Infrared and Raman spectra and normal co-ordinate analysis of dimethyl sulfoxide and dimethyl sulfoxide-d6

SpectrochimicaActa, lB61,Vol. 17, pp. 134 to 147. Pergamon PressLtd. Printedin Northern Ireland

Infrared and Raman spectra and normal co-ordinate analysis of dimethyl sulfoxide and dimethyl sulfoxide-d, W.

D.

HORROCKS,

JR. and F. A. COTTON

Department of Chemistry and Spectroscopy Laboratory, Massachusetts Institute of Technology Cambridge 39, Massachusetts (Receiwd 12 September 1960) Abstract-The infrared spectra from 250-4000 cm-l and the Raman spectra of dimethyl sulfoxide and dimethyl sulfoxide-d, have been determined. From these data a complete assignment-excepting only the torsional modes-has been made and substantiated by a normal co-ordinate analysis carried out using a digital computer. Valence force constants for the C,SO skeleton were calculated and compared with those of the thionyl halides. Potential energy distributions of symmetry co-ordinates among the normal co-ordinates have also been calculated. IntrodllctioIl

IN CONNECTION with a program of study in these laboratories of the ligand properties and complexes of several sulfoxides [l-4], dimethyl sulfoxide (DMSO) in particular [l-3], it became desirable to have a thorough understanding of the infrared spectrum of DMSO in order that infrared studies of its complexes [2] could be most reliably and advantageously used in deducing the structures of those complexes. The present paper reports a detailed experimental study of the infrared and Raman spectra of DMSO-&, from the results of which a complete assignment is made and a set of force constants calculated using the WILSON [5] F- and G-matrix method. The only previous vibrational study, other than cursory examinations of the infrared spectrum and a study of solvent effects on the SO stretching frequency, [6] is the Raman investigation of DMSO by VOGEL-H&JLER [7].

Experimental Chemicals Dimethyl sulfoxide was obtained from the Matheson, Coleman and Bell Co. It was dried either by distillation under reduced pressure (20-40 mm) from BaO or, according to the suggestion of SMITH and WINSTEIN [8], by passing the DMSO through a column of molecular sieves (pellets of type 4-A, Linde Air Products) and then distilling under reduced pressure from powdered type 4-A molecular sieve. DMSO was then stored in the dark, for it tends to turn slightly yellow on long F. A. COTTON and R. FRANCIS, J. Am. Chem. Sot. 82, 2986 (1960). [2] F. A. COTTON, R. FRANCIS and W. D. HORROCKS, JR., J. Phys. Chem. 64, 1534 (1960). [3] F. A. COTTONand R. FRANCIS, J. Inoy. and Nuclear Chem. In press (1961).

[l]

[4] R. FRANCIS and F. A. COTTON, J. Chem. Sot. In press (1961). [5] E. B. WILSON, JR., J. C. DECIUS and P. C. CROSS,Molecda~ Vibratio?~. McGraw-Hill, New York (1956). [6] L. S. BELLAMY, C. P. CONDUIT, R. J. PACE and R. L. WILLIAMS, Trans. Faraday Sot. 55,1677 (1959). [7] R. VOQEL-H~IOLER, Acta Phys. Awtriaca 1, 323 (1948). [S] S. SMITH and S. WINSTEIN, Tetrahedron. 8, 317 (1958); and private communication.

134

Vibrational spectra of dimethyl sulfoxide and dimethyl snlfoxide-d,

Completely

standing when exposed to light. method of COTTONet al. [9]

deuterated DMSO was prepared by the

Infrared spectra Infrared spectra of DMSO and DMSO-&, were taken in the NaCl region on a Perkin-Elmer model 21 double-beam spectrometer equipped with an NaCI prism. The spectra of the liquids were obtained as smears between N&l plates. In this region it was found possible to obtain vapor spectra using a heated lo-cm cell of a design described elsewhere [lo]. A Baird AB-2 spectrometer with KBr prism and calibrated with NH, was used to obtain the spectra of liquid samples in the 800400 cm-l region, and the Perkin-Elmer 21 equipped with a CsBr prism (through the courtesy of Prof. M. K. WILSON, Tufts University) was used to obtain the spectra of the ligands from 450 to 250 cm-l. For practical reasons it was not possible to record gas spectra in the KBr and CsBr regions. The results are collected in Tables 1 and 2 and in Fig. 1. Table 1. Infrared data for dimethyl sulfoxide

-

Calculated (cm-‘)

Observed (cm-l)

Assignment

2973 m 2908 m 2303 w 2183 w 1455 m 1440 ms 1419 m 1405 m 1319 w sh 1304 m 1287 w 1111 s sh 1102 vs 1094 s sh 1016 m 1006 m 929 w 915 w 898 VW 689 m 672 m 382 s liq. 335 m sh, liq. 333 s liq. (308 m Raman only) not observed All are vapor phase values excep

2995,2991,2995, 2994

VlYV-2' v149v15

2934,2935

v3*%3

2 x v, 1449 1443 1418 1403 1328 1302

%7 V13 v4 v5 VlB V6

R-Branch 1109 Pr;;ranch 1034 1008 942 914

%I

vtl %l v3

694 688 378

%3 VlO Vll

336 305

%3 Vl3 Vl39%4

hose marked “liq.”

-

[9] F. A. COTTON,J. H. FASSNACF~T, W. D. HOFCROCKS, JB. end N. A. NELSON, J. Chun. Sot. 4138 (1959). [IO] F. A. COTTON, Modwta Coo~&mtim C&&try (Edited by J. LEWIS and R. G. WILKINS) Fig. 5. p. 320. Interscience, New York (1960).

135

Table 2. Infrared data for dimethvl sulfoxide-d, Calculated (cm-l)

Observed (cm-l)

Assignment

I-

2238,2231,

2250 m 2185 vw 2133 w 1096 vs 1084 s sh 1043 m 1025 m 1015 m 824m sh 814 m 803 m sh 756m sh 750 m 619 m liq. 611 m liq. (555 VW Raman only) 340 s liq. 307 s liq. (262 m Raman only) not observed

2235,223l

v1'v2'v14'y15

2 x v,

2112,2112

'3"16

1083 1080

y7 v19

1040,1038 1020,1034

'6"17 V4'VlS

1014

v5

803 801 745 724 611 600

V6 y20 y9 Y21 v22 VlO V6--y12

344 310 264

'23 y12 V13'v24

All are vapor phase values excep

hose marked “liq.”

)yyTyj '1500

1300

1100

900

750

2500

2000

800

700

600

500

400

300

200

so0

700

600

500

400

300

200

3000

_:I1

Frequency,

cm-’

Fig. 1. The infrared spectra of dimethyl sulfoxide (DMSO) and fully deuterated dimethyl sulfoxide (DMSO-d,).

136

Vibrational

spectra of dimethyl sulfoxide and dimethyl sulfoxide-d,

Raman spectra Raman spectra of both DMSO and DMSO-dE, were obtained on liquid samples of approximately 15 ml using the mercury 4358 A line for excitation. The excitation unit has been well described elsewhere [ll]. Of the three concentric glass tanks surrounding the sample tubes, the outermost was used for circulating cooling water, the next contained an ethanolic solution of Cyasorb UV24 (American Cyanamid Co.) which, after adjustment of the concentration, effectively removed radiation of frequency higher than 4358 A, and the innermost tank contained a saturated aqueous solution of praseodymium chloride to cut down the background in the region of the low-lying Stokes lines. Finally sample tubes were wrapped in cellophane impregnated with ethyl violet to remove lower frequency radiation, especially the mercury 5461 A line. In conjunction with this, a Zeiss three-prism, constant-deviation spectroscope [12] was used. Spectra were recorded on Kodak Spectroscopic Plates of type 103a-0. Best results were obtained using a @12-mm slit width and a lo-hr exposure. The plates were calibrated by juxtaposing an iron-arc spectrum on the plate. The intensities of the Raman lines were estimated by obtaining the trace of the plates on a Leeds and Northrup Co. recording microphotometer. Qualitative depolarization measurements were made by the double exposure method of CRAWFORD and HORWITZ. The frequencies, relative intensities and polarization data of the observed Raman shifts for DMSO and DMSO-d, are given in Table 3, along with the results of VOGELHAGGLER.It will be seen that her data and ours are in excellent agreement except that the weak line she reports at 1141 cm-l was not found by us. Table

3. Rarnan

data

for dimethyl DMSO

sulfoxide

(DMSO)

and dimethyl

sulfoxide-d,

(cm-l) DMSO-d,

Present

work*

308 m 333s 383 m 668 s 700s 952 w 1042s

d d p p d d p

1420s 2915s 3000 s

d p d

305 (5) 334 384 668 698 952 1042 1142 1421 2915 3001

(6) (4) (10) (9) (2) (5,b,dou? (2) (7) (7) (3)

m = medium,

262 ms 306 s 341 m 555 VW 614 vs,b 760m 816vw 1015s 1048 s,sh 2006 VW 2135s 2255s

(0.83) (063)

)

-

(Of13) (0.65) (0.57) (0.50) (OZ3)

d d p p d d p p d p p d

s = strong,

v = very,

b = broad, p = polarized, d = depolarized. t b = broad, dou = doubled, p = polarized, - = no estimate of polarization given. The first column of numbers (integers) represent relative intensities and the numbers in the second column are depolarization ratios.

*

w = weak,

(cm-l)

VOGEL-H~GLER~

/

-

(DMSO-d,)

ah = shoulder,

G. R. HARRISON, R. C. LORD and J. R. LOOFBOUROW, Practical Spectroscopy Fig. 18.3, p. 513. Prentice-Hall, New York (1948). [12] G. R. HARRISON, R. C. LORD and J. R. LOOFBOUROW, Practical Spectroscopy p. 57. Prentice-Hall, New York (1948). [ll]

137

W. D. HORROCICS, JR. and F. A.

COTTON

Table 4. Symmetry co-ordinates for dimethyl sulfoxide A’

s, = 12-l/s(2r, - r2 - rs + 2r, - r5 - r,) 8, = )(rs - r3 + r5 - rs) S, = 6-lj2(r, + r2 + r3 + T4 + r5 + rs) 8, = 12-1’2(2y, - y2 - 73 + 2Y4 - Y5 - l's) 85 = 4cr2 73 + 75 - Y6) s, = 12-qy, + ys + y3 + 74 + Y5 + Y6 - 6, - 62 -

S, s, s, S,, S,,

A”

= = = = =

d, 12-l’2(2S, - S, - S3 + 26, - 6, - 6s) $(S, - 83 + s, - 66) 2-l12(d2 + d3) 2-112(a1 + ct2)

42

=

B

s,,

=

2-l/2(7,

S,, S,, S,, s,,

= 12-1/2(2rI - r2 - r3 - 2r4 + rs + rs) = Q(r2 - r3 - rs + rs) = 6-li2(rI + r2 + r3 - r4 - r6 - rs) = 8(Y2 - 73 - Y5 + 76) = 12-1’2(2y, - y2 - 1/3 - %'4 + Y5 + Ye)

S,,

8,, =

+

‘2)

U-1/2(yl + y2 + 73 -

I/a - 75 - I'6 - 6, - 62 - s3 + '4 + '5 + '6)

S,, =

- S, - 8, - 26, + 6, + 8s)

s,,

- 65 + 66)

s,,

S, s,

EV2(26, = #(S, - 63 = 2-l12(d2 = 2-1f2(a, = 2-1’2(9 -

63 - 64 - 65 - 63)

d,) a2) T2)

Table 5. Approximate descriptionof fundamentals A’

Degenerate C-H stretch Degenerate C-H stretch stretch v3 Symmetric C-H deformation 74 Degenerate C-H deformation v5 Degenerate C-H deformation ve Symmetric C-H v7 S-O stretch V6 Methyl rock va Methyl rock vn, Symmetric C-S stretch vn Symmetric C-S-O deformation v12 C-S-C deformation v13 Symmetric methyl torsion v14 Degenerate C-H stretch v16 Degenerate C-H stretch vn, Symmetric C-H stretch vl, Degenerate C-H deformation vu, Degenerate C-H deformation vls Symmetric C-H deformation vzOMethyl rock v21 Methyl rock v22Antisymmetric C-S stretch vss Antisymmetric C-S-O deformation v24Antisymmetric methyl torsion v1

v2

A”

138

Vibrational

spectra of dimethyl aulfoxide and dimethyl sulfoxide-d,

A normal co-ordinate analysis ~$8 carried out in order to verify the ~ign~en~ of Tables 1 and 2 and to obtain force constants for the molecule. This was done according to WILSON’SP- and #-matrix method 161; solutions of the secular equation were obtained by use of the IBM 704 electronic computer as will be described. DMSO, which has a pyrimidal structure with sulfur at the apex, contains ten atoms and therefore haa twenty-fog vibrational degrees of freedom if the methyl groups are considered not as free rotors, but as undergoing torsional vibrations. The molecule belongs to point group C, with only a plane of symmetry. This aIlows us to

Fig. 2. Internal co-ordinates for dimethyl sulfoxide. Co-ordinates in the second methyl group are r,, t6, rs, y,, ya, ys and 6,, S,, 6, in direct analagy to those shown for the first methyl group.

factor the secular equation into a 13 x 13 A’ factor and an 11 x Xl A” factor, respectively symmetric and antisymmetric to the plane of symmetry. The internal co-ordinates used are illustrated in Fig. 2. The symmetry co-ordinates which aceomplish the factoring are given in Table 4; the numbering corresponds to the vibrational assignments as given in Table 5. In Table 4, internal displacement co-ordinates are to be understood where the internal co-ordinates are written, i.e. rl stands for A.r,. The internal co-ordinate 72and 72refer to the ori~n~tions of the methyl groups with respect to an arbitrary orientation about their individual t&-axes. The symmetry co-ordinates S,, and S,, correspond to torsional vibrations of the methyl groups.

The n~be~ng of the fundamental frequencies corres~n~ to that of the symmetry co-ordinates, and their approximate descriptions are given in Table 5. The assignment of frequencies in both DMSO and DMSO-d, will be discussed together. The bands at 2973 cm-l and 2908 cm-l in DMSO, being respectively depolarized and polarized in the Raman effect, were assigned to the degenerate and symmetric C-H stretching vibrations. From the normal co~~n~~ analysis it appears that the higher band contains four fundamentals: yl, Ye, y14, vlB, and the lower is composed of v3 and y16. The corresponding bands occur at 2250 cm-l and 2133 cm-* in DMSO-&, 139

W. D. HORROCKS. JR.

and F. A. COTTON

and are identically assigned. The very weak bands at 2183 c~n--~in DMSO and 2185 cm-l in DMSO-d, are assigned as the first overtone of the S-O stretching frequency, v?. According to NAKAGAWA and MIZUSHIMA [13] the degenerate CH, deformation frequencies fall in the range 1400-1450 cm-l. In DMSO there are four such fundamentals expected and the four bands observed in this range are assigned to vq, vg, vr,, via, as shown in Tables 1 and 2. Other permutations of these four assignments are of course possible and the present analysis is not sufficiently exact to rule out other assignments. Likewise, the bands about 1300 cm-i are assigned to the two symmetric CH, deformation vibrations, vg and vu,. Force constants which reproduce the deformation frequencies in DMSO as assigned above, when inserted in the secular equations for DMSOd, show these fundamentals to fall close together in the range 1100-1000 cm-l. In the spectrum of DMSO-d, there is not a sufficient number of observed bands in this region to assign all the fundamentals separately, and since the very strong S-O stretching frequency occurs at 1096 cm-l, one or more of these CD, deformation frequencies may be obscured. The normal co-ordinate treatment suggests that the assignments given in Table 2 are not unreasonable. In DMSO the very strong band at 1102 cm-l is undoubtedly the S-O stretching frequency and the value obtained here is in good agreement with that of BELLAMY et al. [6] who report a value of 1103 cm-l for DMSO vapor. This band shows P&R-structure in the vapor phase, the P-branch maximum being at 1094 cm-l and the R-branch at 1111 cm-l, In DMSO-dE, the P&R-structure of the S-O band was not resolved. The remaining vibrations which principally involve hydrogen are the CH, rocking vibrations. There are four of these and in DMSO the bands at 1006 cm-l and 1016 cm-l are assigned to va and vzo, respectively, and those at 915 cm-l and 929 cm-l to vg and vzl, respectively. These bands show a large shift on deuteration as expected. This assignment was suggested by using the same rocking force constants for each vibration initially and noting the calculated frequencies. It should also be pointed out that fundamentals of the same symmetry species seldom lie as close together as do the pairs of bands observed here. For these reasons the above assignments were made, although they are not absolutely certain. The pairs of bands around 805 cm-l and 750 cm-l were assigned to the rocking fundamentals in DMSO-d, as shown in Table 2. The bands at 689 cm-l and 672 cm-l in DMSO were assigned as v22 and vro, the antisymmetric and symmetric S-C stretching frequencies, respectively, on the basis of the Raman polarization data. The former is depolarized and the latter polarized in the Raman effect. The corresponding bands occur at 619 cm -l and 611 cm-l in the infrared spectrum of DMSO-d, but are not resolved in the Raman spectrum. There remain now only the three skeletal deformation fundamentals and the low-lying torsional vibrations to be considered. The band at 382 cm-l, polarized in the Raman effect, is assigned to vll, the symmetric skeletal deformation involving principally bending of the G-S-O angles. This band occurs at 340 cm-l in DMSO-d,. The bands at 333 cm-l and 308 cm-l have been assigned, respectively, to v2a, the antisymmetric bending skeletal deformation involving the C-S-O angles ; and to vi2, the C-S-C frequency. Although both of these bands appear depolarized in the Raman spectrum, the band at 308 cm-l is missing in the infrared and it seems reasonable that v2a,which [13] I. NAKAQAWA and

S.

MIZUSHIMA, Bull. Chem. Sot. Jupan. 28, 589 140

(1955).

Vibrational spectra of dimethyl sulfoxide and dimethyl s&oxide-d,

involves a change in the direction of the S-O dipole, is less likely to be weak in the infrared than is the symmetric C-S-C bending vibration. Also, the reverse assignment would cause a larger discrepancy between the force constants F,, and F,, which would be identical if all interaction constants were negligible. The bands at 307 cm-l and 262 cm-l in DMSO-d, were both depolarized in the Raman spectrum and the 262 cm-r band was again missing in the infrared. These were assigned to vZ3and v12,respectively. This leaves only the torsional vibrations vr3 and vZ4which were not observed in the infrared or Raman spectra. An analysis of the microwave spectrum of trimethyl phosphine 1141predicts torsional fundamentals at 197 f 20 cm-l and 223 f 20 cm-l in that compound. Torsional frequencies of similar magnitude might be expected in DMSO. The shoulder observed in the infrared of DMSO at 335 cm-l is probably due to the water-vapor peak which occurs at this position rather than the first overtone of a torsional fundamental at 168 cm-l. If this shoulder were due to a torsional overtone, the same fundamental should occur at 119 cm-r in DMSO-d, and its first overtone would be predicted at about 240 cm-l which is below the region investigated in the infrared, and thus no check is provided. G-Matrix elements We give here a few comments on the construction of the G-matrix and in Table 6 the algebraic expressions for the elements since there are other molecules [e.g. (CH,),PX] to which they are applicable. The s vectors* for one of the internal torsional co-ordinates, say TV,consist of a vector on each of the three hydrogens pointing in a direction perpendicular to the plane defined by the S, 0 and C atoms. All the other atoms are stationary in this co-ordinate. The magnitude of the vector on each of the H atoms is equal to the reciprocal of the perpendicular distance from the hydrogen to the C&-axis of the methyl group. The internal co-ordinate, ~a, is described by a similar group of vectors on the hydrogens of the other methyl group except that if the vectors on the first methyl group point in a clockwise direction when viewed from the S atom, those of the second methyl group point in a counterclockwise direction. The symmetry co-ordinates S,, and S,, are formed by taking, respectively, the normalized sum and the difference of these two internal co-ordinates. It is a property of these torsional 8 vectors S,, and S,, that the dot products of each of them with all of the other S-vectors vanish, causing the corresponding G-matrix elements to be zero, and this effectively factors the torsions from the secular equation. This reduces the dimension of the A’ secular equation from 13 to 12 and that of the A” equation from 11 to 10. This assures us that incorrect assignment or nonconsideration of the torsional vibrations will not affect the other fundamentals. The results in Table 6 were checked either by comparison with the corresponding G-matrix elements for the thionyl halides [15] or by independent recalculation. G-matrix elements for the vibrations of the methyl group agree with those calculated by NAKA~AWA and MIZUSHEWA[ 131. These elements were calculated assuming tetrahedral angles for the

* See reference [5] for explanation of this notation. [14] D. R. LIDE, JR. and D. E. MANN, J. C&m. Phye. 29, 914 (1968). [15] F. A. COTTONand W. D. HORROCES,JR., Spectrochim. Acta 16, 358 (1960).

141

W. D. HORROCKS, JR. and F. A. GOWN

Table 6. &matrix

A’

elements for DMSO

Gl, = 3% + PI2 G,, = Gl,

G 10.10 = 2 ms2 $ I% + cl0 2

cf 11.11--

sh2

p,,

2P2V

=

d

B cos2 2 -

2 cd

p12po + ccr

a

1

( -

cos Bh

+

2,290

13.13 = YP,2tcH

442

G,, = - 3 G,,

=

PtPo

-42&rpo

G l,lle

-~g&qcos&&+.

G 1.12 =

2d6 --Pt.&

(32, =

%a

Q 2.11 =

-~~sw+,)

G 4.11 =

-

ssin

G4,12 =

-

‘3

G,,

=

G 5.11 =

B

21/G

41/3

PTP2cos a tan 2 ,uc

Prf 2P 0

64s -

PrPz fin 5@c

3246

443 G 6.10 = 3

P&o

c,,

=

B - 2/3pz CO8a tan 2 jI,

G,,

=

-2/3p,

=

d2

_ a,,,,

sin +p8

c_os ale,

G 7.11 = - 4%%! sin tells G 7.12 =

-2P2

G 8,10 =

-

B

cos a tan z cc,

diip2 sin f co8 f ps 142

Q12 + Qz2 ~0s~

B

+ %?,Q,

cos a

pa + ~2’ib

Table 6--(cod.)

G Q

B

+&2Bin~COs~

C

243 8.13 -- -7--sm p p2Y1

2 Q 10*11= - zg Q 1O,1z = a 11.12 =

(

co8

p, -i-

CO8/9) (fos c sin B ps + ~q$&% 2 2

-

G e*ll = ~a~~~~s~~~~

~~~~~s~#~~

Ql 008 a -I- Qz cos2 2 PLs 1

y'%2siwk9 rt&,eosat*~

gap2

&

+&2shB

+&t

B p22tan-eos

2

>

(

A.”

1

B

t+osa

Ql

GM,M = Gn a l&15 - G22 c 10.16 = 633 -G44 2;;:: = G44

G a “z;‘s: G &I a28,az

- Gri, = #p&1

-i- eos /%Q 4- swfc,

+ fr2k

= s?wh + P12M = (1 - 00~Bh4 + k

Q2’(1 - CO8/q/A,-I- f&h

a xt,23 = &

-l- &

(1 - cos B)PO

-G G 24.24 IS.13 G 14,13- aI4 a 14,20- a13

-- 243 COsUtZUlp a,,23 - 3 sin aP2

a l&20 - ass G16.22- tr,S 243 a1,s = 3Pa

B

sin 9%

a 16,lS - %6 a l(l,!xs = to a 17,a1- a46 a,,,,

-- 2d6 - 3sin ,PrP2 s~QI#%

a13.20 =

G46 -- 20 a,3,26 - 3 sina:~r~a

443

G19.22 =

- --y

a 2S.22 =

-

t/i&,

cosutanz

B

y,

P&c sin~cos' 2 Fir

2

B B &2P2 sin 2 rmf3 Tj I% -

a 2(),w = ga

G21.23=

-

G22.23 =

-&1

&

B

cosatan~pc

&PPY

~~Q~s~~~~ - cos&E"s AlI other @matrix

elements

143

aT0 equdti

!&X0.

up0

a

B

tan2pC

W. D. HORROCXS,JR. and F. A. COTTON

methyl groups, that is y = 6 = 109”28’. Fig. 2 is as follows:

The meaning of the symbols not given by

/.A== lfmtl;

m, = mass of the II atom

lu, = WC;

m, = mass of the C atom

pcls= l/m,;

m, = mass of the S atom

cl0 = limo;

m, = mass of the 0 atom

p7 = l/r, = l/r, = l/r* = l/r* = Ifr5 = l/r, ps =

PI = l/21;

Q,=(pz+&.); sin # =

J[

l/is& =

l/d3

Q~=pz-p1~os~;

1 -

i

Q~=P~--P~cos~

B cos2a~cos2 2 )I

The values of the structural parameters employed in computing the numerical values of the G-matrix elements are shown in Table 7. The atomic masses used were those of the American Institute of Physics Handbook [17]. Table 7. Structural parameters [ 161 for DMSO r(C-H)

1.08 A

T(S-O)

1.47 A

f(G-3 /_ (C-O-S)

1.84 A 106’

L (C-S-C)

100”

Solution of the secular equation The G-matrices were constructed and inverted using an IBM 704 oomputer Fortran program. The inverse G-matrix, G-l, satisfied the matrix equation: GG-1 = E. Once the G-l-matrix was obtained, solutions to the secular equations, in the form F - G-12 = 0, were obtained on the IBM 704 computer using a package program developed by QUELLE [18]. This was an extremely efficient program which required only about 3Q min of machine time to solve two 12 x 12 and two 10 x 10 secular equations. This program yielded the eigenvalues, Iz, related to the fun~mental frequencies by the expression, A = 58909 x lo-’ (Y cm-l12. This program which works,on the principle of Jacobi’s method also produces the eigenvectors, the elements of the L-matrix [5]. The L-matrix itself describes the distribution of the symmetry co-ordinates amongst the normal co-ordinates. In matrix language, S = LQ, where S and Q are column vectors of the symmetry co-ordinates and normal coordinates, respectively. The normal co-ordinates may be obtained explicitly from the matrix equation, Q = L-lS, where L-1 is the inverse L-matrix. In order to use this program it was necessary to supply numerical values for the 1161 0. BASTIANSEN and H. VIERVOLL,Ada Chem. Scand. 2,702 (1948); D. W. ALLEN and L. E. Suworu, A&z Cryat. 8, 46 (1950). [l’i’] Ame~iam I;nS&ute of Phyaka ~~~~~~. McGraw-Hal, New York (1957). [lS] F. J. @JXLLE, JR., MITSSIIZTG ProgrctmmingNote No. 17 (1959). (Obtainable from MIT Computation Center.)

144

Vibrational

spectra of dimethyl sulfoxide and dimethyl sulfoxide-d,

F- and G-l-matrix elements. Since it is the F-matrix elements which are the unknowns in the problem, various trial values of the F-matrix elements were used and the secular equations solved until the calculated A values agreed with the observed I’s to within 5 per cent. To start with, only diagonal F-matrix elements were included, but it was found necessary to include certain off-diagonal F-matrix elements in order to obtain satisfactory agreement for both the light and heavy compounds. Details of the refinement of the values, using a Jacobian matrix method will be found in the thesis of HORROCKS [19]. The fina. set of symmetry valence force constants for DMSO are listed in Table 8. Table A’

A”

E;, = P,, = B’= = Eha = F,, = P,, = P,, = Be* = P,, = It’ lo.10 = P 11.11= H 12,12=

8. Symmetry

-

4.76383 4.76125 4.95584 0.48761 0.49274 0.45826 6.54356 0.70051 051598 3.18664 153501 1.55461

valence

mdyn A rade2 mdyn A rade2 mdyn .& radp2 mdynlA mdyn A radw2 mdyn A radp2 mdyn/A mdyn 11 radB2 mdyn L&radp2

force constants

-

for dimethyl

sulfoxide

C-H stretch C-H stretch C-H stretch H-C-H defo~ation H-C-H deformation S-C-H deformation S-O stretch CH, rock CHs rock S-C stretch C---S-O defo~ation C-S-C deformation

P 6.10 = -0.01999 P 8,ll = - 0.03502 P s*rr = 0.35000 P 8.12 = -0~30000 Fa,la = 4.77232 P i5,r5 = 4.77132 P rs,rs = 4.96012 P 17,17 = 0*50826 P is,is = 0.50752 P ls,ls = 0.47352 H ao,ao = 0.71345 P rr,r& = 0*57995 P 22.22= 237290 F s3,zrs= 1.20648

mdyn rad-i mdyn L%rad-2 mdyn A radp2 mdyn A rade2 mdy+% I mdynja mdyn/d mdyn A rade2 mdyn A radp2 mdyn A radw2 mdyn 11 radw2 mdyn d radp2 mdyn/A mdyn A radp2

R-C-H deformation, S-C stretch interaction CH, rock, C-S-O deformation interaction CH, rock, C-S-O deformation interaction CH, rock, C-S-C deformation interaction C--H stretch C-H stretch C-H stretch H-C-H deformation H-C-H deformation S-C-H deform&ion CH, rock CH, rock S--C stretch C-S-O deformation

P r7,sr = 0*02971 F 2032 = -0.08469 F so,= = 0.07176 P 21.22= -0.18224 F 21,23= - 0.24649

mdyn mdyn mdyn mdyn mdyn

CHs CR, CH, CH, CH,

ip rad-2 rad-l il r-ad2 rad-r L%rad-2

rock, rock, rock, rock, rock,

H-C-H deformation interaction S-C stretch interaction C-S-O deformation interaction S--C stretch interaction C-S-O deformation interaction

-

Skeletal force constants It was not considered worthwhile to attempt any sort of complete resolution of the s~metry valence force constants into valence force constants relating to bond [19] W. D. HORROCES, JR., Vibrational AnalysM of Dimethyl SulJoxide and the Th&myl Halides. Thesis, MIT (1960).

2

145

Ph.D.

W. D. HORROC

, SE. and F. A. Corrow

However, it 3s of interest to compare the skeletal force and angle deformations. with those of the thionyl halides [Ml. The nota constant8 of 151 for the thionyl hali same as th& . All interaction cons the C-S4 angle the G-S stretch injection coast, and action constant, were ignored. For DMSO tie S-O stretching force oonatant, H,, equals 6~ mdyn/h ; the C-S stretching force constant, K,, equals 3.03 mdyn/h; the C-S-O bending force constant, k&&d,, equals 0.502 mdyn/h; the C-S-C Treble 9. Distribution

--

Sl

I s _:_ I 0.207 O.i88 -

0~787 0,207

oao2 0.001

1 0.001 OGI 0.002 0.002 ^ O*OOl

0.042 o*9OO

0.L 0.077 0*005 OMl2 0,002 0.006

oG4 ll”.l 0.024 oG4 0.001

0.279 0.702

oao7 o*oO3

oat3 OaY?

0.003 0.040 0.85 1 0.038 0.015 0,022 om%

o.ooj. 0.016 0.028 0.929 0~003 0, 0*001 0~007 o*OO2

0.002

1

d,.DMSO

O*oOl 0.002

0.851 0@40

0.002 DMSO

~-8‘

0.697 0.282 0.001 0~001 0.000 OGO 0.001

I_ /: /,

-

8:E

of potential

-

-

0.002 oG5 0@08

DMSO

s,I

0.639 O-356

0.355 0.640 ___

0.001 0.003 0.716 0.268 -

(I,-DMSO

0.006 0.001 0*008 -

I_-

O*ool _“_^ 0*003 _“__ ~ -lll_^__ 0.267 0.718 L-I...l. O*OOB 0+08 O*ool -

--

0*158 0.023 0*014 0.538 0~014 0.006 O*OOl 0.131 0~019 0.452 -~ OGOI om4 O*OOI o*Oo2 ~__ WI12 oG-25 0.031 0.052 0.002 O.oll 0,656 0.07 1 0.153 0.482 0.073 O-Q28 0.213 0+08 0.041 0.500 O*OOl

0403 0,195 0.306 0.023 0.006 0.004

0.003 0.069 O+o3 -

-

i -

0.<9 O-332 0.038 0.012 0.088 0.051 0~016 oaO3 0.002

A’-vibretione

sI‘

-

s, s, s, - 0.001 - oma OFOl 0.097 oco4 0.001O*OO8 0.051

Is ‘

0.007 0.285 0.444 0.017 0.001 0.008 0.026 0.203 WMS 0032

en@

*s11

rs18

s,,

_111-

-

-

_“_. 0.002 -.I 0.0s8 0.010 0.Z 0.823 0.050 0~010 -. 0.008 0.165 0.096 0,002

0.002 -

3.038 NM6 3.022 3.02 I 3.762 3,363

0.019 0.019 0+01 0.032 0.184 0.894

3@02 3@01

0+04 om2

3.012 3.018

oclo om2 0.006

I.008 3.010 3.101 3.013 I*?10 3.337

oG&.l 0.034 O*623 0.05 0*011

0.001 -

o.G2 0.02 1 0.021 O-l 0.862

h5’I* -

oTS7 0.003 o& 0.985 0.013 OaOI -

’3 1‘

O+ool 0*002 0.032 0.859 0.004 0.099 0.002 oaO2 .0.003 0.007 O.;S 0.010 0.908 oa47 O‘OO5 0+04 0~001

1-

-““x_

I 0*002

o*ooa O*OOl O*SlO O*OOA 0*007 oas7

_- ____ 0.007 O*681 O*O24 0.026 0.183 0.009

s I, w3of

-

/ O.oJl

s 1, O+!Ol -

0.002

0.0040.071om1 0.001 0.821 0.016 0.056 0.01 I

O+Ol 0.077 0.014 o-812 om3 0.843 0a.N 0.220 0.087

0.001 0.004

0.003 O*OOl

O.lol i 0403

0.012 0.001 0.052 0.697 0‘065 0.162 0.015

O.orl

-

0*%8 O.-GM 0.228 0.037 0.00% 0*004 O.-G6 O-040 0.736 ~:~ O*lOO o.zse

0.001 oG2 0*016 0.070 1m5 O-002 -

Vibrational

spectra of dimethyl sulfoxide and dimethyl sulfoxide-d,

bending force constant, k,ld,2, equals 0.459 mdyn/A; k,, = 0.157 mdyn/A; k,.Jd,d, = O-061 mdyn/A. As would be expected, the S-O stretching force constant is considerably lower than in the thionyl halides because of the lower electronegativity of the methyl group compared to the halogen atoms. This tends to increase the electron density around the sulfur which in turn inhibits multiple O-S bonding which occurs by donation of pn-electrons of oxygen to vacant drr-orbitals of sulfur. Character of the vibrations Calculations of the distribution of the potential energy among the normal modes show that there is considerable mixing of the symmetry co-ordinates of the same symmetry ty-pes and further that the distribution often changes markedly on going from DMSO to DMSO-G$. The results are present.ed in Table 9. It is interesting to note here that only about half of the potential energy of v,, the “S-O stretching” vibration is actually associated with S-O stretching, the rest being concentrated in several of the rocking motions in DMSO and in the symmetric methyl deformation and the S-C stretch in DMSO-d,. Ackn@u&dgements-Financial support for this work came in part from the U.S. Atomic Energy Commission undor Contract AT(30-l)-1965, and from the National Science Foundation under Grant No. G-8885, and in t.he form of a summer fellowship to W. D. H., .Jr. The award of 8 Monsanto Chemical Company I’redoctoral Fellowship to W. D. H., Jr. in the academic year 1959-1960 is also gratefully acknowledged. Finally, we express our appreciation to Prof. R. C. Lolru for placing certain facilities of the MIT SpecWoscopy Laboratory at our disposal and to Dr. I. SAKAGAWA for much helpful advice concerning the solution of t,he secular equations.

147