Infrared and Raman spectra of heterocyclic compounds—I the infrared studies and normal vibrations of imidazole

SpectrochimicaActa0Vole24A, pp. 287 to 252. PergamonPreM 1968. Printedin NorthernIreland

Infrared and Raman spectra of heterocyclic compounds--I The i.~ared studies and normal vibrations of imidazole* ~-ARCIA CORDES DE N . D . a n d J . L . WALTER, C.S.Co Department of Chemistry a n d Radiation Laboratory University of Notre Dame, Notre Dame, I n d i a n a

(Received 21 June 1967) A b s ~ t c t - - T h e infrared spectra of imidazole and some substituted imidazoles were obtained from 4000 to 33 em-1. The bands in imidazole are assigned on a basis of comparison with its deuterated a n d trihalogeno substituted analogs a n d its metal complexes as well as other aromatic a n d heteroaromatic systems reported in the literature. A detailed normal coordinate analysis was made for the imidazole molecule considered as a ten-body structure possessing C2~ symmetry. Utilizing a Urey Bradley Force Field an approximate description was given for each vibrational mode a n d values of all the force constants for planar and out of plane vibrations were obtained.

I. INTRODUCTION

THEinfrared spectrum of imidazole has been discussed to some extent in the literature [1-7], but, to date, the complete spectrum has not appeared, nor has an a t t e m p t been made to assign all the bands. The effect of hydrogen bonding on the N H stretching frequencies has been thoroughly studied [3], and assignments have been proposed for the bands observed when the molecule is dissolved in D20 [4]. 2. EXPERIlVIENTAL

2.1 Absorption measurements The infrared spectra were obtained using Perkin-Elmer models 221 and 421 infrared spectrophotometers and the Beckman IR-11. Polystyrene film and water vapor standard peaks were used to cahbrate the 3600-700 cm -1 region. The region 600-250 cm -1 run on the 221 equipped with CsBr optics was calibrated using atmospheric CO 2 and water vapor bands. In regions of strong atmospheric absorption "blanks" were run before and after each spectrum to insure amplifier balance. The * This work based on Ph.D. Thesis of Sister Marcia Cordes de N.D., Notre Dame, June, 1966. t The Radiation Laboratory is operated b y the University of Notre Dame under contract with the Atomic Energy Commission. This is document No. COO-38-535. Acknowledgement is also made for the support b y the N I H grant HE-02218. [1] A. R. KATI~ITZKY(Editor), Physical Methods in Heteroeyelie Chemietry Vol. I and II. Academic Press (1963). [2] W. OTTING, Chem. Bet. 89, 2887 (1956). [3] H. Z I M ~ R ~ , Z. Elektrochem. 65, 821 (1961). [4] R. H. CARLSON and T. L. BROWN, Inorg. Chem. 5, 268 (1966). [5] A. R. KATRITZKY,Quart Rev. London 18, 353 (1959). [6] D. G/~RFr~KET.and J. T. EDSALL, J. Am. Chem. Soc. 80, 3807 (1958). [7] W. C. COBUrg, J~., W. R. LAS~.TERa n d C. V. STEP~NSO~, Technical Report AFOSR-973 (1961). 237

238

M . CORDES DE 1~.D. a n d J . L . W A L T E R

C.S.C.

T a b l e 1. I n f r a r e d f r e q u e n c i e s ( e m -1) a n d a s s i g n m e n t s CsNzH4 (imidazole)

CsN2D4 (imidazole-d 4)

CsNzBrsH

CsN2IsH

CaN2IsD Co(CaNsHs) z 3148 (sh) 3130 (w) 3109 (w)

3124 3105 (sh) 30212587

3075-2630 2372 (sh) 2347 (sh) 23251860

1815 (w) 1665 (w) 1573 (w) 1543 (m)

CsN~BraD

31142450

NHstretehing

23502050

1440 (m) 1525 (s, b)

1440 (w) 1530 (m) 15o5 (m)

22001800

NDstretching

18oo (w) 1632 (w)

1638 (w)

1655 (w)

1445 (s) 1530 (m, b)

1445 (s) 1525 (w)

1598 ira)

1510 iw)

1509 (sh)

1493 (w) 1478 (m) 1445 (s)

1462 (m) 1422 (vs) 1345 (m)

1420 (w) 1388 (vs)

1392 (vs) 1358 (s)

1315

1468 1435 (sh) 1412 (w)

1435 (s) 1430 (s) 1340 ira)

1265 (m)

1485 (vs) 1462 (s)

1300

1328 (s)

1263 (s) 1244 (w)

1300 (s) 1283 ira)

1298 (m) 1283 (m)

1277 (s) 1263 ira)

1268 (sh) 1260 (s) 1232 (s)

1193 is)

1195 (s)

1230 (w) 1170 (s)

1165 (s)

1180 (s)

1180 (sh)

1145 (s)

1148 (m)

1313 (m) 1273 (m) 1230 (s)

1160 (m)

1195 (w) 1145 (m)

CH stretching

CDstretching

1630 (w) 1580 (w)

Assignment

1118 (s, b)

Overtone 2(839) or 8 3 9 + 827, 2(815), 2(825) CC stretching N I t bending 750 × 2 757-{- 736 650+812 Ring stretching Ring stretching ND bending 2(660), 2(650) CI-Ibending 948-]- 34O Ring vibrations 617 × 2 . Ring breathing 592(R) -{- 658(6 ) CD bending N H bending Residual ring vibrations

1105 (sh) 1099 (s) 1053 (vs)

1100 (m) 1078 (vs) 990 (m) 961 (vs)

1000 (m)

990 (s)

034 (vs) 891 (m) 839 (vs) 827 (s)

757 ivs) 736 (vs) 658 ivs) 618 is)

913 (s) 884 (m) 853 (m) 842 (m) 809 (vs) 792 (s) 770 (m) 752 (m) 720 (m) 672 (s) 656 (s) 620 (sh) 555 (sh)

1000 is) 976 (vs) 830 (m)

1000 (vs) 975 (s) 830 (w)

946 (vs) 912 (m) 812 (s)

932 (vs) 915 (sh) 815 (m)

975 (w) 948 (s) 825 (s)

CD bending

660 (m) 625 (w) 513 (m) 457(w)

660 (w) 600 (w) 513(m ) 457 (w)

650 (m) 617 (w) 380(m ) 351 (m)

650 (s)

778 (m) 748 (vs)

~CH yCH ~CD

660 (vs)

Torsion 7NH 7ND CX stretching CX stretching MN stretching NMI~ bending

513 (w) 380(m) 352 (m) 340 is) 280 (m) 194 (m)

177 141 87

CH bending CH bending ND bending CD bending CH bending CD bending Ring bonding

Lattice vibrations

Infrared and Raman spectra of heteroeyclie compounds--I

239

KBr disc technique [8] was used for the region 3600-600 cm-1, and the spectra were checked by comparison with those of nujol and hexachlorobutadiene mulls. Nujol mulls between CsBr or polyethylene plates were used as the sampling technique between 600 and 33 cm -1. 2.2 Preparation of compounds Imidazole was obtained from Aldrich Chemicals Co., Inc., Milwaukee, and was recrystallized from benzene. The resulting white crystals had a melting point of 90°C. Bis(imidazolato)Co(II) was prepared according to the procedure used by BAUd_ANN and WANG [9] for other metal complexes of imidazole. Anal. Calc. for Co(Cstt3N2)~: C, 37.33; N, 29.03; H, 3.14. Found: C, 37.96; N, 28.76; H, 3.23. 2,4,5-Triiodoimidazole was prepared by the method of BRUNrSGs [10]. The melting and decomposition point of 190°C is in agreement with that obtained by him. Because the product slowly loses iodine on standing, a good analysis was not obtained. Anal. Calc. for CaN2IaH: N, 6.28; I, 85.42. Found: N, 8.50; I, 80.00. 2,4,5-Tribromoimidazole was prepared according to the procedure used by WYss [11] with a few modifications. The infrared spectrum is identical to that published previously [7], and the melting point obtained (217°C) is in agreement with that reported byWyss. Anal. Cale. for C3N~BraH: N, 9.19; Br, 78.67. Found: N, 9.15; Br, 78.61. 2.3 Deuteration of compounds It has been found, and confirmed by the authors, that imidazole neither deuterates selectively [12] nor completely [3]. The sample for which a spectrum is given here was treated with a drop of propylamine in D20 and heated at ll0°C, in a sealed vial for several days before evaporating at 70°C in vacuo. This procedure was repeated four successive times. The product is taken to be 1,2,4,5d4-imidazole, probably with incomplete deuteration in all positions. The deuterations of the trihalogenoimidazoles were effected by simple exchange in D~O at 90°C for four days. The solutions were evaporated in vacuo at 60°C. Again complete exchange could not be obtained. 2.4 Results

The infrared absorption frequencies obtained for the foregoing compounds arc listed in Table 1, and spectra are given in Figs. 1 and 2. 3. DISCUSSION

A double minima potential well has been proposed for the imino hydrogen in imidazole [3], and this hypothesis was accepted by the authors for several reasons. [8] 1~. 1~. ST1-MSOl~and M. J. O'Do~r~LL, J. Am. Chem. Soc. 74, 1805 (1952). [9] J. E. BAVMA~rand J. C. WANG,Inorg. Chem. S, 368 (1963). [10] K. J. BRUNINGS,J. Am. Chem. ~oc. 69, 205 (1947). [11] G. WYSS, Ber. 19, 1366 (1877). [12] R. J. GrLLESP~ et al., J. Chem. Soc. 3228 (1958).

240

M. C o ~ s

D~ N . D . a n d J . L. W A L S R

C.S.C.

The molecule is shown below with correct numbering of the ring atoms. H

I

H

N

H

2C

C5

H

Substituents in the 4- or 5- positions are indistinguishable implying equivalence of carbons, and therefore, of nitrogens. NMR studies of the compound yield a single peak for the absorption by the 4- and 5- protons [12]. Intermolecular hydrogen

5O

B o

o

o b-

5c

3500

I

3o0o

I

zsoo

I

I

2000

Frequency

15oo

I

~ooo

I

5o0

(cm")

Fig. l(a). Infrared spectra of hnidazole and derivatives (3500-500 em-Z). A, imidazole: B,2,4,5-triiodoimidazole;C,2,4,5-tribromoimidazole;D,bis-(imidazolato)Co(II).

Tnfeeeocl and Raman spectra of heterooyclic compounds--I

241

bonding in the system is so strong that ebulliometric and cryoscopic molecular weight determinations yield minimum values of 4 times the actual molecular weight [13]. The extensive splitting of the NH stretching ~nfrared bands supports the proposal of a time-averaged molecular configuration of a ten-atom system with U~

50 ~41

A

=

5¢

u

i B

g

rm

g F--

C

50

J94

D I

600

I

500

I

I

400

300 Frequency

33

(cm -I)

Fig. l(b). Infrared spectra of imidazole and derivatives (600-33cm-1). A, imidazole; B, 2,4,5-triiodoimidazole; C, 2,4,5-tribromoimidazole; I), bls(imidazolato) -Co (II).

symmetry, having protons equidistant from the two nitrogens. This distance is taken to be midway between an average NH bond and average N • • • H hydrogen bond. As will be later discussed, there are two bands in imidazole assignable to NH deformations, and these can be accounted for only by a G2~ molecular model. The final model chosen for the assignment of observed bands and the calculation is shown in Fig. 3. The parameters are adapted from an X-ray study performed on histidine [13] K. HO~MAN~, Im~Zazole and I ~ Derivatlve~, Par~ I. Interscience (1953).

242

1K. CORD~.S D~. ~.D. and J. L. WAL~tt C.S.C.

monochloride m o n o h y d r a t e [14]. According to this s y m m e t r y imidazole should exhibit 24 normal modes: 9A1, 8B1, 3A 2 and 4B 2. The subsequent discussion is divided into two sections, the first dealing with the empirical assignments, and in the second part the calculations which permit a more detailed assignment are discussed.

A

~ u 5c

-

B

~ 5c C 500

I 3000

I 2500

I 2000

I 150o

I 1oo0

I 500

I 1500

I I000

I 500

D zOOO

I 400

1 300

Frequency (cm -I)

Fig. 2. Infrared spectra of partially deuterated imidazole and derivatives. A, imidazole; B, 2,4,5-triiodoimidazole; C, 2,4,5-tribromoimidazole; D, bis(imidazola~o)-Co(II).

3.1 Empirical assignment of the observed frequencies The assignment of infrared bands given in Table 1 is based on a comparison of the spectra of imidazole, deuterated imidazole, the trihalogenoimidazoles and their d e u t e r ated analogs and bis(imidazolato)Co II. The halogenated compounds are helpful in t h a t the CH modes are all subtracted; whereas in the complex there are no N H bands. [14] J. DO~AHUV.,L. R. L~.vI~-~ and Z. S. ROLLE~T,Acta Cryst. 9, 655 (1956}.

Infrared and Raman spectra of heterocyelie compounds---I

243

3200-1700 em -1. T h e bands observed in this region are assignable t o h y d r o g e n a n d d e u t e r i u m stretching modes a n d overtones. I n t h e cobalt complex, t h e r e are only t h e C H stretching bands, a n d in the o t h e r compounds, t h e strong, b r o a d absorptions t h a t are a result of strong h y d r o g e n bonding are observed. Overtones and combination bands. I n an early R a m a n s t u d y [15] no bands were observed in crystalline imidazole b e t w e e n 3142 a n d 1543 cm -1. T h e e x p l a n a t i o n t h a t the bands observed in the infrared between 1745 a n d 1445 cm -1 w i t h the H

H

\

,coc C

,. 322 ~,.

C

// N.--"--_

N \

A~'t°

.

1.3o

~,.

.

C ,.o~.

H Fig. 3. Molecular parameters for Csv imidazole. e x c e p t i o n of t h e 1543 cm -1 a b s o r p t i o n are overtones or combination bands has been offered [2]. B e n z e n e [16] a n d pyridine [17], however, h a v e t h e i r highest ring stretching absorptions at 1618 a n d 1580 cm -1 respectively a n d t h a t for pyr~midine is 1570 cm -1 [18]. W i t h less resonance a n d smaller ring size, imidazole can be e x p e c t e d t o e x h i b i t b a n d s o f similar frequencies. I n this s t u d y b a n d s appearing a t a b o u t 1800 cm -1 in t h e free ligands, bands between 3000 a n d 1600 cm -1 in the complex, a n d those occurring consistently in all t h e c o m p o u n d s a t a b o u t 1650 cm -1 are assigned as nonf u n d a m e n t a l . B y comparison with d e u t e r a t e d imidazole, t h e 1493 cm -1 b a n d in imidazole is assigned to a c o m b i n a t i o n of t h e 757 a n d 736 cm -1 bands in a g r e e m e n t with previous work [2]. Likewise t h e b a n d observed in imidazole a t 1244 cm -1 is a combination o f a 592 cm -1 R a m a n b a n d [15] a n d the 658 cm -1 band. 1600-1500 c m - L T h e b a n d at 1573 cm -1 in imidazole has been assigned as a c o m b i n a t i o n b a n d of those a t 839 a n d 736 cm -1 [2]. T h e b a n d remains, however, [15] [16] [17] [18]

K. W. F. KO~AUSCH and 1%. S~.KA,Chem. Bet. 71, 985 (1938). J. R. SCm~RER and J. 0VER~I~rD,Spectroehim. Acta 17, 719 (1961). G. ZERBI, B. CRAW~ORD,J~. and J. OVER~..~D,J. Chem. Phys. 38, 127 (1963). R. C. LORD, A. L. M_AI~STENand F. A. Mrr.T.~R,Spcctrochim. Acta 9, 113 (1957).

244

M. CORD~.SDE :N'.I). and J. L. W~LTER C.S.C.

in the deuterated species where the contributing bands have shifted. On this basis, and t h a t previously mentioned of the highest bands in benzene, pyridine and pyrimidine, this band is assigned to a fundamental ring stretching mode. The spectra of the deuterated compounds indicate t h a t the absorption at 1543 cm -1 probably possesses a considerable amount of NH bending character, with the ND bending modes absorbing at 1340-1360 cm -1, a frequency ratio of approximately 1.15. 1500-1400 cm -1. The two bands at 1473 and 1445 cm -~ are assigned in this work to ring stretching on the basis of their appearance, though at slightly higher frequency in the cobalt complex and somewhat lower in the trihalogenoimidazoles. This latter effect m a y be attributed to the withdrawal of electron density from the ring by the halogens. 1400-1100 cm -1. The 1328 cm -~ imidazole absorption is either slightly shifted or shifted to 1195 cm -1 in the deuterated compound, and would, therefore, seem to be assignable to CI-I or N H bending. Because the band is observed in the cobalt complex and absent in the trihalogenoimidazoles, the CH bending assignment is favored. This assignment is in disagreement with ICCTRIZKY [1] who favors ring stretching for the band. The absorption at 1145 cm -1 has been assigned to NH [7] and CH [1] bending; the former assignment is favored in this study on the bases of an apparent shift in the deuterated species and the presence of similar bands in the trihalogenoimidazoles which likewise shift on deuteration. 1100-900 cm -1. The spectrum of solid imidazole has strong bands at 1053 and 1099 cm -1. Carlson and Brown assign bands observed in DsO solution at 1110 and 1071 cm -1 to CH deformations. K a t r i t z k y assigns the higher vibration to CH bending and the lower one to ring breathing. Ring breathing has been, with some uncertainty, assigned this low in furan [19], thiophene [20] and pyrrole [21]. In partially deuterated imidazole, there is some possibility t h a t the 1099 cm -I band m a y be contained in the shoulder observed at 1105 cm -1, but the 1053 cm -1 absorption has definitely shifted, probablyto 913 cm -I. The cobalt complex has bands in this region, whereas the halogen substituted compounds have none, and this latter fact provides the most conclusive evidence to the assignment of the two bands as CH deformations. The 934 cm -~ band in imidazole seems to shift on deuteration and, therefore, is assigned to CH bending. The absorptions in tribromoimidazole at 976 and 1000 cm -1 and in triiodo- at 912 and 946 cm -~ exhibit the shift expected in a ring vibration on going from bromo to iodo substitution, and similarly for the bands in the cobalt complex at 950 and 995 cm -I. The fact t h a t the ring modes are found lower in imidazole is probably a function of mixing between hydrogen bending and the ring vibrations. The 934 cm -1 imidazole band is assigned to CH out of plane bending by Katritzky. 900-700 cm -I. The three absorptions above 800 cm -~ in imidazole are assigned to in plane ring bending because of their presence or very slight shifts in the deuterated species, and, as explained above, because of the bands present in the halogen analogs and the cobalt complex. The bands in imidazole at 734 and 756 cm -1 are [19] B. B~LI, S. BRODERSONand L. HA~S~, Ac~a Chem. Stand. 9, 749 (1955). [20] M. RICO, J. M. ORZAand J. •ORCILLO, SpecSrovh~,n. Acta 21, 689 (1965). [21] R. C. LORDand F. A. MILLER, J. Chem. Phys. 10, 328 (1942).

Infrared and Raman spectra of heterocyolio oompounds---I

245

assigned to CH out of plane bending in this work, b y Katritzky, b y Coburn, and b y Otting. The set of bands is found at approximately the same frequency in the cobalt complex, and the region is conspicuously e m p t y in the trihalogenoimidazoles, confirming the assignment as a gamma CH mode. 700-500 cm -i. The consistent appearance of the 658 cm -1 band in all of the compounds warrants an assignment to ring torsion. Offing indicates that this band should represent an out of plane vibration and Coburn also assigns it to torsion. The highest non-planar ring mode in pyrimidine [18] is found in this region, and pyrrole has a 7-ring mode at 649 cm -i [1]. The final band in imidazole at 618 cm -i suffers an intensity loss on deuteration with a new band appearing at 555 cm -i and is assigned to N H out of plane bending. The absorption is absent in the cobalt complex and present with shifts on deuteration in the trihalogeno imidazoles. Again this assignment is in agreement with that of Coburn. Below 500 cm -i. There are no bands above 177 cm -i in imidazole, therefore those in the halogen compounds are due to those group vibrations, and those in the complexes to metal-nitrogen modes. The three bands in imidazole below 177 cm -i are absent in the complexes, and can, therefore, be assigned to molecular lattice vibrations, probably through the hydrogen bond, as well as CH interactions analogous to those in crystalline benzene and naphthalene [22]. 3.2 Normal coordinate analysis The normal coordinate analysis was performed as a ten body problem, and all possible internal coordinates for vibrations were included. The calculations were performed on a UNIVAC 1107 computer. Considering the model used in the calculations (Fig. 3), the C--C bond distance is recorded as calculated to ensure ring closure and the obtaining of the correct number of redundant frequencies. In the X-ray work [14] this bond length is given as 1.36 A, so there is a definite discrepancy. For the NI-I bond two rather vastly different values are indicated; one of 1.08 • representing the average value for a free N H bond and another of 1.30, a reasonable estimation for an N - - I t N hydrogen bond. Two separate calculations were run using these values, and the results showed negligible changes in the frequencies concerned with the change in bond length. This fact indicates that although a change in bond length is characteristic of hydrogen bonding, it is the change in force constant which determines the frequency and accounts for the splitting of the N i l stretching band. The observed bands can then be calculated b y changing the NI-I stretching force constant. The frequencies for the infrared active vibrations were calculated using the symmetry coordinates listed in Table 2. Wilson's GF matrix method [23] was used in the construction of kinetic energy matrix elements from the cartesian coordinates and masses of the atoms in the molecule, and the values were calculated using the G matrix evaluation program constructed b y SCHAcrrrscm~mDE~ [24] and coded in [22] I. I-IAnADAand T. SHImANOUOB:I,to be published. [23] E. B. WILSON,d. Chem. Phys. 7, 1047 (1939); 9, 70 (1941). [24] J. I-I. SCHkCHTSCHNEIDERand R. G. S~YDER,Spectrochim. Acta 19, 117 (1963).

M. C O R D E S D E 1~.~). a n d

246

J.

L.

W~TER

C.S.C.

~/H'°

H,~

r ~4

~T~

4

~

,

Fig. H 8~

Table

?i = A R i s i =At i

H7

Ti = A r I

~[: (A"~"( "~AT'[ +

4. Legend

A:7 A:7')/z Table

2. S y m m e t r y

coordinates

Coordinate At: S1=

(83 ÷ 84

÷ 85)/%/3

S 2 = (s 4 -[- 86 - - 28Q/%/6 S 3 ~ (81 -~ 8s)/%/2 S 4 ~ t4 ~ 5 ----- (tl -~- t2 - - t3 - - t5)]2 S~ ~

m7 = = S~ S1o = Six = $12 ~

$8

(t 1 - ~ t 2 -}- t 3 --}- t Q [ 2

((~1-1- ($a)1%/2 (~1 + ~bQ/%/2 ((~a + c$5)/%/2 (¢a + ¢5)1%/2 ~b3 (PX JU to3)/%/2

of imidazole Description

CH str. CH str. ~ str. CG e r r . CN str. CN str. N H def. CNC def. C i l def. N C C def. N C N def. Redundant

$13 = (p4-m-pQ/%/2

Redundant

Sx4 = P3

Redundant

$1~ = (84 - - 85)/%/2 $1~ ~ (8a - - 81)/%/2 $1~ ~ (t 1 - - t 3 -~- t a - - t~)]2

CH str. NH str. CN str. CN str. Nit deL CNC def. C H def.

BI:

Sis ~

Sis Xs0 $31 x3~ $23 $24

(t 3 - - t z -]- t a - - t5)/2

~ (~1 - ~ (~1 - ((~4 - = (~4 ~ c3~ ~ (pl - -

S~5 ~

($s)/%/2 ~ba)/%/2 (~a)/%/2 ~)/%/2 P3)/%/2

(Pa - - Pa)]%/ 2

N c c def. C H def. Redundant Redundant

B3:

Sse = (Ta -{- 7s)/%/2

CH bending

$27 =

NH

(71 ~V 7 3 ) / % / 2 S2s ~ ~2 8~s ~ (Y)s - - tPs)/%/2 Sa0 = (~1 - - ~03)/%/2

bending

CH bending CN t o r s i o n CN t o r s i o n

2.

for

Infrared and Raman spectra of heterocyclic c o m p o u n d s - - I

247

F O R T R A N IV. The potential field used is a modified Urey-Bradley of the following form:

Fi/[ttj2(Ar,) ~ "-k tj~2(Arj) 2 - - 8 0 8 j t ( r 0 Ao~i:1) 2 - - 2ttfl~(Ar~)(Ar~) -k 2t~s~r~(Ar,)(A~) q- 2t~,~r~(Ar~)(A~)] -b P(A~r) 2 -b T(Av) 2

-k

where r0 ----(r~r~)~/2, and r~ and r~ are adjacent bonds, s ~ - - - - ( r , - r~ cos ~)/q~, t~----r~ sin ~%/q~, q~ = distance between atoms i and j which are bonded to a Table 3a. Force constants for C2v imidazole (A~ and B~ vibrations) :F.C. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Description

Value (mdyn/A)

K(CN)x K(CN)r K(CC) K(CH)A K(NH) K(CH)B H(CNC) H(NCC) H(NCN) H(HCN)~ H(HNC)~ H(HNC)~ H(HCN)~ H(HCC) F(HNC)~ F(HNC)~ F(HCN)~ 2'(HCC) F(HCN)~ F(NCN) F(CNC) F(:NCG) p

5.82 5.10 5.83 4.73 4.45-3.00 4.84 0.32 0.55 0.65 0.10 0.29 0.29 0.16 0.24 0.50 0.62 0.28 0.35 0.28 0.90 0.90 0.80 0.25, 0.00

Table 3b. Force constants for C2v imidazolo (A S and B a vibrations) Value F.C.

Description

1 2 3 4 5 6 7

~(CN)x +(CN)r r(CC) ~(NH) ~(CH)~ ~r(GH)n ~(NH)~r(CH)~

8

(mdyn//tx) 0.57 0.52 0.52 0.33 0.35 0.35 --0.03

~-(~rH)cr (CH)B

- - 0.03

9 1110

¢r(CH)Bvr(CH)a /Torsional

-- 0.03 00

12 13 14 15 16 17

],interactions ~r(NH)7(CN)z ¢r(NH)~(CN)r ~r(CH)~(CN)z ¢r(CH)~(CC) ~r(CH)~r (CN)r

0 0.15 -- 0.14 --0.20 0.18 -- 0.18

248

~I. COR~ES DE N . D

a n d J. L

~ R

C.S.C.

R

~

R

,~

4-F

++ + + ;

"1-

I I "'~

I

0

I o,.~

II

r~

4-

~

+

+

~~

+++_,_++ a

~D

\ \ \ \

a

." ~ "

8 +~ '~'~

,~ ,,

+ ""-r- + + + "~: .i_-I-

I n f r a r e d a n d R a m a n s p e c t r a o f he~erooyclic o o m p o u n d s - - I

249

common atom, and the ji terms reverse the subscripts on the r's found in the equation. The r, and ~ , terms are equilibrium bond lengths and angles. 0 is defined as the angle between the plane of the molecule and the atom bending out of the plane. is a torsion about a bond, A~r~A ~ represents out of plane bending of adjacent hydrogens and A~ Ar terms represent the interactions of out of plane bending with adjacent torsions. The force constants are given by ~ (stretching), H (bending), T a b l e 5. P o t e n t i a l e n e r g y d i s t r i b u t i o n s i n s y m m e t r y c o o r d i n a t e s a n d force c o n s t a n t s for t h e c a l c u l a t e d f r e q u e n c i e s in t h e U2~ m o d e l with a resonance parameter Frequency number

~ tale. (cm-*)

1 2 3 4

3102 3060 3077, 2616 1571

5

1444

6

1214

7

1122

8

1065

9

875

10 11 12 13

3108 3072, 2614 1553 1502

14

1367

15

1076

16 17 18

969 887 743

19

708

20

618

21

598

PED in symmetry coordinates (nonnormalized) with signs from the L matrix

PED in force constants ~(PED)~ = 1

F:C

E,(0.72)-}-Sa(0.27) S~(0.74)--~,(0.28) ~a(1.02) ~(0.39)--~(0.37)

K(CN)A : 0.91 K(CH)a: 0.92 K(NH): 0.79, P(HNC)y: 0.11 K(CC): 0.31, K(CN)x: 0.13, H(HNC)~: .16, H(HNC)y: 0.10 S~(0.45)-~S~(0.33)-~-S~(0.23)--Sn(0.11) K(CN)r: 0.31, K(CC): 0.26, H(HNC)y: 0.13 K(CN)x: 0.11, p: --0.11 --Se(0.82) - - Sa(0.11) K(CN)x: 0.28, K(CN)r: 0.25, F(CNC): 0.13 ~qT(0.35)--Sa(0.31)-{-S,(0.15) K(CN)r: 0.17, H(HNC)~: 0.14, F(HNC)~: 0.13, K(CN)x: 0.11 ~g(0.68--$4(0.10) H(HCC): 0.31, F(HCC): 0.18, H(HCN)~: 0.17 F(CNC): 0.17, H(NCN): 0.16, Ss(O.36)--Sn(0.28)--Ss(O.19) F(NCN): 0.16, H(CNC): 0.13, K(CN)r: 0.11 --S,5(1.00 ) K(CH)~: 0.91 --$1s(1.02 ) K(NH): 0.79, F(HNC)y: 0.12 S,7(0.74)--~q~a(0.12 ) K(CN)x: 0.57, K(CN)r: 0.14 --S,8(0.59)--$2t(0.18)--S,o(0.15 ) K(CN)r: 0.30, K(CN)x: 0.13, H(HCC): 0.11 H(HNC)(~: 0.24, H(HNC)v: 0.21, --S,D(0.69 ) -- Sit(0.25 ) F(HNC)(~: 0.14, F(HNC)r: 0.12, H(HCC): 0.11 E2,(0.41) -}- S,8(0.27 ) -- S,o(0.U ) H(HCN)~: 0.18, H(HCN)fl: 0.14 H(HCC): 0.14, K(CN)r: 0.11, F(HCN)fl: 0.10 Ssa(0.58 ) -}- S,s(0.22 ) -}- Ssx{0.14 ) H(HCN)~: 0.39, F(HCN)~: 0.23 S ~ ( 0 . 5 3 ) -}- ~ao(0.25) ~- $17(0.16 ) H(NCC): 0.30, F(NCC): 0.25 S~e(0.86) --~ 8~.(0.81) ~'(CN)r: .81, rr(GN)n: 0.94 •r(CH)~r(CN)r: --0.73 --Sao(1.4 ) -- E2s(1.2) ~'(CN)x: 1.41,~r(CH)A: 1.24 ~(GH)~r(CN)x: -- 1.67 --Sao(0.33 ) -- $29(0.19 ) T(CN)x: 0.33, T(CN)F: 0.19 ~(CHhT(CN)x: 0.28 ~7(0.79) ~r(NH): 0.79,~(CH)B: 0.17, =(NH)T(CN)x: 0.13

P (out of plane bending), T (torsion), p and t (interactions between the latter two) and F (repulsion across three atoms). F ' is a linear term which compensates for the fact that because of repulsions, it cannot be assumed that the actual configuration is at the bottom of the potential well, and is given by --OAF if the repulsion energy is proportional to q-9 [25]. [25] T. StomA*tOUCH1, -Pure Appl. Chem. 7, 131 (1963).

250

~.

CO~DES DE BT.D. a n d J . L . W A L ~ R

C.S.C.

V (resonance) is of the same form used by SCHERER and OV~RV,ND in benzene [16] and GAvA~ in thiophene [26], and is equal to .~. (--1)t+Jpi J AR t ARj where the R's are bonds in the ring, and p is a resonance parameter. As in the case of pyridine [17] only one frequency is strongly dependent on the resonance parameter (see P E D in T a b l e 6. F o r c e c o n s t a n t s f o r s o m e a r o m a t i c c o m p o u n d s Pyridine [15] Value

F.C.

(mdyn/A)

K(CH) K(CN) K(CC) H(NCH) H(COH) H(NCC) H(CCC) H(CNC) F(NH) P(CH) P(NC)

4.54 6.30 4.71 0.36 0.31 1.16 0.68 0.40 0.52 0.43 0.72 O.SO 0.41

F(CC) p

Benzene [48] Value

Thiophene [28]* Value

F.C.

(mdyn/A)

F.C.

(mdyn/A)

K(CH) K(CC) H(CC) H(GH) /,'(OH)

4.790 5.149 0.663 0.356 0.322 0.587 0.351

Ka(CH) .Kfl(CH) K(CC) K(CS) K(CC) H(SH) HI(CH) H(SC) H~(CC) HS(CH) H(CCC) H(CSC) F(CS) /u(cc) F~(CC) lv(SH) /~I(CH) Fs(CH) -~8(CH) p

5.032 4.873 5.520 2.956 4.428 0.235 0.308 o.415 0.308 0.270 1.013 1.678 0.618 0.585 0.585 0.362 0.295 0.295 0.295 0.178

F(CC) p

* I n the superscripts, ~ and 1 refer to bonds and angles of the type which are nearer the sulfur atom, ~ and 2 to those farther away. T a b l e 7. O b s e r v e d 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 02~ i m i d a z o l e

A1

B,

B2

Obs.

Calc.

3105

3102 3060 3077, 2616 1571 1444 1214 1122 1065 875 3108 3073, 2614 1553 1502 1367 1070 969 887 743 708 618 598

3050--2587 1543 1445 1263 1145 1053 839-827 3124 3050-2587 1573 1478 1328 1099 934 891 757 730 658 618

Error* 0.1 --0.88,--1.1 --1.8 0.1 3.9 2.0 --1.1 --5.4 --0.5 --0.75,--1.0 1.3 --1.6 --2.9 2.1 --3.7 0.45 1.9 3.0 6.0 3.2

* (Obs. -- Calc.) × 100 Obs. [26] ft. GAVA1% P h . D .

T h e s i s , U n i v e r s i t y o f M i n n e s o t a (1964).

Infrared and Raman speotra of heterooyclie compounds--I

251

Table 5), so all the e terms were assumed equal as an average resonance contribution to the potential energy of the system. Table 4 shows the results of the calculation with and without the resonance parameter. The imidazole system is complicated both b y resonance and hydrogen bonding, so the calculations were considered satisfactory if the potential energy distributions for given frequencies agreed with the apparent experimental assignments and if the deviation between calculated and observed frequencies did not exceed six per cent (Table 6).

~1

= 3105

~2 = 3 0 5 0

;3

= '.-.3050 - 2 5 8 7

AI

;4 = 1543

;5 ;14,~45

; 7 =1145

T 0 = 1053

;6

=

1263

-~9 = 8 3 9 827

Fig. 6(a). The normal modes of C=v imidazole.

N

N

N ~ll = " 3 0 5 0 - 2 5 8 7

="-I0 = 3124

t,,'12 =

N

1573

~13 =

1478

/--7 ~14 =1328

~N ;,8 = 757

v17 = 891

N..~ ;19= 7 3 0

;20=658

~v21 = 6 1 8

Fig. 6(b). The normal modes of O2~ imidazole.

252

M. CORDES DE N . D . and J. L. W A L ~ R C.S.C.

As a result of the hydrogen bonding and cyclic structure, there are a strong interdependence of force constants among frequencies and a large amount of mixing in mid-region frequencies. For systems thus complicated normal coordinate calculations may not provide absolute values for force constants, primarily because of inadequacies in the force field employed. Since the same basic force field was used, however, imidazole can be compared with thiophene [26], benzene [16] and pyridine [17]. This comparison is shown in Table 5. The CH bending constants decrease in the order CCH ~ SCH ~ NCH as expected from electronegativity considerations. The two values given for the NH stretching force constant calculate the high and low frequency ends of the broad, split band. As in pyridine H(NCC) > H(CNC), and these are smaller for imidazole, as expected for a five membered ring, with repulsion force constants increasing in the opposite direction both within the two molecules and from one to the other. The hydrogen bending force constants in the imidazole calculation increase in the order H(HCN) ~ H(HCC) ~ H(HNC) with repulsion force constants following the same order. Since these angles are of approximately equal size, the principal effect operating is electronegativity and results are as would be predicted. The resonance parameter for imidazole lies between those for pyridine and thiophene, and a greater degree of resonance could be expected with the addition of a second hetero atom and hydrogen bonding. The negative force constants used in the calculation of the out of plane modes have significance only with respect to the manner in which the system was pro° grammed. The internal coordinates have a defined direction, and interactions between these are either positive or negative, but only according to a predetermined convention.