an ab initio study of the structures and the inversion barriers in 1,3-cyclohexadiene,...

Journal of Molecular Structure (Theo&m), 262 (1992) 117-130 Elsevier Science Publishers B.V., Amsterdam

117

An ab initio study of the structures and the inversion barriers in 1,3-cyclohexadiene, 1,2_dihydronaphthalene and 9,10-dihydrophenanthrene

Andrzej Sygula and Peter W. Rabideau

Department of Chemistry, Louisiana State Univeristy. Baton Rouge, LA 70803 (USA)

(Received 2 December 1991; in final form 27 January 1992)

Abstract

Ab initio 3-21G geometry optimization calculations performed for both the half-chair and planar conformers of the title compounds are reported. Vibrational analysis shows the nonplanar conformers to be the minimum energy structures, whereas the planar forms represent the transition states for ring inversion. The calculated geometries are in very good correlation with the experimental data available. The effects of the basis set quality up to 6311G** level in addition to the electron correlation corrections (to the MP4 level) on the calculated barriers for inversion are addressed. The latter effect seems to be more important for the proper description of the barriers in the systems in question. Benxannelation of the l,&cyclohexadiene ring increases slightly the barrier for its inversion. The “best theoretical estimations” of the barriers are 3.7, 4.8 and 8.6 kcalmoll’ for the three title compounds, respectively. Even at the relatively high level of the calculations, the ab initio method tends to overestimate, to some extent, the barriers considered.

INTRODUCTION

There is general agreement that l,&cyclohexadiene (1) is nonplanar in its lowest energy conformation, exhibiting C, symmetry (for a recent review see ref. 1). The benzannelated analogs of 1, i.e. 1,2_dihydronaphthalene (2) and 9,10-dihydroanthracene (3) are also nonplanar in their preferred conformations. In the case of 1 the knowledge was originally based on the results of the microwave spectrum analysis [2,3] which predicted the two ethylene units to be rotated relative to each other around the C2-C3 bond by about 17’. This finding was subsequently confirmed by electron diffraction studies [4-6] and by analysis of the ‘H NMR spectra [7,8]. Although the

Correspondence to: P.W. Rabideau, Department of Chemistry, Louisiana State University, Baton Rouge, LA 70803, USA.

0166-1280/92/$05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.

118 A. ~~gula and P. W. ~ab~~eaul~.

al 3 0

2 3

confo~ational analysis of 2 has attracted less attention than 1, early ‘H NMR studies based on a coupling constant analysis of the hydrogen atoms located at Cl and C2 suggested that the partially hydrogenated ring in 2 may be slightly more puckered than in 1 191. Finally, the central ring of 9,10-dihydrophenanthrene (3) was suggested to be nonplanar as early as 1955 on the basis of chemical arguments [lo] and UV spectra analysis [ll]. Various physical methods reported [l] give an estimation of the rotational angle along the pivotal C4a-C4b bond in the range 20-24’. A recent crystal structure determination of 3 shows the outside rings to be close to planarity and the torsional bond in question to be about 21° (a mean value of the C4-C4a-C4b-C5 and ClOa-C4a-C4b-CSa torsional angles taken from four sy~etry-independent molecules of 3 in the crystal unit cell) [12].

Thus the nonplanarity of l-3 in their lowest energy conformations seems to be well established, and this leads to the question of ring inversion of the nonplanar rings. In 1, for example, this would involve conversion from one C, structure, presumably through a planar transition state, to the other

c2 c2v c2

enantiomer with C, symmetry. Numerous attempts have been made to estimate the inversion barriers for l-3, mainly by ‘H NMR techniques [l]. However, no broadening of the alicyclic hydrogen atom signals was observed even at very low temperatures (e.g. - 50°C for 2 [13] or - 13OOC [14] and - 15OOC [15] for 3). It must be concluded that the barriers for inversion are quite low in the systems under consideration, and thus cannot be measured by NMR methods.

The only experimental estimation of the inversion barrier of 1 comes from the gaseous state Raman spectroscopic study by Carreira et al. [16]. The assumption that the low frequency twisting mode may be described by a double well potential function led to a barrier for inversion of 1 of

A. Sygula and P. W. RabideaulJ. Mol. Struct. (Theochem) 262 (1992) 117-130 119

1099 + 50 cm-’ or 3.1 + 0.1 kcal mol-‘. Such experimental estimates are not available for 2 and 3.

Because of the lack of experimental data, high quality theoretical estimates of the aforementioned barriers become very important. Although a significant number of computational studies have been reported [l], they have generally been limited to empirical molecular mechanics (MM) calculations, presumably because of cost considerations. Herein we present the results of ab initio studies on l-3 focusing mainly on the calculation of the inversion barriers. First 1 is investigated in detail and the influence of the basis set used in addition to electron correlation effects on the quality of the results is addressed at a relatively high level of theory. These results are then used in conjunction with some lower level ab initio calculations performed for 2 and 3 in order to estimate the barriers for inversion with potentially higher accuracy. Finally the correlation of the theoretical results with the available experimental data is discussed.

COMPUTATIONAL DETAILS

All of the ab initio calculations reported herein were performed by using the GAUSSIAN&J program package [17]. Geometry optimization for both planar and nonplanar conformers of l-3 was performed within the Hartree- Fock (HF) approximation at the 3-21G level [18], generally accepted for hydrocarbons as being sufficient for this purpose [19]. Geometry constraints were imposed whenever possible. Thus for 1 and 3 C, and C,, symmetry was kept for nonplanar and planar conformers, respectively; the planar conformer for 2 was optimized with C, symmetry and the nonplanar conformer was ‘optimized with no symmetry constraints (C,). All of the stationary points located on the potential energy surfaces were further characterized by calculations of vibrational frequencies. Single point calculations based on 3-21G optimized geometries were performed with various basis sets up to 6-311G** [20(a)] for 1. For economic reasons the basis set used for 2 and 3 was limited to the 6-31G* level [20(b)].

The post-HF electron correlation effects were assessed employing Marller-Plesset perturbational theory [21] with the frozen core approximation. For 1 the calculations were performed up to the 4th order (MP4 level), whereas MP2 level calculations were performed for 2 and 3.

RESULTS AND DISCUSSION

1,3-Cyclohexadiene (1)

Geometry optimization performed with the 3-21G basis set led to the nonplanar half-chair structure 1A with C, symmetry as the minimum

A. Sygula and P. W. RabideaulJ. Mol. Struct. (Theochem) 262 (1992) 117-130

1 A, nonplanar (C,)

Cl -c2-C3-C4 = 15.2

Cl-C6-C5-C4 - 44.20

HlCl-C266 = 177.00

H2-C261 -C3 -179.3”

H5’-CE-C4-C6 =-122.0”

H5a-C5-C4-C6 = 120.3”

H5-C5-C4-C6 = 122.60

Fig. 1. The optimized 3-21G structures of nonplanar 1A (C, symmetry) and planar 1B (C, symmetry).

energy conformation. Calculated bond lengths and bond angles in addition to some torsional angles for lA, together with conformer 1B (in which the ring is forced to be planar), are presented in Fig. 1. At the 3-21G level 1A is more stable than 1B by 2.2 kcalmolll. Vibrational frequency calculations performed at the same 3-21G level gave positive frequencies only for lA, showing this conformation to be a true minimum on the potential energy surface of 1. In contrast, one imaginary frequency (156i) was calculated for lB, indicating the latter to be a transition state. Closer inspection of the vector conjugated with the imaginary vibration showed that 1B is the transition state for the ring inversion process. This confirms the validity of the previous assumptions about the planar transition state in the ring inversion in 1.

The optimized geometry of 1 (Fig. 1) may be compared with the previously reported ab initio results performed at the STO-3G level [22] and with the

A. Sygula and P. W. RabideaulJ. Mol. Struct. (Theo&em) 262 (1992) 117-130 121

split-valence quality basis set [23]. (The basis set used for the geometry optimization in ref. 23 was the (7,3) + [4.2] set of Roos and Siegbahn for the carbon atoms and the Huzinaga’s (4) + [2] basis set for the hydrogen atoms.) As expected our results are very close to those obtained by Saebo and Boggs [23] with differences in bond lengths and bond angles not exceed- ing 0.005A and 0.4’. The differences are significantly bigger when the STO-3G optimized 1A [22] is compared. Our 3-21G structure is slightly more puckered than both the ones calculated by Saebo and Boggs [23] and by Birch et al. [22]. The torsional angles a, (Cl-C2-C3C4) and ~1~ (Cl-C6-C5-- C4) (15.2 and 44.2O respectively) (Fig. l), are higher than the respective values reported earlier (13.5 and 38.7O [23] or 13.9’ [22] with a2 not reported in this latter case).

Comparison of the calculated structure of 1A with the experimental results derived from electron diffraction studies [4-6] shows a satisfactory correlation. In terms of ring puckering, our structure is slightly closer to the experimental estimates than the previously reported ab initio structures because the electron diffraction experiment suggests 17-18.3O [46] and 46’ [5] for a, and CI~, respectively.

Because 1B is the transition state for the ring inversion, the energy difference between 1B and 1A gives an estimation of the inversion barrier. Such an estimation, however, requires the entropic term to be negligible if the calculated energy difference is to be compared with the experimental AG*. This assumption is expected to be valid for 1 on the basis of the following considerations. First we consider the inversion of the isolated molecule (gas phase) so there are no entropy contributions from the dif- ferent solvation of the substrate and the transition state. Furthermore, in condensed phases (e.g. solutions in nonpolar solvents) this contribution should not be important because both the substrate (1A) and the transition state (1B) are nonpolar molecules. Furthermore, both 1A (C,) and 1B (C,,) possess the same symmetry number of 2 (the symmetry number is the number of indistinguishable spatial arrangements a molecule can have as the results of proper rotations), so the expected contribution to AS* due to symmetry vanishes. Similar arguments are also valid for the inversion of 2 and 3. Thus a comparison of the calculated energy differences between the lowest energy conformers and their respective transition states with the experimental values of AG* seems to be justified in the systems considered.

Table 1 summarizes the results of our calculations testing the influence of the basis set quality on the inversion barrier in 1. Inspection of Table 1 clearly shows that although improvement of the basis set used significantly lowers the calculated total energies, it has very little effect upon the relative stability of 1B vs. lA, i.e. the inversion barrier. Improvement of the flexibility of the atomic orbitals (AOs) when going from the 3-21G to the 6-311G basis set only lowers the calculated barriers for inversion from 2.2

122 A. Sygula and P. W. RabideaujJ. Mol. Struct. (Theochem) 262 (1992) 117-130

TABLE I

The total energies (hartrees) for 1A and the relative energies (kcal mol-‘) for 1B calculated with various basis sets at the optimized 3-21G geometry

Basis set

IA 1B

3-21G - 230.543 2312 ZPE” 14.51

6-31G 6-311G 6-31G* 6-31G** 6-311G* 6-311G-**

- 231.743 6617 - 231.784 285 4 - 231.831604 1 - 231.844 902 1 - 231.812 800 3 - 231.8854870

2.2 74.53b

1.9 1.9 2.0 2.0 2.2 2.1

“Zero point energy (kcalmol-I), scaled by the factor 0.9. b One negative frequency ignored in the calculation of ZPE.

to 1.9 kcal mol-l. However, inclusion of the polarization functions slightly increases the barrier by about 0.1-0.2 kcalmol-’ (Table 1). The above factors work in opposite directions so they almost cancel each other. As a result the inversion barrier for 1 calculated with the highest quality 6- 3llG** basis set is almost identical with the one calculated at the 3-21G level! This is a rather surprising result because it has been believed for some time that a proper description of the inversion processes requires high quality basis sets with polarization functions included in the calculations [19,24]. From an economic point of view our results seem to be encouraging, justifying the use of lower quality basis sets for the calculations of inversion barriers in larger systems. One can also conclude from Table 1 that the zero point vibrational energy correction may be neglected in the theoretical estimation of the inversion barrier of 1 because it is lower than 0.1 kcal mol-‘.

Electron correlation corrections to the calculated inversion barrier of 1 obtained with various basis sets by employment of the Meller-Plesset perturbational theory [21] up to the 4th order are presented in Table 2. Because of the high computer time requirements of the MP4 level of theory, it was applied for 1A and 1B at the 6-31G and 6-31G* levels only. The estimation of the correlation effects with higher quality basis set calculations was made at the MP2 level, which actually is the standard treatment in most applications of the ab initio calculations [19]. Apparently the electron correlation effects have a more pronounced influence on the accuracy of the results than does the quality of the basis set. Generally the inclusion of the electron correlation effects increases the barrier for inversion in 1 as compared with results at the HF level. At the MP2 level this

A. Sygula and P. W. RabideaulJ. Mol. Struct. (Theochem) 262 (1992) 117-130 123

TABLE 2

Electron correlation corrections to the calculated barrier for inversion in 1

Order 6-31G 6-31G* 6-31G** 6-311G* 6-311G**

MP2 1.2 1.5 1.6 1.8 1.9 MP3 0.8 1.0 MP4” 1.0 1.2 1.6b

“All single, double, triple and quadrupole substitutions included, i.e. MP4 (SDTQ) calculations. b Estimated value (see text).

correction is higher than 1 kcal mol-’ and increases slightly, but regularly, with the increasing quality of the basis set used, from 1.2 kcal mol-’ (6-31G) to 1.9 kcal mol-’ (6-311G**). However, MP3 and MP4 results show that the MP2 corrections are somewhat overestimated. Thus going from the MP2 to the MP4 level, the inversion barrier is lowered by 0.2 and 0.3 kcal molL’ with 6-31G and 6-31G* basis sets respectively (Table 2). The results in Table 2 are very consistent so it is reasonable to assume that the expected electron correlation effects at the higher levels not calculated for the highest quality basis sets will follow the same pattern. For example we predict that the correlation correction at the MP4 level with the 6-311G** basis set would be not higher than 1.6kcalmol-‘, i.e. the value of 1.9kcalmolL’ calculated at the MP2/6-311G** level (Table 2) minus the expected 0.3 kcal mol-’ lowering due to employment of the MP4 treatment. Thus the best theoretical estimate of the inversion barrier for 1 at the level of approximation employed in this study would be 2.2 kcal mol-’ (HF/6- 311G**) + 1.6 kcal mol-’ (anticipated MP4 correction) = 3.7 kcal mol-l (no zero point energy nor entropy corrections, see above). This number is only slightly higher than the experimental estimate of 3.1 kcal mol-’ [16].

1,2-Dihydronaphthalene (2)

The optimized 3-21G structures of nonplanar 2A (Cl symmetry) and planar 2B (C,) are presented in Fig. 2. As expected 2A is the minimum energy conformation, as confirmed by vibrational analysis because all the calculated frequencies are positive. Analogous calculations performed for 2B gave one imaginary frequency (162i). Again, inspection of the normal coordinate associated with the imaginary frequency suggests 2B to be the transition state for the ring inversion.

Comparison of the optimized geometry of 2A with 1A reveals some similarities. The torsional angle ~1, describing the deviation from planarity of the “butadiene” part of the molecule (i.e. C3-C4-C4a-CSa in 2) is 15.8°, very close to the value of 15.2’ in 1A. Furthermore, other bond lengths and

124 A. Sygula and P.W. RabideaulJ. Mol. Strut. (Theochem) 262 (1992) 117-130

4

2A, nonplanar (C,)

Hl ‘-Cl -C2 = 106.6”

H29C2-Cl = 109.8”

C3-C4-C4MXa = 15.8”

C3-C2-Cl -C8a = 48.2’

Hl ‘-Cl-C2-C8a =-119.1’

Hl ‘-Cl -C268a = 122.70

H29C2-Cl -C3 =-120.3’

H2’-C2-Cl C3 = 121.7’

28, pkmr (Cs)

Hl-Cl-C2-C8a= 121.9’

H2-C2-Cl-C3 = 122.1’

Fig. 2. The optimized 3-21G structures of nonplanar 2A (C, symmetry) and planar 2B (C, symmetry).

angles in the partially reduced ring of 2A are very close to the correspond- ing values in lA, except for the C4a-C8a bond, which (being a part of the aromatic ring in 2A) is significantly longer than the analogous Cl-C2 bond in 1A (1.397 vs. 1.322& see Figs. 1 and 2). As a consequence of the longer C4a-C8a bond the torsional angle a2 (C3-C2-Cl-C8a in 2A) is slightly higher than CQ in 1A (48.2 vs. 44.2’).

The lack of experimental data precludes strict evaluation of the quality of the calculated structure of 2A. However, the general acceptance of the 3-21G structures, in addition to the good correlation of the computed structure of 1A with the experimental data (see above), lead us to believe that 2A is a reasonable representation of the optimum energy conformation of 2. Moreover, in the early NMR study based on the coupling constant ratio Jtrans : JciS for the CH,-CH, fragment in 2, Cook et al. [9] estimated the torsional angle a2 to be 50°. This number is in very good agreement with the calculated value of 48.2’ (Fig. 2).

1A is more stable than 2B by 3.5 kcal mol-’ at the 3-21G level (Table 3). Comparison of the geometrical features of 2A and 2B (Fig. 2) allows an

Basis set 2A ‘LB 3A 813

3-21’S - 382.362 263 5 3.5 - 534.176 755 5 7.4 ZPE” 103.64 20S.B4b 132.62 182,51b

6-31C - 536.979 779 X 6.5 MP2/&31C - 536.1893438 6.2 6-31G* - 384.503 749 2 3s - 53‘7.1706238 6.6 M~2~~3~~* - 365.769 is35 2 4+7

explanation for the difference in stability. Apparently the bond angles in the reduced ring of 2B are forced to be significantly larger than the standard values in order to conform to the planar conformation of the ring. This causes an extra strain destabilizing the molecule by more than it can gain by better conjugation of the C3-C4 double bond with the rest of the aromatic system in the planar conformation of 2,

The results of the calculations for the inversion barrier in 2 are presented in Table 3. The barrier is eaIculated to be 4.7 k&al mall’ at the highest level applied (~~~~~G~~~3-2~G). Closer execution of the results for 2 reveals a strong correlation with the results discussed above for 1. For example, when going from the 3-2fG basis set to the 6-31G level the barrier for 2 is lowered by 0.3 kcalmoll’ whereas in 1 this lowering was 0.2 kcalmol-l. Furthermore, the MP2 electron correlation correction for the inversion barrier calculation at the 6-31G* level is l-5 kcal mall’ (Table 3), identical to the analogous correction for 1 (Table 2). It is therefore tempting to use the results of the higher level calculations performed for 1 in order to make an estinmtion of the barrier for 2 with higher accuracy. Thus if basis set quality is considered, the barrier for inversion of 2 at the 6-31lC”” level is expected to be about 3.3 kcaf molVt (because of the 0.1 kcalrn~I_~ increase when going from 6-31G* to 6-31IG** (Table 1)). At the same time the efectron correlation correctiun shoukl be about 1.6 kcalmol-” (Table 2). Zero point energy correction (Table 3) lowers the barrier by 0.1 kcal mall’ and so the ‘Lbest theoretical estimate”’ for the barrier in question is 48kcalmol-‘. This number is actually very close to the MP2/6-3l.G*//3~2lG result.

The experimental determination of the inversion barrier in 2 is not available so we cannot precisely address the question of the reliability of the computed result. However, taking the results for I into aceount, we

126 A. &&a and P. W. R~~~d~~~~J. Mol. Struct. (T~e~~e~~ 262 (1992) 117-130

3A, nonplanar (C2)

C8a-C4bC4a-ClOa = 23.3’

C8a-CS-ClO-ClOa = 57.0’

HS’-CS-C&-C10 = 119.5’

HS’-CS-C8a-Cl0 = -121.5”

38, planar (C,,)

HS-C9-C8a-Cl0 = 122.6’

Fig. 3. The optimized 3-21G structures of nonplanar 3A (C, sy~et~) and planar 3B (C, symmetry).

expect the value of 4.8 kcalmol-’ to be a reasonable estimation of the barrier for 2. Moreover, the lack of changes in the ‘H NMR spectrum of 2 upon cooling the solution down to - 5O*C [13] also suggests a rather low barrier for the ring inversion.

9,1@Dihydrophenanthrene (3)

Figure 3 presents the results of the 3-21G geometry optimization calculations for 3. The central partially reduced ring in 3A is more puckered than the analogous rings in both 1 and 2. The torsional angles CI~ (CSa-C4b-C4a- ClOa in 3) and a2 (CBa-C4bC4a-ClOa) are 23.3 and 57.0°, respectively, these values being significantly higher than those reported above for 1 and 2. These numbers are in good agreement with the recent results of both MM [25,26] and semiempirical molecular orbital (MO) calculations [26], and with the earlier predictions based on various physical methods which gave an estimation of q in 3 of 20-24’ [l]. The calculated geometry of 3A may also be compared with the recently published results of the X-ray crystal structure determination of 3 [12] (details of the crystal structure of 3 were derived from the archive file available from the Cambridge Crystallograph- ic Database). The crystal unit cell of 3 contains four symmetry independent molecules so the compa~son was made using the average bond lengths and

A. Sygula and P. W. RabideaulJ. Mol. Strut. (Theo&m) 262 (1992) 117-130 127

angles. (It must be stressed however, that the determined crystal structure of 3 exhibits large fluctuations of the bond lengths and angles which are supposed to be identical by symmetry in the isolated molecule. For example a1 values lie in the range of 18.9-21.9°, ap in the range 53.~56.4’, the Cl-C2 bond length in the range 1.3731.417A, etc.) For example, the average torsional angles a1 and a2 determined in the crystal are 20.2 and 55.5’ respectively, in satisfactory agreement with our calculated values (Fig. 3). Furthermore, the average values of the experimental bond lengths and angles are in good correlation with the calculated data, the differences in bond lengths and bond angles being not greater than 0.015 A and lo respectively.

In full analogy with both 1 and 2, nonplanar 3A with C, symmetry is a minimum on the potential energy surface whereas planar 3B of C,, symmetry is the transition state for the ring inversion with one imaginary frequency of 182i. The planar transition.state for the ring inversion in 3 was also recently deduced from both MM and semiempirical MO calculations [25,26]. The difference in total energy between 3A and 3B is 7.4 kcal mall’ at the 3-21G level in favor of 3A (Table 3). Improvement of the basis set from the 3-21G to the 6-31G lowers the barrier more significantly than observed in the case of 1 (0.9 vs. 0.3 kcal mall’). However, the comparison of the barrier for 3 calculated at the 6-31G and 6-31G” levels (Table 3) reveals similar effects to those observed for 1. That is, further improvement of the basis set causes only a very slight increase in the calculated barrier. We then conclude by analogy with 1 that the expected limit for the barrier in 3 calculated at the HF approximation may be estimated as about 6.7 kcal mall’.

Because of computational time requirements, the influence of electron correlation effects on the inversion barrier in 3 was assessed at the MP2 level with the 6-31G basis set only. This calculation gives the correction to the barrier to be 1.7 kcal mall’ (Table 3), slightly higher than that obtained for both 1 and 2. Thus at the MP2/6-31G//3-21G level the calculated barrier for inversion in 3 is 8.2 kcal mall’. The inclusion of the zero point energy correction (Table 3) lowers the barrier to 8.1 kcal mall’.

If the influence of the correlation effects in 3 parallels its behavior in 1, one can estimate the limit of the correction at the MP2 level with a higher quality basis set to be higher than the MP2/6-31G correction by about 50% (see Table 2), i.e. about 2.5 kcal mall’. On the other hand the MP2 treatment overestimates the electron correlation corrections by about 20%, as we concluded from the results of the calculations made for 1 (Table 2). Thus the estimated limit for the electron correlation correction will be about 2.0 kcal mall’. The “best theoretical estimation” of the barrier for 3 will then be 6.7 (the basis set limit estimation) + 2.0 (the electron correlation

128 A. Sygula and P. W. RabideaulJ. Mol. Struct. (Theochem) 262 (1992) 117-130

correction limit) - 0.1 (the zero point energy correction) = 8.6 kcal mall’. This is slightly higher than the MP2/6-31G barrier of 8.1 kcal mall’.

Both the calculated and the estimated values for the inversion barrier of 3 are higher than the recent results of both MM (5.25 [27] or 5.5 kcal mall’ [26]) and MO (2.4 kcal mall’ [26]) calculations. This seems to be a general feature for such systems because ab initio calculations for the inversion barrier in 9,10-dihydroanthracene at the 4-3lG level [27] gave a significantly higher value than both MM and MO calculations [28]. The recent ‘H NMR experiment suggests AG* for the ring inversion of 3 to be lower than 6 kcalmoll’ [15] if there is no accidental isochrony of the pseudoaxial and pseudoequatorial hydrogen atoms attached to C9 and ClO. If this is a good estimate, then the ab initio calculations also overestimate the barrier for ring inversion in 3.

CONCLUSIONS

The ab initio 3-21G calculations provide very reasonable minimum energy structures for l-3 as shown by comparison with the experimental data available. As expected, the nonplanar half-chair conformers are generally found to be more stable than the planar ones. The latter structures are shown by vibrational analysis to be transition states for the ring inversion processes.

Surprisingly, the calculated inversion barriers for l-3 seem to be rather insensitive towards the quality of the basis sets used. On the other hand the electron correlation effects appear to be important, systematically increasing the barriers by more than 1 kcal mall’ in all the cases considered. The widely used MP2 level of post-HF treatment seems to overestimate the barrier heights by about 20% compared to the more elaborate and time- consuming MP4 level.

The “best theoretical estimates” for the barriers in l-3 are 3.7, 4.8 and 8.6 kcal mall’ respectively, showing that the benzannelation of the 1,3-cyclohexadiene ring increases the tendency of the molecules to be nonplanar in proportion to the number of benzene rings. This is in full accord with the behavior of the isomeric 1,Ccyclohexadiene system (for a review on 1,4-cyclohexadiene, 9,10-dihydroanthracene and related compounds see ref. 28).

Comparison of the “best theoretical estimates” for 1 and 3 with the experimental data (3.1 kcalmolll for 1 [16] and an upper limit of 6 kcal mall’ for 3 [15]) suggests that even at relatively high levels of calculations, the ab initio method tends to overestimate to some extent the barriers for the ring inversion in l,&cyclohexadiene and related systems. Similar conclusions were drawn from the ab initio study of the rotation barrier in benzaldehyde [29]. The authors found the STO-3G calculations to give the closest agreement with experiment, with the higher quality basis sets

A. Sygula and P. W. RabideaujJ. Mol. Struct. (Theo&m) 262 (1992) 117-130 129

overestimating the barrier by about 3.6 kcal mall’ [29]. We also performed single point STO-3G calculations at the 3-21G geometries, obtaining 0.7,2.1 and 5.1 kcalmoll’ as the inversion barriers for l-3 respectively. When the electron correlation and zero point energy corrections were included (see above) the values for the barriers were 2.3,3.6 and 7.0 kcal mol- ’ respectively. These numbers are lower than the “best theoretical estimates” discussed above. However, comparison of the value of 2.3 kcal malll with the experimental value of 3.1 kcalmoll’ for 1 shows that the employment of the STO-3G basis set does not improve the agreement between theory and experiment in this system. Instead of overestimating the barrier, calculations at this level underestimate it to nearly the same extent. Thus the use of the lower quality basis set cannot be recommended, at least for the systems in consideration. The better agreement of the lower level calculations with the experimental results for some systems must be considered as purely accidental.

ACKNOWLEDGMENTS

This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences of the U.S. Department of Energy and by SNCC (Louisiana State University) with allocation of computer time.

REFERENCES

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an ab initio study of the structures and the inversion barriers in 1,3-cyclohexadiene,...

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