Vibrational spectra and molecular conformation of cyclenes—I Vibrational assignment and valence force field of cyclohexene and cyclohexene-d10.

Spectrochimica Acta, 1967, ¥ol. 23A, pp. 1763 to 1774. Pergamon Press Ltd. Printed in :Northern Ireland

Vibrational spectra and molecular conformation of eyelenes--I Vibrational assignment and valence force field of cyclohexene and cyclohexene-dlo. N. NETO a n d C. DI LAURO Istituto Chimico, Universitk di l~apoli Via Mezzocannone 4, Napoli, Italy and E. CASTELLUCCI a n d S. CALrFANO Laboratorio di Spettroscopia Molecolare, Universit~ di Firenze, Via G. Capponi 9, Firenze, Italy (Received 27 July 1966) Abstract--The infra-red and Raman spectra of cyclohexene and cyclohexene-dlo have been

studied between 4000 and 200 cm-1. A vibrational assignment is given which is consistent with both the i.r. rotational band shapes and Raman depolarization data. The assignment is supported by a theoretical prediction of the fundamental frequencies calculated with a zero order valence force field. This force field was transferred from previous calculations on hydrocarbons and cyclohexadiene 1-4, and it gave a correct interpretation of the experimental results. The force constants were then refined by the method of steepest descent. The resulting new force field can be used to predict the vibrational spectra of other cyclenes. INTRODUCTION THE vibrational spectra o f cyclenes h a v e been studied v e r y little in t h e past, despite the useful i n f o r m a t i o n t h e y can s u p p l y for the identification o f t h e actual molecular conformations o f these molecules. Only cyclopentene [1] a n d cyc/ohexene [2, 3] h a v e been, in fact, investigated in detail until now, whereas o n l y few spectral correlations h a v e been established for t h e larger rings. F o r these molecules the generally low molecular s y m m e t r y , t h e possibility o f existence o f several conformational isomers a n d the c o m p l e x i t y of the vibrational spectra, h i n d e r a n y serious a t t e m p t of i n t e r p r e t a t i o n , unless a confident m e t h o d o f identification o f the f u n d a m e n t a l modes can be found. An a p p r o a c h to t h e problem, which seems p r e s e n t l y v e r y promising a n d has been in fact used with success for o t h e r classes o f molecules, is the theoretical prediction o f t h e f u n d a m e n t a l modes, c o m b i n e d with t h e e x p e r i m e n t a l evidence o b t a i n e d f r o m s t a n d a r d techniques such as R a m a n depolarization m e a s u r e m e n t s , v a p o u r phase b a n d c o n t o u r analysis, etc. A priori calculations o f t h e f u n d a m e n t a l s o f large molecules are n o w possible once a reliable p o t e n t i a l f u n c t i o n is available. F o r aliphatic h y d r o c a r b o n s a workable [1] C. H. BECKETT, IV. K. F R E E ~

and K. S. PITZER, J . Am. Chem. Soc. 70, 4227 (1948). L. M. SV~RDT.OVand E. 1~. KR~,INOV, Opt. Spectry 6, 214 (1959). [2] F. F. CriEr-ELAn-D,J. Chem. Phys. 11, 301 (1943). [3] K. SAKASHITA,J. Chem. Soc. Japan 77, 1094 (1955). 1763

1764

I#. NETO, C. DI LAURO, E. CASTELLVCCI and S. CALYFAI~O

valence force field has been established by SNYDEI~ and SCHACHTSCHNEIDER [4] and the same force field has been extended later with great success to branched and cyclic hydrocarbons as well as to vinylpolymers. For cyclenes one can reasonably expect t h a t a satisfactory form of the force field can be obtained by using the "aliphatic field" for the aliphatic part of the ring and an "ethylenie field" for the --H2C--CH---~CH--CH 2 - group. Obviously this field must first be established by using enough certain experimental frequencies and then be tested on some specific examples in order to ascertain its euristic power in predicting the fundamentals of other members of the series. In our laboratory we have collected a large body of experimental results on several cyclenes with one, two or three double bonds in the ring, ranging from cyclohexene up to cyclododecatriene. In order to interpret their spectra we decided to follow the procedure discussed above and to begin the analysis of the force field with cyclohexene which has a large enough ring to be free from strain. I n addition, since it was necessary to have at our disposal a great number of fundamentals for the proper refinement of the force field, we decided to investigate also the spectra of cyclohexene-dlo. The present paper describes the vibrational assignment of CsH10 and CeD10 based on a zero order calculation and on the analysis of the infra-red and R a m a n spectra, as well as the final refinement of the force field. Future papers will deal with the interpretation of the spectra of other members of the series. EXPERIMENTAL The infra-red spectra were obtained between 4000 and 400 c m -1 on a PerkinElmer Mod. 225 grating speetrophotometer or alternatively on a B e c k m a n IR-9

spectrophotometer. The far-infra-red spectra were registered on a Perkin-Elmer 301 instrument. Spectra were detected in the vapour, liquid and solid phases. The vapour and crystal spectra are limited to 400 cm -1. A conventional low temperature cell was used to obtain the spectra of the solids. R a m a n spectra were obtained with a Cary 81 R a m a n spectrophotometer. Depolarization measurements were made with standard Cary polarizers. The cyclohexene was a reagent grade compound purified by gas-chromatography. Cyclohexene-dlo was prepared according to the following procedure: 10 g of sodium pentachlorophenoxide, dissolved in 25 ml of D20, was added to 25 ml of 6N N a 0 D containing about 4 g of N i - R a n e y catalyst and reduced with D 2 at 90°C under a pressure of 50 lb/in ~. In this way pentachlorophenoxide was reduced directly to perdeuterocyclohexanol which was extracted with anhydrous ether, dried over Na2S04 and distilled. Cyclohexene-dlo was then obtained by dehydration of C6DllOD over P205 in petroleum solvent at a temperature of 180°C. The final product was purified by gas-chromatography. ZERO ORDER CALCULATIONS

Force constant calculations were performed on a Control Data G-20 computer with a normal co-ordinate programme described in a previous paper [5]. Calculations [4] R. G. SNYD~Rand J. H. SCACHTSCH~ID~R,Spectrochim. Acta 21, 169 (1965). [5] N. NETO, Gazz. Chim. ItaL, 96, 1094 (1966).

Vibrational spectra and molecular conformation of eyclenes---I

1765

w e r e m a d e for t h e s t r u c t u r e w i t h a C~ s y m m e t r y a n d w i t h t h e m o l e c u l a r p a r a m e t e r s g i v e n in T a b l e 1. Details on t h e calculations will n o t be g i v e n here, since t h e y were s t a n d a r d processes which h a v e a l r e a d y b e e n described in o t h e r p a p e r s f r o m this laboratory. T h e zero order force c o n s t a n t s were t a k e n f r o m t h e p a p e r b y SNYDER a n d SCHACHTSCHNEIDER [4] Oil aliphatic h y d r o c a r b o n s a n d b y p r e v i o u s calculations on 1-4 cyclohexadiene [6], a n d t h e y are s h o w n in T a b l e 2 u n d e r t h e label ¢0. T h e n o m e n c l a t u r e o f t h e force c o n s t a n t s a d o p t e d in t h e t a b l e is consistent w i t h t h a t u s e d in Ref. [4] a n d refers t o t h e choice of i n t e r n a l co-ordinates o f Fig. 2. Table 1. Molecular parameters and moments of inertia of C6Hlo and C6Dlo R(CIC~) = R(C2Cs) = R(CsC4) = R(C1C6) = R(C1HT) = R(C2Hs) = CeHlo CeDlo

1.52 A 1.54 A 1.54 • 1-35 A 1"08/~ 1"93/~

~(C1C2Ca) = 111°34 ' u(C2CaCa) = 109°30 ' a(C1C6C5) = 123 °

169.0 311.5 215.7 385.3 I(g • cm 2 . 10--4°)

178.5 229.0

T

4

!

Fig. 1. Half chair conformation.

Fig. 2. Internal co-orcUnates.

T h e zero order frequencies of cyclohexene a n d cyclohexene-dlo , calculated w i t h t h e force field o f T a b l e 2, are listed, t o g e t h e r w i t h t h e e x p e r i m e n t a l d a t a in T a b l e s 3 a n d 4. MOLECULAR STRUCTURE A l t h o u g h t h e m o l e c u l a r s t r u c t u r e of cyclohexene in t h e solid s t a t e has n o t y e t b e e n i n v e s t i g a t e d , definite conclusion a b o u t t h e m o l e c u l a r c o n f o r m a t i o n h a s b e e n o b t a i n e d f r o m c o n f o r m a t i o n a l calculations of m o r e or less empirical c h a r a c t e r . T h e s e calculations [11] h a v e s h o w n t h a t t h e half-chair c o n f o r m a t i o n o f Fig. 1 w i t h C 2 s y m m e t r y is m o r e stable b y a b o u t 2.7 k c a l / m o l e t h a n t h e b o a t c o n f o r m a t i o n . B o n d [6] 1~. NETO, C. DI LAIYROand S. CALIFANO,to be published.

1766

N. NETO, C. DI LAURO, E. CASTELLUCCI and S. CA~IFANO Table 2. Zero order and refined force constants of c y c l o h e x e n e *

N

F. Const.

1

Kt

2

Ka

3

KD

4

K~ ~

5

He

6 7 8 9 10 11 12 13 I4 15 16 17 18 19 20

KR ~

H¢o H~ H~b H~ HO

Hy HF ~'D vT TR ~ TL FR2 = Fnz F~T F0T F ~ ~ FrL

F~

Kz

~o 5.055 4.554 8"7 4"387 0"91 1.13 0"55 0"5 0"5 0'656 0.656 0.21 0.24 0.024 0-024 0.101 0.101 0"328 0.328 0.364

~ 5.06765 4.55162 8.69955 4"38409 0-91726 1"05149 0"54399 0"50357 0"47669 0"66687 0.66071 0.22129 0"22203 0.02019 0-02379 0.12375 0.09830 0"36026 0.34143 0.31913

N 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

F. Const. F5D F'Ty F'T~ = F ' ~ F ~ c o ~ F~,8 ~ F~, ~ F00

FDe

F'Tr ~ F~yO F~ F?¢o ~ F0~ Fe~ ~ Fe~ Frr(tr ) Fry(g) ~ For(g) FtTr(tr) F~7(g) F~yy(tr)

F~rr(g) F~w(tr) Fr~(g )

Fcom(g) F~b~b Faa

(I)o

Or

0.364 0-079 0-079 0"417 0'021 0"012 0-012 --0-031 --0"031 0.127 --0"05 0.002 0.009 --0.014 --0.025 0"049 --0'032 O'011 0.14 0-006

0.36509 0.04750 0.07713 0"42296 --0"01937 0'01928 0'03267 --0'03410 --0"04305 0.135 --0.00736 0.00536 0.02549 0.01090 --0.00731 0.06164 --0-07004 --0"01716 0.12247 0-00530

F'r7 = F'n~ = F'zr = F'n0; F'no~= F T~ = FL~; FroJ = Fe~v= Fe~; F'yy(tr ) = F'djw(tr) = Fr0(tr); .F'rr(g) = F'0~(g) = F'vo(g); F"r,r(tr ) = F"rO(tr ) = F~,p; F"r>,(g)= F"yd~(g) = F"eo(g); Fea~(tr) = F~pco(tr) = F~be(tr); Frw(g) = Foe(g); Fa~w(g)= F~oe(g) = Fee(g) * For the symbolism of the f o r c e c o n s t a n t s see ReL [4]. Stretching c o n s t a n t s a r e in units of mdyn/A; stretching interactions in units of mdyn/rad; bend constant in units of mdyn.A/rad 2. lengths, bond angles and torsion angles for the half-chair structure have been reported b y C O R E ¥ a n d SI~EEN [7] a n d b y BOUCOURT [8]. R e c e n t l y CHEN et a L [9] h a v e m e a s u r e d t h e m o l a r K e r r c o n s t a n t a n d t h e a p p a r ent dipole moment of cyclohexene. They confirmed the half-chair conformation b u t s u g g e s t e d t h a t a f l a t t e r s t r u c t u r e is p r o b a b l y m o r e a p p r o p r i a t e . A N E T a n d H A Y [10] h a v e s t u d i e d t h e N M R s p e c t r a o f c y c l o h e x e n e and of cyclohexene-cis 3,3,4,5,6,6-d s at low temperature and have shown that a very rapid conversion between a half-chair conformation and its mirror image takes place at ordinary temperatures. They suggested a transition mechanism from one half-chair structure to the other which goes through the boat form, and calculated a n a v e r a g e l i f e t i m e o f 10 -9 s e c a t 2 0 ° C f o r a c y c l o h e x e n e m o l e c u l e b e f o r e i n v e r s i o n . In addition they postulated a transition state between the half-chair and the boat form in which five carbon atoms are coplanar. A s f a r a s t h e i n f r a - r e d s p e c t r u m is c o n c e r n e d , t h e r e is n o e v i d e n c e o f m o r e t h a n one conformational isomer in the liquid state. Also the spectrum of the solid at --194°C shows no disappearance of bands that could be ascribed to another form. It should be pointed out however that the Raman spectrum contains less polarized bands than expected for a C 2 symmetry, in agreement with the occurrence of a rapid i n t e r c o n v e r s i o n b e t w e e n t h e h a l f - c h a i r f o r m w i t h C~ s y m m e t r y a n d t h e b o a t f o r m [7] [8] [9] [10] Lll]

E. R. C. F. C.

J . CORE:~ a n d R . A . S~rEEN, J . A m . Chem. Soc. 77, 2505 (1965). BOUCOURT, B u l l . Soc. C h i m . . F r a n c e 1262 (1963). V. CHEN, R . J . W. LE FEVR~. a n d K. M. S~DA~AM, J . Chem. Soc. 553 (1965). A. L. A~ET a n d M . Z. H A ~ , J . A m . Chem. Soc. 87, 3147 (1965). W. BECKETT, :~r. K. FREEMAN and K. S. PITZ~R, J . A m . Chem. Soc. 70, 4227 (1948).

Vibrational spectra and molecular conformation of cyclenes---I

1767

with Cs symmetry. Under these conditions we expect in fact to find only the bands originating from molecular modes which belong to the totally symmetric irredueible representations of both point groups to be really polarized. Such modes belong to the representation A I of the C~. super-group. I t is therefore convenient, in discussing the vibrational spectra, to introduce the pseudosymmetry C~ in order to account for the non-rigid structure of the molecule in the liquid state. In what follows we shall use this concept in the discussion of the vibrational assignment and show that it affords a correct understanding of the spectra. DISCUSSION OF THE SPECTRA The infra-red and R a m a n spectra of cyclohexene have been studied in the past b y several authors. A detailed discussion of the vibrational assignment, based on the previous R a m a n polarization measurements of CLEVELAND [2] and on his own infra-red data, was given later b y SAKASHXTA[3]. References to earlier work can be found in this paper. The comparison of the assignment of Sakashita with the calculated frequencies of Table 3 convinced us that some changes were necessary. Owing to the low resolution of the vapour spectrum of Ref. [3] and to some incongruencies between R a m a n and the infra-red evidence we decided to re-investigate under higher resolution the infra-red and R a m a n spectra. We found indeed that the depolarization ratios reported b y CLEVELAND [2] and used b y Sakaschita were markedly different from our results. Cleveland found as many as 24 polarized R a m a n bands over a total of 27, whereas we have found several bands definitely depolarized. I t is easily seen that the rotational band envelopes in the vapour spectrum are often in disagreement with the depolarization data of Cleveland whereas they confirm our results. Sakashita has already met this difficulty in the discussion of the assignment and in several cases has preferred the infra-red evidence. The infra-red spectra of cyclohexene-do and cyclohexene-dlo in the vapour and liquid phases are shown in Figs. 3-6. For cyclohexene-do we have also obtained a crystal spectrum at --194°C. The peak frequencies and relative intensities, together with the R a m a n frequencies and polarizations are listed in Tables 3 and 4 respectively. The selection rules for the C~ point group, predict 22 A and 20 B fundamentals all infra-red active and those of A species are R a m a n polarized. The vapour spectrum, despite the low molecular symmetry, is of considerable help in the vibrational assignment. Cyclohexene is a slightly asymmetric top with the greatest inertia axis (see Table 1) perpendicular to the plane formed b y the double bond and b y the binary axis, and the medium inertia axis parallel to C~. We expect therefore vibrations of species .4 to give vapour bands with a P R envelope of the B type and vibrations of species B to give rise to hybrid bands between the .4 and C types of an asymmetric top. The latter vibrations should show a PQR envelope with a more or less prominent Q branch. We conclude then that all vapour bands which show a central Q peak can be confidently assigned to the B species. Both the R a m a n and the infra-red spectra of cyclohexene are in excellent agreement with the predictions of the force field of Table 2. All bands which appear as polarized in R a m a n as well as all bands which show a Q branch in the vapour spectrum correspond within few wavenumbers to calculated frequencies of species

1768

N.

Table

•ETO,

C. DI

3. I n f r a - r e d ,

Raman

I . R . (gas)

I . R . (liq)

450m

Q

175 280 324 393 452

636 vs 660 s 718 vs

Q Q Q

640 v s 670m 720 vs

810 w

vs w vw vw s

LAURO, E.

spectra

and

CASTELLUCCI and

calculated

frequencies

R a m a n (liq)

Q

919 s

Q

878m 905 w 917m

175(1-5) d p 281(4"5) d p

186 B 285 A

394(10) p 455(2-5) d p 495(3) d p 643(2) d p

399 474 521 634

721(1.5) d p 789(2) p

706 B 779 A

822(40) p 878(3) d p 905(9) d p

811A 869 B 902 A 907 B 973 A

A B A B 495(A) q- 175(B) = 670(B)

640(B)-}- 1 7 5 ( B ) =

966(4.5) d p Q Q

998 v w 1009 w 1038m 1060 v w 1068 v w

175(B) q- 822(A) ~ 997(B) 1040(8) d p 1068(12) d p

1054 A 1084 A

Q

1112 v w 1138 s

1139(3-5) d p

1240m

PR

1222 v w 124Iw

1222(40) p 1241(11) p

1269m

Q

1265(15) d p

1325m 1343m

Q Q

1264m 1310 w 1321m 1338 w

1131B 1124 A 1233 A 1250 A 1227B 1278 B

1343(5) p 1353(5) p

1357 1425 1369 1403

1445 vs(sh) 1450 s Q 1455 vs Q

1438 vs 1447 s 1456 s 1530 v w 1603w 1633 v w 1653 s 2840 vs 2860 vs

1604 v w

Q

1660m

PR

2858 vs

Q

2878 v s 2890 v s

Q Q

2942 vs

Q

2882 2898 2929 2940

PR Q

2960 s 2993m 3022 vs 3065 w

vs vs vs vs

1436(40) p 1455(20) d p

1656(40) p 2839(30) p 2865(21) p 2886(19) d p ? 2916(40) p 2940(40) p

3040 vs 3078w

815(A)

967B 1043 B

1140 vs

1350w 1392m

of cyclohexene-d o Calc.

810 w

877 s

1009 w 1039 s

S. CALIFANO

2990(4) d p 3026(27) p 3065(2) d p

394(A) + 7 2 0 ( B ) =

1114(B)

495(A)-]- 721(B)=

1316(B)

1222(A) q- 1 7 5 ( B ) =

1397(B)

395(A) q- 1 1 3 7 ( B ) =

1532(B)

B B A A

1435A 1454 A 1446 B 1467 B

1667 A 2854A 2853 B 2855A 2854 B 2925A 2925B 2934A 2929B 3050A 3048B

Several w e a k a n d v e r y w e a k b a n d s b e t w e e n 1650 a n d 3500 c m -1 w e r e e m i t t e d i n t h e t a b l e .

Vibrational spectra and molecular conformation of c y c l e n e s - - I

I

i

I

2000

1800

1769

!111~ L

~,

I

I

H~

300~

1600

1400

1200

1000

800

600

400

200

600

400

200

Fig. 3. Infra-red spectrum of gaseous cyclohexene-d o.

2000

3000

1800

1600

1400

1200

1000

800

Fig. 4. Infra-red spectrum of liquid cyclohexene-d o.

i

V i

2000

1800

1600

1400

1200

1000

800

600

Fig. 5. Infra-red spectrum of gaseous cyclehexene-dlo.

400

200

1770

1%. 1%ETO, C . D I

Table

4. Infra-red,

I . R . (gas)

375m

Q

497 vs Q 608m

712m

Q

Q

Raman

LAImO,

E.

spectra

and

CASTELLUCCI a n d

calculated

Q

375 m

230(2) d p 327(3) p 378(0.5) d p 457(1) d p 497(0.5) d p

182 B 232A 337 A 384 B 472 A 489B

618(0"5) d p

606 B 616 A

494 vs 529vw 605m 634 w 71Om 730 s 739 w 772 w

737(4) p

Q

799(25) p 845(7) p 868 v s

917 w

911 ra

1052 w

1048 m

1069 m Q

1064 s

1083 vs Q

1080 s

1174m Q

1099 w 1170s

1630m

874(0"5) d p 899(1) d p

1225 1250 1382 1590 1619 vs 2044 v w

2102 vs Q

2093 v s

2110 vs Q

2115 v s

1066(4) d p 1079(1.5) p

1103(1.5) p 1171(1) d p 1206(1) dp~

1621(22) p 2039(1) p 2087(30) p 2105(22) p

2191 vs Q 2211 vs Q 2268m

2182 v s 2206 vs 2229m 2263 s 2302w

695 715 710 742

B A B A

752 749 767 858 850 885 885

A B A A B B A 457(A) × 2 = 914(A)

923(3) p 962(1) d p 998(1) p

961 m Q

cyclohexeno-dio

457(A) + 327(A) = 784(A)

791m

872 vs Q

of

Calc.

R a m a n (liq)

779(12) p 795m

frequencies

I . R . (liq)

727(8) p 731m

S. C A L I F A N O

2119(17) 2140(30) 2165(18) 2184(16) 2210(16) 2221(16) 2264(14)

p p p dp dp p p

2343(2-5) p

922 A 965 B 1001A 1054 B 1051A 1077 B 1062 A 1088 B 1150 B 1183 A 1217 B 1235 A 737(A) + 4 9 4 ( B ) =

1231(B)

795(B) + 7 9 9 ( A ) =

1594(B)

1621A 1206(A) + 845(A) = 2051(A) 2087 2084 2090 2087

A B A B 1066(B) X 2 = 2 1 3 2 ( A )

2180 A 1080(B) X 2 = 2 1 6 0 ( A ) 2182 B 2191B 2205 A 2271 2260 B 1171(B) X 2 = 2 3 4 2 ( A ) o r 1621(A)+ 727(A)=2348(A)

Vibrational spectra and molecular conformation of cyclenes--I

ri !, .

2300

2100

1900

1700

1500

1300'

.

.

1771

.

11100 ' 9 0 0

' ?00

I

' 500

' 300

' '

Fig. 6. Infra-red spectrum of liquid cyclohexene-dlo. A and B respectively. The correct correspondence between the theoretical predictions and the experimental evidence shows undoubtedly t h a t the force field used is essentially correct and makes us confident in the predictions for those modes which, owing to their weak infra-red or R a m a n activity, are doubtful.

CycloH~.XENE-d o I n the R a m a n spectrum there are 15 polarized lines at 394, 789, 822, 905, 1222, 1241, 1343, 1353, 1436, 1656, 2839, 2865, 2916, 2940 and 3026 cm -1 which are undoubtedly fundamentals of species A. In addition there are four depolarized lines at 281, 495, 966 and 1068 cm -1 which have very weak counterparts in the infra-red spectrum of the liquid and fit, within few wavenumbers, the calculated frequencies of species A. Owing to the C~ pseudosymmetry and to the agreement with the calculation, their assignment to the A species seems unquestionable. I n the infra-red spectrum of the vapour there are 18 bands at 450, 636, 718, 877, 919, 1009, 1039, 1140, 1269, 1325, 1343, 1450, 1455, 2858, 2878, 2890, 2942 and 3078 cm -1 which show a well resolved Q branch and belong therefore to the B species. Their close correspondence to calculated fundamentals definitely proves the correctness of their assignment to B fundamentals. I n addition there is a very strong band in the infra-red spectrum of the liquid at 175 cm -1 which corresponds to a weak depolarized band in Raman. Although the rotational envelope of this band has not been observed the agreement with a calculated B fundamental at 186 cm -1 seems sufficient to establish its assignment to this species. There are still three A and one B fundamentals left unassigned. Definite spectroscopic evidence are absent for these modes either because t h e y are expected in regions of strong absorption or because they have a too weak i.r. or R a m a n activity to be identified with certainty. Their assignment must therefore rely only on the prediction of the force field. The present assignment differs in several points from t h a t of Sakashita. This author has assigned to the species A the R a m a n lines at 175 and 1039 cm -1 which Cleveland reported as polarized but in our R a m a n spectrum are definitely depolarized. I n addition, the 1039 cm -1 band has a well resolved Q branch in the vapour spectrum, a fact which is inconsistent with the assignment to the A species, and the 175 cm -1 band is very strong in the liquid spectrum. The joint evidence of the experimental

1772

1~. I~]ETO, C. DI LAURO, E. CASTELLUCCIand S. CXLIF~XO

results and of the calculations of Table 3 shows undoubtedly t h a t Sakashita's assignment is incorrect, both bands being clearly B fundamentals. Another fundamental of species A was assigned by Sakashita to a weak band at 1007 cm -1. As reported previously this band has a strong Q branch and again cannot belong to the A species. Finally Sakashita assigned to the B species the depolarized R a m a n bands at 279 and 966 cm -1 as well as the infra-red band at 1395 cm -1. The first band has a very weak counterpart in the infra-red spectrum whereas the second is completely missing, an argument which is clearly in favour of their choice as A fundamentals in view of the C2, pseudosymmetry. The agreement with calculated fundamentals of this species gives further support to our choice. As far as the last band is concerned it fits very well the assignment to the combination 175 + 1222----1397 cm -1 whereas lies far out from a n y calculated value to be accepted as a fundamental. In addition it is absent in the spectrum of cycloheptene and cyclo-octene and is therefore difficult to accept its choice as a = C H deformation mode as suggested by Sakashita.

CycloHEXENE-dlo The 16 polarized R a m a n bands at 327, 727, 737, 779, 799, 845, 923, 998, 1079, 1103, 1621, 2087, 2105, 2140, 2221 and 2264 cm -x are undoubtedly A fundamentals and the 15 infra-red vapour bands at 375, 497, 608, 712, 731, 795, 872, 961, 1069, 1083, 1174, 2102, 2110, 2191 and 2211 cm -1 all with a well resolved Q branch are clearly B fundamentals. Again they all correlate within acceptable errors with the zero order calculated frequencies. In the R a m a n spectrum there are six depolarized lines at 230, 457, 618, 899 and 1206 cm -~ which are either absent or have very weak counterparts in the infra-red spectrum of the liquid. As for the light species they originate from molecular motions which for the C2v pseudosymmetry would belong to the A S species. Their assignment to the species A of the C 2 point group is substantiated by the agreement with calculated values of this species. I n the infra-red spectrum of the liquid there are two bands of medium intensity at 1048 and 1098 cm -1 and one weak band at 2301 cm -1 which agree with calculated frequencies of B species and therefore have been accepted as fundamentals. THE REFINED FORCE FIELD The vibrational frequencies of cyclohexene and cyclohexene-dlo identified in the previous section were used to refine the zero order force constants with a steepest descent method discussed in a previous paper [5]. Weighting factors of 1/2ohs were used in the refinement procedure. The refined frequencies are compared with the experimental data in Table 5. An approximate potential energy distribution is also included in order to characterize the normal modes. For simplicity only contributions greater than 10 per cent are reported in the table. The excellent agreement between observed and calculated frequencies obtained with numerical values of the force constants consistent with well established data, shows t h a t the type of force field used is correct and t h a t no important interaction terms have been omitted. The complete valence force field of cyclohexene would actually include an inpracticable number of independent force constants (260) and it is obvious t h a t several

Vibrational spectra and molecular conformation of cyclenes--I T a b l e 5.

Vibrational assignment and refined calculated frequencies for cyclohexene-d o and cyclohexene-dlo Cyclohexene.d o

~"

A

?~obs ~'calc

1 3026 2 2940 3 2916 4 2865 5 2839 6 1656 7 8 1436 9 1353 10 1343 11 1 2 4 1 12 1 2 2 2 13 14 15 1068 16 966 17 905 18 822

3054 2934 2924 2854 2853 1656 1463 1440 1355 1328 1249 1222 1141 1095 1085 967 905 813

19 20 21 22

789 495 394 281

791 507 392 277

23 24 25 26 27 28 29 30 31 32

3067 2960 2898 2882 2860 1450 1443 1338 1321 1265

3053 2928 2925 2853 2852 1455 1442 1344 1314 1269

Cyclohexene.d~ o P.E.D.

0"99K t 0"99K d 1-0Kd 0.99K~ 0.99Kd 0.79K~-4- 0.12KR 0.76H~ -~ 0.22Hr 0.80H~ -{- 0-14H~, 0.21K2-{- 0.14//0 -~ 0.60Hr 0.18KR-[- 0'21H0 -~ 0.67H~, 0-21H0-{- 0'65Hv 0.16KR-~- 0.21H~ -~- 0.21H~ -[- 0.33H~, 0.27H0 -~- 0-77Hr 0.70KR 0"38H0 -]- 0"30H~, -]- 0"I3HF -~- 0"31~ 0"44HF -{- 0"12H~ 0"69KR~ 0.12Hr -~- 0"10K b 0.83KR 0.18KR ~- 0'15H0 -~ 0.64H~ 0-11He -{- 0.58H~ -~- 0.11Hr 0"31HF -]- 0.34r~ -~ 0 . 1 ~ -~- 0"I~R 0.49H¢o~- 0"l~'b -~ 0.27~-~

33 34

0.99K t 0.99K~ 0.99K d 0"99K~ 0-99K~ 0.77H5 -]- 0.14H~, 0.79H~ -]- 0.16Hr O*ISHo-~ 0-80Hr 0.19H0 ~ 0"65H~ 0-11KR -4- 0.11H~ -I- 0-1H~ 0"13H0 -~ 0"56Hv 1214 0-67KR ~- 0-25H~b -~ 0"16/-/0 ~- 0.18Hy 1 1 3 9 1 1 3 2 0.1K R-~- 0-39H0 -~ 0"58Hy

35

1040

36 37 38 39 40 4I 42

1 0 6 8 0.20K~-~ 0.13H~ ~- 0.26H~ ~- 0.1H0-]- 0.24Hy 1009 985 0.16H~ ~- 0.27H~ -{- 0-13H0 -4- 0"28Hv 917 917 0"21H0 -~- 0.72Hy 878 861 0*81KR 721 643 455 175

1773

716 645 463 179

0.14K2 -~ 0"18He -t- 0.37Hy -]- 0.14HF 0.66HI" 0.57Hw -~- 0.34H~ 0-24H~ -~- 0-28~'T -4- 0.350"r2

robs

Ycalc

P.E.D.

2264 2221 2140 2105 2087 1621 1206 1103 1079 998 923 899 845 799 779 737 727

2273 2225 2179 2090 2087 1618 1200 1125 1070 1055 1001 921 892 842 805 770 740 718

615 457 327 230

626 459 330 225

0.94K~ 0.96Kd 0.98Kd 0.97Kd 0-96Kd 0.79K~-~- 0.16K2 0.97KR ~- 0.32H7 0.51K2 -~ 0"22H0-{- 0.44H~ 0.11K2-~- 0.77H~ -{- 0.14H~ 0-77H~-{- 0-20H~, 0.1K2 ~- 0"60H~ 0.65H~, 0"60/-/0-~- 0.27HF 0.1KR -~ 0.41H~ ~- 0.34H~ 0.21H0 -~- 0.74H~, 0.53K~ -~- 0.19/-/~, 0.35KR -4- 0-26H~ -~- 0*16HF 0.23KR -]- 0.11H0 -~- 0.22Hr -~ 0.21HF -]- 0 ' 1 3 ~ 0-15H0 -~- 0.59HV 0.50H~ -[- 0.24H~ 0-24HF -~- 0.43~'/) -~ 0*10"r 0.50KR -~ 0.31~'R

2302 2206 2182 2115 2093 1170

2265 2190 2182 2087 2084 1180 1105 1080 1080 1064 1 0 5 8 1048 1 0 4 7 962 868

963 881 852

79I 730 710

772 706 698

605 497 378

618 493 377 146

0-96K t 0.97Kd 0.98K~ 0.97Kd 0.97K a 0"94KR-4- 0"20Hv 0-18K2-~ 0.14H~ -]- 0.50Hy 0.1Hw @ 0"59118-~ 0"16H0 0.76H~-~ 0"I8H0 0.13H~ ~- 0.14H~ -4- 0.13H~ -~ 0.10H0 0.67Hr 0"17He ~- 0.22Hw -~ 0.1H~-{- 0.26H V 0-73H0 -4- 0.19Hr 0.12H~ ~- 0-26H0 -I- 0.49H~ 0.99H~, 0.21H~ -~ 0.25H~ -4- 0"36KR-{- 0*13H7 0.13K2 -4- 0.21He -~- 0.36H~, 0"70HF 0"46H~ -~- 0.55Hr 0"23H~ ~- 0.30~-~, -{- 0.36v~

simplifications are necessary to reduce the number to one acceptable in actual calculations. Happily, the paper by Schachtsehneider and Snyder already gives the force constants of the aliphatic part of the ring that must be included as independent terms in the force field and there is no reason, owing to the staggered conformation of the CH 2 groups and to the absence of effective ring strain in the C~ form of cyclohexene, to assume that other force constants should be added for this part of the field.

1774

N. N~To, C. DI LAtmo, E. CASTEImUCCIand S. CAnlI~A~O

The terms involved in the ethylenic part, as well as the interaction terms between the aliphatie and the ethylenie field have been introduced while trying to preserve the internal consistence of the field. For instance, since the force field of Ref. [4] includes interaction terms between CC bonds only if t h e y have one common C atom, no interactions between the CC double bond and no-adjacent CC bonds are included. Although this procedure has no a priori justification, it is clearly supported a posteriori b y the excellent results obtained. The refined force constants are listed in the last column of Table 2 under the label (I)r and have all numerical values which make physical sense; those of the aliphatic part being ver y close to the corresponding terms of Ref. [4] and those of the ethylenic p ar t being in line with previous calculations on ethylenie compounds. For this reason we believe t h a t a detailed discussion of the force constants would be redundant. The validity of this force field has been tested on larger rings such as cycloheptene and cyclo-octene and it has been found t h a t the field is correctly transferable. The occurrence of new steric situations, such as the eclipsed CH 2 groups, required only ver y few additional terms.

Acknowledgements--This study was supported by the U.S. Department of the Army, through its European Research Office, under contract No. DA-91-591-EUC-3543 and by the Italian Consiglio Nazionale delle Ricerche.