This document is © Elsevier Science, 1994

Cross-conjugated compounds:
microwave spectrum and ring planarity of
3-methylene-1,4-cyclohexadiene

Wolfgang Hutter, and Andreas Koch

Abteilung Chemische Physik, University of Ulm, D-89069 Ulm (Germany)

Presented in part at the 13th Colloquium on High Resolution Molecular Spectroscopy, 13-17 September 1993 in Riccione.

Abstract

The unstable 3-methylene-1,4-cyclohexadiene, an isomer of toluene, has been prepared from benzoic acid. The hydrocarbon can be handled quite easily in the solid state and in the gas phase at low pressures. Rotational transitions have been measured from 12 to 40 GHz. 64 lines were assigned with J-quantum numbers up to 60. From the least-squares fit with a standard deviation of 23 kHz the three rotational constants and all five quartic centrifugal distortion constants from Watson's A-reduction could be determined as A = 5177.8216(37) MHz, B = 2613.1518(10) MHz, C = 1755.8422(9) MHz, DJ = 0.1384(65) kHz, DJK = 0.135(16) kHz, DK = 1.074(50) kHz, dJ = 0.0440(11) kHz and dK = 0.333(24) kHz (representation IR used). The dipole moment was found to be 0.8645(31) D from in total 32 frequency shifts of the M components of the transition 8(35)-7(34). The 6-monodeuterated species has also been prepared and its microwave spectrum measured. Using Kraitchman's equations, the coordinates of the ring methylene hydrogens could be determined. The pseudoinertial defect was found to be -0.1435(56) amuÅ2 which proves that the molecule possesses a planar ring. The results are compared with the data for 4,4-dimethyl-2,5-cyclohexadien-1-one.

Introduction

Molecules with cross-conjugated bond systems are of great interest for both theoretical and applied chemistry. Most of them are characterized by a high reactivity. Some members of this class of molecules are even rather unstable. The reasons for this instability are however not always related to the cross-conjugated bond system. During the past years our group has been working on some of the cyclic representatives.

The compounds with five-membered rings include fulvene (I) and cyclopentadienone (II). They are unstable, but it is possible to obtain microwave spectra of both molecules. In the case of fulvene extensive work has been done [1] so that an almost complete rs structure is available. For cyclopentadienone the work on a reliable structure is still in progress [2].

Cross-conjugated compounds with six-membered rings are of special interest since they represent tautomeric forms of aromatic counterparts. The oxo-compound 2,5-cyclohexadienone (IIIa) is a keto-tautomer of phenol. This is also the reason of its high instability which has made it impossible up to now to study this molecule by microwave spectroscopy. We were, however, able to record and assign the spectrum of the corresponding dimethyl-compound (IIIb) [3].

In this paper we wish to present our investigations on the methylene compound 1-methylene-2,5-cyclohexadiene* (IVa) - a tautomer of toluene. An electron diffraction paper [4] on 4,4-dimethyl-1-methylene-2,5-cyclohexadiene (IVb) claims a non-planar ring structure with dihedral angles within the ring of about 8 degrees. One of our aims in this work was to check this by microwave spectroscopy.

*The correct nomenclature for (IVa) would be 3-methylene-1,4-cyclohexadiene. However, for easier reference to various substituted cyclohexadienes we will use "2,5-cyclohexadiene" as the basic unit. The unsaturated exocyclic group is referred to as position 1, the saturated carbon atom on the opposite side of the ring is referred to as position 4.

Unless denoted otherwise whenever a value is given with error limits (in parentheses) these denote the standard deviation or the uncertainty resulting from error propagation in units of the last digits given.

Preparation

1-Methylene-2,5-cyclohexadiene (IVa) has been prepared following the method of Plieninger and Maier-Borst [5] with the modification proposed by Gajevski and Gortva [6]:

First benzoic acid (V) is hydrogenated in a Birch reduction [7]. The dihydrobenzoic acid (VI) is then converted to the corresponding amine by standard procedures: formation of the acid chloride (VII) with oxalyl chloride [5]; the acid chloride is allowed to react with dimethylamine to give the dimethylamide (VIII) [5] which is in turn reduced to the amine (IX) with LiAlH4 [5]. The amine is oxidized with H2O2 according to Cope et al. [8]. Thermolysis of the amine oxide (X) finally gives methylenecyclohexadiene (IVa) and dimethylhydroxylamine [6].

The thermolysis was monitored by a quadrupole mass spectrometer. Thus it could be observed that even at temperatures barely above room temperature a noticeable amount of the amine oxide decomposes. The main part was, however, thermolyzed at about 65°C. The products were collected in a trap cooled with liquid nitrogen. From this trap the pyrolysate could easily be separated by fractional sublimation. The most volatile compound was the desired hydrocarbon. For the microwave measurements methylenecyclohexadiene could thus be passed directly from the original cooling trap into the cell.

As long as the contents of the trap were kept cool enough so as to prevent melting of the contents, the hydrocarbon could be handled quite easily and no significant decomposition, oligomerization or tautomerization could be observed. However as soon as the trap was warmed enough to melt the contents, practically no methylenecyclohexadiene could be recovered.

Microwave Spectrum and assignment

The measurements were carried out at -30°C and about 3 Pa (0.03 mbar) using a conventional Stark spectrometer with a 3m cell. The compound was found to be sufficiently stable for static measurements. For the aforementioned conditions we determined a half life within the cell of about 4 hours. Ab initio and semi-empirical calculations were very helpful for first guesses of the rotational constants. It turned out that the calculated constants deviated from the experimentally determined ones by as few as some tenths of a percent. This is in agreement with the experiences from 4,4-dimethyl-2,5-cyclohexadienone (IIIb) [3].

Due to the relatively small dipole moment first trials of assignments were made in the region between 35 and 40 GHz where the most intense transitions could be expected. Since a powerful computer (a DEC VAX 9000-410 of the computational center of the University of Ulm) was available we tried an "automatic assignment". First we determined reasonable ranges for each of the rotational constants by investigating the derivatives of these constants with respect to the different molecular parameters. Using these ranges it was possible to calculate ranges for some intense low-J-transitions for which the contributions of centrifugal distortion should be below 1 MHz. Now all lines found in these ranges were fed into a computer program, which succesively fitted each possible combination to a rigid rotor model. Combinations resulting in a standard deviation of less than 1.5 MHz and leaving the rotational constants within the given ranges were printed. After some unfruitful trials we found the correct assignment for four transitions. The rotational constants that resulted from this fit were accurate enough to assign many other transitions within a relatively short period of time.

As expected the spectrum followed a-type selection rules and we were able to assign 63 transitions between 12 and 40 GHz with a maximum J of 60 (cf. Table 1). The least squares fit showed a standard deviation of 23 kHz and yielded the three rotational constants and all five quartic centrifugal distortion constants (see Table 2).

The dipole moment was determined from a least squares fit of 32 measurements of Stark shifts of the M components of the transition 8(35)-7(34) and was found to be 0.8645(31) D along the a axis. The cell was calibrated using the dipole moment of OCS [9]. The figure below shows a sample spectrum of the transition 8(35)- 7(34) along with a calculated spectrum.

Spectrum of the transition 8(35)-7(34) recorded at a static field of 825 V/cm with a modulation field of 1025 V/cm (above) and calculated using Lorentzian line-shapes with line-widths (FWHM) of 250 kHz (below). The zero-field frequency of the transition is shown (---). The signals are labeled with their respective values of M. The signals marked with an asterisk represent the Stark lobes.

As mentioned earlier, one of our aims was to find out whether the ring of this molecule is planar or not. When the ring is planar the molecule possesses C2v symmetry. This would result in four pairs of identical hydrogens which would lead to a spin weight ratio of 17:15. However such a small difference could not be ascertained with the technique used.

The planar moment Pc was found to be 1.58785(49) amuŲ (using the conversion factor 505379.1 amuŲMHz). This is what would be expected for a planar ring with one pair of hydrogens out of the plane. This value is also in good agreement with the values found for planar four-membered and five-membered rings with only pairs of hydrogen atoms out of the plane (cf. Table 3). The methylene geometry should be suspected to change systematically when moving from four- to six-membered rings. As the C-C-C ring angle increases the H-C-H angle gets smaller, thus reducing the planar moment. The elongation of the C-H distance that also has to be expected has much less influence. So the planar moment per pair of hydrogens should get smaller with increasing ring size. Taking into account the effect of out-of-plane vibrations on the planar moment - which should be expected to be higher for six-membered rings than for five-membered rings, thus making the value of Pc larger - this corresponds quite well with the experimental values.

However a slight bending of the cyclohexadiene ring to form a very shallow boat cannot be ruled out by the planar moment Pc alone. If the observed value is to be reproduced the dihedral angles within the ring can be as large as about 3 degrees if the C-H bond length and the H-C-H angle are to remain within acceptable limits (cf. figure below). Yet, a value of almost 8 degrees, as determined by Trætteberg et al. [4] for the 4,4-dimethylated species, is not reconcilable with these results.

Dependence of the H-C4-H angle and the C4-H distance on variation of the dihedral angles (C6-C1-C2-C3 and C2-C3-C4-C5) in the ring. The abscissa represents the H-C-H angle in degrees, the ordinate the C-H distance in Å. For nine dihedral angles (varying between 0 degrees and 8 degrees) the data points show the possible values of the methylene geometry to reproduce the experimental planar moment Pc. The dashed lines denote extreme values between which the parameters should be expected to lie.

For a final decision it was therefore desirable to be able to calculate the actual contribution of the two hydrogens in position 4 to the planar moment. This can be done if their coordinates (especially the c coordinates) are known. So we decided to synthesize and measure 4-monodeuterated 1-methylene-2,5-cyclohexadiene.

Deuteration

First we tried to deuterate the amine (IX), but it turned out that no significant exchange of deuterium for hydrogen could be achieved. Therefore we prepared a p-deutero substituted benzoic acid (XI) according to the following reaction scheme:

Starting from p-bromo-toluene deuteration was achieved via a Grignard compound which was treated with deuterium oxide. The methyl group is easily oxidized by potassium permanganate. From the resulting 4-deutero- benzoic acid (XI) the preparation of 4-deutero-1-methylene-2,5-cyclohexadiene (IVc) was carried out as mentioned above for the non-deuterated compound.

Purity and degree of deuteration were checked by mass spectrometry and NMR. Both methods showed that the degree of deuteration was well over 90%.

The rotational constants that were predicted by ab initio calculations for the parent molecule were compared to the experimental data. The relative deviation for each constant was multiplied with the corresponding constant for the deuterated molecule obtained from the ab initio geometry (cf. Table 4). The rotational constants thus calculated predicted rotational transitions near 39 GHz (J=9) with deviations of less than 1 MHz. So the spectrum of the deuterated compound could be assigned with no substantial difficulties. We measured 44 transitions between 28 and 40 GHz with a maximum J of 49 (cf. Table 5). The least squares fit showed a standard deviation of 18 kHz and yielded the rotational constants as well as all five quartic centrifugal distortion constants (see Table 2).

By a qualitative evaluation of the observed spectra first indications for a planar ring can be obtained. As Avirah et al. [13] have pointed out there are several possibilities with respect to the potential function of the ring-bending vibration (and thus to the planarity question):

A first possibility would be a double minimum potential with a high barrier (> 500 cm-1). In this case the rotational spectrum in the ground state of the normal isotopomer would possibly show no indication of the barrier (except the planar moment, which would be higher than expected). The 4-monodeuterated species, however, would exist in two distinct conformers (flagpole or bowsprit deuterium) which would have different microwave spectra. It cannot be definitely ruled out that only transitions of one of the conformers have been assigned and the others have gone unnoticed, but the probability would be rather small, as the transitions that were predicted using rotational constants calculated for a planar conformation were correct within 1 MHz. This would be very unlikely if the ring were not planar. So this possibility can be ruled out.

A second possibility is a double minimum potential with a medium height barrier (~100-500 cm-1). In this case the interaction between the two degenerate vibrational levels would become so strong that the splittings caused in the microwave spectrum should make it impossible to fit the observed transitions to a planar model.

The third possibility is a double minimum potential with a barrier below the vibrational ground state energy. An example of such a case is cyclobutanone [14]. Without investigation of the microwave spectrum in the excited vibrational states such a case cannot be distinguished from the fourth possibility, a single minimum potential.

So the only potentials that would be consistent with the observed microwave spectra are either a single minimum potential or a double minimum potential with a barrier below the vibrational ground state. In either case, however, the vibrational ground state structure would have to be considered planar.

Theoretical calculations

Just as for the analogous oxo-compound 4,4-dimethyl-2,5-cyclohexadienone all ab initio and all semi-empirical calculations predicted a planar ring for methylene-cyclohexadiene. It is a well-known fact that particularly semi- empirical methods (we used MINDO/3 [18], MNDO [19] and AM1 [20] with the software package MOPAC [21]) are too much in favor of planar rings. But ab initio calculations with GAUSSIAN86 [22] gave the same result with both smaller (STO-3G) and larger (6-31G*) basis sets. Rotational constants, dipole moment and the geometry of the ring methylene group were predicted remarkably well by a RHF-SCF ab initio calculation with a 6-31G* basis set. A survey of some of the results is given in Table 6.

Geometry

If the molecule is planar it possesses C2v symmetry, the ring lying in the ab plane with a being the twofold axis defined by the two methylene carbon atoms. The substituted hydrogen would then lie in the ac plane and the b coordinate should be zero. Using Kraitchman's equations [23] for singly substituted molecules the b coordinate was 0.060(52) Å*. So it seemed to be justified to use the formulas that apply to atoms that lie in a plane of inertia. The resulting a and c coordinates were identical with the previously obtained values within the error limits (a = 2.5550(12) Å, c = 0.8673(36) Å). The agreement with the ab initio calculated structure (planar) is striking (cf. Table 7). The contribution of the two hydrogens in position 4 to the planar moment Pc can now easily be accounted for to give the pseudoinertial defect:

Dc = 2(2m(H)c² - Pc) = -0.1435(56) amuÅ

This value is definitely too low to allow for any significant non-planarity of the ring skeleton. The lowest vibration was calculated at 127 cm-1. It is an out-of-plane vibration that should give quite a large negative contribution to the pseudoinertial defect, so that possible contributions of a non-planar equilibrium structure can be ruled out.

* The error limit was determined using the relation proposed by van Eijck [24].

Summary

It could be shown unambiguously that the toluene tautomer 1-methylene-2,5-cyclohexadiene (IVa) possesses a planar ring. The pseudoinertial defect of -0.1435(56) amuŲ is well accounted for by a low-lying out-of-plane ring vibration. This result is confirmed by theoretical calculations which also predict a planar ring structure. These theoretical results (especially those gained by ab initio RHF-SCF calculations with a 6-31G* basis set) can be regarded as quite reliable, since they also predicted the rotational constants (signifying the structure as a whole) as well as the coordinates of the out-of-plane hydrogens (a specific substructure) with remarkable accuracy.

Based on these results the previously published data for 4,4-dimethyl-2,5-cyclohexadienone [3] (IIIb) may also be interpreted as indicative of a planar ring structure. This would be in agreement with the observations on 4-pyranone (XIIa) and its three sulfur analogs (XIIb-d) [25] as well as on 1,4-cyclohexadiene (XIII) [26] which were all found to be planar.

These results are, however, in direct conflict with the structure published by Trætteberg et al. [4] for 4,4-dimethyl- 1-methylene-2,5-cyclohexadiene (IVb). That work claims a bent ring with dihedral angles of about 8 degrees. Such a bent ring structure can be definitely ruled out for 1-methylene-2,5-cyclohexadiene both from the pseudoinertial defect and from the qualitative arguments discussed above. The effect of the two methyl groups should be negligible and the investigations on the oxo-compound 4,4-dimethyl-2,5-cyclohexadienone suggest a planar structure for 4,4- dimethylated species, too.

Acknowledgements

Financial support by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie is gratefully acknowledged.

Note added in proof
Additional information on this work is contained in the dissertation thesis of W.H. (German).

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TABLE 1
Rotational transitions of 1-methylene-2,5-cyclohexadiene (frequencies in GHz)
________________________________________________________________________

 N    J   KP   KO    J'  KP'  KO'    nexp.    ncalc.    exp.-calc.
________________________________________________________________________

 1    3    0    3    2    0    2    12.429251    12.429252    -0.000001
 2   51   18   33   51   18   34    14.715834    14.715845    -0.000011
 3    4    1    4    3    1    3    15.460635    15.460645    -0.000010
 4   54   19   35   54   19   36    15.572041    15.572044    -0.000003
 5    4    0    4    3    0    3    16.005919    16.005928    -0.000009
 6    8    2    6    8    2    7    16.283481    16.283494    -0.000013
 7   37   13   24   37   13   25    16.362626    16.362610     0.000016
 8   57   20   37   57   20   38    16.426237    16.426213     0.000024
 9   60   21   39   60   21   40    17.278182    17.278140     0.000042
10    4    2    3    3    2    2    17.333277    17.333276     0.000001
11   26    9   17   26    9   18    17.356299    17.356290     0.000009
12   40   14   26   40   14   27    17.574459    17.574477    -0.000018
13   18    6   12   18    6   13    17.741738    17.741684     0.000054
14    4    3    2    3    3    1    17.776629    17.776620     0.000009
15    4    3    1    3    3    0    17.919963    17.919899     0.000064
16   13    4    9   13    4   10    18.181990    18.181925     0.000065
17    4    1    3    3    1    2    18.746576    18.746577    -0.000001
18   43   15   28   43   15   29    18.780095    18.780092     0.000003
19    4    2    2    3    2    1    18.800557    18.800524     0.000033
20    5    1    5    4    1    4    19.118405    19.118380     0.000025
21    5    0    5    4    0    4    19.446452    19.446470    -0.000018
22   46   16   30   46   16   31    19.979716    19.979698     0.000018
23   44   15   29   44   15   30    27.187218    27.187203     0.000015
24    6    3    3    5    3    2    27.773132    27.773151    -0.000019
25    6    2    4    5    2    3    28.661582    28.661586    -0.000004
26   47   16   31   47   16   32    28.778581    28.778626    -0.000045
27    8    1    8    7    1    7    29.796033    29.796035    -0.000002
28    8    0    8    7    0    7    29.830023    29.830003     0.000020
29   50   17   33   50   17   34    30.358727    30.358765    -0.000038
30   20    6   14   20    6   15    30.499962    30.499953     0.000009
31    7    3    5    6    3    4    31.013539    31.013501     0.000038
32    7    5    3    6    5    2    31.234962    31.234983    -0.000021
33    7    5    2    6    5    1    31.249771    31.249780    -0.000009
34    7    4    4    6    4    3    31.378332    31.378296     0.000036
35    7    4    3    6    4    2    31.671998    31.672038    -0.000040
36   53   18   35   53   18   36    31.928011    31.928056    -0.000045
37   28    9   19   28    9   20    32.178425    32.178411     0.000014
38    7    2    5    6    2    4    33.214239    33.214227     0.000012
39    8    1    7    7    1    6    33.627072    33.627073    -0.000001
40   42   14   28   42   14   29    34.918624    34.918620     0.000004
41   59   20   39   59   20   40    35.035341    35.035315     0.000026
42    8    3    6    7    3    5    35.215607    35.215638    -0.000031
43    8    7    2    7    7    1    35.527630    35.527617     0.000013
44    8    6    3    7    6    2    35.650366    35.650315     0.000051
45    8    6    2    7    6    1    35.652343    35.652326     0.000017
46   14    4   11   14    2   12    35.734408    35.734440    -0.000032
47    8    5    4    7    5    3    35.838096    35.838062     0.000034
48    8    5    3    7    5    2    35.894886    35.894940    -0.000054
49    8    4    5    7    4    4    35.940927    35.940899     0.000028
50    9    2    8    8    2    7    36.640094    36.640108    -0.000014
51    8    4    4    7    4    3    36.665233    36.665244    -0.000011
52   10    1   10    9    1    9    36.830340    36.830337     0.000003
53   10    0   10    9    0    9    36.836095    36.836085     0.000010
54   21    6   15   21    6   16    36.837313    36.837282     0.000031
55   45   15   30   45   15   31    36.952841    36.952889    -0.000048
56   26    8   18   26    8   19    36.975724    36.975698     0.000026
57    9    1    8    8    1    7    36.984799    36.984803    -0.000004
58    8    2    6    7    2    5    37.394574    37.394562     0.000012
59    8    3    5    7    3    4    38.185981    38.185974     0.000007
60   48   16   32   48   16   33    38.968831    38.968813     0.000018
61   15    4   12   15    2   13    39.019105    39.019136    -0.000031
62    9    8    2    8    8    1    39.955112    39.955133    -0.000021
63    9    7    3    8    7    2    40.067614    40.067563     0.000051
________________________________________________________________________
Standard deviation: 23 kHz.

TABLE 2
Spectroscopic constants (Watson's A-reduction, representation IR) of 1-methylene-2,5-cyclohexadiene.
Numbers in parentheses are standard errors of the last digits given.

______________________________________________________________

          parent molecule             4-d-molecule
______________________________________________________________

   A     5177.8216(37)   MHz        5139.5303(23)   MHz
   B     2613.1518(10)   MHz        2518.7678(14)   MHz
   C     1755.8422(09)   MHz        1716.9106(14)   MHz
DJ    0.1384(65)   kHz           0.1159(78)   kHz
DJK   0.135(16)    kHz           0.128(15)    kHz
DK    1.074(50)    kHz           1.030(53)    kHz
dJ    0.0440(11)   kHz           0.04111(68)  kHz
dK    0.333(24)    kHz           0.273(12)    kHz
k    -0.4989                    -0.5314
   Ia      97.604577(70) amuŲ        98.331766(44) amuŲ
   Ib     193.398290(74) amuŲ       200.64536(11)  amuŲ
   Ic     287.82716(15)  amuŲ       294.35376(24)  amuŲ
  m      0.8645(31)   D


TABLE 3
Planar moments per pair of hydrogens for some planar molecules

______________________________________________________________

     Molecule  Number of pairs of hydrogen  Pc/n    Reference
                           n               (uŲ)
______________________________________________________________

                      2               1,643      [10]

                    2               1,639      [11]

                    2               1,699      [12]

                     2               1,652      [13]

                    3               1,663      [14]

                    1               1,551       [15]

               1               1,523       [16]

                 1               1,520       [16]

           1               1,531 (35Cl) [17]
                          1               1,583 (37Cl) [17]

                    1               1,588     This work
_________________________________________________________________________ 

TABLE 4
Ab initio geometry (RHF/6-31G*) of 1-methylene-
2,5-cyclohexadiene (distances in Å, angles in degrees)
___________________________________________

  distances                  angles
___________________________________________

C1=C7    1.32820      C2-C1-C7    122.2037
C1-C2    1.47336      C2-C1-C6    115.5927
C2=C3    1.32291      C1-C2=C3    122.4289
C3-C4    1.50310      C2=C3-C4    123.3792
C2-H     1.07639      C3-C4-C5    112.7911
C3-H     1.07697      C3=C2-H     120.2803
C4-H     1.09030      C2=C3-H     119.8276
C7-H     1.07548      H-C4-H      105.0704
                      H-C7-H      116.6545


TABLE 5
Rotational transitions of 4-deutero-1-methylene-2,5-cyclohexadiene (frequencies in GHz)

_______________________________________________________________________

 N    J   KP   KO   J'  KP'  KO'     nexp.    ncalc.   exp.-calc.
_______________________________________________________________________
 1   37   12   25   37   12   26    27.988563    27.988565   -0.000002
 2   23    7   16   23    7   17    28.114744    28.114796   -0.000052
 3   40   13   27   40   13   28    28.938139    28.938129    0.000010
 4   18    5   13   18    5   14    29.401027    29.401030   -0.000003
 5   43   14   29   43   14   30    29.784465    29.784461    0.000004
 6   26    8   18   26    8   19    30.130810    30.130793    0.000017
 7   46   15   31   46   15   32    30.532730    30.532734   -0.000004
 8   49   16   33   49   16   34    31.187715    31.187716   -0.000001
 9   29    9   20   29    9   21    31.989909    31.989942   -0.000033
10    8    3    6    7    3    5    34.179731    34.179758   -0.000027
11    8    7    2    7    7    1    34.383956    34.383915    0.000041
12   14    4   11   14    2   12    34.388253    34.388214    0.000039
13    8    6    2    7    6    1    34.491518    34.491497    0.000021
14   15    5   11   15    3   12    34.542001    34.542008   -0.000007
15    8    5    4    7    5    3    34.656267    34.656286   -0.000019
16    8    5    3    7    5    2    34.695873    34.695903   -0.000030
17    8    4    5    7    4    4    34.772776    34.772796   -0.000020
18   24    7   17   24    7   18    34.913316    34.913309    0.000007
19   19    5   14   19    5   15    35.026986    35.027051   -0.000065
20   35   11   24   35   11   25    35.277119    35.277113    0.000006
21    8    4    4    7    4    3    35.331438    35.331427    0.000011
22   10    1   10    9    1    9    35.994871    35.994876   -0.000005
23   10    0   10    9    0    9    36.002813    36.002795    0.000018
24    9    1    8    8    1    7    36.155225    36.155214    0.000011
25   17    4   13   17    4   14    36.303803    36.303810   -0.000007
26    8    2    6    7    2    5    36.332733    36.332733    0.000000
27   16    5   12   16    3   13    36.663570    36.663576   -0.000006
28   38   12   26   38   12   27    36.720779    36.720764    0.000015
29    8    3    5    7    3    4    36.792976    36.792945    0.000031
30   27    8   19   27    8   20    37.396433    37.396426    0.000007
31   41   13   28   41   13   29    38.039685    38.039691   -0.000006
32   22    6   16   22    6   17    38.331662    38.331675   -0.000013
33    9    8    1    8    8    0    38.670260    38.670279   -0.000019
34   17    6   12   17    4   13    38.698089    38.698104   -0.000015
35    9    6    4    8    6    3    38.918640    38.918631    0.000009
36    9    6    3    8    6    2    38.924479    38.924492   -0.000013
37    9    5    5    8    5    4    39.132139    39.132137    0.000002
38    9    4    6    8    4    5    39.153041    39.153041    0.000000
39   44   14   30   44   14   31    39.239351    39.239348    0.000003
40    9    5    4    8    5    3    39.254453    39.254462   -0.000009
41   17    5   13   17    3   14    39.331922    39.331910    0.000012
42   11    1   11   10    1   10    39.430066    39.430069   -0.000003
43   11    0   11   10    0   10    39.433323    39.433348   -0.000025
44   18    6   13   18    4   14    39.705167    39.705155    0.000012
_______________________________________________________________________

Standard deviation: 18 kHz.


TABLE 6
Comparison of theoretical calculations and experimental values for 1-methylene-2,5-cyclohexadiene.
(Rotational constants are in MHz, dipole moments in Debye, coordinates for the 4-methylene hydrogens in Å).

___________________________________________________________________________

       GAUSSIAN86                  MOPAC                 exptl.
      6-31G*    STO-3G     MNDO    MINDO/3     AM1
___________________________________________________________________________


 A   3338.80   3276.33   3260.03   3306.67   3370.32    3332.16
 B   1205.23   1178.95   1165.69   1151.86   1197.24    1193.07
 C   1092.49   1067.37   1061.41   1050.04   1084.41    1082.21
m    4.8       2.9       3.6       4.3       4.2        4.45
___________________________________________________________________________


 A   5194.16   5100.61   5167.73   5181.18   5254.50    5177.82
 B   2645.64   2634.15   2559.82   2523.76   2621.14    2613.15
 C   1771.38   1755.56   1730.68   1714.79   1768.96    1755.84
|a|     2.538     2.543     2.567     2.600     2.541      2.555
|c|     0.865     0.872     0.892     0.873     0.904      0.867
m    0.8       0.6       0.1       0.1       0.5        0.86


TABLE 7
Substitution coordinates of the 4-methylene hydrogens without assumptions and with the hydrogens assumed to lie in the ac plane (in Å).

__________________________________________________________________________

 "general" case   H in plane of inertia   error*   calculated (6-31G*)
__________________________________________________________________________
a     2.5551             2.5550           0.0012        2.538
b     0.060              0.0              0.052**       0.0
c     0.8673             0.8673           0.0036        0.865
* according to van Eijck [24]
** value refers to column "general case" only, as the b coordinate is exactly zero if the hydrogen lies in the plane of inertia.


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