Vibrational spectra of cubane and four of its deuterated derivatives

JOURNAL O F T H E AMERICAN CHEMICAL SOCIETY Regiprerrd i n U S Parenr Office

0 CopJrighr. 1979. by the American ChemrcalSocie/j

VOLUME 101, N U M B E R25

DECEMBER5 , 1979

Vibrational Spectra of Cubane and Four of Its Deuterated Derivatives E. W. Della,Ia E. F. McCoy,Ia H. K. Patney,Ia Gerald L. Jones,1b3C and Foil A. Miller*Ib Contribution from the School of Physical Sciences, The Flinders University of South Australia, Bedford Park, South Australia 5042, and the Department of Chemistry, University of Pittsburgh. Pittsburgh, Pennsylvania 15260. Received April 9, I979

Abstract: Vibrational spectra are reported for cubane, cubane-dl, sym-cubane-d2, S~m-CUbane-d6,and cubane-dg. Infrared spectra are from 400 to 3600 cm-' for CS2 and CC14 solutions, and for a solid deposited from the vapor a t -I00 K. Raman spectra are for the same solutions and for the polycrystalline solid at room temperature. Vibrational assignments have been made for all the fundamentals of all five compounds, 120 modes in all. The fortuitous crystal structure of cubane and cubaneds was an important aid. Of the 18 fundamentals of cubane, only one or two are not certain. The spectra show almost no effect of the severe bond angle strain. Also there are no low molecular modes; the lowest for cubane is 617 cm-].

Introduction Cubane, CgHg, has the carbon skeleton shown in Figure 1 .* I t is an exceptionally interesting molecule because of having the unusual cubic cg cage, very high symmetry, and a great deal of strain. The C-C-C angles are decreased from 109.5 to 90' at each of the eight corners, and this might be expected to produce some unusual vibrational frequencies. Hence a thorough study of its vibrational spectrum seemed desirable. Cubane was first prepared by Eaton and Cole in 1964.3 An X-ray diffraction study by Fleischer4 showed that, within experimental error, the carbon frame is a cube and the hydrogen atoms lie on extensions of the cube diagonals. The C-C distance is 1.55 A, almost exactly the same as in cyclobutane. Very little is known about the vibrational spectrum. There are no published Raman data, and the only infrared results are from a survey spectrum obtained a t the time of the original ~ y n t h e s i sOnly . ~ three bands were observed-just the number of fundamentals permitted by cubic symmetry. Recently some unpublished data of King, Cole, and Gayles has been quoted by other^.^ Both the data and the interpretation differ considerably from ours. Thus there is very little usable information on the vibrational spectrum of cubane in the literature. This work is a cooperative project between our two laboratories. Della and Patney did the chemical preparations, Jones and Miller made the spectroscopic measurements, and McCoy is responsible for the normal coordinate calculation (to be published separately). We have studied five isotopic forms of cubane: cubane-do and -dg (oh symmetry), sym-cubane-d2 and -dg ( D 3 d ) , and cubane-dl ( C 3 ) .For brevity these will be referred to as do, dl, dr. d g . and dg. The d2 and d g will always mean sym-d2 and sym-dg. Their full names are 1,4-dideuteriocubane and 1,2,3,4,6,7-hexadeuteriocubane.

Experimental Procedures and Results Origin and Properties of the Samples. The syntheses have been described by Della and Patney.6 Between 40 and 200 mg of each compound was available for our work. Cubane is a colorless solid. It melts at 130- I3 I "C, and decomposes above the melting point. It is soluble in CS2, CC14, CHC13, and benzene. Surprisingly, it is not sufficiently soluble in cyclohexane to make that a useful solvent for vibrational spectroscopy. It sublimes fairly easily, and is readily transferred on a vacuum line.' A small sample left in the open will disappear overnight. One can readily lose cubane while handling it, and we had great difficulty in recovering samples after our experiments. I n part this was because the cubane also vaporized when a solvent was evaporated. We suspect, too, that the vapor dissolves readily in stopcock grease. The purity of the samples will be discussed later. Infrared Procedures. Initially quite a bit of do was lost in vain attempts to make KBr pressed disks. It just disappeared. We believe now that it may have sublimed when the sample-KBr mixture was evacuated prior to and during the pressing. Solid samples were therefore prepared by depositing the vapor onto a cold window (-100 K) in a conventional low-temperature cell. Solutions in CS2 and CC14 were also used. Spectra were obtained from 400 to 3600 cm-l with a Beckman IR-12 spectrophotometer. The lower limit was set by KBr cell windows. In addition a thick deposit of do was measured down to 200 cm-' in a Csl cell. Since no infrared bands were found, the range 200-400 cm-' was not examined for the other compounds. The spectral slit widths were 1-2 cm-' in all cases. Raman Procedures. Raman spectra were obtained with a Spex Ramalog instrument which has been described elsewhere.* Samples were held in thin-walled glass capillary tubes. They were examined as polycrystalline solids at room temperature, and as solutions in CS2, CC14, or benzene as needed to observe each band. Depolarization ratios were measured for the solutions. Excitation was with either the 488.0- or 514.5-nm line of an Ar+ laser. We took the precaution of keeping the laser power at the sample less than 100 mW, and of ro0 1979 American Chemical Society

7441

Journal of the American Chemical Society

1442

/

101.25

/ December 5 , I979

Table 1. Cubane-do Infrared and Raman Bandse infrared solid (-100 K ) CS2 soh cm-l int cm-l int 617

CC14 soh cm-1 int

*

vw

Raman solid (-295 K ) CS2 soh CC14 soh cm-1 into cm-1 into pb cm-1 into

8 665

{Z 824 I829 839

w m m

852

1030

vw

-1030

3

24 21

* 821'

667

*

20

16

2 0.75

* * *

*

assignments

15 18 4 12 for I3C compd

s

912 996 1002 -I 026

vw

1000 899 sh -996 970 1001 1 -1028

235 sh 1000 1

899 -996 1001

280 0.76 sh P 1000 0.00

12 6 2 for I3C compd 2 imp 17

-1078

vw 1083 1 I30

-I I33 I144

4 8

1078

3

-

'!

I078

5 9

1

'? ?

vvw

vw

{E vw I168 W

7

vw

1184

VW

I{ ;;:

vvw

-1183

-I 223

95 60

1182

2 -1224

45

1 I85

40

0.78

2 X 617 ( I ) = 1234? or imp. 1 1 for '3C compd or imp. II

2

* 1230 1235 1283 -1638 1701

1799 1819

vs m w

1698 -1717

w vvw

-1746

vvw

-1794 1817

vvw w

-1850

vvw

-1895 -1952 -1961 -1970 -1983

vw w vvw w vw

1965 1982

vw vvw

2965

vvw

w

S

'!

+ + + + + + + + + + + + + ? 821(R) + I151(1) = 1972 1130(R) + 853(1) = 1983 2X 1036(1) = 2072 839(1) + 1230(1) = 2069

665(R) 617(1) = 1282 2 X 665(R) = 1330 815(R) 829(1) = 1644 2 X 82l(R) = 1642 665(R) 1036(1) = 1701 899(R) 829(1) = 1728 (soln) 899(R) 851(1) = 1750 (soln) 1130(R) 617(1) = 1747 665(R) 1130(R) = 1795 I179(R) 617(1) = 1796 665(R) 1151(1) = 1816 821(R) 1036(1) = 1857 (soln) 1001(R) 851(1) = 1852 (soln) 665(R) 1230(1) = 1895 1130(R) 829(1) = 1959

vvw

w

vw w

1231

* -1276

*

vw

2210

s

w

1895

2148

1228

*

*

1700

1820

imp.d 14

-1330

1

-1640

1

-1795

1

vw

vw

1 -206 I

I

-2154 -2205

I 2

2241 {-2257 -2309

4 2

-2363 -2454

2

-206 I

1

1002(R) + 1151(1) = 2153

'!

-2205

?

1

1179(R) -2252

2 X I 130(R) = 2260

I

1130(R) 2312

1

-2328 -2365

I I

0.0

s

2970

180

2973

200

+ l182(R) =

'!

2 X I185(R) = 2370 (soln) 2 X 1230(1) = 2460 3 and I O (a,Jd

1

300 240

+ 1036(1) = 2215

0.75

13

Miller et al.

/ Vibrational Spectra of Cubane

1443

Table I (Continued) infrared CS2 soh solid (-100 K ) cm-1 int cm-1 int 2978 2992

vs vs

2977

vs

CC14 s o h cm-1 int 2982

Raman CCI4 s o h solid (-295 K ) CS2 soln cm-1 into cm-1 into cm-I into pb

assignments 10 (%I 3 and I O (a#

vs 2995

395

2994

295

2999

280

0.0

1

Raman intensities are relative peak intensities on a scale of 0-1000, uncorrected for instrument response. p = depolarization ratio. For depolarized lines, we obtain 0.75 f 0.03. p, d p = polarized, depolarized. Numerical value of p could not be obtained. 821 cm-l is a shoulder on the side of the CS2 band at 796 cm-1. d See text. e Notes (also apply to Tables 11-V): w, m, s = weak, medium, strong; v = very; b = broad; sh = shoulder; = approximate ( f 3 - 5 cm-I), due to breadth, weakness, or being a shoulder; *, solvent interferes; R = Raman value; I = infrared value; imp. = impurity; dl,d7 = cubane-dl, cubane-d7, etc.; ( ) = estimated from product rule; FR = Fermi resonance.

-

Table 11. Cubane-dg Infrared and Raman Bandse solid (-100 K ) cm-l int 448 vw 527 vw (532 vvw

infrared CS2 soln cm-1 int

*

CC14 s o h cm-1 int

Raman solid (-295 K ) CC14 soh cm-1 into cm-1 into

571 586 623 v w , b 638 w

I-;:

686 vs z,sh

-716

vw,sh

768 m 777 vvw 791 vw

* *

*

8 IO

570

11

0.0

606

2

0.0

635 684

10 585

636 669 674

4 135 sh

sh

683

vs

684

709

w

*

710

55

710

*

150 6 55

716

m

715 739 766

vvw

*

164 -790

assignment

06

* * *

* *

807 vvw

imp.c 8 8 for d7 imp.< 16 imp.< ? d7 6 6 for d7? 12

0.75 0.78

m

-802

1

-842 884 923

2 8 8

950 956 960

55 1000 140

995 1004

3 20

*

766b

35

d7 0.75

15 ? d7 ? d7? *? 4 ? 9 d,? 17 (also in Raman. d7?) 2 for I3C compd 2 2 for d7 7 (and 2 for d7)

-d

20d 0.75

924 vw 950 954 958

sh 1000 140

0.0 0.00 0.00

972

45

0.0

1004 1028

3 75

0.78

1073

40

0.76

1155

4

0.74

960 vw I005 vw

1083 m 1094 vw

1081

vw

* *

(;:;I 2;: 1072 130 -1144

1154 1156 I I69 I185 -1504 1534 1598 -1698

Q

? d7 5 5 for d7 14 II doublet with 1083? '!

2

w m vvw vvw

1154

vw

I188

vw

* *

vw vw vw vw

1801 vvw

-1695 -1795

1154

15

* *

+ +

vvu vvu

f

1865 vvw

1963 w

1962

vw

d7 imp.c d7 586(R) 924(1) = 1510 ? 1072(R) 527(1) = 1599 1027(R) (674)' = 1701 715(R) t 1083(1) = 1798 884(R) ', 924(1) = 1808

+

+

1908

5

2 X 956(R) = 1912 884(R) 1027(R) = 191 I

1936 1952

5 5

?

+

1072(R) t 884(R) = 1956 884(R) 1083(1) = 1967

+


1444

/

101:25

/ December 5, 1979

Table I1 (Continued) solid (-100 K ) cm-l int

I

2001 w 2005 vw,sh 2029 vvw 2046 2052 2060 2069

w vvw w vvw

infrared CS2 s o h cm-1 int 2000

vw

2029

vvw

2044 2060

CC14 soh cm-' int

?

2036

IO

2040

3

0.11

2052

18

2054

5

0.60

2093

8

2096

3

0.75

2133 2141

10 IO

2137 2146

7 7

0.0 0.71

2158 2180

5 5

2162

3

0.0

2226 (2232

300 545

2230

9

* *

2238

+ +

9

vs

2242

175

0.75

13 3 and I O (aJC 10 (4 3 and I O (a,)C

m 2259

760

2265

340

0.00

1

?

* 2926

vw

2973

s

-3305

586(R) t 2240(1) 684(R) 2240(I) 2232(R) 686(1) 715(R) 2240(1) d7, also 2259(R)

+ + +

2976

vw

-2980 w,sh 2993 w 3216

+

1072(R) 1027(R) = 2099 1027(R) 1083(I) = 21 I O ? ? 2 X 1072(R) = 2144 l072(R) 1083(1) = 2155 2 X 1083(1) = 2166 ? ?

*

2185 vvw 2215 vvw

3224 vvw 3303 vw 3346 vw

+

d7, also 2 X 1027(R) = 2054(R) ?

vw

*

+

1072(R) 960(1) = 2032 960(1) 1083(1) = 2043

vw

*

2149 w

2261 w 2815 vvw,b 2918 vvw,b

assignment

pb

?

2105 w 2124 vvw

2229 m 2240 vs 2248 m

Raman solid (-295 K) CC14 s o h cm-1 into cm-1 into

2975

40

2990

IO

2918

IO

0.20

= 2955

+ 715(R) = 2974(R)

d7 956(R) 2240(1) = 3196 2259(R) 960(1) = 3219

+ +

vw vvw

1072(R) 2259(R)

See footnote a , Table 1. See footnote b, Table I. See text.

= 2826 = 2924 = 2918

+ 2240(1) = 3312

+ 1083(1) = 3342

Benzene solution. e See footnote e , Table I.

Tahle 111. svm-Cubane-d, Infrared and Raman Bands!

solid (-100 K ) em-' int 574

w

infrared CS2 s o h cm-I int 568

CC14 s o h cm-' int 568

Raman solid (-295 K ) CC14 s o h cm-1 into cm-I into 632 651

691 711 724 737

vw m

770

vw

20 6

0.76 0.33

706

m 721

5

vw

sh

890

vw

s s

m

w

838

839

738c

I30

136

85

0.75

821

25

820d

1 Od

0.74d

0.74 -0.73 dp? -0.73 dp?

*

* 875 600 888 80 900 15 983 55 991 1000 994 1 1 5

866 887 -900 983 990 994

220 15 2 45 1000 65

55 230

I002 1016

15 95

0.0 0.0 0.0

994 1001

18b di g fund. 15b'? 15b '?

* * *

s

1016 1020 1036

63 1 65 1

8 16b 16a '?

706

vw

-X27 838 L44 851

995

30 6

assignment

Ph

w

0.0 0.76

15a 18a 4 12b 12a 6 di ?

2 for I3C compd 2 2 for dl 17b 2 for do 5

vw

'?

w

17a

Miller et al.

1 Vibrational Spectra of Cubane

7445

Table 111 (Continued) solid (-100 K') cm-I int 1109 I169

CC14 s o h cm-' int

I100

20

I099

4

0.73

1133 1168

6 125

I I34 1 I70

4 36

0.10 -0.57

I174

80

1 I76

24

-0.72

assignment 9b 7 >

14a imp.c 14b 1la 632(R) 574( I ) = I206 Ilb 738(R) 574( I ) = 13 I2 632(R) 71 l ( 1 ) = 1343 632(R) 995(1) = 1627 651(R) 1036(1) = 1687 1 l74( R) 574( I ) = 1748 651(R) I109(1) = 1760 738(R) 1 109( I ) = I847 632(R) 1222(1) = 1854 l016(R) 838(1) = 1854 I IOO(R) 838(1) = 1938 2 X 991 ( R ) = 1982 875(R) I IOO(R) = 1975

vw s w,sh s vw vw, b vw,b vw, b vw,b vw, b vw, b vw, b

-1933

vw, b

I204

s

1205

I220

s

1221

+

+ + + + + + + + + + +

*

1975

3

1977

2

2024

3

2100

3

2027 2062 2101

2 2 2

2197

2

2199

6

2212

2

w

'?

* * * *

2122 2156 2162 2188 2194

vw vw vw w w

*

2195

vw

2210

m

*

2214

m

2220

vw

*

2240 2248 2278 2968

s w vw s

2977

vs

2992

s

-3255 -3410

Raman solid (-295 K ) CC14 s o h cm-1 into cm-' into Ph

w

1201 -1208 1222 1308 -1342 -162.5 -1683 -1744 -1762 -1845 -18.53

1991

infrared CS2 s o h int cm-1

-2239

+ +

+ + + +

0.10

+

?

s

2243

vs

2980

2237

280

2246

50

2241

130

13a I Oa

0.23

S

*

2977

2 X 1016(R) = 2032 839(1) 1221(1) = 2060 ( s o h ) 995(1) I109(1) = 2104 1016(R) 1109(1) = 2125 1168(R) 995(1) = 2163 ( I 130) 1036(1) = 2166 991(R) 1201(1) = 2192 1168(R) + 1036(1) = 2204 2 X I 1 OO(R) = 2200 991(R) + 1222(1) = 2213(1) 995(1) 1222(1) = 2217(R)

2970 2976

400 300

2985

180

2993

440

? I 174( R)

297 I

130

+

I I09( I ) = 2283 3 13b 738(R) + 2237(R) = 2975; FR with 2970 10b

dp

vs

? d , '!

299 1

280

1

-0.12

1016(R) I174(R)

b vw,b VW,

+ 2240(1) = 3256 + 2240(1) = 3414 ~

See footnote a , Table I . See footnote b, Table I . 738 cm-' is asymmetric on low-cm-I side; unable to resolve. solution. See footnoted, Table I . See footnote e , Table I . tating the capillary, to avoid decomposition. It was not possible to obtain the spectrum of molten cubane because it decomposed when slightly above the melting point and under laser illumination. The spectral slit widths were 5 cm-I for survey spectra, and down to 1 cm-l when possible for frequency measurements. Results. Survey spectra are shown in Figures 2-5 and numerical data are given in Tables I-V. The wavenumber calibration of the instruments was checked just before or after each measurement. The tabulated infrared wavenumbers are thought to be accurate to f l cm-I, and the Raman ones to f 2 cm-I, unless a band is marked broad, shoulder, or approximate. It is noteworthy that the bands seldom change by more than 3 cm-I between solid, CS2 solution, and CC14 solution. This simplifies comparison between these spectra.

Theoretical Considerations We find that in solution cubane-do follows the selection rules for oh symmetry, whereas in the polycrystalline solid it follows

~~

820 cm-I. In CHCl3

those for the crystal. Solutions. Consider first the expectations for the free molecule (gas or solution). I f cubane-do and -dg are cubic (oh symmetry), their vibrations are 2al,(R) i- 2e,(R) -I-Iflg 4f2,(R) 2a2, 2e, 3fl,(I) 2fzu, where R and I mean Raman and infrared active. Note that only three of the nine u modes are active. sym-Cubane-dz and -dg then have symmetry D 3 d , and their fundamentals are 6alg(R) lazg 7e,(R) 2a1, 5azu(I) 7e,(I). Finally cubane-dl is C 3 L , with 1 lal(R,I) 3a2 14e(R,I). Table VIA gives the correlation of the vibrations as the symmetry changes from o h to D3d to C3u Product Rule. The Teller-Redlich product rule9 is a powerful and useful check on the assignments. We prefer to use the reciprocal of the equation given by Herzberg so that the ratios are > I . Data used for calculating the theoretical ratios are given in Table VII. Both theoretical and observed product rule

+

+

+

+ +

+

+

+

+

+

+

+

Journal of the American Chemical Society / 101.25

1446

/ December 5, 1979

Table IV. sym-Cubane-ds Infrared and Raman Bandsg infrared solid (-100K) CS2 soln cm-I int cm int

538

Raman -solid (-295 K) CCI4 s o h

vw

579 598 -623 633 -643 651 662

w

)

645 66I

m

)

vw

704 716 725 738 758 786

s s

786

m

m

804

m

vw

I100

{

'?

305 10

35 35 245 6

696

I IO

0.78

IO IO

0.48 0.80 0.78

-1

725l' 736' 753'

70

1

4 847 884

35

844

8

0.76

1

55

40

962 966 97I

IO00 160

978 985

15

96I 967 97I

IO00

978 985 992

15 90 15

1029 I035 I067 1083

15 I55 5 25

1036 1065 1083

45 3

I145

100

1146

250

0.0 0.01 0.0 I

7

0.0 0.75

I I64

s

'?

5

IO

30

0.77

14b

I I83

W

I183

1

VVW,

VW,

-1728 -1769

VVW,

2006

w

2032

2043 2053

vvw w vvw

207x 2114

w vvw

2142

vw

2172

vw

+ 786(l) = 1384 + 786(1) = 1544 + 975(I ) = 1554 + 651(1) = 1618 '? l145(R) + 538(1) = 1683 1083(R) + 651(1) = 1734 758(R) + 1014(1) = 1772 884(R) + 1035(R) = 1919 786(1) + 1164(1) = 1950 985(R) + 975(1) = 1960 975(1) + 1014(1)= 1989 1035(R) + 975(1) = 2010 985(R) + 1035(R) = 2020 '? 884(R) + 1164(1) = 2048 1083(R) + 975(1) = 2058 2 X 1035(R) = 2070 985(R) + I lOO(1) = 2085 1145(R) + 975(1) = 2120 2 X 1067(R) = 2134? 985(R) + I145(R) = 2130'? 975(1) + I I64( I ) = 2 I39? 985(R) + I164(1) = 2149 598(R) 758(R) 579(R) 967(R)

b b VVW, b

VW.

-1680

2 X 538(1) = 1076 14a Ilb imp.' I I b for ds'!

m

m

vvw,b vw.b

9a I7a 2 for I3C compd 2 2 fords'? 17b 2 for d d ' ? 9b 9b for dS? 7

0.80 0.0 0.65

vw,sh

m

ds'?

I la

vw vw,b

vw

15b

?

*J

w

1955

ds?

'!

-1

vvw

VW.

I2a 6 6 for dg? I5a

1

-1642

-1615

I

12b

806

927

671

ni

vw vw,b

vvw vw

4

18a

688

s

807 832 849

-1144 1164 I169 1184 11x7 -1384 -1536 -1554

8 16a I6b

m w

717

1014

0.o 0.78

18b

vw

975

3 15

? ?

674 690

786 (792

578 597

vvw,b vvw w,sh

67I

736 -757

6 35

b b b

1917 1947

1

I

-1917 -1947

I, b 1,b

I987

3

-1987

I,b

2019

1

-2020

l1b

2061

6

2062

4

0.59

2134

3

2135

2

0.0

2162

5

2163

4

0.0

2 X 1083(R) = 2166 1

Miller et al.

Vibrational Spectra of Cubane

1447

Table 1V (Continued)

infrared solid (-100 K ) CS2 soh cm-’

2194

{ 2196

int

cm-1

int

Raman solid (-295 K ) cm-’ into

2176

5

2196

5

CC14 soh

cm-1

into

+ 1164(1) = 2178 + 1 l 4 5 ( R ) = 2180

1014(1) l035(R)

W

+

0.0

1035(R) 1164(1) = 2199 2 x 1 lOO(1) = 2200

0.75

? ? 13b

W

2196

4

vw vw

320 90 223 I

{ 2236 2239 { 2242

2230

100

S

vs

2234

vs

2245

s

1 Ob

VS

vs

2254 2275 2319

2974

vs

299 I

S

3226 -3378

assignment

Pb

2972

495 6 I

2257

335

0.02

3 1 )

2

X

I164(1) = 2328

1 Oa

s

2978

330

2992

80

vw vvw. b

2919

f’

I IO

0.19

13a 758(R) t 2236(1) = 2994 758(R) 2229(R) = 2987. FR with 2978 2229(R) t I lOO(1) = 3229 I145(RI t 2236(1) ~, = 3381

+

\

,

(‘See footnote a , Table I. See footnote b, Table I. I n benzene solution. 806 cm-I. Both CC14 and benzene interfere. e See footnoted, Table 1.i 2992 cm-’ is not observed in solution, even a t 0.5-cm-’ resolution. R See footnote e , Table I . [

ratios (7’s) are listed in Table V I I I . The observed ratios are expected to be less than the theoretical ones because of anharmonicity. A crude guide is that the difference is about 1% for each C-H(D) stretching mode and about 0.5% for each C-H(D) bending mode. Effect of Crystal Structure. Fleischer showed that the space group is R3 (or C 3 i 2 )with , only one molecule per unit The factor group is C3i = S g . This has several useful consequences. (a) Under it, all the fundamental modes of do and dg become formally allowed. The correlation between modes of the free molecule and of the factor group is shown in Table VIB. (b) There is still a center of symmetry in the factor group so the g-u distinction is preserved and the rule of mutual exclusion still applies. (c) In principle the triply degenerate modes of oh split into two spectroscopically active components in the crystal. I n fact most of them are observed to do just that. The finding that there is only one molecule per unit cell also has three pertinent consequences. ( I ) There are no correlation field splittings due to interactions between molecules in the same unit cell. Therefore any observed splittings are due to lowering of the symmetry from the molecular group to the factor group (Oh to Sg). Consequently they will be a dependable guide to locating triply degenerate modes of o h . (2) There are no translatory lattice modes. (3) There are only two rotatory lattice modes, having symmetry ag and eg of s 6 . These are Raman allowed, but we found no evidence for them down to 30 cm-’. This is understandable, for they are probably very low in both frequency and intensity. I f the molecule were truly cubic in the crystal, rotation or libration would not change the polarizability, and it would be spectroscopically inactive. The molecule is not exactly cubic but the distortion is very small so the librational bands are probably very weak. The above considerations do not necessarily apply to the intermediate deuterated species. The d l , d2, and d6 molecules have a unique molecular symmetry axis, but it is not necessarily directed along the Sg axis of the unit cell. The C3 symmetry axis of these molecules does not present a very different external aspect to neighboring molecules than the other cube diagonals, so some randomness is possible. This will lead to a further relaxation of selection rules in the solid.

Figure 1. The carbon skeleton of cubane.

Purity of the Samples A discussion of the purity has been deferred until after presenting the selection rules for solution and solid. We now must consider it before starting on the assignments. First of all, the infrared spectrum of every solid sample has a very weak band a t 1 168 or I 169 cm-I. It is not in the empty cell. Although it is hard to imagine how the same impurity can be in every one of the isotopic compounds, we believe that this band must be due to something extraneous to the samples. do. Gas chromatography indicated I-2% of a chemical impurity whose identity is unknown. A few bands in Table I that we cannot explain may be due to it. The only band that we are certain is an impurity is 1030 cm-’ in the infrared, because it appears in solution as well as the solid. Only f,, modes are allowed in solution (i.e., for the free molecule), and all three f l ufundamentals are known with certainty. It cannot be a sum tone because no frequencies are low enough, and it cannot be a difference tone because the solid spectrum was obtained at 100 K. Hence the infrared band is due to an impurity. The Raman band at -1026 cm-I may have the same origin. The remaining samples contained the same I-2% of chemical impurity found in do, although it may have been partially deuterated. The isotopic purity seems much more significant, and will now be discussed.


7448 Table V.

Cubanc-dl Infrared and Raman Bands"

infrared solid (-100 K ) CS2 solnu11-' int cm-' int 590 654

w

585

*

w

\4

7 24

m

721

rn

828 834 847 853 -878 892 995 IO02 IO26 I036 I Oh2 I098 I145

I168 117.5 -1 179 I184

VS

587 652 -659 722

I1 7 sh 55

816

826

25 25

cm-l

585 652 -659 722 818'

CCIJ soln int['

4 4 sh 20 10

m

0.82 0.75

8 16b 16a

0.76 0.7 I

18b

844

7

843

4

0.56

885

m

898 -902 996 I002

780

887

200

0.73

'! 6

1000 I00

995 I002

1000 40

0.00 0.26

2 2 of do, PIUS I 7bd

1027

28

I028

5

0.0 I

'!

I 062 1101 I132 I 145

18 13 5

I 062

7

1100

3

0.76 0.75

I174 1 I79

70 50

1217

7

1001

1

sh

17b

W

w U'

vw W

I175

w

4

vw

-1722 -1762

w,

VS

1217 1223

7

I303

W

S

11:: 1219

40) sh

0.76

*

VW

w,

b

0.73

*

b

w, b

-1880

v\+, b

-1935 -1962 I984 -2025 -2056 -2 I 08

vw. b u. b v \v vu. b vu. b vw, b

V\

w

\v m u. sh ni

-1959

w,

*

* *

m

\c

S

vs \

2975

imp." I4a 14b I la Ilb 590 659 = 1249 590 724 = 1314 659 t 724 = 1383 659 1002 = 1661 590 I098 = I688 654 t 1036 = 1690 847 844 = 1691 724 t I002 = 1726 590 I I74 = 1764 724 IO36 = 1760 { 5 9 0 + 1219 = 1809 892 996 = 1888 659 t 1225 = 1884 724 t 1225 = 1949 816 t 1145 = I961 2 X 996 = 1992 847 I I79 = 2026 996 1062 = 2058 892+ 1219=21ll 898 1217 = 2115 996 I145 = 2141 996 I I74 = 2170 2 x 1101 = 2202 1062 1145 = 2207 996 t 1217 = 2213 1101 I I32 = 2233 1 Oa 1101 t 1145 = 2246 I101 I174 = 2275 2 X I I74 = 2348

b

1982

-1

I984

I

2054

2

2056

3

21 14 2143 2168

I

2145

1

2

2212

IS

2240 -2247 2269 2349 2969 2977

X5 sh

2214 -2233 2243

10 sh 36

2270 2352

I I

280

2973

150

dp'?

2YY.I

590

2995

260

F

I

+

+

+ + +

+

* *

224 1

9b 9J. 7

+ + + + + + + +

w. b

-1 806

172 5

'!

4

VW

W

I 5b 18a 4, 12bd 12a

VS

vw

vw w vw. sh

1 Sa

844

vw

w

assignment

P"

w

w, b

(I

int"

s, sh

-1690

2992

:m-I

W

VS

2967 2978

Ranian

jolid (-295 K )

w

1219 I225 I248 I308 1381 -1659

2170 2199 2204 2212 -2230 2239 2250

/ 101.25 / December 5, 1979

vs

2 2

0.22 0.19

+ +

13a.13b 3,10b I

See footnote ( I . Table I . " See footnote h , Table I . ' (818). I n CHCIj solution. ('See footnoted. Table I . "See footnote e , Table I .

ds. N M R showed that the deuterium content is 96 f 1% of the total [D HI. I f the figure is 96%, and if the distribution is statistical, then there is 72% dg, 24% d7, and 4% dg (not all of which is s y m - d g ) . The spectrum of dg does show a considerable amount of isotopic impurity. This not only gives many extraneous bands; it also dilutes the dx and makes many of its

+

bands appear to be very weak. Evidence for isotopic impurity in dx consists of the following: (a) Bands which appear in both the infrared and Raman spectra (agreeing within 3 cm-I) (not permitted for oh or Sg symmetry except by accident). Examples are 638, 7 1 1, 768, 924,960, 1005, 1 156, 2052,2975, and 2993 cm-I. We do not

Miller et al.

7449


- * .

-' + I

'kR

I .

c

__ *

I

- r

3600 3 2 0 0

I

"

I

2800 2400

_ - ~- _..

I I 2000 1 8 0 0

*

I

f

1600

CM"

- - I

1200

"

-

---a-

I

I

I

I

I

1000

800

600

400

200

0

I

t I

3600 3200 2800 2 4 0 0

2000

I

"

1800 1600

I

CM"

1200 lo00

800

600

400

1

200

7

0

Figure 2. Spectra o f cubane. (There is a 2X scale change at 2000 cm-I.) Upper, infrared of solid at -100 K ( 1 -2 cn1-l slits): ( A ) absorption by water on cell windows; (B) absorption by KBr windows; (E) discontinuity due to grating change. LoNer. Rainan of solid at room temperature, 4880-A excitation, 5-cm-' slits; (C) Hg line from room lighting; (D) bands due to glass o f sample tube.

attribute 686 (I) and 684 (R) to d7 because each is very intense. The infrared band is assigned to an allowed flu fundamental. Also the I R and Raman values in CC14 solution differ by 15 cm-I. (b) Weak bands which appear a few cm-I higher than stronger bands of dg. The former may be due to d7. Examples are 532,674, and 1032 cm-I. (c) Some infrared bands which appear in both solid and solution. Assuming that the effective symmetry in solution is oh, only modes of flu symmetry are permitted. The three flu modes are easily identified (see later). Other infrared bands in solution which cannot be explained as Flu combination tones are probably due to d7. Examples are 71 1,768,791, 1156, and I185 cm-I. Two of the above frequencies will actually be assigned to dg fundamentals later in spite of the suspicion that they are due to d , (924 and 960 cm-I). The Raman bands of ds in solution at 570 and 606 cm-' are attributed to an impurity because they are highly polarized. For dg there are only two polarized fundamentals, and they are certainly 956 and 2259 cm-l. There is no way that totally symmetric combination tones can be obtained at 570 and 606 cm-I. These bands must therefore arise from some extraneous substance. Furthermore, a Raman band was observed a t 570 cm-' in the CC14 solution of every sample of every cubane that we have examined in this work. (This was not true for the solids, however.) For dg, the intensity of the 570-cm-' band in

solution increased with time, further suggesting that it was due to a chemical impurity. Finally, the 448-cm-1 infrared band of d8 is attributed to an impurity because there is no reasonable corresponding band in any of the other cubanes. Its counterpart in do must not be greater than 448 X 1.35 (the maximum isotopic shift ratio) = 605. The only bands between 448 and 605 cm-l in all the other cubanes can be nicely accounted for in other ways. d1. N M R indicated the isotopic labeling to be 99 f 1% complete.6 The Raman band at 1002 cm-' could be due to do, but if so it seems to also coincide with another mode. This will be discussed later under "Assignments for d l " . There are no other places in the spectrum where one can get a sensitive test for do impurity in d l . d2. N M R indicated the deuterium content a t the labeled positions to be 99 f The spectrum of dl provides a useful check on the purity of d l . For example, thc very strong Raman-active band of each compound near 1000 cm-I, due to the "cube breathing" mode, gives evidence in dz for some d l (994 cm-!) and a little do (1001 cm-I). Infrared-Raman coincidences should not occur in d l except by chance, but several are observed (agreement within 3 cm-I). Two of these are attributed to dl impurity: 724 and 890 cm-I. These bands are a t least moderately strong in d l , and for it the coincidence is allowed.

7450


3600 3200

2800

2400

2000

1600

1800

/ 101:25 / December 5. 1979

CM-'

1200

1000

800

600

400

200

0

CY-'

1200

1000

800

600

400

200

0

Figure 3. Spectra of sj,m-cubane-dz.See Figure 2 for full caption

Table V i . Correlation of the Vibrations"

Table VII. Data for Calculating Product Rule Ratios"

-

A . On Deutcrium Substitution in the Free Molecule

Oh illF

DM

----t

+ fZg

21

+ + f?u a?g + f l , e, + f,, + f Q SIu

alu

C"

C'31

3 l U

a?

a2J

+ fl" + flu

e, cg

1

e

B. On Crystallization 01'Cubane-do and -dg mol sym Factor group 01,

+

Sh

('c'3i)

"R = Raman ilctivc; I = infrared active; - = forbidden; p = pol ; ~r i7ed. db. N MR showed the deuterium content at the labeled positions to be 96 f 2%.6 The spectra show considerable evidence for isotopic impurity, viz.: (a) Several strong bands assigned as fundamentals for d b have weaker satellite bands a few

cornpd

M

I;

I,,,

cubane-do sym-cubane-d? sym-cu bane-db cubanc-dx

104. I5 106.17

146.6 146.6 177.6 177.6

146.6 158.4 166.1 177.6

110.19 112.21

I' M = molecular weight: 1 = moment of inertia (in ainu A?). r(C-C) = 1.551 A; r ( C - H ) and r(C-D) = I .06 A.

wavenumbers higher which are assigned to dg. The best example is the very strong Raman cube breathing mode at 967 cm-l, which has highly polarized satellite bands a t 971 and 978 cm-' that are attributed to dS and dq, respectively. Other examples are 7 16 and 992 cm-I. (b) Several bands which are observed in both the infrared and Raman spectra are attributed to d5 (7 16, 847, 1 184 cm-I).

Assignments for the g Modes of do and d8 Now having removed a t least some of the extraneous features from the data, we are ready to start on the assignments. The g modes for do, d ~d g, , and d8 will be considered first, followed by their u modes. Since dl does not have a center of symmetry, it will be postponed until last. The assignments are included in Tables I-V, and are summarized in Table IX. i n the discussion the frequencies quoted will usually be those for the solid because many frequencies do not appear i n solution, especially i n the infrared spectra.

Miller et al.

/

Vibrational Spectra of Cubane

745 1

Table VIII. Theoretical vs. Observed Product Rule Ratios

for the Cubunes

(T's)

Oh Species

ale?

e,

f l &I

f?g

2?U

e,

flu

f?u

1.414 1.390

1.414 1.406

1.285 1.278

2.000 1.912

1.414 1.383

1.414 1.404

1.927 1.877

1.414 1.379

isotopic pair tl0/dx theor obsd

D3d

a 29

alg

d&

2

d$dh rl?/d6

dddx dc,/dx

I .ooo

1.414 1.389 2.000 1.949 1.414 1.404 2.000 1.913 1.414 1.363

t h eor

obsd theor obsd t heor obsd theor obsd theor obsd

Species e, 1.361 I .345 2.658 2.577 1.953 1.915 2.67 I 2.555 1.367 1.334

1 .ooo 1.285 1.278 1.285 1.278 1.285 1.278 1 .ooo

1 .ooo

q

alu

a2U

eu

1.000 1.002 1.414 1.375 1.414 1.371 1.414 1.376

1.401 I .37 1 1.944 1.912 1.388 1.394 1.945 1.894 1.401 1.359

1.401 1.378 2.750 2.690 1.963 1.952 2.75 I 2.637 1.401 I .35 1

I.000 1.003

q

C U BAN Ed6 INFRARED SOLID

I

I

3600 3200 I 1

I

2800 I

i 2400

' I

-100K

I

I

I

I

2000

1800

1600

I

I

I

CM-' I

I

I

I

I

I

I

1200

1000

800

600

400

200

I

I

I

600

400

I

.

I

-

4

I

RAMAN, 4000 A

'

4

2 .

i?

cn

-4 800

200

0

Figure 4. Spectra of sym-cubane-ds. See Figure 2 for full caption.

+

For oh symmetry the g fundamentals are 2alg(R,p) 2eg(R) I f , , + 4f2g(R). A. g Modes for do. It is simplest to start with do because one does not have to worry about incomplete deuteration for it. It does have I-2% of an unknown chemical impurity which may be responsible for a few weak bands that we cannot explain any other way. We reiterate that the solution follows oh selection rules, and the solid follows Sg. By examining Table VIB one sees that the g modes for do and dg can, in principle, be sorted

+

out in the following way: aig bands are polarized in solution; f i g bands are forbidden in solution but allowed in the crystal: bands are allowed in both, and give doublets in the crystal: eg bands are allowed in both, but give singlets in the crystal. 1. ale Depolarization ratios and intensities clearly indicate that these two fundamentals are at 2995 and 1002 cm-l. Note that because the molecule is cubic, p should be zero, and that it is so within experimental error. 2. fl,. There is only one mode in this species, a C-H bend.

74 52

L3600 3200


2000 2400

2000 1000

1600

CM"

1200

lo00

800

/

101:25

600

/ December 5,1979

400

200

Figure 5. Spectra of cubane-ds. See Figure 2 for full caption.

It is forbidden in solution but allowed in the crystal. There is only one candidate: the weak band a t 1130 cm-I. Although it should be a doublet in the crystal, it is not. The assignment will be verified by d6 and dg results to be given later. 3. fZ8..These four fundamentals should occur in both solution and solid, and be doublets in the latter. The doublet property suggests 2970, 1182, and 821 cm-" (all solution values). The fourth one is not obvious and we defer it for a bit. 4. eg. These two modes are allowed in both solution and solid, but are singlets in the latter. The extremely intense 912-cm-' band is a clear choice, but the second one is not obvious. There are only five candidates for the two missing g fundamentals: 665, possibly 827 (the separation between 8 15 and 827 is larger than for any other doublet in do or ds), -1026, 1083, and -1223 cm-l. We will turn to the deuterium derivatives for help in making the selection. B. g modes for dg. 1. alg. Polarization and intensity clearly indicate that these two fundamentals are a t 2259 and 956 cm-l. The product rule ratio is satisfactory (Table VIII). Vibration u2, the cube breathing mode, can easily be located in all the intermediate deuterated compounds except d3, because it decreases linearly by 5.75 cm-l per D atom (Table X A ) . Adding one atomic mass unit by substituting a I3C for a I2C atom has exactly the same effect as substituting a D for a H atom, viz., v2 is lowered by about 6 cm-l. Thus in do u2 is lowered from 1002 to 996 cm-l in the '3C compound, and in d8 from 956 to 950 cm-'. The concentration of molecules

containing one I3C atom is 8.2% of the total, so the intensities are reasonable. 2. fl,. This one mode is expected in the solid only. Since the mode is at 1 130 cm-' in do, the product rule unequivocally selects 884 cm-' in do. This choice will be verified later by the data for d6. 3. fZg. These modes should give doublets in the crystal. Possibilities are 71 5 (the 710 component is also in the infrared, but the two Raman bands are quite intense for d7 impurity), 1027, and 2232 cm-l. Again one is missing. It will turn out, too, that we shall later be forced to assign 1027 cm-l to eg in spite of its being a doublet. Therefore two more f2g fundamentals are needed. 4. eg. These modes are permitted in both solution and crystal, and are singlets in the crystal. The very strong 684-cm-I band is an obvious choice. It seems to be the counterpart of 9 12 cm-] in do on the basis of (a) high intensity, (b) the unusually large frequency shift between crystal and solution (1 3 cm-l for do and 15 cm-I for d8). This mode can easily be traced through the intermediate compounds (Table XB). W e are therefore confident that 912 cm-I in do should be paired with 684 cm-l in dg. The large decrease shows that they belong to a C-H bend. This leaves an eg and one or two f2g fundamentals to be identified in both do and d8.It is helpful now to look at the data for d l , d2. and dg. C. Help from the Raman Bands of d l , d2, and d g . The

0

Miller et al.


7453

Table IX. Assignments for the Fundamental Vibrations of Cubane-do, -d2, -d6, and -dxh D3d

o h

species

species

3 1 ~ R(P)

a i g R(P) f2g

3 ?&

f 1&

eg R

e8

R

R

flg

f2g

R

azu

I

e, flu

1

2 13a 14a 15a 16a

1

f 2u

schematic descripn

do

C-H str C-C str C-H str

C-H bend C-C str C C, def

I

~ym-dz

sym-ds

dx

2995 I002 2970 I182 82 1 665

2993 99 I 2237 I168 821 65 1

2254 967 2978 I083 725 579

2259 956 2232 1072 715 586

9a

C-H bend

I I30

(1130)

884

884

5 6 9b 13b 14b 15b 16b

C-C C-H C-H C-H

1083 912 I I30 2970 1182 821 665

1016 875 2970 I174 738 632

1035" 704" 98Sa 2229 758" 598

IO27 684 884 2232 1072 715 586

1036 8 29

I036 -827

927 674

924 (674)

[--29781 839 2978 1230 853

2968 838 2240 1201 85 1

2242 807 2974 I100 690

[-22391 807 2240 1083 686

I151 617 2978 i 230 853 1036 829

1109 574 2977 1222 844 995 71 I

1014 538 2236 I164 786 975 65 1

960 527 2240 1083 686 924 (674)

17a

f2u

flu

no.

str bend bend str

C-H bend C-C str C C3 def

18a

Cbend c-cH str

3 4 12a

C-H str C C i def C-H str C-C str C-H bend

7 8 10b Ilb 12b 17b 18b

C-H C-C3 bend def C-H str C-C str C-H bend C-C str C-H bend

1 Oa 1la

I I

I 1

1100

1145

To satisfy the noncrossing rule, 1035 and 985 cm-' in dg should be interchanged, and so should 704 and 758 cm-l. See text. Values in parentheses were estimated From the product rule; values in brackets were estimated from the resonance pair. 'I

Table X. Some Details for Several Fundamentals vibration no. A . V ? (obsd) I)?

B.

I002

996 996 898

912 13

(solid) - V 6 (soh)

c. V l h

665 ~

(I

di

(estd)

Uh

Vh

do

~

11

-659 sh 652 dD

d3

d4

ds

985

978" 979

9710 973 716"

d2

99 1 99 1 875 9 651 p 632 d p

d6 967 968 704 8 598 dp 579 p

di

dx

960h 962

956 684 15

586

~~~

From isotopic impurity in the d g sample, See Table IV. From isotopic impurity in the dg sample. See Table I I

665-cm-' band of do can be traced through the intermediate compounds to 586 cm-I in dg as shown in Table XC. In d l , d2. and d6 it gives two bands, and in d2 and d6 one of each pair is polarized. This is just what is expected if, and only if, 665 cm-l is an f2g mode, for on going from oh to D 3 d symmetry an fzg mode splits into al,(p) and e,(dp). An eg mode does not give two components when the symmetry is lowered to C3c ( d l ) or D 3 d (dz and d6). Therefore we have good evidence that 665 (do) and 586 cm-' (dg) are f2, modes, and since they are the lowest Raman bands they must be V l 6 . This is nominally a cube deformation, and the numerical value seems reasonable. D. Completing fzg and eg. W e now know all four f2g fundamentals for do and three of them for dg. The product rule indicates that the fourth in dg is about 1050 cm-l. There is nothing there, but this is roughly midway between the strong depolarized Raman lines a t 1072 (singlet) and 1027 cm-' (doublet). One would like to use 1027 cm-l because it is a doublet in the crystal, but it gives a product rule ratio of 1.996, which is too high compared to the theoretical 2.000. We therefore adopt 1072 cm-' (which gives a ratio of 1.912, too

low), and assign 1027 cm-' to us (e,) of dg. However, an eg mode should not give a doublet, so we suggest that the 1032cm-l component, which is much weaker, is due to d7. An alternative possibility is that 1027 and 1072 cm-' in dg may be a Fermi resonance pair. Their average is 1050 cm-l. There is a very weak infrared band at 527 cm-' which will later be assigned to an e, fundamental. It is possible that 2 X 527 = 1054 cm-I (Alg Eg) could interact with the missing eg fundamental at about 1050 cm-' to give the two observed bands. However. it is an f2, fundamental which the product rule suggests is about 1050cm-l, and it would not interact with this overtone. Consequently we reject this possibility. Turning now to the eg modes, we have assigned 9 I 2 cm-' in do and 1027 and 684 cm-l in dg. The product rule suggests that the missing one in do is about 1070 crn-'. There is a weak band at 1083 cm-' which we adopt. I f we had interchanged the assignments of 1072 and 1027 cm-I (putting 1072 cm-' in e, and 1027 cm-I in fzs), we would have had two problems: (a) a high T for f2g (1.996) and (b) finding a satisfactory frequency for us of do. The product

+

7454


rule indicates that it should be around 1120 cm-I. The closest Raman bands are 1130 cm-I, which is surely 4,and 1083 cm-I. The latter gives a 7 for eg of 1.347, which is too low compared to T(theor) = 1.414. More important is that there are no reasonable Raman frequencies for U S in d2 and d6 between 1083 (do) and 1072 cm-' (ds).Hence we reject this alternative too. This completes the g fundamentals for do and dg.We now turn to those for d2 and d6.

g Modes for d2 and d6 When giving wavenumbers for the four compounds do,d2. dg, and dg,we will for brevity list them in that order without specifying the compounds explicitly. For example, u t is 1002, 991,967, and 956 cm-I. Vibrations u2, U6, !-'16a9 and U16b have already been traced through the series (see Table X). alg for D3d. This species contains two C-H stretches. One of them involves the stretching of the H's (or D's) on the C3 axis. Its frequency will therefore be high for do,low for d2,high for dg,and low for ds.We arbitrarily designate this one as ~ 1 3 The other C-H stretch ( V I )will then be high-high-low-low. The observed depolarizations make it easy to select these. ul is 2995-2993-2254-2259, and u 1 3 is~ 2970-2237-2978-2232 cm-l. It is also easy to trace ~ 1 and 4 ~ 1 through 5 ~ the series because they are polarized in d2 and dg. Values for U14a are 1182-1 168-1083-1072, and for ~ 1 are 5 821-821-725-715 ~ cm-I. The d2 band a t 821 cm-' is actually depolarized, but this is permissible and the numerical value is appropriate. a2g for D3d. There is only one mode in this species (U9a). It is forbidden in solution, but is allowed in the crystal. Since it involves a C-H bend in which H's on the C3 axis do not participate, its frequency should be the same for do and d2,and also for d6 and dg.W e have already assigned it to 1 130 cm-' in do and 884 cm-' in dg. In d2 there is a band a t 1133 cm-I, but it is present in both solution and solid and it is polarized. It therefore cannot be due solely to uga. We do not know its origin. However, dl has a band a t 1132 cm-' in the Raman spectrum of the solid which adds support to the assignment. In dg there is a very weak band in the solid a t 884 cm-I. This also is helpful confirmation of the assignment. eg modes for D3d. Vibrations u6 and ul6b have already been identified (Table X). The C-H stretch V 1 3 b is straightforward. It will be high-high-low-low, and the values 2970-29702229-2232 cm-l seem reliable. For ul4b the choices 11821 174- 1 145- IO72 cm-I are fairly obvious. There are three nominal C-H bends in this species. One of them ( u g ) has been identified. One of the other two is a bend of the C-H's that lie on the C3 axis, so in zero approximation it should go high-low-high-low. For V15b we select the values 821 -738-758-71 5 cm-l for the following reasons. In d2 the only candidates are 821 and 738 cm-I. Since 821 cm-' has already been used for ulsa, we try 738 cm-' for Ulsb. In d6 there are six bands between 82 1 and 7 15 cm-I. The strongest by far is 758 cm-l, so we shall try it. The above sequence goes high-low-high-low, so it may have considerable contribution from the axial C-H bend. For u5 three values are easily selected: 1083-?-1035-1027 cm-I. In d2 nothing was observed between 1100 and 1016 cm-I. This may be a case of first-order interaction in d2,with u5 being pushed down to 1016 cm-' and v 9 b up to 1100 cm-I. We adopt these two assignments. In d6 u9b should be higher than 884 cm-I, the value in dg. The next higher depolarized band is 985 cm-I, which we use. This completes the assignments of the g modes for all four molecules. The product rule ratios for all the various isotopic pairs are given in Table VIII, and are generally satisfactory.

/

101:25

/ December 5, 1979

In species eg there are two crossings i n going from d2 to d6. Vibration v9b is higher than u5 in d2 and lower than u5 in dg. Similarly Ug is higher than V 1 5 b in d2 and lower than VISb in d6. Although in principle this cannot occur because of the noncrossing rule, and we should interchange the designations in d6 to remove it, in fact it makes no difference. There are advantages to the present arrangement because it is easier to follow a mode through the sequence of molecules. For example, for V g of dg, 704 cm-' was chosen rather than 758 cm-I because of its greater intensity and greater solid-solution frequency shift. However, the two have mixed i n dg and share these identifying characteristics to some extent. Thus A; is 8 cm-' for 704 cm-I and 5 cm-I for 758 cm-I, whereas for 684 cm-' in dg it is 15 cm-l. The noncrossing rule does not hold in going from d6 to dg if the two modes that cross are in different species in dg.

~ .

Remaining Raman Bands Explanations for the remaining Raman bands are included in Tables I-IV. Only binary sum tones were used; ternary combinations were not tried. Difference tones are improbable because even the lowest fundamentals are fairly high. (Even for dg all the fundamentals are greater than 525 cm-I). Furthermore, the infrared spectra of the solids were obtained a t -I00 K, making difference tones originating from u levels highly unlikely. All the sum tones which are given are symmetry allowed for our assignments. In many cases there are additional explanations which could be given but which we have not bothered to list. A few comments will be made about each molecule. do. There are only three Raman bands of do which cannot be explained: 2154,2205, and 2328 cm-I. Since they are all very weak, they do not offer an obstacle. ds. Many of the remaining bands may be due to d7.The only one we wish to comment on is 2052 cm-I, for which p = 0.60. For ds p should be either 0 or 0.75. W e therefore believe that two bands are superimposed here: the overtone of 1027 cm-I with p = 0 and a band of d7 with p = 0.75. d2. The most serious unanswered questions are how to explain 2985 (intensity 180) and 2246 cm-' (intensity 50). Neither is due to dl,for we know its spectrum. dg. The worst problems here are presented by 738 (intensity 35), 847 (35), and 1029 cm-' ( 1 5). The first two may be due to d5. On the whole we are well satisfied with the assignments for the g modes. We turn now to those for the u fundamentals. Assignments for the u Modes of do and ds For o h symmetry the u fundamentals are 2a2, 2e, 3fl,(I) 2f2,. Only the three flu modes are active. All other u fundamentals are forbidden for o h , but allowed in the crystal (Table VIB). W e assume that the crystal structure of the samples at -I00 K used for the infrared measurements is the same as the crystal structure of the solid a t room temperature, so that the s6 factor group applies also for the infrared data. This is a key assumption. We have no proof that it is correct except that it seems to work. It is going to be more difficult to assign the u modes than the g ones because most of the u modes are forbidden for o h symmetry. Even when allowed in the crystal by the s6 symmetry, they will probably be weak. Also there is no experimental feature to separate a2, and e, vibrations (Table VIB). flu. These three fundamentals are the only u ones allowed for o h symmetry. They are therefore expected to be relatively intense in solution as well as for the solid. In do they are easily identified as 2978, 1230, and 853 cm-I. In dg 2240 and 686 cm-I are surely two of them. Candidates for the third are 1 156

+

+

+

Miller et al.


and 1083 cm-I, and the product rule shows that 1083 cm-' is the correct choice. These modes should be doublets in the crystal, and all of them are. (See below concerning the C-H stretch.) C-H Stretches. There are only two u-type C-H stretches for oh symmetry: v3 in a2, and V I O in f l u . They present an interesting situation. In do only one C-H stretch is observed in solution as expected (2977 cm-I), but there are three in the solid: 2965 (s), 2978 (vs), and 2992 cm-l (vs). It is impossible to account for the third one as a binary sum tone, so another explanation is needed. We recall that, when the symmetry is changed from oh to Sh. f l u modes split into a, and e, components and a2, modes go to a, (Table VIB). Thus in the crystal three frequencies are allowed. We believe that the e, component is 2978 cm-', close to the solution value of 2977 cm-'. We further believe that the two a, components have interacted to give 2965 and 2992 cm-I. This would explain why no one of the three is weak; the a, mode derived from the Oh-forbidden a2, has picked up intensity from the a, mode derived from the Oh-allowed f l u . It also explains why the separations from 2978 cm-l are nearly equal ( 1 5 and 14 cm-I), and rather large compared to our other doublets. In Table I we have designated these a, bands 2965 and 2992 cm-' as "3 and I O(a,)" to imply that each is a mixture. It then appears that the unperturbed a, fundamental would have been about 2978 cm-I, almost coincident with the e, component. In dg the situation is analogous. There is one band in solution (2238 cm-I) but three in the solid: 2229 (m), 2240 (vs), and 2248 cm-' (m). Again it seems that the e, component is 2240 cm-I, nearly coincident with the solution value, whereas the a, components have interacted and split to give 2229 and 2248 cm-l. We take the unperturbed value to be about 2239 cm-I and use this for v3. us (e,,).In do, d l , d2, dg, and d8 there are bands at 61 7, 590, 574, 538, and 527 cm-I, respectively, which cannot be ignored. Although they are weak, they are in every compound and are well isolated from other bands. In do 6 17 cm-' is so useful in explaining sum tones that this alone indicates it to be a fundamental. Since these are the lowest observed bands in each of the compounds, they are probably either v4 or vg. These are nominally cube deformations, and are expected to be the lowest of the fundamentals. Species a2, of oh has only two fundamentals: a C-H stretch which we have just assigned for both do and dg. and a cube deformation. The product rule can therefore be used to see whether 617 and 527 cm-l belong to v4 of this species. It is quickly found that they do not. Therefore 61 7 and 527 cm-I probably belong to the other nominal cube deformation, V g of e,. This gets some further support from the following observations. ( I ) In do 61 7 cm-l is not a doublet in the solid. This is consistent with not being an f mode (although by no means proof of it). In d8 527 cm-l is a doublet, but the higher component (532 cm-I) is much weaker and can be due to d7. (2) The bands of d2 (574 cm-I) and d6 (538 cm-I) are singlets in the solid. If they had originated from f2, in do, they should be pairs of bands. Therefore they seem to have originated from a2, or e, i n do. Since we have just seen that the product rule eliminates a2,, the only possibility left is e,. We therefore assign 6 17 and 527 cm-' to vg. fi,, Modes ( v i 7 and V I S ) . In do doublets in the solid are significant. (Unfortunately this is not necessarily true fords because of the isotopic impurity.) Species f l u and f2, of oh should give doublets. Since we know the f l u assignments, we can look for candidates for the two fz, modes of do which are (a) doublets in the solid and (b) absent in solution. Possibilities are 829 (m), 1036 (m), and 1 1 5 1 cm-l (w). In d2 and d6 the f2" modes split into two components because of lowering of the symmetry. W e have designated these a and b. Consider the component that is in a', of D3d. We note that

7455 the product rule ratio for do/dz is I , and also for dg/dg. Consequently one looks in the infrared spectrum of d2 to see whether any of the above three bands is present there too. Two -827 (sh) and 1036 cm-l (w, solid only). This gives us the assignments for V 1 7 a and v18a in do and d2. Next we look in dg and d8 for bands which ( I ) have the same wavenumbers i n these two compounds (to give 7 = I ) and (2) satisfy the product rule for do/dg. There is only one pair with the same wavenumbers in dg and dg: 927 (vw) and 924 cm-l (vw). Unfortunately, the Raman spectrum of dg has a band a t 923 cm-I, so this could be due to d7. However, let us try it. We then have 1036 and 829 cm-I in do, and 924 and x cm-l in ds. By using the product rule, x is estimated to be 670 cm-I. A weak band here might be hidden under the very strong one at 686 cm-l. However, in dg there is no interference, and there is a band at 674 cm-l, very weak and in the solid only. Therefore we adopt 927 and 674 cm-' for "178 and visa in d6, and 924 and 674 cm-I (postulated) in dg. Both assignments for dg are uncertain. az,, Modes ( v 3 and v4). We already know v3 in both do and dg. The product rule then gives the ratio V4(dO)/V4(dg) N I .045. One can therefore search the spectra for bands giving this ratio. They should be singlets i n the solid and missing in solution. The bands may be weak in the solid because they are made allowed only by the crystal symmetry. Furthermore, v 4 is nominally a CC3 deformation so it is expected to be < 1000 cm-I. An examination of the infrared spectra of do and dg gives several possibilities. An additional restriction is that one ought to find the mode in dz and dg also. A suitable choice seems to be 839 (m)-838 (s)-807 (m)-807 cm-l (vvw). This gives a satisfactory 7 for do/dg (1.383 vs. 1.414). It also follows the expected selection rules. In solution v4 is forbidden for do and dg, but is allowed for d2 and dg. The observations for solution are absent, s, w, absent. e, Modes (v7 and vs). We already know v g in both do and dg. The product rule then gives the ratio v 7 ( d 0 ) / ~ 7 ( d g=) I . 185. These modes are forbidden in solution and should be singlets in the solid. The only observed bands which satisfy these requirements are 1144 or 1 1 51 in do and 960 cm-' in dg. Unfortunately, 1 15 1 cm-I is a doublet, but it is more intense than 1 144 cm-' and more useful in explaining sum tones so we use it in spite of its weaker companion at 1153 cm-I. In dg 960 cm-I is also observed in the Raman spectrum (intensity 140, p = 0.00). The Raman band is assigned as v 2 for d7. This mode of d7 is also infrared allowed, and this may account for some of the observed infrared intensity. However, by analogy with the infrared and Raman intensities of v 2 in d l , where the symmetry is the same as for d7, the infrared intensity of 960 cm-l seems to have another contribution. We therefore believe that 960 cm-' is also v7 of dg. u Modes for d2 and d6

These have already been selected for (quite certain), ~ 1 and v l g a (from 7 = I ) , and v4. There are three C-H stretches: two in a2, of D3d (v3 and vloa) and one in e, (VlOb). ,411 are a\lowed for D3d. One of the a2, modes involves stretching of the C-H or C-D groups lying on the C3 axis. It will therefore be high-low-high-low. We arbitrarily designate this one vloa. The other two C-H stretches will be high-high-low-low. The following assignments seem reasonable: for v3, [--297812968-2242-[-22391; for vlpa, 2978-2240-2974-2240; for VlOb, 2978-2977-2236-2240 Cm-'. Selection of the remaining u modes for d2 and dg is a matter of looking for bands with reasonable wavenumbers between those of do and dg, and then checking with the product rule. Given the assignments for do and dg, there is not a great deal of choice. Our values are given in Table IX, but do not warrant discussion.

7

~

7456


Table XI. Assignments for the Fundamental Vibrations of Cubane-dl Compared w i t h -do and -df

assignment

c',,. sym

snccies sel rules ~

no.

~~~

;)I

R(pL I

I 2 1321 14a

R(dp), I

~

2993 996 2969 I I74 816 -659 2977 844 2240 1219 853

2993 99 1 2237 I168 821 65 I 2968 838 2240 1201 85 I

9rl 17a I 8a

1 I30

1132 1036 834

(1130) I036 -827

5 6 9b 13b 14b

I083 912 I I30 2970 1182 82 1 665

I062 898

1016 875 I100 2970 I I74 738 632 I109 574 2977 I222 844 995 71 I

I6a 3 4 1 Oa I la 12a 'I 2

d,

di

2995 1002 2970 I182 821 665 [--29781 839 2978 1230 853

15a

L'

dn ~~~~

I5b 16b 7 8 I Ob IIb 12b 17b I 8b

I036 829

I151 617 2978 I230 853 1036 829

1101

(29691 I179 826 652 I I45 590 (2977) 1225 847 I002 722

[' Braces indicate value used twice. See footnote b, Table IX. It may be noted that u1gb is 651 cm-' in dg and rises to 674 cm-l in dg.This can be rationalized as follows. The 651-cm-I value is abnormally low in d6 because V1gb has had first-order interaction with Vl2b in the same species, making the latter abnormally high a t 786 cm-I. In dg this interaction does not occur because u1gb and u l 2 b are in different species. Consequently U1gb moves up from 651 to 674 cm-I, and U12b has a 100-cm-l drop from 786 to 686 cm-I. This completes the assignments of the u modes. The product rule ratios in Table Vlll are on the whole quite good. The weakest assignments for do and d8 are (a) 1151 cm-' for do and (b) 960,924, and 674 cm-I for d8.

Remaining Infrared Bands Explanations for most of these are included in Tables I-IV. The general comments concerning remaining Raman bands apply here too. For do there are six infrared bands for which we cannot supply an explanation. The only serious problem is presented by 1235 cm-l because of its medium intensity. The other five bands are all very weak. For d8 there are a number of infrared bands for which we cannot account, but all are weak and we know that there is considerable isotopic impurity. Similarly dZ and dg do not present any serious problems. Assignments for dl Because this molecule has a different symmetry from the others, it is discussed separately. Under C30the fundamentals are 1 la1 (R,I) 3a2 I4e(R,I). Our assignments are given in Tables V and XI. The assignments for do and d2 provide a useful guide because they will bracket those for d l ; they are therefore included in Table XI. One of the C-H stretches of do will drop to about 2250 cm-l in d l . We arbitrarily call it v~o,,although it could equally well be termed ~ 1 3 The ~ . other C-H stretches are fairly obvious: V I 2993, u3 and UlOb 2977, and V13, and V13b 2969 cm-I.

+

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/ 101:25 /

December 5 , 1979

There is no doubt that u 2 is 996 cm-l. From the large solid-to-solution shift of the 898-cm-l band, this is clearly ug (Table XB). The large infrared intensities confirm 1219 and 1225 cm-' as V I l a and vi [b, and 847 and 853 cm-I as Y l 2 b and ~ 1 2 , .The reasons for these particular a-b assignments are as follows. (1) zql.The polarized Raman sum tone at 221 2 cm-' can be explained as 996 12 17 = 22 13 cm-l. Since both 996 and 22 13 cm-1 are totally symmetrical, 12 17 cm-I must be also. Therefore 12 I7 cm-l ( 1 2 I9 cm-I in the infrared) is assigned to V I l a , leaving 1225 cm-l for V I Ib. (2) v12. The Raman band a t 844 cm-' has p = 0.56. AIthough this value is possible for a C3r molecule, the deviation of dl from oh symmetry is small enough so that all the other observed p's are either 0.75 or

Vibrational spectra of cubane and four of its deuterated derivatives

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