Force-field and vibrational spectra of oligosaccharides with different glycosidic linkages—Part I. Trehalose dihydrate, sophorose monohydrate and laminaribiose

Spectrochimica Acta, Vol. 50A, No. 1, pp. 87-104, 1994

0584-8539194 $6.00+0.00 Pergamon Press Ltd

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Force-field and vibrational spectra of oligosaccharides with different glycosidic iinkagesmPart I. Trehalose dihydrate, sophorose monohydrate and laminaribiose MANUEL DAUCHEZ, PHILIPPE DERREUMAUX, PHILIPPE LAGANT a n d GI~RARD VERGOTEN* I.N.S.E.R.M. U279, C.E.R.I.M., Groupement Scientifique I.B.M.-C.N.R.S. "Mod61isation Mol6culaire', Universit6 des Sciences et Technologies de Lille, 1 rue du Professeur Calmette, 59019 Lille, C6dex, France and MAJDA SEKKAL a n d PIERRE LEGRAND L.A.S.I.R., Universit6 des Sciences et Technologies de Lille, Bat. C5, C.N.R.S. UPRA 2631 L, 59655 Villeneuve D'Ascq, C6dex, France

(Received 12 September 1992; in final form 10 February 1993; accepted 11 February 1993) Abstract--Tbe vibrational spectra of the disaccharides, trehalose dihydrate, sophorose monohydrate and laminaribiose, have been recorded in the crystalline state in the 4000-100cm -~ spectral region for the IR spectra and in the 4000-20 cm-1 spectral range for the Raman spectra. These three disaccharides exhibit the same monosaccharide composition (i.e. glucose residue), but differ in the position and configuration of the glycosidic linkage (a, 1-1; fl, 1-2 and fl, 1-3 for trehalose, sophorose and laminaribiose, respectively). Most of these spectra have not yet been reported, particularly in the low frequency range. They constitute the basis of theoretical calculations of normal modes of vibration. Normal coordinate analysis has been made in the crystalline state using a modified Urey-Bradley-Shimanouchi intramolecular potential energy combined with a specific intermolecular potential energy function. The force field parameters are transformed from initial works on both anomers of glucose. The vibrational assignments of the observed bands are made on the basis of the potential energy distributions. It appears that the greatest part of the vibrational modes is very highly coupled vibrations. The calculated vibrational frequencies agree very well with the observed frequencies in the whole spectra, particularly in the "fingerprint" regions and in the low frequency range. The bands observed at 733, 773 and 755 cm -~ for trehalose dihydrate, sophorose monohydrate and laminaribiose, respectively, are calculated at 728, 772 and 755cm -l and are due to bending modes of heavy atoms involved in the corresponding glycosidic linkage Ci-Or-C'. Moreover, some known characteristic structural regions may be divided into different parts that have a specific significance. The standard deviation between calculated and observed frequencies below 1500 cm -t leads to values of 3.0, 3.7 and 4.2 cm -~ for the three disaccharides, respectively.

1. INTRODUCTION CARBOHYDRATES r e p r e s e n t o n e o f t h e m o s t w i d e s p r e a d classes o f o r g a n i c m o l e c u l e s . M o n o s a c c h a r i d e s a n d d i s a c c h a r i d e s , o l i g o s a c c h a r i d e s a n d p o l y s a c c h a r i d e s [1, 2], glycan m o i e t i e s o f g l y c o p r o t e i n s [2, 3], a r e p r e s e n t in n u m e r o u s p l a n t tissues a n d / o r living o r g a n i s m s a n d p l a y k e y r o l e s in a w i d e r a n g e o f b i o l o g i c a l p r o c e s s e s . A n a t t e m p t to u n d e r s t a n d t h e s e p h e n o m e n a o n t h e m o l e c u l a r level r e q u i r e s a k n o w l e d g e o f t h e d e t a i l e d t h r e e - d i m e n s i o n a l s t r u c t u r e o f o l i g o s a c c h a r i d e s . N u c l e a r m a g n e t i c r e s o n a n c e ( N M R ) is a p o w e r f u l e x p e r i m e n t a l m e t h o d to access t h e s t r u c t u r a l i n f o r m a t i o n b u t has to b e u s e d in c o m b i n a t i o n with t h e o r e t i c a l c a l c u l a t i o n s [4, 5]. U p to n o w , it has b e e n difficult to o b t a i n t h r e e - d i m e n s i o n a l s t r u c t u r e s f r o m X - r a y o r n e u t r o n d i f f r a c t i o n results for o l i g o s a c c h a r ides [5, 6]. T h u s , m o l e c u l a r m o d e l l i n g p r o v i d e s a p r o m i s i n g m e t h o d for s t u d y i n g t h e c o n f o r m a t i o n s o f c a r b o h y d r a t e s . N e v e r t h e l e s s , t h e c o m p u t a t i o n a l results a r e s t r o n g l y d e p e n d e n t a b o u t t h e r e l i a b i l i t y o f t h e f o r c e field used. A n a c c u r a t e f o r c e field c o u l d be d e t e r m i n e d o n t h e basis o f v i b r a t i o n a l s p e c t r o s c o p i e s a n d o f n o r m a l m o d e calculations. C a r b o h y d r a t e s h a v e b e e n i n t e n s i v e l y s t u d i e d b y using v i b r a t i o n a l s p e c t r o s c o p y (for a r e c e n t r e v i e w s e e R e f . [7]). A s a result o f s t u d y i n g t h e I R s p e c t r a , t h e i m p o r t a n t r o l e * Author to whom correspondence should be addressed. ~ A ) so:14

87

88

MANUELDAUCHEZet al.

played by the anomeric centre has been demonstrated [8-11]; because of the high complexity of the recorded spectra, the interpretation of the data leads to considerable difficulties, particularly below 1500cm -1. In order to have access to the structural information that is contained in vibrational spectra, theoretical calculations are performed using the methods of normal coordinate analyses. Numerous calculations on carbohydrates have been published [12-22]. Almost all these calculations deal with monosaccharides, particularly for a and fl glucose molecules. Only a few extensions have been obtained to disaccharides [15, 16, 19], using monosaccharide results without further refinements [19]. Moreover, apart from the calculations of HUVENNE et al. [20], all the calculations have been obtained for an isolated molecule. Nevertheless, it is well known that it is impossible to reproduce perfectly some characteristic regions of the vibrational spectra of carbohydrates without taking into account the intermolecular and the hydrogen bond contributions [23, 24]. We have recently completed a study in a crystal state model on both a and fl anomers of glucose [24] and galactose [25]. The aim of this series of papers is to obtain vibrational assignments and accurate information for disaccharides and to extend the analysis for the different glycosidic linkages that exist in the field of carbohydrate chemistry. The choice of the disaccharides was made for the following reasons. In order to avoid problems of vibrational assignments, due to epimeric forms, the disaccharides are constituted with the same monosaccharide composition (i.e. glucose). They exhibit different glycosidic linkages, in position and in configuration. They also have to be solved by crystallographic methods and have to be commercially available. Moreover, it is important to underline that the initial force field used in these calculations was transferred directly from our previous works that were carried out on both a and fl anomers of glucose [24]. The refinement was done only on specific force constants and will be described in detail elsewhere [26]. In this work, vibrational IR spectra (4000-100cm -x) and Raman spectra (4000-20 cm-1) were recorded in the crystalline state for the following three disaccharides: trehalose dihydrate, sophorose monohydrate and laminaribiose. They are used to perform normal mode analyses and the vibrational assignments of the observed bands are made on the basis of potential energy distributions. These three disaccharides differ in the position of the glycosidic linkage, 1-1, 1-2 and 1-3 for trehalose dihydrate, sophorose monohydrate and laminaribiose, respectively. Part II of this series will describe similar data and results for three other disacchrides that exhibit the remaining positions 1-4 and 1-6, of the glycosidic linkage and with both a and fl configurations for the 1-4 position.

2. EXPERIMENTAL

2.1. Samples The samples of trehalose dihydrate and laminaribiose were supplied from Sigma Cie (France) and the sophorose monohydrate was purchased from Koch-Light (U.K.). Infrared and Raman spectra of these three disaccharides were recorded using the commercial powder, without further purification. 2.2. Material Raman spectra were obtained for powdered samples contained in capillary tubes. The 90° scattered light was collected using a triple monochromator "CODERG T800" Raman spectrometer, and the 488.0 or 514.5 nm excitation lines of a Spectra-Physics Ar + laser were used. The slitwidths were adjusted for a resolutions of ~4 cm - ~and ~ 1 cm- 1in the 4000-200 cm- I range and in the low frequency range (below 200cm-1), respectively. The laser power on the sample was between 250 and 400roW, depending upon the spectral range, and 16 to 64 scans were accumulated, depending upon the compound studied. The IR spectra were recorded by using an IFS l13V Bruker FFIR spectrometer, working under vacuum to eliminate water and COz vapour. This apparatus is equipped with two detectors, an

Force fieldand vibrationalspectra of oligosaccharides--Part I

89

MCT for the 4000-400 cm -~ range and a DTGS for the 500-100 cm -I range. The samples were pressed in KBr discs for the former region and in polyethylene in the latter one. For both regions, the spectral resolution is of 2 cm-1. One hundred scans were accumulated for the mid-IR and 200 scans for the far-IR. 3. COMPUTATIONALMETHODS

3.1. General In order to determine the frequencies and the normal modes of vibration, the method used is obtained from the Wilson GF method [27]. For the three disaccharides, internal displacement coordinates are determined from the Cartesian coordinates and then are transformed into non-redundant symmetry coordinates. The details of computations and strategy to remove the redundant coordinates are given and discussed elsewhere for the glucose molecule [24]. In this study, the same method is used for both the reducing unit and non-reducing unit of each disaccharide. Nevertheless, the redundancies which are generated in a ring that involved both monosaecharide units by one or more hydrogen bonds, such as for instance between 05 of the non-reducing unit and O~ of the reducing unit in laminaribiose, are not removed. The complete U matrices of each disaccharide are available from the authors. The vibrational assignments of the observed bands are made on the basis of the potential energy distributions (PEDs). The normal coordinate treatment is performed using both a modified Urey-Bradley-Shimanouchi intramolecular potential energy function [28] and an intermolecular potential energy function. Van der Waals interactions, described by a Buckingham type function, electrostatic contributions with a charge distribution [28] computed by the AM~ quantum-mechanical procedure [29] and an explicit hydrogen bond function, are included in the latter energy term. All the calculations were carried out on an IBM 3090 computer at Circe (Orsay, France). 3.2. Geometry A vibrational analysis requires accurate knowledge of the atomic coordinates. The molecular geometries used were taken from the X-ray diffraction data of TAOA et al. [30] for crystalline trehalose dihydrate, of OnANESSIAN et al. [31] for crystalline sophorose monohydrate, and of TAKEOA et al. [32] for crystalline laminaribiose, and are shown in Fig. 2. However, when some bond lengths and bond angles between the heavy and the hydrogen atoms were too short and/or too large, the corresponding hydrogen positions were recalculated by AM~ semi-empirical geometry optimization calculations [29], retaining the experimental orientations. 3.3. Force field The normal mode calculations were performed for each disaccharide in a crystal model. The initial force field was transferred from results obtained for a-D-glucose and r-o-glucose [24]. Force constants were applied, respectively, to each corresponding monosaccharide unit of the disaccharides. Thereafter, refinement of the force constants is made until a satisfactory agreement between the observed and the calculated frequencies is obtained. Details of the crystal models, of the refined force constants and of the computational procedures of this series of papers will be published elsewhere [26]. 4. RESULTSAND DISCUSSION 4.1. General Figure 1 shows a schematic representation of a disaccharide and the atom designation for the glycosidic linkage between the non-reducing residue and the reducing residue.

MANUELDAUCHEZel al.

90

HO~

H2OH 5 O 3I

/"

,,

,,

R'IfH, R;---OH, Alpha Non-ReducingUnit

,,

~. N ~' - - ~ I O' q ~.m-.--~\

Re~eing Unit

,

l~t=OH, R'2=H, Beta

I i, R2

Fig. 1. Schematic representation of a disaccharide and atom designation for the glycosidic linkage between both non-reducing and reducing residues. In this figure, the non-reducing unit has its anomeric carbon C~ in the ~ configuration. All the atoms of the reducing unit are marked with a prime. The value of C" depends upon the position of the glycosidic linkage: in this paper, x has the value 1, 2 or 3 and in Part II x will have the value 4 or 6.

The value of Cx depends upon the position of the glycosidic linkage: in this paper, x has the value 1, 2 or 3. All the atoms of the reducing unit are marked with a prime. The three disaccharides studied in this paper, using the previous nomenclature for the glycosidic linkage, are listed in Table 1 and are represented schematically in Fig. 2. From these figures, drawn from crystallographic data [30-32], it is seen that both trehalose dihydrate and laminaribiose exhibit intramolecular hydrogen bonds between the two pyranose rings. In the former case, a complex hydrogen bond network is established between some hydroxyl groups and water molecules. However, it is well known [7] that vibrational data of such interactions are sensitive to the local environment of the chemical bonds. Therefore, all these intramolecular hydrogen bonds are treated in the calculations as intrinsic coordinates of the disaccharide. The following section will discuss the experimental vibrational data and the computational results for the three disacchaddes studied. 4.2. Vibrational assignments for the three disaccharides Before our analysis of the IR and Raman spectra and the results of our normal mode analyses are discussed, it is important to underline that except for the CH stretching frequency region of trehalose [33], no vibrational spectra of these disaccharides have been published. These spectra have been deposited with the British Library Document Supply Centre at Boston Spa, Wetherby, West Yorks LS23 7BQ, U.K., as supplementary publication No. SUP 13068 (11 pp). For purposes of discussion, the Raman and IR spectra and the corresponding assignments will be divided in different regions that have a specific significance in the structural analysis of carbohydrates [34]. Tables 2, 3 and 4 present the observed Raman and IR data compared with the calculated frequencies for the different species and a description of each mode of vibration for the crystalline trehalose dihydrate, sophorose monohydrate and laminaribiose, respectively. As described previously [24, 26], considering the fact that the Table 1. Position of the glycosidic linkage and configuration of both units of each studied disaccharide

Molecule Trehalose, 2H20 Sophorose, H~O Laminaribiose

Configuration Non-reducing unit Reducing unit a ~ /~

a a ~

Position 1--* 1 1--,2 1--* 3

Force field and vibrational spectra of oligosaccharides--Part I

91

\

o

1

a-D-glucopyranosyl-(l-lt)-a-D-glucopyranose,2H20

~-D-glucopyranosyl-(l-2~-a-D-glucopyranose,H20

O ........

•-D-glucopyranosyl-( l-3')-D-D-glucopyranose Fig. 2. Schematic figure obtained from crystallographic data of trehalose dihydrate [30] (a-Dglucopyranosyl-(1-1')-a-D-glucopyranose, 2H20), sophorose monohydrate [31] (/~-Dglucopyranosyl-(1-2')-a-D-glucopyranose, H20) and laminaribiose [32] (~-D-glucopyranosyl-(13')-//-D-glucopyranose). The hydrogen bonds are drawn in dashed lines. The oxygen atom of water molecule is labelled W.

symmetry coordinates are very complicated, the description of each mode of vibration is given from the PED for force constants. Nevertheless, for a better knowledge of the low frequency range, external coordinates are used instead of force constants for non-bonded interactions. In these tables as shown for Fig. 1, the force constants of the atoms involved in the reducing unit are written with a prime. For molecules as complex as disaccharides, the PED of each table shows that almost all the modes are very highly coupled

92

MANUEL DAUCHEZet t//.

Table 2. The observed Raman and IR frequencies (cm-m), the calculated vibrational frequencies (cm -~) in the four symmetry group species and the potential energy distributions of each mode of vibration for crystalline trehalose dihydrate Observed frequencies (cm -~)

Raman

IR

1487 1472 1467

1466

1453

1451

1444

1423

1425

1411

1408

1397

1400

1385

1385

1370

1369

1356 1347 1329 1309

1356 1334 1311

1290 1242

1241

1213

1212

1188 1166

1147 1129 1121

1150 1128

1100

1111 1099

1081

1085

1060 1045 1019

1032 1015

996

999

976 955

957

Calculated frequencies (cm -m) Species

A 1485 1482" 1472 1467 1466 1458 1457 1452§ 1448" 1445" 1438 1435" 1430" 1423" 1417 1414 1409§ 1398 1389" 1388 1386 1384 1368 1367 1361 1358 1349 1333 1305 1299 1295 1287 1238 1223 1216" 1192 1189' 1171" 1169" 1156 1151" 1132§ 1125 1113§ 1092§ 1087§ 1077" 1066" 1063" 1061" 1044" 1007" 999 997* 990* 971 948*

Bi 1485 1482 1472 1467 1466 1458 1457 1453 1448 1445 1438 1435 1430 1423 1417 1413 1410 1398 1389 1388 1386 1384 1368 1367 1361 1357 1349 1333 1305 1299 1295 1288 1238 1223 1216 1192 1189 1171 1168 1156 1151 1132 1125 1113 1092 1087 1077 1066 1063 1060 1044 1017 999 997 990 971 949

B2 1485 1482 1472 1466 1458 1457 1457 1454 1447 1445 1438 1435 1430 1423 1416 1414 1410 1397 1389 1388 1387 1384 1368 1367 1361 1357 1350 1333 1306 1299 1296 1287 1237 1223 1216 1192 1189 1171 1169 1156 1151 1130 1129 1114 1092 1087 1077 1066 1063 1060 1044 1017 1000 997 991 971 948

B3 1485 1482 1472 1467 1458 1457 1456 1454 1447 1445 1438 1435 1430 1423 1417 1414 1410 1398 1390 1388 1386 1384 1368 1367 1361 1357 1350 1333 1306 1299 1295 1288 1237 1224 1216 1192 1189 1171 1169 1157 1151 1130 1126 1114 1091 1087 1076 1066 1063 1060 1044 1017 1000 997 991 971 949

Potential energy distribution H ' C ' O ' + C ' C ' H ' + H'C[O; HCIO1 + HC105 + CCH + H ' C ' O ' HC505 + CCH + HCO + C4OH H'C~,I-I'+ H'C~O' + C'C~H' C4OH + HC60 + CCH + CC505 CC~H + HC~O5 + CCH + H ' C ' O ' HCd-I + HC60 + HC505 + CCH H ' C ' O ' + C ' C ' H ' + CCH + C ' O ' H ' C'C~H' + C ' C ' H ' + C ' O ' H ' + C~O'H' C ' C ' H ' + H ' C ' O ' + H'C'O; + H'C;O' HCO + CCH + C4OH C'C'H' + H'C'~O~ + C ' O ' H ' + H'C;O' C~O'H' + HCO + H'C[O' + CCH HCO + CCH + C~O'H' + C4OH C ' O ' H ' + H ' C ' O ' + C ' C ' H ' + HCO C ' O ' H ' + C'C'H' C2OH + C ' O ' H ' + CCH + HCO H'C'O' + C'C'H' + C'O'H' COH + C ' O ' H ' + CCH + HCO C~O'H' + C6OH + C'C'H' C'C'H' + C6OH C~O'H' + C-6OH C'C'H' + H'C'O' + C'O'H' CCH + HCO + C4OH + C6OH CCH + COH + HCO + CC6H COH + CCH C'C'H' + C ' O ' H ' + C~O'H' + H ' C ' O ' C'C'H' + H ' C ' O ' C'C~H' + H'C~O' CCr,H + HC60 CCH + COH + HCO CCH + COH H'C~O' + C'C~H' HC60 + CC6H + CCH + C5C6 C'C'H' + H ' C ' O ' + C ' O ' H ' + C'C'rg C ' C ' H ' + CCH + C'C'rg CCH + CCrg + CO + HCO CCH + HC60 + CC6H + CCrg C'C'rg + C~O~+ C;O~ + C'O' C'C'rg + C;C~ + C ' C ' H ' + C'O' CCrg+ CO + CCH + CtOs C~O~+ CCrg + C'C'rg + C'O' CiO~+ CO + CCrg +CIO5 CIO~+ C~O~ + CCrg + C'O' C~O~+ CO + CCrg + C606 C~O~+ CO + CCrg + C'~O~ CO + C606 + CCH + CCrg C~O~+ C'O' + C'C/8+ C;O; CCrg + C606 + C'O' + CIO5 C~O~+ C'O' + CiO~ + C,O~ C'O' + C'C'rg + C~O; + C;O; CO + C606 + C~O5+ CCrg CO + C'O' + CCO + CCrg C'O' + CO + C ' C ' O ' + C'C'rg C'O' + C~O; + C ' C ' O ' + C;C~ CO + C~Ot + CCO + CCrg CiOi + C'O' + C'C'rg + C ' C ' O ' continued on facing page

93

Force field and vibrational spectra of oligosaccharides--Part I Table 2. c o n t i n u e d Observed frequencies (cm -~) Raman

IR

924~h 912 848 84O 805

92# h 911 852 842 804

733 698 674

731 697 679 669

641

644

620 6O7 603 596 581

613

582 573

543

538

523

519

485 475 452 442 433

443 428

410 391 378 371 355

410

338 330

332

297 285 260 247 223 214

299 281

202

202

183 171

181

159

131

370 359

247

Calculated frequencies (cm -t) Species A

B~

B2

920 847 835 807 784§ 728§ 689§ 681" 670* 664 638 632 627 611 602* 597* 588* 571§ 567 543 537* 521 516 499 483 471 459* 453 443 436 420 415 393 380 367 350 342 339 324 316 308 298§ 282 273 244* 224

919 847 835 808 783 728 69O 682 671 666 636 630 626 618 601 595 589 571 566 543 537 517 516 502 482 472 458 454 443 436 419 413 394 380 365 350 341 340 326 317 309 297 278 274 247 221

208 202* 189 180 173" 166" 155" 148" 141' 132§ 120§

207 197 193 180 177 165 158 148 137 127 122

919 920 847 847 835 835 807 807 784 784 729 729 687 687 682 685 677 676 667 667 639 643 630 629 621 620 612 616 603 603 593 593 591 591 573 573 565 565 546 545 535 536 519 520 516 517 500 497 484 484 471 471 460 461 451 451 446 446 437 436 421 418 413 413 395 395 384 384 366 365 352 352 338 339 334 336 324 325 319 321 311 313 298 301 287 285 278 275 248 243 218 213§ 214 208 197 198 189 185 183 181 170 172 167 167 153 159 147 155 139 143 136 137 125 127

216

168 150 147 135 124

B~

Potential energy distribution

CiOi+ C105 + CIO|C~ + CCO C'C~H' + H'C~O' + C;O; CC6H + HC60 + rC606 + rC5C6 rC~O~+ OHO,,, + HO,,,H + rCO C;O; + CO5C + C'O~C' + C~C~Ot CO5C + C'O~C' + OC~O + CCO CCO + CIOIC~ + CC1OI + rC202 CCO ÷ C5C60 ÷ rC606 ÷ ClO 1 C~ HO,,H + OO,,H + C~O~C~+ CCO OO,,H + HO,,H + OOwH tC606 + C'C'O' + CCO + C~C~O~ rC606 + TC'O' + C ' C ' O ' C'C'O' + rCO rC606 + CCO + r C ' O ' TC'O' + C'C'O' + CCO + OC10 OOwH + rCO + HO,,H + O'C~O' OO,,H + HO,,H + rCO + r C ' O ' r C ' O ' + HOwH+ CCO + rCO r C ' O ' + CCO + C5C60 + C'C'O' TC'O' + rCO C ' C ' O ' + C~C~O' + r C ' O ' + CCO C'C'O' + CCO + C~C;O; + rCO CCO + C5C60 + OC~O + rCO CCO + OO.,H + rCO + r C ' O ' rCO+CCO C'C'O' + C'C'C' + rC~O~ C'C'C' + C'C'O' + C;C~,O' + C~C~O; CCO + C'C'C' + C'C'O' + rC~O~ OHO +rC~O~+ CCO + C ' C ' O ' CCC + CCO + rCO HO,,H + OO,,H + COH,, + r C ' O ' C'C'O' + C'C'C' + C~C[O' + C;C~O' HO,,H + COHw + rC202 C'C'O' + CCO + C~C~O~ CCO + C ' C ' O ' + C2CIOt + CsC60 C'C'O' + C[C~O' + CCO CCO + C'C'O' C ' C ' O ' + CCO + C;C~,O' CCO + C'C'O' + CCIO~ + Hbint~ C ' C ' O ' + CCO + C~C;C~ + Hbi.t~ CCO + C6C50 + C ' C ' O ' + C~O~C'~ C6C505+ CCO + CC~O~ + CC~O5 C;C~,O' + Hbintra + rC~O~ Hba,.a + C1OIC', + O'C',OI + C'O;C' Hbi~t,~+ C~O~C~+ CCO + C'C'O' Hbimra+ CCO + CCC + C'C'O' Hbintra + C'C'O' + CCO + C'C'C' CCO + CCC + rCC + rC~C6 C'C'O' + CCO + CCC + CO~C Hb~.t,~+ C'C'C' + C'C'O' + r C ' C ' Hbl.t~ + C C O + rC'O'

Hbi,.¢.+ CCO + C'C'O' + C'C~,O' rC;C~,@rCsC 6 ÷ CCO ÷ rC606 C'C'O' + C'C'C' + C'O[C' + Hb~.t,~ rC;C~,+ Hbint~+ rC~C~+ rC606 CCO + rC~C~ + rCC + rCO C ' C ' O ' + Hbintta+ CIOIC'I + rC'lO1 C'C'O' + Hbintra+ CCO + CO~C continued on next page

MANUELDAUCHEZet al.

94

Table 2. continued Observed frequencies

(cm-') Raman 117 97 82 75 68 63 51 48 40 35 28 19

IR 118 113 103

Calculated frequencies (cm -1) Species A

Bj 119"

115" 102§ 100" 85§ 73 68* 56§ 52§ 46*

105 96* 91 75 64 63§ 60

B3

120 111 102

120 113

93

99 93 81

73 69 62

67 59

53

55

47 38* 35

37§ 29 19"

B2

35 26

Potential energy distribution C'C'O' + CCO + C'C'C' + rCC C'C'O' + C'C'C' + C~CIO~+ tC'C' C'C'C' + tC5C6 + rC'C' + rC'O' C'C'O' + CCC + C'O~C' + rC~Ot Tr+Tx+C'C'C'+Rc Rc + C'C'C' + C'C'O' + rC~O~ R~ + rC;C~ + CCO + rCO Tx+Rc+RA+rCIO 1 Ty + Rc + CCO + rC~O~ Tv+ Tx+ Rc+C'C'O' Tr+Rn+tCO+HOwH Ra+Rc+ Tv+ Tx+ CCO Rs + Tx+ Rc + RA + CCO RA+rCO+Tx+rC[OI Tx+Rc+RA+Tr Tz + Rc + RB + ~:CC

Ow is the oxygen atom of the water molecule. Hbinuais the contribution of the hydrogen bond between the two units of the disaccharide. Hb is the contribution of an intermolecular hydrogen bond. Sh is for a shoulder and rg is for the atoms belonging to the ring. Tx, Tv, Tz are respectively translational lattice vibrations along the X, Y, Z crystallographic axes. RA, Rs, Rc are respectively rotational lattices vibrations around the principal axes. The modes marked with an asterisk are highly coupled and involved more than the four contributions described in the PED. Similarly, the modes marked with a § are highly coupled modes with more than four motions which involved atomic groups belonging to the glycosidic linkage. Considering the fact that symmetrical coordinates are very complicated, the description of each mode of vibration is given from the PEDs for force constants, taking into account only the intramolecular force constants of bond lengths, bond angles and torsions. Nevertheless, for a better knowledge of the low frequency range, the external coordinates involving in the corresponding modes are used with the PEDs for force constants description. The eigenvalues, the eigenvectors, the U matrix, the PEDs in terms of local symmetry coordinates and the Lx matrix (displacements of the atoms for each mode) for this disaccharide and the following ones are available from the authors.

v i b r a t i o n s . N e v e r t h e l e s s , s o m e m o d e s t h a t a r e highly c o u p l e d involve o n l y a t o m i c m o t i o n s c o n c e r n i n g o n e o f t h e t w o p y r a n o s e rings. T h e r e f o r e , t h e e x p l a n a t i o n s for t h e s e m o d e s arise f r o m t h e p r e d o m i n a n c e o f an i s o l a t e d r e s i d u e t h a t c o n s t i t u t e s the d i s a c c h a r ide, a n d i n t e r r e s i d u e c o u p l i n g has to b e n e g l e c t e d , a l t h o u g h , in a few case, t h e m o d e s can b e c o n s i d e r e d to arise f r o m o n l y o n e t y p e o f m o t i o n a n d to be a l m o s t p u r e . It m a y b e s e e n f r o m T a b l e s 2 - 4 t h a t t h e r e is a v e r y g o o d a g r e e m e n t b e t w e e n c a l c u l a t e d f r e q u e n c i e s a n d o b s e r v e d d a t a . B e l o w 1500 cm-1, this a g r e e m e n t l e a d s to a v a l u e o f the s t a n d a r d d e v i a t i o n b e t w e e n o b s e r v e d f r e q u e n c i e s a n d c a l c u l a t e d f r e q u e n c i e s o f 3.0, 3.7 a n d 4.2 cm-~ for t r e h a l o s e d i h y d r a t e , s o p h o r o s e m o n o h y d r a t e a n d l a m i n a r i b i o s e , r e s p e c tively. U p until n o w , t h e r e h a v e b e e n no c a l c u l a t i o n s p u b l i s h e d in t h e l i t e r a t u r e for t h e s e t h r e e d i s a c c h a r i d e s a n d it is i m p o s s i b l e to c o m p a r e o u r results a n d to b e sure o f o u r v i b r a t i o n a l a s s i g n m e n t s . In 1991, ABBATE et al. [33] p u b l i s h e d a w o r k b a s e d o n v i b r a t i o n a l a n d t h e o r e t i c a l i n v e s t i g a t i o n s o f a , a - t r e h a l o s e , b u t o n l y for t h e C - H stretching region. Our assignments are based upon known attributions of carbohydrates a n d p a r t i c u l a r l y o f m o n o s a c c h a r i d e s [ 1 2 - 2 1 , 24, 25]. T h a t is w h y w e h a v e c h o s e n d i s a c c h a r i d e s c o n s t i t u t e d o n l y o f b o t h a n o m e r s o f glucose which a r e t h e c a r b o h y d r a t e s which h a v e b e e n s t u d i e d t h e most. W i t h o u t t a k i n g into a c c o u n t w a t e r m o l e c u l e s , a d i s a c c h a r i d e c o n t a i n s 45 a t o m s a n d c o n s e q u e n t l y 129 (3No6) m o d e s a r e p r e d i c t e d . F o r t h e f r e q u e n c i e s which a r e o b s e r v e d , it is i m p o s s i b l e to p r o p o s e a definitive o n e - t o - o n e c o r r e s p o n d e n c e b e t w e e n o b s e r v e d d a t a a n d c a l c u l a t e d results. C e r t a i n l y , t h e f r e q u e n c y m a t c h c a n n o t be e x p e c t e d in s o m e cases to b e r e a l l y p e r f e c t , b u t the a g r e e m e n t is in m o s t cases within a few w a v e n u m b e r s . M o r e o v e r , all t h e d i f f e r e n t s p e c t r a l r a n g e s a r e r e p r o d u c e d in totality. W e will n o w d e s c r i b e the results o f t h e calculations for e a c h different region of frequencies.

Force field and vibrational spectra of oligosaccharides--Part I

95

Table 3. The observed Raman and IR frequencies (cm-t), the calculated vibrational frequencies (cm -~) in the four symmetry group species and an approximated description of each mode of vibration for crystalline sophorose monohydrate; the notes used for trehalose dihydrate (Table 2) are the same in this case Observed frequencies (cm -~) Raman

1474 1469 1449

IR

1471 1464 1436

1421 1414 1408

1381

1391 1379

1369

1366

1349

1355

1332 1324

1338

1317 1303

1301

1278 1269

1275 1260

1250 1234 1210 1179 1170

1230 1206

1155 1139

1151 1136

1116

1110

1169

1097 1086 1078 1071 1056 1048

1042

1022 1012

1024 1014

Calculated frequencies (cm -~) Species A

1474 1469 1451 1434 1433 1423 1416 1407 1405§ 1403" 1396 1381 1377" 1367" 1362 1359" 1355 1350 1344 1337§ 1322" 1319" 1315 1307" 1303 1297 1284" 1272" 1270" 1262 1257 1247 1241 1227 1206 1176" 1166" 1163 1161" 1137" 1124 1123" 1103" 1101" 1089§ 1078" 1073 1061§ 1051§ 1046 1039" 1027§ 1013"

B~

1474 1470 1451 1434 1433 1424 1416 1406 1405 1403 1396 1381 1378 1364 1362 1356 1355 1352 1344 1341 1321 1319 1316 1308 1304 1297 1284 1271 1270 1262 1257 1247 1241 1228 1206 1176 1165 1164 1161 1138 1124 1122 1103 1101 1088 1078 1075 1061 1051 1047 1039 1027 1013

B2

1474 1470 1451 1435 1433 1423 1416 1406 1405 1403 1396 1381 1377 1367 1362 1359 1354 1349 1344 1337 1322 1319 1315 1307 1303 1296 1285 1271 1270 1261 1257 1247 1241 1230 1206 1176 1165 1164 1161 1137 1124 1121 1103 1101 1088 1079 1075 1060 1050 1046 1039 1027 1014

B3

1474 1469 1451 1435 1433 1425 1416 1406 1405 1403 1396 1381 1378 1364 1363 1356 1355 1352 1344 1340 1321 1319 1316 1308 1303 1296 1284 1272 1270 1261 1257 1247 1241 1230 1206 1176 1165 1163 1161 1137 1124 1122 1102 1101 1089 1079 1073 1061 1051 1047 1039 1027 1014

Potential energy distribution H ' C ' H ' + H'C~O' HCH + HC60 H'C;O' + C'C'H' H'C~O1 + HC101 + CCIH + C'C[H' HC505 + CCH + HC105 + H'C~O1 C'C~H' + C'C~H' + H'C'~O~ COH + HCO + CCH + HC10~ C~O'H' + COH H ' C ' O ' + C ' O ' H ' + HCO + C ' C ' H ' HCO + C~O'H' + C ' O ' H ' + CCH H'C'O' + C'C'H' HCO + COH + CCH H'C;O' + C'C~O~ + H ' C ' O ' + CC~H' C6OH + COH + HCO + HC~O5 HCO + HC~O5 + CCH + COH C6OH + H'C[O' + H'C~O~ + H'C~O~ C ' C ' H ' + C'C~H' + H'C~O' + C ' O ' H ' CCH + COH + C6OH H'C'O' + C'O'H' + C'C'H' C6OH + COH + CCH + HC~O~ COH + CCH + HCO + HC60 C~O'H' + H ' C ' O ' + C'C'H' + C'C~H' CCH + COH + HCO CC6n + HC60 + C6OH + COH CCH + COH + HCO C ' C ' H ' + C ' O ' H ' + C'C~H' + H'C~O C ' O ' H ' + C~O'H' + C ' C ' H ' + C'C~H' CCH + C ' O ' H ' + C'C'H' + C~O'H' CCH + COHC + HC60 + C ' O ' H ' C ' C ' H ' + C ' C ' H ' + H'C~O' + C ' O ' H ' HC60 + CCott + COH + CCH CCH + COH C'C'H' + C ' O ' H ' + CCH H'C~O' + C'C~H' C'C~H' + CCIH + CCH CCrg + C'C'rg + C~C~+ CCH C ' C ' H ' + C;C~ + C~O~+ CC'rg CCH + CCrg + CO + C'C'H' C'C'rg + C~O~+ CC'rg + C5C6 C~Ot+ C~Oj + CCrg + C'C'rg CCH + CCrg + C'C'rg + CO C'C'H' + C~O~ + C'C'rg + C~O~ CCrg + C'~O'~+ C'C'rg + C ' C ' H ' C505+ CCrg + C~O~ + HC60 CCrg + CCH + C~O; + C'C'rg C~O~+ C~OI + C~O~+ C~O~ C'C'rg + C'O' + C'~O;+ C'C'H' CO + C'O' + C'C'rg + C~O~ C'O' + CO + C;O; + C~O~ C~O6+ C~O5 + CCrg + CsO~ C~O~+ C~O[ + CCrg + C~O[ CCrg + CO + C~O~+ C~O~ C'O' + CO + C~O~+ C~O~ continued on next page

96

MANUEL DAUCHEZ et al.

Table 3. continued Observed frequencies

(cm-b

Calculated frequencies (cm -~) Species

IR

A

B~

B2

997

994

988 939 921 901 853 773 712

970 933

999§ 998 986* 959* 917" 894 861 772 715" 694 690§ 682 652 645* 640 626* 612 602 589 566* 550 535* 529* 511 498 485 476* 468 444 431 425 419" 406 388 377 360§ 347* 336 330* 320 309 299 286* 255* 253

999 998 985 959 918 894 861 772 716 691 691 680 653 647 641 625 613 602 589 564 550 539 529 516 493 484 477 471 445 434 425 419 407 390 369 357 345 334 332 323 305 297 283 262

999 998 986 959 917 895 861 772 718 693 689 684 655 648 640 620 612 604 588 564 552 536 528 511 493 485 478 468 444 433 425 415 408 390 376 358 340 332 327 320 313 297 286 260 250

Raman

647 640

597 580 570 553

897 849 770 714

640

589 553

529

527

491

495 482

474 452

447 424

409 394

391

365 347

360 351 336

309

313

277 267

282

236

245 231 222

222 199 195 182

194

224* 221 210§ 193 192 178

241 221 220 211 195 189

226 222 205 201 190 178

B3

Potential energy distribution

1000 998 986 959 917 894 861 772 719 692 691 681 654 648 640 626 614 604 589 565 551 539 529 509 497 482 475 470 444 433 426 414 408 389 370 354 341 335 325 321 309 296 287 257

C'O' + CO + C5C6+ CCrg CO + C'O' + CCrg + CCO CO + CCrg + C5C6+ CCH C'O' + C~O~+ C;C~ + C'C'rg C'C'rg + C~O~+ C;C~ + C'~O~ CC6H + H C 6 0 + C505 + ~C606 C'C~H' + H'C~O' + C~O~+ rC~O~ C'C~O~ + C'O;C' + C'C~O; + C~O~C~ C~C~O~ + C~O~C~+ C'C'O' + C'C~O' 'rC606 + C C O -Jr-CC101 C C O + CC101 -~ ~C606 + C'C~O~ rCO + r C ' O ' r C ' O ' + rCO + C;C~O, + O'C;O' CtC~O' -[- C4C50 + C C O q- C C i O 5 CCO + rC;O; + C~C~O~+ C~C~O~ C'C~O' + rC~O; + r C ' O ' + CCO rC;O~ + CCO + C ' C ' O ' OOwH + HO~H + HB + CCO CCO + rC~O; + O'C~O' CCO + C~C~O' + C4C50 + C ' C ' O ' rC~O~ + C ' C ' O ' CCO + C ' C ' O ' + OC~O + O'C'~O' C'C'O' + O'C~O' + C'C~O' + C~C~O' C'C'O' + CC60 + CC~Os + OC~O r C ' O ' + CCO + C4C50 + C'C'C' rCO + r C ' O ' + CCO r C ' O + rCO + CCC + C~C~O' rCO + C'C'O' + C4C50 + r C ' O ' CCC + CO5C + CCO + r C ' O ' rCO C'C'C' + CCO + C'C'~O~+ O'C;O' CCO + C'C'C' + C'C'O' + C'C~O~ C'C'C' + C'C'O' + C'C~O~ + rCO C'C'O' + C'C~O~ + C~C~O' CCO + CCC + CC60 C C O + C'C~O'1+ C5C60 -[- C6C50 CCO + C'C'O' + C4C~O + CC60 C ' C ' O ' + CCO + C~C~O' + rC~C~ CCO + CC60 + C'C'O' + C~C~O' CCO + C'C'O' + C'C;O; C C O + C ' C ' O ' + r C C + rC5C6 C'C'O' + CCO C'C~O' + CCO + C;C~O[ + O'C'tO' C'C~O' + C'O~C' + O'C'~O' + C'C'O' rCsC 6 + C C O + CCiO 1 CCO + rC~C6 + rCC + CC~O~ C6C50 + C4C5C6 -~-C C O -[- CClO 1 C~C~C~,+ C~O~C~+ CCO + C'C~O' C6C~O + OC~O + rCC + rC5C6 C~C~O' + zC5C6 + r C ' C ' + rC~C~ C4C5C6 -]- C C O + CO5C "[- C~C20 I OCtO + C~C~O; + C~C~C~+ CtO~C~

244 228 221 210 193 188 178

continued on facing page

Force field and vibrational spectra of oligosaccharides--Part I

97

Table 3. continued

Observed frequencies

Calculated frequencies (cm -])

(era-1)

Species

Raman

164 150 145

IR

176 160

A

B1

160§ 156"

173" 155 154

145 137 131

135"

136 132"

120 111 105

123" 112 109

122 112

126 105 93 84 73

96* 88§

37 32

B3

158 151 141§

162 154 143 138

128"

118

113 105

99§ 97

111 97 91

87

75

78§ 71

67*

69

62 54 47

B2

57§

61

46 40* 37§ 30*

50 42

76 67

62* 61 56§ 50 44

62 51

Potential energy distribution c101c~ + ocmo + c~c~o; + c c o rc5c6 + rCC + rC'C' + CCO rC'C' + tC'O' + C'C'C' + C'C'O' rCC+ rC5C6+rC'C' + rC;C~ rCC + ~C5C6+ rC~O~+ CCC tCC + rC'C' + rC5C6+ tC;C~ rCsC6+ rC;C~+ rC'C' + CC~Om tC;C~ + rCC + rC5C6+ tC'C' CCO + rCO + TC;C~+ rCO CCO + C'C'C' + rC'C' + HB R8 + rCC + R c + rC5C6 RA+ rC~O~+ rC1Ot + C~O1C~ RB+ rCC + rCO + CCO Rc+ R,4 + tC'C' + rCC RA+ rC'C' + rC~O1+ rC~O~ Tz+RA+ICC+RB Re + Tz + tCC + rC5C6 Re+ Ty+ tC5C6+ Tz Tz+Tx+TC'C'+rCsC6

Ra + RA+ Tz + rC;O; 38 30

Tx+Tv+rC~O~+tC606 TZ+RA+Rc+rCC+tC'C' Rc + Tr + Ra + rC'O'

O H and C H stretching regions. T h e results of the calculations determined for the three disaccharides are in fairly good agreement with experiments in these ranges and are able to reproduce the different parts of the spectra. In the 3700-3200 cm -1 frequency region, the P E D s show almost pure modes (contribution of 98-100% in the P E D ) corresponding to the O H stretching modes. It is well known that the character of the spectrum in this range is strongly influenced by intermolecular hydrogen bonds. The use of a specific potential energy term for hydrogen bonds in the calculations allows us to calculate frequencies that are differentiated. For trehalose dihydrate and sophorose monohydrate, frequencies arising from water molecules are observed in a higher range and are correctly reproduced in the calculations. In the 3000-2850 cm -1 frequency region, modes due to the valence vibrations of CH groups are calculated. From the comparison of the data obtained for the three disaccharides, it is possible to differentiate in this region two different "hills", one with bands observed between 3000 and 2930 c m - 1 and the other one between 2930 and 2850 cm -~. All these vibrational modes are described correctly by the calculations with only one force constant. The purpose of this work is not to attribute unequivocally each C H stretching modes as was done by ABBATE et al. [33], but to reproduce the overall spectral range. Nevertheless, it is important to point out that the calculated frequencies in this spectral range are coupled modes. The four lowest calculated frequencies should be attributed to antisymmetric and symmetric valence vibrations of the two primary hydroxyl groups of each disaccharide. 1500-1200 c m -1 region. This spectral region exhibits numerous bands and is one of the richest in structural information. As was underlined by MATHLOUTHI and KOENIG [7], the assignment of the observed bands by classical group frequencies correlations is difficult, because the calculated frequencies exhibit highly coupled modes. In both R a m a n and I R spectra, these quite closely spaced lines of medium and strong intensity are distributed in three different spectral parts: ~1500-1425, ~1425-1300 and ~1300-1200 cm -]. Only a few bands are found in the former region; most of the strong

98

MANUEL DAUCHEZeta!.

Table 4. The observed Raman and IR frequencies (cm-~), the calculated vibrational frequencies (cm -l) in the two symmetry group species and an approximated description of each mode of vibration for crystalline laminaribiose; the notes used in the trehalose dihydrate (Table 2) are the same in this case Observed frequencies

Calculated frequencies

(cm -I)

(cm -1)

Raman 1466 1449

IR 1489 1451 1433

1416 1401

1401 1390

1377

1373

1363

1364

1350

1346

1327 1315 1301 1291

1337 1324 1314 1299

1283

1285

1264 1253

1263

1224

1221

1199 1180

1199

1153 1138 1126 1119

1165 1153 1137 1128 1118

1101

1106

1089 1079 1070 1059 1052 1041 1021

1041 1030

A 1466 1453 1431 1422 1419" 1409" 1400" 1392 1386§ 1379" 1366 1363" 1355§ 1346§ 1344" 1366" 1330" 1308" 1297 1290" 1286" 1282" 1275" 1266 1265" 1259 1245" 1241" 1227 1223 1205 1190 1178" 1174" 1171" 1160§ 1147" 1141" 1133" 1121 1110 1107' 1097§ 1091" 1085' 1076" 1066§ 1051" 1049" 1036 1030" 1023§

B

Potential energy distribution

1466 1451 1431 1421 1419 1410 1398 1393 1385 1378 1365 1363 1355 1347 1344 1336 1330 1308 1297 1289 1286 1282 1275 1266 1265 1257 1243 1240 1225 1221 1205 1191 1178 1173 1172 1161 1146 1141 1133 1120 1109 1107 1098 1090 1085 1075 1066 1051 1049 1036 1030 1023

HCH + HC60 + CC6H H ' C ' H ' + H'C~O' H'C;O' + C ' C ' H ' + C'C~H' HC505 + CCH + HCO HC505 + HCIO1 + CCH + CCIH HCxO1+ HCO + H ' C ' O ' + CCH HCO + CCH + CCtH + HCsO5 H ' C ' O ' + C'C'H' + C ' O ' H ' + H'C~O1 HCO + COH + CCH + CCIH H'C~O' + C'C~,I-I'+ H ' C ' O ' HCO + COH + CCH H'C]O~ + H ' C ' O ' + C ' C ' H ' + C'C~H' H'C;O~ + H'C~O' + C ' O ' H ' + C'C;H' HC~O5+ CCH + HC60 + CCIH C'C[H' + H'C;O' + H'C;O~ + C'C~H' HClO 5+ HClO~ + CCH + CC6H C ' C ' H ' + H'C~O l + H ' C ' O ' + C'C~H' C ' C ' H ' + C'C~H' + C'C~H' + H ' C ' O ' C6OH + CCH + C ' C ' H ' + C~O'H' CCH + C'C'H' + C'C;H' + HCO C~O'H' + CCH + CC_x,H+ C ' C ' H ' CCH + C ' C ' H ' + C'C)H' + HCO C6OH + C ' C ' H ' + CCH + HC60 CCH + C'CH' + C~O'H' + C ' O ' H ' CCH + C ' C ' H ' + CCt,I-I + HC60 COH + CCH + HCO CCH + C ' O ' H ' + C ' C ' H ' + H°C'O ' CCH + C ' C ' H ' + C ' O ' H ' + COH COH + CCH + HCO + C ' C ' H ' C ' C ' H ' + COH + H ' C ' O ' COH + CCH + HCO C[O'H' + C'C'H' + C'C~H' + C'C;H' C'C~H' + H'C~O' + C'C~-I' + C;O; CC61-I+ C'C~-I' + C5C6+ C505 CCrg + C~O~+ C~O[ + C'C~H' CCrg + C'O' + C'C'rg + C;Ot + CCH C'C'rg + CO + C~Ot + CCrg + CCH C'C'rg + CCrg + C'O' + CiO~ + CO CCrg + C505 + CO + CCH C'C'rg + C'C'H' + CCrg + CCH C'C'rg + CCrg + C;O~ + C~Ot C'C'rg + C~O} + C;O; + CCrg C'C'rg + CCrg + CCH + C ' C ' H ' CCrg + C505 + CCH + HC60 C'C'rg + C;O~ + C~O; + CCrg CiO 5+ CCrg + ClOt + C606 CO + C~O~+ CIO5 + CCrg C'O' + C;Oi + ClOt + C;C~, C'O' + CO + C;Ol + CtO~ C606+ CIO5 + C~O~+ C;O~ C~O~ + C~,O6+ CO + CCrg C~O~ + CO + C~O6+ C~O~ continued on facing page

Force field and vibrational spectra of oligosaccharides--Part I

Table 4. continued Observed frequencies

Calculated frequencies

(cm -~)

(cm -~)

Raman 1010

IR 1012 997

974 894

845 755 735 677

969 895

751 671 662

649 636 623 602

619

591

582 560 529 491 472

555 505 492 464 446

436

420 405

B

Potential energy distribution

1016" 1004§ 995 992* 979 964* 892

1013 1005 995 992 978 964 892

846 75O 734

845 749 731

682§ 658§ 646* 632* 631" 613§ 601" 596 591§

682 658 646 630 627 619 603 595 589

586

586

579 552 532§ 499* 494 471" 446 435§ 428 426

575 556 532 498 491 471

CCH + CCrg + C'C'rg + CsC~ C ' O ' + CCH + CIO; + C5C6 CO + CCrg + C~O6 C'O' + C;O; + C~O; + C'C'rg CO + CCrg + C;O1 + CCH C,Oi + C~O;+ C'O' + C~C~ CC6H "F C5054" HC60 -I"1"C606 H'C~O' + C'C~,H' + C;O; + rC;O~ C,OIC; + C'C'O' + CCO + C~C~OR rCiO; + CCO CCO + CC,O, + CO5C + C~C~O~ CCO + C ' C ' O ' + C~C~O~+ C~CiO; rC606 + CsC60~ + r C ' O ' + rCO rC606 "[-rC~O~ + r C O "[-C'C~O; rC~O~ + OsH'O~ + rCO + CCO rC606 -F r C ' O ' "-I-CCO -k C ' C ' O ' CCO + O'C~O' + rCO + rC~O~ rCO + rC~O~ + OC,O rCO + OC,O+ CCO+ rC606 C~C~O~+ rCO + C'C'O' + C~C~O~ CCO + rCO + C ' C ' O ' rC~O~ + O'CiO' + C ' C ' O ' CCO+ CC60+ CCt05+ CCC C5C60 + C'C[O~ + C'CIO' + CCC C ' C ' O ' + CC~O5 + C4CsO + C'C~O' C'C'C' + CCO + CCC + CCtO5 rCO + r C ' O ' + CCO C ' C ' O ' + C'C'C' + CCC + CCO r C ' O ' + C ' C ' O ' + C ' C ' O ' + CCO CCC + CCO + C O ~ r C ' O ' + rCO + CCO + C'C'O' r C ' O ' + C ' C ' O ' + CCO CCO + C~C~O; + C ' C ' O ' + OC~O C ' C ' O ' + C'C;O' + CCO + rC'O' C ' C ' O ' + CCO + r C ' C ' + rC~C~ CCO + C'C'O' + rCO + CsC60 C ' C ' O ' + CCO + O ' C ' O ° C ' C ' O ' + CCO + C~C;O~ + O'C~O' C ' C ' O ' + CCO + CC60 + C,CsC6 c ' c ' o ' + C'C~O' + C~C~C~+ Hbm~ CCO + CC60 + rCC

A

403 397

358

334

383 358

329 319

314 285 267 248 224 214 197 186 175 160 148 141 134

278 265 249 228

195 180 176 166

381" 359 348 345 338* 321" 317 304 267* 260 239§ 226 208 195 188§ 172" 159" 154§

436 431 419" 408 401 394* 378 354 348 342 329 317 315 305 270 266 245 226 208 184 182§ 177 159

144§ 137"

c c o + c ' c ' o ' + c ~ c i o i + rCsC6 C6C50 + CCO + rCsC6 + rCC r C ' C ' + rC;C~ + C~C;O' + O'C;O' C4CsC6 + CCO + CC~O~ + C~C~O CC,01 + C~C;O' + C~C;O, C~C~O, + C~C~O' + C C C + r C ' C ' rC~C6 + rCC + r C ' C ' + C'C'C' rC;~ + Hb,.,r, + rCsC~+ C~C;O, rCsC-.s+ rCC + H b ~ + C~C~O, rC'C' + Hbm~,+ C ' O ' C ' + CC~O~ l'CC -}-C4C5C6 + CCO -}-C,OiC 3 rC~C~ + r C ' C ' + rCC + OC~O rCC + CCC + rC~C~+ rC'C' rCC + r C ' C ' + rC~C~ + CCC c o n t i n u e d o n next p a g e

99

100

MANUEL DAUCHEZet al. Table 4. continued

Calculated frequencies (cm-')

Observed

frequencies (cm-') Raman

118 107 94 91 85 76

69 62

IR

B

124

128 117§ 108"

rCC + ~C5C6+ rCO + C~C;O~ rCC + ¢C;C~+ rC'C + CCC rC'C' + rCO + Rc+ RA rCC + rC5C6+ rC;C~+ rC'C'

90§

Hbi,tra + rCO + rC606 + T C I O I

98

86 76§ 75

74 69§

63§ 55§

51 40 35

Potential energy distribution

A

38* 34

52* 49* 40

rCO + rC~O~+ rC'C' + Hb Rs+ rC5C6+ rC;C~+ rC'C' Tx + rCsCo+ RB+ rCO RA + rCO+ Rc+rC'C' R8 + Rc + rCO + rC~Ol Rc+RA +rCO+ Tx

R8 + Ra + rC~Ol + ~CC Ty+ rCsC6+ rC;C~+ rC'C' Tz + RA + Rc + rCO RA + Tz + Rc + rCO

bands are observed in the second one and the third one exhibits some bands, more or less broad and with medium intensity. As expected, the bands appearing in this region are due to H--C-H, C - O H and endoand exo-cyclic H--C-O and C - C - H bending vibrations and are highly coupled modes. In the former group of observed frequencies, modes that involved primary hydroxyl groups are found. Scissoring deformations are calculated at 1467 and 1457cm -1, 1474 and 1469 cm -~, and 1466, 1453 cm -1 for trehalose dihydrate, sophorose monohydrate and laminaribiose, respectively. Moreover, additional bands observed at higher frequency (1487 and 1472 cm -~) for trehalose dihydrate (see above) are calculated at 1485 (or 1482) and 1472 cm- ~ and assigned to H - C - O bending deformations of both anomeric carbons that are involved in the glycosidic linkage. Frequencies with a significant contribution if the C - O - H bending deformations are mostly calculated in the region 1280-1410cm -~, correspond almost to the second observed group of frequency described above. Calculations are carried out taking into account a specific term for the hydrogen bonds. Without this term (i.e. performing calculations on an isolated molecule) it is very difficult to fit perfectly the calculated spectra with the observed spectra. In such a case most of the assignments are modified and contributions of the C - O - H bending modes are shifted to lower frequencies. Wagging and twisting modes of the primary hydroxyl groups are calculated around 1350 and 1310cm -~ and 1220-1200cm -~ (and below) for the three disaccharides. The band observed for sophorose monohydrate at 1210 cm -~ is calculated at 1206 cm -~ and is assigned to C - C - H deformations of the two carbon atoms involved in the glycosidic linkage. 1200-950 c m -~ region. Between the previously described frequency range and this region, one can observe a brief clear region. Then, two closely spaced groups of bands, 1180-1100 and 1080-1000 cm-1, also separated by a brief clear region, are observed. The Raman spectra of the three disaccharides show numerous intense bands. Below 1000 cm- 1, only a few bands of weak intensity are observed. This spectral range shows very highly coupled modes that involved valence vibrations of C - C and C - O bonds and some C--C-H and H - C - O bending deformations. Because carbohydrates are constituted with numerous endo-cyclic and exo-cyclic C - C and C - O bonds, it is very difficult to reproduce perfectly this range of frequency and to assign unambiguously all the observed frequencies. Nevertheless, from the PEDs it is seen that the 1200-1100 cm -~ preferably involved C - C rather than C - O stretching elongations,

Force field and vibrational spectra of oligosaccharides--Part I

101

whereas below it is the contrary. The calculated frequencies at 1169 and 1151 em -t, at 1176 and 1161 cm -~ and at 1171 and l l 6 0 c m -~ could be attributed to endo-cyclic C--C and C - O valence vibrations of both pyranose rings, for trehalose dihydrate, sophorose monohydrate and laminaribiose, respectively. These modes show a high degree of mixing. Observed bands of high intensity at 1111, 1139 and 1119 era- 1, for the three disaccharides, respectively, are calculated at 1113, 1137 and 1110 cm -~, respectively. Even if these calculated bands are highly coupled modes, an important contribution of the C-O valence stretching modes that involved the inter-residue glycosidic oxygen atom is seen. Such contributions also exist for calculated modes around 1050era -~, particularly for laminaribiose (Table 4). The observed bands at 976 and 955 cm-~ of trehalose dihydrate (Table 2) and 974 and 969 cm-~ of laminaribiose (Table 4) are calculated at 971 and 948 and 979 and 964 cm -~, respectively. The assignments of these frequencies give C - O stretching modes that involve the anomeric carbons and the carbon participating in the corresponding glycosidic linkage. 950-800 c m -~ region. For a long time this region has been known to show the characteristic bands of the anomeric atoms [8-11]. TuL'CmNstv et al. [23], from studies on model compounds and on disaccharides, called this spectral range the "fingerprint" or the "anomeric" region. In both IR and Raman spectra, the bands having more or less intensity are more widely spaced and most of them do not overlap. This very sensitive region is perfectly reproduced by using our previously determined force field for carbohydrates [24]. For the three disaccharides, the expected bands corresponding to the different anomers are calculated correctly. Moreover, additional modes observed for example at 939 cm -1 in the Raman spectra of trehalose dihydrate are quite well reproduced (959 cm-1). For a,a-trehalose dihydrate, the bands observed at 912, 848 and 840 cm -1 are calculated at 919, 847 and 835 cm -~ and are assigned for the two latter modes to rocking deformations of the primary hydroxyl groups. The former vibration involved stretching elongations of the anomeric C - O bonds and a contribution of the bending deformation of the C - O - C glycosidic angle (Table 2); however, it is impossible to calculate the shoulder observed at 924 cm -~. The two calculated modes in the corresponding region for both sophorose monohydrate and laminaribiose are also assigned to coupled modes that involve the rocking deformations, the endo-cyclic C-O elongations and the torsional modes around C-O of the primary hydroxyl groups (Tables 3 and 4, respectively). It is important to point out that for both compounds, the coupled modes do not involve inter-residue vibrations. 8 0 0 - 6 0 0 c m -~ region. In this spectral range, the Raman and IR spectra show few widely spaced bands of weak and medium intensity. TuL'CruNS~:V et al. [23] have called this region "the region of crystallinity" because the spectra should be under the control of the packing of the molecule in the crystalline lattice. This region recorded on solid samples for the three disaccharides leads to fairly good resolution. As noticed above, it is impossible to reproduce perfectly this region without taking into account the intermolecular interactions and the hydrogen bonds in the potential energy function. As seen for trehalose dihydrate and sophorose monohydrate, some calculated vibrations are due to modes that involved the angle deformations of the hydrogen bond network. Moreover, numerous exo-cyclic torsional r(C-O) vibrations participating in the hydrogen bonds are found in the PEDs. The bands observed at 733,773 and 755 cm -~ for the three disaccharides are calculated at 728, 772 and 755 c m - l and are due to bending modes of heavy atoms involved in the corresponding glycosidic linkage C1-O~-C" or in the hemi-acetal fragment. 600-200 cm-~ region. For the three disaccharides studied, the Raman and IR spectra differ greater from each other. Closely spaced bands, having very high Raman intensity and medium or high IR intensity, are found between 600 and 350 cm-L It is possible to

102

MANUELDAUCHEZel al.

separate this region into three parts with a small clear region beyond ~400 and ~290 cm- 1. Most of the bands observed in this spectral range are fairly well reproduced using our force field. As for the other regions, the calculated modes are very highly coupled modes due to endo- and exo-cyclic heavy atoms skeletal deformations (C-C-O, C - O - C or O - C - O ) and to internal rotations about endo- and exo-cyclic C O . Moreover, contributions of the "intramolecular" (Fig. 1) hydrogen bonds and intermolecular hydrogen bonds are present in numerous calculated frequencies. It is well known [7] that below 600 cm- 1each carbohydrate examined has distinct features in its Raman and IR spectra. The PEDs show that the frequencies are greatly influenced by the relative arrangement of the groups (particularly the hydroxyl and hydroxymethyl groups) and their neighbouring fragments. Nevertheless, it is very difficult to obtain a one-to-one correspondence between observed frequency and calculated frequency for this region. Most of the calculated frequencies may be assigned to pyranose ring motions and sometimes to interresidue modes. Below 200 c m - 1. It is well known that the low frequency IR and Raman studies play an important role in the determination of the conformation of the biological molecules [35] and help us to elucidate the nature of the intermolecular interactions of the molecules studied. Most of the motions expected in that region involve internal modes, lattice vibrations and overall vibrations for large systems. Up to now, only a few investigations have been reported in this spectral range for saccharides [20, 35-39]. As pointed out for both glucose molecules [24], it is impossible to reproduce and to fit perfectly the low frequency range without carrying out the calculations in a crystal model with a combination of an intramolecular potential energy function and an intermolecular potential energy, constituted with a coulombic energy term, van der Waals non-bonded interactions and a specific hydrogen bond function. For the three disaccharides, the frequencies observed in this range are calculated with less than two wavenumbers of standard deviation. Most of the motions involve internal modes, lattice vibrations and for the lowest calculated frequencies some torsional contributions of the different parts of the glycosidic linkage that may correspond to "overall vibrations". The internal modes are due to skeletal deformations with a predominant part for the endo- and exo-cyclic C--C-C and C - C - O angle bendings and to internal rotations around C-C and C - O bonds. Moreover, the intramolecular hydrogen bond, joining the two pyranose molecules, is involved in numerous calculated bands between 200 and 100cm -1. The assignments of the observed (Raman and/or IR) bands at 182 and 176cm -l, and 186 and 180cm -1 for sophorose (Table 3) and laminaribiose (Table 4), calculated at 178 and 173 cm -1, and 188 and 182 cm -~, respectively, are due to C-C-O, O - C - O and C - O - C bending vibrations around the glycosidic linkage. For trehalose dihydrate the corresponding motions are calculated at 132 and 120 cm-L The lattice vibrations below 100 cm -~ are coupled mostly with internal rotations around most C-C bonds and C-O bonds and with bending deformations. Moreover, some of the calculated modes involved the internal rotations around the different parts of the glycosidic linkage. Thus, in trehalose the calculated bands at 85 and 37 cm-1 involved r(C1-O1) and r(C'I-O1) and four other bands involved one of the two mentioned torsions. In sophorose monohydrate the calculated modes at 37, 52 and 96 cm -I are assigned with r(C1-O1) and ~(C'2-O1) contributions. Moreover, for the latter calculated frequency the C - O - C ' glycosidic bending mode is also involved. For laminaribiose, the corresponding frequencies are calculated at 63 and 52 cm-1. For each disaccharide, the lowest observed frequency is predicted correctly.

5. CONCLUSION

In summary, this comparative study of three disaccharides constituted with glucose molecules that exhibit three different positions of the glycosidic linkages has shown that

Force field and vibrational spectra of oligosaccharides--Part I

103

the I R and R a m a n spectra possess quite similar features. Nevertheless, the characteristic structural regions [7, 34] m a y be divided into different parts that have a specific significance. The 1500-1200cm -~ region may be separated into three parts, ~ 1 5 0 0 1425, ~1425-1300 and ~1300-1200 cm -~. T h e 1200-1000 cm -~ region may be divided into two parts, -~1200-1100 and ~1080-1000 cm -~. The spectral range between 950 and 800 cm -~ depends upon the configuration of both units of a disaccharide. Between 800 and 6 0 0 c m -~, some characteristic bands are found and correspond to the glycosidic C - O - C " bending angle deformation. Below 600 cm -~, each disaccharide has its own features. With this experimental background, we have performed for each disaccharide a normal m o d e analysis in a model of crystal structure, including intramolecular potential energy function, van der Waals non-bonded interaction term, electrostatic function and an explicit hydrogen bond potential energy function. Using this combination of intramolecular and intermolecular force fields, the n u m b e r and density of vibrational states are correctly reproduced for all the different spectral ranges. Moreover, it is important to point out that without these terms it is m o r e difficult and sometimes impossible to reproduce perfectly most of the observed regions. Because of the lack of computational results in the literature for these carbohydrates, it is impossible to compare the veracity of our assignments. Nevertheless, the assignments seem to agree with published works on monosaccharides [12-25]. The initial force field, transferred from our works on a and fl glucoses [24], leads to good agreement between observed data and calculated results, even if it is difficult to m a k e a definitive one-to-one correspondence. The value of the standard deviation between calculated and observed frequencies, below 1500 cm-1, is of 3.0, 3.7 and 4 . 2 c m -1 for trehalose dihydrate, sophorose monohydrate and laminaribiose, respectively. This point underlines the viability of our force field [24] and will be confirmed in Part II that concerns maltose, cellobiose and gentiobiose. These three disaccharides possess the remaining position (1-4 and 1-6) and the two configurations (a, 1 - 4 and fl, 1-4) of the glycosidic linkage.

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