E L S E V I E R Spectrochimica Acta Part A 52 (1996) 1803 1814

SPECTROCHIMICA ACTA

PART A

Density functional theory study of vibrational spectra. 8. Assignment of fundamental vibrational modes of

9,10-anthraquinone and 9,10-anthraquinone-d8

Bryan Ball, Xuefeng Zhou, Ruifeng Liu* Department ~[" Chemistry, East Tennessee State University, Johnson City, TN 37615-0695, USA

Received 12 February 1996: revised 15 June 1996; accepted 15 June 1996

Abstract

Density functional theory (using Becke's exchange and Lee-Yang-Parr ' s correlation functionals (BLYP)) and ab initio Hartree-Fock calculations were carried out in order to investigate the molecular structure and vibrational spectra of 9,10-anthraquinone and its perdeuterated analog. The calculated structural and spectral features are in good agreement with the available experimental results. Most of the BLYP/6-31 G* non-CH(D) stretching frequencies are slightly lower than reliable experimental assignments; the mean absolute deviation is about 14 cm 1. On the basis of agreement between calculated and experimental results, assignments of the fundamental vibrational modes were examined and some reassignments were proposed. The calculated results can serve as a guide for a future experimental search for the missing fundamentals of the target molecules.

Keywor&': 9,10-Anthraquinone; Density functional theory: Hartree Fock theory; Vibrational spectra

1. Introduct ion

9,10-Anthraquinone (AQ) (Fig. l) has been the subject o f many experimental and theoretical in- vestigations [1-10]. Its vibrational spectrum has been studied by infrared absorpt ion [1-3] and Raman scattering [4,5,8,10] spectroscopy as well as phosphorescence [6-8] techniques, and empiri- cal normal coordinate analysis [9] was carried out to assist assignment of the fundamental vibra- tional modes. However, up to now the fundamen-

* Corresponding author.

tal vibrational spectral features o f A Q are still not fully unders tood and there are some controversies on assignments o f the fundamental vibrational modes [10].

In our recent theoretical studies o f the vibra- tional spectra o f many organic compounds [11,12], it was found that density functional the- ory (DFT) using Becke's exchange and Lee Yang Parr 's correlat ion functionals (BLYP) reproduces the observed fundamenta l vibrational frequencies o f non -XH stretching modes very well, with a mean absolute deviation o f about 15 cm 1 between the calculated and observed results [12]. This accuracy is desirable for resolving dis-

0584-8539/96/$15.00 Copyright ~5 1996 Elsevier Science B.V. All rights reserved PII S0584-8539(96)01769-2

1804 B. Ball et al./ Spectrochimica Acta Part A 52 (1996) 1803 1814

~J

H 11.196

119.9 C C

" ~ £ 5 - / lZ0.2 ~ / 1175 C ...... C 117,4(4)

119.9 I 119.7 120.1(2)1

I

1.382

c .

1 393 1.389 HF 1.421 1.411 BLYP

EXPT I 1.400(2) 1.400(2)

C C C C

119.0 1087(4) 118.2 1.499(2) 1.400(2) 1.073

. . . . . 1.092 1.087(4)

H H o

Fig. l. Comparison of the calculated and electron diffraction [23] structural parameters of 9,10-anthraquinone. The bond lengths are given in A, ngstr6ms, and angles in degrees.

putes in vibrational assignments and provides valuable insight for understanding the observed spectral features.

In order to better understand the vibrational spectra of AQ and to clarify uncertainties in the vibrational assignments, we have carried out density functional theory and ab initio Har t ree- Fock calculations to investigate its structure, quadratic force field, and fundamental vibra- tional modes. The calculated results are in good agreement with available experimental data and indicate that some previous assignments of the fundamental vibrational modes need to be re- vised.

2. Computational details

The molecular structure of AQ was fully opti- mized by the ab initio Har t r ee -Fock (HF) method and density functional theory using Becke's exchange functional [13] and the correla- tion functional of Lee et al. [14] as transformed by Miehlich et al. [15]. The 6-31G* basis set [16] was used in all the calculations as smaller basis sets were shown to be unreliable [17] and larger basis sets are too expensive for a molecule of

this size. For the BLYP equilibrium structure, quadratic force field and dipole moment deriva- tives were calculated by BLYP/6-31G*. The quadratic force field was used to calculate nor- mal vibrational modes by the GF matrix method [18], and the dipole moment derivatives were transformed into the normal modes to ob- tain infrared intensities. As analytical evaluation of polarizability derivatives by DFT is not avail- able with the current version of the Gaussian program that we use, we carried out HF/6-31G* vibrational analysis at the HF/6-31G* geometry and combined the HF/6-31G* Raman intensities with BLYP/6-31G* frequencies in our discussion of vibrational assignments. It should be noted that the 6-31G* basis set is perhaps not flexible enough to give a good description of the dipole moment and polarizability derivatives [19]. Therefore, the calculated spectral intensities can only be regarded as being qualitatively correct. On the other hand, spectral intensities are also difficult to measure accurately. As shown in Fi- gs. 2-4 , both the calculated IR and Raman in- tensities are in satisfactory agreement with experimental results.

The normal modes calculated from the BLYP/ 6-31G* force field were approximately character-

B. Ball et al. / Spectrochimica Acta Part A 52 (1996) 1803-1814 1805

A

B

A

500 400 300

V "- --I - - -J

200

U 100

_y L J < I I

500 300 200 400 100

Fig. 2, Comparison of a theoretical Raman spectrum of AQ-h 8 (simulated from the calculated frequencies and Raman intensities in Table 1) and the experimental Rarnan spectra of Lehmann et al. [8]. A, B, and C are powder Raman spectra obtained at 5 K, 100 K, and room temperature, respectively, and D is the theoretical spectrum.

ized by total vibrational energy distribution (TED) analysis [20,21]. The ab initio and density functional theory calculations were carried out using the Gaussian-94 program package [22]. The vibrational analysis was carried out using the TX90 program package [23,24].

3. Results and discussions

3.1. Structure

In agreement with expectation, geometry opti- mization of AQ by both the HF and BLYP

1806 B. Ball et al. / Spectrochimica Acta Part A 52 (1996) 1803.~1814

P 1800

I 1700

I

1601

I , I

1500 (cm_l) 1300

t

1400

i

I 1201

A

1100 900

13

r

lOOO 800

L I

700 500

[ .... [

600 400

Fig. 3. Comparison of a theoretical IR spectrum of AQ-h 8 (simulated from BLYP frequencies and IR intensities) and experimental polarized IR spectra [1]. (A) Experimental spectra of the bc crystal plane. Solid line, electric vector perpendicular to the b axis; broken line, electric vector parallel to the b axis. (B) Theoretical spectrum.

methods results in a planar equilibrium structure of D2h symmetry. A comparison of the calculated- structural parameters and the results of an elec- tron diffraction analysis [25] is presented in Fig. 1. In this figure, bond lengths are given in Angstr6ms and angles in degrees. It should be pointed out that the electron diffraction study could not determine all the independent structural parameters. As a result, all the CH bond lengths were assumed to be the same and bisecting the external C - C C angle, and all the C - C bond lengths of the two benzene rings were assumed to be equal in analyzing the electron diffraction pat- terns. Fig. 1 shows that these assumptions are quite reasonable, as the electron diffraction results are in good overall agreement with the calculated structural parameters. The calculations show in- deed that distortion of the two benzene rings from the regular hexagonal structure is very small, as all the CC distances of the two benzene rings are

very close to 1.40 A and all the CCH angles are close to 120 °. Compared with the electron diffrac- tion results, all the HF bond lengths are slightly too short and all the BLYP bond lengths are slightly too long. These deviations may have re- sulted from neglecting electron correlation in the HF theory and slight exaggeration of electron correlation by BLYP. The reliable bond distances of similar molecules are, therefore, expected to be between the values predicted by HF/6-31G* and BLYP/6-31G*.

3.2. Vibrations

Under the D2h point group, the 66 normal vibrational modes of AQ belong to the following symmetry species: 12ag + 4big + 6b2g + 1 lb3g +5au + llblu + llb2u + 6b3u. Among them, the ag, big, b2g, and b3g modes are Raman active and infrared inactive, the b~u, b2u, and b3u modes are

B. Ball et al. ' Spectrochimica Acta Part A 52 (1996) 1803 1814 1807

I

1700

I 1800 160(

i i

i I I

1500 (c -~ ) 1300

I 1400

A

~ I i I i I

1 I00 900 700

B ;

I I 1200 1 ooo 800

I I 5O0

I I

600 400

Fig. 4. Comparison of a theoretical IR spectrum of AQ-d 8 (simulated from the BLYP frequencies and IR intensities) and experimental polarized IR spectra [1]. (A) Experimental spectra of the bc crystal plane. Solid line, electric vector perpendicular to the h axis; broken line, electric vector parallel to the b axis. (B) Theoretical spectrum.

infrared active and Raman inactive, and the au modes are inactive in both infrared and Raman spectra. A comparison of the calculated frequen- cies and Raman activities of the Raman active modes with available experimental results for AQ- h8 is given in Table 1, a comparison of the calcu- lated and experimental results of the Raman inactive modes of AQ-hs is given in Table 2, a comparison of the calculated and experimental results of the Raman active modes of AQ-d~ is given in Table 3, and a comparison of the calcu- lated and experimental results of Raman inactive modes of AQ-d~ is given in Table 4. It is shown in these tables that most of the calculated non- CH(D) stretching frequencies are slightly lower but are in overall good agreement with available experimental results. They also show that some symmetry assignments of the observed frequencies given in previous studies are inconsistent with the calculated results. A comparison between a theo- retical Raman spectrum (simulated with BLYP

frequencies and HF Raman intensities in Table 1 by assuming Lorentzian band shape) and experi- mental Raman spectra of AQ is presented in Fig. 2. A comparison between theoretical IR (simu- lated with BLYP frequencies and IR intensities) and experimental IR spectra of AQ and AQ-d~ is presented in Figs. 3 and 4, respectively. These figures show clearly that not only the frequencies but also the IR and Raman intensities are repro- duced satisfactorily by the calculations. In the following, we will discuss assignments of the fun- damental vibrational modes based on agreement between the calculated and observed results.

3.2.1. Raman active modes of A Q-hs The calculated results indicate that most of the

ag modes have fairly high Raman activities. Therefore, they should be easily identified in the Raman spectra. Indeed, for most of the ag modes, the two experimental assignments are consistent with each other. Minor inconsistencies between

1808 B. Ball et al. / Spectrochimica Acta Part A 52 (1996) 1803 1814

Table 1 Comparison of calculated and observed Raman active vibrational frequencies tbr 9,10-anthraquinone

Symmetry v Calculated ~ Experimental Reassignd/ Mode description e

Freq./ IR . . . . . / Freqb./ b I R ...... / Freq'./ (cm i) (era-i) (,~4 a.m.u.-i) (cm-i) (A 4 a.m.u, l) (cm i)

ag 1 3140 321.4 3075 - 3076 3076 CH str. 2 3118 364.4 3067 - 3069 3069 CH str. 3 1645 196.4 1665 100.0 1673 1673 CO str. 4 1567 14.12 1596 20.00 1603 1603 C-C str. 5 1473 1.29 1317 2.30 1480 1480 C-Cstr .+ CH bend. 6 1351 5.17 1212 1.20 1318 1318? C-C str. 7 1171 98.42 1178 31.40 1178 1178 CH bend. 8 1145 41.16 1144 19.00 1156 1156 CH bend. 9 1026 76.79 1030 21.00 1035 1035 CC str.

10 697 14.86 684 7.00 683 683 Ring def. 11 466 19.58 475 12.20 479 479 Center ring def. 12 354 2.70 301 1.50 362 362 Center ring def.

big 13 956 0.64 978? 0.50 978 CH wag. 14 761 1.84 770 1.85 770 CH wag. 15 442 0.65 440 0.87 440 Ring tor. 16 225 12.46 239 4.10 - 239 Butterfly

b2g 17 975 0.46 990? 0.52 - 990 CH wag. 18 897 5.77 819 0.60 900 f CH wag. 19 794 0.84 654? 0.40 819 CO wag.+ ring tor. 20 645 0.43 449 0.92 654 Ring tor.+ CO wag. 21 421 1.60 419 0.23 449 Ring tot. 22 128 3.85 156 4.10 156 Center ring tor.

b3g 23 3137 30.61 3082 - (3076) 3076 CH str. 24 3103 149.9 3043 (3069) 3069 CH str. 25 1584 164.1 (1653) 1584 1584 C-C str. 26 1451 3.58 1584 2.40 1440 1440 CH bend. 27 1287 21.95 (1326) 0.35 1324 1324? Ring def. 28 1206 8.11 , (1308) 0.70 1212 1212 CH bend. 29 1082 3.08 (1082) 0.60 1082 1082 Ring def. 30 907 3.55 924 1.20 978 924 Ring def. 31 672 0.12 678 2.00 679 679 CO bend.+ ring def. 32 408 1.23 364 2.10 419 419 Ring def. 33 294 1.88 250 4.70 258 301 Ring def.

~The frequencies are calculated by BLYP/6-31G*, and Raman intensities by HF/6-31G*. bThe experimental assignments of Lehmann et al. [8]. The parentheses denote marginally detected bands. The Raman intensities are relative to v 3. CAssignments of the fundamental vibrational modes of Girlando et al. [9]. aAssignments of the fundamental vibrational modes proposed in this study. ~Based on total vibrational energy distribution analysis. fFrom Ref. [8].

t he e x p e r i m e n t a l a s s i g n m e n t s we re f o u n d f o r t he

w e a k R a m a n m o d e s , vs, v6 a n d v12. L e h m a n n et

al, [8] a s s i g n e d v5 to a w e a k R a m a n b a n d a t 1317

c m 1, w h i l e G i r l a n d o et al. [9] a s s i g n e d it t o 1480

c m - 1 o n t he b a s i s o f a n e m p i r i c a l n o r m a l c o o r d i -

n a t e ana lys i s . O u r c a l c u l a t e d f r e q u e n c y o f n5 is

1473 c m 1, s u p p o r t i n g t he r e su l t s o f t h e e m p i r i c a l

n o r m a l c o o r d i n a t e ana lys i s . F o r v6, L e h m a n n et

al. [8] a s s i g n e d it to a b a n d a t 1212 c m 1, b u t

G i r l a n d o et al. [9] a s s i g n e d it to 1318 c m l. O u r

c a l c u l a t i o n s p r e d i c t t h i s m o d e a t 1351 c m - ~, sup -

p o r t i n g t he a s s i g n m e n t o f G i r l a n d o et al. F o r Vl2,

Tab

le 2

A

co

mp

aris

on

of

the

calc

ula

ted

an

d

ob

serv

ed R

aman

in

acti

ve

vib

rati

on

al f

req

uen

cies

of

9,1

0-a

nth

raq

uin

on

e

Sym

. v

Cal

cula

ted

a E

xp

erim

enta

l (c

m

L )

Rea

ssig

n. b

M

od

e d

escr

ipti

on

c

Fre

q.,

li

p ̀

Ref

. [1

] R

ef.

[2]

Ref

. [3

1 R

ef.

[8]

Ref

. [9

] (c

m -

I)

(kin

to

ol

i)

Ref

. [1

0]

(cm

')

a~

34

973

0.0

1010

vw

10

10 v

w

1010

35

887

0.0

8867

vw

36

715

0.0

750

vw

75

0 v

w

750

37

485

0.0

(670

) vw

38

11

0 0.

0 -

- bn

, 39

31

38

6.54

30

81

3080

vw

30

80 v

w

40

3103

10

.20

3068

30

40 v

w

3040

vw

41

16

62

181.

4 t6

76

16

81

vs

1681

vs

1682

42

15

76

129.

5 15

93

1594

s

1594

s

1585

43

1445

2.

7I

1454

14

55

w

1455

w

1456

44

12

56

1.83

12

87

13

10

?m

13

10

m

1320

45

1156

11

.72

1173

1

30

47

m

13

04

m

1307

46

10

84

0.00

10

96

1t6

8m

1

16

8m

11

70

47

780

0.1

l 91

3 79

2 vw

{1

053)

vw

48

605

1.69

62

6 40

7 In

62

0 49

22

3 1.

75

237

236

w

m

236

w

228

b2u

50

3139

30

.29

3074

30

75 v

w

3075

vw

51

31

18

49.0

6 30

45 v

w

3045

vw

52

1558

0.

11

1574

15

76 w

15

76 w

15

76

53

1461

0.

66

1474

14

75

w

1475

w

54

1340

15

.22

1373

13

30 s

13

30 s

13

39

55

1264

61

6.5

1335

12

85

s 12

85

s 56

11

63

21.7

6 12

07

1146

w

12

05 w

57

1034

1.

41

1034

vw

11

45 w

11

55

58

926

67.0

0 93

9 9

35

m

935

m

945

59

622

7.97

6

24

m

62

4m

60

383

24.4

0 38

7 4

07

/39

0 m

3

90

m

b3u

61

959

2.82

97

0 97

0 w

97

0 w

62

801

20.1

7 81

6 81

5 s

815

s 79

5 63

69

7 75

.16

708

693

m

693

m

705

64

400

0.01

49

1 49

0 vw

49

0 v

w

65

157

1.86

37

5 w

37

5 w

66

50

5.60

16

7 16

7 w

16

7 w

I6

7

3078

3056

16

76

1593

1450

12

85

1169

1097

79

1

627

230

3078

3056

15

82

1475

13

32

1285

1163

10

54

939

(627

) 38

4

1679

1595

1169

(625

)

1580

1329

12

84

1050

938

693

973

808

699

1010

? C

H

wag

. 88

6 C

H

wag

. 67

0?

Rin

g t

ot.

490

Rin

g t

or.

Cen

ter

rin

g t

or.

3078

C

H

str.

30

56

CH

st

r.

1679

C

O

str.

15

95

C-C

st

r.

1450

C

H

ben

d.

1285

C

H

ben

d.

1169

C

C

str.

10

97

Rin

g d

ef.

791

Rin

g d

ef.

625

Cen

ter

rin

g d

ef.

230

Rin

g d

ef.

3078

C

H

str.

30

56

CH

st

r.

1580

C

C

st

r.

1475

C

H

ben

d.+

C

C s

tr.

1329

C

C

st

r.

1284

C

C

st

r.

1163

C

tt

bend

. 10

50

CC

st

r.

938

CC

str

.+

CO

ben

d.

627

Rin

g d

ef.

384

CO

be

nd.

973

CH

w

ag.

808

C1-

1 w

ag.

+

CO

wag

. 69

9 C

O

wag

.

375

Rin

g t

ot.

16

7 B

utt

erfl

y

73

Rin

g t

or.

e~

@

e~

4.

~'B

oth

the

freq

uen

cies

an

d

the

IR i

nte

nsi

ties

are

cal

cula

ted

by

BL

YP

,'6-3

1G

*.

bA

ssig

nm

ents

of

the

fun

dam

enta

l v

ibra

tio

nal

mo

des

pro

po

sed

in

this

stu

dy

.

~B

ased

on

tota

l v

ibra

tio

nal

en

erg

y d

istr

ibu

tio

n a

nal

ysi

s.

1810 B. Ball et al. / Spectrochimica Acta Part A 52 (1996) 1803-1814

Table 3 Comparison of the calculated and observed Raman active frequencies of 9,10-anthraquinone-d8

Sym. v Calculated a Experimental/(cm ~)

Freq./ le . . . . / Ref. [9] Ref. [8] ( c m - b (A a.m.u. -1)

Reassign.b/

(era ~)

ag 1 2331 164.7 2 2311 124.3 - 3 1642 192.1 1664 1660 4 1544 16.23 1570 1569 5 1374 4.83 (1203) 6 1347 29.14 1340 (1203) 7 852 18.35 1096 1095 8 822 14.98 851 814 9 1084 154.1 822 854

10 641 12.21 652 645 11 464 18.68 474 475 12 343 3.04 289

bl~ 13 775 0.09 14 589 0.03 - 609? 15 393 0.81 389 16 212 9.84 224

b2~ 17 777 1.62 18 681 0.09 599 19 839 2.07 20 591 0.49 400 21 394 0.84 ' 410 22 121 2.59 - 143

b3g 23 2325 16.51 - - 24 2296 54.29 - - 25 1550 172.4 - - 26 1370 6.02 1561 27 118l 24.16 (1208) 28 1005 0.27 29 826 0.28 - (830) 30 895 3.93 901 31 647 0.16 - 651 32 400 1.58 - 351 33 283 1.49 - 234

1660 1569

1340 854 814 1095 645 475 351

609 389 224

599 400 t43

1561

1208

830 901 651 410 289

~The frequencies are calculated by BLYP/6-31G* and Raman intensities by HF/6-31G*. bAssignments of the fundamental vibrational modes proposed in this study.

our calculated frequency agrees very well with the assignment of Girlando et al.

For the out-of-plane Raman active big and b2g modes, the only experimental assignments we found were those of Lehmann et al. [8]. For the b~g modes, both the calculated frequencies and Raman intensities are in good agreement with the experimental assignments. For the beg modes, there are some inconsistencies between the calcu- lated results and the experimental assignments of

modes v18 through v21. Careful inspection shows that the two observed frequencies, 819 cm-1 and 654 c m - 1, are in good agreement with the calcu- lated results for v19 (794 cm - l ) and v20 (645 cm-1), respectively. Therefore, they should be reassigned accordingly. For v21, the calculated frequency, 421 cm -1, is between two observed candidates at 449 and 419 cm- l , respectively. Although the latter agrees better with the calcu- lated frequency, the intensity pattern supports

B. Ball et al. / Spectrochimica Acta Part A .52 (1996) 1803 1814 181 l

Table 4 Calculated and observed Raman inactive frequencies of 9,10-anthraquinone-ds

Sym. v Calculated ~

Freq./ llr / (cm 1) (km mol 1)

Experimental/(cm - ~)

Ref. [1] Ref. [2] Re['. [3] Ref. [9]

Reassign.b/

(cm i)

a u 34 809 0.0 35 726 0.0 36 637 0.0 37 439 0.0 38 100 0.0

bLu 39 2326 8.15 2281 40 2296 5.44 2272 41 1658 205.6 1676 42 1545 98.10 1565 43 1342 2.60 1395 44 1016 1.56 1020 45 1098 5.26 1120 46 861 3.06 871 47 736 1.02 815 48 582 1.37 605 49 209 0.65 222

b2u 50 2330 35.40 2296 51 2311 14.55 52 1528 0.00 1530 53 1371 120.5 1403 54 1333 0.66 1311 55 1225 499.9 1246 56 844 4.44 965 57 911 67.38 - 58 803 1.61 922 59 600 6.98 - 60 380 24.36 381

b3u 61 803 0.00 846 62 559 54.64 744 63 728 2.24 570 64 357 0.29 398 65 153 1.99 348 66 49 5.25 161

800vw 755vw 638w

2295vw 2275vw 1675vs t568s 1400% l120m 1021m 872m

222w 2295vw 2279vw 1550w t405?s 1310m 1243vs 955w 818vw 922s 601m 395/382m 845w 562s 743m 465vw 348 w 160w

800vw 755vw 638 w

2295vw 2296 2275vw 2275 1676vs 1671 1568s 1566 1400s 1354 l120m 1120 1021m 1023 872m 868

(895)vw (742) 395m 604 222w 222

2295vw 2296 2279vw (2275) 1550w (1528) 1405s 1402 1310m 1310 1243vs 1243 955 w 918 828 w 922 s 835? 601m (604) 382m 381 845w 562s 743m 398vw 348w 160w

806 755 638

2326 2296 1671 1566 1354 1023 1120 868 742 604 222

2296 2275 1528 1402? 1310 1243 846 922 828 6O4 381 818 562 743 348 160 7O

~Both the frequencies and the IR intensities are calculated by BLYP/6-31G*. bAssignments of the fundamental vibrational modes proposed in this study.

assigning 449 cm -1 to this fundamental. For v~s, the calculated frequency of 897 cm-~ is too far from experimental assignments o f the bzg modes. In the Raman spectrum of Lehmann et al. [8], there is a band at 900 cm-~ which was explained as a combination of v48 and v64. On the basis o f agreement between the calculated and observed frequencies, it seems this band is a reasonable candidate of v~8.

Significant differences between the two experi- mental assignments [8,9] and our calculated re-

sults are found for the b3g modes. For v25, v26 , v28 , and v32, the two experimental assignments are inconsistent with each other. For these four modes, our calculated results are in good agree- ment with the assignments of Girlando et al. [9]. Our calculated result o f V3o is in agreement with the assignment of Lehmann et al. [8], while the assignment of Girlando et al. is 70 cm l higher than the calculated result. Both of the previous studies assigned v33 to a band at about 250 c m - 1, but it appears too low compared to the calculated

1812 B. Ball et al./ Spectrochimica Acta Part A 52 (1996) 1803 1814

frequency, 294 cm ~ On the other hand, the calculated frequency is in good agreement with a Raman band at 301 cm 1 which was assigned by Lehmann et al. [8] to the ag fundamental v~. Their assignment was refuted by Girlando et al. and not supported by the calculated result. On the basis of agreement between the calculated and observed results, it is reasonable to assign the Raman band at 301 cm i to v33.

With the reassignments proposed above, the mean deviation between the calculated and sug- gested assignments of the non-CH stretching Ra- man active modes of AQ-h~ is 14 cm ~. This mean absolute deviation is of similar magnitude to those of many other organic compounds that we have studied [11,12].

3.2.2. Raman inactive modes of AQ-hs Compared with the number of experimental

studies on the Raman active modes, there are many more experimental studies on the infrared active modes. Although there were significant dif- ferences among the early assignments of the bh, and b2o modes, our calculated frequencies of these modes agree closely with the assignment of Gir- lando et al. [9], thus supporting their assignments. For the b3u modes, all the experimental assign- ments of v61, v62, and v63 are in good agreement with our calculated results, but discrepancies are found for v64, v65, and v66. All previous studies assigned a weak infrared band at 167 cm l to V66. Our calculations predict indeed a weak infrared feature at 157 cm 1, but the calculations indicate that it is v65 instead of v66. The latter is predicted to be a stronger infrared band at 50 cm i. In the infrared spectrum of crystalline AQ-hs, there is a strong infrared band at 73 cm t [1], which was attributed to lattice vibrations. According to the calculated results, it is probably v66. This band was found to have a deuterium isotopic shift of 3 cm 1 in AQ-d8 [1], which is in reasonable agreement with the calculated isotopic shift of 1 cm ~. The fact that this band was also observed in the Raman spectrum of the crystal [5] may be ex- plained by a lowering of the symmetry due to intermolecular interactions in the condensed phase. The experimental assignment for v65 is a weak infrared band at 375 cm 1 , which is in

reasonable agreement with our calculated fre- quency for v64. The experimental assignment of v64 to a very weak infared band at 490 cm t is, on the other hand, too high compared to the calculated result, but the observed frequency is in good agreement with our calculated aL, mode v37. With the reassignments for v64 , v65 , and v66, the mean absolute deviation between the calculated and observed non-CH stretching frequencies of the infrared active (b~u, b2u, and b3u) modes of AQ-hs is 13 cm ~, which is again consistent with the mean deviations of many other organic com- pounds

The au modes are inactive in both the infrared and Raman spectra and therefore are the most uncertain. Our calculated frequency of v37 agrees closely with the frequency of a very weak Raman band observed at 490 cm ~ which was assigned to v64 , but has been shown to be incorrect. The calculated frequency of v~ 5 agrees closely with the experimental assignment of Gazis and Heim [2], but the experimental assignments of v34 and v36 differ significantly from the calculated results. More experimental studies on these modes are desirable in order to clarify these uncertainties.

3.2.3. Raman active modes of AQ-d8 There are very few studies of the Raman spectra

of AQ-d8. Lehmann et al. [8] assigned 23 Raman bands to the Raman active modes, and Girlando et al. [9] assigned 8 Raman features to the ag modes. The experimental assignments are com- pared with the calculated results in Table 3. It is shown that most of the symmetry assignments of the Raman features given by Lehmann et al. [8] are in agreement with the calculated results, but some assignments need to be revised. For example, a band at 289 cm ~ was assigned by Lehmann et al. [8] to the lowest ag mode v12, but it is 54 cm lower than the calculated result. On the other hand, the calculated lowest b3g mode v33 is at 283 cm J which is in excellent agreement with the 289 cm ~ band. The calculated frequency of v12 (343 cm- 1) agrees very well with a Raman band ob- served at 351 cm ~ which was assigned by Leh- mann et al. [8] to the b3g mode v32. The calculated frequency of v32 (400 cm 1) is 49 cm ~ higher than the experimental assignment (351 cm - I )

B. Ball et al. / Spectrochimica Acta Part A 52 (1996) 1803 1814 1813

but agrees reasonably with an observed Raman band at 410 cm 1 which was assigned t o b2g symmetry. On the basis of the agreement be- tween the calculated and observed results, it is reasonable to reassign the observed frequencies at 289 cm-~, 351 cm ~, and 410 cm ~ to v33 (b3g), v12 (ag), and V32 (b3g), respectively. There are also some discrepancies between the empiri- cal assignments and the calculated results for other modes. On the basis of the calculated re- sults, our suggested reassignments of the ob- served Raman frequencies of AQ-d~ are given in the last column of Table 3. There are some missing frequencies in this column and more ex- perimental studies of AQ-d~ are required in or- der to give a complete assignment of all Raman active modes. The calculated frequencies of the missing modes can serve as a guide for future experimental search and assignments of the missing bands.

3.2.4. Raman &active modes of AQ-d~ Comparison between the experimental assign-

ments and the calculated results of the Raman inactive modes of AQ-d8 is given in Table 4. There are many experimental studies of the in- frared active modes of AQ-d~ [1-3,9]. The cal- culated results for most of these modes are in good agreement with the experimental assign- ments. As in the case of the parent molecule, the most significant difference between the cal- culated and observed results of the infrared ac- tive modes is in the assignment of v~,~,. According to the calculated result, this mode should be around 50 cm - j and is tentatively assigned to the 70 cm 1 observed in the crystal spectrum. The weak infrared band observed at 160 cm ~ which was assigned to v6(~ should be reassigned to mode v65. The calculated frequen- cies of the aL, modes v34 , v35 , and v3~, are in good agreement with available experimental as- signments. On the basis of the calculated results, our suggested assignments of the observed fre- quencies are given in the last column of Table 4. For the non-CD stretching infrared active modes, mean absolute deviation between the cal- culated frequencies and our suggested assign- ments is 13 cm 1

4. Summary

Density functional theory BLYP and ab initio HF calculations have been carried out in order to investigate the molecular structure and vibrational spectra of AQ and its perdeuterated analog. Both the calculated structural parameters and the vi- brational spectral features are in good agreement with available experimental results. The mean ab- solute deviation between the calculated vibra- tional frequencies and the reliable experimental assignments is about 14 cm ~. On the basis of agreement between the calculated and experimen- tal results, assignments of the fundamental vibra- tional modes of AQ-h~ and AQ-d8 are examined and some reassignments are proposed. The calcu- lated results can serve as a guide for future exper- imental searches for and assignments of the missing fundamentals. This study shows that the density functional theory BLYP/6-31G* calcula- tion is a much more promising approach to un- derstanding the vibrational problems of organic molecules than the empirical normal coordinate analysis.

Acknowledgements

This study was partially supported by the Re- search and Development Committee and the Honors Committee of East Tennessee State Uni- versity and by Research Corporation.

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