An in-plane force field for some benzene derivatives having unsaturated substituents

Specrrochimico Acrrr, Vol. 44A. No. 2, pp. 141-156. Prmted in Great Britain.

OSR4-8539:8R

198X.

$3.00 + 0.00

Pergamon Press plc

An in-plane force field for some benzene derivatives having unsaturated substituents L.-O. PIETILA, University

of Helsinki, Department

B. MANNFORS

and K. PALMS

of Physics, Accelerator Laboratory, Helsinki, Finland

(Received 22 April

1987; accepted

Siltavuorenpenger

20 M, SF-00170

18 June 1987)

Abstract-A simplified in-plane overlay valence force field has been developed for some benzene derivatives that have unsaturated substituents. The molecules used in the optimization of the force constants are

benzene, styrene, benzaldehyde, ethynylbenzene and m- and p-diethynylbenzene. The force field comprises 57 force constants, out of which 33 have been transferred from our other overlay calculations and 24 are optimized on about 600 experimental frequencies, giving an rms frequency deviation of 10.5 cm-’ which includes the C-H stretching vibrations. Some revisions in the assignments have been made. For comparison a fully independent overlay force field has been optimized for some methyl substituted benzenes using the same approximations in the force field. The transferability of force constants and limitations of the transferability are discussed.

I. INTRODUCTION

developed overlay force fields for a series of conjugated molecules including e.g. butadiene, acrolein, vinylacetylene, diacetylene and methylacetylene [4, 51. Since the molecular geometries are not exactly known we have optimized some of the stretching force constants of the substituents. The final values of these force constants then give information about the corresponding relative bond lengths in the different molecules. We have also introduced some “new” interaction force constants not available from the previously studied molecules.

For large molecules the amount of assigned experimental frequencies does not allow a reliable force field to be determined. As a matter of fact, the problem here is in most cases the reverse and the force field is used to assist in making the assignments of the experimental frequencies [ 11. When force field calculations are used for this purpose, a reliable force field must, of course, be available. The best, if not the only, way to find well defined values for the force constants is to use the overlay technique, that is, to assume that the force constants are transferable between related molecules and groups [l, 21. The force constant values may then be taken from overlay calculations done for smaller analogous molecules. In conjugated molecules there are some problems with the stretching force constants. These may have different values in different conjugated systems and they are also often correlated with interaction force constants. These difficulties can, however, be mastered by studying systematically a group of structurally related conjugated molecules. Certain interaction force constants can then be assumed to be equal which allows an optimization of the stretching force constants. Further, the stretching force constants are related to the bond lengths, and this can be used either as a constraint or as a check. In this work, which is part of our studies of transferable force fields for weakly coupled conjugated systems [3-61, we present an in-plane force field for benzene (B), styrene (S), benzaldehyde (BA), ethynylbenzene (EB) and m- and p-diethynylbenzenes (mDEB and p-DEB). Benzene is probably the most studied conjugated molecule [7-161. Thus, there is plenty of information accessible about the approximations that can be used in the force field of the benzene ring. The force constants for the substituents are also readily available because in previous papers we have

2. COORDINATES

AND THE FORCE FIELD

The definitions and sign conventions for the internal coordinates and for the force field are the same as those used in the previous papers of this series [3-6]. The notation for the coordinates is given in Fig. 1. The local redundancy existing in planar systems between the three valence angle bending coordinates sharing the same apex atom has been avoided by defining only one valence angle bending coordinate z and one in-plane wagging coordinate 8, instead of the three valence angle bending coordinates. Apart from the numerical factor in fi the same choice has been made in many ot the recent papers dealing with force fields for benzene derivatives, e.g. bb is defined as the difference between the two CCH angles multiplied by l/2. Thus. /jb is the angle that the C-H bond makes in the plane with its equilibrium position. Many authors interpret the inplane wagging coordinate as a local symmetry coordinate and multiply the difference between the two valence angles by a normalization factor l/ J2. The different definitions cause no problems in a comparison, however, since the force constants differ only by a factor of 2 or J2. As indicated in the Introduction the approximations used in the force field are based on the assumption that the molecules studied in this work can be treated as 141

L.-O. PIETILA et al.

142

o hydrogen 0 carbon oxygen

Fig. 1. Notation for the internal coordinates.

weakly coupled conjugated systems. Thus, e.g. in styrene, we assume that the force constants for the phenyl ring can be transferred from benzene and those for the vinyl group from butadiene, except F(R,) and F(R,) since these are sensitive to the bond lengths which are not well known. The approximations used in the force field for the benzene ring have been influenced by the ab initio results published by PULAYet al. [ 14,161, and are close to those commonly applied to benzene derivatives. As regards the force constants for the ethynyl group the question about the C-C=C linear angle bending force constant was raised. It is not a priori clear that the same force constant can be used here as in the out-ofplane force field. However, it was shown in Ref. [5] that the same linear angle bending force constant can be used in the different hybridization cases C(sp3)-C EC, C(sp)-Cd and C(spz)-Cd (in-plane and outof-plane). Thus, the same value for F(6) can be used in the present case too. Evidently then, the H-C=C linear angle bending force constant F(E) is also directly transferable from Ref. [5]. 3. CALCULATIONS

AND RESULTS

The calculations were done with the program MOLVIB written by SUNDIUS [17, 181. The geometrical parameters used were the same as those applied in the calculation of the out-of-plane force field for the present set of molecules [a]. Thus, the structure of the ring in all the molecules treated was assumed to be the same as in benzene [ 191, while for the substituents the geometrical parameters were transferred from butadiene [20], acrolein [21] and vinylacetylene [22]. The calculations followed closely the same path which we have found practical in the previous papers of this series [36]. Thus, the obvious starting point was benzene, since the assignments of its vibrational spectra are well settled [23]. There is also a general agreement about the main pattern of the force field for the benzene ring in the recent literature.

In the next step we added styrene to the calculation. For this molecule there are experimental frequencies from ten isotopic species available [24-281. The force constants for the vinyl group were taken from butadiene [4], modified as described in Ref. [S]. Actually, the only difference with respect to Ref. [4] is that a reoptimization has been made where FM,) for butadiene was allowed to vary independently of the corresponding force constant in acrolein and pbenzoquinone. For F&-c) we tested different values and found that it must be larger than F&-) for toluene, or about 2 mdynA/rad’. There is some disagreement regarding the recent assignments of the fundamentals of styrene. CONDIRSTON and LAPOSA[25] have assigned a band near 640 cm - ’ as an out-of-plane fundamental and a band near SSOcm-’ as an in-plane fundamental. GREEN and HARRISON[26] have assigned the band near 550 cm- 1both as an out-of-plane and an in-plane fundamental, while MARCHANDand QUINTARD [28] have reversed the assignments made by CONDIRSTON and LAPOSA. Our calculations suggest that there should be an in-plane fundamental near 560 cm- ’ while our out-of-plane force field showed that the band at 640 cm-’ is an out-of-plane fundamental [6]. Thus, our calculations support the assignments made by CONDIRSTONand LAPOSA [25], and in general our calculations are in good agreement with their assignments. The only significant difference is in styrene-ds where CONDIRSTONand LAPOSAhave assigned a band at 841 cm-’ twice, while our calculations give only one fundamental there. Instead, the results suggest that the band at 789 cm-’ corresponds to an in-plane fundamental in addition to the two out-of-plane fundamentals already assigned to it in our calculation of the outof-plane vibrations [6]. Thus, three fundamentals are represented by this band. GILSON et al. [27] have based their assignments of the vibrational spectra of CsHSCHCD2 on the work by CONDIRSTON and LAPOSA [ZS] and their assignments are in good agreement with our calculations. Their assignment of

Force field for benzene derivatives

the band at 1024cm-‘, about which they were not certain, is confirmed by our calculations. GILSON et al. have assigned the band at 837 cm-’ both as a “/I’mode” and as an out-of-plane fundamental. The force field calculations suggest, however, that the band at 907 cm ml corresponds to the “p-mode”. GILSON et al. also assigned this band to an out-of-plane fundamental, in agreement with our calculations [6]. In C6H5CHCH2 the band at 909 cm-’ corresponds to two out-of-plane fundamentals [6,25] which probably is the reason for the different depolarization ratios ot this band in CbHSCHCH: and C6H5CHCD2 [27]. The experimental frequencies for the styrene deuteromers not studied in Refs [25] and [27] were taken from the paper by MARCHAND and QUINTARD [28], but their assignments have been revised to correspond to those in Refs [25] and [27], as modified in this work. The vibrational spectra of benzaldehyde and three of its deuteromers have been assigned by ZWARICH et al. [29]. With a few minor exceptions our calculations are in good agreement with their assignments of the inplane fundamentals. The assignments of the in-plane and the out-of-plane modes in the region 210-250 cm-’ have been reversed as discussed earlier [6]. ZWARICH et al. [29] have assigned the strong band seen at 832 cm-’ in the i.r.-spectrum of BA-d6 as an out-of-plane fundamental. However, our out-of-plane force field suggested that this fundamental should be at 814 cm-’ [6]. A comparison with S-d5 and S-d*, as well as our calculations suggest that for BA-d6 there should be three in-plane fundamentals in the region 815-840 cm _ I, all of which are rather pure ring modes. An obvious choice is 839,832 and 814 cm- ‘, with the last band assigned twice. Our calculations give no inplane fundamental near 770cm-’ as assigned by ZWARICH et nl. [29]. Ethynylbenzene and the diethynylbenzenes have received only little attention and the only systematic study of their vibrational spectra we are aware of has been carried out by KING et al. [30. 311. Our preliminary calculations on these molecules suggested, though. some revisions in the existing assignments. The most serious disagreement concerns the in-plane C-C=C linear angle bending vibrations. In ethynylbenzene and its deuteromers this mode has been assigned to be at 50&530cm-’ [30], and in the diethynylbenzenes at 474-560 cm-’ [31]. The calculations indicated, however, that the modes which predominantly represent C-C-C in-plane linear bending 6 (having a considerable contribution of pee) should be located at 110-200 cm-‘. The calculated frequencies are not far from those calculated for the corresponding out-of-plane fundamentals in this region [6]. and their average values are close to the frequencies observed in the liquid state Raman spectra [30, 311. Thus, it seems that the Raman bands in question should be assigned both to the in-plane and to the out-of-plane vibrations. The single vibronic level fluorescence spectra of ethynylbenzene analysed by

143

Table 1. The force constants.

The units are mdyn/A for stretching, mdy&rad2 for bending and mdynjrad for stretching-bending force constants. Parameters with missing uncertainty have been transferred from analogous molecules Parameter

Value

I. F(r) 2. F(r,) 3. F(r,) 4. F(Tb) 5. F(R,) 6. FW,) 7. FW,) 8. F&J 9. F(R,), 10. F&J,, 11. F(Rti k~.m-DEB. 12.

13 f(q) 14. F(rb) 15. F(Z’) 16. F(B,) 17. F(BJ 18. F&J 19. F@CC)BA.s 2”. FU~C)EB.~-DEB. 21. F(B’) 22. F(s) 23. F(6) 24. f’(R,, R,) 25. JR,. R,) 26. f(R,. R,) 27. f(Rb, R,) 28. flR,. R,; 0) 29. f(R,. R,; m) 30. f(Rb. R,; p) 31. f(E,. a’) 32. ./‘(p,, B’, 33. .,(&,. k,; 0) 34. f(,$,. &,; m) 35. f(n,. B’) 36. f(x’. Ir,, 37. f(%. kc) =/(q Bee) 38. ./@b. pb) 39. j(6, z) 40 f’(R,, q,) =_f(R,. as) 41. f(R,. a’) 42. /‘(R,. q,) 43, =$Rw. 44. 45. 46. 47. 48.

~-DEB

F‘(3Lo)

p-~~~

5.9492 5.0826 4.2422 5.1451 12.3799 15.9047 9.2785 6.601 I 4.7015 4.6828 5.585’) 1.2893 1.1507 1.2817 0.6803 0.9949 I .2378 1.0326 2.2700 1.6041 1.1123 0.2045 0.3173 0.7779 0.7747 0.59 I8 0.3624 0.7785 -0.3761 0.2700 - 0.0367 -0.0716 0.0154 - 0.0254 0.0890 0.0366 - 0.200 1 -0.1051 0.0744 0.4227

Uncertainty

0.007 1 0.05 10 0.0691 0.0782 0.1134

WI 10

0.004 1 0.0847 0.0396

0.0329 0.0199 0.0349 0.0227 _ 0.0029 0.0025

0.0358 0.0093

- 0.2687 0.1507

rs) ab)BA.

S

f(R:: ab) EB. m-DEB. f(R,. ab) fK,. B,) .fW,. B,, j(R,. B,) =I(&, 8,) 49. _/(R,, &,; 0) 50. f&v &; m) 51. j‘(&,. /%Jc) 52. /(r,. rr) 53. f(r,, R,) 54. ./(r, R,) 55. fV,, R,) 56. f(r,, aO) =I@-,. CI& 57. _/@I,. ab)

p-DEB

- 0.3529 -0.5821 0.3 138 - 0.6759 -0.3813 -0.1419

0.0602 0.0382 0.0484

~ 0.2506 - 0.0594 - 0.4272 0.0255 0.2960 0.0656 0.0642 - 0.0673

0.0071 0.0056 0.0282

-0.1325

0.02 12

144

L.-O. PIETILii er al.

et al. [32] also support this interpretation. Since in these modes the frequencies may be significantly shifted by intermolecular interactions they have been left out of the fit. The bands at 500-530 cm-’ in the EBs, previously assigned as 6 modes [30], are so strongly mixed that it is not justified to give them any simple description. The main components in their PEDs are F&-J or F(a) with a large contribution of F(6). The calculations gave no bz fundamentals at 320-350 cm-‘, where the lowest bZ fundamentals of the DEBs have been assigned and described as &HOLLAS

modes [30]. Similar revisions had to be made in the assignments of the lowest a1 and b2 fundamentals of the m-DEBs and in the assignments of the lowest b3, and bzu fundamentals of the p-DEBs [31]. The other changes in the assignments are of less importance and need not be discussed here. The force constants are given in Table 1, and the frequencies and the potential energy distributions in Table 2. The force field contains 57 force constants out of which 33 have been transferred from our previous calculations and 24 have been optimized on about 600

Table 2. The observed and calculated frequencies (cm- ‘) and the most significant terms of the PED. The numbering of the force constants is Riven in Table 1

b,. bzr

e1.

ObS.

CA.

h

3074 993 1350 3055 WOO) 1177 607 3057 1010 1309

3080 996 1354 3065 1598 1175 611 3064 1013 1295

+6 +3 -l-4 +10

1146 (3068) 1482 1037

1154 3072 1483 1037

+a

2303 946 1059 2275 1558

2292 946 1053 227 1 1547

-11

868 579 2285 970 1282

857 584 2269 967 1285

-11 +5 -16 -3 +3

824 2288 1333 814

822 2279 1329 810

-2 -9 -4 -4

2282 lGiI4 956 1322 3063 2282 1580 1414 1101 833 594

3072 2280 1006 955 1307 1268 908 3069 2276 1574 1418 1095 830 597

3106 3091 3084 3061 3055 3029 3009 2981

3098 3078 3072

-2 +4 +7 +3 - 14

+1 0

0 -6 -4 -11

PED

4(99) 8(85) 28(20) 18(lb2). ’ 4(W 8(78) 14(11) 18(27) 49(- IS) 8(20) 18(69) 49( 12) 14(91) 4(lW 14(99) S(153) 18(29) 28( - 36) 29( - 17) 49 ( - 25) 8(18) 18(84) 49(15) 4(99) S(32) 18(69) 8(57) 18(27)

8i82j 28(19) lS(102) 4(97) E(88) 14(10) 18(14) 28(- 10) 49(-11) 8(10) 18(77) 14(90) 18(13) 38( - 11) 4(9a) 14196) 8(169) lE(10) 28(-40) 29( - 19) 49( - 16) 18(103) 4(96) 8(58) 18(39) 8(29) 18(57)

Benzene-l,3,M, 0;

e’

Styrene-hs a’

zzz 3064 3053 3010

-2 +2 -1 -15

+6 -6 -6 +4 -6 -3 +3 f8 -13 -12 +a +10 +35 +44 f29

4(99) 4(97) 8(27) 14(68) 8(57) 14(30) 28(13) E(73) 18(74) 28( - 17) 49(- 19) S(96) 18(40) 28(-23) 29(- 11) lE(102) 4ww 4(96) 8(81) 14(10) l8(23) 49(- 14) 8(42) 18(57) 8(41) 18(46) 8(22) 18(64) 14(90) 18(10)

4ilob) 4wO) 4wO) 2(99) 2(99)

Force

field for benzene

derivatives

145

Table 2 (Conrd ) Obs

Calc

A

1630 1600 1575 1494 145u 1411 1334 13OZN 1289 120:’ 1181 115t1 108:’ 103; 1019 99s’ 77CN 621 554 44: 241

1628 1606 1585 1496 1451 1414 1328 1314 1289 1185 1172 1161 1086 1034 1028 lW3 781 623 561 433 232

-2 +6 +10 +2 +I +3 -6 +I1 0 -18 -9 +5 +3 +2 +9 t4 +5 +2 +7 -9 -9

7(72) 15(19) 8(72) 14(12) 18(26) 49(- 14) 8(77) 14(11) 18(23) 49( - 12) X(35) 18(62) 8(36) 18(53) 15(63) 18(87) 8(44) l6(35) 28(-IO) 8(105) 18(15) 28(-24) 29(-12)49(-13) 8(26) 9(21) 14(14) 16(16) 18(19) 8(17) 18(62) 8(21) 18(78) 49(15) 8(43) 18(37) 8(30) 16(14) 18(12) 21(36) 8(28) 14(27) 21(24) 8(51) 14(39) 28(12) 8(21) 9(26) 14(36) 14(87) 13(32) 14(38) 19(15) 9(11) 13(13) 14(31) 19(28) 13(42) 19(38)

232(1 229; 229; 227; 2267 2261 225Cl 2215 1574 1563 1536 137i 1327 1285 1179 105G 1028 1001 958 870 841 825 810 789 699 594 498 408 212

2322 2289 2280 2275 2272 2269 2269 2204 1573 1552 1538 1371 1326 1286 1187 1050 1025 995 956 862 841 829 820 793 708 597 505 401 205

+2 -3 -12 -2 +5 +8 + 19 -11 -I -11 +2 -6 -I fl +8 0 -3 -6 -2 -8 0 +4 + 10 +4 +9 +3 +7 -7 -7

2(98) 4(96) 4(89) 4(96) 2(52) 4(44) 4(98) 2(35) 4(61) 2(95) 7(23) 8(58) 9(15) 7(38) 8(49) 7(19) 8(70) 8(56) 9(12) 18(29) 8(60) 18(26) 8(168)28(-40)29(-19)49(-13) 8(15) 9(33) 14(13) 18(10) 15115) 18f761 l4il7j 15&j 16(10) 18(15) 15(29) 16(20) 21(18) 8(45) 14(43) 28(11) 8(14) 18(65) 8(12) 18(78) 8(23) 18(54) 8(13) 18(82) 16(46) 21(34) 8(15) 9(18) 14(36) lS(18) 21(13) 14(85) 13(22) 14(37) 19(12) 21(18) 13(15) 14(24) l9(30) 13(44) 19(36)

3092 3009 2983 2292 2283 2277 2271 2262 1629 1575 1539 1425 1377 1328 1305 1284 1154

3053 3010 2289 2280 2275 2270 2269 1627 1566 1543 1424 1365 1327 1307 1280 1142

+6 +44 +27 -3 -3 -2 -1 t7 -2 -9 f4 -I -12 -1 t2 -4 - 12

2(1W W9)

1054 1006 958 871 841 (825) 825

1057 1012 957 864 841 832 820

PED

Styrene-da a’

Styrene-ds a’

(&,D&HCHJ

+3 +6 -1 -7 0 -5

VW WV W6) 4(97) 4(97) 4(98) 7(77) 15(21) 8(84) 14(13) 18(13) 49( - I I) 8(88) 28( - 10) 9(14) 15(61) 16(10) 8(48) lS(12) 18(26) 8(56) 18(24) 8(5l) 16(37) 28(- 10) 8(120) 28(-28) 29(-13) 8(21) 9(25) 14(20) 16(18) lS(12) lS(56) 21(21) 16(14) 18(36) 21(42) 8(41) 14(48) 8(16) 18(60) S(12) 18(78) 8(23) 18(56) 8(13) 18(83)

L.-O. PIETILA et al.

146 Table 2. (Contd.) Obs.

Calc.

A

729 595 541 433 231

737 598 548 420 225

+8 +3 i-7 -13 -6

3104 3084 3061 3051 3026 2329 2244 2207 1602 1585 1562 1491 1445 1332 1290

3078 3072 3069 3065 3064 2322 2272 2204 1609 1586 1555 1492 1447 1327 1293

-26 -12 +8 +14 +38 -7 +28 -3 +7 +1 -7 +1 +2 -5 c3

1225 1181 1156 1081 1048 1027 1003 1003 831 735 622 510 420 220

1229 1174 1161 1085 1045 1028 1004 998 804 742 622 516 414 211

+4 -7 +5 +4 -3 +1 +1 -5 -27 +7 0 +6 -6 -9

PED 8(21) 9(19) 14(27) 18(23) 14(86) 13(32) 14(40) 19(13) 9(11) 13(15) 14(30) 19(25) 13(39) 19(40)

Styrene-d3 (C6H,CDCDz) a’

Styrene-dl (C6HXDCHD

cis) 3078 3072 3069 3065 3064 3057 2214 2256 1609 1588 1576 1493 1448 1328 1294 1276 1227 1174 1161 1084 1045 1027 1003 810 748 622 535 421 221

(II

2281 2241 1611 1583 1574 1495 1450 1337 1287 1224 1185 1162 1086 1030 1026 1008 815 742 625 523 430 Styrene-dz (CeH&DCHD a’

2264 2238 1604

4i106) 4(W 4(lW 2(98) 2(94) 2i95j 8(73) 14(12) 18(26) 49( - 14) 8(79) 14(11) 18(22) 49(-12) 7(73) 9(11) 8(34) 18(63) 8(38) 18(58) 8(12) 18(88) 8(150) 18(20) 28(-35) 29(- 17) 49( - 16) 8(16) 9(42) 14(14) 8(19) 18(70) 49(12) 8(21) 18(78) 49(15) 8(44) 18(38) 8(23) 15(34) 16(16) 18(11) 8(34) 14(34) 15(11) 18(12) 8(37) 14(39) 15(11) 8(20) 15(29) 16(15) 21(15) 16154121(24) S(i3) b(ld) 14(39) 21(21) 14(86) 13(21) 14(34) 19(15) 21(19) 9(10) 13(13) 14(25j 19(31) 13(47) 19(34)

-13 +15 -2 +5 +2 -2 -2 -9 +7 +3 -11 - 1. -2 +15 +1 -5 -5 f6 -3 + 12 -9

4(99) 4(99) 4(W 4(100) 4W) 2(99) 2(94) 2(97) 8(69) 14(12) 18(25) 49(- 14) 7(14) 8(68) 18(18) 7(59) 8(21) 8(34) 18(64) 8(38) 18(58) 8(10) 18(86) 8(146) 18(20) 28( - 34) 29( - 16) 49( - 17) 15(68) 8(14) 9(34) 14(12) 21(12) 8(19) 18(70) 49(12) 8(21) 18(78) 49(15) 8(45) 18(38) 8(26) 16(23) 18(12) 21(15) 8(30) 14(40) 18(10) 8(55) 14(33) 28(13) 16(58) 21 (25) 8(15) 9(21) 14(39) 21(16) 14(86) 13(30) 14(29) 19(19) 21(14) 9(13) 13(12) 14(31) 19(25) 13(44) 19(37)

tram) 3078 3072 3069 3065 3064 3057 2288 2240 1609

+24 i-2 +5

4(99) 4(99) 4(100) 4(W 4(W 2(99) 2(93)

2W’)

8(69) 14(12) 18(25) 49( - 14)

Force

field

for benzene

147

derivattves

Table 2. (Contd.) Obs

Cak

A

1590 1570 1490 1443 1333 1333 1291

1588 1577 1494 1447 1331 1327 1293 1182 1170 1161 1085 1031 1009 1001 836 762 622 529 416 220

-2 17 t4 +4 -2 -6 +2

1174 1155 1080 1029 1010 IotKl 845 760 617 413 230 Styrene-dl

+3 - 10

7(14) 8(68) 18(18) 7(62) 8(21) 8(34) 18(64) 8(38) 18(58) 9(15) 15(55) 21(15) 8(12) 18(87) 8(149) 18(20) 28( -35) 29( -17) 49(~16) 8(23) 9(16) 14(10) 15(11) 18(27) 8(16) 9(13) 18(51) 8(21) 18(78) 49(15) 8(45) 18(38) 8149) 14(18) 18(21) 14(39) 16(19) 21(14) 8(53) 14(15) 28(12) 16(56) 21(36) 8(18) 9(24) 14(40) 14(86) 13(24) 14(39) 19(13) 21(13) 13(14) 14(25) 19(32) 13145) 19(35)

+12 0 +9 -5 -3 0 +2 -3 +9 0 -23 -8 +8 +5 +1 -1 +5 0 +7 +4 +9 -4 -6

4(99) 4(99) 4(l@J) 4(lW 4(lW) 21991 2i98i 2(92) 8(72) 14(12) 18(26) 49( - 14) 8(71) 18(18) 7(65) 8(16) 8(34) 18(64) 8(37) 18(57) 18(86) 8(86) 16(30) 18(14) 28( - 20) 49( - 12) 8(67) 9(15) 16(20) 18(11) 28(- 14) R(25) 9(20) 14(13) 16(24) 18(14) 8(18) 18(65) 49(10) 8(21) 1X(77) 49(15) 8(44) 18(38) 8(46) 14(16) 15(10) 18(19) 14( 11) 15(75) 8(49) 14(41) 28(11) 8(16) 13(13) 21(43) 8(U) 9(19) 14(38) 21(22) 14(86) 13(20) 14(36) 19(14) 21(21) 13(14) 14(25) 19(33) 13(47) 19(33)

-4 +6 +5 +2 -1 +1 -9 i? +5

(CeHKHCDl) 3078 3072

a’

2308 2214 1600 1595 1570 1494 1445 f331 1300 1280 1210 1180 1153 1080 1030 1024 999 907 735 618 513 426 218 Styrene-d,

PED

3064 3052 2320 2214 1609 1590 1567 1494 1447 1328 1309 1280 1187 1172 1161 1085 1031 1023 1004 907 742 622 522 422 212

(G,H&DCH;)

2(lW

3098 3078 3072

a’

2240 1615 1598 1570 1485 1442 1401 1330 1295

3064 3011 2265 1618 1603 1585 1495 1449 1409 1327 1294

i25 +3 t5 +15 + 10 +7 +8 -3 -1

1215 1178 1153 1109 1076 1025 1001 886 767

1228 1174 1161 1109 1083 1030 1003 871 767

+13 -4 f8 0 +7 +5 +2 -15 0

4(99) 4(99) 4(ltw 4(ltw 4(1OO) 2(99) 2(96) 7(55) 8(21) 9(13) 15(16) 7(19) 8(58) 18(20) 49( - 11) 8(78) 14(11) 18(23) 49(-12) 8(35) 18(62) 8(38) 18(56) 7(11) 15(68) 8(11) 18(88) 8(150) 18(20) 28(-35) 29(-17) 49( - 17) 8(12) 9(29) 14(10) 21(17) 8(20) 18(69) 49(12) 8(21) 18(78) 49(15) 8(15) 14(14) 21(41) 8(45) 18(37) 8(47) 14(26) 18(19) 8(50) 14(40) 28(12) 16(69) 21(26) 8(19) 9(23) 14(38)

L.-O.PIETIL~et al.

148 Table 2. (Cm&.) Obs.

Calc.

A

618 550 425 235

623 552 424 231

+s

Styrene-d, (GHKHCHD a’

cis) 3078 3072 3069 3065 3064 3058 3052 2263 1611 1597 1582 1495 1448 1360

-

2260 1611 1600 1512 1492 1445 1279 1228 1186

1183 1171 1161 1085

1156 1082 -

930 769 622 537 424 221

940 163 619 532 423 230 Styrene-d, (C6HsCHCHD

(I’ -

f2 -1 -4

f3 0 -3 f10 +3 +3

+20 -20 -3 +5 +3

-10 +6 +3 +5 +1 -9

1290 1280 1200 1179 1157 1078 1029 loo0 923 743 622 439 224

4(99) 4(99) 4(W 4W) 4(W 2(99) 2(99) 2(9S) 7(17).8(59) 9(11) 14(10) 18(21) 49(- 11) 7(43) 8(41) 18(11) 7(23) 8(58) 18(20) 8(35) 18(63) 8(38) 18(57) 9(12) 15(40) 16(27) 21(14) 18(87) 8( 141) lE(20) 28( -33) 29( - 16) 49( - 17) lS(31) 16(43) 8(26) 9(20) 14(13) 18(24) 8(17) 9(11) 18(57) 8(21) 18(77) 49(15) 8(45) 18(38) 8(48) 14(23) 18(20) 8(48) 14(43) 28(11) 8(11) 13(12) 15(11) 16(10) 21(49) 8(18) 9(25) 14(37) 21(14) 14(87) 13(22) 14(42) 19(11) 21(14) 13(14) 14(24) 19(34) 13(45) 19(34)

tram) 3072

2279 1612 1598 1575 1492 1448

PED 14(87) 13(34) 14(34) 19(17) 9(12) 13(12) 14(31) 19(25) 13(42) 19(39)

2266 1610 1596 1581 1494 1448 1330 1316 1289 1182 1171 1161

926 749 622 543 429 222

-13 -2 -2 +6 +2 0

-1 -4 - 18 -8 +4 +5 +2 +4 +3 +6 0 - 10 -2

4(99) 4(99) 4(W 4(99) 4W) 2(98) 2(100) 2(9S) 7(15)8(60) 14(11) 18(22)49(-12) 7(39) 8(42) 18(11) 7(26) 8(54) 18(19) 8(35) 18(64) 8(38) 18(57) lE(84) 8(49) 16(40) 28( - 11) 8(87) lS(12) 18(13) 28(-20) 49(-11) 8(18) 9(14) 15(59) 8(25) 9(14) 14(10) 16(20) 18(22) 8(17) lE(57) 8(21) 18(77) 49(15) 8(4S) 18(37) 8(49) 14(23) 18(20) 8(47) 14(44) 28( 11) 8(15) 16(11) 21(42) 8i14j 9(i1)‘14(jE)il(lE) 14(87) 13(29) 14(31) 19(18) 21(16) 9(12) 13(12) 14(31) 19(27) 13(44) 19(36)

Bemaldehyde-hr a’

306s 3065 3065 3065 3065 1701 1601 1588 1496 1458 1394

3078 3072 3069 3065 3064 2784 1721 1607 1588 1495 1454 1387

+13 fl +4 0 -1 f20 +6 0 -1 -4 -7

4(99) 4(99) 4(W 4(100) 4(W 3(W 5(99) 8(76) 14(13) 18(27) 49(- 15) 8(79) 14(11) 18(22) 49(- 12) 8(35) 18(64j 8(35) lE(52) 8(10) 17(72) 18(16)

Force field for benzene

derivatives

149

Table 2. (Conrd.) Obs.

WC.

A

1314 1292

1325 1287

fll -5

1206 1171 1164 1075 1026 1004 831 650 619 442 245

1196 1173 1161 1084

- 10 +2 -3 +9 +4 0 - 13 - 14 -7 - 12 +13

2298 2298 2298 2298 2298

2289

1004 820 636 612 430 258

PED 8(21) 18(83) 8(132) 18(18)28(-30)29(-15) 49(- 13) 8(27) lO(35) 14(18) 18(13) 8(18) 18(68) 49(11) 8(21) 18(78) 49(15) 8(45) 18(38) 8(48) 14(23) 18(20) 8(48) 14(43) 28(11) 8(25) lO(23) 12(15) 14(28) 12(27) 14(66) 8(il) 12(i4)‘14(63) lO(15) 12(11) 14(36) 19(21) 12(28) 19(50)

Bemldehyde-d, a’

1685 1564 1547 1373 1329 1298 1177

962 872 839 832 814 747 618 594 428

2275 2269 2076 1698 1565 1543 1371 1327 1288 1172 1049 1011 957 863 841 831 820 743 608 587 411 247

-9 -18 -23 -28 - 29 +13 +1 -4 -2 -2 - 10 -5 t2 -5 -9 t2 -1 +6 -4 - 10 -7 -17

4W) W6) 4(97) 4(97) 4(98) 31931 5i92j 8(86) 14(13) 18(14) 49(-11) 8(89) 14(10) 28( - 11) 8(57) lO(14) 18(29) 8(60) 18(26) 8(167)28(-39)29(-19)49(-13) 8(18) lO(38) 14(17) 17(12) 18(11) 17(11) 18(83) 14(17) 17(58) 18(10) 8(43) 14(45) 28(10) 8(16) 18(62) 8(12) 18(78) 8(23) 18(55) 8(13) 18(83) 8(20) lO(l5) 14(22) 18(22) 12(25) 14(67) 18(10) 8(11) 12(17) 14(57) lO(15) 12(11) 14(37) 19(16) 12(25) 19(53)

Benzaldehyde-4-d, li

3066 3066 3066 3066 2276 1703 1597 1577 1415 1384 1304 1275 1205 1166 1104 1020 989 882 821 643 617 442 238

Benzaldehyde-7-d, GHSCDO) 3066 a’ 3066 3066 3066 3066 1690 1599 1585

3075 3072 3067 3065 2784 2277 1721 1601 1578 1487 1418 1381 1310 1284 1196 1173 1111 1029 984 870 817 633 607 427 257 3078 3072 3069 3065 3064 2076 1699 1606 1586 1494

t9 t6 t1 -1 t1 1-18 t4 t1 t3 -3 t6 +9 -9 t7 t7 t9 -5 - 12 -4 - 10 - 10 -15 t 19 t12 t6 t3 -1 -2 t9 t7 t1 0

4(99) 4(99) 4(lOO) 4(lW 3((W 4(96) 5(99) 8(75) 14(12) 18(27) 49(- 15) 8(83) 14(12) 18(16) 8(34) 18(65) 8(34) 17(26) 18(34) 8(23) 17(55) 18(25) 18(85) 8(148) 28(-34) 29(- 16) 49(- 12) 8(28) lO(35) 14(18) 18(12) 8(18) 18(68) 49(11) 8(32) 18(60) 49(10) 8(42) 14(32) 18(18) 8(55) 14(33) 28(12) 8(13) 18(73) 8(24) lO(23) 12(15) 14(29) 12(27) 14(66) 8(11) 12(14) 14(63) lO(14) 12(10) 14(36) 19(20) 12(27) 19(50) 4(99) 4(99) 4(lW 4(100) 4(1W 3(93) 5(92) 8(76) 14(12) 18(27) 49(- 15) 8(80) 14(11) 18(23) 49( - 12) 8(35) 18(65)

150

L.-o.

PlETILii et al.

Table 2. (Contd.) Obs.

Calc.

A

PED

1451 1315 1283

1448 1327 1295

-3 +12 +12

1217 1171 1164 1075 1046 1025 1003 793 638 620 437

1218 1173 1161 1085 1035 1022 1003 785 632 605 422 256

+1 +2 -3 f10 -11 -3 0 -8 -6 -15 -15

3332 3078 3067 3047 2120 1601 1488 1192 117.5 1028 998 760 465 3096 3058 1573 1447 1330 1282 1157 1070 649 613 513 (162)

3333 3078 3069 3064 2115 1605 1494 1195 1172 1030 1004 765 467 3072 3065 1578 1437 1321 1277 1161 1079 627 616 506 168

+1 0 +2 +17 -5 +4 +6 +3 -3 +2 +6 +5 +2 -24 +7 +5 -10 -9 -5 +4 +9 -22 +3 -7

1(96) 4(99) 4(W 4(10@ 6(89) ll(14) 8(76) 14(12) 18(27) 49(- 15) 8(35) 18(65) 8(28) ll(36) 14(18) 18(15) 8(18) 18(66) 49(11) 8(48) 14(24) 18(19) 8(45) 14(47) 28(10) 8(23) 11(27) 14(42) ll(14) 14(63) 4(99) 4(100) 8(79) 14(11) 18(27) 49(- 13) 8(38) 18(62) 8(33) 18(82) 8(137) 18(22) 28(-31) 29(-14) 8(21) 18(78) 49(15) 8(47) 18(37) 14(28) 22(68) 39( - 11) 14(59) 22(37) 20(49) 23(32) 20(36) 23(67)

2610 2300 2292 2284 1980 1571 1378 1136 952 867 838 707 448

2585 2289 2275 2269 1981 1563 1368 1131 957 863 831 717 452 2279 2269 1531 1312 1274 1034 840 820 596 534 443 153

-25 -11 -17 -15 +1 -8 -10 -5 +5 -4 -7 +10 +4

l(71) 6(29) 4(96) 4(96) 4(98) l(28) 6(63) ll(14) 8(86) 14(13) 18(14) 49( - 11) 8(58) ll(11) 18(31) 8(26) ll(34) 14(26) 18(10) 8(36) 14(54) 8(16) 18(62) 8(25) 18(56) 8(20) ll(20) 14(36) 18(22) ll(14) 14(63) 4(96) 4(97) 8(91) 14(10) 18(11) 28(-11) 8(75) 18(28) 8(158) 28(-34) 29(- 17) 18(93) 8(12) 18(79) 8(13) 18(82) 14f841 20(26) 22(54) 23(37) 39( - 26) 20(23) 22(55) 39(10) 20(35) 23(65)

3333 2289 2276 2269 2115 1563

+1 -11 -15 -13 -7 -9

8(38) 18(58) 8(10) 18(89) Silk) li(2i) 28(-35) 29(-17) 49(- 171 8(i9) id(46) 14(17) 8(19) 18(70) 49(12) 8(21) 18(78) 49(15) 8(45) 18(38) 8(42) 17(24) 18(19) 8(11) 14(37) 17(45) 8(55) 14(32) 28(13) 8(20) lO(22) 14(31) 17(12) 12(19) 14(74) 8(12) 12(25) 14(48) 19(11) lO(16) 12(10) 14(36) 19(19) 12(28) 19(51)

Ethynylbenzene-he

Ethynylbenmne-d, QI

bz

1556 1323 1275 1034 841 821 601 (513) 477 (146)

-25 -11 -1 -Y -1 -5 -34

Ethynylbenzene-d~ (G.DsCCH) (11

3332 2300 2291 2282 2122 1572

1(96) 4(96) 4(96) 4(98) 6(89) ll(14) 8(86) 14(13) 18(14) 49(-11)

Force

151

field for benzene derivatives

Table 2. (Contd.)

62

Ethynylbenzene-d, 01

bz

PED

Ohs.

CdC

A

1379 1136 956 x6X 839 716 454 .~

1370 1136 958 864 831 720 457 2279

-9

1557 1323 1274 1034 842 822 648 602 502 (161)

1531 1312 1274 1034 840 820 624 595 494 163

m~26 -11 0 0 -2 -2 -24 -7 -8

3078

0 +3 +1x -24 -3 +4 +6 -3 -4 +5 +6 +3 +3 -24 +7 1-5 ~ IO -8 -1 +4 +9 -3 +11 -34

4(YYI 4(lW) 4( 100) l(71) 6(2Y) 1(2x) 6(62) ll(15) x(77) 14(12) 1X(27) 49(- 15) X(35) 1X(65) X(2X) ll(32) 14(16) 18(1X) X(18) 1X(63) X(48) 14(25) 18(1Y) X(45) 14(46) 2X(10) x(22) 1 l(26) 14(43) ll(l5) 14162) 41’)“)) 4(IUO) 8(7Y) 14(11) 1X(27) 4Y(- 13) X(38) 18162) X(33) 18(X2) 8(137) 18(22)2X(-31) 2Y(- 14) X(21) 1X(78) 4Y(l5) 8(47) 1X(371 14(x6) 20(32) 22(46) 23(3X) 3Y( ~ 25) 20(22) 22(63) 20(34) 23(67)

+ 30 -12 +4 +36 +7 +7 -7 +5 -I t6 -2 +4 +13 - 14

I(961 4(YY) 4llW 4(lW) 6(X7) ll(l4) X(75) 14(11) 18(2X)49(-12) X(62) 1X(25) 20(12) X(24) ll(45) 14(25) 1x(10) X(47) 1X(34) x(38) 14(56) X(17) ll(l7) 14(56) 22(106) 39( - 16) ll(11) 14(36) 20(16) 23(20) X(13) ll(11) 14(14) 20122) 23(26) 20(44) 23(56) 1196) 4(1(W) 6(x9) 11(13) X(76) 14(13) 1x(27) 49( - 14) 8140) 181601 X(54) 18(7Y) 2X(- 12) 49(- 15) 8(119J 18122) 2X(-26) 29(- 12) X(24) 18(71) 49(15) X(27) 1 l(29) 18(3Y) X(23) ll(41) 14(19) 22(1W) 23(11) 3Y(-20) 20(52) 23121) ll(l1) 14(66) 20(30) 23(75)

0 +2 -4 -8 +4 +3

X(58) ll(12) 18(30) X(25) ll(36) 14(26) 1X(11) 81361 14154) xii7j ixi62j X(24) 1X(56) X(21) ll(19) 14(35) 1X(22) ll(l3) 14(64) 4(96) 4(Y7) X(91) 14(10) 1X(11) 2x(-11) X(75) 18(2X) 8(158)2X(-34)29(-17) 1X(93) X(12) 18(7Y) X(13) 1x(82) 22(102) 39( ~ 16) 141841 2Oi45j 23(35) 20(37) 23(65)

(C,H,CCD) 3078 3066 3046 260’) lYX4 1600 1488 1193 1175 1025 YYX 758 45’) 3OY6 3058 1573 1447 132’) 1278 1157 1070 623 531 4x2 (154)

25x5 19x1 1604 1494 1190 1171 103u 761 462 3072 3065 1578 1437 1321 I277 1161 1079 620 542 44x 158

m-Diethynylbenzene-h, UI

bz

3303 3088 3065 3028 2109 1571 1405 I236 IO90 YYX 703 618 4x0 455 (122) 3303 3088 2108 1592 1475 1311

8Y4 647 557 455 (1x5)

3333 3076

2116 157x 1398 1241

701 622 493 441 122 3333 3068 2115 1598 1476 1312 1257 116X 1128 902 626 550 462 194

+30 - 20 +7 +6 +I +I

+X -21 -7 +7

152

L.-o.

PlET1L.i

et al.

Table 2. (Contd.) Obs.

Calc.

A

3076 3069 3064 2585 1981 1577 1397

-12 +4 +36 -3 +3 +6 -8 +2 fl +7 -2 +3 -4 -30

PED

m-Diethynylbenzene-d2 (&H&CD),) al

bz

3088 3065 3028 2588 1978 1571 1405 1233 1088 997 700 522 475 442 (117) 3088 2590 1979 1592 1473

894 560 470 457 (172)

1089 1004 698 525 471 412 113 3068 2585 1598 1476 1312 1257 1168 1124 896 574 472 452 183

-20 -5 +1 +6 +3 +2

+2 + 14 +2 -5

4(99) 4(W 4(W l(71) 6(29) l(28) 6(62) ll(15) 8(75) 14(11) 18(28) 49(- 12) 8(62) 18(26) 20(12) 8(24) ll(43) 14(25) 8(46) 18(34) 8(38) 14(56) 8(17) ll(16) 14(57) 20(17) 22(64) 23(37) 39( -28) ll(18) 14(38) 22(20) 20(23) 22(25) 23(15) 39(12) 20(43) 23(56) 4(100) l(71) 6(29) l(28) 6(63) ll(14) 8(76) 14(13) 18(27) 49(-14) 8(39) 18(60) 8(54) 18(79) 28( - 12) 49( - 15) 8(119) 18(22) 28(-26) 29(- 12) 8(24) 18(71) 49(15) 8(28) ll(27) 18(39) 8(22) ll(42) 14(20) 20(50) 22(23) 23(34) 39( - 16) 14(30) 22(58) 14(38) 22(28) 20(28) 23(74)

p-Diethynylbenzene-h6

b38

L

bzu

3300 3064 ilO8 1601 (1195) 1176 812 385 3054 1306 653 618 535 (197) 3305 3040 2110 1489 1015 646 3080 1401 1260 1100 615 486

3333 3075 2116 1610 1193 1168 809 383 3064 1547 1301 641 618 542 193 3333 3067 2115 1506 1195 1027 654 3072 1384 1262 1111 622 472 128

+33 +11 +8 +9 -8 -3 -2 + 10 -5 -12 0 +7 +28 +27 +5 +17 + 12 +8 -8 -17 +2 +11 +7 -14

1(96) 4(99) 6(89) ll(14) 8(75) 14(13) 18(27) 49( - 15) 8(47) ll(31) 8(22) ll(13) 18(60) 8(38) ll(27) 14(29) 44(-10) ll(14) 14(61) 44(11) 4(100\ 8{86)‘14(12) 18(18) 28(-10) 8(12) 18(81) 14(48) 20(11) 22(31) 14(31) 22(71) 39(- 13) 20(53) 23(23) 20(29) 23(74) U96) 4(100) 6(89) ll(14) 8(37) 18(60) ll(42) 14(35) 18(21) 44(-12) 8(34) 14(45) 18(15) 8(12) ll(40) 14(26) 44(10) 4(99) 8(55) 18(52) 49( - 13) 8(165) 28(-36) 29(-17) 51(-12) 8(34) 18(55) 22(107) 39(-17) 20(40) 23(43) 20(44) 23(58)

p-Diethynyknzene-d6 %

b3,

1018 630 547

2585 2285 1981 1575 1166 865 764 376 2268 1511 1019 617 547

(177)

456 176

2597 2291 1985 1575 1168 870 763 380 229 1

- 12 -6 -4 0 -2 -5 +1 -4 -23 +1 -13 0

l(71) 6(29)

W4

l(28) 6(62) ll(15) 8(86) 14(14) 18(14) 49(-11) 8(45) 1l(43) 8(20) 18(60) 8(29) ll(24) 14(26) 18(27) ll(15) 14(61) 44(11) 4(97) 8(94) 14(11)28(-11) 18(88) 14(72) 14(14j 20(32) 22(36) 23(35) 39( -21) 20(18) 22(72) 20(29) 23(7 1)

Force field for benzene derivatives

153

Table 2. (Contd.)

b,.

Obs.

Cak.

A

2590 2285 1981 1403

2585 2272 1981 1403 1107 850 617 2279 1305 1254 822 524 428 118

-5 -13 0 0

851 2296 1320 1258 819 520 464

b,.

p-Diethynylbenzene-d, %

b,,

b,,

b,.

bdo

1018 631 619 511 (186) 3305 2286 2110 1404 851 2297 1320 1258 820 615 484

bl.

51(-16)

3333 2285 2115 1576 1172 865 767 382 2268 1511 1019 631 607 519 187 3333 2272 2115 1406 1111 851 624 2279 1305 1254 822 622 470 127

+33 -6 +7 +1 -3 -4 +1 +12 -23 +1 0 -12 +8 +28 - 14 +5 +2 0 - 18 -15 -4 +2 f7 - 14

l(96) 4(96) 6(89) ll(l4) 8(86) 14(14) 18(14) 49(-11) 8(44) 1 l(45) 8(21) 18159) 8i29j lli24j 14(24) 18(27) ll(l4) 14(62) 44( 10) 4(97) 8(94) 14(11)28(-11) 18(88) 14(19)22(71) 39(-13) 14(58) 22(34) 20(47) 23(27) 20(31) 23(72) 1(96) 4(97) 6(89) ll(l4) 8(57) 1 l(21) 18(26) ll(31) 14(53) 18(16) 8(15) 14(24) 18(46) 8(16) ll(32) 14(22) 4(96) 8(101) 18(20) 49( - 14) 8(140)20(14)2X(-24) 29(8(10) 18(86) 22(107) 39( - 16) 20(40) 23(43) 20(44) 23(58)

11) 51(-16)

(C,H,(CCD),)

3066 2596 1984 1600 (1196) 1171 809 380 3053 1305 650 (547)

b,.

-17 -15 -4 +3 +4 -36

(C,,D,(CCH),) 3300 2291 2108 1575 1175 869 766 370 2291

p-Dn%hynylbenzene-dz a,

-1

PED l(71) 6(29) 4(97) l(28) 6(63) ll(l4) 8(57) ll(l9) 18(27) ll(30) 14(54) 18(15) 8(151 14(231 18(471 8(16j lli33j 14i22j 4(96) 8(101) 18(20) 49(- 14) 8(140) 20(14) 28(-24) 29(-11) 8(10) 18(86) 20(18) 22(69) 23(36) 39(-29) 20(25) 22(40) 23(13) 39(14) 20(42) 23(58)

(1821 3039 2591 1980 1490 1014 _ 3080 1401 1260 IlOO 520 464

3075 2585 1981 16139 1188 1166 806 377 3064 1546 1301 636 566 463 182 3067 2585 1981 I505 1190 1027 645 3072 1384 1262 1111 525 429 119

+9 -11 -3 +9 -5 -3 -3 +11 -4 - 14

+28 -6 +1 fl5 +13 -8 -17 +2 +11 +5 -35

4(99) l(71) 6(29) l(28) 6(62) ll(15) 8(76) 14(13) 18(27) 49(- 15) 8(45) ll(24) 18(16) 8(25) 11(17) 18(54) 8(37) 11127) 14(30) 44( - 10) ll(15) 14(60)44(11) 4(lW 8(86) 14(12) 18(18) 28(- 10) 8(12) 18(81) 14(73) 14(13) 20(43) 22(25) 23(35) 39(- 17) 20( 15) 22(83) 20(27) 23(73) 411001 li71) b(29) 1(28)6(63) ll(14) 8(37) 18(61) ll(41) 14(35) 18(20) 44( - 12) 8(33) 14(46) 18(15) 8(12) ll(40) 14(25) 44(10) 4(99) 8(55) 18(52) 49(- 14) 8(165) 28(-36) 29(-17) 51(-12) 8(34) 18(55) 20(19) 22(68) 23(37) 39( - 29) 20(25) 22(41) 23(13) 39(13) 20(42) 23(58)

154

L.-o.

PETILk

Table 3. The force constants for the methyl substituted benzenes. The units are as in Table 1 Parameter 1. F(rb) 2. Qr,,,) 3. F(&,) 4. F&J 5. F(Q) 6. F&,-,) 7. F(Bb) 8. F(Bcc) 9. F&J 10. f(&,, R,; 0) 11. f(&,, R,; m) 12. f(&> R,; p) 13. f(% R,,,) 14. .f@b, Pb; O) 15. f@b. hbi m) 16. _0P,,,>8,; P) ‘17.!(ab? fib) 18. I(%,, ab) 19. _f(R,, ab) 20. f(&,, ,&; 0) 21. f(&,, &; m) 22. f(R, Bee) 23. f(~,, B,) 24. f(r,, rm) 25. f(rb. ab)

Value 5.1280 4.7828 6.5567 4.6256 1.2813 0.5460 1.0460 1.5359 0.6248 0.8188 - 0.3793 0.2830 0.1816 0.0036 - 0.0240 - 0.0356 - 0.0739 0.2618 -0.5101 - 0.2223 - 0.0548 -0.3457 0.2493 0.0670 -0.0818

Uncertainty 0.0153 0.0850 0.0545 0.0097 0.0024 0.0047 0.0244 0.0047 0.0205 0.0398 0.0290 0.0278 0.0032 0.0028 0.0032 0.0157 0.0569 0.0340 0.0087 0.0077 0.0257 0.0138 0.0368

frequencies. The rms frequency deviation was 10.5 cm-‘. For comparison we made an independent overlay calculation for benzene, toluene, m- and p-xylene and mesitylene (and some of their deuteromers) using the same approximations for the force field as in Table 1. The experimental frequencies were taken from a work by LALAU and SNYDER [33], and the geometrical parameters were the same as those used in a similar calculation for the out-of-plane vibrations [6]. The force field, which gave an rms frequency deviation of 7.9 cn- ‘, is shown in Table 3. The calculated frequencies and PEDs are close to those obtained by LALAU and SNYDER[33] and by DRAEGER[34], and are not reproduced here. 4. DISCUSSION

Out of the 24 optimized force constants 14 are shared with benzene. Although there is a general agreement about the benzene fqrce field there has been some discussion about the bzu species [9,14,16-J where two alternative solutions for the symmetry force constants exist [9]. The difference between these two solutions is not large enough to allow discarding either of them by clear physical reasons. Nor can a definite choice be made by studying the transferability of the force constants as both solutions gave about the same rms value for the present set of molecules. We chose the solution (a) by DUINKER and MILLS [9] mainly because this solution is supported by the ab initio results due to PULAY et al. 114, 163. DUINKER and MILLS preferred solution (b) because if it is assumed

et d.

that f(Rb, &; m) and f(Rb, &; p) are much smaller than f(Rb, /lb, 0) then F1+ L5= 2/,/3F,., (in their notation) which supports solution (b). When we used only the ortho interaction, small changes in the initial values often caused a convergence towards solution (b). Similarly, some of the recent overlay force fields belong to solution (b) [35,36]. When the convergence was towards solution (a) the interaction force constant f(Rb, c$,) had a small value as compared to that obtained by PULAYet a/. [14] and also to those of the “similar” force constants F (R,, us) and f(R,, a,). When f(Rbr fib; m) was added a reasonable agreement with PULAYet al. was achieved. A comparison between the symmetry force constants is given in Table 4. For further comparison some other empirical force fields optimized on different sets of molecules are also included in the table. The revised DUINKER-MILLS force field due to PULAY et al. [14] was optimized on data from benzene only, while the force field by BARANOVlC et al. [35] was optimized on frequencies from benzene, phenylacetylene (ethynylbenzene), diphenylacetylene and diphenyldiacetylene (and some of their deuteromers). PULHAM and STEELE [36] optimized their force field on frequencies from biphenyl and 4,4’-difluorophenyl and their fully deuterated isotopomers. The two last mentioned force fields belong to solution (b) in the bj?, species while the other force fields in Table 4 belong to solution (a), and this is the only significant difference between these force fields as far as the benzene ring is concerned. The differences between the conjugated systems are most readily seen in the stretching force constants. These are, though, strongly correlated with certain interaction force constants so that care has to be taken when optimizing them. However, in closely related cases, as e.g. for the vinyl groups in butadiene and styrene, it can be assumed that the interaction force constants are transferable with high accuracy. The stretching force constants F(R,) and F(R,) for styrene could therefore be optimized independently of those of other molecules. The results show that F(R,) for styrene (4.70f 0.11 mdyn/& is slightly smaller than for butadiene (5.02 f 0.13 mdyn/A) while F(R,) is slightly larger for styrene (9.28 + 0.07 mdyn/A) than for butadiene (9.12 + 0.05 mdyn/A). This indicates that in styrene the C=C bond is shorter and the C-C bond is longer than in butadiene, and thus the vinyl group in styrene is less affected by the conjugation than the vinyl group in butadiene. The stretching force constant F(R,) for the ethynyl group was also independently optimized. It became slightly larger (15.90 f 0.05 mdyn/A) than for vinylacetylene (15.70 + 0.27 mdyn/&, or for diacetylene (15.52 f 0.10 mdyn/A), but smaller than for methyl acetylene (16.41 +O.ll mdyn/A) [5]. All the force constants for the aldehyde group in benzaldehyde were transferred from acrolein [4], modified as in Ref. [S]. No optimization of these force constants was made, as the experimental frequencies were taken from liquid state spectra [29] and may be

Force field for benzene derivatives

Table 4. [7]. The in-plane constants

155

Symmetry force constants of benzene in terms of the symmetry coordinates by WHIFFEN C-C-C bending coordinates have been multiplied by the C-C bond length and the C-H wagging coordinates have been multiplied by the C-H bond length so that the force are in units of mdyn/A. The notations for the force constants are the same as in Ref. [14] I

II

-

-

111

IV

V

VI

7.50 0.15 5.2

7.600

7.504

5.089

5.073

0.863

0.850

0.829

0.656

0.659

5.089

5.073

7.676

7.719

5.145

5.128

7.609 0.110 5.218

0.862

0.855

0.855

0.657 -0.095 5.145

0.657 - 0.059 5.128

0.650 -0.184 5.154

4.022 0.353 0.809

3.878 0.309 0.843

3.917 0.290 0.811

3.94 0.30 0.822

4.294 0.637 0.816

4.368 0.666 0.859

0.657 - 0.095 0.225 -0.120 5.145

0.657 - 0.059 0.187 - 0.085 5.128

0.656 -0.139 0.204 -0.136 5.158

0.656

0.630 -

0.158 -0.110 5.089

0.265 - 0.078 5.073

6.469 - 0.400 0.887

6.400 -0.355 0.908

0.639 -0.123 0.28 -0.125 5.156 0.061 0.028 6.70 - 0.421 0.881

6.427 -0.416 0.901

6.814 -0.551 0.832

7.084 - 0.577 0.848

7.364 0.221 0.095 0.913

7.479 0.222 0.059 0.914

7.34 0.219

7.354 0.209

7.102 0.255

0.91

0.890

0.947 -

5.145

5.128

7.270 0.221 0.175 0.910 0.006 5.185

5.15

5.089

5.073

b 1”

Fiz.~zW FLZ.13

F13.1369 b2” F,4,dR) F14.15

F,LI#)

0.65 - 0.20 5.2

%I

Fc,.s(a) F6.7 F6.8 F6.9

FT.&-) F7.8 F7.9 F8.8W F8.9 F9,9(P) eh FIR F19.18

,9(R)

I. This work, from Table 1. II. This work, from Table 3. III. PULAY et a/. set 11 [14]. IV. Revised DUNKER-MILLS [14]. V. BARANOVIC et al. [35]. VI. PULHAMand STEELE [36]. shifted due to hydrogen bonding. The approximation is justified by the smallness of the changes in the stretching force constants for the vinyl and ethynyl groups. All the angle bending force constants for the substituents were transferred directly from related molecules [4,5] and in the vinyl and aldehyde groups this caused no problems. However, regarding the ethynyl group modes that have a large contribution of the H-C =C linear angle bending (c) there arose some difficulties, especially in those modes that in addition involve the &coordinate. For these modes the largest discrepancies between the assigned and calculated frequencies occurred. An easy way to improve the fit on this point would be to optimize F(E) and to include the interaction force constantf(e, /ICC). However, we have not done so for the following reasons. In the out-ofplane force field [6] F(E) as well as F(6) were successfully transferred directly from an overlay force field developed for a set of simpler molecules containing the C=C group [5], and F(S) has also been transferred

without refinement to the present in-plane calculation. Further, although f(& E) is large, some other ‘related’ interaction force constants involving the linear group have been found to be negligible. This is the case for f(S, 6) in diacetylene [5] and for f(S, ycc) [6] and f(S, PC,-) in the present molecules (ycc is the C-C out-ofplane bending coordinate). These results suggest that f(s, &,-) also is negligible. Thus, we have transferred F(E) from Ref. [S] and assumed that f(s, PC.) = 0. Another view was taken by BARANOVI~: et al. [35] in their overlay force field for phenylacetylene (ethynylbenzene), diphenylacetylene and diphenyldiacetylene. They included f(s, bee) in the optimization and they also optimized F(6) and F(E) for the in-plane vibrations independently of the corresponding out-ofplane force constants [35]. An interesting case where transferability breaks down is represented by the force constant F&c). Its value in toluene is close to that in ethynylbenzene (1.54 + 0.02 and 1.60 f 0.04 mdynA/rad’, respectively), while for styrene and benzaldehyde it is much larger

L.-O. PIETIL~~et al.

156

(2.27 f 0.08 mdyn&rad’). As F(ycc) in all these cases could be considered to have the same value [6], the apparent explanation for the different values of F&-) is the effect of nonbonded interactions. Thus, according to this explanation, it would be doubtful to transfer F&,) from styrene to nonplanar substituted styrenes unless the effect of nonbonded interactions is explicitly taken into account in the same way as in the molecular mechanics method [37,38]. Similarly, in biphenyl the same value for F&c) cannot be used both in the crystal phase and in the gas phase, since in the former case the molecule is planar while in the latter case the torsion angle between the phenyl groups is about 40

PI G. ZERBI, in Vibrational Spectroscopy-Modern Trends, p. 261 (edited by A. J. BARNESand W. J. ORVILLETHOMAS).Elsevier, Amsterdam (1977). c31 L.-O. PIETIC, K. PALMS and B. MANNFORS,J. molec. Spectrosc. 112, 104 (1985). and B. MANNFORS,J. molec. c41 L.-O. PIETILA, K. PALMER Spectrosc. 116, 1 (1986).

c51 B. MANNFOR~,L.-O. PIETILAand K. PALM& J. molec.

Struct. 144, 287 (1986). PALM& B. MANNFORS and L.-O. PIETILA, Spectrochim. Acta 42A, 1265 (1986). D. H. WHIFFEN, Phil. Trans. R. S&z. A248, 131 (1955). N. NETO, M. SCR~CCOand S. CALIFANO,Spectrochim. Acta 22, 1981 (1966). J. C. DuINKERand 1. M. MILLS, Spectrochim. Acta 24A, 417 (1968). J. FAVROT,P. CAILLETand M. T. FOREL, J. Chim. Phys. 71, 1337 (1974). P. C. PAINTERandJ. L. KOENIG,Spectrochim. Acta 33A, 1019 (1977). P. C. PAINTERand R. W. SNYDER, Spectrochim. Acta 36A, 337 (1980). K. OHNO, J. molec. Spectrosc. 72, 238 (1978). P. PULAY, G. FOGARASI~~~J. E. BOGGS,J. them. Phys.

C61 K.

[391. 5. SUMMARY

This study concludes a series of papers where we have developed an overlay force field for some simple weakly coupled conjugated molecules [3-6]. Our main purpose has been to investigate systematically the transferability of force constants in these kind of molecules. The transferability turned out to be good and even the stretching force constants for similar bonds change only little from one molecule to another. Such small but perceptible changes can be used as indications of differences in the bond lengths. However, due to correlations between the force constants conclusions must be drawn with care and only in cases where the corresponding interaction force constants

have

been

directly

transferred

without

reoptimization.

74, 3999 (1981). A. G. OZKABAK,L. GOODMAN,S. N. THAKURand K. KROGH-JESPERSEN, J. them. Phys. 83,6047

(1985).

Cl61 P. PULAY, J. them. Phys. 85, 1703 (1986).

T. SUNDIUS,Commentat. Phys.-Math. 47, 1 (1977). ;::3 T. SUNDIUS,J. molec. Spectrosc. 82, 138 (1980). Cl91 A. LANGsETHandB. P. STOICHEFF,Can. J. Phys. 34,350 (1956).

c201 K. KUCHITSU,T. FUKUYAMA~~~Y. MORINO,J. molec.

Struct. 1, 463 (1968). [21] K. KUCHITSU,T. FUKUYAMAandY. MORINO,J. molec. Struct. 4,41 (1969). [22] T. FUKUYAMA,K. KUCHITSUand Y. MORINO, Bull. Chem. Sot. Japan 42, 379 (1969). r231 S. BRODERSENand A. LANGSETH,Mat. Fys. Skr. Dan. Vid. Selsk. 1, 7 (1959). ~241W. D. MRoss axid G.‘ZUNDEL, Spectrochim. Acta 26A, 1109 (1970). ~251D. A. CONDIRSTONand J. D. LAPOSA, J. molec. L--A

When developing transferable force fields for large molecules, one of the greatest difficulties is the influence of nonbonded interactions on the force constants. This also became evident in several phases of the present calculations. The most serious cases are easy to detect and one solution is then to optimize the affected force constants independently, as was done e.g. for F(ficc). The nonbonded interactions are explicitly taken into account in the molecular mechanics method [37,33] and it would therefore be appealing to use this method for calculating vibrational frequencies and force fields. However, the approximations to be used in the potential energy functions for weakly coupled conjugated molecules are not necessarily very obvious and, in fact, one of the motives for the present work was actually to obtain information about the approximations to be used in molecular mechanics calculations on these kinds of compounds. Acknowledgements-We thank Dr TOM SUNDIUSfor many valuable discussions and for reading the manuscript. Financial support from the Academy of Finland, the Heikki and Hilma Honkanen Foundation and from the Magnus Ehrnrooth Foundation are gratefully acknowledged. REFERENCES

[l]

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