J . Phys. Chem. 1992,96, 3709-3712 3709

Molecular Orbital Study of the Structures of Hydroxamic Acids

LAsz16 Turi, J. J. Damenberg,*

Department of Chemistry, Ciry University of New York-Hunter College and the Graduate School, 695 Park Ave., New York, New York 10021

Jose Rama, and Oscar N. Ventura*

Instituto de Quimica, Facultad de Ciencios y CIftedra de Quimica Curintica, Facultad de Quimica, Gral. Flores 21 24, C.C. 1 1 57, I I800 Montevideo, Uruguay (Received: October 7, 1991)

Semiempirical (AM1 and PM3) and ab initio Hartree-Fock and Moeller-Plesset (MP2) calculations using the 3-21G, 3-21G(d), 6-31G(d,p), 6-31 lG(d,p) basis sets are reported for the E and Z conformations of both the keto and iminol tautomers of formohydroxamic acid. Semiempirical and Hartree-Fock calculations are also reported for several substituted hydroxamic acids. The HF calculations tend to favor the non-hydrogen-bonding E forms, while the MP2 calculations predict both of the Z forms to be close in energy. AM1 predicts the (Z)-imino1 to be the global minimum, while PM3 predicts this to be the least stable structure. The Z-keto structures are predicted to be stabilized upon substitution by methyl, cyano, and phenyl groups by all methods. The results are discussed in terms of electronic effects and known experimental results.

Hydroxamic acids have several interesting properties.' In addition to being unusually strong, they can dissociate to different anions, behaving as either oxygen or nitrogen acids. They are known to be potent and specific inhibitors for urease (urea am- inohydrolase, EC 3.5.1.5) activity.* Boric acid reverts the in- hibition by reversibly binding to the hydroxamic acids forming anions of boron heterocycles under basic condition^.^

Hydroxamic acids can exist in two tautomeric forms, keto, 1, or iminol, 2. In addition, both 1 and 2 can be present in either the E or Z orientation about the C-N bond. The X-ray diffraction of crystals of formohydroxamic acid4 shows it to be in the (a-1 form with the C&H bond in the anti orientation (better suited for intermolecular H bonding). The dihedral angle defined by the four heavy atoms is 5 . 4 O . X-ray diffraction of the hemihydrate of acetohydroxamic acid also indicates (a-1 to be the s t r u c t ~ r e . ~ An 170 N M R study of benzohydroxamic acids has similarly concluded that the keto, 1, form is predominant in various solvents at concentrations of 0.346 M.6 More recent NMR results have shown that monoalkylhydroxamic acids exist in both Z and E keto as well as iminol forms.7 Substitution on the carbon of hy- droxamic acids might have a profound effect upon the energetic ordering of the different tautomers as well as their conformational preferences. A similar but greater effect might be expected upon the conjugate bases of these suhstituted acids which would be quite important in predicting and understanding the acidities of com- pounds such as these. Recent reports on strategically substituted acetohydroxamic acid suggest it to be a nitrogen acid whose conjugate base has an internal H bond both in DMSO* and in the gas phase.g

(1) (a) Bauer, L.; Exner, 0. Angew. Chem. In?. Ed. Engl. 1974,13, 376.

(2) Kobashi, K.; Terashima, N.; Hase, J. Chem. Pharm. Bull. 1973, 21,

(3) Das, M. K.; Chakraborty, S . Synth. React. Inorg. Met.-Org. Chem.

(4) Larsen, I. K. Acra Crystallogr. E 1988, 44, 527. (5) Brccher, B. H.; Small, R. W. H. Acra Crysrallogr. 1970, 826, 1705. (6) Lipczynska-Kochany, E.; Iwamura, H. J . Org. Chem. 1982.47, 5277. ( 7 ) Brown, D. D.; Glass, W. K.; Mageswaran, R.; Girmay, B. Magn.

(8) Bordwell, F. G.; Fried, H. E.; Hughes, D. L.; Lynch, T.-Y.; Satish, A.

(9) Decouzon, M.; Exner, 0.; Gal, J. F.; Maria, P. C. J . Org. Chem. 1990,

(b) Lipczynska-Kochany, E. Chem. Reu. 1991, 91, 477.

2303.

1989, 18, 225.

Reson. Chem. 1988.26, 970.

V . ; Whang, Y. E. J . Org. Chem. 1990,55, 3330.

55, 3980.

TABLE I: Relative Semiempirical Eotbalpies and ab Initio Energies of tbe Tautomers of Formohydroxnmic Acid (In kcal/mol)

total (E)-la" (Z)-la' ~ - (E)-2a (Z)-2a energyof

method P nP P nP P P (E)-la(nP)c AM 1 3.7 1.8 5.6 2.7 4.2 0.0 -49.23 PM3 5.2 0.0 5.6 1.4 5.1 6.1 HF/3-21G 7.8 0.0 2.5 2.3 6.9 2.7 MP2/3-21G 9.0 0.0 0.8 0.4 7.3 1.8 HF/3-21G(d) 10.4 0.0 3.6 2.8 8.2 5.1 MP2/3-21G(d) 11.1 1.0 1.2 0.0 7.7 2.9 HF/6-31G(d,p) 9.3 0.0 3.0 1.8 7.1 4.0 MP2/6-31G(d,p) 9.5 0.0 0.7 1.3 5.2 1.0 HF/6-311G(d,p) 9.6 0.0 2.9 1.7 7.2 4.3 MP2/6-311G(d,~)~ 9.4 0.0 1.1 1.3 5.1 1.3

-48.53 -242.35821 -242.80458 -242.482 54 -243.120 82 -243.73247 -244.403 62 -243.79641 -244.577 33

'Two minima, planar (p) and nonplanar (np), were found at all levels. bMP2/6-31 lG(d,p)//HF/6-31 lG(d,p) calculations. cTotal energies are in hartrees, except for AM1 and PM3 calculations where the heats of forma- tion are shown in kcal/mol, respectively.

Previous theoretical studies on formohydroxamic acid include INDO'O and ab initio ca1culations.l' The highat level calculations (Huzinaga DZ basis) were performed on ( E ) - h and (a-h only.

H / H 0 \ \

R-(N-H

,-("OH \

0 0

12 1E

l a R = H lc R = C N

Ib R = Id R=Ph CH3

/h

"-O

"-"\ 0 --H

0 - H 22 2E

20 R = H 2c R = C N

2 d R = P h 2b R = CH3

0022-365419212096-3709$03.00/0 0 1992 American Chemical Society

3710 The Journal of Physical Chemistry, Vol. 96, No. 9, 1992

TABLE 11: Ontimized Structures of ( Z b l a of Formohvdroxamic Acids at Different Levels of Theon"

Turi et al.

3-21G 3-2 1 G(d) 6-31G(d,p) 6-31 lG(d,p) Darameter AM 1 PM3 H F MP2 H F MP2 H F MP2 H F r(CN) 1.418

4ON) 1.335

d o c ) 1.236

r(HO) 0.977

r(HC) 1.114

r(HN) 1.013

O(0CN) 123.2

O(H0N) 105.8

O(HC0) 130.8

O(0NC) 116.1

O(HNC) 113.4

O(HN0) 108.0

devb 22.5 b(ONC0) -17.4

b(HONC) 78.6

b(HNCH) 36.7

1.437

1.438

1.212

0.950

1.103

0.993

120.0

102.0

127.0

116.5

114.3

104.3

24.9 -22.4

76.1

35.8

1.366 1.338 1.433 1.440 1.205 1.220 0.970 0.978 1.083 1.079 0.998 0.993 125.6 122.3 104.9 102.0 123.5 124.1 116.0 117.4 122.0 129.4 111.2 113.2 10.8 -17.2 0.0 88.7 0.0 21.6 0.0

1.378 1.361 1.492 1.482 1.258 1.261 1.010 1.012 1.094 1.095 1.015 1.010 121.7 121.5 98.1 97.5 124.8 124.9 11 3.6 116.0 124.0 130.6 110.3 113.4 12.1 -13.4 0.0 12.7 0.0 32.1 0.0

1.369 1.360 1.325 1.334 1.386 1.420 1.386 1.406 1.178 1.224 1.195 1.229 0.964 1.003 0.972 1.005 1.099 1.103 1.094 1.103 1.008 1.023 0.999 1.014 126.5 122.0 123.2 121.4 103.6 97.5 100.1 96.2 124.0 125.1 124.7 125.6 114.4 112.9 118.4 116.5 115.5 118.4 127.4 129.1 109.6 110.0 114.2 114.4 20.5 18.7 -18.7 -13.7 0.0 0.0 103.0 7.3 0.0 0.0 32.6 39.4 0.0 0.0

1.366 1.330 1.370 1.370 1.186 1.201 0.945 0.951 1.093 1.089 0.996 0.990 125.6 123.0 106.1 103.8 123.4 124.0 116.9 119.6 117.6 126.7 110.8 113.7 14.7 -18.1 0.0 94.2 0.0 26.2 0.0

1.379 1.369 1.343 1.332 1.409 1.366 1.398 1.366 1.219 1.179 1.235 1.194 0.967 0.942 0.978 0.948 1.101 1.094 1.095 1.090 1.010 0.996 1.003 0.990 125.0 125.9 121.6 123.3 103.1 106.1 99.7 104.1 124.4 123.5 125.1 124.0 116.0 117.2 118.0 120.0 117.4 117.0 128.3 126.2 109.2 110.9 113.7 113.8 17.4 14.9 -22.1 -18.0 0.0 0.0 85.3 95.3 0.0 0.0 31.9 26.6 0.0 0.0

'Distances in angstroms and angles in degrees. The first entries correspond to the nonplanar structure, the second entries to the planar structure. *Deviation of the sum of the three angles around the nitrogen from 360O.

TABLE III: ZPVE of the Isomers of Formohydroxamic Acid at HF/6-31G($p) Levelo

ZPVE ( E ) - l a planar 33.16

nonplanar 34.49 (Z)-la planar 33.60

nonplanar 34.37 (E)-2a planar 34.22 (Z)-2a planar 34.63

isomer

' Energies in kcal/mol.

To the best of our knowledge, no calculations that correct for electron correlation have been reported.

In this paper we present the results of both semiempirical (AM1 and PM3) and ab initio (HF and MP2) calculations with various basis sets on the relative energies of the parent hydroxamic acid and several substituted derivatives.

Methods Semiempirical calculations were performed using the AM 1 ,I2

and MNDO-PM3I3 approximations to molecular orbital theory. All species reported were geometrically optimized in all internal coordinates using the AMPAC'~ computer program on I386 based workstations. Ab initio calculations were performed on the neutral species using the 3-21G, 3-21G(d), 6-31G(d,p), and 6-31 lG(d,p) bask Sets Using the MONSTERGAUSS, GAUSSIAN86, and GAUSSIANSB''

(10) Hilal, R.; Moustafa, H. Inr. J . Quontum Chem. 1984, 26, 183. (11) (a) Nguyen, M. T.; Ha, T.-K. J . Mol. Srrucr. THEOCHEM 1982,

88, 127. (b) Fitzpatrick, N. J.; Mageswaran, R. Polyhedron 1989,8, 2255. (c) Reference 5, footnote 32.

(12) Dewar, M. J. S.; Zoebisch, E. G.; Healy, E. G.; Stewart, J. J. P. J . Am. Chem. SOC. 1985, 107, 3902.

(13) Stewart, J. J. P. J . Compur. Chem. 1989, 10, 209, 21 1. (14) AMPAC including various updates was obtained directly from M. J.

S. Dewar and E. Healy and modified by J. J. Dannenberg for use on I386 and IBM RS/6000 computers.

TABLE IV: Relative Energies of Substituted Hydroxamic Acids method/ basis

substituents set (E)-1 AM 1 0.4 PM3 0.0 3-21G 0.0 3-21G(d) 0.0 6-31G(d,p) 0.0

CN AM 1 0.3 PM3 0.0 3-21G 0.0 3-21G(d) 0.0 6-31G(d,p) 0.0

phenyl AM1 1.1

CH3

PM3 0.5

(Z)-1 (E)-2 0.6 2.7 0.3 5.0 2.2 7.5 1.5 8.7 1.4 7.5 0.0 2.2 0.0 5.7 1.5 7.8 1.8 8.4 0.7 7.1 0.1 2.9 0 6.1

( 2 ) - 2 0 6.4 4.8 4.8 5.6 0.1 6.7 4.0 5.0 3.2 0 7.2

programs on HP/Apollo DN10000, IBM 3090, and IBM RS/ 6OOO computers. MP2, as well as HF, calculations were performed where computationally practical. All species were fully optimized at each level of calculation, unless otherwise noted. All stationary points were fully characterized by calculation of the force con- stants.

Results and Discussion The calculated relative energies and major geometric features

for the optimized structures of the parent formohydroxamic acid are collected in Tables I and 11. The results are clearly dependent upon the calculational method chosen. Among the semiempirical methods, AM1 finds the iminolic form with the internal hydrogeQ bond ((Z)-2a) to be the global minimum, followed by the keto forms, @)-la, and ( a - l a , with the other iminolic form, (E)-%, the least stable. PM3, on the other hand, predicts (Z)-2a to be the least stable isomer, with the other three in the same order as AM1. la has two distinct minima (characterized by calculation

(1 5) The GAUSSIAN series of programs is available from GAUSSIAN, Inc., Pittsburgh, PA.

Structures of Hydroxamic Acids

TABLE V Charge Density on Selected Atoms of Different Substituted Hvdroxamic Acids Calculated by A M P

The Journal of Physical Chemistry, Vol. 96, No. 9, 1992 3711

R = H R = CH3 R = CN R = Ph atoms @)-la (Z)-2a ( 2 ) - l b (2)-2b ( 2 ) - l c G9-k (Z)-ld (Z1-U

-317 -272 -317 -278 -259 -249 -313 -274 235 12 235 65 34 1 148 280 1 1 1

O(C) C N -202 -142 -202 -143 -1 79 -8 3 -196 -138

-243 -271 -243 -279 -231 -265 -242 -278 R 129 20 1 88 156 -137 -55 28 -140 OW)

'Charges are X103.

of all force constants as noted above), planar and nonplanar, for each of the E and Z forms. From the data in Table 11, one can see that the nonplanar form is pyrimidalized at the N, with the 0-H bond twisted out of the plane defined by the bonds to the carbon.

The Hartree-Fock calculations find (@-la to be the most stable isomer by at least 1.8 kcal/mol at all the levels calculated. The iminols are calculated to be more energetic than either of the keto forms, with (Z)-2a about 3 kcal/mol lower than (E)-2a, pre- sumably due to the internal H bond. However, the MP2 calcu- lations significantly change the situation. At the highest level studied with complete geometrical optimization, MP2/G-3 1G- (d,p), three isomers ((E)-la, (z)-la, and (z)-2a) are predicted to be within 1.0 kcal/mol of each other. The MP2/6-311G(d,- p)//HF/6-31 lG(d,p) calculations give a slightly larger range (1.27 kcal/mol). In particular, the relative energy of (z)-2a (which is the global minimum predicted by AM1) markedly decreases upon correction for electron correlation, as does (Z)-la. This behavior is quite reasonable as the two Z forms contain internal H bonds which require the oxygens to be closer to each other than in the E forms, thus increasing the electron-correlation error of the H F calculations. Furthermore, while the nonplanar structure of ( a - l a is calculated to be more stable than the planar form for all HF, the MP2/3-21G, and MP2/3-21G(d) calculations, the planar MP2/6-31 lG(d,p)//HF/6-31 lG(d,p). is predicted to be more stable by MP2/6-31G(d,p) and MP2/6-31 lG(d,p)//

Zero-point vibrational energies (ZPVE) calculated at the HF/6-31G(d,p) level are presented in Table 111. The greatest effect of incorporating the ZPVE correction would be to lower the relative energies of the planar forms of @)-la and (Z)-la. It is not clear that these values are applicable to the MP2 cal- culations, as the relative energies and geometries are somewhat different from those obtained using H F (see below). However, calculation of the ZPVE's at the MP2/6-31G(d,p) level was not computationally practical. Planar (E)-la is sufficiently more energetic than the nonplanar form that the ZPVE correction does not affect the qualitative results. However, if one applies this ZPVE correction to the MP2/6-31G(d,p) and MP2/6-311G- (d,p)//HF/6-3 1 lG(d,p) calculations, the energy difference be- tween the nonplanar @)-la and planar (z)-la forms essentially disappears.

One cannot be certain the energetic ordering of the species in question would not change if higher levels of theory be applied. Nevertheless, the results demonstrate that small basis set and uncorrelated ab initio calculations are inadequate to describe the relative energies of the possible forms of formohydroxamic acid. The AM1 calculations seem to have a bias for the (z)-2a form compared to the best correlated calculations. Since both Z forms (particularly, (Z)-2a) seem to significantly improve in stability upon correction for correlation error and improving the basis set, the possibility remains that better ab initio calculations might predict (n-20 to be the global minimum. Inspection of the geometric parameters collected in Table I1 indicates that, upon application of MP2, the geometries of the species tend to change in the direction predicted by AM1. This is particularly evident from the lengths of the bonds (especially, N-O) in the various species.

Since we cannot practically use those ab initio calculations that are sufficiently accurate to calculate the stabilities of the larger substituted hydroxamic acids, we are forced to choose one of the

HF/6-31 lG(d,p).

TABLE VI: Charge Density on Atoms of Substituents of Substituted Hydroxamic Acids Compared to CH3CN and Toluene Calculated Using the AM1 Methoda

H . . - \

4W0-S

5 6

(a -1 db

(2)-1 (2) -2 substituent atoms R-CH, charge diff charge diff

N -50 40 90 21 71 R = C N C -144 -177 -33 -76 68

R = phenyl C, -70 -125 -55 -44 26 C2 -131 -101 30 -88 43 C3 -127 -135 -8 -143 -16 C4 -135 -104 31 -110 25 C5 -127 -135 -8 -142 -15 C6 -131 -75 56 -87 44 Hz 130 132 2 150 20

H4 130 138 8 134 4

H6 130 153 23 152 22

H3 130 139 9 136 6

H5 130 141 1 1 136 6

OCharges are X103. bThe f(C2CICN) tetrahedral angle is 44.8'.

semiempirical methods. One can certainly eliminate PM3 on the basis of its poor description of (Z)-2a. Thus, AM1 appears to be the method of choice. We also present HF calculations on some of the smaller substituted hydroxamic acids for comparison with the AM1 results which are presented in Table IV.

Significantly, all the methods used clearly predict the (z)-1 form to decrease in relative energy upon substitution with methyl, cyano, or phenyl groups. Due to the expected increase in positive charge (see Table V) on the carbonyl carbon upon internal H bonding, one might expect. only electron-donating groups to sta- bilize (2)-1; however, cyano and phenyl are not normally con- sidered to be electron-donating. Nevertheless, these results can be rationalized by considering resonance structures such as I for the cyano and I1 for the phenyl derivatives. In these structures,

H H \

0- 0-

N-0 N+-C-( 1 H

I II

positive charge is developed in n-systems of the substituents, while the carbonyl oxygen becomes more negative, which should increase the stabilizing effect of the hydrogen bond. The atomic charge densities collected in Table V also illustrate this effect. In this table the difference in positive charge on the carbonyl carbons of (a-1 and (2)-2 is seen to decrease upon substitution with any of the substituents. In Table VI the atomic charges on the cyano and phenyl groups are compared with those on the analogous atoms of acetonitrile and toluene (where the hydroxamyl group is replaced by methyl). The ortho and para positions of the phenyl

3712 J. Phys. Chem. 1992, 96, 3712-3116

group become more positive in (Z)-ld compared to toluene, while the N of the cyano group in (2)-lc behaves in a similar manner when compared to that of acetonitrile.

The calculations are in reasonable agreement with the NMR studies’ that indicate benzohydroxamic acid to exist predominantly in the (Z)-1 form, while monoalkylhydroxamic acids exist in several forms. Hopefully, the data presented here will encourage the further work necessary to provide a more appropriate com- par ison.

Conclusion

The ab initio results clearly show that Hartree-Fock calculations are not sufficient for describing the conformational preferences of formohydroxamic acid. At the highest levels optimized with

MP2/6-31G(d,p) @)-la is predicted to be most stable, but two other conformations ((Z)-la, and (Z)-h) are so similar in energy that careful experimental work might be needed to accurately determine the structural preference of this molecule in the gas phase. The presence of substituents on the carbon of formo- hydroxamic acid is predicted to strongly affect the structural preferences of the acids. Therefore, experiments performed on the substituted acids may not be relevant to the parent.

Acknowledgment. This work was supported in part by grants from the National Science Foundation, PSC-BHE, and IBM Corp.

Rdstry NO. 1, 4312-87-2; (E)-2, 77269-31-9; (Z)-2, 77269-30-8; H$CONHOH, 546-88-3; NCCONHOH, 140177-1 1-3; PhCONHOH, 495-18-1.

Closs’s Diradicai: Some Surprlses on the Potential Energy Hypersurface

C. David Sherrill, Edward T. Seidl, and Henry F. Schaefer III*

Center for Computational Quantum Chemistry, University of Georgia, Athens, Georgia 30602 (Received: December 5, 1991)

The singlet and triplet potential energy surfaces for 1,3-~yclopentanediyl (Closs’s diradical) have been investigated using ab initio electronic structure theory. The triplet C, structure previously postulated to be an intermediate in the ring inversion of bicyclo[2.1.0]pentane (BCP) is found to correspond to a saddle point, rather than a minimum, on a potential energy surface more complex than that originally proposed by Closs. The singlet and triplet surfaces share several qualitative features, but the triplet stationary points lie - 1 kcal/mol below the corresponding singlets. The BCP ground state and the singlet and triplet stationary points for Closs’s diradical have been fully optimized using a DZ + d basis set at the SCF and CISD levels of theory.

introduction

Because they have so often been proposed as reaction inter- mediates,’ diradicals have become a principal subject of inves- tigation in physical organic chemistry. In 1975, Buchwalter and Closs became the first to characterize a “localized” diradical, 1,3-~ycIopentanediyl.~ Their ESR and CIDNP results suggested that 1,3-cyclopentanediyl has a triplet ground state which is planar or near-planar, and the triplet decay kinetics led them to propose the schematic potential energy surface in Figure 1. The shaded region represents the barrier to quantum mechanical tunneling, which Buchwalter and Closs believed responsible for the tem- perature independence of the triplet decay rate a t low tempera- tures. The barrier height was estimated to be 2.3 * 0.2 kcal/mol. Despite Benson-type thermochemical calculations that suggest a minimum on the singlet surface with a well depth of 5 k~al /mol ,~ Buchwalter and Class depicted the singlet diradical as a transition state on its potential energy surface because they found such a deep well inconsistent with the observed instability of the triplet diradical. A more recent study by Goodman and Herman using time-resolved photoacoustic calorimetry also suggests that the

(1) (a) Borden, W. T., Ed. Diradicals; Wiley-Interscience: New York, 1982. (b) Berson, J. A. In Rearrangements in Ground and Excited Stares; de Mayo, P., Ed.; Academic Press: New York, 1980; Vol. I, pp 31 1-390. (c) Gajewski, J. J. Hydrocarbon Thermal Isomerizations; Academic Press: New York, 1981. (d) Wagner, P. J. In Rearrangements in Ground and Excited States; de Mayo, P., Ed,; Academic Press: New York, 1980; Vol. 111, pp 381-444. (2) (a) Buchwalter, S. L.; Closs, G. L. J . Am. Chem. Soc. 1975, 97, 3857.

(b) Buchwalter, S. L.; Closs, G. L. J . Am. Chem. Soc. 1979, 101, 4688. (3) (a) Beadle, P. C.; Golden, D. M.; King, K. D.; Benson, S. W. J . Am.

Chem. Soc. 1972,94, 2943. (b) ONeal, H. E.; Benson, S. W. Inr. J . Chem. Kiner. 1970,2,423. (c) Luo, Y.-R.; Benson, S. W. J . Phys. Chem. 1989,93, 3304.

0022-365419212096-3712$03.00/0

singlet diradical is a transition state or a shallow local minimum! Conrad et al. have previously studied 1,3-~yclopentanediyl with

ab initio electronic structure theory,s using the spin-restricted self-consistent field (SCF) method with a double-l (DZ) basis set. They performed a partial geometry optimization of the triplet diradical, subject to the constraints of C, symmetry, 1.09-A C-H bond lengths, and 109’ methylene bond angles. At the constrained triplet geometry, the lowest lying singlet state, treated with tweconfiguration self-consistent field (TCSCF) theory, was found to lie 0.9 kcal/mol above the triplet ground state, in good agreement with the work of Buchwalter and Closs.

In this work we seek to better characterize the singlet and triplet potential energy surfaces, and to answer the long-debated question of whether the singlet surface contains a local minimum. Using a DZ + d basis set, we optimize the geometries of the ring-closed ground state of bicyclo[2.1.O]pentane (BCP) and the diradical stationary points on the singlet and triplet surfaces at the SCF, TCSCF, CISD, and TC-CISD levels of theory. We perform harmonic vibrational frequency analyses at the SCF level to help determine the relationships among the stationary points on the schematic potential energy surface.

Theoretical Methods The basis set used in this study includes Dunning’s6 double-l

contraction of Huzinaga’s’ 9s5p primitive set for carbon and 4s primitive set for hydrogen. The basis set for carbon was aug-

(4) Herman, M. S.; Goodman, J . L. J . Am. Chem. SOC. 1988,110,2681. ( 5 ) Conrad, M. P.; Pitzer, R. M.; Schaefer, H. F. J . Am. Chem. Soc. 1979,

(6) Dunning, T. H. J. Chem. Phys. 1970, 53, 2823. (7) Huzinaga, S. J . Chem. Phys. 1965, 42, 1293.

101, 2245.

0 1992 American Chemical Society