Vibrational spectra of cyclopropenium ions

Sp~trochimica Acta,

Vol.$0A,pp. 1105to 1114. PergamonPress1974. Printedin Northern Ireland

Vibrational spectra of cyclopropenium ions Z~.~-ICHI YOSHIDA, SHIDZUE HIROTA and HISANOBU 0GOSHI Department of Synthetic Chemistry, Kyoto University, Yoshida, Kyoto 606, Japan (Rece/ved 29 May 1973) Abstract---The i.r. spectra of trimethylcyclopropenium hexachloroantimonate and its d e u t e r o analog have been measured from 4000 em-1 to 100 em-1. The Raman spectrum of the fluoroborate has been obtained in the solid state. Normal coordinate analyses have been carried out on the Csv model of trimethylcyclopropenium ion and the Ds~ model of cyclopropenium ion (CElls+). The calculation of trichloroeyclopropenium ion has been examined to compare t h e s u b s t i t u e n t effect on the cyelopropenium ion. The i.r. absorption at 1490 cm-1 and Raman line at 1878 cm-1 of trimethylcylopropenium i o n a r e assigned to the degenerate a n d t h e totally symmetric Cs+ ring vibration modes respectively. The Urey-Bradley force constants of the rin{g C-C and Ca+--CH a stretching have been estimated to be 6.315 mdyn].~ and 3.886 mdyn/A respectively. INTRODUCTION S~AT.r. ring systems with high strain energy such as cyclopropenium ion are of interest in current chemistry. Among the physico-chemieal methods, i.r. and R a m a n spectroscopy have been used as reliable tools to characterize structures and to determine molecular symmetries. The first preparation of the C3I-I3+ion b y BRESLOW [1] has especially invoked us to carry out normal coordinate analysis of the various eyclopropenium ions and to elucidate t he substituent effect on t he cyclopropenium ion. The normal coordinate analysis of trichlorocyclopropenium ion has been reported b y W~.ST an d his coworkers [2] using the U r e y - B r a d ] e y force field. T h e y have discussed th e force constants without showing the calculated frequencies and the potential energy distribution, although their assignments seem to be reasonable. KREBS has also made the calculations on trichlorocyclopropenium ion and t he simplified model of triphenylcyclopropenium ion based on the G V F F [3]. Empirical band assignments have been made for the i.r. absorptions of Calla+ and CaDa+ ions b y BR~.sT,ow and his coworkers [4]. Trimethylcyclopropenium ion has been known to be one of the most stable ions from its high pKR÷ value [5]. However, the vibrational spectrum of this ion has never been reported. I n order to investigate the novel structures of these smallest nonbenzenoid aromatic systems (3C2~) at the ground state, we have made rigorous normal coordinate analyses of Ca(CH3)3+ (1), Cs(CDa)a + (1)-dg, Calla+ (2), CaDa+ (2)-da and CaCla+ (3). The observed frequencies of (1) and (1)-d 9 have been described on the basis of the potential energy distribution. [1] [2] [3] [4] [5]

R. BRESLOW,J. T. G]~OrESand G. RYAN, J. Am. Chem. So¢. 89, 5048 (1967). 1~. WEST, A. SA.D5and S. W. TOBEY,J. Am. Chem. Soc. 88, 2488 (1966). F. H6~EI~, B. SCHRADERand A. Ka~.BS, Z..No~urforach. 24a, 1617 (1969). R. BRESLOWand J. T. GROVES,J. Am. Gherf~. Sot., 9'~ 984 (1970). J. CI~BATTO~Iand E. C. NATrrA~, HI, Tetrahedron Letters 4997 (1969). 1105

1106

Z. YoS~DA, S. HmoTx and H. Ooosm ~']XPERIMENTAL

Trimethylcyclopropenium fluoroborate [C3(CH3)3]+[BFa]- (1') was prepared according to the procedure reported by CLOSS [6]. The fluoroborate of (1) is hygroscopic and gives a poorly resolved spectrum. To obtain a better i.r. spectrum, the hexachloroantimonate (1), [C3(CHs)s]+[SbCIe]% was prepared by the reaction of 1,2,3-trimethyl-3-methoxycyclopropene with methyloxocarbonium hexachloroantimonate [CHsCO] + [SbCle]-. The hexachloroantimonate recrystallized from acetoneether was fairly stable in exposure to air during spectral measurements. The deuterated compound (1)-d 9 was prepared using 3-methyl-da-2,4-pentadione-d7 [7] obtained from acetylacetone-ds [8] and methyliodide-da. The percentage of deuteration was determined by the I~MR spectrum of the precursor of (1)-dg, 3,4,5trimethyl-dg-5-methoxy-3H-pyrazol (98% deuteration). The i.r. spectra were recorded on a Beckmann model 12 from 4000 to 300 cm-' as a K B r pellet. The far i.r. spectra were obtained as a nujol mull using a Hitachi_ Perkin-Elmer FIS-3 spectrophotometer. The R a m a n spectrum of the fluoroborate of (1) in the solid state was measured by a JASCO J0003 spectrophotometer. PROCEDURE OF CALCULATION

The molecular symmetries of (2) and (3) are considered to be Ds~ point group according to the i.r. spectra. This model has 12 (6 × 3 -- 6) normal vibrations which are classified into 2A 1' ÷ A 2' + A2" + 3E' + E" species. I n our calculation, we have calculated the five in-plane vibrations (2A 1' -}- 3E') by using Wilson's GF matrix method [9]. The G-matrix elements were evaluated by the molecular parameters for (2) and (3) as is seen in Table 1. Figure 1 illustrates the internal coordinates and Table 2 shows the six s y m m e t r y coordiates used in the calculations of (2) and (3). This set of the s y m m e t r y coordinates includes one redundancy which gives a zero frequency in the final results. For trimethylcyclopropenium ion, the molecular s y m m e t r y can be approximated to the Dab point group, if we assume t h a t the methyl group is a single atom. I n this paper, we have assumed the Ca~ model for (1) as is shown in Fig. 2. One hydrogen Table 1. Stuctural parameters of CsXa+ ( x = H, Cl) Bond length (A) d (C---C) 1.373(a) d (C---H) 1 . 0 7 0 " d (C--C1) 1.790"

Angle /_CCC 120° / _ C C X 150°

* Assumed. {a) Reference [10]. [6] [7] [8] [9]

G. L. CLOSS,W. A. B6LL, H. HEY~ and V. DER, J. Am. Chem. So~. 90, 173 (1968). Org. Synth. Vol. 42, p. 75. John Wiley, [New York (1963). G. T. BsH:~r,a: and K. NAX_~OTO,Inorg. Chem. 6, 433 (1967). E. B. WILSOn,J. C. D~.cxus and P. C. CROSS,Modular Vib'fa~ions, McGraw-Hill, NewYork (1955).

Vibrational spectra of eyclopropenium ions

1107

Table 2. Symmetry coordinates of CsXs+ A1 t

E'

S 1 = A ( R 1 + B= + R3)/V'3 5'2 = A(R= + B 5 + R 6 ) / V 3 S a = A(2R 1 -- R= -- R a ) / V 6 ~4 = A ( 2 R e -- Re -- .R4)/V6

1, C - - C ~ C--X • C---C ~ C---X

~q5 = A(4~s -- 2~b0 -- 2~8 -- 2~2 + ~7 + ~bs

~ CCC

--2~1 "}- ~s -F ~,)/6 $ 6 = A ( ~ 7 - #e - #6 + #~)/2

~C--X

The symbol ~ and ~ denote stretching a n d bending respectively.

R6

R4/~

5/I

R~

5

Fig. 1. Structure and internal coordinates of C8X8+ (X = H, CI).

(3)

H

H

R3

Rz

,h *5 (I) y

I I I I I

.~s

" I

~'(2)

! I I I

F i g . 2. S t r u c t u r e a n d i n t e r n a l coordinates o f Cs(CHs)8 +.

1108

Z. YOSKLUA, S. H m O T X a n d H . O 6 o s m

atom is on a s y m m e t r y plane and two hydrogen atoms are separated by a s y m m e t r y plane. Its normal vibrations are grouped into 8A 1 (Raman and i.r. active), 5A~ (inactive) and 13E (Raman and i.r. active) vibrations. We have calculated the seven A 1 and the eleven E modes by using seven and twelve s y m m e t r y coordinates as is shown in Table 3. The local s y m m e t r y coordinates were adopted for each methyl group belonged to the C3, s y m m e t r y as is shown in Table 4. Their definitions are refered from the calculation of the acetylacetonato complexes by SHrM~NOUCH~et al. [11]. The molecular dimensions of the Ca+ ring of (1) are same as those of (2) and (3) except for the methyl group. The geometry of the methyl group is assumed as d(C-H) = 1.094 ~, d(C3+-CH3) = 1.480 A, /_Ca+CH = 109028 '. The potential energy was expressed by the simple Urey-Bradley force field [12]: V = ~ [K,'r,o(Ar,) -~ (1/2)K,(Ar,) ~] -~ Z [H,'r,.2(A°~,) + (1/2)H,r,~2(Ao~,) ~] -~ ~ [F/q,o(Aq,) ~- (1/2)F,(Aq,) ~] i T a b l e 3. S y m m e t r y c o o r d i n a t e s Al

S I = A ( R 1% R z%/~8)/%/3 Sz = A ( R , + R 6 + R6)/~/3 S s = A(S~(1) ~- ~ ( 2 ) -~ S~(3))/%/3 ~4 = A(S,(1) + Sq(2) ~- Sq(3))/V3 $5 = A(Sr[1] ~ ~r(2) -~ Sr(3))/~/3 S s A ( S , ( 1 ) -~- ~(2) -{- ~ , ( 3 ) ) / ~ v / 3 S~ : A(~,(I) -~ ~,(2) -~- ~,(3))/%/3

y C--C v C--0H, Ys CHs ~'s Oils ~, CH, prCH~ (~, CH,

5'~ = A(2R~ -- / ~ - - R~)1%/6

~ C--CH s

5';a = ~t = Sz~ = S]~ = S~ =

v CH, ~t. CH~ .or CH, (~, CH, y'.OHa

E

s,o = A(~.-- 2~0 -- 2~, -- 2~, + ¢, + ~. -- ~ + ~. + ~,)/e A(2Sq(3) -- 5,(2) -- ~'q(1))/V6 A(2Sr(3) -- St(2) -- Sr(1))/~/6 A(2.(3) -- ~q.(2) -- ~.(1))/%./6 A(2~,(3) -- ~¢(2) -- 8,(1))/%/6 A(Su(2) -- ~'u(1))IV2

5'~, ~ A(S.o(2 ) -- ~ ( 1 ) ) / V ' 2

a OCO

gt~' CHa

The number in the bracket indicates the number of the methyl group. The symbols y, ~ and Pr denote stetching, bending and rocketing respectively. T a b l e 4. L o c a l s y m m e t r y c o o r d i n a t e s o f C H s o f g r o u p S p ; A(r 1 -t- r2 + rQ/ V 3

Sq; 5(2r 1 - r~ - rs)/ V 6 St; h(~ 1 + ~2 + ~3 -- fll - fl~ - f13)/V6 S s ; A(2fll -- fl2 - - f l a ) / V 6 St; A ( 2 ~ 1 -- ~2 -- ~ 3 ) / V 6 Su; A ( r 2 - - r a ) / V 2 Sv; A(fl z - - f l a ) / V 2 Sw; A ( g 2 -- % ) / V 2

symmetric degenerate symmetric degenerate degenerate degenerate degenerate degenerate

s t r e t c h i n g ~sCHa s t e t c h i n g ~aCHa d e f o r m a t i o n ~sCH3 rocking prCH 3 d e f o r m a t i o n ~aCHa s t r e t c h i n g uarCHa rocking p/CH 3 d e f o r m a t i o n ~a'CHa

[10] M. S U ~ D A P . A ~ G ~ a n d L . H . G~NSEN, J. A m . Chem. See. 88, 198 (1966). [11] M. M;~Am(, I . I~A~rAGAWA a n d T. S H I ~ ' ~ O U C H I , Spaztrochim. Acts 2 3 A , 1037 (1967). [12] H . C. UREY a n d C. A . BB~LvI~Y, Phys. Rev. 38, 1969 (1931).

Vibrational spectra of cyclopropenium ions

1109

Here, Ar o A~t, and Aq~ are the changes of the bond lengths, bond angles and the distances between non-bonded atoms. The symbols Ki, Ki', Hi, Hi', Fi, Fi'represent the stretching, bending and repulsive force constants, respectively. Moreover, r~0, r~a and q~ are the values of the distances at equilibrium position, and are inserted to make the force constants dimensionally similar. The values Ki' and Hi' vanish in the final result, since t h e y can be expressed in terms of F ' by the equilibrium condition. F ' was taken as --(1/10) • F by assuming that the repulsive energy between the non-bonded atoms in proportional to (1/rg). RESULTS AND DISCUSSION Table 5 and 6 list the observed frequencies [1, 2], the calculated frequencies and the prominent potential energy distributions expressed in terms of s y m m e t r y coordinates for (2), (2)-da, and (3). The infrared absorptions at 3105, 1276 a n d 908 cm -1 of (2) are interpreted to be the C - - H stretching, the C--C stretching and the C - - H in-plane bending modes, respectively, b y BRESLOW etal. [4]. The present calculation seems to support their empirical band assignments of (2) and (2)-da. A band at 1276 cm -1 is assigned to the ring stretching vibration (E') coupled with the C - - H in-plane bending mode. Table 7 lists the values of force constants of (2) and (3), which were adjusted several times b y refering to the Jacobian matrix elements, and were further refined b y the least square methods. The Cla--H coupling constant of (2) in n m r measurement shows clearly the sp hybridization of the C---H bond. This result gives a satisfactory explanation for slightly higher force constant of (5.048 mdyn/A) t h a n those of the Table 5. Observed and calculated frequencies of the E' type vibration of Calla+ and CaDa+ (om-1)

Calla + Cai)s+

Obs. ta~

Caled.

P.E.D. (%)

Assign.

3105 1276 908 2327 1239 665

3118.7 1285.5 906.0 2307.8 1231.6 663.7

$4(100) Sa(74) Se(24 ) Sa(20) Se(76 ) ,~4(98) $a(82) Se(13 ) Sa(lO ) 8e(87 )

v C--H v C---C $ C---H ~ C--D ~ C---C ~ C---I)

(a) From Ref. [4]. Table 6. Observed and calculated frequencies of CaCI3+(em-1)

AI' E'

Obs. (a)

Calcd.

~1 ~a ~a

1791 459 1312

1791.0 459.0 1312.0

$1(91) $2(22) $2(83 ) Sa(89 ) $4(29 )

v C---C v C--C1 v C---C

~4

735

735.1

~'s(lO) 8s(10 ) ,94(71) Ss(12)

v C--C1

%

200

200.0

S s ( l l ) Se(79 )

(~C---CI

Ca)From Ref. [2].

P.E.I). (~o)

Assign.

1110

Z. YOSmDA, S. HIROTA and H. OOOSHI Table 7. Force constants of CaXa+ (mdyn]A) X =H

K(C--C) K(C--X) B(CCC) H(CCX) F(C--C--X) C(X. • • X)

6.590

X =CI 6.221

5.048 0.033 0.180 0.148

3,345 --0.484 0.284 0.702

--

--

(6.31

6 . 7 4 ) (a)

(2.99 5.08) (--0.248 -- 0.497) (0.385 0.990) (0.808 -- 0.145) ( 0 . 0 - 0.008)

(a) From Ref. [2]. sp 2 t y p e C - - H bond such as eyclopentadienide anion (4.99) [13] and benzene (4.76) [14].

I n the calculation of (3), the set of force constants given b y the previous workers did not show satisfactory agreement of the calculated frequencies with the observed values (average error, 4.16~/o; maximum error, 12.2~/o). The present calculation b y using the new set of force constants shows fairly good agreement of the calculated frequencies with the observed frequencies as is seen in Table 6. Slightly smaller values for K(C--C) and larger K(C--CI) have been obtained in comparison with those estimated b y WEST [13]. The negative value of bending force constant, H ( ~ ) was also found in our calculation. The large stretching force constant K(C--C1) is explained b y stronger C8~--C1 bond than ordinary C~.--C1 bonds such as tetrachloroolefine (2.66 mdyn/A) [15] and ehlorobenzene (2.30) [16]. The absorption at 1312 cm -1 is assigned to the E ' type ring stretching vibration coupled with the C--C1 stretching vibration. Figure 3 illustrates the i.r. spectra of (1) and (1)-d 9 from 4000 to 300 cm -1 in K B r pellet. Figure 4 shows their far i.r. spectra in Nujol mull. R a m a n spectrum of the fluoroborate salt (1') is shown in Fig. 5. The degenerate ring stretching vibration of the alkyl and aryl substituted cyclopropenium ion has been reported for phenyl (1409 cm -1) [3], t-butyl (1465 cm -1) [17] and n-propyl (ca. 1400 cm -1) [18]. The ion (1) exhibits three bands at 1490 (medium), 1450 (strong), and 1414 cm -1 (weak) in this region. However, it is very difficult to make empirical band assignment of the ring stretching vibration owing to appearance of the bending vibrations of the methylene and methyl groups. The position of the ~(Ca+) is evidently confirmed b y deuteration of the CH 3 group. The deuterated analog (1)-d 9 shows only medium strength band at 1446 cm -1. The first band of medium intensity at 1490 em -1 is assigned to the degenerate ring stretching vibration ($8) strongly coupled with the C - - C H a stretching vibration ($9) and the CH a asymmetric deformation mode ($19). The next band at 1450 em -1 is mainly due to another CH a asymmetric deformation mode (Sle). The third band at 1414 cm -1 is assigned to the CH a asymmetric deformation ($19) coupled with the C - - C H a stretching ($9). Therefore, the band at [13] [14] [15] [16] [17] [18]

A. SAD6, R. W~ST, H. P. FRITZ and L. SC~FER, Spectrochim. Acta 22, 509 (1966). J. R. SCHERERand J. OVE~E~D, ibid., 17, 719 (1961). I). E. MA~, T. Sgr~rAo~rc~, J. H. MEALvand L. FAz~o,J. Chem. Phys. 27, 43, 51 (1957). J. R. SC~RER, ~pectrovhim. Aeta 20, 345 (1964). J. CIABATTOZCIand E. C. I~IATHA~,III, J. Am. Chem. Soc. 91, 4766 (1969). R. BREST,OW,H. H6BF~Rand H. W. CEA_WG,J. Am. Chem. Soc. 84, 3168 (1962).

Vibrational spectra of cyelopropeninm ions

l 111

== ._

E m D

l--

4000

~500

5000

2000

1600

1200

800

400

250

cm -I

Fig. 3. I n f r a r e d s p e c t r a o f Ca(CHa)a+SbCI6-(1) a n d

Ca(CDQa+SbCle-(1)-d 9

)d9

t

400

|

I

|

500

|

200 ~,

|

|

iO0

c m -~

Fig 4. Far-infrared spectra of Cs(CH~)a+SbC1e- (1) and Ca(CDQs+SbCle- (1)-d 0. 1446 cm -1 o f (1)-d 9 is definitely assigned to t h e ring stretching m o d e (Ss) coupled w i t h t h e C---CD 3 ($9). T h e C H 3 a s y m m e t r i c d e f o r m a t i o n modes (Sz6) a n d ($19) are shifted t o lower f r e q u e n c y region a n d superposed a t 1018 c m -1 due to t h e deuteration. T h e b a n d s a t 1346 cm -1 o f (1) a n d 1083 c m -1 o f (1)-d 8 are assigned t o t h e C H s a n d CI) 8 s y m m e t r i c d e f o r m a t i o n modes respectively. Two absorptions a t 1069

1112

Z. Y o s m D A ,

S. H I R O T A a n d

H.

OOOSHI

"/ 4000

3000

[000

2000 cm -I

Fig. 5. Raman spectrum of Cs(CHa)s+BF4-(I').

and 954 cm -1 of (1) are attributed to the rocking deformations (Sz9) and (Sz6) modes. The strong absorption at 814 cm -z is due to the C---CH a stretching mode coupled with the ring stretching ($8) and the CH 3 rocking (Sz9) vibrations. The band at 208 cm -1 sensitive ~o the deuteration of the CH a group is assigned to the Ca+--CH a in-plane bending mode (Szl). These band assignments above mentioned have been made on the basis of potential energy distribution. The characteristic lines of the BF 4- ion in R a m a n spectrum are observed a~ 1016, 982, 769, 524 and 353 cm -~, whose positions are quite similar to those of

T a b l e 8. O b s e r v e d

A'z

B'

vz ~2 va v4 vs V0 ~T Vs ~'9 vz

Vll vl= ~)13 v14 ~15 via Vl~ ~19

and calculated

Obsd.

Calcd.

2985 2935 1878 1445 1370 -680 -2964 2915 1490 1450 1414 1346 1069 954 814 208

2964.7 2923.6 1876.1 1436.1 1356.8 995.5 697.3 2965.5 2964.7 2913.1 1472.9 1436.1 1429.2 1352.3 1031.0 995.5 811.3 210.8

frequencies of Cs(CHa)a + (cm -1) P.E.D. (~o) $4(100) 5,a(100) 5,1(78) 5,B(30) 5,e(10) 5,7(88) 5,s(10O) 5,6(92) 5,~(12) 5,1(22) 5,9(69) 5,1~(100) 5,xa(100) 5,~9(100)

5'8(44) 5'9(39) 5,1a(12) 5,15(10)$1s(88) 5,D(11) 5,Z9(75) 5"94(98) 5,9(17) 5,1s(69) 5"19(10) 5,15(92)Sis(12) 5,~(33) 5,s(37) 5,1s(20) 5,11(90)

Assign. v v ~ ~= ~s Pr y v ~'

CH s CH s C--C CHs CHa CHs C---CH 9 CH 9 CH 9 v CH s v C---C ~= CHs ~=' CHa ~B CH9 Pr' CHa Pr CHs V C-~-~CHs ~i C---CH s

Vibrational s p e c t r a o f cyclopropenium ions

1113

Table 9. Observed a n d calculated frequencies of Ca (CDs)s+ (em-x) Obsd. A1

'vx vI

---

vs

--

v4 vs

~, E

V, vs •o • 1o z'xl

Calod.

P.E.D. (~o)

Assign.

----2210 2165 2090 1446

2196.9 2098.8 1875.0 1068.3 1029.2 777.1 617.6 2199.0 2196.9 2097.7 1461.9

E4(100 ) Ss(99 ) ~Sx(78) 8 s ( 3 0 ) ~qz(19) Es(92 ) ~q, (95) 81(19 ) 8 z ( 5 6 ) S s ( l l ) ~ (100) S~s(100 ) ~qlz(100) Es(54 ) B1(48 )

z, CD 8 ~ CD s v C---C ~, CD s ~a CD8 pr CD, ~ C--CD, v CD, ~ CD 8 ~ CD$ ~, C - - C -~

1083 1018 1018 870

1078.8 1029.3 1028.5 865.0

~qs(12) ~q~(20) ,S'~t(72 ) ~S~s(92 ) ~ze(91) ~q,(20) ~ ( 2 1 ) ~Is(36)

~ CD s t~ CD s (~a' CD8 Pr"CDs ~-

770 696

777.1 681.2

,~15(95)

p~ CDs

Bs(20 ) ~ . ( 1 6 ) ~18(53)

p/CD s

182

184.3

Sz1(89 )

~ C,---CDs

~7(92)

C---CD8 Vx= ~Âs

vas V~ vxe ~17 ~zs

÷ ~. CD,

KBF~ [19]. The presence of the SbC1e- ion is confirmed by the far i.r. absorptions at 340, 180 and 177 cm -1 [20]. As has been described before, the C8o model has been applied to assign the absorptions due to the CH 3 group. The R a m a n spectrum of (1) shows a strong new band at 1878 cm -1, which is not observed in its infrared spectrum in this region. This fact indicates t h a t molecular symmetry of (1) neglecting hydrogen atoms is essentially grouped into D3~ symmetry. This R a m a n line can be assigned to the totally symmetric ring stretching ($1) coupled with the C--CH a stretching mode ($2). A strong R a m a n line at 680 cm -1 is interpreted as the C3+--CHs stretching vibration (Sa), which is coupled with ring stretching mode ($1). Table 10 shows the final set of the Urey-Bradley force constants of (1). The force constant of the Ca+--CHa bond shows higher value t h a n those of the C--C single bond. Generally, the C - - C t t a bond length decreases with the higher s-character of the carbon atom attached to the CH 3 group. The bond length of the C,~8--CHa, C,~r-CHs, and C,~--CH a are 1.534, 1.488 and 1.439 A respectively [21, 22]. This trend gives a plausible explanation of larger K(C3+--CH3). Table 10. Force constants of Ca(M%)a+ (mdyne/A) K(C---C) 6.315 K(C---Me) 3.886 K(C---H) 4.429 H(CCC) --0.026 H(CCMe) 0.159 H(CCH)

H(HCH) F(C--Me) F(C--H) F(H--H) K

0.394 0.228 0.487 0.103 --0.031 (mdyne.A)

0.222

[19] N. N. GREENWOOD,J. Chem. Soc. 3811 (1959). [20] K. N ~ o ~ o , Infrared Spevtra of Inorganic and Coordination CompouncD. J o h n Wiley, :New York (1963). [21] Interatomiv Distances, SP :Pub. :No. 11, (Edited b y L. E. SUTTON).Chem. Soe. London (1958). [22] Interatomiv Distanoes, Sp. Pub. :No. 18, (Edited b y L. E. Su~-xoN). Chem. Soe. London. (1965).

1114

Z. YOSHIDA, S. HIROTA and H. Ooosm

The negative value of the bending force constant of the Ca+ ring has been obtained in our calculation, l~or the degenerate vibration mode, the procedure of transformation from internal coordinates to symmetry coordinate gives a relationship between the C--C stretching and the C--C---C bending force constants of the Ca+ ring. The following equation is found in the Jacobian matrix elements, 3 • Jilt = J ~ where d~j = O2i/afj, 2i and fj denote i-th eigen value and j-th force constant. Therefore, K(C--C) can not be determined from the i.r. frequencies only. In the case of AI', totally symmetric ring stretching does not involve the bending vibration ( J ~ ---- 0). The R a m a n spectrum o f t h e cyclopropenium ion is required to determine the K(C---C). Thus obtained K(C--C) from the R a m a n spectrum is used to calculate the E ' t y p e frequencies b y adjusting the H(C--C--C) until the calculated frequencies show good agreement with the observed frequencies. The H(C--C---C) of (2) has been estimated as a tentative value from the reason above mentioned. However, if the R a m a n spectrum of (2) is available, the more improved K(C--C) will be obtainable. Relatively larger value of the K(C--C) of the cyclopropenium ion has been usually attributed to its shorter C---C bond length than those of another nonbenzenoid aromatic systems and benzenoid systems. The linear harmonic oscillator approximation has been generally applied to the ~-bent bond of the eyclopropenium ion. Therefore, the calculation gives a force constant for the linearly bonded C---C linkage of the C3Xa+. However, the present results indicate that approximation is still useful to characterize the vibrational spectra of highly strained small ring systems. Acknowle,dgemer*t~--The authors wish to express their thanks to Professor K. MACKrDAand

Dr. Y. SAITOfor cordial discussions and Mr. J. KZNCArDfor his aid in spectral measurements.