The n-π transitions of the pyrazine molecule

ChemicalPhysics 8 North-Holland

ll(1975) 151-172 Publishing Company

THE n--n TRANSITIONS 11.Polarizedspectrum David L. NARVA Depwrmenr

OF THE PYRAZINE MOLECULE.

in benzene

crystal, and anharmonicity

in the upper singlet state potential

function

*

and Donald S. McCLUFUZ

of Chemisrry.

Princeron

Universiry,

Princeron, Ntw Jcrsqv 05540.

US.4

Revised manuscript received 16 June 1975

The polarized absorption specua of pynzinc (h4 nnd do) in single bcnzcnc crystals hdve been masured at high rcsalurian at 2 K. Vibratiorwl assignmcms in the t Ag + ‘Bg,, (nn’) transition have been confirmed and corkdenbly cxtcnded. The quutic potenthl component of hydrogen bending mode tO3 has been found to originate primarily from vibronic coupling with the nearby t Bzu (nn*). The coupling between in-plane 63 and out-of-plane 10a modes is dcrcribed theareticW, and leads to further spcchal assignments. 0th~; out-of-phne modes 4 and 5 are identified and shown to hrve combination defects with 63r A quartic component found for the out-of-pine ring bending mode 4 could not be cxplSncd by vibronic coupling.

1. Intmduction

In a previous paper [ I] (henceforth calle’d I) the vibrations excited in the nn transitions of pyrazine were assigned and deductions concerning the potential surfaces of the ground and first singlet excited state were made. The major conclusion was that the mode lOa, the big out-of-plane H-bending mode, has a strongly quartic oscillator component in the ’ B,, rm state. In another paper, Suzuka et al. reached the same conclusion [2] _We also observed a strong coupling between 6a and 10a [I]. We felt that these properties are especially characteristic of nfl excited states and that it would he worthwhile to strengthen the previous con-

clusions by further experimentation, and to look for other significant facts about the excited state. This paper presents

the results of a detailed

in single oriented

benzene

study of pyrazine

crystals.

The vibrational assignments in the excited ’ Bg, state of pyrazine were made quite definite by several methods. First, it was possible to use polarization ratios quantitatively, and thereby to assign a line to one of

the three possible directions of elect:ic dipole transitions within the pyrazine molecule. Second. the isotope product rule was used fcr h, and d4 isotopes as before [ 11. Third, the extremely narrow lice widths mqde it possible to use the isotope shifts due to 'SN and 13C innatural abundance to confirm several crucial assignments. Fourth, accurate intensity measurements of a line relative to the origin made it possible to use Franck-Condon intensity calculations quantitatively. The quartic anharmonicity of the out-of-plane modes, 4 and 10a was measured. Modes 4, 10a and another out-of-plane mode. 5, add 6a anharmonical[y. The analysis of these anharmonicities enables us to extend the spectral assignments in the pyrazine spectrum. We are of IOa able to account for the quartic anharmonicity by vibronic coupling with the nearby I B,, state, but for the mode 4 the major part of the anharmonicity must be an in-state effect. These anharmonicities ap pear to be a significant feature of the nrr* states of heterocyclic molecules.

2. Experimental l

-

This work was supported by a grant from the Natioxd ence Foundation.

ki_

The experimental greater than 99%

results to be shown

later prove that are oriented

of the pyrazine molecutes

152

D.L. Natva. D.S. McClure/The n-n nansiriofis of the pymzine moleade. II

Table 1

Thb ratiosof the squares of the projectiorrsof the three symmetry axes of pyrazineon the benzene aystal ax& for the orientation

with the N-N axis along the b ayrtal

axis

Crysialaxes [4 ] c/b

otb

olc

z Y

11780 13.411

118.6 11.011

91/l l/1.22

X

7.16/l

7.711

1.08/l

aystai to a dry ice bucket and then slowly lowering it into a Dewar which had begun to cool doim to 77 K. The spectra wer? taken with a JaneLAsh 3.4 meter grating spectrograph using the third order of a grating having 180 000 lines in a 6 inch width. Photographic plates, usually Kodak 103a-0, were used. Narrow lines 0.3 cm-l apart were observed to be clearly resolved. Line positions are given to 0.1 cm-*. Iron arc lines were used for calibration. The sample was immersed in liquid helium below the A-point. The source of light was a high pressure xenon arc, filtered to permit only ultraviolet light to pass through the sample.

2.1. Measuremertt of relcrtive intensities arrd pokzrizations in a single way in the benzene crystal. They are coplanar with the replaced benzene molecule and the N-N direction is nearly along the b-axis as for the two opposite CH groups of the replaced benzene molecule. Hong and Robinson [3] suggested that the pyrazine molecules line up with their N-N axis almost along the b crystal axis of benzene because of the similarity of the spectra of pyrazine in benzene and pyrazine in pyrazine-d4. Table 1 shows the ratios of the squares of the projections of the three symmetry axes of pyrazine on the benzene crystal axes for the case of this particular orientation 14). The table shows that three types of polarized lines should be observed. The a and c axes were not distinguished and an ub or bc face was always photographed. Therefore, only columns c/b and u/b

Accurate polarization ratios were needed in order to distinguish the hvo transition moment directions perpendicular lo the N-N direction. and this meant that accurate intensities were necessary. It was also important to establish the intensity ratios 12,g’Im for nontotally symmetric vibrations since these ratios could be used as a test of assignments by ccmparing the observed and calculated ratios. The calculated ratio using the Frzmck-Condon principle is

Izo/foo = * [(a” - o’)/(w”

+ w’)] 2.

(1)

A third reason for having accurate intensity measuremcnts is to be able to identify fiiy the lines due to molecules containing 13C and 15N in natural abundance. These lines are useful for verifying vibrational assignmcnts. Since the photographic method of recording was used

are important; they are approximately the same. The crystals were grown by lowering a Bridgeman tube into ice water over a period of 24 hours. Starting in order to get good wavelength measurements, it was concentrations of pyrazine in benzene ranged from necessary to be careful not to exceed the linear range lWs molar lo 1W3 molar. At the higher end of this of the plates These were !ra&d with a Joyce-Lcehel range. there was a large difference in concentration bemicrodensitometer, and lines within the linear range of tween the top and bottom of the boule. the plate were &iy identified. Samples of many difThe finished crystal was examined in convergent poferent concentrations were studibd, and a wide range hrized light with a polarizing microscope in a cold of exposures %is taken for each ,The resulting speck ioom at -2O”C, and was cut with a razor blade until were compared: spectra of crystals of differing concen,‘ the-acute bisectrix feure was located. It was not always tiation but the -&me ex@url made possible the conpossible to distinguish the u and c axes, but this “s struction of a relative scal; of intensities, using the f&t not necessary, as is shown in table 1. After the acute. tit .the true relative inte&ities of all l&r of 8 spee . bisectrix and, therefore, the b-axis was lopted; the cry& trum are f&xl. Since the l&strengths range’over -many $4 was cut along the b-axis so that polarized syctra orders of magnitude. the concetitratio~ Ii&thick&s .lD and UI could be taken. in Grder It was important to get hnooth surfaces in aider to ’ wa; also varied over &aiiy _orders_of&&de to &y within the Ii&t& ra&e of the plates. : : - : tkve cqrrst polarizations Thiiwas accomplished b) - wingnewrazor bkdes, qiiickly t&nsfe_~‘the’c& : .‘@epl&es icsed~@&ost~~f the w&k-w&e &$k. Y : .‘.-_., J ,_ < I‘ .;.’ . - .: ;, :: __ :‘. I ._ . .\,’ _” I : L _. 7. : ::_ 1 . ,, -, _,_ . . ,_ 1 _’ ~. _: :.. _. ..” ‘\. - .‘I.:.. _:,, ,., ;_I ,--. _. __ . -. i_: .: .:.-_..-. _,, . _._. -’ .___I. .‘_-_;,__

D.L. Nary

D.S. McfXue~Thc

n-w rmnsitions of rhe pymzine nwkade.

Fig.1.Pohrizedspcclrumofh~ pynzine

If

153

'Bm nn*inbenzcneat2K.

103a-0 which have a linear range from 0.2 to 1.7 optical density and are quite fast. The speed was important when working with very narmw slits (10.~) and when many exposures were necessary. The results obtained were quite adequate for both relative intensity and polarization. As has already been mentioned, the crystal surfaces must be smooth for good polarization measurements, and this turned out to be the most importnat factor. A single calcite Clan-Thompson prism was used as a polarizer.

10a 430

?.cm

NNAHDL-

-1

3. Description of the spectra

RING

F&. 2;. 100 and 6a $I ihe polarized spectrur: of pyrazine hq 2 K at a concqtration where only three peaks are visible.

The appearance of the spectra is illustrated in fii. 1 for h4 and in fii. 3 for d4 _ Tables 2 and 3 list the lines in h4 and da. The frequency corrected to vacuum is listed first, followed by the energy difference from the origin, the absorption intensity at the line maximum, the line width at haIf height, and the product of the intensity and line width_ This product is a good measure of the true line strength. Next the polarizatioa ratio is

at

given as f(u or cl/I@). Most of these ratios are.around 6/l, corresponding to the out-of-plane polarization.. The last column in the tables gives the interpretation of the line. The justification of these assignments is given in I tid in the following section of this paper.

154

D.L. Narw, D.S. McClure/The

n-n

transitions of rhe pymzine

molea&.

II

Table 2 Pynrine hg, 2 K. in benzene

em-1

29 883.1

A (cm-‘) -11.1

894.2

0.0

Au

I

430 63000

30000

Interpretation

1

NN-2

>4

origin

236

0.55 0.46

Polarizalion ratio

Pduct

898.6

4.4

400

0.55

220

7

900.3

6.2

1400

0.50

700

5

900.5

6.4

1400

0.50

700

5

origin site al

lSN origin 13C, origin

902.1

8.0

.4.0

0.8

3.2

-4

“N2

origin

904.1

10.0

11.0

0.:

a.8

-4

“CZ

origin

1.4

11.2

-4

“Cz

origin

0.72

11.0

-4

NN-3 origin site? a)

8.0

906.1

12.0

908.6

14.5

941.6

47.5

340

12

4 100

6

lattice fJ)

947.8

53.6

450

lli

4 500

6

lattice b,

953.9

59.7

300

5.5

1650

6

httice b,

957.1

63.0

260

3.3

860

6

htliee b,

970.9

76.8

85

II

940

5

htriee b,

981.1

86.9

90

12

1080

s

htticc b,

30 297.9

403.7

18

2.7

49

6

310.4

416.3

37

9.4

350

4

322. I

428.0

42

0.v

324.2

430.1

328.6

434.4

329.5

15

32.0

l/10

NN-2 10a site a)

0.46

4 100

20

0.58

12

435.4

160

0.58

90

372.2

478.0

30

14

420

3

1Oa btticeb)

379.7

485.6

36

14

500

3

1Oa lattice b, 55 cm-*

9000

1s -10 12

1OP 1Oa “N,

(4.3)

1oa SC, ‘

(5.3) 48 cm-’

1.7

136

11100

i .a5

407

l/10

1950

6

2X

3

2 X 16b OC, ‘

6

NN-2 6a site a)

399.8

505.7

80

411.4

517.3

220

429.6

535.4

1500

434.3

540.2

40

0.92

469.0

574.8

60

2.3

1.3

3? 138

4 16b (4.8)

478.5

584.3

2.0

18000

6

6a

52a.1

633.9

200

10.3

2060

5

6a ~rtiee b) so

534.4

640.3

240

10.3

3 120

s

6a httiee b) 56

539.8

645.6

iao

4.7

a50

5

6a lattice b, 61

9000

555.8

661.6

68

14

950

3

6a lattice b, 77

567.5

673.3

s2

14

72s

3

6a krtice b, a9

613.0 627.6

7:8.8 733.4

18 8

694.6

800.4

120

1.2

21.6

1.2

9.6

1.05

777.9

883.8

4

788.8

894.7

600

792.9

898.8

so

1.1

835.4

941.3

350

1.2

837.3

943.2

20

1.5

126

2.k

10

2.24

1340

55 ,

420 30

l/7

j

-l/10

3 .S -5 6 6‘

_

--

1

h-2

2 x lcla site 1).

2X-10&(2X430)+35 2 x 91oa lSc,

(4.1)

_‘

~_

: :’ :_.,_

_

_ .-

D.L NOIM. D.S. h¶cClurejThe

n-n rransiliotu of rhe pymzihe molecuk

15s

II

Table 2 f%zine

ha. 2 K, in benzene (continued)

A (cm-‘)

cd

1

Au

Roduct

107

863.1

968.9

70

1.53

866.4

972.3

700

1.65

881.8

987.7

200

3.5

885.1

991.0

280

4.7

904.0

1 009.9

40

1.8

72

1150

lblariwtion ratio 312 12

1320

6

1.8

135

Cl15

1.8

117


1027.7

1.8

400

1046.0

300

2.6

780

12 4

1052.5

35

1.9

67

I

921.8 940.1 946.7

oi3.a

953.1

1059.0

40

24

96

>5 P-3

960.1

1066.0

35

2.4

84

>2

966.0

1071.8

28

2.5

70

l/l5

981.3

i

80

1.3

95

087.1

4+6b,517+733(est)+28 2X4,(2X517)+12

4+6a.517+584-28

3 4

9a

1 126.9

300

2.0

600

a

63+(2X

044.0

1 149.9

20

4.8

96

==5

057.0

1162.8

30

4.8

144

5

065.6

1171.5

3.3

4 630

4

310

4

997.5 31021.0

1 103.3

1.72

1


75

1012.6

907.9

6a+10a.584+430-40

6

700

65 220

906.7

Interpretation

imo

1400

2060

088.5

1194.4

65

4.8

LOS.3

1211.1

320

4.8

120.2

1226.0

25

5.4

135

4

134.1

1 240.0

40

2.4

96

4

142.6

I 248.4

140

3.6

500

6

154.2

1 260.0

180

1.8

320

6

163.2

1269.1

640

3.0

1920

5

188

1294

4

36


202.8

1 308.6

3s

2.4

a4

2

206.4

1312.2

9

3.6

320

110.75

211.7

1317.6

100

1.4

140

5

224.8

1 330.7

120

4.8

580

6

248.0

1353.8

65

3.4

220

4

263.8

1369.6

70

3.4

240

4

275.0

1380.8

130

4.3

560

>12

305.3

1411.1

20

3.8

76

4

1418.2

9

1540

140

7.4

1439.4

3s

3.9

136

318.2

1444.1

60

3.9

234

345.2

1451.0

15

3.8

57

-4 111.5

1040

2 5

1460.0

14

3.8

53

380.4

1486.3

45

3.8

170

20

- 385.2

1.491-o

110

4.9

550

39O.i

1496.7

‘40

3.8

?O 3

152

X ~CIsite 3) 2X6&584+584+3 2x 11

63 * 5.584

3x

+ 719 - 9

1oa.430+455+486

1oa+1.430+991-3

4

3,-l

.

NN-2.2

5

333.6

-312.3

16b)?584+7+535

2 X 1Oa + 69.894.7

+ 584.3

- 345

156

D. L. Narm, D.S McClure/The

n-n mnsifions

of the pyrarine

.

molecule. II

Table 2

-tine

hq. 2

cm”

K. in benzene (conrinacd)

accm-‘)

AU

I

31 395.7

1501.6

2s

S

400.9

1 506.7

10

2-s

404.2

1510

18

412.4

L 518.2

3.8 3.8

414.4 449.5

1520.2 1524.9 1555.3

60 1.5 30 170

458.1

1564.0

14

460.8

1 566.7

37

466.2

1572.1

SO

476.1

IS82

20

480.1

I

586

17

485.5

1591.3

60

496.6

1 602.4

30

498.2

1604

419.0

3

3.8 6.2 4.3 3.8 3.8 2.8 3.8 3.2 7.6 5 4

Polarization ratio

Roduct

68

l/4 20

228 55.1

l/2

186

I

730

100

53

5

140

l/l0

140

5

76

3

54

114 3

456 150

1623.5

30

6.2

531.1

1 627.0

20

2.7

544.8

1 650.6

I20

SS4.0

1659.9

80

560.7

1666.6

115

566.9

1672.8

15

572.9

1 678.7

90

585.3

1691.1

25

5905

1696.3

2s

3.8

95

6

594.1

30

1.5

22s

6

596.6

1699.9 1 702.4

10

3.8

611.4

1717.2

80

4.5

360 ”

3

186-300 54

111 4

6.2

744

6

7.5

600

6

S

516

4

38.1

3.8

900

l/3 4

9s

6

38

628.3

1734.1

2s

S

125

2

I 740.2

22

5

110

S

653.4

1759.3

165

4.4

725

661.8

I 767.6

12

3.c:

46

674.9

1780.7

35

7.5

262

3

690.5 692.6

I 796.4

45

4.4

198' I

4

1798.5

4s

4.4

198'

4

708.6

1814.9

30

4.4

132

720.6

1 826.5

10

6.0

60

741.2

I 847.0

7s

7.5

563

6.3

284

30

5.0

MO_

800.2

1906.0

70

6.3

441

807.7

1913.6

2s

s

125 ::

831.9

1937.7

840.7

1946.6

40 ‘a.

“..._ - _

,_ ‘

_

.

.: _I

i -,_‘ .

_. ‘

584+6

4+9a,719+1103+4 1269 + 584 - 6

3

45

__i ’

3X 6a.3~

5+(2X4),719+1046+2

5

1 897.0

.

1+5,991+719-8

l!S

1866.2

22iJ”,

1+6a,1103+584-9

3

760.3

.a@

+S84 -3

3x4.517+529+541

l/l

791.1

312.

1 +6a.991

l/2

634.4

.s.3

6a + 6a + lOa. 430 + (2 x 561)

l/2

517.7

25

65+941.584+941

111

12

10

Inteipretation

S 5

L

S .

s

’

‘I’ ‘3.5

.j

’

‘.

_:-

:

,-.

.

.

.;

1.10..

; .- :

_ _ -- (3 x tori +61.~1381‘+ Ma . .. ,_ _.. , -_-_ __- ;.- _.. ,- _.,. ..: .:. ‘ ._ _. .,._. -_-,-.; _. _ :_‘.

_ _. --

-3,.

D.L Nanu. D.S. McCh/The

n-a rransitiow

of rhe pyrarine

L57

nmLecuk If

Table 2 Pynzinc ha, 2 K. in benzene (cant&d) cni1

a(cm-‘)

I

Pohrizatian

Roduct

Au

Interpretation

rrlio 856.9

1962.1

25

12.5

312

111

867.2

1914.0

25

I2

300

L/3

880.9

1986.7

30

264

4

a99.2

2005.1

34

340

2

885.3

1991.2

20

6.3

126

2.5

913.8

2 019.6

8

12.5

100

934.7

2 040.6

8

8.8

70

5

942.6

2048.4

10

7.5

75

5

8.8 10

>4

I /l or l/2

950.5

2 056.3

4

5

957.6

2 063.4

34

13.8

20

978.1

2 084.0

5

7

980.1

2 086.6

1s

8.8

132

986.8

2 092.7

22

8.8

194

>S

997.0

2 102.9

10

14

140


32 004.1

2 110.0

10

10

100

022.5

2 128.4

16

12.5

042.9

2 148.8

7

IO

70

044.8

2 150.7

15

12

180

053.2

2 159.0

21

15

316

087.7

2 193.6

9

9

81

4

098.1

2 204.0

18

135

2

109

2 215.4

22

220

5

114.6

2 220.5

113

2 232.0

15 4

7.5

126.2

6.3

252

136.5

2 2423

10

6.3

63

460

5 l/2?

35

7.5 10

1418+2+584

5 9a-c 1.1103+991+

I

3

75

4.5 l/l 111 2.5

(2% m+

1.+991+(2x

2x93.2x

1103-2

5 >2

1103+ 1126+2 4

145.5

2251.3

28

12.6

354

3

156.1

2 262.0

10

I.5

15

6

1269+2+991

166.0

2 271.9

14

7.5

105

6

~2x6a)+9~.117l-?c1103

173.1

2 279.0

18

7.5

135

5

184.1

2 289.9

22

1.5

165

4

190.8

2 295.6

20

7.5

150

192.6

2 298.4

8

6.5

52

112

194.4

2 300.2

7

6.5

45

207.3

2313.2

3

8

24

112 3

224.7

2 330.6

233.0

2 3483

24 16

17 12

410 193

10

247.8

2363.7

22

10

220

3

264.2

2 370.1

20

8

160

3

>5

4

4x

584-6

1269+2+1103

a) Site refers to a second orientation of pyrazinc in benzene with the NN direction not along the 6 aystab iti the plane of the mokcuk. (See experimental section.) b) &ice refers to interactions (vibrations) of pyrazinc with its neighboring benzene mokcula t, 972’ and 1027 apmi to be split due to Fermi rcsomnce (see 1Oa + 60 assignment).

_

-

1. : .

.,

.

_. -

: .:

-

584)

axis. but with no cbngc

158,

:-

D. L Narw. D.S McClure/The

.

Tabk 3 Pyrazhc d4, 2 K. in benzene -___ cm-1

.A(cni’)

AU

----40.0

-38.1

033.2 047.5 052.1

-14.3 0.0 4.7

053.2

5.8

0.68 0.68

750

0.5s

“Nl

2.6

13Cl origin

3.43

690 5 530 5 600 73.0

2.6 4

371.0 382.0

329.6 334.6

100 4400

527.5 530.7

480.0 483.2 505.8

640 220

550 55

0.70

385

110 140 3600

1.9 3.8 3.8 2.72

105 420 530 9 800

21 12 1.9 0.71 0.96 0.93

3 800 1930

0.96

672

878.3

830.8

700

849.1 876.0

50 90 230

882.8

360 90

030.1 0j2.5 037.2 069.0.

989.7 1021.6

-0922 096.6

1044.7 ‘I 049.1

20

origin

so

0.91 0.49

896.6 900.3 923.5

025.9

OS

700 450

180 160 180 370 130 9000

958.6 972.0

0.6 1 0.660 0.68

569.5 622.5 686.8 706.5 719.8 815.1 826.2

006.1 019.5

12.3 10.6

250

617.0 669.9 134.3 753.9 767.3 862.6 873.1

955.5

NN-2

4

324. I

998.9

silt of dlh origin site of dsh

690

1600 4310

6.5

origin

0.43

371.5

31 003.0

3.2 3.5

510

0.37

530 120

893.8 951.5

510

410

53.9 303.2

930.3 941.3

Intc&=t$ion

1600

101.4 350.6

8528

Pokriwtion r33fio

413 30 000 152

6.1 47.0

509.7 536.3 557.0

Roduct

--__

750 150

053.5 094.4

553.2 557.1 583.8 604.5

molcqule. I1

-__----__~------I

ti 007.4 CO9.48

n- z rmnsirions of the pymrike

2 900 170

origin

ori@

‘Jc,

ori&l

htticc b, lattice b,

4 12

d$

1110 >5

NN-2 103 site a) 103

If 1.5 115 l/l -5 5 7

10a

1OiI ‘%I 2x 4

16b’

pohriwtion

NN-2 6a 6a

ratio varies

siteal

bttice VI 53.0 cm-’ 2 x 1oa. (2 x 330) + 27

345

285 125 8 360

9a site 8) 93 9a “Ct

5

100 90 1150

lilttice

3.3

1 200

lOa+ 61.330

1.0

1.33

b) 50 cm-’

120 135 600

100

1.34

900 70 1200

0.67 1.3s 1.1

1300

978.4

150

1.35

205

982.6

200

1.0

985.0

800

2.34

150 120. .9_c 120

1.ss 17 20 2.7

site a)

c)

9.5

200 I 87s 235 2050 190

1 2X4

.

-

+ 553

D. L Narw, D.S. McClurc/lIhe

II- (I transitions of the pymzinc

mdtmde

Ii

Table 3 Pyrazine

d4,

cm-’

2 K,in benzene (continued)

A (cm”)

I

Au

PXOdUCl

Pobrization

Interpretation


4 + 63.483

1051.9 1054.8

85 160

2.0 2.7

170 430

1092.8 1101.2 1136.1

60 50 520

6.1 4.8 4.0

365

>S

148.6 183.5

240 208

>4 5

201.5

1 154.0

370

3.4

125

1s

1 165.4

30

12123 1223.1

100 30

2.0 3.4 2.0

60 340 60


099.3

102.3

140.2

21i.9 259.8 270.6

+ 569

2 x 63. (2 x 569)-2 9a + lOa. 826 + 330 - 2 4+(2X

lOa),

-4+689

271.2

1 229.1

230

1.7

390

304.2 310.7

1 256.7 1263.3

420 200

2.7 2.0

1135 400

6 S

318.7 328.3

1271.3

55

3.4

185

1 280.9

90

2.0

180

5 4-8

342.4

1295.0

60

5.4

350.1 351.4

1 302.6

180

2.4

325 430

1 >s

1 303.9

150

2.7

405

(111.3

352.4

1304.9

210

358.6 385.8

1311.1 1338.4

120 40

2.4 2.7 6.8

500 325 275

>2 >7 4

422.2 438.8

1374.7 1391.3

454.4

1 407.0

480.4 485.9 494.2

1433.0 1438.5 1446.8

110 160 40 10 23 17

2.4 4.1 28 2.5 11.7 1.4

265 3 250 1120 25 1350 120

497.4

1450.0

17

5.5

470

7

513.5 519.7 5629

1466.1 14123 1514.5

80 35 50

4.2 4.2 245

335

570.1

1522.7

150

3.24


587.6

1540.2 15428 1559.8

41s 425 120

3.5 4.2 lo.s

145 1780 1250

5 6

so

661.5

1593.6 1614.0

12.0 4.2

600 10s

2 1

691.1

1643.7

130

4.9

640

3

696.2

300 60

12.6 14.0

3 77s 850

5 3

2 X 9a, (2 X 826) - 3 3 X 65. (3 X 569) - 7 9a + 956.826

590.3 607.2 641.0

25

150 123 480

7.5

4 5 1
5

.

748.1

1648.8 1700.6

.

828.3 836.4

1780.8 i 788.9

130 so

5.8

750

6

2.9

145

3

845.5 864.9

i 798.0 i 817.4.

625 60

4.3 6.5

2700 390

.S 10

2 x 10a + 6a, 686.8 + 569.5 - 26.6

IOn + 956,330

+ 956 - 4

1+1os,972+330+1 9a+u,826-S+483 loa + 985.330

+ 985 - 3

6a + 9a. 569 + 826 - 4 4+955.483+955-s

103 + (2 x 6a). 330 + (2 x S53)

1+4.972+483+11

956 + 6a. 956 + 569 - 2 6a+1,si9+972-1 6a+1.972+569+1 6;r+986.569+986+5 very broad

9a+1.826+972

+ 956 - I

LS9

160

D. L. Nor RI, D.S

McClurejThe

n-n framitions of Ihe pyasinc

mOkcuk. If

Table 3 Pnatine da, 2 K. in benzene konlinucd)

_-___L---

cm-’

Ahmi’)

Interpretalion

Pohrizatim

ROdUCt

Av

i

~~ti0

872.8

1 825.3

85

3.6

30s

902.3

1 854.9

100

5.0

SOD

9

911.4

1 870.0

15

5.0

75

Cl/?-

928.3

1880.8

65

5.8

375

10

980.1

1 932.6

70

11.5

800

4

956+1.956+972+5

32 008.6

1961.1

160

7.9

1250

5

(2x

064.1

2016.6

40

7.2

290

8.8

141.1

2 093.6

40

156.1

2 108.7

120

9.5

1150

175.2

2 127.3

40

12.4

500

191.2

2 143.8

2s

5.1

125

32 262.3

2 241.9

70

13.2

910 ---.

>Y

lOa46a+956,330+569+956+2 9a+6a+4.826+569-8 10a+6a+9a.330+569+972+8 6a)+9s,(2x

569)+826-4

350 6a + (2 X 11,569 +

6a + (2 X 9a),

(2 X 972) - 5

569 + (2 X 826) - 7

tables 2 and 3. Intensity assumed same as in ha_

a*b) Have the same meaning in c)

Some of the lines in the spectrum of pyrazine in benzene are under 0.5 cm-t in width at half height, while others are several cm-l wide. Fig. I shows some of these features: For example, 584 is quite wide and 430 is narrow. These two lines are shown 0;1 a better scale in fig. 2. The origin of the h4 spectrum at 29 894.2 is so intense and narrow that its true shape is only observed on our plates when all otherlines have

nearly vanished. A 0.5 mm crystal using the iowest concentration (under 1W5 M) was used to observe this line in rhe polarization perpendicular to the b-axis. It is impossible to show these relative intensities in the figures, and one must refer to the line list, table 2, for the actual measurements. One can, however, see the evidence for the intensity ratios in fig. 1, by referring to the 15N and 13C lines near +5 cm-l. The assignments of these lines

. fig. 3. Pot&ed ‘-

spectruin of pynzine d+“Bu

ny* in bf”ti

_.

.’ _I,’ -

at 2 K. _

‘. .’

‘. . :

7.

_.-_

..,.-.

:. , 1

:

- ._ :_ __:.:.

.

.

. -_:

:

-,_ , _ : . .

D.L. Narw.

will be discussed

D.S. l&Ciure/llze

n-n

later. The 13C line in fii. 1 should be

25 times smaller than the origin, but it appears there to be only 2 times smaller in polarization lb. The polarization ratios shown in fig. 1 are sometimes distorted also. The intense origin, of course, shows no polarization, but the 13C origins are close to the linear range of the plate. The polarization ratios fall into three classes, approximately 12: 1,7: 1 and 1: 10. The line lists, tables 2 and 3 bear out this generalization quite well for all the more prominent lines. The true polarization ratios are illustrated for the impor:ant 430 and 584 lines in fig. 3. where it is shown that 12: 1 can be distinguished from 7: I.

4. Vibrational

analysis

The main features of the vibrational analysis were shown in I. Some new assignments and confirmation of previous assignments will be made in this section. We must first discuss in detail the matter of multiple sites for pyrazine in the benzene lattice. and the effect of the natural abundance of 13C and 15N on the spectra. 4. I. erazine

sites in the benzene crystal

In I, the additional lines in the phosphorescence spectrum at +85.4 and +22.4 cm-’ in the line lists (i.e.. at higher energy than the origin) were interpreted as the emission origins of molecules located at different sites in the benzene host crystal. Hong and Robinson [3] made a tentative identification of these sites. Note that the crystals used in their investigations were rapidly frozen polycrystalline materials. The extra tines due lo these sites are almost unobservable in absorption in the slowly grown single crystals. We have identified two other weak lines as belonging to differently situated molecules, and the type of site can be inferred from the polarization and vibrational data. As noted in the Iast section, three different polarization ratios are found among the main lines of the spectrum. If a pyrazine molecule were rotated about an axis perpendicular to the ring in its site in the benzene lattice, lines polarized perpendicular to the mole* ular plane would have t3e same polarization ratio, but l&s polarized along the other two directions muld have different ratios.

mrnsitionc of

rhe pyrazine

mdccule

II

161

The different environment could not only cause a shift in the origin position but also, in the case of the solvent-sensitive vibrations discussed in I, could cause o change in vibrational frequency. The 10a mode is a good case for such a test. To identify a line as being due to a molecule at a dimerent site can be done by using its intensity ratio to the parent line in spite of the unknown frequency shift. Lines at - 1 I (d,) (see tables 2.3 and 4 and fig. 4) are assigned to pyrazine molecules with the N-N direction rotated into one of the two other possible cubon positions (N-N-2). Since the benzene crystal has Ci site symmetry [4], there are three possible pyrazine nitrogen positions. Table 4 shows that the energy shifts for the N-N-2 site for A, vibrations are small. This is expected since the benzene lattice has little effect on the A, modes as shown by the small energy shifts from the vapor. Evidence for the molecular orientation in the N-N-2 site comes from the polarization of N- N-2 for the LOa vibration. This N-N-2 line is highly polarized opposite from the N-N-I line as shown in fig. 5 for (r, and as reviewed in table 4.Oppositc polarization is predicted by direction cosines of either of the other two N-N sites not along the b crystal axis in a ratio of I/l.S to l/500. The energy separationbetween N-N-l and N-N-2 for IOa is -2.1 cm-l, much less than at the origin, -11 WI-~. However, unlike & modes, 10a shifts 47 cm-* as the molecule goes from vapor to benzene solution due to the effects of the benzene matrix and, therefore, a shift of IOa due to a new N-N orientation is expected. The intensity ratio N-N-I/N-N-Z is the same for the origin and 10a. The evidence that site N-N-2 is a rotation in the plane of the molecule is that the polarization ratios for the A, vibrations (1 polarized to the ring plane) are the wme as for the N-N-I site. Oppositely polarized N-N-2 is between a 60” and 120” rotation. Because it is probable that the pyrazinc nitrogens would fit in the lattice positions of benzene carbons, N-N-2 is probably either a 60° or 120° rotation. A line at +14.5 about 3000 times weaker than the origin is tentatively ascnaed to a third site, but we have no information about it. except that it appears to be polarized in the same way as the origin.

162

D.L. Nanq D.S. McClure~~e

n-n transitions of the pymrine wleculc

II

Table 4 Evidence for the NN-2 lattice site of pynzine in the benzene aystJL A molecule in the NN-2 site occupies the sme lattice space as a molecule in the NN-1 site. However, the NN axis is along the b axis in NN-1 and not along the b axis in NN-2 A (cm-' ) is the dishnce between the NN-1 site and the NN-2 site for the absorption peak being considered

4

h, Vibration

OIigiIl

-11.1

LOa 6a 9a

-

2x

Ioa

2x 6a

Folarimtion ratio

A (clIiL)

7

2.1 9.5

-10.6 -

4.2. Lines due to molemles rmturalabundance

11127 l/130

=5

l/140 l/60

containing 13Cand

l/13(1

15N in

Some of the weak and sharp lines near the origin are due to molecules containing tsC or lSN in their natural abundance of 1.1% and 0.37% respectively. The

DaH -40.0

O,H -38.

I

A(Ctli')

Polarization

I (siteM

(parent)

ratio

l/l0 6

5

8.7

I (site)/1 fpxcnt)

-14.3 - 5.5

6.5 If10

t/70 llS0

-12.5 -11.1 Tao broad

I 10

I/20 1167

vibrational spectra of these molecules can be found and verified by the intensity ratio, which must be the same as that at the origin. Fig. 4 shows these lines. The vibration frequencies of these molecules can be estimated fairly well with the help of the Teller-Redlich product

rule and with information about details of the normal

D.L

Narw.

D.S hfcClure/l%c

SC,

n-n

10.

334.5

I

NN AND

IRING ==N

lOa

_- 343.6 -

i

5. 10~1 in the polarized spearurn of pynzine d4 a highly concentrated crystal showing the NN-2 site. nrbd 13C, line.

Fig.

a1 2 *‘N,

K in line

mode. Conversely, the isotopic molecule lines can be used to verify assignments of vtbrations, since their intensity ratio is a good indication of their identity. This procedure gave some important assignments. An origin doublet for 13C1 12C3 N2 H4 (13Cl) is assignedal +5.7 and +5.9 cm-1 to higher energy from the or&hi. A similar 13C assignment at +5.8 and +6-l cm-l is made in 4. A t J_C2 I?C2 N, b (13C9) doublet origin is assigned in hg at +lO and +12 cm-l .-The -’ .

transilionc

ofthe pyrazinc

molecule. 11

163

basis of these assignments is: (1) The calculated intensity ratio of 13CI to the origin is 0.044; that of the observed doublet in it, is 0.047. The d4 doublet also has an intensity ratio of 0.047. (2) The calculated ratio of the r3C2 origin is 6/10000 and the experimental ratio adding both lines together is 7/10000. (3) The 13C2 lines center at +l I .G cm-’ which is close to twice the energy shift of 13Ct. 3s is expected in analogy with the deuterium isotope effect [Sj . (4) Benzene C6H, in host crystal C6D6 [6) has a 13C origin at +3.6 cm-1 and a ‘SC2 origin at l7.6 cm- \ . (5) The t3C I line is doublet, as expected: Since the crystal has Ci symmetry [4] there are two different positions with respect to neighboring molecules for molecules in the N-N-I site. Consequently. a doubIet is seen. Another example of this is the d3f1 molecule which has a doublet at -40, -38 cm-I as seen in fig. 4. (6) There are three molecular isomers containiag two I%! atoms. Theoretically. three zero point energies are possible. The line at +I 2 is brad with a shotddcr which may represent the energy of the third isomer. (7) The 1211 polarization of the t3CI 1Oa lint proves this line is not due to molecules in rotated N-N orientation which would have oppositely polarized spectra. AC4 lsN, 14N, H, origin is located at +4.4 A,, +4.7 d4_ The calculated intensity ratio of lsNl to the origin is 0.0074; the experimental ratio is 0.0073 1:~. 0.0050 1,. The t5N, line is displaced from the origin in the same direction and slightly less than the 13Ct line as expected (see later). A line at 8 cm-t has the intensity expected for lsN2 and has approximately double (51 the lsN, energy shift, adding support to the t5Nt assignment. The 10/l pohrization of the tsNI 1Oa line (see fig. 5) proves that this line is not due to a different N-N orientation, making assignment to another lattice site doubtful. The ratio of the lsNl intensity to 13Ct is 116.4 (origin), l/7.5
164

D. L. Narw. D.S. MKiuref

Fig. 6. 103

plus 9a in

771~n-n fransinhu

the pokwizcd

4.3. Vibmtiotzal assigtmenzs

Both new assignments and supporting evidence for previous assignments are made in this section. bl, IOa = 430 IQ, 330 d4

This assignment was made in the previous paper [ 1] but there is considerable supporting evidence to be added here. 1CJais the only vibration of symmetry class Eta_ BI, vibrations couple 1 Bs, nn*. 10a should be visible because I B2u is the closest rrn* state (+ ~8000 cm-l ,f= 0.1) [7]. A polarization ratio of 13.4/l to 11.0/l is expected (since the u and c axes were not distinguished). Fig. 2 shows that 430 has the correct polarization. In 4 there are two lines below 1000 CIII-~ with a polarization ratio greater than 8.972 (12) and 430 (14). Among other reasons, 972 is ruled out as 10a because it would be an increase in energy from the ground state. In d4 330 is much more polarized than its equally intense neighbor 6a. Additional proof in d4 is that it combines with. 9a to give 1154 and 6a to give 883 both of which are

clearly more highly polarized than the surrounding bands. Fig. 6 shows the comparison between the polarizationsoi’2x6a(1136)and10a+9a(11S4)ind4. The t5N 10a satellite line at 430 + 4.3 has the same separation as at the origin (t4.4) (see fig. 5). This means 15N 1Oa has no isotope shift as expected since 1Oa has a node through the nitrogens. A-2.0 cm-t tsN shift _would be expected for alternative assignment 5.. -. .

of fhc pyrazine moletile.

II

specrrum of pyrezincd~ at 2 K.

The 13Ct line 10a at 430 + 5.3 is a drop of 1.0 cm-t from the origin (6.3). The frequency ratio calculated from the product rule for a molecule with four 13C is 1.010. If we assume that the zero point shift for one 13C is one fourth of that for four, we obtain a drop of 1.08 cm-l in agreement with experiment. The product rule applied to the d4 molecules also supports the 10a assignment. 2 x I On = 895 4,687 d4 This line was also assigned in the previous paper [ 11. Additional confuming evidence is the observation of S/l poIarization ratio. Also, an intensity calculation using eq. (I), and disregarding the small quartic component predicts Izo/I,-,o = O.C%l_The observed values of 0.045 for h, and about 0.06 for dq are within experimental error. Other possible assignments, 2 x 5 or 2 x 11 are ruled out because the vapor line at 823 does not shift with one t5N substituted 181.2 x 11 and 2 x‘5 should have a small 15N shift whereas 2 x 10a has a node through the nitrogens and no tSN shift. is expetted. The 687 cm-t-Yine” in d4 is unkally broad and irregularly shaped. We-have no good explanation for this but suggest that 2 x 10a may axrple strongly with 6a plus lattice overtones. The measurement of _its in.1 ten&y is les$c&tain than for the other lines. The -%, 2 x 1Oa line is.at 895 + 4.1 which is a 2.2 cm-l drop in frequericy n@sured_from thebrigirr. ‘&is drop_is in exa$:agre@nei& with _&at cakulaikd from ._ I._. ‘ - :: I,_,, .‘..,T ~.I._:._ -.i _I., .~ . . : _ _,. _‘_-._ -, _-.

D.L. Narua. D.S. hfcClure/The

n-n rransilions of rhc p)m:ine

the product rule. The l5 Nt line, six times weaker than the C3Ct line cannot be observed in this case, and would be expected to be obscured by the t3CC line. Agreement with the d4 product rule, the t5N product rule in the vapor, a solvent shift similar to that for lOa, and its appearance in fluorescence are other arguments presented in the previous paper [ I] in support of the 2 x 10a assignment. b2, 4 = 517 h+ 483 dq: 5 = 719 hd. estimated 561 d4 These assignments are based on their polarization and combinations with A, symmetry vibrations. 4 and 5 are the only two vibrations of symmetry Bz,. They are expected CO be visible with a polarization ratio of l/780-1/8.6 because Baa couples 1B3e na* with the intense CB lu err*. The only oppositely polarized band below loo0 cm-l in dq is 483 (excepting the N-N-2 lattice site line of 10a at 324 explained earlier). There are three oppositely polarized bands in hq at 505,517, and a weak line at 719 (not counting the weak 10a N-N-2 line at.428). The intensity and polarization of the 505 h4 line varies in different crystals and 505 does not add harmonicaUy to Aa vibrations. Therefore, 505 is considered to be an impurity. The theoretical product rule for Bk is 1.37 calculated from rotational constants in the excited state as given by Thakur and lnnes [S] . Using the remaining three lines 517,719 h4 and 483 dq, a line at 561 d, is calculated. This line could easily be covered by 6a at 569.5. We have no evidence for this line in combinations. Mode 5 is very weak in h4 and may be even weaker in d, _ 517,719 h4 and 483 da aU add A, vibrations to give oppositely poiarized lines. An interesting aspect is that both h, lines add 6a anharmonically; 719 + 584 - 9 = 1294 and 417 = 584 - 28 = 1072. Out-ofplane vibration 10a adds 6a anharmonically and, therefore, it is reasonable that out-of-plane modes 4 and 5 do also. 517 combines with 1 and 9a harmonically. 719 adds to 9a plus 4 cm-C and to 1 minus 8 cm-*. Although 5 plus 1 and 5 plus 9a are slightly anharmonic, the assignments are reliable because there are so few oppositely polarized lines. 2 x 4 = 1046 h.,, 986 d., This assignment is-based on the presence of ha and d4 lines near the expected R = 2 positions having the

same isotope shifts as for the n = 1 vibrational level .

molecule. II

165

(517/483 = 1046/986), and that there is no other unassigned line of the correct polarization and close to the correct intensity within 150 cm-f. An intensity ECUCation [eq. (I)] using a grtiund state value of 4” = 690 predicts fZo/foo = 0.0105. If a value of 4” = 753 is used f&,8 = 0.017. The expcrimcntal vaCues are 0.020 da, 0.026 h,. These values arc somewhat too high and there does not seem to be any simple explanation for the disagreement. These assignments give the overtones higher frequencies than twice the fundamental by 12 and 20 cm-t for h4 and d4 respectively. 2 x 16b = 535 h4, 480 d, This assignment is based on its polarization ratio. the fact that there are only two possible ground state modes with such low energy, and the Desktndres tab&e for h4 and d4 of Innes (LO]. The pohrivtion ratio shows that it mmes from two times a non-symmetric mode. It seems doubtful that modes above 700 in the ground state will drop Co 267,235 vapor. Therefore, only 16b having a gorund state frequency of 416 and 16a at 389 are possibilities [IO]. 16a istuledout because the line in the ‘5N-substituted molecule is at 464 in the vapor, 5 cm-l less than the t4N 469 line [S] _ No t5N shift is expected for 16~1. The Deshndres tables for 2 x 16b in vapor at 469 ir4 and 422 da are accurate and give the lines 16bf, 8, 9 ands[ll].Th e b enzene assignment correlates with the d, drop of 2 x 16b in the vapor: 535(benzcne h4) x 422(vapor d4)/469(wpor h4) = 482(benzene de). This line is also shown in Ito’s durene crystal spectrum [2], and it shifts to higher energy going from durene to benzene as an out-of-plane mode should. it also showed the 13CC shift of 1.5 cm-1 as expected. An f3 cm -* drop is calculated for four C3C for the 63, class of 11 and 16b. Since 16b is C-N bending whereas I C is CH bending, 16b should drop more. Therefore, a drop of 1.S cute1 for one t3C is reasonable.

The IsNt satellite line of 535 is not seen. The region 537 + 539.2 is clear. Since there is a 5 cm-1 drop in 16b for one r5N substitution the frequency should shift by 5 cm-l ; but with the 4.4 cm-t origin shift, the satelhte would be within 0.6 cm” of the parent Line, and should not be resolved. The intensity calculation for 2 x 16b is within expel-fmental error for d4 (0.02 talc. versus 0.03 ohs.), but the calculated intensity for 535 h4 is less than one half

166

D. L. Narva, D.S. McClurefThe n-n transitions d/the pyra:ine molecule. II

the experimental value. This discrepancy is similar to that found for 2~4; in this case the assignment is quite firm on many other grounds, and the Franck-Condon factors may not be adequate.

I[k + 6a = 972 or 1027 it+ 883 d, The polarized spectrum of d4 confii

rhis assign-

ment, which was made in the previous paper [l ] . The line at 883 = 330 + 553 is clearly highly polarized as is a second 6a addition st 1438 = 330 + (2 x 554). At frequencies higher than that of IOa in h,. two of the three most intense highly polarized bands are at 972 and 1027. 10a + 6a in the vapor is 10a + 562 (the normal 6a vapor frequency is 583; ;he same as in benzene host); therefore a line is expected at 430 + 562 = 992. Instead. two highly polarized bands are found at 992-20 and 992 + 35. This appears to be a case of Fermi resonance since 10a plus a decreased 6a is seen in all other hosts and isotopes. The other partner in the resonance must have B,, symmetry; therefore it can be Blu plus B3, or %2, plus B vibrational combinations. 4(%& 517 plus estimated 6$%,,) 483 is the best possibility. The estimate for 6b(483) is reasonable since the ground state is 516 and 6b is an in-plane C-C bending mode. (qong and Robinson [3] however, give 603.5 for 6b). Two other inplane C-C bending modes are 1 which drops from 1010 to 991 and 6a which drops from 591 to 584. NO other B% plus B combination is possibIe since the Bsg ground state ? requeccies are above 1100 LJTI-~.A possible %zu + Bj, sum is 16b(B3,) 267 and estimated 15(BzJ 733. Mode 15 is 1022 in the ground state and is a CH in-plane bending mode. A similar CH bending mode 9a drops 130 cm-t in t Bju. Therefore, a 289 cm-l drop by 15 may not be out of the question. Also, although 15 may not drop 289 cm-l, it may add to 16b anharmonically. In summary, 16b + 15 is unlikely but possible and 4 + 6b is a good assignment for the band in Fermi resonance with 6a + 10a.

The line at 955 in d4 has 2.5 times the calculated intensity. However, 2 x 16b in d4 has one third of the intensity of the corresponding 114line, so it appears that the IWOsymmetry coordinates in 16b and 11 mix differently in the two isotopic species in ground and excited states. The frequency of 2 x 1 I can be estimated by comparison with pyridine where its assignment is quite certain [13]. 484(excited pytidine) x 786(ground pyrazine) irOO(ground pyridine) = 534(excited pyrazine). Thus the assignment 2 x 11 = 1194 is reasonable.

5. Discussion 5. I. Vibratiotutl assignments

The polarization and isotope data confirm the assignments of 10a and of 2 x 10a beyond doubt. The polarizations have also confumed the additions of 6a to 10a. These are particularly interesting because mode 6a in combination with 10a has a much depressed frequency, and cannot be assigned simply on the basis of

adding harmonic frequencies. The bk modes 4 and 5 arc also assigned with confidence because of their reverse polarizations. The overtone 2 x 4 shows an ap preciable positive anharmonicity. It is also interesting to have 2 x 16b assigned. In pyridine 16b is much more strongly decreased in the excited state than in pyrazine [I 31. The identification of the weak lines due to different crystal sites and to isotopes leaves no lines below 600 cm-t unassigned. In the complex region between 900 and 1300 cm-l in h,, only the prominent lines 941,121t and 1269 are not assigned. It is not likely that the missing fundamena1 8a could be one of these since it does not appear in fluorescence. These could be two quanta or even 2 x/I = II94 h.,. 995 d4 combinations of odd parity modes. There are a fair The product rule for B% IGbrations 16b and 11 is number of weak lines in this region whi+ remain un-1.38. The assignment of 535 as 16b has already been assigned. In di the assignments are easier to make be- . tiimly established. The experimental product rule is cayse the vibrations are more nearly hannonid. Mosi (535/480) (1194/95S) = 1.39. No other unassigned ha tine‘fiom 800 cm-t to 1200 cm-l agrees with the’prodof the~anharnionicity, appears in out-of-plane hydrogen vibrationi, and~be~usethedispka~en~ oft&e uct rule. I1 is 786 in the ground state ofh4 112) giving a caIcuIated intensity ratio of lo-J& = 0.009. I I?4 has _: -dsutetium at?ms are”s&ller $an of hydrogek the perturtiationsaresm&r.*: ,:-.. : _-- -_. _ .- : _‘. f()&) _y0.0 I‘. . . ~.-, _._. 1 . _.__:: _‘._ . . , . ._‘.~ __ :1 -_., ._I’ ,I : _: j c : ->. ;./-ALi I.‘_ . .._ -y :. .-..L. _- . _: -_ I , ..: :._-..

D.L. Narw. D.S. McClure/77re n-r

rmnsirions ofrhc p_vo:ine maleak

It is worth pointing out here some striking differences between the nl; spectra of pyrazine and pyridine. Ramsay [I31 has shown that pyridine in its fist nn state becomes slightly non-planar in the mode 16b. Only even quanta of 16b appear in the vapor spectrum and this mode drops from itsground state value of 403 to 70 cm-*. Brown& [14J has found that pyridine in benzene single crystals shows no double minimum in 16b and that single quanta appear very weakly. The mode 16b also rises to 150 cm-l due to the effect of the crystalline solvent. The solvent effect here is similar to that in pyrazine. In pyrazine there is a center of symmetry and the odd parity 16b can only appear in even quantum numbers; however, this mode is not any more strongly depressed in excited pyrazine than it is in the first excited state of benzene. The strongly depressed mode in pyrazine is lOa, and it is this mode which has the strongly quartic oscillator behavior. This comparison raises some questions. Why do only even quanta of 16b appear in the pyridine spectrum, while odd quanta of 1Oa are prominent in the pyrazine spectrum? Part of the answer is that Herzberg-Teller coupling brought about by 16b connects the nn state of pyridine to a 1A state, 17 000 cm-l away, while in pyrazine, 10a connects the rnr state to the’l Bz, state only 8000 cm-l away. Still it is surprising that the outof-plane carbon bending is active in pyridine in preference to out-of-plane hydrogen bending as is present

in pyrazine. Presumably the mixing with the corresponding ?r state in pyridine only 4000 cm-t away could have been brought about by the hydrogen bending modes, but it is not. The carbon bending takes over instead. Furthermore, the carbon bending in pyridine does not introduce much transition probability in the onequantum levels of 16b, yet the distortion in this mode is quite strong, while in pyrazine a somewhat smaller distortion in 1Oa is accompanied by a substantial trausition moment. This comparison shows that even in closely related molecules the perturbations causing shape changes and transition moments can be quite different. In pyridine it does not seem to be correct to ascribe the out-of-plane distortion to interaction with one or a few nearby states, while in pyrazine it seems at least qualitatively correct to do this. In the following section, we will show to what extent the principal features of the nn spectrum of pyrazine can be explained by the interaction between the I B3, and nearby mr states.

167

II

Another way to view the occurrence of quartic anharrnonicity in pyrazine and pyridine is to ascribe it to the need to relieve ring bond angle strain. The excihtion of the non-bonding electron into the R system of the ring sets up forces favoring sp3 hybridization to a small extent around the ring atoms. This effect would be described by in-state or diagonal quartic matrix elements. Benzene does not show quartic anharmonicity in any of its vibrational modes in the tB2u state as it does not add an extra 71electron in this state [ 151. The nn* state of other aza aromatic compounds should also show either quartic anharmonicity or double minimum potentials. 5.2. Thco~

of the anhwmonic

modes

in this section we will carry out the perturbation theory describing the interaction between ‘Bju and either 1 B,, or tBlu nn states, and apply it quantitatively to the perturbations involving the mode 10a. The theory is similar to that of Hochstrasser and hhrzzxco

1161. We consider the portion of the potential function of pyrazine involving one symmetric mode, A, and one nonsymmetric mode, B, such as ICJa. In view of the discussion at the end of the last section it is desirable to include diagonal quartic potenti terms. There are enough &ta so that these terms cau be evaluated separately from the contribution due to the nn-nn interaction, which also produces a quartic contribution to the potential of the nn state. Thus the potential to be examined is: V(QA.QB)

= VO + VA&,

+ ‘ABQAQB +%B&;

+ g %AA Q3 A + 1 v,,,Q,@, + hvAA,A&

+ bVAABBQ:Qi

The matrix

+ veQB +!vAAQ;

+&-&,Qi

ftVhsQ; f 1-v,,,Q&?;

+%AAB&~B

+hf&B@B-

(2)

of this potential will be written in the LBS,, tBz,, basis. The abbreviations 3 and 2 will designate these states in matrix elementsand in subscripts. The basis wavefunctions are vibronic and we mnst choose a set of nuclear equilibrium positions to which they refer. The gerund itate geometry is probably the most reasonable since it is completely known. There is some ponibinty that with the moments of inertia now known

168

D-L. Namz D.S McChuejlRe n-n

for the excited states and with the help of the FranckCondon factors, the geometry of the nk state can be worked out. It does not differ much from that of the ground state. For convenience, however, we choose excited state functions so that diagonal linear terms can be ignored and diagonal quadratic terms have the meaning of force constants which can be evaluated from the data. On physical grounds, and also to keep the problem tractable, we neglect diagonal third order terms and retain only the last of the fourth order terms of eq. (2) in the na state. Thus the matrix equation to be considered becomes e

+ &AQi

+ lb@

--e

LSQB+ ~ABQAQB

transifiom

of the pyazine

mokcule.

It

is the effective force constant for 10a. Since the perturbation terms subtract from the diagonal term, the observed strong reduction in frequency of 10a is explainable. The fourth power terms are both diagonal and off diagonal, and their relative magnitudes will have to be determined from experiment. The mixed terms can be fitted to the 6a-t0a combination bands, and their signs are such as to explain their reduction in frequency. A reasonably accurate solution of eq. (5) could be obtained by perturbation theory, but here we will get approximate values of the matrix elements by using some simplifications. First, in order to tit the 10a series, we will assume that the mixed terms in Q,Qi and QiQi can be neglected. This leaves us with a potential function for 10a of the form used in our previous

USQB+ ~ABQAQB 4 + fk3AQ;: + tkJBQi +e’Qi-e

paper [l]:

=O,

(3)

where~=(31VB12~,~AB=(31YAB12),u’=

(31 V,,,,13). k% = (21 VAA12), etc. The roots of this equation to fourth powers of QB are

V = $kQE +aQi,

k = kgB --2$,‘dE= a =

+ (Vi /m3)04, + ~‘a’,

(4)

and a similar result for E2. There are five unknown matrix elements here. We know that AE = E2 -E, = 8000 cm-l. The expression for Es(QA.QB) is the unperturbed electronic energy of the 1 Bj, state E3(0,0) plus the vibrational potential energy, and *he energy levels it leads to could be found by inserting it into the Schroedinger equation K”A+Tg +~~(QA,QB>l~‘(Q~.Qg)=~(QA~QB)’

(9 TA and TB are the vibrational kinetic energies. Qualitatively the potential surface of eq. (4) con: tains all of the features we need in order to explain the behavior of IOa and of 1Oa in combination with 6a. The combination ,-2[lk,,-u~IdE--(~%LIABfdE~*-(U2ABt~*]

-_

,: .

“_k& .-

(6)

where, comparing (6) and (4): k;,

v41AE3 + :(k 28 - k,,)~lAE* B

(74 + a’.

(7b)

We have already measured k, a and AE, and can get un from the intensity of 10a compared to the origin. We need one more piece of information to find the three unknowns km, k,, and a’. The value of kzB should be nearly the same as the force constant for mode 10 in the lB2” state of benzene. The value of mode 10a in the fhU state of benzene is 584 cm-l. We scaled this up to 630 cm-l by the ratio of 10a in the ground state of pyrazine (918) to that of 10 in the ground state of benzene (851). Assuming that the geometry is the same as in the ground state we fiid (8) ‘2B =18.8x10‘12erg. (In order to obtain km from the frequency, the effective mass of the normal mode 10a is needeu. ‘Ibis mode is a rotation of the hydrogens against the carbons around the N-N (or C-C) axis and therefore the effective mass is or.= I,J,/(l, +.I& where fH,fc are the moments of inertia of hydrogens or carbons around the N-N axis. The value. using the ground state structure, is i = . 13.3 x lo-r0 gm cm2. The force constants have dimensions of ergs because of ths w of angular displacemen+) Values of k and P were it actually quoted in 1. but we can now find them. by fittin the energy leveli in the . -

D.L h’arvo. D.S. McClure/The

n-n rmnsirians of the pymrine

which favors non-planar geqmetry and would there-

10a series to the theory OF Cban et al. [ 171. For the vapor a value u = 0.218 was found and a 1 Oa frequency of 383 cm-’ corresponds to a reduced frequency from Chan’s table 4 of 4.53. Using eqs. (7-9) of Chan we find for lOa in the ’ B,, state of pyrazine: k = 4.22 x lo-t2

erg.

a=44_0x10-12er&

(9)

if all of the intensity of mode 10a and the series built on it arises from the perturbation by the ‘BzU state we have: AlOa)//(Bz,)=

[(l/A.E)u,

(01Q,13)12.

(10)

we have evaluated the vibrational integrals using harmonic oscillator functions. The one quantum state of * B3, interacts with 0 of the ground state. The vibrational integral in terms of harmonic oscillator functions becomes 20;‘4~;‘4/(o,

+ 03)3’2 = d ,

(11)

where a3 = c$tB3J = mffi. o. = a(’ A,,), and k; is the actual value of the force constant. The experimental value of thefinumber ratio is I(lOa)/j(BZu)

= 0.0166.

(12)

This is found from the intensity measurements given in table 2 for the ratio of the 10a line to the origin line f(lfh)/f3(Origin)

=

0.137 and using the ratio of

tatalf

numbers f3/f2 = 0.140 which we measured in n-pentane solution. f3/f2 was adjusted to 0.121 when the intensity of 10a was deducted fromf3. Since we cannot find the frequency of 10a in the ‘Bzu state (the spectrum is diffuse), we must use the upper root of eq. (3) to find k;. Thus k; = kZB + 2v;/AE.

(13)

We now have four equations to solve VahJeSOf Ug, k;, ksg and 11’.namely, (ll), (13). using the data in (8) (9), AE=XlOOcm-t. The solution yields the following s

= 4.96,

c - a’ = 73.4,

k,,

for consistent eqs. (7a). (7b), (12) and a value results = 35.0

and k; = 49.6. all in units of IO-l2 ergs. AU reklts are listed in table 5. Since a = 44.0 x lo-” ergs, the diagonal quartic termu’ is -29.4. A physical interpretation of this result could be that the lBgu state has an intrinsic force

:

169

molecule. iI

fore cause the system to go to lower energy during the 10a motion except that other planar restoring forces are greater. A more likely explanation is that the c&uIation of a’ is incorrect by this amount. TO cakuiate eq. (10) it was necessary to make the Condon approtimation that the ratio of thefnumbers of the pure electronic transitions’j(B~u)/f(B2u) equals the ratio of the /numbers for the total vibronic states. This ignores vibration changes in going from the ground state to the t B,, and *B2,, states. The fact that the calculated quartic term is within 60% of the observed quartic term is significant however. The values of the force constants seem reasonable. The matrix element ug is 3.1 ev, a value consistent with the a--n interaction involved. We conclude that the perturbation between the nrr and nrr states has been described semi-quantitatively. Up to this point, we have analyzed the vibrational levels ignoring the coupling terms between levels of different symmetry, in particular the 6a-10s coupling. We will now treat this coupling via perturbation theory using the results of the previous analysis as the unperturbed problem. These two modes, 6a and lOa, on mix in the out-ofplane configuration having f& sytmnetry since they both belong to the symmetric representation of C2h. The physical reason for the mixing wa~x~l~ined in I. In eq. (4), there is a coupling term$QAQu -(&&E’)Q~$B. This term has the correct sign to explain the low value of 6a in combination with 10a. The matrix element uAB cannot be evaluated independently of the 6a-10a mixing, and since there is also a potential term 1 VA,+guQiQi in eq. (2), we cannot be sure whether the coefficient of @AQi is a dtigonal or an offdiagonal electronic matrix eiement. The other term in eq. (4), q’QAQi = -(2ukuAB/AE)QAQ~ could only be off-diagonal electronically. Both terms can be estimated from the data, giving 6~’ = 4’. However, q’ is off diagonal in the vibrational basis, so its effect is quite small. We later found its effect to be 10 tlmcs smaller than the effect of the other term. Therefore, the problem is reduced to solving a Schroedinger equation: @A f TB + VA + VB +P’Q@@

=W,

_

(14)

where TA + ,VA is the harmonic oscillator hamiltonian for Q,, TB + VB is the mixed barmonicquartic hamil-

‘.

170

D.L.. Narva. D.S. McClwe/Thc II--A rransirions of the pymzine molecule. II

Table 5 Values of matrix elements in the ’ 63, stateoi pyrazine tx 1cP* erg)

k3B = 2t31YBBl3)

k& = kobs = kaB - Zv;laE “B = (31 YB12) 0’ = (31 vBBBB13) a(obr)

Mode 103 kwor)

Mode 4 tbcnzene)

35.0 4.22 4.96 -29.4 44.0

19.5 15.5 2.82 63.0 64.0

U~‘=U~/PE’+:(k*B-kJB)“2B/aE2

73.4

1.0

k2B = 2(2 1VBB! 2 )

18.8 49.6

25.1 29.1

k:B = k2B + 2ri)IpE

Table 6 Coefficients of p and of p’ for 6~1-105 couplirrg. and the level shirts in h4 pyrzinc ror low lying levels

tonian for Qe andp’Q:Qi is the coupling term. We will solve this equation using products of uncoupled wavefunctions:

(1% where NA and NB represent the quantum numbers of the levels of QA and QB. Eq. (14) is thereby reduced to a secular matrix involving the coupling matrix elements and the energy shifts of a level; each level is now labelled by the integers NA and NB representing the principal term in eq. (15):

The diagonal and off-diabonal matrix elements WAIQ INil are well known [ 181. The values of U&IQ !! I&) can beobtained from Ghan’s paper 1171 using the experimental value Q = 0.218 from I. For the off diagonal elements UV,IQ~lN& we used harmonic oscillator values since their contribution to the final resuk is not large. A fiit order perturbation solution was obtaikd’instead of diagonaiizing the entire matrix and the results are of the form

E - @,Q?EN~ -4~~ -EoB) =--P
sNB)P2,

where qB is the non-integer

(17) needed to give &B and

“Ah

4NAqA

0

10

0 3.11 0 6.22 11.16 0 5.58

01 11 20 21 22 02 12

f(NA.&+

-AE @(h‘d = 5.8 cm-‘)

0.0269 0.0218 0.116 0.070 0.219 0.180 0.074 0.279

0.91 0.73 220 2.3 43.4 73.2 2.5 41.8

f(N*, NB) is the coefficient giving the contribution of the off-diagonal matrix elements. The parameter p is p’(Qft)o(Q@o. The values of 48 are: q = 0,0.778, 1.395, 1.902 for NB = 0. 1,2,3. for a = 0.218. The theory can best be compared to experiment by defming a level shift due to the perturbation:

-f(OA

.NB)I3

(18)

where ENA,NB

- ENA,OB - EQA,NB is an experimental quantity obtainable from three spectral lines. The value of p can be obtained from the measurement of DE(1,1):

AE(l,l)=Ell-EIO-EO, -20.4

cm-‘,

=945.0-582.7-382.7= 09)

with frequency values established in the vapor by lnnes [8] - Thus from table 6, -3.1 lp - 0.067~2 = -20.4 giving dJz4) = 5.80 cm-l. The value-sof the level shifts using this vaIue of p are given in the last column of table 6. The, corresponding value of p for (Is pyrazine is obtained from E y -y% = 852.5 - 546.6 -Eo, = 3.60 cm-l. 301.4 z-13.7 cm’ gnfingp(+) Tfie deuterjum isotope effect on p +n be seen from its definition to be (in the harmonic approximation): (20)

D.L. No1,ur.D.S. M~llucllhcn-nrronsirionrof Table 7 Comparison between alcuhtcd

NANB

obs.

10

582.7

01

3827

shifted levels of 10a and 63, and probable da Vapor

ha Vapor Cxlc.

ohs. 564.6

-

wk. -

II

945.0

852.3

1168.0

1129.3

-

21

1508.2

1510.3

1402.0

1405.8

1916

1918

1724

1710.4

1367.6

1178

882.7

12

1372.0

cxpcrimcntnl v3lucs

ohs.

mlc.

1169.2

while the observed value from the previous paragraph is 1.61. This corresponds to a 1 cm-’ accumulated error in measuring the various line intervals involved, and it may be within the experimental error, since eight line positions enter into the experimental value of p. The other check on the theory is to predict the position of the lines 63 + 2 x lOa, (1 2) and 2 x 6a + 2 x IOa, (2 2). These lines have not been assigned, so the theory is used to help locate reasonable possibilities. The results are shown in table 7. Here measurements on both it4 and d4 and in vapor and benzene solution are given. The table also shows the values of the measured fundamentals. The 2 1 and 1 2 lines seem to be given correctly by the theory. The 2 2 lines are not as definite since there are several possibilities for an assignment. Thus, while the theory is not perfect, it does have nearly the correct quantitative and qualitative features to describe the coupling between the in-plane 6a and out-of-plane 10a modes. This coupling seems to be a feature of electronic spectra not encountered before, but may very well be a common occurrence in other n + n states if one looks for it. One of the shortcomings of the theory is that the relative bases of QA and QB have been ignored by S using CQE> instead of ((QAQB)2>. If the physical interpretation for the coupling expressed earlier is correct, this correlation term should be significant, and may account for the discrepancies. _ We can now see that the neglect of the coupling terms in eq. 7a could not have caused much error.

obr

504.3

569.5

430.1

329.6

994.4tesL)

-

1555.3

1444.1

cltc.

882.8 1136.1

1561.2

1438.5

1440.6

1229.7

1434.3

686.8

894.7

630.6

Benzene

4

1171.5

22

171

II

ha Benzene

301.4

20

02

rhcpyrarincmlenrlc.

1225.5

Table 6 shows that Eol = 0.7 cm-l, and this represents only a negligible change in the effective force constant, ci5. It was therefore justified to write k = k$. 5.3. Gzuses of quartic pokwtial

compottettts

Eq. (7b) is the expression for tl~e quartic force constant ~7.The first two terms in eq. (7b) result from vibronic coupling with the 1 B2, state. These two terms explain the n(obs.) within a factor of 2. Therefore, the results of the previous section show that the perturbation due to the lBzu (7777’)state is large enough to explain the qurtic anharmonicity in 10a. We have also shown that mode 4 and probably 5 have quartic potential components. and couple to 6a in the same way as does lOa, but with smaller level shifts. The low spectral intensity of these modes shows that the perturbation caused by the lBlu state is smaller than that suffered by the lOa mode. The results of a calculation of the cause of the quartic component for mode 4 in the benzene host is shown in table 5. The starting parameters are~(4)/fi1Blu) = 0.0011,~ = 17.6 x lo-40 gm cm2 kzB = 25.1 x IO-*2 erg and Q = 0.04. The equations for IOa were used to calculate the results. p was calculated by treating modes 4 and 5 as rotations in the same way as described for 10a. A more exact ~1could be found by a normal coordinate analysis. However. a change by a factor of 3 in p would not signi!kantIy change our conclusion about the cause of the quartic potential component in 4. Fermi iesonance ls a possible cause of anharmonicities in the

172

D.L. Narva. D.S. McClure/l?te

n--R transitions of the byrarine molecule

overtone of 4. But the fact that 4 has a significant quartic potential component in the hd and 64 spectrum makes it hard to explain this component by Fermi resonance. Table 5 shows that a(obs.) is not explained by vibronic coupling as it is for 10a. a is larger for 4 than 1Oa although 4 has a much smaller Q value. This can be explained by the larger k and g values for 4. Table 5 shows that the cause of the quar:ic component in 4 is the diagonal& term and therefore the quartic potential is intrinsic to the t B3, nn* state. The occurrence of a sizeable quartic potential component in the excited state is a phenomenon requiring a special explanation in aromatic molecules. These same modes in the *B 2” excited state of benzene are nearly harmonic. If we ask whether or not a quartic component of the magnitude found in the lB3u state of pyrazinc could be present but masked by the large quadratic poential in the ground state. a calculation shows that it could not. We have shown that there are two different sources of the quartic potential component in heteroaromatic molecules. The presence of the quartic component in the out-of-plane hydrogen bending mode 10a has been explained here by vibronic coupl;ng with the close by lB2,, state. But the quartic components of out-of-plane ring bending modes 4 in pyrazine and 16b in pyridine cannot be explained vibronic coupling (the one quan-turn level of 16b in pyridine vapor has no detectable intensity). The diagonal a' term is the source in the case of these two out-of-plane ring bending modes. (1'may be explained by the presence of the extra R electron in nn* states. Wadt and Goddard [ 191 have calculated that in the ‘nl~* state the extra ITelectron is distributed to 6.8% on each carbon and 36.4% on each nitrogen. The 36.4% extra electron on the nitrogens must strain the ring to change the 90” angle between the nitrogen pn orbital and the carbon nitrogen bands. 16b and 4 both cause the carbon nitrogen bonds to become nonplanar. The repulsion between this extra pn electron density and the bonds could be responsible for the reduction‘ of the quadratic force constant of 16b and 4 and the appearance of the quartic term. Similarly, the presence of qua&c potentials in smaller ring molecules has beea~explained by the need for relief of ring strain 1171. Since there is only an extra 68% electron at each carbon, @e quartic component in IOa, which o$y chan&esthe carbon hydrogen bond.angle. is not’ caused .by.the e&a n electron.

-.

_.-

L :

:‘

_

II

Therefore, there appear to be two causesof the quartic potential component. In 10a it is caused by vibronic coupling and in 4 (and 16b of pyridine) the ring strain due 10 the extra electron density on the Arogens may be the cause. Acknowledgement We wish to thank Professor K.K. lnnes for providing data on the vapor spectrum from the theses of J.D. Simmons, S.G. Tilford and S.N. Thakur, and for several valuable discussions. We also wish to thank Dr. J.C. Baum for his help with the first experiments using single crystal benzene samples. References

[ 11 E.F. Zalewski, D.S. McClure and D.L. Narva, J. Cbem. Phys 61 (1974) 2964.

[ 2 1 Ismu

Suzuka. Naohiko hlikami and Mitsuo Ito. J. MoL Spcctry. 52 (1974) 21-37. (31 C. Hong and G.W. Robinson, J. hfoL Spectry. 52 (1974) 1.

(4 ) G.E. Bacon, N.R. Curry and S.A. Wilson. Proc. Roy. Sot. A279 (1964) 98. [S I CC Nieman and D.S. Tinti, J. Chem. Phys. 46 (1967) 1432; F-M. Carforth. C.K. Ingold and H.G. Poole. J. Cbem. Sor (1948) 508. [6] E.R. Bernstein, S.D. Colson. D.S. Tinti and G.W. Robinson, J. aem. Phys. 48 (1968) 4632. [7] S.P. Mason, J. Cbem. Sot. (1959) 1240. (31 K.K. hnes, private communication. 191 S.N. Tbakur and K.K. Innes, J. Mol. Spectry. 52 (1974) 130. [lOi J.P. Simmons, K.K. lnnasand CM. Begun. J. MoL Speclry. 14 (1964) 190. [ 11 I KK. Inner, J.D. Simmons and S.G. Tilford, J. MoL Spectry. 11 (1963) 257. [ 12 j S. Califano, G. Adembri and G. Sbrana. Spectxochem. Acta 20 (1964) 385. I131 J.P. Jesson. H.W. Kroto. D.R. Ram&. J. Ctwm. Pbyr 56 (1972) 6257. 1141 J.T. Bro~~~igg. R.D. Thesis, University of Chicago (1974). [IS] J.N.C8Llomon,T.M.DunnandI.M.Mills.PhilTranrRoy. Sot. A259 (1966)499. [ 161 R.M. Hochstrassa andCA. Mar&co, Molecular Luminek eence. ad. E.C Iim Beqiamis New York, 1969) p. 631; G-C. Ni-n and DS. Tinti. J. C%m. Pbys. 46 (1967)

1432. [ 17] S. CIun, P. Stelm& a-&. L Tho&on, (iSI

1: C&m. Phys 41

(1964) 2828. -_ I&B. WiIsom. J.C. Deciusand i!.C Qoss, tions (MA;raw-HiU, New York; 1955).

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