Raman Spectra and the Phonon Dispersion of PolyglycineEnoch W. Small, Bruno Fanconi, and Warner L. Peticolas Citation: The Journal of Chemical Physics 52, 4369 (1970); doi: 10.1063/1.1673659 View online: http://dx.doi.org/10.1063/1.1673659 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/52/9?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Phonon dispersion in graphene J. Acoust. Soc. Am. 123, 3453 (2008); 10.1121/1.2934282 Phonon dispersion of graphite AIP Conf. Proc. 723, 397 (2004); 10.1063/1.1812116 Acoustic phonon peak splitting and satellite lines in Raman spectra of semiconductor superlattices Appl. Phys. Lett. 62, 267 (1993); 10.1063/1.108985 Raman phonon spectra of partiallydeuterated crystalline ethylenes J. Chem. Phys. 68, 2151 (1978); 10.1063/1.436038 Vibration Spectra of Polyglycine J. Chem. Phys. 48, 3008 (1968); 10.1063/1.1669565

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THE JOURNAL OF CHEMICAL PHYSICS VOLUME 52, NUMBER 9 1 MAY 1970

Raman Spectra and the Phonon Dispersion of Polyglycine

ENOCH W. SMALL, BRUNO FANCONI, AND WARNER L. PETICOLAS*

DepartmMlt of Chemistry, University of Oregon, EugMle, Oregon 97403

(Received 24 November 1969)

The Raman spectra of the two crystalline modifications of polyglycine, I and II, and of N-deuterated polyglycine II have been recorded. The results of a normal-coordinate analysis of polyglycine II and N­deuterated polyglycine II are presented along with the phonon dispersion curves of polyglycine II. Assign­ments are made on a number of bands not observed in the infrared. Some previous band assignments are found to be inconsistent ",ith the Raman data.

I. INTRODUCTION

The molecular vibration spectral region of the poly­peptides has been extensively studied by ir spectros­copy.l-a In contrast to the large amount of ir data, very little Raman data has been reported. It has long been recognized that to make detailed vibrational assignments it is desirable to have both ir and Raman data. There are variations of intensity between ir and Raman spectra especially when the molecule has a high degree of symmetry. For example, some of the ir in­active E2 modes of helical a polY-L-alanine have recently been observed by Raman spectroscopy.6 Also, in the extended {3 form of polyglycine (PGI) there are modes which are ir inactive but Raman active. For the isolated chain PGI with C2v symmetry, these modes

on both forms of polyglycine by Krimm et al. lO •n have been used to verify the existence of CH· . ·O=C hydro­gen bonding. As the Raman spectra should be consistent with the ir data, the CH2 stretching region was examined in detail.

Herein we report the Raman spectra of PGI, PGII, and N-deuterated PGII. The results of a normal­coordinate analysis on PGII and N-deuterated PGII are presented and the assignments of several bands not observed previously are made. The phonon dispersion curves of PGII have been determined and the frequency regions which possess a high density of states agree with the inelastic-neutron-scattering data.

II. EXPERIMENTAL

belong to the A2 species whereas for the antiparallel- Polyglycine was obtained from two sources, Mann chain, pleated-sheet structure with D2 symmetry they Research Laboratories and Miles Laboratories. The belong to the A species. Both of these models of PGI greatest difficulty encountered in obtaining Raman have been considered in normal-coordinate analyses,2.7.8 spectra of these samples was their luminescence. They and the Raman data will be helpful in correlating the were purified (described in detail below) to reduce results. The other crystalline modification of poly- this luminescence to acceptable levels. glycine (PGII) is a helix with a threefold screw axis. The Mann sample (molecular weight ",,15 000) was The corresponding factor group is isomorphous with the dissolved in hexafluoroacetone sesquihydrate (HFA), C3 point group; the normal modes may be classified as treated with activated charcoal, filtered, precipitated A or E and in either case are active in the ir and Raman. by addition of water, washed with water, and dried.

Infrared spectroscopic studies on the polypeptides It was then redissolved in saturated LiBr solution, have been mainly concerned with correlating the spectra treated with charcoal, filtered with a millipore filter, with polymer conformation. In the low-frequency mixed with water until just before precipitation, and region the normal modes consist mainly of skeletal poured into excess water. The resulting PGII precipitate bending and internal rotation. Subsequently the was centrifuged and washed several times, and dried. frequencies of these bands are very sensitive to chain The Miles sample was of unspecified and presumably conformation. Normal-mode calculations2.7.8 and ir lower molecular weight. It appeared to contain a larger studiesl.2 on the two forms of polyglycine indicate that amount of low-molecular-weight material that was the band due to torsional motion about the peptide insoluble in saturated LiBr solution. The sample was, bond occurs at 217 cm-l in the extended {3 form, poly- however, considerably cleaner, requiring merely treat­glycine I, and at 363 cm-l in the helical form, poly- ment with charcoal and precipitation from saturated glycine II. We have also observed these bands in the LiBr solution, by the procedure described above, to Raman spectra. Although no bands at frequencies reduce the luminescence to acceptable levels. lower than that of the torsional motion about the pep- Although only the Miles sample could be used for the tide bond have been observed in the ir spectrum of Raman work, both samples were satisfactory for the ir polyglycine, several additional bands are observed in and gave identical ir spectra. the Raman spectra. N-Deuterated PGII was prepared from the PGII by

Recently Ramachandran et al.9 have proposed that a procedure identical to the one described above with hydrogen bonds of the type C-H·· ·O=C can be formed D20 substituted for water. The exchange was virtually in PGII. Infrared studies in the CH2-stretching region complete as evidenced by the lack of all but a few of the

4369

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4370 SMALL, FANCONI, AND PETICOLAS

8 iii ~ g .,.

oo oo

most intense Raman bands of nondeuterated PGII in the spectrum of N-deuterated PGII.

PGI was made from the PGII by casting films from dichloroacetic acid (DCA) or HFA solution. Films from DCA possessed higher luminescence; the solvent could not be completely removed from the HFA films.

The PGII sample was prepared by making a soft pellet of pure material using mild pressure on a KBr pellet press. Pellets made in this way were free-standing and could be placed directly in the laser beam. Although almost clear pellets of pure PGII could be prepared, the soft pellets were preferred since the softness appeared to facilitate burning off the luminescence, which generally required 2-3 h.

PGI films were placed directly in the laser beam. The Raman spectrometer, which has been described

elsewhere/ was modified for greater accuracy in band frequencies, and for the detection of very weak Raman bands. A Varian Data 620ji digital computer is used to store the output in a specified time interval of the Ortec integral discriminator at each increment of wavelength in a preselected wavelength range. The time interval is generally chosen to be 1(}--20 sec; the minimum wavelength increment is 0.1 A or approxi­mately 0.4 cm-I • The monochromator stepping motor (Slo-Syn Driving Motor type HSS(4) is controlled by a Slo-Syn Preset Indexer which is interfaced with the 620/i. At the end of the scan, the averaged counts per second and associated wavelengths are printed out by teletype.

With this system, very weak Raman bands or Raman bands in the presence of a high background are detected by using narrow slitwidths and long time intervals. For an example of the advantage of this method of data collection compare the low-frequency spectrum of PGI plotted from the 620/i output (Fig. 2) with the spectrum obtained by continuous scanning (Fig. 1).

All Raman spectra were taken using 5145-A excita­tion, except for a few regions of the PGII spectra taken with 4880 A for comparison to aid in elimination of emission lines interfering with low-intensity Raman bands.

The ir spectra were taken on a Beckman IR-7; PGII was examined as a KBr pellet and PGI as self­supporting films from DCA or films from HFA on CaF2 •

01 0 0 ~ 0, oo 0

~, '" '" oo oo oo

'01

~I 'I I

FIG. 1. Raman spectrum of poly­gycine I.

III. NORMAL-COORDINATE ANALYSIS AND PHONON DISPERSION CURVES OF

POLYGLYCINE II

The normal vibrations of PGII were calculated by the Wilson's GF methodI2 as described by HiggsI3 for infinite helical polymers. This method reduces the dimensionality of the problem to that of the chemical repeat unit consisting of N atoms. Using this method, it is not much more difficult to solve the secular equation for an infinite homopolymer than it is to solve the secular equation for the corresponding monomer or repeat unit. Although this method has been described in the literature previously/,14 we believe that the adap­tation which we have developed in much simpler and easier to use than the methods previously described, so we will discuss this method in some detail.

To use our adaptation of Higg's method, one merely calculates the B matrix by standard procedures for a given chemical repeat unit. Thus the internal co­ordinates Rn of the nth chemical repeat unit are related to the Cartesian displacement coordinates by the rela­tion

+M Rn= L Bn,n+8Xn+., (1)

where Rn is a vector consisting of the internal co­ordinates of the nth repeat unit in the helical polymer, Xn+s is a vector of the Cartesian displacement co­ordinates of the atoms in the chemical repeat unit s removed from n, but in the unrotated Cartesian co­ordinate system of the nth unit cell, and Bn,n+8 is the usual B matrix which transforms the Cartesian dis­placements in the n+s unit into the internal coordi­nates of the nth unit. The maximum value of s for which is B~O M.

If there are no redundant internal coordinates, then there will be 3N internal coordinates in a chemical repeat unit. These 3N internal coordinates will be connected to the 3N Cartesian displacements in each of the neighboring chemical repeat units along the chain, s=O, ±1,···, ±M. The matrices Bn,n+. will be of dimension 3NX3N if there are no redundant coordi­nates. If there are redundant internal coordinates, then these matrices will not be square, but the corresponding G matrices will be square and possess as many zero eigenvalues as there are redundant internal coordinates.

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RAMAN SPECTRA OF POLY GLYCINE 4371

If there are k residues in m turns of the helix, then we may arbitrarily choose any repeat unit for n= 0; then the units n= 1, 2, "', k-1, are fixed. If the z axis is taken as the helix axis and we hold the x and y axes of the helix in an arbitrary but fixed position, then Bn,n+s will be different for n= 0, 1, ... , k-l. Although a bond stretch coordinate between units 0 and 1 will be identical to the equivalent internal coordinate between units 2 and 3, the x and y Cartesian co­ordinates will be quite different because each repeat unit is obtained from the previous one by a rotation through an angle l/; and a translation through a distance Zl' This translation rotation through r nearest neighbors takes the Cartesian coordinates of the ath atom in the n= 0 unit into the Cartesian coordinates of the equiv­alent atom in the rth unit by the relation

(2) where

Ha"(l/;)= (::~o:~ :), Tz = (~). (3)

o 0 1 Zl

Only the rotational part of Eq. (3) need be considered because the internal coordinates are invariant to simple translation. The vector XT consisting of the co­ordinates of all of the atoms in the rth unit are related to XO by a relation of the form

XT=WXO,

where W is a matrix of the form

For n=O, Eq. (1) becomes +M

RO= L BO,sXs.

(4)

(5 )

(6)

~ U> ... U> I­Z

8000

7000

is 6000 o

5230 5220

.... o N

5210 5200 WAVELENGTH (A')

.:" •••• 0'

f'-- -::",:'w

~ w

5190

FIG. 2. Low-frequency Raman spectrum of polyglycine 1.

are independent of the value of n and hence

L BO"X'= L Bn,n+sHnX'.

5180

(9)

Equating coefficients of X' gives the important relation­ship

(to)

Let r=n+s and we may write

and

(12)

Since Hn (l/;) is easily calculated, all of the values of Bn,r may be obtained from BO,r-n by means of Eq. (11). This greatly simplifies the calculation. Once the BO" matrices are calculated for all s, the Gm matrix may be calculated,

(13)

or

where M-l is the inverse mass matrix. It can be shown14 that the full G and F matrices for

an infinite polymer reduce to

G (0) = GO+ L ei88GS+ ris8 Gts ( 15 )

One first fixes the x and y axes of the helix so that the matrices BO,s are particularly easy to calculate. Now and the Cartesian displacements n+s units away are related

(16) to the coordinates Xo+s by the relation

(7)

Putting Eq. (7) into Eq. (1) we have

Rn= L Bn,n+8HnXs. (8)

The internal coordinates of any chemical repeat unit

where Gts is the Hermitian conjugate of G8, and the GB matrices are given by Eq. (14).

The i, j element of the FB matrix is the component in the Urey-Bradley force field of the ith internal co­ordinate of the zero repeat unit and the jth internal coordinate of the s repeat unit. The Urey-Bradley

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SMALL, FANCONI, AND PETICOLAS

L-__ ~-----t----112 INELASTIC NEUTRON SCATTERING PEAKS

6

l\\\SSS'S!

__ -:t----! 5 1\\\1\\\\1\1

~-.lr----I :3 t\\'\\'(\\\\l

2 ~~~~~~T-r~~~1

.2 .3 14 .5 .6 .7 .8 .9.". 8 .". 0 .". k

FIG. 3. Phonon dispersion curves for polyglycine II.

force field2 used in this calculation is of the form

V= L Kjk'rjk(ml(llrjk(ml)+1/2Kjk(llrjk(ml)2 m,j,k

m,i,j,k

+ 1/2Hijkri/mlrjk(ml (t1cxijk(ml)2

+ L Fi ,k'qik(ml(t1qik(ml) m,i,j k

m,j

where t1rjk(ml, t1cxijk(ml, t1T/ml , t1w/ml are the internal coordinates corresponding to bond stretch, angle bend, torsion, and wag, respectively. The subscripts on the first two internal coordinates label the atoms involved and the superscript m labels the chemical repeat unit. The torsional coordinate t1T/ml is the sum of all cis and trans torsions about the jth bond.

The phonon dispersion curves are found by solving the secular equation

I G(()F(()-w2] I =0 (18)

for values of () between 0 and 7r. The angle () is the phase difference of the vibration between neighboring chemical repeat units. The associated Brillouin zone is larger by the number n of chemical repeat units which con­stitute the translational unit cell. For polyglycine II with a threefold screw axis, this number is 3. The

true Brillouin zone may be constructed from the extended Brillouin zone by n-l successive reflections about ()=7r/n and ()=O. The arrangement of the phonon dispersion curves in the true Brillouin zone for PGII is indicated by the range of k in Fig. 3. The points on the dispersion curves in the extended Brillouin zone which are ir active are ()= 0 and 1/;, and the Raman active points are ()=O, 1/;, and 21/;. All these points are at k=O in the translational Brillouin zone.

Computer programs used in this calculation were modified from a set of programs written by Schacht­schneider.l5,l6 To overcome difficulties in handling complex numbers the G (() and F (() matrices in Eq. (18) are transformed to their real equivalent matrices by a similarity transformation. l7

To simplify the calculation the methylene groups in PGII were treated as single mass units. This has proven to be a good approximation in a number of normal­coordinate calculations on PGP,7,8 Although it may be justified within the single-chain approximation for PGII, the methylene group should be considered explicitly in the crystal calculation because of the possibility of CR·· ·OC hydrogen bonding.

No attempt was made to find a best set of force constants; instead they were taken from recent calcula­tion on PGI by Fukushima et al.8 (in plane) and Gupta et al.2 (out of plane). The bond distances and bond angles were taken from the crystal structure of PGIU8

Torsions about the C-N, N-M, and M-C bonds were treated as separate internal coordinates. In each case the internal coordinate was the sum of all cis and trans torsions and an average force constant was used.

In Fig. 3 are shown the extended phonon dispersion curves for PGII. The ir and Raman active points (1/;= 120°) are at ()=o and 27r/3. The observed Raman frequencies assigned (Table II) to these dispersion curves are indicated by the open circles. The frequency distribution for PGII has been calculated from inelastic neutron scattering by Gupta et al.2 Peaks in the inelastic neutron spectra correspond to regions of high density of states in the phonon dispersion curves. The frequency range of these peaks are indicated by the hatched areas in Fig. 3 and the corresponding high density of states region in the dispersion curves by heavy lines. As seen from Fig. 3 there is good agreement between the inelastic neutron spectra and the phonon dispersion curves.

In Tables II and III are listed the calculated fre­quencies for ()= 0, 27r/3 along with the observed irl and Raman bands for PGII and N-deuterated PGII. These results are discussed in the next section

IV. RESULTS

A. Polyglycine I

Figure 1 shows a Raman spectrum of PGI, cast from RFA, taken directly from the recorder chart. The very narrow bands throughout the spectrum are emission

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RAMAN SPECTRA OF POLYGLYCINE 4373

lines from the Ar+ laser and the bands labeled S are due to the solvent. The PGI sample may contain a very small amount of PGII as evidenced by the weak band at 1034 cm-l characteristic of PGII. The high back­ground obscures low-intensity bands but the more prominent bands are readily discernible. The fre­quencies given under the bands are averages of a number of repetitive scans at different resolution on films cast from both HF A and DCA.

The low-frequency region of PGI was examined by computer controlled scanning and is shown for a film case from DCA in Fig. 2. Wavelength increments of 0.1 A and a time interval of 15 sec were used. Emission lines were suppressed by using a 1O-A narrow-bandpass filter. The band labeled G is a grating ghost that appears in all our spectra.

Table I is a summary of the Raman results, the ir observed by Suzuki et al} and calculated frequencies reported by Gupta et al.2 The calculated in-plane frequencies in Table I are in agreement with those reported by Fukushima et al.8 Both of these calculations assume an isolated-chain model. Miyazawa et aU have calculated the ir-active amide bands for the anti­parallel-chain pleated-sheet structure (two-dimensional crystal), D2 symmetry, including interchain interactions through the hydrogen bonds.

The force constants used by Gupta et al.2 were varied to obtain the best fit with the ir data. Thus interchain interactions have been included in a circuitous manner. If the interaction between the same mode in different chains is weak, as it probably is for vibrations localized in the methylene group, then classification according to the isolated chain symmetry is valid. However, for modes in which the interaction is appreciable classifica­tion in this manner is suspect. For example, Gupta et al.2 assign the amide VII band, observed in the ir at 217 cm-I, to an A2 vibration which derives its intensity from nonplanarity of PGI; Miyazawa et al,7 assign this band to a BI vibration (D2 symmetry group) which is ir active.

The frequencies of the ir-inactive A modes were not reported for the crystal calculation, therefore we assign the Raman bands in Table I using the isolated-chain model subject to the above considerations.

There are several differences between the ir and Raman spectra. Frequency differences of less than 6 cm-l are probably insignificant because of instrumental error in the ir and Raman measurements. The error range in the Raman band frequencies was determined to be from approximately 1-2 cm-l for narrow intense transitions to 4-6 cm-l for the weaker broad transi­tions. Since the ir spectrum of P GI (v> 700 cm-l )

taken in our laboratory agrees with that reported by Suzuki et al.! except for only a few additionallow-inten­sity peaks, the differences between the ir and Raman are not due to impurities or differences in sample preparation.

No ir bands have been observed below 217 cm-l with

TABLE I. Observed and calculated vibrational frequencies of polyglycine I.

Band frequencies (em-I)

Raman ira Caleb Assignmentsc

3301 M 3308 S 3311 (AI, BI) Amide A 3088M AmideB 2978W CR2 antisym. str.

2955 M CR2 antisym. str. 2932 S 2929W CR2 sym. str. 2869M 2869VW CR2 sym. str. 1674 S 1685M 1687 (AI) Amide I

1636 S 1647 (BI) Amide I 1564 W 1524 (BI) Amide II 1515 W 1517 S 1516 (AI) Amide II 1460 S CR2 bend

1432 S CR2 bend 1410M 1408W CR2 wag 1341 W 1338 Wd 1295 W 1255 M CR2 twist 1234 S 1236M 1303 (AI) Amide III 1220W 1214 W 1294 (Bl ) Amide III 1162 M

1112 We 1112 (AI) I'NM, rMC

1057 W 1034W 1021 VS 1016M 1014 (Bl ) rCN, rNM, "'CNM

985 (AI) rMC, "'MCN, "'CNM

874 (Bl ) rNM, 'MC

884M 888 Wd CR2 rock 737 (Bd Amide IV

708 S 703 (B2 ) Amide V 699 (A 2) Amide V

628W 614 (B2 ) Amide VI 614M

601W 618 (A 2) Amide VI 589M 600 (AI) Amide IV

541 (B I ) "'NMC, "'MCN

410 (B2) Amide VII 277(Bd "'CNM,"'NMC

220 (AI) "'MCN, "'CNM, "'MCO

207W 217 f W 231 (A 2) Amide VII 167W 173 (AI) "'NMC,"'CNM

146 (B2) 3 torsions 91 (A 2) TeN, TNM, TMC

• From Suzuki et al. (Ref. 1). b From Gupta e/ al. (Ref. 2). Mode symmetry in parentheses. cr. bond stretch; a, angle bend j T. torsion. d From our ir data. e From Fukushima e/ al. (Ref. 8). fFrom T. Miyazawa. Bull. Chern. Soc. Japan 34, 691 (1961).

the exception of a questionable band at 142 cm-l

reported by Gupta et al. There are two Raman bands at 167 and 207 cm-l in this region. The Raman band observed at 167 cm-l can be tentatively assigned as the Al mode calculated at 173 cm-l which involves skeletal bending of the N-M-C and C-N-M angles. The Raman band observed at 207 cm-l is sufficiently re-

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4374 SMALL, FANCONI, AND PETICOLAS

TABLE II. Observed and calculated vibrational frequencies of polyglycine II.

Band frequencies (cm-l) Band No. Raman ira Calcb AssignmentsC

3305 W 3303 S 3342 (A, E) rNH(l00) Amide A 3278 M Amide A 3085 M 3086 M AmideB 2979 S 2983 W CH2 asym. str. 2940 VS 2944 W CH2 sym. str. 2868 W 2848 W 2831 W 2742 VW 2652 VW 1654 VS 1644 S 1657 (A, E) rco(80) , rCN(16) Amide I 1582 VW 1560 W

1554 S 1543 (1<:) rCN (33), ¢NH (70) Amide II 1547 (A)

1421 S 1420 M CH2 bend 1383 S 1377 M CH2 wag 1334 VW

12 1283 M 1283 M 1281 (E) rCN (35), rMc(23) , Amide III ¢NH(19)

1261 S CH2 twist 12 1244 S 1249 M 1265 (A) rCN( 40), rMc(19), Amide III

¢NH(24) 11 1134 M 1132 VWe 1079 (A) rNM (70), rMc(21)

1060 W 11 1031 VS 1028 M 1009 (E) rNM(42) , rCN(14) ,

rCM(15) 1017 Wd

10 968 W 971 VWe 959 (A) rCM (23), ¢ocN(17), ¢CNM(17), rco(12)

10 952 W 944 (E) rNM(35), rCM(21), ¢ocN(lO)

897 VW 884 VS 901 M CH2 rock 864 W 862 VWe

9 752 VW 751 We 778 (A) 1I"NH(41) , 1I"co(20), Amide V ¢NMc( 10), TNM (12)

9 742 VW 740 M 741 (E) 1I"NH(43),1I"co(10), TCN(18), TNM(20) ,

8 707 W 698 S 665 (E) ¢NMc(35), ¢Co(12) II 673 Mf 662 (A) rMc(14), ¢co(18), Amide IV

¢NMC(14) 7 643 (E) rMc(13), ¢co(24), Amide IV, VI

1I"co(26) 578 W

7 566 M 573 S 576 (A) 1I"co(54),¢Co(23) Amide IV, VI 6 496 W 460 (E) ¢MCN (36), ¢co(16) 6 424 VW 416 (A) TMc(27), ¢CNM(16),

1I"NH (10), TNM (10) 383 VW

5 353 VW 363 S 373 (E) ¢Co (26) , TMc(20), Amide IV ¢CNM (15)

340 M 313 VW 297 VW

5 272 W 282 (A) ¢NMd27), ¢Co(21), ¢CNM (11), TMc(12)

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RAMAN SPECTRA OF POLY GLYCINE 4375

TABLE II (Continued)

Band frequencies (em-I) Band No. Raman ira Caleb

4 234 (E) 4 217 W 189 (A)

3 126 (E) 2 79 (E)

3 76 (A)

a From Suzuki e/ al. (Ref. I). b Mode symmetry in parentheses. C Potential energy distribution among diagonal elements of the force

matrix; T, bond stretch; <P. angle bend; 'Jr, out-of-peptide-plane bend; T,

moved from the ir band at 217 cm-l (Amide VII) to suggest that it is due to a different normal mode. Since the Amide VII is composed of torsions about the C-N bond, it is not surprising that there would be significant interchain interactions through the hydrogen bonds giving rise to a splitting of the C2v ir-inactive A2 mode into the Dz modes A and B1• Miyazawa et al.7 assign the ir band at 217 cm-I to the BI mode, and the ir-inactive mode apparently occurs in the Raman at 207 cm-I .

The BI vibration, although allowed in the Raman, IS

not observed. Raman bands which do not correspond to any ir

bands or calculated frequencies occur at 1034(W), 1162 (M), 1255(M), 1295 (W), 1341 (W), 1460(S), 1564(W), 1674(S), and 2955 (W) cm-I. (The letters in parentheses represent the relative intensities: W = weak, M = medium, S = strong.) Three of these bands may be assigned to vibrations of the methylene group. The Raman band at 1255 cm-I is assigned to the CH2 twist which is expected to occur in this region and to have little ir intensity. The strong ir band at 1432 cm-I, assigned to the CH2 bend, is not observed in the Raman, but a strong band is observed at 1460 cm-I

and is presumably also due to a CH2 bending vibration. The two methylene bending modes per unit cell are split into an Al and BI mode, and if the above assign­ments are correct, there is significant interaction between the methylene groups. There is also evidence of interaction between the methylene groups in the CH2 stretching region. A comparison of the ir and Raman data indicates there are four bands in this region at 2869 (ir, R), 2932 (ir, R), 2955 (R), and 2978 (ir) em-I. A single methylene group would have an asymmetric and symmetric CH2 stretch. As above, the interchain interaction would split the symmetric mode into an Al and BJ, while the asymmetric mode would be split into an A2 and B2• All modes would be Raman active but only the AI, BJ, and B2 modes would be ir active. On this basis we assign the two symmetric vibrations to the bands at 2869 and 2932 cm-I and the

Assignments·

<PNMC (35) , <l>cNM (15) <PMCN (40), <l>co(23),

TNM (12) TMc(35), TNM (30) TCN (27), TNM (16),

TMc(24) TCN (39), nm (27),

TMc(25)

tonlion. d Could be {3 form. e From OUf if data.

Amide VII

Amide VII, V

f Intensity varies from sample to sample.

asymmetric vibrations to the bands at 2955 and 2978 cm-I since the asymmetric vibrations would be ex­pected to be of higher frequency. It is interesting that the Raman intensities of the symmetric vibrations are greater, as generally observed. The band at 2955 cm-I

could correspond to the A2 mode of the asymmetric stretch which would be ir inactive, and the ir band at 2978 em-I could correspond to the B2 mode. The 2978-cm-1 band is present as a shoulder in Fig. 1.

The weak band at 1564 cm-lis in the Amide II region. Although the bands show little intensity in the Raman, the Amide II region is of particular interest due to the higher resolution. In addition to the 1564-cm-1 band the familiar Amide II band is observed at 1515 cm-I. Since the frequency of the first overtone of the Amide II band (2X 1515) would not be sufficiently high for Fermi resonance with the N-H stretch giving rise to the Amide A and B bands, Suzuki et al.1 postulated the existence of a band at about 1558 cm-I. The band observed at 1564 may be the Amide II band whose overtone is responsible for the observed splitting. However, a band in PGII similar to the 1564 band in PGI does not disappear upon N-deuteration and therefore cannot be assigned to an Amide II vibration.

Interchain interactions are expected to be strong for the Amide I vibrations, and the additional splitting gives rise to four frequencies. The Amide I band ob­served at 1674 cm-I probably corresponds to one of these frequencies. The shape of this Raman band sug­gests the presence of additional bands at higher and lower frequencies, but attempts to split the band into its components were unsuccessful.

The medium intensity band at 1162 cm-I is assigned to the N-M-C asymmetric stretching mode which was calculated at 1112 cm-I to fit a weak ir band observed by some workers. (This band would shift little upon N-deuteration, and there is a medium intensity band in PGII at 1134 cm-I which shifts to 1131 cm-I in N-deuterated PGII.) The ir band at 1112 cm-I as well as the weak Raman bands at 1034, 1295, and 1341 cm-I

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4376 SMALL, FANCONI, AND PETICOLAS

TABLE III. Observed and calculated vibrational frequencies of N-deuterated polyglycine II.

Band frequencies (em-I)

Raman ira Calcb P.E.D.c Comments

3068 W 2980 VS 2975 W CH2 asym. str. 2940 VS 2940 W CH2 sym. str. 2866 VW 2850 W 2809 VW 2472 M 2464 W 2440 (A, E) TNo(100) Amide A' 2419 M 2416 S AmideB' 2330 W 1640 VS 1639 S 1649 (A, E) TCN (23), Tco(83) Amide I' 1582 VW 1558 W

1423 (A) TCN(56) , TNM(l1), Amide II' TMC(12) , <l>No(24)

1470 M 1476 S 1422 (E) TCN(51), TNM(13), Amide II' TMC(14) , <l>No(22)

1448 W 1419 S 1420 M CH2 bend 1412 W 1347 W 1350 M CH2 wag 1333 VW

1277 M 1267 S 1262 M CH2 twist 1231 W 1150 W 1131 M 1100 W 1029 M 1034 M 1112 (A) TNM(43) , TMc(32),

<l>No(17) 1075 (E) <l>NO (46), TMC (15) Amide III' 976 (E) TNM(21), TCN(16)

995 VS 987 M 971 (A) TNM (20), <l>No(59) Amide III' 984 VW 952 W 945 (A) TMc(20), Tco(l1),

<l>co(16) , <l>CNM(12) 913 (E) TNM (33), rMc(15),

<l>NO(17) 887 W 886 W CH2 rock 875 VS CH2 rock 857 W 734 W 729 (A) 7l"co(39) , <l>NMc(21), Amide VI'

7l"No(17) 693 S 680 (E) 7l"co(67) Amide VI'

653 (E) <l>co(34) , TMc(23), Amide IV' <l>NMC(15)

576 M 597 (A) <i>co(37),7l"co(22) Amide IV', VI' 537 (E) 'lrNO( 44), TCN (19), Amide V'

TNM(16) 520 S 504 (A) 7l"No(33) , 'lrco(24) , Amide V', VI', VII'

TCN(26) , TNM(13) 491 VW 446 (E) <l>MCN(35) , <i>co(21)

414 (A) TMc(25), TNM(12), <i>cNM(16)

356 S 364 (E) <l>co(23) , TMc(19), Amide VII' <i>cNM(13) , TCN(l1)

335 W 314 VW

274 (A) <l>NMc(27), <i>cNM(lO) , TNM (10), TMc(11)

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RAMAN SPECTRA OF POLYGLYCINE 4377

TABLE III (Continued)

Band frequencies (em-I)

Raman ira Caleb P.E.D." Comments

227 (E) <PNMc(37), TCN(W) 188 (A) <PMCN (41), <f>co(22) ,

TNM(12) 116 W 124 (E) TMC(34) , TNM(32)

79 (E) TCN (27), TCM (25), TNM(17)

75 (A) TCN (39), TMc(25), Amide VII' 1I"ND(27)

• From Suzuki et al. (Ref. 1). b Mode symmetry in parentheses. C Potential energy distribution among diagonal elements of the force

may be due to short chain segments where the k=O selection rule no longer applies.

B. Polyglycine II

The Raman spectra of PGII and N-deuterated PGII are shown in Figs. 4(a), 4(b). Raman frequencies are given under the more prominent bands. A narrow-band­pass filter was used to eliminate emission lines. Tables II and III list the Raman and ir bands, and the cal­culated frequencies for PGII and N-deuterated PGII, respectively. As with PGI the Raman frequencies were obtained from a series of repetitive runs at different resolution, including computer controlled scanning of several regions of interest. The only Raman band that could be detected below 200 cm-1 was the band at 116 cm-1 in N-deuterated PGII.

The results of our calculation are in agreement with those reported by Miyazawa et aU The normal modes of PGII can be classified as either A or E of Ca and are in either case both ir and Raman active. We have ob­served several weak bands in the ir which, although not previously reported, correspond to Raman bands and are therefore included in Table II. These and other differences between the Raman spectra and the reported ir frequencies we believe not to be due to impurities or differences in sample preparation. Only a very small amount of PGI may be present as evidenced by the weak shoulder at 1017 cm-1 in the spectrum of P GIl. The CH2 stretch region was examined in detail for com­parison with the work of Krimm et al. lO •ll in which the two additional bands in the ir of PGII were assigned to the vibrations of a hydrogen-bonded methylene group. A high sensitivity spectrum of this region is shown in Fig. S. The results of the ir studies by Krimm et al.lO •ll

and the Raman data for both PGI and II are compared in Table IV. It was concluded from the ir studies that the two CH2 vibrations of PGI indicate there is very little interaction between the methylene groups and that the additional two bands in PGII are attributable to methylene groups in a different environment. The

matrix; r. bond stretch; <p. angle bend; 11". out-of-peptide-plane bend; T'

torsion.

three prominent Raman bands in the CH2 stretching region and the frequency difference of 28 cm-1 between the Raman and ir CH2 bending modes of PGI may indicate significant interaction between neighboring CH2 groups. From Fig. 5 it is evident that although there are more bands in the Raman of PGII than PGI, the intensity argument10 •ll used with the ir data is not substantiated by the Raman results. Also it is prob­able that some of the weaker bands in Fig. 5 arise from combination and overtone bands.

We were unable to obtain a high-sensitivity spectrum of PGI in this region and therefore cannot rule out the existence of the weak bands seen in PGII. We conclude that in view of the Raman results the previous assign­ments of the CH2 stretching bands are suspect and additional research including a PGII crystal calcula­tion would be desirable.

The Raman bands at 3305 and 3278 cm-1 disappear upon N deuteration andean be assigned toNHstretching modes. The two bands may arise from the splitting of the NH stretching mode into an A and E mode or may indicate two different environments of the amino hydrogen. No such splitting is observed in PGI and the calculated splitting is less than 1 em-I. These findings rule out the first interpretation. Environmental differences may arise from NH· •• OC hydrogen bonding to direct or inverted chains or from bonding to oxygens participating in CH·· ·OC hydrogen bonding. Rama­chandran et al.9 have found that NH·· ·OC hydrogen bonds of approximately the same strength are formed between direct-direct and direct-inverted chains and that CH·· ·OC hydrogen bonding is possible only between direct-direct or inverted-inverted chains. They also have shown that ",,1/3 of all interchain bond­ing is between like chains and therefore ",,1/3 of the oxygens will be participating in N-H···O and CH···O hydrogen bonding. Formation of the CH···O hydrogen bond will tend to weaken the N-H···O hydrogen bond, and hence the NH stretching frequency should be higher in these cases. Assuming that the intensity is unchanged by the difference in bonding environments, the ratio

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4378 SMALL, FANCONI, AND PETICOLAS

of intensities between the two N-H stretching fre­quencies should be 1: 3 with the lower-intensity peak occurring at higher frequency. This is in qualitative agreement with the experimental results. The amide B band, 3086 cm-I, in PGII is not observed in the Raman spectra of either PGI or a-polY-L-alanine.

Neither of the two bands in the Amide II region, 1560 and 1582 cm-I, disappear upon N deuteration and therefore cannot be assigned to the Amide II mode. The 1261-cm-1 band, not observed in the ir, is assigned to the CH2 twist and shifts slightly to 1267 cm- l in N-deuterated PGII. The Raman bands at 1582, 1560, 1334, 1060, 897, 864, 383, 340, 313, and 297 cm-l have not been assigned. Some of these bands may arise from

r~!' I 'I.I I I '8' Ii 1.1' ""g"-" ',"" o 0 (j) <.0 <.0 LO

C\I It)

ID 'C\I

FIG. 5. Raman spectrum of polyglycine II in the CH2-stretching region.

FIG. 4. (a) Raman spec­trum of polyglycine II. (b) Raman spectrum of N-deuter­ated polyglycine II.

short chain segments or from the folding of long chains which invalidates the k = 0 selection rule. With the exception of the 340-cm-1 band, all the un­assigned bands have little intensity, which is charac­teristic of k~O Raman transitions from short chain segments.

The lowest observed ir band, 363 cm-I, has been assigned by Miyazawa et al.7 to a combination of the Amide VII (torsion about the CN bond) and Amide IV (in-plane bending of CO). We find that torsion about CM bond contributes more to this mode than torsion about the CN bond. We calculate a frequency shift of -9 cm-l for this mode upon N deuteration and the observed ir band shift is -7 cm-l • The medium inten­sity Raman band at 340 cm-l shifts to 335 cm-l in N-deuterated PGII and is probably of different origin than the ir band at 363 cm-l • This band may arise from the A mode calculated at 282 cm-1 reflecting an error in the calculation. The Raman band at 217 cm-l is assigned to the A mode calculated at 189 cm-l . This mode consists mainly of the skeletal angle MCN deformation and the NM bond stretch. The calculated

TABLE IV. C-H stretch region of polygiycines.

Polygiycine I Polyglycine II

Raman Raman

2978 W 2983 W 2977 VW 2979 S 2955 M 2944 W 2935 W 2940 VS

2929 W 2920 W 2932 S 2869 VW 2850 VW 2869 M 2848 W 2850 W 2868 W

2805 VW 2831 W

a From Suzuki et al. (Ref. 1). b From Krimm et al. (Ref. 11).

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RAMAN SPECTRA OF POLYGLYCINE 4379

lowest frequency mode of PGI consisting of the same deformation occurs around 550 em-I. Finally, the band at 116 cm-I in N-deuterated PGII is assigned to a mode involving torsion about the M-C and N-M bonds. This mode is calculated at 126 cm-I in PGII and at 124 cm-I in N-deuterated PGII and may correspond to a prominent low-frequency ir band observed by Shimanouchi and co-workers4,6 in other polypeptides.

Note added in proof: Since this paper was accepted for publication, a paper on the Raman spectrum of polyglycine II has been published.I9

* The authors acknowledge support of NIH Grant No. 5-R01-GM15547-07.

1 S. Suzuki, Y. Iwashita, and T. Shimanouchi, Biopolymers 4, 337 (1966).

2 V. D. Gupta, S. Trevino, and H. Boutin, J. Chern. Phys. 48, 3008 (1968).

3 C. H. Bamford, A. Elliott, and W. E. Hanby, Synthetic Polypeptides (Academic Press Inc., New York, 1967), Chap. V.

THE JOURNAL OF CHEMICAL PHYSICS

4 K. Itoh, T. Kakahara, and T. Shimanouchi, Biopolymers 6, 1759 (1968).

6 K. Itoh and T. Shimanouchi, Biopolymers 7,649 (1969). 6 B. Fanconi, B. Tomlinson, L. A. Nafie, W. Small, and W. L.

Peticolas, J. Chern. Phys. 51, 3993 (1969) 7 T. Miyazawa, in Poly-a.-Amino Acids, G. D. Fasman Ed.

(Marcel Dekker, Inc., New York, 1957), Chap. 2. 8 K. Fukushima, Y. Ideguchi, and T. Miyazawa, Bull. Chern.

Soc. Japan 36, 1301 (1963). 9 G. N. Ramachandran, C. Ramakrishnan, and C. M. Venkata­

chalam, in Conformation of Biopolymers, H. N. Ramachandran Ed. (Academic Press Inc., London, 1967), Vol. 2, p. 429.

10 S. Krimm, K. Kuroiwa, and T. Rebane, in Ref. 9, p. 439. 11 S. Krimm and K. Kuroiwa, Biopolymers 6, 401 (1968). 12 E. B. Wilson, J. Chern. Phys. 7, 1047 (1939). 13 P. W. Higgs, Proc. Roy. Soc. (London) A220, 472 (1953). 14 L. Piseri and G. Zerbi, J. Chern. Phys. 48, 3561 (1968). 16 J. H. Schachtschneider, Shell Development Company,

Emeryville, Calif. Tech. Rept. Nos. 57-65 and 231-64. 16 We are grateful to Dr. Schachtschneider for these programs. 17 H. J. Hannon, F. J. Boerio, and J. L. Koenig, J. Chern. Phys.

50,2829 (1969). 18 F. H. C. Crick and A. Rich, Nature 176, 780 (1955). 19 M. Smith, A. G. Walton and J. L. Koenig, Biopolymers 8,

29 (1969).

VOLUME 52, NUMBER 9 1 MAY 1970

Light Scattering from Optically Active Fluids*

L. BLUM

Department of Chemistry, University of Puerto Rico, Rio Piedras, Puerto Rico 00931

AND

H. L. FRISCH

Department of Chemistry, State University of New York at Albany, Albany, New York 12203

(Received 13 October 1969)

A rigorous theory for the light scattered from a solution of an optically active species is presented. The theory is based on the quantum-mechanical time displaced correlation function for the suceptibility tensors. This formalism leads to the correct form of the Kronig-Kramers relations. Otherwise, the procedure follows the usual theory of light scattered from inactive solutions. The result shows that the parameters usually associated with the optical rotatory power and the ellipticity are linear combinations of two rotational invariants of the fourth-rank tensor formed by the direct product of the dielectric polarizability tensor and the pseudotensor that gives the optical activity. Only for isotropic molecules do we recover the classical result. The depolarization of the light (or ellipticity) is due both to the dielectric polarizability and to the optical activity pseudotensor. If the scattering experiment is done at an angle different from zero, then information about the anisotropy of the molecular susceptibility tensor be obtained. Also, when the system is opalescent, it could be more convenient to look at the scattered light instead of the "transmitted" one.

I. INTRODUCTION

In recent years much progress towards the under­standing and application of optical rotatory dispersion (ORD) has been achieved.I It has been stated in several places2.3 that it should be considered from the point of view of the theory of light scattering. How­ever, no attempt has been made to use as a starting point the rigorous theory, based on the time-dependent correlation functions of van Hove4 as applied to light scattering by Komarov and Fisher and Pecora.5 The main difference that this procedure introduces is in the angular averaging of the molecular parameters, or tensor contraction. The usual procedure takes the

angular average of the susceptibility tensors indi­vidually, and then multiplies them to obtain the intensity of the scattered light.

The need of using a time-dependent formalism can be understood considering that the optical rotation is due to the variation of the incident field over the realm of the molecule.6 Therefore, retardation effects have to be taken into account for consistency. This will make our treatment consistent with the phenomenological Kronig-Kramers relations.7,8 However, the parameters involved will have a different microscopic interpretation.

As stated above, our angular averaging does not follow the usual one of the ORD literature. As is done in the theory of light scattered from optically inactive

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