Conformational analysis of divinylketones by molecular mechanics (MMPI)

Journal of Molecular Structure (Theochem), 136 (1986)351--359 Elsevier Science Publishers B.V., Amsterdam --Pr inted in The Netherlands

CONFORMATIONAL ANALYSIS OF DIVINYLKETONES BY MOLECULAR MECHANICS (MMPI)

LUIS CARBALLEIRA

Colegio Universitario de Vigo.Apdo. 8 74, Vigo (Spain)

RICARDO A. MOSQUERA and MIGUEL A. RIOS*

Departamento de Qufmica F~sica, Facultad de Qufmica, Universidad de Santiago de Compostela, Galicia (Spain)

(Received 12 August 1985)

ABSTRACT

AUinger's molecular mechanics method, as implemented in the program MMPI, has been applied to the conformational analysis of divinylketone. The various conformers found are described, together with the corresponding interconversion processes and transition states, and the results are compared with those of ab initio calculations pre- viously obtained by Skancke. In general, the two methods yield very similar findings, though the more intensive exploration of the potential surface possible with MMPI has allowed the location of new singular points. Results for the mono- and dimethyl- derivatives are also presented.

INTRODUCTION

Divinylketone (DVK, 1,4-pentadien-3-one) belongs to a series of thermally unstable compounds which are difficult to s tudy experimentally. Although it has been used as a Michael acceptor for organic synthesis [1, 2 ] , its structure has scarcely been investigated, the only published research on it being a recent theoretical s tudy by Skancke [3] in which various conformational possibilities are analysed by ab initio calculations.

The present article aims to add to the description of DVK by reporting the results of its conformational analysis by a molecular mechanical (MM) method, and at the same time to enable comparison with Skancke's results and thus contr ibute to the relative assessment of ab initio and MM methods [4, 5] . In addition, the influence of methylat ion has been investigated by studying the mono- and dimethylated derivatives (MDVK and DMDVK, respectively), no conformational analysis of which has hitherto appeared.

METHOD

Among the possible MM [6, 7] methods now available, the one chosen for the present work was that due to Allinger and co-workers [8] , whose

*To whom correspondence should be addressed.

0166-1280/86/$03.50 © 1986 Elsevier Science Publishers B.V.

352

application to molecules with delocalized ~ systems is implemented by the program MMPI [9, 10] . This program is widely used at present and has been successful in the analysis of analogous systems (a,~-unsaturated ketones) for which experimental data exist [11, 12] .

The DVK molecule (Fig. 1) presents only two non-redundant torsion angles susceptible to significant modification without prohibitive cost in terms of the steric energy of the system. Possible conformers have been sought by optimizing a series of input conformations differing mutually only with regard to the initial values of the two modifiable torsion angles ¢o, (1--2--3--6) and ~2 (6--3--4--5), the former of which was assigned values v between --180 and 180 ° and the latter values between --v and v. These ranges were chosen bearing in mind the symmetry of the system, which obviously has the same energy in the conformations (v 1,v2), (--v2,--v 1), (v2 ,v,) and (--v 1,--v2). The speed of the MMPI program allowed the potential surface of the DVK to be explored more intensively than in the earlier ab initio study [3] , which only used 7 different initial conformations as compared with the 297 considered in thepresen t work.

The calculations were carried out in two stages. In the first, singular points were located using the standard MMPI criteria for convergence (the use of stricter criteria with DVK and MDVK was found not to produce any improvements). The second stage consisted in using the MMPI driver procedure to determine whether the singular points identified in the previous stage were true conformers or saddle points, the superior eigenvalue method [ 13] not being available.

RESULTS AND DISCUSSION

Divinylketone

The results obtained using MMPI (Table 1) [14] show DVK to possess five conformers: CC,TC(++), TC(----) , TT(+--) and TT(--+), were the + and -- signs indicate the position of the ethylene groups with respect to the 2--3--6 plane (regardless of whether the torsion angles are positive or negative).

Conformer CC(s-cis, s-cis) (Fig. 1) is energetically the most stable. Geo-

O6

HJsc iJc iSc H8 HIO H9

Fig. 1. DVK conformer CC (s-c/s, s-c/s).

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TABLE 1

Geometries a and relative energies (in kJ tool -1) of the various singular points found for DVK (ab initio [3 ] results are shown in parentheses)

Parameters Conformers

CC TC(++) TT(+-) TC TT TO(++) OC(+-)

1.349 1.347 1.346 1.348 1.346 1.349 1.338 1--2 (1.321) (1.321) (1.321) (1.320)

1.348 1.350 1.338 1.350 4--5 (1.321)

1.486 1.489 1.493 1.490 1.491 1.482 1.527 2--3 (1.477) (1.478) (1.479) (1.480)

1.488 1.486 1.532 1.478 3--4 (1.473)

1.215 1.222 1.220 1.223 1.225 1.219 1.217 3--6 (1.223) (1.221) (1.224) (1.224)

120.2 124.0 122.3 126.1 130.8 122.4 118.9 1--2--3 (122.1) (126.5) (127.4) (130.9)

119.6 119.7 118.9 120.4 3--4--5 (121.4)

122.1 120.1 120.3 118.8 115.9 121.7 121.6 2--3--6 (121.5) (118.8) (117.1) (116.4)

121.0 120.6 121.3 123.9 4--3--6 (122.5)

115.8 118.8 119.3 120.5 128.2 117.0 114.4 2--3--4 (117.0) (122.4) (120.3) (127.1)

0.0 --165.1 148.3 180.0 180.0 --179.5 97.6 1--2--3--6 (0.0) (151.2) (180.0) (180.0)

0.0 25.4 148.3 0.0 180.0 92.2 1.2 6--3--4--5 (0.0) (151.2) (0.0) (180.0) AE 0.0 1.88 5.10 3.55 31.22 9.11 14.84 (AE) (0.0) (19.2) (7.5) (31.7)

aDistances in A and angles in degrees. Torsion angles ( i - - j - -k-- l ) are referred to the c/s conformation, the angle being positive when atom l must move anticlockwise to be con- cealed by atom i when looking along j - - k axis. Only the absolute values of torsion angles obtained by ab initio calculations are given.

metr ical ly the molecule is perfec t ly flat, with C2h s y m m e t r y and absence o f any impor t an t steric in terac t ions causing significant d i s tor t ion o f the b o n d angles, which like t he bond leng ths remain close to their natural values.

C o n f o r m e r TC(++) and its enan t iomer T C ( - - - - ) (Fig. 2) are the nex t m o s t stable and lack any s y m m e t r y at all. Both the molecule as a whole and the e thylenic groups and ~ sys tem are n o n planar. In general, the con- fo rmer is m o r e d is tor ted in tha t part o f the molecule which is s - t rans to the ca rbony l group.

C o n f o r m e r T T ( + - ) and its enan t iomer TT( - -+) (Fig. 2) are the least stable. T h e y possess C2 s y m m e t r y in which bo th the u sys tem and the e thylenic groups are non-planar . The bond leng ths undergo no great changes,

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TT(+ - ) TC (++) TT TO (+ Jr )

TC CO(+-) TT(++)

Fig. 2. Skeletons of the conformers and saddle points conformations of DVK found by MMPI (except CC), together with the conformation TT(+ +).

180" ~ O T (++) ~ /TT "~,,~QT (--1 ~ ]

w r O - ~ - C (

[ CO(- +) TO (++) CO(- +)

: -+ CT (++),-~ / / ~ . " CT(++)~

C T"~'--"'~OT ( + + ) T(--) CT C T ( - - ) " ~ T T ( + - ) CT(--

0 90 180 -90 0 0., 2

Fig. 3. Conformational interconversion paths traced for DVK by MMPI's driver procedure. (o) Conformer, (e) saddle point.

but the bond angles differ more widely from their natural values than in the other conformers, specially the C--C--C angles, which widen so as to reduce the repulsion between H7 and H12.

Six saddle points were located (Figs. 2 and 3), four by direct optimization (TC, TT, TO(----) and the latter's enantiomer) and two during the driver procedure (OC(+--) and OC(--+)) . Two groups may be distinguished, those

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TABLE 2

Interconversion processes traced by MMPI for DVK, with energy barriers (AE t) with respect to the most stable conformer and the differences in energy (AE) between initial and final states

Process Saddle A E t z~ E p o i n t (kJ too l -1 ) (kJ too l -1 )

CC -~ TC(+ +) OC(+--) 14.84 1.88 CC-~ TC(----) OC(--+) TC(+ +) -~ TT(--+) TO(----) 7.23 3.22 TC(----) -* TT(+--) TO(+ +) TC(+ +) ~ TC(----) TC 1.67 -- TT(--+)-~ TT(+--) TT 26.12 - -

mediating interconversion between enantiomers (TC and TT), which are planar and present significantly distorted bond angles; and those lying between conformers of differing symmetry (TO(----), OC(+--) and their enantiomers), in which bondlength and bond angle distortion is slight but whose skeletons are non-planar, ¢o 1 or ¢o 2 at times approaching 90 °.

The conformers described above are interconverted via the processes summarised in Table 2. Two points may be noted. Firstly, no direct pathway between CC and TT(+--) was found, and the absence of such a path is sup- ported by the fact that neither has it been found in any of the monomethy l derivatives, in which the lack of symmetry allows the w 1- and ~2-driven paths from CC and TT(+--) to be distinguished. Secondly, the process TT(+--) -~ TT(--+) could not be studied with the driver procedure, although the geometric characteristics of TT and the results of optimizing TT conformations in MDVK and DMDVK suggest that it could exist. The driver procedure exhibits the same snags as were pointed out by Burkert and Allinger [15].

Comparison o f MM and ab initio results

Using ab initio calculations, Skancke [3] deduced the existence of three conformers and their enantiomers (CC, TC and TT(+--), in descreasing order of stability) and of one saddle point (TT), to justify which he also provided the geometry and energy of a TT(++) conformation. He further ruled out the existence of any local minima in the CC(+ +) or CC(+--) regions.

Inspection of Table 1 shows the ab initio and MMPI calculations to coincide as regards the existence of four of the singularities detected by the latter (CC, TT(+--), TC and TT). However, TC is described as a conformer in the ab initio results, whereas the MMPI driver procedure identifies it as a saddle point, the reason the discrepancy probably being that the TC(+--) and TC(++) regions were not explored in the ab initio work, which that also failed to discover the conformer TC(++) found by the present MM calcula-

356

tions. The other saddle points brought out by the MM method, TO(+÷) and OC(+--) and their enantiomers, were understandably missed by the necessarily coarser exploration used in the time consuming ab initio calculations. The geometric data calculated by the two methods for the conformers located by both agree very well. The energies of these conformers follow the same relative order, but there are the same quantitative differences as are usual when the two methods are compared [4, 5] .

The above considerations suggest the conclusion that for divinylketone both ab initio and MMPI calculations lead to very similar results. The uncer- tainty attending the conformers identified by one of the methods but not t h e other cannot be cleared up until further evidence is forthcoming either from experimental studies or from ab initio calculations filling in the gaps in the earlier work.

Monomethyl derivatives

The monomethyl derivatives of divinylketone comprise the Z and E isomers of 1,4-hexadien-3-one (henceforth referred to as 1Z-MDVK and 1E-MDVK, respectively) and 2-methyl-l ,4-pentadien-3-one (henceforth referred to as 2-MDVK). Their conformational analysis reveals no conformers not basically corresponding to those of DVK itself {Table 3). Nevertheless, as in all monomethyl derivatives, the loss of symmetry in the molecule gives rise to separate CT(----) and TC(++) conformers; TC(++),

T A B L E 3

Angu la r d i s to r t ions a and ster ic energies o f t he c o n f o r m e r s o f each o f the t h r e e m o n o - m e t h y l derivat ives b

C o n f o r m e r P a r a m e t e r 1 Z - M D V K 1 E - M D V K 2 -MD V K D V K

CC ~ 1 25.7 0.0 18.5 0.0 ~ 3.4 0.0 11.3 0.0

¢v 3 26.7 0.0 - -17 .1 - - E 43 .60 34 .40 35 .70 31 .85

TC(+ +) ¢v i 141.4 165.3 161.9 165.5 co 2 - -20 .2 - -25 .8 - -25 .9 - -25 .4

3 - - 1 9 . 9 - - 2 . 8 5 . 9 - - E 48 .82 36 .24 31 .85 33 .73

CT(+ +) ~ , 40 .2 22.7 47 .4 25.4 w 2 --167.8 --164.3 --160.7 --165.5

3 - -20 .1 0.5 1.5 - - E 42 .97 36 .87 4 0 . 6 2 33 .73

TT(+--) ~ , 125.4 149.8 145.2 148.3 ¢o 2 163.6 146.4 149.5 148.3 w 3 - - 8 . 9 - - 3 . 8 9 . 5 - - E 46 .02 38 .75 33 .77 36 .95

acv 3 is t h e l eas t o f t h e a n g l e s H---C--C1---C 2 b e t w e e n t h e m e t h y l g roup a nd t he C,---C 2 b o n d (Fig. 1). bAng les in degrees a n d e n e r g y in kJ mo1-1.

357

CT(++) and T T ( + - ) are deformed with respect to the corresponding unsubsti tuted conformed to an extent which depends on the position of the substituent; and no derivative has been found to have conformers which differ only in the or ientat ion of the substituent, ¢~ 1 and c02 being similar for both.

The main difference among the three derivatives concerns the small degree to which replacement of Hs (1E-MDVK) affects the molecule as compared with 1Z-MDVK and 2-MDVK, in which the unsubst i tuted CC conformer has become non-planar and has shifted to CC(+--), leading a saddle point at CC, and the order of the conformers ' energies is also altered, the differences between 1Z-MDVK and 2-MDVK largely amount to the distort ions in the former being larger but more localized.

The interconversion paths found for these molecules (Table 4) imply that, as for DVK all the conformers are present in a mixture in conformat ional equilibrium. Methylat ion, at whichever position, causes no great changes in the inter-conformer energy barriers present in the unsubsti tuted molecule, and in keeping with the remarks of the previous paragraph, this is especially t rue in the case o f 1E-MDVK.

Dimeth yl derivatives

In what follows the dimethyl derivatives of DVK are denoted by DMDVK preceded by the numbers of the carbons to which methyl groups are attached. The results of their conformat ional analysis (Table 5) generally support the findings already discussed, particularly as regards the effect of replacing Hs.

TABLE 4

Conformational interconversion in monomethyl derivatives of DVK (symmetric processes omitted)

Derivative Process Saddle point A E t a A E a

1Z-MDVK CC(+--) -~ TC(+ +) OC(+ 0) 10.24 3.38 CT(----)-~ CC(+--) CO(+--) 15.26 2.47 TT(--+) -~ TC(+ +) TO(+ +) 17.81 2.80 CT(+ +) -* TT(+--) TO(+--) 3.84 3.05 CC(+--) -* CC(--+) CC 1.84 --

1E-MDVK CC -~ TC(+ +) OC(+ 0) 14.96 1.84 CC -+ CT(+ +) CO(0+) 14.34 4.35 TC(+ +) -~ TT(--+) TO(--+) 6.77 2.51 CT(+ +) -~ TT(+--) OT(+--) 8.11 1.88

2-MDVK TC(+ +) -~ CC(+--) OC(+ +) 11.58 3.84 CC(--+) -~ CT(+ +) CO(+ +) 10.24 4.93 TC(+ +) ~ TT(--+) TO(--+) 7.44 1.92 TT(--+) -~ CT(+ +) SCT(+ +) 7.11 6.94 co(+--)-* co(--+) c c 0.58 --

aExpressed in kJ tool-'.

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TABLE 5

Most significant angular geometric characteristics a and total steric energies b of the singular points located by MMPI for the various dimethyl derivatives of DVK

Derivative Singular point c~ ~ cv ~ ~ 3 c~4 E

1,1-DMDVK CC 0.0 0.0 0.1 0.1 51.71 CC(+--) 28.5 4.4 27.1 2.9 49.12 TC(+ +) 142.0 --22.1 20.0 7.4 53.63 TT(+--) 127.0 162.1 10.8 5.4 50.83 CT(+ +) 38.9 --166.4 22.6 2.0 48.28

1Z,2-DMDVK CC 0.1 0.0 0.1 0.1 55.72 CC(+--) 39.7 10.8 25.0 26.8 47.15 TC(+ +) 136.8 --18.4 19.1 5.0 47.28 TT(+--) 121.5 165.5 10.5 5.7 43.85 CT(+ +) 70.1 --168.7 6.9 14.0 45.10

1Z,4-DMDVK CC(+--) 34.0 18.8 23.8 18.8 46.11 TC(+ +) 118.7 --27.2 3.3 11.6 51.62 TT(+--) 127.7 158.8 11.2 5.8 42.76 CT(+ +) 40.3 --165.1 20.5 4.9 40.50

1Z,SE-DMDVK CC 0.0 0.0 0.0 0.0 48.28 CC(+--) 29.1 4.4 25.9 0.2 46.15 TC(+ +) 140.6 --20.8 19.8 0.7 51.16 TT(+--) 127.5 161.8 10.9 2.2 47.44 CT(+ +) 40.1 --167.1 20.5 2.6 45.23

1 Z-SZ-DMDVK CC 0.1 0.2 0.1 0.2 59.90 CC(+--) 25.7 26.5 27.0 26.7 55.47 TC(+ +) 148.4 --36.3 23.9 21.2 57.98 TT(+--) 141.1 139.2 16.6 15.8 59.40

1E,2-DMDVK CC(+--) 28.5 4.4 27.1 2.9 49.12 TC(+ +)I 154.8 --27.9 16.3 37.3 39.35 TC(+ +)II 159.9 --29.2 31.4 17.8 39.96 TT(+--)I 139.7 151.8 10.5 42.3 40.04 TT(+--)II 144.3 150.3 28.0 17.6 40.96 CT(+ +) 48.3 --159.9 1.0 59.5 43.43

1E,4-DMDVK CC 0.0 0.0 0.0 0.0 39.33 CC(+--) 9.5 0.1 20.0 17.9 38.58 TC(+ +) 159.8 --46.8 3.7 55.6 42.30 TT(+--) 149.9 144.3 3.9 9.6 35.57 CT(+ +) 24.2 --159.9 0.4 6.4 34.78

1 E,5E-DMDVK CC 0.0 0.0 0.0 0.0 37.41 TC(+ +) 164.7 --27.0 2.8 0.7 39.08 TT(+--) 149.3 146.6 3.3 3.8 38.75

2,4-DMDVK CC(+--) 33.8 34.4 35.9 36.2 43.35 TC(+ +)I 155.8 --44.8 6.8 53.3 37.95 TC(+ +)II 161.7 --61.2 5.4 14.1 36.53 TC(+ +)III 148.9 --47.2 8.0 25.4 38.33 TT(+--) 146.4 146.4 9.8 9.8 30.64

aAngles in degrees, w3 and c~4 are absolute values, w4 being the torsion angle of least absolute value between a C--H bond of the methyl group replacing the highest-numbered H and the C~--C 2 or C4--C s bond, whichever is appropriate (Fig. 1). I, II and Ill distinguish between conformers differing in the orientation of the methyl group, bExpressed in kJ mol -I .

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The derivative 1E-DMDVK, for example, has a planar CC conformer. How- ever, unlike the monomethyl derivatives include members (those in which the methyl groups are adjacent, such as 1E-DMDVK and 2,4-DMDVK) which possess optimal conformations differing only in the orientation of the methyl groups, ¢o l and ~o2 being similar for both conformers. As for the unsubsti tuted and monosubst i tuted molecules, the conformers of the disub- sti tuted derivatives span a rather narrow range of steric energies, in no case differing by more than 14 kJ mo1-1.

REFERENCES

1 H. A. P. de Jong and H. Wynherg, Recl. Tray. Chim. Pays-Bas, 82 (1963) 202. 2 D. Spitzner, Angew. Chem., 90 (1978) 213. 3 P. N. Skancke, J. Comput. Chem., 4 (1983) 142. 4 U. Burkert, J. Comput. Chem., 1 (1980) 285. 5 N. L. Allinger and S. Profeta, J. Comput. Chem., 1 (1980) 181. 6 U. Burkert and N. L. Allinger, Molecular Mechanics, Am. Chem. Soc., Washington,

1982. 7 D. N. J. White, Molecular Structure by Diffraction Methods, Vol. 6, Chem. Soc.,

London, 1978, Chap. 2. 8 N. L. Allinger, Adv. Phys. Org. Chem., 13 (1976) 1. 9 N. L. Allinger, MMIfMMPI, Q.C.P.E., 404.

10 N. L. Allinger, J. T. Sprague and T. Liljefors, J. Am. Chem. Soc., 96 (1974) 5100. 11 T. Liljefors and N. L. Allinger, J. Am. Chem. Soc., 98 (1976) 2745. 12 T. Liljefors and N. L. Allinger, J. Am. Chem. Soc., 100 (1978) 1068. 13 O. Ermer, Tetrahedron, 31 (1975) 1879. 14 Readers may request more detailed geometric information from the authors. 15 U. Burkert and N. L. Allinger, J. Comput. Chem., 3 (1982) 40.

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Conformational analysis of divinylketones by molecular mechanics (MMPI)