away from the C1-C2bond. Conversely, the charge transfer from the CF2 groups to the oxygen via the SS (schematic VI) and S A (schematic VII) symmetry orbitals of oxirane draws the oxygen toward the C-C bond. Since the charge changes induced around the carbons in oxirane and C1 and C2 in cyclopropane move them in the same direction, the C-0 bonds and C3-C1,2 bonds are affected differently by tetrafluoro substitution. As shown previously in this work and the earlier paper,1° these results are also applicable to the disubstituted species. G. The Electron Donor-Acceptor Scheme. Hoffmann13 has postulated that the predominant interaction determining the effect of a a-donating substituent on a cyclopropane ring would be the interaction between the a-donor and the unoccupied SA C-C-C antibonding orbital (M010) of cyclopropane. Extending this

MOlO

postulate to oxirane yields the conclusion that the predominant interaction would be between the a-donor and the unoccupied SA C-0-C antibonding orbital (M010) of oxirane. Inspection of the MOs reveals that MOlO is partially occupied in all of the fluorinated molecules studied in this work and in the earlier work.IO However, the F-Mol0 interaction is such that only the 2s and 2px AOs on the substituted carbons make a significant contribution to the resultant MO. (As an example, see M 0 1 3 for tetra-

-

M013

fluorooxirane.) There is also a small gain in charge density around C3 and the oxygen, but it is too small to affect the C-O or C3-C1,2 bond lengths. The net effect of this interaction is to increase the antibonding character of the bond between the substituted carbons. However, we find that this effect is overridden by the interactions between the a-donor and the occupied SS and SA symmetry orbitals of cyclopropane and oxirane. Consequently, the C1-C2 or C-C bond shortens rather than lengthens. We reached a similar conclusion on the inability of this scheme to explain overall substituent effects in our study of cyclopropanone and methylenecyclopropane.10 H. Generalization to Other Systems. In the absence of steric effects, the above analysis of oxirane substituent effects should be general for electronegative substituents because it is based solely on induced charge redistributions. Indeed, we showed previously10 that our approach explains the bond length changes in the cyclopropane ring due to F, 0,and CH2 substitution. In addition, our suggested geometry for I,l-dichlorocyclopropane'Owas later confirmed via ab initio optimization of the structure of this m~lecule.~ Thus, our approach should be applicable to chlorinated oxiranes as well, if steric effects can be ignored. Politzer et aL21 have determined optimized geometries for oxirane, cis- and trans- 1,2-dichlorooxirane, and tetrachlorooxirane at the STO-3G and STO-SG level^.^^,^^ Their results indicate that all of the ring bond lengths in cis-1,2-dichlorooxirane and trans- 1,2-dichlorooxirane are essentially unchanged, at 1.31 A (C-0) and 1.49 A (C-C), compared to these bond lengths in oxirane. The C-0 bonds in tetrachlorooxirane are also the same length as the C-0 bonds in oxirane, whereas the C-C bond in tetrachlorooxirane lengthens to 1.51 A. Clearly, all of the ring bonds in these chlorinated oxiranes are longer than predicted by the above analysis, suggesting that steric effects are important for these molecules. This result is not especially surprising, since the C-C bond in oxirane is one of the shortest observed carbon-carbon

J. Phys. Chem. 1984,88, 5981-5986 single bonds and the distance between the fluorines in cis- 1,2difluorooxirane is approximately equal to the sum of two fluorine van der Waals radii.19 Since the sum of two chlorine van der Waals radii (3.53 A) is larger than that of two fluorine van der Waals radii (2.70 A), this could prevent the C-C bond in the chlorine-substituted oxiranes from shortening. IV. Summary In summary, the following points have been made: (1) 1,2difluoro substitution or tetrafluoro substitution of oxirane shortens all of the ring bonds, with tetrafluoro substitution shortening them more than difluoro substitution. (2) Fluorination of oxirane generates charge shifts which draw the oxygen toward the C-C bond and move the carbons toward the opposite C-0 bond. (3) The charge density difference plots reveal the group of symmetry orbitals responsible for the relevant charge transfers; the orbital diagrams reveal the dominant orbital within the pertinent group. (4) The observed bond length changes are accounted for by interactions between the ?r-donor and occupied ring orbitals. (5) trans- 1,2-Difluorooxirane will be more stable and have a shorter C-C bond than cis- 1,2-difluorooxirane. ( 6 ) The charge redistributions induced by fluorine substitution and, therefore, the resulting geometry changes are different for oxirane and cyclopropane. (7) Steric effects may be important in determining the geometries of chlorinated oxiranes.

5981

After completion of this article, it was brought to our attention that preliminary results from the laboratory of Dr. Charles W. Gillies indicate that our predictions that the C-C bond in trans- 1,2-difluorooxirane and in tetrafluorooxirane and the C-0 bonds in tetrafluorooxirane are shorter than these bonds are in oxirane and cis-l,2-difluorooxirane will be substantiated. (C. W. Gillies, personal communication.) Note Added in Proof: The work on trans-l,2-difluorooxirane and tetrafluorooxirane has now been completed by Gillies et a1.62 The only discrepancy between our predicted trends and their results is in the relative lengths of the C-0 bonds in cis-1,2-difluorooxirane and trans- 1,2-difluorooxirane. We predicted that the C-O bond lengths would be essentially equivalent in the two isomers. They find that the C-0 bonds are shorter in the trans form. Acknowledgment. We thank Dr. Peter Politzer for data from his oxirane and trans- 1,2-dichlorooxirane calculations and Dr. Charles W. Gillies for data from his microwave studies of trans- 1,2-difluorooxirane and tetrafluorooxirane prior to publication. We also thank Dianne c. Wood and Richard B. Salmonsen for carrying out some preliminary work on this project. The support of the College of the Holy Cross Data Processing Center is gratefully acknowledged. Registry No. I, 75-21-8; 11, 54943-69-0; 111, 80397-37-1; IV, 69417-7; FZ, 7782-41-4; Clz, 7782-50-5.

Polarized Infrared Spectra of Hydrogen-Bonded Systems by the Stretched-Polymer Method. 2. Transition Moment Directions of the Vibrations of Normal and Deuterated Acetlc Acid Dimerst Martti Ovaska Division of Chemistry, School of Pharmacy, University of Helsinki, Fabianinkatu 35,SF-00170 Helsinki 17, Finland (Received: May 30, 1984)

Transition moment directions of the vibrations of dimers of CH3COOH, CH3COOD, CD3COOH, and CD3COOD have been measured by using the stretched-polymer orientation method. 0-H, C-0, and C = O stretching vibrations are directed almost parallel to the respective bonds. The OCO bending is observed to be directed above 30° from the long axis of the dimers. The rocking OCO vibration is directed almost parallel to the long axis of the dimers in each species. The OH (OD) bending is the only vibration which shows noticeable differences in the directions of transition moments between different isotopic forms. The obtained results are compared to theoretical directions for carboxylic ring in-plane vibrations calculated by the fixed partial charge model using the formic acid dimer as a model system.

Introduction Much work has been devoted to experimental and theoretical determination of the magnitudes of vibrational transition moments of molecules, because vibrational intensities are proportional to the square of the transition moment.’ Both magnitudes and directions are needed in calculations of vibrational optical activity. The methods used in calculations of infrared vibrational circular dichroism (VCD) include the fixed partial nuclear charge (FPC) mode12p3and the localized molecular orbital (LMO) model.e6 For polymers an exciton coupling model has been used which requires experimental knowledge on magnitudes and directions of the coupled vibrations.’ The FPC and L M O models require knowledge of the molecular force fields in order for the atomic displacements in vibrations to be calculable. The uncertainties in force fields of molecules severely restrict the usefulness of these methods for highly mixed modes.3 Experimental knowledge on transition moment directions can be used in searching for a reliable force field for a molecule. Reference 16 is taken at part 1 in this series.

The experimental determinations of transition moment directions for nonpolymers have been few and limited to solid-state measurements.6-10 However, in the solid state the crystal field perturbations can severely affect the transition moments and, besides, it is often difficult to prepare single crystals suitable for polarization measurements. The stretched-polymer orientation method has proved to be a valuable method for obtaining information about the directions of the electronic transition moments (1) “Vibrational Intensities in Infrared and Raman Spectroscopy”; Person, W. B., Zerbi, G., Eds.; Elsevier: New York, 1982. (2) Schellman, J. A. J. Chem. Phys. 1973, 58, 2882; 1974,60, 343. (3) Singh, R. D.; Keiderling, T. A. J . Chem. Phys. 1981, 74, 5347. (4) Nafie, L. A.; Walnut, T. H. Chem. Phys. Lett. 1977, 49, 441. (5) Walnut, T. H.; Nafie, L. A. J . Chem. Phys. 1977, 67, 1491, 1501. (6) Nafie, L. A.; Freedman, T . B. J . Chem. Phys. 1981, 75, 4847. (7) Snir, J.; Frankel, R. A.; Schellman, J. A. Biopolymers 1975, 14, 173. (8) Sandeman, I. Proc. R. SOC.London, Ser. A 1955, 232, 105. (9) Abbot, N. B.; Elliott, A. Proc. R. SOC.London, Ser. A 1956, 234, 247. (IO) Kyogoku, Y.; Higuchi, S.;Tsuboi, M. Spectrochim. Acta, Part A

1967, 23, 969.

0022-3654/84/2088-598 1%01.50/0 0 1984 American Chemical Society