the structure of organophosphorus compounds
TRANSCRIPT
L I T E R A T U R E C I T E D
1. K. Bras s and E. Klar, Chem. Ber . , 65, 1660 (1932). 2. Z . A . Starikova, T. M. Shchegoleva, V. K. Trunov, et al., Kris ta l lograf iya , 24, 1211 (1979). 3. R . S . Mulliken, J. Chem. Phys. et Phys . -Chem. Biol., 6_!1, 20 (1964). 4. Z . A . Starikova, T. M. Shchegoleva, V. K. Trunov, et al., Zh. Strukt. Khim., 2__1_1, No. 2, 73 (1980). 5. Z . V . Zvonkova and I. V. Bulgarovskaya, Itogi Nauki Tekh., Kristal lokhimiya, 1._~3, 144 (1979). 6. Yu. V. Zef i rov and P. M. Zorkii , Zh. Strukt. Khim., 1_~7, 994 (1976). 7. A . C . Hazell , Acta Crys ta l logr . , B34, 466 (1978). 8. C . K . l>rout and J. D. Wright, Angew. Chem., 8_00, 688 (1968). 9. C . K . Prout and S. C. Wallwork, Acta Crys ta l logr . , 2_~.1, 449 (1966).
10. I . V . Bulgarovskaya, Z. V. Zvonkova, and O. V. Kolninov, Kris ta l lograf iya , 2_33, 1175 (1978).
T H E S T R U C T U R E OF O R G A N O P H O S P H O R U S C O M P O U N D S .
XVIIL* CRYSTAL AND MOLECULAR STRUCTURE OF THE
TETRAMER OF 2-OXO-5-t-BUTYL-1,3,2-OXAZAPHOSPHOLE,
CONTAINING AN EIGHT-MEMBERED PHOSPHAZANE RING
M. Yu . A n t i p i n , Y u . T . S t r u c h k o v , UDC547.26'118+547. Y u . V. B a l i t s k i i , a n d Y u . G. G o l o l o b o v 79+548.737
An x - r a y s t ruc tura l study of [P(O)OC(tBu)=C(H)N]4 has been car r ied out (di f f ractometer , Mo, 454 ref lec t ions , record ing a t -120~ heavy atom method, anisotropic fu l l -mat r ix re f ine-
ment, R =0o064). The c rys ta l s a re te t ragonah a =12.41, c=21.09 A, Z =4, space group I41/a. The molecule of the t e t r a m e r has a cyclophosphazane s t ruc tu re and occupies a special position of symmet ry -4 in the crys ta l . The e igh t -membered ring has the saddle conformation with the P and N atoms displaced f rom the average plane of the r ing by �9 0.163 and �9 0.721
respec t ive ly . The bond lengths are: P - N 1.68 and 1.66, P---O 1.45, and P - O 1.60/~; the valence angles at the P atom are c lose to t e t rahedra l (angle NPN 107.8 ~ angle NPO in the r ing 94.1~ The coordination of the N atom is planar tr igonal, C - N 1.45 A, PNP 128 and PNO 123 ~ The oxazaphospholine r ing is planar to within 0.01 A.
I N T R O D U C T I O N
The react ion of a -aminopinaco l ine hydrobromide (I) and PC13 in the p resence of t r ie thylamine gives a mixture of crys ta l l ine o l igomers of 5- t -bu ty l - l ,3 ,2-oxazaphosphole (C6H10NOP)m, where m=2 , 3, or 4 (II), identified f rom the infrared, NMR, and mass spec t r a [2]:
A t-BuCOCH2NH 2 HBr -b PC13 -~ 4Et3N > (CsHI~ Vo~ (C6HI0NOP)'~On"
I --3Et3N. HE1 II~ re=S, 3, 4 I I I . m=3,4 --Et3N �9 t t B r n ~ l - - 4
It might be assumed that the compounds II consis t of phosphazane r ings of different dimensions [3]. The extract ion of the mixture II with boiling toluene in air for 4 h gives a mixture of crys ta l l ine substances III with mp> 300 ~ which according to the mass spec t ra have the overa l l formula (C6H10NOP)mOn, where m =3 or 4 and n =1-4. The inf rared and 1H and 31p NMR spec t ra of the mixture III do not contradict the cyclophospha- zane s t ruc tu re . The main bulk of the mixture III consists of very fine c rys ta l s together with a smal l quantity
* F o r Pa r t XVII, see [1].
Institute of ge te roorgan ic Compounds, Academy of Sciences of the USSR. Institute of Organic Chemistry, Academy of Sciences of the Ukrainian SSR. Trans la ted f ro m Zhurnal Strukturnoi Khimii, Vol. 22, No. 4, pp. 98-102, July-August , 1981. Original a r t ic le submitted F e b r u a r y 28, 1980.
0022-4766/81/2204-0557507.50 �9 1982 Plenum Publishing Corporat ion 557
c 2"~c) c I" 1,~88<18).~
." 6 i l )s
" J \ \ I1 , , # ~ : ,AM ^ rD
o
O
F i g . 1. G e n e r a l f o r m of t h e m o l e - c u l e wi th the bond leng ths and p r i n c i p a l v a l e n c e a ng l e s . T h e ' 4 ax i s of s y m m e t r y is v e r t i c a l .
T A B L E 1. gen a t o m s and x 104 fo r t h e o t h e r a t o m s *
Atom x y z Atom x y z
P o O(P) N C0) C(2) C(3) C(4) C(5) C(6)
--89(4) 386(7)
-5~(8) 930(7)
--60(I) -780(9)
37000) -8o(to) t58o(1o)
4000)
C o o r d i n a t e s of the A t o m s (•
1172(2) t784(4) 692(5)
t592(,f) 2350(5) 2259(5) 2927(6) 349~(7) 29~6(7) 2928(6)
H(2) H(4,1) H6,2) H(4,3) H(5,t) H(5,2) H(5,3) H(6,9 H (6,2) n(6,3)
03 fo r t he h y d r o -
4197(3) 4788(7) 4900(10) i592(8) 437000) 3635(9) 4910(i0) 4340(10) 485000) 6070(10)
329 ~50 354 I 459 401 5f9 I 5i7 659 65O 619
--147
--89 t73 t92 t91 35
--80
247 381 3~,4 353 293 333 255 247 332 293
* The h y d r o g e n a t o m s a r e g iven the n u m b e r s of t he c a r - bon a t o m s to which they a r e jo ined .
of l a r g e r (0 .10-0.15 m m d i a m e t e r ) w e l l - f a c e t e d c r y s t a l s of o c t a h e d r a l shape . The l a t t e r w e r e s e l e c t e d fo r x - r a y s t r u c t u r a l a n a l y s i s , wh ich p r o v e d tha t t h e s e c r y s t a l s c o n s i s t of the t e t r a m e r (C6Hi0NOP)40 4 (IV) wi th the c y c l o p h o s p h a z a n e s t r u c t u r e .
E X P E R I M E N T A L
The c r y s t a l s of compound IV a r e t e t r a g o n a l ; a t - 1 2 0 ~ a = 1 2 . 4 1 ( 1 ) , c = 2 1 . 0 9 ( 2 ) / ~ , V=3248(5)A 3, d e a l t = 1.309 g / c m 3, Z =4, s p a c e g r o u p I4~ /a . S ince the c r y s t a l s of compound IV showed only weak r e f l e c t i o n at r o o m t e m p e r a t u r e , l o w - t e m p e r a t u r e r e c o r d i n g was used to i n c r e a s e t he i n t ens i t y of the d i f f r a c t i o n p a t t e r n . The i n t e n s i t i e s of 599 independen t r e f l e c t i o n s w e r e m e a s u r e d at a t e m p e r a t u r e o f - 1 2 0 ~ on a Syntex P2i a u t o - m a t i c f o u r - c i r c l e d i f f r a c t o m e t e r ( M o I ~ r a d i a t i o n , g r a p h i t e m o n o c h r o m a t o r , 0/20 scann ing , 20 -< 40~ 454 r e f l e c t i o n s wi th I > 2~ (I) w e r e used in t he s t r u c t u r a l c a l c u l a t i o n s . The s t r u c t u r e was d e t e r m i n e d by the h e a v y - a tom method and r e f i n e d in t h e a n i s o t r o p i c f u l l - m a t r i x a p p r o x i m a t i o n . A l l the h y d r o g e n a t o m s w e r e d e t e c t e d in the d i f f e r e n c e s y n t h e s e s and inc luded in the r e f i n e m e n t wi th f ixed p o s i t i o n a l and t h e r m a l p a r a m e t e r s wi th B i so =6 A 2. With a l l o w a n c e fo r t h e s e , the f ina l va lue s w e r e R =0.0641 and RG = 0.0752 (R = 0.0910 and R G = 0.0768 r e s p e c t i v e l y f o r a l l 599 r e f l e c t i o n s ) . The g e n e r a l f o r m of the m o l e c u l e of compound IV wi th t he num- b e r i n g of the a t o m s and the m o s t i m p o r t a n t bond l eng ths and v a l e n c e ang l e s a r e g iven in F i g . 1, and the co- o r d i n a t e s of the a t o m s and the bond l eng ths and v a l e n c e a n g l e s a r e g iven in T a b l e s 1 and 2.*
* T h e t a b l e of a n i s o t r o p i c t e m p e r a t u r e f a c t o r s can be ob ta ined f r o m t h e a u t h o r s ,
558
TABLE 2. Bond Lengths and Valence Angles*
Bond d, ~ Angle w, deg Angle oJ, deg
P - - N '
P--N P--O(P) P--O c( t ) -o C(i)--C(2) C(t)--C!3) C(3)--C{4) C(3)--C(5) C(3)--C(6) C(2)--N
t,65800) t,68t (t0) t,447(t3) t,597(9) t,4t6(14) 1,288(t8) t,490(t8) 1,499(20) t,5t2(22) t,496(2t) t,447(t4)
OPO(P) 0PN' 0PN O(P)PN' O(P)PN NPN' POC(1) oc(t)c(2) oc(i)c(3) c(2)c(1)c(3) C(t)C(2)N
tt5,5(7) to5,o(5) 94,1(5)
t13,4(7) 118,8(7) 1o7,s(5) 1it,5{7) 113,9(t,t) 1t2,4(t,0) i35,5(i,2) 11t,8(t,0)
C(2)NP" PNP" C(2)NP c(1)c(3)c(4) c(l)c(3)c(~) C0)C(3)C(6) c(4)c(3)c(5) c(4)c(3)c(6) �9 C(5)C(3)C(6)
t23,0(7) i27,9(6) i08,6(7) i07,7(i,2) t10,8(t,2) tlo,1(t,t) to9,50,2) t10,5(t,2) t08,3(t,2)
* The coordinates of the a toms N' and pn a r e re la ted to the coor - dinates of the a toms N and P by the t r an s fo rma t ions ( 0 . 2 5 - y , 0.25 + x, 0 . 25 -z ) and ( - 0 . 2 5 +y, 0 . 2 5 - x , 0 . 2 5 - z ) .
D I S C U S S I O N OF R E S U L T S
The presen t work proved conclusively that the compound IV studied has a t e t r a m e r i c s t ruc tu re with an e i g h t - m e m b e r e d phosphazane r ing. In accordance with the spec ia l position of the molecule in the c rys ta l , the phosphazane r ing P4N4 has "4 s y m m e t r y , which co r responds to the boat (S4) and saddle (D2d) conformat ions or conformat ions in te rmedia te between them.
The s t ruc tu r e s of cycl ic phosphorus-n i t rogen compounds with single P - N bonds (cyclophosphazanes) have been studied in much less detai l than the cor responding cycl ic phosphazenes, cha rac t e r i zed by a l te rnat ing fo rma l ly double and single P - N bonds in the r ing. At the p resen t t ime, the s t r u c t u r e s of the s i x - m e m b e r e d [MeNP(O)OMe] 3 (V) [4] and the e i gh t -m em bered [MeNP(O)OMe]4 (VI) [5] cyclophosphazanes a re known. These compounds, of genera l f o rm u l a [RNP(O)OR]n, a r e r e m a r k a b l e in that they can be obtained by the r e a r r a n g e - ment of the cor responding alkoxyphosphazenes [NP(OR)2] n [6]. F o r example, compound VI is fo rmed f r o m [NP(OMe)2] 4 (VII) in the p re sence of methyl iodide [7]. The s t ruc tu r e s of H4[HNPO2] .2H20(VIII ) [8], K4[HNPO214"4H20(IX),andCs4[HNPO2] "6H20 (X) [9], containing the cyclic phosphazane anion [HNPO2]~- , have also been establ ished. In addition, the s t ruc tu r e s have been studied for a whole s e r i e s of t e t r aphosphazenes [NPR2]4, differ ing in the nature of the subst i tuents R on the phosphorus a tom (R =F , C1, Me, NMe2, OMe, etc.) (XI-XIV) [3, 10-14]. Table 3 c o m p a r e s var ious geomet r i c p a r a m e t e r s of the cyclophosphazanes and cyclophosphazenes for which s t ruc tu ra l studies have been ca r r i ed out.
It can be seen f r o m Table 3 that the P - N bonds in the cyclophosphazanes a r e approximate ly 0.1 A longer than those in the cyclophosphazenes . This is due to the d e c r e a s e in the mult ipl ici ty of the P - N bonds, but
o
the i r length does not r e a c h the value 1.77 A, cha r ac t e r i s t i c of a s ingle P - N bond [3], and is s m a l l e r than it o
by approx imate ly 0.1 A. Most authors a t t r ibute this d e c r e a s e in the length of the fo rmal ly single P - N bonds in phosphazanes to the par t ic ipat ion in the in teract ion of the unoccupied d -o rb i t a l s of phosphorus and the un- shared pair of e lec t rons of the nitrogen, leading to an inc rease in the mult ipl ici ty. The possibi l i ty of this additional interact ion is indicated by the planar t r igonal coordination of the ni t rogen a tom in the phosphazanes studied, including compound IV.
The geome t r i c p a r a m e t e r s of the phosphazane s y s t e m IV a re typical and l ie in the range of values found for other phosphazanes (see Table 3). The angles N - P - N a r e c lose to t e t r ahedra l , unlike those in the phos- phazenes , where the ave r age value of the angle N - - P = N is 120 ~ The angles at the ni t rogen a toms a re also s m a l l e r than those in phosphazenes , but the s ca t t e r in the individual values is ex t remely l a rge (122-132~ and this poss ib ly re f l ec t s the f lexibi l i ty of the PN r ings .
It is of in te res t to c o m p a r e the conformat ions of the e igh t -membered r ings in the phosphazenes and phosphazanes. These conformat ions a r e ex t r eme ly var ied, and, with the exception of compound XI, all the r ings have a nonplanar s t ruc tu re . According to [3], a s y s t e m of a l te rnat ing double and single P - N bonds does not impose r ig id r e s t r i c t i o n s on the conformat ion of the PN r ing, and its nonplanari ty does not prevent the rea l iza t ion of both delocal ized and " isola ted unit" 7r-systems, as a r e su l t of which equlization of the P - N bond lengths takes place. A decis ive influence on the conformat ion of the r ing is apparent ly exerted by nonvalence in teract ions ( t r ans -annu ta r in teract ions of the subst i tuents , packing effects , etc.). F o r example, the anion [HNPO2144- in the s t r u c t u r e of compound VIII has the boat conformation, whereas in s t r uc tu r e s IX and X, that is in the K and Cs sa l t s of the acid H4[HNPO2]t, it takes the chai r and saddle f o r m s respec t ive ly . The cation
559
TABLE 3. zane and Phosphazene Rings
Compar ison of the Geomet r i c P a r a m e t e r s of Phospha-
Litera- . Compound P--N, ~ ~:: :-N' ture
cited
[P(O)OC(t- Bu) = t,658(t0) c(H)Nh t,68t(10) [MeNP(O)OMe ]a t,663 [MeNP(O)OMe ]4 1,673(3) [NP(OMe)2]4 t,57 H4[HNPO2]4.2H~O 1,661 K4[HNPO2h.4H20 1,673 Cs4 [HNPO2]~.6H20 t,676(7) (NPF2)~ t,5t (2)
(NPMe2h t ,596 (3)
[NP(NMe.2)e ]4 1,53 [NPCl2]4 1,56
1,56
No.
IV
V vI
VII VIII
IX
x x I
x I I
xIII xIr
107,8(5)
t05,2 106,9(2) 121,0 107,4 108,t 106,9(5) i22,7(t,0~
it9,5
120 121
12t
Conforma- P--N--P, tion of the
deg ring
t27,9(6) Saddle
t21,7 t22,5(2) Boat t32,2 Saddle t25,6 Boat 13t,9 Chair t28,8(6) Saddle t47,2(1,4) Planar
ring t32,0 Bent
ring ta3 Boat 131 Boat
(K-form) 134,I38 Chair
(t-form)
Data �9 ~ presented
4 5 7 8 9 9
t0
tl
12 13
t4
[NP(Me)2]4H + exists in the boat and saddle conformat ions in the s a m e c rys t a l s t r u c t u r e [15], and in the case of compound XIV, two modif icat ions with different conformat ions of the r ing have been detected: the K- fo rm (boat) and the T - f o r m (chair) [14]. These data apparent ly indicate that t he re is only a slight energy d i f ference in the conformations of the e i gh t -m em bered PN r ings . This conclusion is conf i rmed by a recen t conforma- tional calculation for a number of cycl ic phosphazenes [16] and agrees with data on the high mobil i ty of the PN r ings in the liquid s ta te [17].
It is known that e i g h t - m e m b e r e d PN r ings may be planar and also take the crown, chair , saddle, and boat fo rms [18]. In cyclophosphazanes and cyclophosphazenes , the boat and saddle conformat ions a r e most frequently encountered. In the ideal case for the la t t e r , the values of ~P/6N, where 6P and ~N a re the devia- tions of the P and N a toms f r o m the average plane of the r ing perpendicular t o the ~ axis , is equal to 1 for the boat fo rm and 0 for the saddle f o r m [5]. F o r compound IV, 5P-- -0 .163 A, 5N = ~-0.721 A, and 5P/(~N =0.22. F o r s t ruc tures VI, VII, and XIV (K-form) , 5P/~N has the values 0.48, 0.20, and 0.75 re spec t ive ly . Thus the conformation of the e igh t -membered r ing in compound IV is c lose to the saddle f o r m (as in compound VII), whereas in compotmd XIV it has the boat fo rm; the r ing in compound VI has an in te rmedia te conformat ion . The values of the tors ional angles PNPN and NPNP (*66.5 and 51.89 also indicate that the conformat ion of c o m - pound IV is c lose r to the saddle f o r m *
In contrast to the previously studied [19] 2 - o x o - 2 - m e t h y l - 3 , 5 - d i - t - b u t y l - A q3 ,2-oxazaphosphol ine (XV), the molecule of which has the envelope conformation with the P a tom displaced f r o m the plane of the other atoms of the f ive -membered r ing by 0.206 A towards the O(P) atom, the f i v e - m e m b e r e d oxazaphospholine r ing in compound IV is planar to within 0.01 A. The bond lengths in the f i v e - m e m b e r e d r ings of compounds IV and XV coincide within the l imits of e r r o r . The only d i f fe rence is observed in the valence configurat ion of the nitrogen atom, which is planar t r igonal in compound IV (sum of the angles 359.5~ but which is apprec iably nonplanar in compound XV (sum of the angles 354.9~ As in compound XV, the phosphorus atom in compound IV has a distorted te t rahedra l coordination. The OPN angle within the r ing is dec rea sed to 94.1(5 ~ (to 94.5(1) ~ in compound XV), and the angles involving the "double-bonded" phosphoryl a tom O(P) a r e g r e a t e r than the ideal t e t rahedra l values: O(P)PN' 113.4(7) ~ O(P)PN 118.8(7) ~, andO(P)PO 115.5(7 ~ (the las t two angles in compound XV are 118.2(1) and 115.6(1)~ h noteworthy fea tu re is the inc rease in the exocycl ie angle C(2)C(1)C(3) at the C(1)-C(2) double bond to 133.5(1.2) ~ in compound IV and 133.7(3) ~ in compound XV, evi- dently due to the repulsion of the t -butyl group f r o m the H(2) atom. The slight d e c r e a s e inothe length of the C - C single bonds in the t -butyl group compared with the genera l ly accepted value of 1.54 A can be at tr ibuted to the neglect of l ibrational cor rec t ions .
The crysta l s t ruc ture of compound IV is made up of d i s c r e t e molec ' l les , separa ted f r o m one another by the usual van der Waals dis tances .
* The tors ional angles a re �9 73 ~ in the ideal boat fo rm, and • 52 ~ in the ideal saddle f o r m [20].
560
L I T E R A T U R E C I T E D
1. M. Yu. Antipin, Yu. T. Struchkov, N. A. Tikhonina, et al., Zh. Strukt. Khim., 2__22, No. 2, 93 (1981). 2. Yu. G. Gololobov and Yu. V. ]3alitskii, Zh. Obshch~ Khim., 4_44, 2356 (1974). 3. H . R . Allcock, Phospho rus -N i t rogen Compounds, Academic P r e s s (1972)o 4. G . B . Ansell and G. J. ]3ullen, J. Chem. Soc. (A), 3026 (1968). 5. G . J . ]3ullen, N. L. Paddock, and D. J. Pa tmore , Acta Crysta l logr . , ]333, 1367 (1977). 6. ]3. W. F i t z s immons , C. Hewlett, and R. A. Shaw, J. Chem. Soc., 4459 (1964). 7. G . B . Ansel l and G~ J. ]3ullen, J. Chem. Soc. (A), 2498 (1971). 8. T. Migchelsen, R. Olthof, and A. Vos, Acta Crysta l logr . , 1_99, 603 {1965). 9. ]3. ]3erking and D. Mootz, Acta Crysta l logr . , ]327, 740 (1971).
10. H . M . McGeachin and F. R. Tromas , J . Chem. Soc., 4777 (1961). 11. M.W. Dougill, J. Chem. Soc., 5471 (1961). 12. G . J . ]3ullen, J. Chem. Soc., 3193 (1962). 13. R. Hazekamp, T. Mighelsen, and A. Vos, Acta Crysta l logr . , 1_5.5, 539 (1962). 14. A . J . Wagner and A. Vos, Acta Crysta l logr . , I324, 707 (1968). 15~ J. T r o t t e r and S. H. Whitlow, J. Chem. Soc. (A), 460 (1970). 16. R . H . ]3oyd and L. Kesner , J. Am. Chem. Soc~ 9_99, 4248 (1977). 17. Ao C. Chapman and N. L. Paddock, J. Chem. Soc., 635 (1962). 18. N . G . ]3okii, Yu. T. Struchkov, A. E. Kalinin, et al., P ro g re s s in Science. Crys ta l Chemistry , Vol. 12,
VINITI, Moscow (1977). 19. Yu. V. ]3alitskii, Yu. G. Gololobov, V. M. Yurchenko, et al., Zh. Obshch. Khim., 5__00, 291 (1980). 20. J. ]3. Hendrickson, J. Chem. Soc., 8._9_9, 7043 (1967).
CRYSTAL STRUCTURE OF ORGANOSILICON COMPOUNDS.
XXVI.* cis-l, 7-DIPHENYL-3,3,5,5,9,9,11,11-
OCTAMETHYLBICYCLOHEPTASILOXANE AND eis-I,I,7,7,9,9-
HEXAME THYL-3,5,1 I, 13-TE TRAPHENYLTRICYCLONONASILOXANE
V. E . S h k l o v e r , Y u . T , S t r u c h k o v , N. N. M a k a r o v a , a n d A. A. Z h d a n o v
UDC 548.737
The molecular s t ruc tu re in the c rys ta l of the two s implest cyc lo- l inear organopolysi loxanes has been de te rmined . The geometry of the siloxane r ings present in these molecules , and also the cha rac t e r i s t i c fea tures of thei r s t ruc tu re as the s imples t cyc lo- l inear o l igomers , has been discussed.
INTRODUCTION
After Brown's r epo r t [2] of the synthesis of macromolecu la r polyphenylsi lasesquioxanes, the chemis t ry and physical chemis t ry of the organosi lasesquioxanes began to develop rapidly. Of considerable importance for an understanding of the s t ruc tu re of these polymers is information on the charac te r i s t i c fea tures of the s t ruc tu re of thei r e lementary unit, that is the f ragments of the cyc lo- l inear condensed siloxane rings. Of par t icu la r in te res t is the s t ruc tu re of te t ras i loxane rings present in a t rans and in a cis environment, as f rag- ments of the two cyc lo - l inea r polymers (a) and (b) (Fig. 1), which have actually been obtained [2, 3]. The s t ruc tu res of various molecules with te t ras i loxane r ings included in a polycyclic sys tem are already k n o w n
* F o r Par t NXV, see [1].
Insti tute of Heteroorganic Compounds, Academy of Sciences of the USSR, Moscow. Trans la ted f rom Zhurnal Strukturnoi Khimii, Vol. 22, No. 4, pp. 103-112, July-August , 1981. Original a r t ic le submitted F e b r u a r y 27, 1980.
0022-4766/81/2204-0561507.50 �9 1982 Plenum Publishing Corporat ion 561