Equilibrium Structure, Stabilized Transition State, or Disorder in the Crystal? Studies of the Antiaromatic Systems Tetra-tert-butyl-s-indacene and Tetra-tert-butylcyclobutadiene by Low-Temperature Crystal Structure Analysis

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C O M M U N I C A T I O N S

graphic) molecular site symmetry is only C,

(T),

the molec- ular geometry (Fig. I ) shows no significant deviations from DZh symmetry.

Equilibrium Structure, Stabilized Transition

State,

or Disorder in the Crystal?

Studies of the Antiaromatic Systems

Tetra-tert-butyl-s-indacene

and

Tetra-tert-butylcyclobutadiene

by Low-Temperature

Crystal Structure Analysis**

By Jack D. Dunitz,* Carl Kriiger, Hermann Irngartinger,

Emily F. Maverick, Yu Wang, and Matthias Nixdorf

The crystal structure of 1,3,5,7-tetra-tert-butyl-s-inda- cene 1 as determined a t room temperature"] shows effec- tive DZh symmetry of the carbon skeleton. Similarly, the

Fig. I . O R T E P [27] drawing of I at 100 K; parameters from the H O refine- ment [3]. Bond lengths [lo' prn] and angles ["] are indicated. Ellipsoids are scaled to enclose 50% probability.

presence of only four 13C-NMR signals that show no per- ceptible line broadening down to - 130°C for the twelve C atoms of the perimeter is consistent either with a very low energy barrier between the valence isomers o r with a com- pletely delocalized twelve-electron 71 system. According to

calculations"' ( M I N D 0 / 3 method), the energy barrier is only about 8 kJ mol-' for the tetrasubstituted molecule 1 ,

although it is considerably larger for the parent hydrocar- bon."]

We now report results of a new, more accurate low-tem- perature (100 K) X-ray analysis of 1, which substantiate and extend these

indication^.^^.“^

Although the (crystallo-

I*] Prof. Dr. J . D. Dunitz

Laboratory of Organic Chemistry, Swiss Federal Institute of Technology

Universitststrasse 16, CH-8092 Zurich (Switzerland) Prof. Dr. C. Kruger

Max-Planck-Institut fur Kohlenforschung

Kaiser-Wilhelrn-Platz 1, D-4330 Miilheim a. d. Ruhr (FRG) Prof. Dr. H. Irngartinger, Dr. M. Nixdorf

Organisch-chernisches Institut der Universitat Irn Neuenheirner Feld 270, D-6900 Heidelberg 1 (FRG) Prof. Dr. E. F. Maverick

Los Angeles City College Los Angeles, CA 90029 (USA) Prof. Dr. Y. Wang

Department of Chemistry, National Taiwan University Roosevelt Road, Section 4, Taipei (Taiwan)

[*'I This work was supported by the Swiss National Science Foundation, the Deutsche Forschungsgemeinschaft, and the Fonds der Chemischen In- dustrie. We thank K . H . Claus (MPI Miilheim) fur experimental assist- ance.

Moreover, as described below, a detailed analysis of the anisotropic displacement parameters U'' (ADPs)"] of the

carbon atoms gives no evidence for disorder between two sets of atomic positions for the skeletal atoms. We con- clude that either the equilibrium structure of 1 has Dzh symmetry with a localized system or we are observing not the ground-state molecular structure in the crystal but rather the transition state for the valence isomerization, which may be stabilized by crystal packing forces. The ex- ample of biphenyl, planar in its crystal structure, nonpla- nar as a free molecule, can serve as a precedent."]

Analysis of the ADPs with Trueblood's THMA pro- g r a d 8 ] leads to the following indications:

(1) Calculation of mean-square displacement amplitudes (MSDAs)I9' along all interatomic vectors shows that the molecule does not behave as a rigid body in the crystal. The MSDAs between nonbonded pairs of atoms-and in- deed the ellipsoids in Figure I-reveal appreciable mo- tions of the tert-butyl groups relative to the indacene skel- eton. On the other hand, the rigid-bond criterion'"] is satis- fied reasonably well, especially for the indacene skeleton, for which (A(MSDA)2)"2=7 pm'.

(2) The translational ( T ) and librational ( L ) analysis," 'I including allowance for internal libration of the tert-butyl groups about the exocyclic bonds C4-C7 and C6-C8, leads to mean-square libration amplitudes, (q52), of 9 and 20 (")', respectively,['21 considerably larger than the eigen- values of the L tensor (4.9, 0.9, 0.4 ( O ) ' , with the major

eigenvalue approximately along the long axis of the mole- ~ u I e ) . ' ' ~ l

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(3) Although the above model leads to reasonable agree- ment between observed and calculated U tensors (((A U”)’)’’‘ = 15 pm’), the residual discrepancies show sys-

tematic features. In the direction perpendicular to the ring plane, Uoh,d is significantly larger than Ucdlcd for the ring atoms C2, C3, and especially C5 (AU33=51 pm‘); for C7 and C8, the reverse is true. Thus the model tends to ascribe too much motion to the quaternary C atoms C7 and C8, and too little to the ring atoms that are not attached to tert- butyl groups. This suggests that the ring atoms (especially

C 5 ) are moving in a direction perpendicular to the plane.

Allowance for out-of-plane bending or buckling of the ring skeleton, as inferred in a variable-temperature study of would reduce these discrepancies. Within the molecular plane there are no significant differences be- tween U&,d and Uc.,lrd components for the ring atoms,

whereas in a n averaged structure involving superposition of two valence isomers with localized single and double bonds, we would expect U&d> Ucalcd to allow for the ef-

fect of disorder.’I6’ If the observed structure were such a superposition, the two sets o f atomic positions could not differ from the averaged positions by more than about 3 pm.

The observed structure, if it is indeed the transition state for interconversion of the free molecules, may be stabilized relative to the structures with localized bonds by better packing of the tert-butyl groups. Model calculations sug- gest that the packing energy would be reduced by about 4 kJ mol-’ per tert-butyl group for the small in-plane dis- placements of these groups that would be associated with the reorganization of the indacene skeleton.

I n contrast, a comparable analysis of the ADPs from a low-temperature study of tetra-tert-butylcyclobutadiene 2[”] shows that in this crystal a t 123 K there is still residual

disorder of the atoms of the central four-membered ring, corresponding to the coexistence of both valence isomers (although not in equal amounts).

The room-temperature X-ray analysis of 2 led to a struc- ture in which the sides of the slightly nonplanar four-mem- bered ring were almost equal (146.4 and 148.3 pm).[I8] This result was in conflict with those obtained for other cyclo- butadiene derivatives where much larger differences (14- 26pm) between the ring bonds were ob~erved.l’~] On the basis of quantum-mechanical model calculations, Borden and Davidson‘201 suggested that the bulky tert-butyl groups could exert a considerable “quadratization effect,” but this was countered by Ermer and Heilbronner,[2‘1 who argued from photoelectron spectroscopic evidence and force-field calculations that 2 must have a rectangular structure with appreciably different ring bond lengths. They proposed that the nearly square arrangement of the ring atoms found in the room-temperature analysis did not correspond to the actual molecular structure but rather to averaged atomic positions resulting from disorder among two rectangular structures. Indeed, ring bond lengths found in the subse- quent low-temperature crystal structure analysis at 123 K were different (144.1 and 152.7 pm),‘”] but the question of whether residual disorder was still present at this tempera- ture was left open. From a detailed analysis of the aniso-

tropic displacement parameters U‘J151 of the carbon atoms in the 123 K structure, we now conclude that residual dis- order is indeed still present at this temperature. The results are compatible with an averaged superposition of two mu- tually perpendicular rectangular rings with sides approxi- mately 160 and 134 pm,IZ2] and with one orientation several times more probable than the other.

ADPs from the 123 K structure determination were ana- lyzed, as for the indacene derivative l , with THMA.IX1 Standard deviations of U tensor components are of the or- der of 5 pm2. Casual inspection of the probability ellip- soids (Fig. 2) shows that those of the methyl group carbon atoms are systematically larger than those of the other atoms. Calculation of M S D A S ‘ ~ ~ along interatomic vectors shows that in contrast to the indacene derivative 1 the ri- gid-bond criterion”*] is not obeyed for 2. For example, for the CILC6 bond A(MSDA) is 19 pm’. This in itself is an indication of possible disorder. However, MSDA differ- ences between nonbonded pairs of atoms are much larger (up to 100pm’) and indicate appreciable motions of the tert-butyl groups relative to the inner

Fig. 2. ORTEP [26] drawing of 2 at 123 K. Ellipsoids are scaled to enclose

50”h probability. Hydrogen atoms are omitted for clarity.

The T, L , and screw tensor (S) analysis, including inter- nal libration of the two independent tert-butyl groups about the ClLC2 and C6-C7 bonds, leads to mean-square libration amplitudes

(4’)

of 14 and 23 ( o ) 2 for the two in-

ternal motions, These are several times

larger than the eigenvalues of the L tensor (4.4, 2.4, 2.2 ( O ) * , with the lowest value along the crystallographic two- fold rotation axis; the molecule has effective D2 symmetry but only one of the symmetry elements is imposed by the space gro~p).‘‘~]

The residual discrepancies between observed and calcu- lated U tensors show systematic features. One of these is the striking excess of 51 and 31 pm2 of the observed over the calculated tangential components of C1 and C6 (Table 1). This feature cannot be attributed to underestimation of the overall molecular libration (this would affect the outer atoms rather than the inner ones), but it is qualitatively in

Table I. Calculated and observed mean-square displacement amplitudes [prn’] for the ring atoms C1 and C6 in 2 along the tangential, radial, and ring-normal directions. Observed Calculated CI C6 221, 126, 170 210, 126, 164 170, 166, 154 179, 157, 145

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accord with the disorder model proposed by Ermer and Heilbronner (see Fig. 1 in Ref. [21]). I n the crystal it is not necessary that the two perpendicular orientations of the rectangular ring have a common center (indeed, the above- mentioned A(MSDA) of 19 pm2 between C1 and C6 sug- gests that they d o not). However, if we wish to make a rough estimate of the proportions of major and minor orientation present, it simplifies the argument somewhat if we assume this condition to be satisfied and use the aver- aged tangential MSDA excess of 41 pm2.

For equal occupancy of the two perpendicular orienta- tions of a rectangular ring with sides of 134 and 160 prn'"' and a common center, we expect a n excess MSDA of 84 pm' in the tangential direction (in agreement with Ermer and Heilbronner's estimate of 80 pm2["I). For other occupancy factors p , the excess is then 336p(l - p ) and hence ~ ~ 0 . 8 6 for the observed excess MSDA of 41 pm2 at

123 K.[261

These examples, 1,3,5,7-tetra-tert-butyl-s-indacene with indications of delocalization consistent with a stabilized transition state between two valence isomers, and tetra- terl-butylcyclobutadiene with evidence for disorder among the two isomers, show how ADPs derived from high-qual- ity diffraction data can provide information about the na- ture and extent of mean displacements of atoms from their equilibrium positions and hence allow differentiation among alternative models compatible with these posi- tions.

Received: July 7, 1987; revised: December 28, 1987 [Z 233212333 IE]

German version: Angew. Chem. I00 (1988) 415

CAS Registry numbers:

I , 101998-70-3. 2, 66809-05-0.

[ I ] K. Hafner, B. Stowasser, H. P. Krimmer, S . Fischer, M. C. Boehm, H. J. Lindner, Angew. Chem. 98 (1986) 646; Angew Chem. I n / . Ed. Engl 25

(1986) 630.

121 For HMO arguments showing that 1 should have a more delocalized r[

system than the unsubstituted s-indacene, see also E. Heilbronner, Z.-z-

Yang, Angew. Chem. 99 (1987) 369; A n g e w Chem. Int. Ed. Engl. 26 (1987) 360.

Crystal structure of 1 : monoclinic, space group P2,/n, Z = 2 , a=970.0(3), b= 1174.6(3), c= 1085.8(2) pm, [j= 107.67", T = 100 K,

pc,blLcs= 1.06 g cm-', MoKn radiation (A=71.069pm),,u=0.52 c m - ' (no

absorption correction applied), 22 565 measured reflections, reduced to 5636 independent reflections (R,p, =0.022), 4383 observed ( / > 2 m ( I ) ) , 207 parameters refined, R=0.043, R,, =0.039, R,,<,=0.030 (sinO/A> 0.0065 pm-I). Measured reflections: f h ? k I 0 < 8 < 4 2 " , w = O " ;

f h ? k l 0 < 8 < 4 2 " , w = I S " ; k h f k I O < O < 16". y = -45/45O. Nor- mal data set 45 kV/32 mA: attenuated reflection set SO kV/8 mA, 40 kV/8 mA. Further details of the crystal structure investigation may be obtained on request from the Fachinformationszentrum Energie Physik Mathematik, D-7514 Eggenstein-Leopoldshafen 2 (FRG), by quoting the number CSD-52900, the names of the authors, and the complete ci- tation o f the article.

We thank Prof. K . Hafner for supplying samples and Prof. H . J . Lindner

for sending the room-temperature crystal data and other information.

U ' J are the components of the symmetric second-order tensor U which defines the matrix of second moments of the probability distribution function for each atom. They are obtained along with positional coordi- nates of the atoms by least-squares analysis of the experimental struc- ture amplitudes from X-ray or neutron diffraction. The interpretation of ADPs is discussed in some detarl in a recent review [6].

J. D. Dunitz, V. Schomaker, K. N. Trueblood, J. Phys. Chem. (1988), in press.

W. R. Busing, Acta Crystallogr. Secr. A 39 (1983) 340.

K. N. Trueblood, Acta Crystallogr. Sect. A 34 (1978) 950. Several ver- sions of this program are in circulation, the latest being THMA I I.

The mean-square displacement amplitude in the direction of a unit vec- t o r n is given by n'Un, where the components o f n are referred to unit- length reciprocal basis vectors.

F. L. Hirshfeld, Acra Cryctallogr. Sect. A32 (1976) 239.

For the analysis of I described here, the screw tensor Svanishes because

of the molecular site symmetry. I n the T, L analysis we used the param-

eters from refinement of the full data set, but results obtained with pa- rameters from the HO refinement [3j are practically the same. [I21 As discussed by V. Schomaker and K . N . Trueblood. Acta Crvsrallogr.

Secr. A 4 0 Suppl. (1984) C-339 (see also [6j), these values correspond strictly not to ( @ > ) b u t to ( $ J ~ ) + ( $ A " ) . where ( @ A " ) is the parallel compo- nent of the overall molecular libration. However, since the overall Iihra- tion is here small compared with the internal libration, their quadratic aberage must also be small.

[I31 Values of mean-square lihrdtion amplitudes (4') were also estimated by numerical integration o f

j d 2 e x p ( - V(d)/RT)dd/l e v - V ( d ) / R T ) d d

where Y ( @ ) was obtained from calculated potential energy curves [I41 for step-by-step rotation of the tert-butyl groups about the appropriate axes without relaxation of the surrounding crystal structure. The calcu- lated values o f (4') are about 5Ooh too small, but larger for C6-C8 than for C4-C7, as found in the A D P analysis.

[I41 U. Shumueli, P. A. Kroon, Acta Crystallogr. Sect. A 3 0 (1974) 768. [IS] C. P. Rrock, J. D. Dunitz, Acra Cr>~sm//ogr. Sect. 8 3 8 (1982) 2218. [I61 The 0 components arising from this kind of disorder would not be com-

pletely absorbed in a model involving additional librational motion. [I71 H. Irngartinger. M. Nixdorf, Angeu-. Chem 95 (1983)415: Angew. Chem.

Int. Ed. Engl. 22 (1983) 403.

[I81 H. Irngartinger, N. R~egler, K.-D. Malsch, K.-A. Schneider, G. Maier,

Angew. Chem. 92 (1980) 214: Angew. Chem. Inr Ed. Engl. 19 (1980) 21 I .

[I91 a) H. Irngaflinger, H. Rodewald, Angew. Chem. 86 (1974) 783; Angew. Chem. Int. Ed Engl. 13 (1974) 740; b) L. R. J. Delbaere, M. N. G. James, N. Nakamura, S. Masamune, J . A m . Chem. Soi. 97 (1975) 1973.

I201 W. T. Borden, E R. Davidson, J. A m Chem. Soc 102 (1980) 7958. [21] 0 . Ermer, E. Heilbronner, Angew. Cliem. 95 (1983) 414; Angew. Chem.

In! Ed. Engl. 22 (1983) 402.

[22] These bond lengths are chosen to agree with values found in other cy- clobutadiene derivatives [IS, 19a, 231.

123) H. Irngartinger, M. Nlxdorf, N. H. Riegler, A. Krebs. H. Kimling. J.

Pocklington, G. Maier, K:D. Malsch, K:A. Schneider. Chem. Eer.. in press.

[24] R. E. Rosenfield, K. N. Trueblood, J. D. Dunitz, Acra Crystallogr. Sect. A 3 4 (1978) 828.

1251 Calculations [ 131 reproduce the difference in internal motion between these groups but the values of (4:) are too small. However, since the intramolecular overcrowding among the iert-butyl groups IS so severe,

allowance for correlated motion will certainly need to be included in a more realistic model.

I261 From the observed bond lengths of 144.1 and 152.7 pm we would esti- mate ~ ~ 0 . 7 , assuming the same rectangular ring. For a more thorough discussion of the disorder on d(MSDA) values see K. Chandrasekhar, H. B. Burgi, Acra C r ~ ~ . ~ t o l l o g r . Secr. 8 4 0 (1984) 387 )

1271 C. K. Johnson: ORTEP-II: A FORTRAN Thermal-Ellipsoid Plot Pro- gram for Crystal Structure Illustrations (report ORNL-5 138). Oak Ridge

National Laboratory. Oak Ridge, TN, USA 1976.

Reaction of 1,3-Azaphosphinines

with 2-tert-Butyl-1-phosphaethyne:

9-Aza-2,4,6-triphosphatetracyclo-

[5.3.0.0294.03~61de~a-8,10(

1)-diene

By Gottjiried Markl,* Stefan Dietl, Manfred L. Ziegler, and Bernd Nuber

Recently, we reported the synthesis of 1,3-azaphosphin- ines 1 from 3-azapyrylium salts by O / P exchange with (Me3Si)3P.['1

In contrast to phosphinines, which only undergo Diels- Alder reactions with highly reactive alkyne dienophiles (e.g., hexafluorobutyne) under drastic reaction conditions to give 1 -phosphabarrelenes,['] 1,3-azaphosphinines 1 react with all alkynes so far investigated even under mild condi- [*I Prof. Dr. G. Markl, S. Dietl

lnstitut fur Organische Chemie der Universitlt Universitritsstrasse 31, D-8400 Regensburg (FRG) Prof. Dr. M. L. Ziegler, Dr. B. Nuber

Anorgdnisch-chemisches lnstitut der Universitit Im Neuenheimer Feld 270, D-6900 Heidelberg (FRG)

數據

Fig.  I .   O R T E P  [27] drawing of  I  at  100  K; parameters  from the  H O  refine-  ment  [3]
Fig. I . O R T E P [27] drawing of I at 100 K; parameters from the H O refine- ment [3] p.1
Fig.  2. ORTEP [26] drawing of  2  at  123 K.  Ellipsoids  are scaled  to  enclose  50”h  probability
Fig. 2. ORTEP [26] drawing of 2 at 123 K. Ellipsoids are scaled to enclose 50”h probability p.2
Table  I.  Calculated  and  observed  mean-square  displacement  amplitudes  [prn’]  for the  ring  atoms  C1  and  C6  in  2  along  the tangential,  radial, and  ring-normal  directions

Table I.

Calculated and observed mean-square displacement amplitudes [prn’] for the ring atoms C1 and C6 in 2 along the tangential, radial, and ring-normal directions p.2

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