Review of optically pumped FIR laser observations and FT-spectra-assisted FIR laser assignments for 13CD3OH

INFRAREDPHYSICS &TECHNOLOGY ELSEVIER

Infrared Physics & Technology 38 (1997) 357-372

Review of optically pumped FIR laser observations and FT-spectra-assisted FIR laser assignments f o r 13CD3OH Li-Hong Xu *, Daniel Hurtmans Department of Physical Sciences, Universi~ of New Brunswick, Saint John, N.B., Canada E2L 4L5 Received 25 April 1997

Abstract The 13CD3OH methanol isotopomer is known to be an efficient FIR lasing molecule when optically pumped by a CO 2 laser. One hundred and eighty-nine (189) FIR laser lines have been detected in laboratories to date and the frequencies of 80 of these have been accurately measured by heterodyne techniques. They include the third most efficient FIR laser line at 127 /zm (the first and second most efficient FIR laser lines are at 123.5 ~m and 118.8 /xm for CH3OH) and a very long wavelength line at 2615/xm. The present work extends the identification of IR-pump/FIR-laser line systems with assistance from high-resolution F-T-spectra. New assignments with full quantum numbers have been made for 44 FIR laser lines and partial J-assignments for 7 additional lines. This brings to 100 the total of FIR laser lines spectroscopically assigned to date for J3CD3OH. In the course of this work, we have compiled and updated all known information on the IR-pump/FIR-laser observations and spectroscopic assignments for ~3CD3OH, and have made some substantial corrections to the existing literature on assignments. Very close FIR laser doublets reported for one system are associated with asymmetry splitting for K = 8 A levels in the excited ~3CO-stretching state, representing the highest K state for which asymmetry doubling has been resolved for methanol and suggesting the presence of interesting vibrational perturbation and mode coupling. © 1997 Elsevier Science B.V.

1. Introduction Like its parent ~2CH3OH species, the 13CD3OH isotopomer of methanol is known to be an efficient far-infrared (FIR) lasing molecule when optically pumped by a CO 2 laser. During the last thirteen years, this species has been examined extensively over a range of experimental conditions and spectral regions by several research groups around the world for the detection of new FIR laser emissions [1-15]. Briefly, the first successful generation of FIR laser

* Corresponding author. E-mail: [email protected].

radiation f r o m 13CD3OH by optical infrared (IR) pumping with a CO 2 laser was reported by Inguscio et al. [1], who used a 1 m open-structure FIR resonator and a 1 m high-pressure cw quartz waveguide (WG) CO 2 laser of 150 MHz tunability. Many FIR laser lines were observed including an extremely efficient one at 127 /zm, later identified by Mukhopadhyay et al. [3] on the basis of calculated energies. A study of the efficiency and Stark effect for this 127 /xm FIR laser line by Ioli et al. [4] revealed that the 127/zm FIR laser line was second in efficiency only to the 119 ~ m FIR laser line of normal CH3OH. Furthermore, the different polarization and Stark behavior of the 127/zm FIR laser line

1350-4495/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S 1 3 5 0 - 4 4 9 5 ( 9 7 ) 0 0 0 3 0 - 3

922.9143

922.9143 922.9143

924.9740 924.9740 924.9741) 924.9740

929.11174

931.0014

931.0014 931.1X114 931.(X114

934.8945

938.6883

IOP(42) IOP(42)

111P(401 111P(41)) 10P(411) 10P(411)

IOP(361

111P(34)

10P(34) 10P(34) I11P(34)

11)P131))

10P(26)

84

-61

17 100 1181

- 119

- 38

- 57 72 130 131)

5

5

2519122.5

16112861.1) 21)23188.3

51.92 132.19 16.53 53.4657 67.4863

281.7

255.7

125.3 241.6 145.4

149.6

225.1

393.3 281).0 2115.4 2110.4

280.3 40.3

35.50

39.11

79.83 41.39 68.76

66.83

44.43

25.42 35.71 48.68 49.91

35.68 248.1

119.111167 84.0289

75.7 6114.9 187.1)358 148.1782

192.6

II

II

± Z II

±

w S M

1511

180 180

VW

M

M

200

200 201)

M

181)

W w S S

120 1211 251) 250

±

M

1811

II ± .L II II .L

s

w M M,20 S,811

w

141)

2111) 150 150 1511

2oo

II

II II Z ±

II

[5]

[51

[5] [5] [5]

[5]

[5]

D21 [5] [51 [51 [5]

[111

[1,5,14]

[5] {5] [5,111] [I,5,10]

[5]

h I); 1; O;

14) 141 14) 14)

P(I, 1, 6; 29) P ( l , 1, 6; 29) P(I, 1, 6; 29)

P(n, t, K; 32)

P(I, 1, 2; 34) P(I, 1,2; 34)

P(I, 1, 4; 34) P(I, I, 4; 34) P(I, 1, 4; 34)

P(II, 2, 15; 39) P((), 2, 15; 39)

P ( l , 3, 11; 14)

2, 3, 2, 3,

2, h 3,1); 2, 1; 3, O;

13)r 131V? 13)r 13)V?

(I, 1, 6; 28),:o (1, 1, 6; 281cn (1, I, 6; 28)(:o

(n, t, K; 311co

(1, 1, 2; 33)(:0 (I, 1, 2; 33)co

(1, 1, 4; 33),:0 (I, 1, 4; 33)(:o (t, 1, 4; 33)co

(0, 2, 15; 38)c0 (0, 2, 15; 38)c0

(1, 3, O; 13)V?

(I, (1, (1, (1,

10P142)

-49 5 5 5 P(I, P(I, P(I, P(I,

922.9143 922.9143 922.9143 922.9143

20

920.8291

l(I)r IO)r lO)r lO)r 10)I" 111)r lO)r l(I)r lO)r

10P(42) 1011(42) 10P(42) 10P(42)

2, 5: 2, 5; 2, 5; 2, 5; 2. 5; 2, 5; 2, 5; 2.5; 2, 5;

10P(44)

H)) 101 i0) 10) 10) 11)) 10) 1111 11))

(1, (1, (1, (1, (1, (I, (1, (1, (I,

2, 5; 2, 5; 2, 5; 2, 5; 2, 5; 2, 5; 2, 5; 2, 5; 2, 5;

Q(I, Q(I, Q(I, Q(I, Q(I, Q(1, Q(I, Q(I, Q(1,

9112.2315

10HP(29)

Ref.

upper state (n t, t', K'; J')V'

P lnt (mTorr)

FIR laser transition

Pol

transition P/Q/R (n, t, K; J)

wavenumber (cm -1)

IR pump wavelength (/zm)

li'equency (MHz)

wavenumber (cm -1 )

ID

offset (MHz)

Spectroscopic assignment FIR laser

pumped by a CO 2 laser

CO 2 pump

for 13CD3OHoptically

lR-pump/FIR-laser measurement

Table 1 FIR laser line observations and spectroscopic assignments

h 12)r

(l, 1, 6; 271c0 (1, 2, 5; 281¢u --, (1, 2, 5; 27)co

(n, t, K; 3111cu

(1, 1, 2; 32)cn --*(1,2, 1; 33)c0

(1, 2, 3; 33),,:0 (1, 1, 4; 32)co (1, 2, 3; 32)(:o

--,* (11, 2, 15; 371cn (0, 3, 14; 381co

~(1,2,

(0, 1, 2; 14)co (1, 3, II; 12)r (n", t", K" ; 13)V" --* (1, 2, 1; 13)t

--* (1, 2, 5; 9)r ~ (1, 3, 4; 9)r (1, 3, 4: lO)r •-.* (1, 1, 6; 10)r --* (1, 1, 6; 1 l)r ---, (0, 3, 4; 10)cn --. (0, 3, 4; 9)(:0 --* (1), 1, 6; l l ) c e (0, 1, 6; 10)ce

lower state --~ (n", t",K"; J")V"

II [± ] [11]

II

[11] [±]

.t. [11] [ll]

I1 ±

II

II II l ±

[±] [[I]

Ill] [ .t ]

[±] [Z] [I] [11] [±]

Pol

35.61129 [57.4745] [93.0249]

41.922 71.779

67.11332 [41.9272] [1118.8956]

84.11289

67.4867

16.5488

[t2.7251)] [54.21511] [41.4968] [19.0514] [5.11363] [121.82121 [134.5893] [72.9189] [86.9577]

loop calc (cm-t)

[17] [17] [17]

new

new new

[16] [16] [16]

new

new

[17] [16,17] [17] [16,171/ [1,5.1o] [16,17]/ [1,5,141

[22] {22] [22] {22l [22] [221 [22] [22] [22]

Ref.

L~ ..q I

ov

o~

g

- 98

-115 - 67 56 73 73

84

136

101 0 0 0 116

942.3833

942.3833

942.3833

947.7420 947.7420

949.4793 949.4793 949.4793 949.4793 949.4793 949.4793

951,1923 951.1923 951.1923 951.1923

952.88118

952.88118

952.88118

952.88118

954.5451 954.5451 954.5451

101:)122) 10P(22) 10P(22)

10P(16) 1011116)

1011114)

10P(121 10P(12)

IOP(H)) I0P110) lOP(10) I(1P(101 10P(10)

ioP(1O)

10P(lO)

954.5451

966.2504

967.3643

967.71172 967.7072

967.71172

10SR(l 1)

10R(81 10R(8)

10R(8)

954.5451

10R(6)

952.8808

952.88118

952.8808

10P(8) 10P(8) 10P(8) 10P(8)

1oP(8)

lOP(12)

lop02)

10P(14) 10P(14) 10P(14) 10P(141

1oP(14)

- 98

940.5481

10P(24)

940.5481

940.5481 9411.5481 940.5481

-

940.5481 9411.5481 9411.5481 940.5481

55 1118 1(18

411, 55

28, 30

-15

24. 37

-

-

- 55

105

-75 8O 80 80

-88

-17 -15

99

29 21 21 21 21 99 99

155

-

10P(24) 10P(24) 10P(24) 10P(24) 10/'1241 10P(24) 10P(24) I0P(24)

155

-

9411.5481 940.5481

10P(24) 10P(24)

4796751.6 1065407.3

1163665.7

5792881.7

6485(11.6 1712097.5 2360174.8

2O52029.8 2243269.0

1844839.3

88(1119.7 899571.7

11169614.9 1315594.8

147216(1.2 2526691.4 1O3O536.3 1385645.4 2412757.4

35.63 46.73

97.9

62.4991 281.3877

257.6276

51.7519

811.8

127.0213

128.3 462.2848 175.11124

127.2 142.(I 53.4 87.11 72.1 87.0 151.6

146.11956 133.6409 84.7 70.0

56.(I 196.2 162.51133 115.1 112.3 414.6

3411.6269 333.2613

336.9 313121 46.4

510.0

102.15

160.01124 35.5382

38.8157

193.2297

77.94 21.6317 57.11194 78.72711 123.76

78.62 711.42 187.27 114.94 138.70 114.94 65.96

68.4483 74.8274 118,06 142.86

178.57 50.97 61.5372 86.88 89.115 24.12

29.3576 30.0065

29.68 31.95 215.5

19.61

203.6412 49.1060 118.65112 84.2814 290.9092 34.37511 216.3558 46.2202 124.2530 80.48119 38.6 259.1)7 280.2807 35.6785 227.8760 43.8835

28(1.7 214.0

2(~) 100

1211 (20

3(x) 1211

II

l} II

II

± , II

II

~1

II II

±

30o

2511 1511

II(1

15o

311 2311 15(1

1811

(5(1

170 1811

1911

1911

II

~1

2(X1 1511 170

±

1511

1511

±

II

21111 21)11

II II

15(1

15o

II II

1511

3.

± , II 151)

[I U

II II

II II II

13(1

21111 20o

±

250

LJ II II

200 3o0 25o 2511

2o0 20o

II II ± II

1[ II

t51

[51 [5]

[5,11,14] [11] [5] [51 [5,1111 [5,1o] [51 [5[ [5]

[11]

[(,5] [51

[1,5,14]

[5,9] till [12]

[5,91

[1,5,9,1ol [121 [5,9] [5,91

[I,5,9,111] [5,9,111]

[1(11 [5,9,1o]

D ,91 [5,9]

4

M VS

1.2

M

14(1 VVS W

[15]

[1.51 [51 [5.11,151 (15] [) ),15} [5.11]

[4,5,111]

[5] M (5) W (5] W, 3511 [1,5,1ol M

M W

M

W W

S, 15 S, 30 W W

W S M W W W

S VS

M W

M

S S

511 M, 3O S, 12(1 M, 3511 M, 175

S S

P(O, 3, 9; 10) P(0, 3, 9; 10)

P(0, 1, 9; 10)

P ( I , 1, 6; 18) P ( h 1, 6; 181 P ( I , 1, 6; 18)

P(I, 3.4; ]9)

P(2, 2, 5; 19) P(2, 2, 5; 19)

P ( n , t, K; 21) P(n, t, K; 21)

P(O, 1, 3 + ; 24) P(0, 1 , 3 + ; 2 4 )

P(n, t, K; 26)

P ( 0 . 2 , 3; 29) P(0, 2, 3; 29) P(0, 2, 3; 29) P ( I , 3, 1 + ; 2 8 ) P ( I , 3, 1 + ; 2 8 1 P ( I , 1, 8; 28) P ( I , 1, 8; 28) P(I, l. 8; 28) P ( I , 1, 8; 28) P(0, 1, 5; 29) P((I, I, 5; 29) P(0, 1, 5; 29) P(0, 3, 7; 29) P((I, 3, 7; 29) P(0, 3, 7; 29) 3; 28)(:o 3; 28)(:0 3; 28)(:0 1 + ; 27)co 1 + ; 27)co 8; 271co 8; 27)co 8; 27)(:o 8; 27)(:o 5; 28)co 5; 28)(:o 5; 281co 7; 281co 7; 28)(:0 7; 281co

(0, 3, 9; 9)co (o, 3, 9; 9)co

(11, 1, 9; 9)co

(1, 1, 6; 17)(:o (1, 1, 6; 17)co (1, 1, 6; 17)(:o

(I, 3, 4; 181co

(2, 2, 5; 18117o (2, 2, 5; 181co

(n,t,K;201co

( n , t, K ; 2 0 ) c o

(0, 1, 3 + ; 231co (0, 1, 3 + ; 23)(:0

(n, t, K; 25)(:0

((I, 2, (I), 2, (0, 2, (1, 3, (1, 3, (1, 1, (1, 1, (1, 1, (1, 1, (0, 1, (0, 1, (0. 1, (0, 3, (0, 3, (11, 3,

(n,

t. K -

1; 2 0 ) c o

~ (0, 1, 8; 8)co ~ (11, I, 8; 9)co

--) (0, 2, 8; 8)co

~ (I, 1, 6; 161co ~ (1, 2, 5; 17)co ~ (1, 2, 5; 161co

~ (11, 2, 5; 18)def

--) (2, 1,6; 191co ~ (2, I, 6; 18)co

~(n,t,K-l;19)co

+

---)(0,1,3+;22)(7o ~ (0, 2, 2 + ; 22)co

---) (n, t, K; 24)co

~ (11, 2, 3: 271co ~ (0, 3, 2; 27)co --+ (0, 3, 2; 28)co -'-) (0, 2, 2 + ; 27)def --) (11, 2, 2 - ; 26)def ~ (1, 1, 8; 26)co ~ (1, 2, 7; 27)co ~ (1, 2, 7; 261co ~ (11, 2, 7; 261co ---) (11, 1, 5; 27)(:0 ---) (0, 2, 4; 2 7 k o --* (0, 2, 4; 28)(:o ~ (0, 1, 6; 28)(:o ~ (11, 3, 7; 27)co ~ (0, 1, 6; 271co

II [± ]

l[

II ± II

±

II ±

II

±

II 1[

II

II 11 [± ] ± [111 till

II

II

[± ] [±] II II ±

II

11

35.5384 [24.11538]

38.8153

21.6318 57.11187 78.7269

66.504

29.3575 30.0065

35.6582 46.7769 [111.8816] 49.1126 84.2789 34.3737 46.2180 80.4791 259.251 35.6783 43.8825 [8.22271 19.6137 [35.6814] [55.2795]

[17,2tl] [17,20]

new

[3,17] [171 [3,17]

new

[2ol [2o1

new new

[3,17] [3,17]

new

[9]'

[21)]

new new [3,9,17,211] [9,17,20] t3,9,17,20] new [9] '[17,211] [91 '[17,2(11 [17,2(11 [20I [211]

[2o]

I9,17,20] [9,2111

oo

970.5472 970.5472

975.9304

977.2139 977.2139 977.2139 977.2139 977.2139 977.2139 977.2139 977.2139 977.2139 977.2139 977.2139 977.2139 977.2139 977.2139 977.2139

977.7623 977.7623 977.7623 977.7623 977.7623 977.7623

978.4723 978.4723

978.4723 978.4723

978.4723 978.4723 978.4723 978.4723 978.4723 978.4723 978.4723 978.4723 978.4723

978.9517 978.9517

10R(12) IOR(12)

It)R(20)

10R(22) IOR(22) 10R(22) 111R(22) 108(22) 108(22) 108(22) 108(22) 10R(22) 10R(22) 10R(22) 10R(22) 10R(22) 10R(22) 10R(22)

111SR(27) 111SR127) 11)SR(27) 111SR(27) 10SR(27) 10SR(271

10R(24) IOR(24)

111R(24) 11)R(24)

10R(24) I08(24) 11)R(24) 10R(24) 10R(24)

I (ISR(29) 10SR(29)

108(24) 108(24) 108(24)

IOR(24)

969.1395 969.1395 969.1395 969.1395 969.1395

IIIR(II)) IOR(III) II)R(10) IOR(IO) IOR(IO)

4080637.2

- 26 - 13 - 13 27 27

-24 -28

126 126 126

40 I(X) 100

- I(I 12 40

- 10 - I11, - 25

2059531.6

486O288.7 4669448.0

44968811.8

4262687.4 18631138.2 2396985.6

-39 -24 - 8 3551805.8 14 2348438.4 25 60 611 60 74 74

100

135 126 t181

- 1117 - 1117

-

16

3642651.6

- 6 3 4182256.6 -2, - 5 4454427.9 40 916011.1 40 11)7

Requency (MHz)

wavenumber (cm - ~ )

ID

offset (MHz)

FIR laser

CO 2 pump

lR-pump/FIR-laser measurement

Table 1 (continued)

469.4 219.8

t28.1 145.5634 90.3 82.5 286.6 152.9 367.3 327.5 173.4

61.6820 64.2030

1411.4 128.9

125.0706 234.0 127.6 66.6668

16(I.9159

70.3294

110.0

144.5 81.8 193.3 129.9 84.4 86.5 84.4056 127.6561 257.4 462.6 37,437 150.7 1(11.8 83.O

73.4671

82.30116 67.8

71.682{I 67.31121 327.2804 145.7 91.0

wavelength (/xm)

45.5(I

21.3(I

78.06 68.6986 110.74 121.21 34.89 65.411 27.23 30.53 57.67

162.1218 155.7560

71.23 77.58

142.1879 62.1443 79.9548 42.74 78.37 149.9998

69.20 122.25 51.73 76.98 118.48 115.61 118.4755 78.3355 38.85 21.62 22.88 66.36 98.23 120.48 90.91

136.1154

147.49

121.5058

139.5051 148.5837 3O.5548 68.63 IO9.89

wavenumber (cm - 1)

II

II ±

± ii ± ±

It

, ± ± Z

120

160

1711 1811 180 130

150 17o

1711 180 130

± , II 1511

12(I

2511

± ±

~81,

1311

21111 130

ii

11

II

130

z911

2511 191)

II 1 II ±

2211 220

]1

2OO

±

±

1511

180 15o

200 201)

0.1 0.2

[15] [15]

[5,8] [5,8] [5,8] [5,8] [5,8]

[111

[5,8,1 I]

[5,8]

[1,51

M W M W S M W S

[5,8,111,11] [11,15] w

S, 3(H) M, 0.2

M

[5,8] [5,8]

[151

11.3 M

0.5 11.05 0.15

[5,8] [5,8] [5,8] [5,8] [5,8] [I,5] [15] [15] [15] [15] [15]

w 6 (i.5

M

W M

w w

W W W S W W

32O 180

[1,51 [5,81

[5,8] [5,8] [5,8] [1,5]

W

2OO 200

180

[5,81 [5,81 [5,81

[I,51

[1,51

I151

[5,10] [5,15] [5,1(I] [51 [51

W M

M

M

0.08

VS

M

VS, 25 M, 11.3 S, 8

Ref.

190

180

11X1

3OO 200 151) 1811 220

P Int (mTorr)

II II

± .1.

±

±

±

± Z II II ±

Pol

2, 2; 1, 5; 1, 5; 1, 5; 1, 5;

I, I; 3,9; 3, 9; 1. I; 1, I; 3, 9; 23) t41 14) 141 14)

16) 18) 18) 16) 16) 18)

Q(I), 3, 8; 19) Q(O, 3, 8; 191

3, 13; 24) 3, 13; 24) I, 9; 24) 1, 9; 24) Q(O, I, 9; 24)

Q(O, Q((I, Q(O, Q(0,

Q(I), 3, 3; 24)

Q(I, 1, 2; 5) Q(I, 1, 2; 5) Q(I, 1, 2; 5) Q(2, 3, 4; 51 Q(2, 3, 4; 5) Q(2, 3, 4; 5) Q ( I , 2 , 1: 17)

Q(I, Q(I, Q(I, Q(I, Q(I,

Q(2, Q(I, Q(I, Q(2, Q(2, Q(I,

P(2, 3, 1 + ; 2 1 P(2, 3, I - ; 2 )

P(2, 2, 3; 7) P(2, 2, 3; 7)

transition P/ Q/R (n, t, K; J)

IR pump

2, 2; 1, 5; 1, 5; I, 5; 1, 5;

23)co 141co 141¢o 14)co 141co

1711:o 18)co 18)co 16)co 16)co Igloo

(11, 3, 8; 19)(:o (0, 3, 8; 191co

(0, 3, 13; 241¢o ((1, 3, 13; 24)(:o (I), I, 9; 24)(:o (0, 1, 9; 24)co (0, I, 9; 24)co

(0, 3, 3; 241co

(1, 1, 2; 5)co (1, 1, 2; 5)co (1, I, 2; 51co (2,3,4;5),:0 (2,3,4;5)(:0 (2, 3, 4; 51co (I, 2, I; 171co

(1, (1, (1, (I, (1,

(1, 3, 2; (I, 3, 9; 11,3,9; (2, I, 1; (2, I, 1; (1,3,9;

(2,3, 1 + ; l)co (2,3, I - ; l)co

(2, 2, 3; 6)co (2, 2, 3; 6)co

upper state (n', t" K'; J')V"

FIR laser transition

Spectroscopic assignment

3, 2, 2, 2, 3,

1 - ; 22)r 4; 141co 4; 131co 4; 15)co 6; 14)def

(0, 1,7; 191co --'* (0, I, 7; 18)co

(0, 1, 12; 24)co (0, 1, 12; 231co (0, 2, 8; 24)(:o (0, 1, 9; 231co (1), 2, 8; 231co

(0, 2, I; 25)r

-*(1, 2, 1; 5)co "* (1, 2, 1; 41co (1, 1, 2; 41co (1, 1, 3; 4)co (1, 1, 3; 5)co --*(2,3,4;4)(:o (0, 3, (I; 16)def

~(1, ~ (1, (1, (1, (0,

(I, t, 8; 18)co

~ (I, 3, 2; 16)co

16)co 17)co 19)co 17)on

1,0; l)co

~ (I, 3, 2; (1, 3, 9; (I, 1,8; 4--*11,3,2;

~(2,

.L

II

±

±

II ± II

±

l [± ] ± [111 [±] [± ]

II

.L I[ ± [± ] II

n

II

± ±

I[

[z]

±

II

±

(2, 1, O; 2)co

[11]

(2, I, 4; 6)co

Phi

(2, 1, 4; 7)co

h)wer state "* (n', t",K" ; J#)V"

21.317 45.545

27.2526 30.5739 57.8355

111.713

71.2853 77.6514 [6.3654] 162.1213 [155,7558] [6.3561] 77.668

142.184 62.14511 79.955(I 43.0627 7 .5288

21.663 22.9112 65.871 97.836 119.469 9(i.ii57

loop calc (cm - J)

new new

[8] ", new [8] ", new [8.17] [8.17] [8:7]

new

[161

[161 [161

[2(11

[2o1

12ol

BCW

new new new new

new new new new new new

new new

new new

Ref.

u

t.~ Oc

~,

~"

77 77

- 43

987.6202 987.62112

9911.6196

9911.6196 9911.6196

992.4848 992.4848 992.4848 992,4848

993.3764

1018.91R57 1018.91X17

1018.9007 1018.9(1)7

1029.4421

1033.48811

11135.4736 11135.4736

11137.4341

1039.3693 1039.3693 11139.3693 11139.3693

10R(40)

10R146)

10R(46) 10R(46)

10R(50) IOR(50) 10R(50) 10R(50)

IOR(52)

9P(48) 9P(481 9P(48) 9P(48) 9P(48)

9P(38)

9P(34)

9P(32) 9P132)

9P(311)

9P(28) 9P(28) 9P(28) 9P(28)

1018.911(17

982.11955 982.0955

10R(30) 10R(30)

10R(40)

9811,9132

10R(28)

191171)57.8

2(1488113.6

948141.4

639264.6

15214311.9

-91 --91 -65 - 65

- 95

"

'

24 24

4

- 11

42

421532.0 714824.2

999657.8 1258766.4

999676.2 1258774.6

9245122.6

36611888.4 4979742.5 5852719.7 5852724.11

63111)397.4 19111282.4

H) 4527932.5

132 132

- 74 - 74

182

- 110 -3(1 -- 25 - 25 -- 25 - 25 --25 98/-25 -- 12 - 12 184 184 184

979.7054 979.7054 979.71)54 979.71154 979.71154 979.71154 979.7054 979.71154 979.71154 979.71154 979.71154 979.71154 979.71154

10R(26) 1(1R(26) 10R(26) 10R(26) 10R(26) 10R(26) 10R126) 10R(26) 10R(26) 10R(26) 10R(26) 10R(26) 10R1261

- 159

979.7054

10R(26)

167.79 172.12

411.911

77.9 69.7 78.t 711. I

87.0

399.8 711.1974 419.3933

156.t)

299.8896 238.1621 133.0 299.8951 238.1637

32.4271

81.89116 611.2024 51.2228 51.2227

128.37 143.47 128.114 142.65

114.94

25.111 14.0608 23.84411

64.10

33.3456 41.9882 75.19 33.34511 41.9879

308.3841

122.1141 166.1063 195.2257 195.2259

2111.1586 63.421511

66.21196 151.11356

47.5831 157.6791

±

I1 ± I1 ±

II

± 11

II

II

II

I[

II

II

J_ fl

II II

II

fl .L

J_ I[

±

58.93 ± 50.7495 ]L .L 15.27 ± 21.3236 [[ 36.52 .t. 3.82 ± 31.6266 II 67.811 ± 47.85 II 68.34117 ± 17.85 .I. 22.37 I[ 411.23 l

30.30

188.0 53.19 157.21116 63.6126

59.6 58.1

244.5

169.7 197.0464 655.0 468.9646 273.8 2615 316.1896 147.5 2119.11 146.3256 560.3 447.11 248.6

330.0

150 1511 711 711

1811

100 100 1011

511

811 811 711 811 811

2111

31111 880 27(1 2711

2411 75

150

120 1211

31111 31111

130

140 1411 1211 1411 1411 150 1411 150 150 1411 90 90 91)

190

M M M M

s

M S S

M

75 8(1 W 65 711

11.113

4 5 05 0.5

[5] [5] [5] [5]

[5]

[I,5] [5] [5]

[2,5]

[111] [5] [111] [10]

[10]

[15]

[15] [15] [15] [15]

7 [151 100, (I.24 [10,15]

[151

[51

5

151

M

[51 [51

[5,81

[5,81

[5,8,11] [5,8.15] [1,5,11] [I,5,11] [5,8] [5,8]

/zzl

[1,5,11] [111 [I,5,11] [5,8,1 l]

[5,8]

[5,81

s

M M

s

M M M s w M M M M M

w

VS

vs

M

2, 5; 2, 5; 2, 5; 2, 5; I, 7; 1, 7; 1, 7;

8) 8) 8) 8) 8) 8) 81

R(0, R(O, R(0, R(O,

2, 2, 2, 2,

8; 8; 8; 8;

32) 32) 32) 32)

R(0, 2, 8: 32)

g(l, R(I, R(I, R(I, R(I, R(I, R(I.

R{I, l, O; 6) R(I, I, 11: 6) R(I, 1, 0; 6)

R(2, 3, 2; 2)

R(2, 3, 2; 2)

Q(o, 3, I11; 11) Q(o, 3, Io; 11) Q(I), 3, 111; 11)

1, 13; 16) 1, 13; 16) 2, 5; 14) 2, 5; 141 2, 5; 14)

(11, 2, (11, 2, (0, 2, (11, 2, (0, 2,

8; 8; 8; 8; 8;

(I, 2, 5; (I, 2, 5; (I, 2, 5; (I, 2, 5; (I, 1, 7; (1, 1, 7; (I, 1, 7;

33)',:o 33)co 33)co 331co 33)c,o

9)co 9)co 9)co 9)co 9)co 91co 91co

(1, 1, 11; 71co (l, 1, 0; 7)co (1, 1, 0; 7)co

(2, 3, 2; 3)co (2, 3, 2; 3)co

(11, 3, I11; ll)co (O, 3, 10; I l)co (0, 3, I(1; ll)co

1, 13; 16) 1, 13; 16) 2, 5; 141co 2, 5; 141co 2, 5; 14~o

(0, (0, (0, (0, (0,

12; 15)co 8; 12)(:o 8; 121co 8; 121,,:o

Q(O, Q(O, Q(0, Q(O, Q(0,

(0, 3, (11, 3, (11, 3, (0, 3, (0, 3, 12; 15)co

3, 12; 15) 3, 8; 12) 3, 8; 12) 3, 8; 12)

(11, 1, 6; 14)(:o (0, 1, 6; 141co (0, 1, 6; 14)co

Q(O, 3, 12; 15)

Q(O, Q(o, Q(0, Q(o,

Q(o, 1, 6; 14) Q(o, 1, 6; 14) Q(O, I, 6; 14)

12; 161Co 12; 15)co 5; 13)(:o 4; 141co 4; 1311:o

(0, 3, "-) (11, 2, (0, 3, (0, 3, (11, 2,

7; 8; 7; 7; 8;

331co 32)co 32)co 33)co 32)co

--'-) (0, I, 6; I0)CO --) (I, 2, 5; 8)co (0, 1, 6; 91co (0, 3, 4; 8)co -+ (1, 2, 6; 81co -'-) (1, 2, 6; 9)co (1, 1, 7; 81co

~(1,3,1+;81co "-') (1, 3, 1 - ; 7)co (I, 1, 11; 6)co

~ ( 1 , t, 1; 3k'o ---) (I, 1, I;211:o

(0, I. 9; 10)(:o ---) (0, 3, 1{1; 101Co ---)(0, I, 9; ll)co

(11, 2, ~ (0, 2, (0, 2, (0, 3, ---) (11, 3,

~(11, 1, 11; 151co

+111, I, 11; 14)co (11, 3, 8; 11)co (If}, I, 7; 121co ---)(11, 1, 7; ll)co

(0, 2, 5; 13)co (t), 2, 5; 14)c',1 (0, 1, 6; 13)co 2-

I.LI [Ill II [±] [II]

[11] II [11] t±l II n [±] till

.k

[±1 [11

±

±

II ±

II

±

[±1 [11]

.L

Ill1 t±]

[2151, new new new

[20], n e w [20], new

116] 01.4524]

[33.3446] [41.9877] 75.37116 33.3446 41.9877

new [161 [16]

12111 [20] 12o1 [2o1 [2o1 [17] [171 [171

[171 [17]

[17]

new new [81 a[17] [8] '[17] [81 ~[171

new

[171 [171 [17]

new

[211] [2111 [20]

151.11358 [11.4519] [161.7987] 210.1587 63.4199 [52.111173]

53.5040 63.6124 [8.9122]

168.11175 171.9266

411.9506 [14.0246] [26.9175]

68.3389 17.8658 22.3732 40.2487

31.6278

511.7523 [15.311981 2[.3229 36.6362

311.3175 [12.4521] [17.8654]

1

t.,n -.q

oo

11174.6465

11175.9878

11177.3025

11178.59116

11179.8523 IO79.8523

1081.0874 1081.11874

1082.2962

11183.4788 11183.4788

11184.6351

1084.6351 11184.6351

1085.7654 1085.7654

1086.8698 11186.8698

9R(141

9R(16)

9R(18)

9R(20)

9R(22) 9R(22)

9R(24) 9R(24)

9R(26)

9R128) 9R(28)

9R(311)

9R(301 9R(30)

9R(321 9R(321

9R(34) 9R(34)

4587083.11

1070.4623 1070.4623 111711.4623

9R(8) 9R(8) 9R(8)

11171,8838

11158.9487 11158.9487

9P(6) 91116)

11174,6465 1074.6465

11155,6251 1055.6251 1055.6251 1055.6251

9Rill))

1045.11217

9P(I(I) 91111111 9P(l(I) 911110)

9R(14) 9R(141

7696811.11 13562117.4

-78 - 1211

11145.0217

9111221 9P(22)

2616992.5 7591236.8

0

- 17

- 24

2

8311112)

(1

II

46

- 19

-45

3650380.0

5376677.3

1318533.5 1996261.6

891339.3 19511581.6

3982631.9

I 115461.4 1197005.1

12411925.7

5731794.1

36(156116.5

- 211 - 211 2528773.8 23 311611318.9

- 14

-4 -23

- 1311 - 1117 - 1117

1041,2791 1041.2791 11141.2791

9P(26) 9P(26) 9P126)

11611451.9 1214686.4

frequency (MHz)

wavenumber (era - l )

ID

offset (MHz)

FIR laser

CO z pump

IR-pmnp/FIR-laser measurement

Table I (continued)

155.28

43.14

183.49 162.611 183.49

wavenumber (cm - I )

98.5 82.1264

55.7579 52.1

3(19.7 227.3681 1511.1769

336.3393 153.6939

91.8

75.27511

79.4

268.76119 2511.4521

241.5878

52.31134

83.1462

97.9612

353,5 118.5525

65.3558

389.51127 221.11521 196.2

114.5561 39.4919

11)1.52 121.7636

179.3466 191.94

32.29 43.9815 66.5881

29.7319 65.11644

1118.93

125.94 132.8463

39.9278

37.21178

41.392g

191.1921

1211.2701

28.29 84.35118 1112.0813

153.1X186

25.6738 45.2382 511.97

87.2935 253.2164

258.3411 38,7085 246.81165 40.5176 126.1 79.30 72.9 137.17

64.4

231.8

54.5 61,5 54,5

wavelength (~.m)

1711

2_ [I

I[ 2_

I[

2511

1811

2111)

31HI

225

110

1911

21X1 21X1 [I

2111

II II

21x) 31111

50 511

21111

100

21X1

1511 ]511 2511

31X1

1211 IIXI 911

2511 31111

[1,5,111] [1,5]

[11]

[15] [15]

[10] [lO]

[11,15]

[1,5,15]

[15]

[151

[5,11] [1,5,11]

[I,5,15]

[l,5,l()] [1,5,111] [1,51

[15] [15]

[1o] [10] [i,51 [1,5]

[5]

[51

[51

[5] [5]

Re(.

M 2.5

M, 3.0 M

[l,5] [15]

[1,5,15] [1,5]

M [11] 71) [11)] VS, 150 [1,5,111]

W, 311 S

M

11.2 0.6

311 3o

M, 11.3

M, 11.2

11.2

S $ 2.11

M, 11.5

S, 1110 M

M

0.1 I).2

211 s VS

l(X)

195

18

M

M

W M

M

lix1

180

IgO

2181 21x1 2o11

P Int (mTorr)

2_

II

II

2_

g.

II

II l

Pol

Pin, t, K; 33)

P(O, 3, Pill, 3, P(O, 2, P(O, 2,

13; 24) 13; 24) 12; 26) 12; 26)

P(O, 2, O; 311) P(O, 2, 0; 3(1)

(0, 3, (0, 3, (0, 2, (0, 2,

13; 23)de( 13; 23)de( 12; 25)de( 12; 25)de(

(0, 2, 0; 29)de( (0, 2, O; 291def

in, t, K; 32)de(

in, t, K; 22)de(

(n, t, K; 20)de(

upper state

(n ~, t! K'; J')V'

P/ Q/ R in, t, K; J)

FIR laser transition

transition

IR pump

Spectroscopic assignment

(0, 2, 12; 24)de( ---)(0,3, I I; 25)de(

(0, 3, 13; 22)de( (0, I, 12; 22)de(

-) (11, 2, 11; 28)de( ((1, 1, h 28)def

-'~ in, t, K; 31)de(

--, in, t, K; 21)de(

~ in, t, K; 19)de(

(n ~, t",K"; J")V#

lower slate

H [I]

H I[

[If]

[11]

II

II

II

Pol

37.2118

h)op calc (cm - t)

new flew

new new

new new

new

new

new

Ref.

ol

oo

i,o

1(X12.4778

9P(18) h

149.7

45.5

36+2

232.3514

542.748~1 317.5569

387.2 151.0 177.6 54.58111

66.811

219.78

277.78

43.11383

18.4248 31,49114

25.83 66.23 56.31 183.2140

[[

21111

51~ 5O

35{I

140 2(10 1811

VS

S

W

(1.2

46

111

o.4

MW W w

[6]

[6]

[6]

[15]

I1111 [10]

I1,5] [15l

[I,5] [1,5]

(11, 1, 6; 14)def (11, l, 6; 14)def (0, 1,6; 14)def

(0, I, (I; 19)def

P(0, I, 11; 2(1)

P(D, 1,6; 15) P((I, 1, 6; 15) P((I, 1,6; 15)

(11, 3, 6; 231def (0, 3, 6; 23)def (0, 3, 6; 231def (11, 3, 6; 23)tier ((1, 3, 6; 231def (4,3,4;21110 14,3,4;211)O (4,3,4;211)O (4, 3, 4; 21110 (4, 3, 4; 21110 (4,3,4;21110 (4, 3, 4; 21110

P((I, 3, 6; 24) P111, 3, 6; 24) P((I, 3, 6; 24) P((I, 3, 6; 24) P((I, 3, 6; 24) P(O, 3, 4; 21) P(11,3,4;211 P((1,3,4;21) P(II, 3, 4; 21) P(tl, 3, 4; 21) p((I, 3, 4; 21) P(0, 3, 4; 21)

--~ 111, l, 6; 13)del" ---*(0, 2, 5; 13)def --,(0,2,5; 14)def

~ (1, 3, 1 - ; 20)r

~ (11, 3, 6; 22)def ~(11, 1, 5; 23)def ~ (0, 1, 5; 22)de( ~ (1, 1, 5; 23)r --* (1, I, 5; 221r --*(4,3,4; 19)O ~(0, 1,3+;2(I)def "-~((L 1 , 3 - ; 2 ( l ) d e f ---, ((I, 1, 3 + ; 19)def ~ 111, 1, 3 - ; 19)def ~ ( 1 , I, 3; 2(11r ~ 11, 1, 3; 19)r

[]]) [11] [±]

II

[1[] [J-] [11 [± ] [11] [11] [1] [l] (Ill [11] [.1_] [[~l

18.4248 31.4901 [13.1974]

25.5429

[29.9787] [184186] [48.35114] [89.111(14] [118.2592] [25.9133] [13.5490] [13.4641] [39.5845] [39.5225] [71.11193] [96.5559]

[16] [16] [16]

new

[22] [22] [22] [221 [22] [22] [22] [22] [22] [22] [22] [221

lines assigned incorrectly, b l a c o 2 pump.

Offset' and" indicate two different pump offsets. Int. Three ways are used in literature to report relative intensities for a FIR laser Line: (i) W = weak, M = medium, S = strong, VS = very strong; (ii) In [10], the intensities listed are proportional to the rectified voltage detected on MIM diode, and for comparison, the very strong 118.8 /zm line of CH3OH and the 127/xm line of taCD3OH had relative strengths of 4200 and 3000; (iii) In [15], the intensities listed are proportional to the rectified voltage detected on MINI diode, and for comparison, the 119 p.m [9P(36)-pumped] CH3OH line from this laser has a relative intensity of 10. Transitions in brackets, [], are predicted, a References mean

998.7883

9P122) ~

16

12911254.6

1096.5164

991.11715

9R(54)

U195.6636 11195.6636

9R152) 9R152)

9P(311) b

5523611.3 9441159.11

11189.111111 11189.11011 1|19~1.11284 1093.8847

9R(38) 9R(38) 9R1411) 9R(48) 5492616.2

11188.4034

9HR(23)

t.zo

"-.I I

c~

364

L.-H. Xu, D. Hurtmans / Infrared Physics & Technology 38 (1997) 357-372

made it an advantageous alternative to the 119 /~m FIR laser line, and it was soon utilized for diagnostics on the Princeton Tokamak. Later on, Moraes et al. [5,8,9,11] reinvestigated the 13CD3OH molecule in greater detail in a 1 m Fabry-Perot FIR cavity pumped by a waveguide CO 2 laser of 300 MHz tunability, paying particular attention to the Q-branch region of the CO-stretch fundamental. How one can achieve the maximum number of FIR laser emissions for a molecule under study? Pereira et al. [6] turned to the 13CO2 laser to obtain different pump coincidences. Recently, efforts devoted to designing a CO 2 laser with extended line coverage and higher resolution have dramatically increased the chances of coincidence between CO 2 pump lines and molecular absorptions. Many new FIR laser lines have been observed in a metal-dielectric rectangular WG FIR cavity pumped by a high-resolution CO 2 laser system with broader J-range, sequence-band lines and hot-band transitions [10,12,15]. This brings the total of FIR laser lines observed to date for the 13CD3OH species to 189, including the very efficient line at 127 /xm and an extremely long wavelength line at 2615 /zm. In addition, FIR laser frequency measurements have been pursued for improved FIR laser line precision. Altogether 80 out of the 189 13CD3OH FIR laser lines have now been measured in frequency [1,5,8-10,13-15] by the heterodyne technique. All known IR-pump/FIR-laser observations for 13CD3OH are summarized in Table 1. The observed 13CD3OH FIR laser lines are widely distributed over the wavelength range from 32 /zm to 2615 /zm (or wavenumber range from 308 cm -~ to 3.8 c m - t ) . Thus, they play an important role in bridging the full gap of radiation between the microwave and optical regions for applications such as laser magnetic resonance (LMR) spectroscopy, tunable FIR (TuFIR) spectroscopy, plasma diagnostics, etc. A statistical summary is presented in the bar graph of Fig. 1 to give an overall picture of the distribution of 13CD3OH FIR laser lines with respect to wavenumber. The success of 13CD3OH as an excellent FIR laser medium arises from several factors, including the presence of large permanent dipole moment components along both a and b axes giving a strong FIR spectrum and liberal transition selection rules, the rich FIR and IR spectra arising from the complexity of the energy level structure due to the

-]

# ~ IAa~

0-50

50-100

100-150

150-200

200-250

250-300

>300

Wavaatm~r ia cm-I

Fig. 1. Statistical bar graph with number of FIR laser lines observed in each 50 cm- i interval.

large-amplitude torsional motion, and the excellent overlap between the CO 2 laser bands and the methanol IR absorption bands. The subject of FIR laser line assignments has been of great interest to a number of groups around the world for two principal reasons: (i) Excited vibrational state energy level structures are important from the points of view of both theoretical Hamiltonian modeling and practical understanding of vibrational energy dynamics [16]. Since FIR laser transitions occur either within an excited vibrational state or between two nearby vibrational states, observations of FIR laser lines give first-hand information about the excited states which is difficult to obtain by other means; (ii) 13CD3OH is one of the heavier methanol isotopomers hence its IR spectra are extremely congested due to the smaller rotational B-value. The situation with overlapping transitions is serious in the 13CO-stretch fundamental and has tended to limit full confidence in the IR assignments. We have benefitted greatly in the past from clear confirmation of many of our IR results arising as a by-product of the assignments of a variety of IR-pump/FIR-laser transition systems [17]. This work has continued to expand the list of FIR laser line assignments, based on the knowledge gained from the high-resolution Fourier-transform

L.-H. Xu, D. Hurtmans / lnfrared Physics & Technology 38 (1997) 357-372

( F r ) spectroscopic studies [16-23] carried out over the last several years in our group. For the present investigation, the 13CD3OH IR spectrum was revisited and a number of new systems were spectroscopically assigned. Particularly noteworthy are several systems with high-K levels a n d / o r high torsional-n levels for which the FIR laser excited-state information provided crucial clues needed to identify the corresponding weak IR subbands in the spectrum. Most of the new assignments presented in this work have been rigorously checked by forming closed combination loops with known high resolution data to confirm FIR laser assignments in some cases and to give predictions for improved FIR laser line wavenumbers in other cases. The present paper is divided into the following parts: Section 2 briefly reviews general features of 13CD3OH FTFIR and FTIR spectra; Section 3 describes the closed transition loop technique, the triad pattern of FIR laser wavenumbers, and the p u m p / l a s e r polarization relations all contributing to the detective work used for assignment and confirmation of the FIR laser lines; then Section 4 reports our 44 new FIR laser line assignments in the context of a comprehensive review of all known 13CD3OH FIR laser line observations and spectroscopic assignments, including substantial corrections to a number of literature FIR laser line assignments. Lastly, the final Section 5 presents discussion and concluding remarks concerning the difficulties in identifying the transition systems for the ~ 50% of known 13CD3OH FIR lines which still remain unassigned.

2. 13CD3OH FTFIR and FTIR spectra The torsional energy of the methanol molecule can be approximately expressed as Etor=(H°)=F(PvZ)+½V3(1-

cos3y)

(1)

where ( ) denotes an expectation value in the basis of the eigenfunctions of H °, F is the reduced rotational constant equal approximately to the inverse of the reduced moment of inertia for the methyl top (13CD3) and framework (OH), Pv is the torsional angular momentum conjugate to the torsional angle y, and V3 is the torsional potential barrier. (For the deuterated species, F and V 3 are approximately 25 c m -

365

and 370 cm -~, respectively.) The eigenvalues of H ° represent the torsional energies for A and E torsional symmetries of different torsional states n, which are then superimposed on top of the zero-order rotational energy Ero t

=

½(B-[-C)J(J+ 1) + {A - ½(B+ C)}K 2, (2)

where A, B and C are the rotational constants and K is the projection of the overall angular momentum J along the a axis parallel to the methyl top axis. (For the deuterated species, ½(B + C) and { A - ½(B + C)} are about 0.64 cm -1 and 1.71 cm - l , respectively.) The IR and FIR spectra of methanol are very rich, due on the one hand to the torsional complexity and on the other to the liberal selection rules that allow transitions both within a K energy ladder with A K = An = 0 (a-type) or between different K stacks with A K = + 1 and no restriction on the change A n of torsional quantum number (b-type). The same selection rules apply to IR transitions between different vibrational states. As well, transitions with A K >_ 1 can occur for some systems due to perturbations and level mixings arising from vibrational intermode coupling. In the course of this study, high-resolution FT spectra of J3CD3OH were recorded in various spectral regions from 10 cm -1 to 1400 cm -I under different experimental conditions. In terms of increasing wavenumber, the lower end of the FIR spectrum contains a mixture of a-type J multiplets ( J + 1 ~ J and A K = 0) and b-type A K 4~ 0 transitions within the ground vibrational state. Above the 45 c m - 1 FIR region, most of the a-type J multiplets die away ( J would be greater than 35 above 45 cm -1, since 2 B ( J + 1) = 1.28 × 36 = 46 cm - l ) and the FIR spectra then contain mainly b-type transitions within or between torsional states. Assignments of these ~3CD3OH FIR spectra are in an advanced stage with more than 10,000 lines now identified [21,22] including high K and n levels for A and E torsional symmetries. The FIR assignments in the ground vibrational state form a solid base for the confirmations of FIR laser line assignments. The IR spectrum of 13CD3OH in the 9 / x m and 10 /zm CO 2 laser regions, displayed in low resolution

L.-H. Xu, D. Hurtmans / Infrared Physics & Technology 38 (1997) 357-372

366

in Fig. 2, consists of fundamentals of the in-plane 13CD3-rocking, 13CO-stretching and symmetric 13CD3-deformation modes (denoted as V = r, co and def in the following text), as well as weaker bands of the out-of-plane 13CD3-rock and the two asymmetric 13CD3-deformation modes. Substantial spectroscopic work has been carried out for the former three stronger fundamentals [16,18,19,23], and the general features are highlighted below. For the latter three weaker fundamentals, on the other hand, there are still no convincing assignments obtained. However, as seen in Fig. 2, the CO 2 laser spectrum overlaps with all of these bands to some extent hence interest in identifying the FIR laser transitions provides a practical motivation for studying these fundamentals. At high resolution, the in-plane 13CD-rocking fundamental centered around 851 cm-1 shows parallel a-type features in R, P and Q subbranches associated with each K subband. The torsion-rotation energies for the excited in-plane 13CD3-rock have been mapped through K = 16 and 6 for the ground and first excited torsional levels (n = 0 and 1), respectively, for A and E torsional symmetries. Roughly speaking, the observed energies of the ground torsional state in the 13CD3-rocking vibration can be explained by the torsion-rotation Hamiltonian in Eqs. (1) and (2) with a large increase in the height of the torsional barrier V3. However, the increased V3 value is not consistent with the observed energy structure for the first excited torsional state of the 13CD3-rocking vibration. Here, the oscillatory energy pattern as a function of K shows a reversal of the ~" ordering of the torsional energy curves. (The index ~- cycles through the values 1, 2, and 3 as K changes and labels the torsional symmeout-of-plane 13CD3-rocking

in-plane 13CD3-rocking

tries through the relation (~'+ K) = 3 N + 1, 3N and 3 N - 1 for A, E 1 and E 2, respectively, where N is an integer.) Thus, it appears that the conventional torsional effective Harniltonian of Eq. (1) cannot be applied directly to the excited in-plane 13CD3-rocking Vibration. The CO-stretch vibrational state is where most FIR laser emissions occur for all methanol isotopomers. In contrast to the in-plane 13CD3-rocking fundamental, the strong 13CO-stretch fundamental centered at 980 cm-1 is a well-behaved a-type band with a clear R-, P-, and Q-branch pattern, as seen in Fig. 2. The fact that the Q-branch and the R and P J-multiplets are very compact indicates similar torsion-rotation energy structures for the ground and the excited ~3CO-stretch states. More than 60 subbands have been identified through K = 10 and 8 for the n = 0 and 1 torsional states, respectively, for A and E torsional symmetries, and a few weak n = 2 assignments have also been obtained. Apart from several K-localized Fermi resonances with the fourth excited torsional state of the ground vibrational state, the observed torsion-rotation energy pattern in the excited ~3CO-stretch vibration follows in general the effective Hamiltonian. The symmetric 13CD3-deformation band is located near 1111 cm- 1 with reasonably wellbehaved a-type features. The rotational B value is larger for this mode than the ground state, resulting in many intermode interactions with J-localized level crossings which lead directly to fragmentation of the spectrum. Two types of perturbations are observed in the spectrum, namely the Fermi type with mainly the fourth excited torsional state (n = 4) of the ground vibrational state and the Coriolis type with the first

a s y m m e t r i c 13CDy-deformations

/

13CO-stretching

~

s y m m e t r i c 13CD3-deformation

- ~ ~..~;. ~.~v....-_~,.~

,

,

lOP(60) - 9R(58) 13CO2 regular band , 10HP(55) - 9HR(55) CO 2 hot band ~ 10SP($5) - 9SR(53) CO 2 Ist seq. band , 10P(60) - 911(58) CO 2 regular band

, , s I

I

820 840

I

860

I

t

I

I

880 900 920 940

I

I

I

t

I

I

I

I

I

I

I

I

960 980 1000 1020 1040 1060 1080 1100 112011401160 l l S 0 c m "l

Fig. 2. L o w r e s o l u t i o n I R s p e c t r a o f J 3 C D 3 O H s u p e r i m p o s e d on the C O 2 laser s p e c t r u m .

L-H. Xu, D. Hurtmans / lnfrared Physics & Technology 38 (1997) 357-372

excited torsional state (n = 1) of the in-plane ~3CD3-rocking vibration. So far, assignments of the deformation-band subbranches have been made for K values up to 6 for A and E torsional symmetries in the ground torsional state. Although the majority of the series suffer from local perturbations, deperturbed subband origins have been obtained for the ground torsional state. These define the torsional energy pattern in the excited deformation state, and show a regular sinusoidal K-oscillation behavior similar to that of the S3CO-stretch vibration which can be modeled with a decreased torsional barrier V3 value. The out-of-plane ~3CD3-rocking fundamental is predicted to lie between the in-plane 13CD3-rocking and the strong S3CO-stretch fundamentals. A search has been conducted, but due to the weak nature of the band only one K-subband [16] has been assigned in the region and no other obvious structures have been found. The predicted band centers for the two asymmetric 13CD3-deformation bands are located between the strong ~3CO-stretch fundamental and the symmetric ~3CDa-deformation fundamental. Some series have been recognized in this region but determination of the full quantum number labelling still remains a challenge.

3. FT-spectra-assisted FIR laser assignment techniques In the general scheme of an optically-pumped FIR laser, molecules are pumped to a specific excited vibration-rotation-torsion level (n, r, K, j)v by a selective CO 2 pump laser line which is in coincidence with a molecular IR absorption line. Population inversion is then achieved relative to lower rotational levels in the excited vibrational state, where the population is very small prior to the optical pumping. Stimulated emission can thus occur between those levels with inverted populations. The FIR laser lines can be of either a- or b-type and a typical pumping scheme and the possible FIR emissions are shown in Fig. 3 with just the K and J rotational quantum numbers indicated. In a real system, the vibrational and torsional quantum numbers, V and n, would not necessarily be the same for the K - 1, K and K + 1 stacks of energy levels of Fig.

K-1

367

K

K+I

A

Fig. 3. Schematic diagram of t R - p u m p / F I R - l a s e r energy level scheme with possible FIR laser transitions.

3. The FIR radiation is linearly polarized either parallel ([D or orthogonal ( ± ) to the pump radiation depending on the sum of A Jpump and A JFt R, the J-value changes in the pump and FIR laser transitions. The rule for the relative polarizations of the pump and emission fields was stated in a convenient form by Henningsen [24] as [ even odd

A )'pump q- A JFIR = ~

~ ~

[[

±

(3)

The spectroscopic detective work involved in FT-spectra-assisted assignments for a given FIR laser system starts with a search for a coincidence between the CO 2 laser pumping line and an identified molecular IR absorption to within the pumping offset tolerance defined by the tuning range of the CO 2 laser. In the most favorable cases, this search is successful and then we can immediately apply the FIR lasing scheme of Fig. 3 to predict the wavenumbets for all of the potential allowed FIR laser lines and compare them with the observations. A predicted FIR laser wavenumber VFIR comes from a closedloop combination difference calculation in which the two vertical sides, %ump and vA, are known from our IR observations and the bottom one, v.d, is a FIR transition within the ground vibrational state. /"FIR = /}pump -{- Pa -- UA"

(4)

As the Vpump, vA and va wavenumbers are all determined from our high-resolution FT spectra, the FIR laser wavenumber VFIR can be predicted to an accu-

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racy between 0.001 and 0.005 cm - l , depending on the transition involved, of the same order as the precision of the FI" data. In more challenging cases, either the identified IR pump transition leads to loop-calculated laser predictions that do not agree with the reported observations, or else there is no assigned IR line seen at the pump position. This implies one of the following situations: (i) the IR absorption coincident with the CO 2 pump is an overlapped feature where more than one IR transition contributes to the absorption profile and the presence of the hidden pump absorption has not been realized, or (ii) the IR pump absorption is a very weak feature which has not been assigned or even observed. In both cases, identification of the FIR laser transition system can be of great assistance in untangling IR assignments in doubtful cases where line series are perturbed, strongly blended, or very weak. However, such identification is much more problematic when the pump transition is not known, hence more ingenious approaches must be used for the detective work in which clues from the FIR laser observations themselves are analyzed first. The first and most useful clue comes from the observation at the same pump offset of three related FIR emission lines, normally referred to as a triad. The three lines of the triad are labelled as L a, L b and L c in Fig. 3, and because the A K = 0 a-type lines do not vary strongly with K, their wavenumbers obey the approximate combination relation La +

L~ -

Lb =

0

for the case with A K = - 1 (5a)

L a - Lc + L b = 0

for the case with A K = + 1 (Sb)

Now in a triad, L a and L b will have the same values of A JFIR and therefore have the same polarization, while L c, the Q-branch transition in the excited state, will have the opposite polarization. Thus, observation of a triad greatly aids the FIR laser assignment since the value of A Jpump follows directly from the polarization of L c, and the J value of the upper pumped level can itself often be determined from the a-type laser emission frequency L a using the approximate relation Jupper = L a / 2 O ' ,

(6)

where B' is the excited-state rotational constant. As well, the L c Q-branch transition is sensitive to the (n, r, K) quantum numbers, and we were able to exploit this to deduce several assignments in the present study by comparing the observed L c wavenumbers against a data base of approximate excited-state transition frequencies which we calculated from our spectroscopic data as described below. In the most difficult cases, a triad of FIR laser lines is not observed and only a single FIR laser line is reported for a specific CO 2 laser pump. However, the FT spectroscopic data may still provide sufficient evidence to tie down an assignment. For example, suppose the CO 2 laser line pumps in the R- or P-branch of the 13CO-stretch band. In this event, the upper-state J-value can be estimated from our spectroscopic knowledge of the band. Furthermore, an orthogonally (_t_) polarized FIR laser line must here correspond to the Q-branch transition Lc in Fig. 3, while a parallel (11) polarized FIR laser line would have to be L, or L b. Since Jupper is known, Eq. (6) can be used to distinguish between the Z a and L b possibilities for the latter case. If the laser line is L b, then this fact plus Eq. (6) can further be used to estimate the L c wavenumber as L c = [ L b - 2 B' X J ] for the A K = - I case o r L ~ = [ L b + 2 B ' X ( J + 1)] for the A K = + 1 case. The L~ wavenumber would then allow a search for (n, r, K) candidates from our data base. On the other hand, if the C O : laser pumps in the 13CO-stretch Q-branch region, a parallel (11) polarized FIR laser line would have to be L c (Q-branch transition) and an orthogonally (_1_) polarized line must be L a o r L b. In the former case, the Q-branch wavenumber could be matched to our data base to find the (n, r, K ) identification, but in the latter case the J-value would not be determinable in the very dense Q branch so that the L~ wavenumber could not be calculated directly from L b. Thus, one would have to fall back upon a series of trials with different J-values to seek a match for the calculated Q-branch wavenumber in our data base. It is possible through persistent detective work, therefore, to follow the trail of spectroscopic clues to find a plausible FIR laser assignment scheme even for systems in which there is only a single FIR laser line pumped by an unknown IR absorption. Once

L.-H. Xu, D. Hurtmans / lnfrared Physics & Technology 38 (1997) 357-372

such a proposed assignment scheme is determined, then if one or more of the observed FIR laser lines are frequency measured we can go back and use those accurate FIR laser frequencies in combination loops in order to tie down and disentangle any doubtful IR assignments for overlapped or weak features in the spectrum. In the present work, the IR spectrum of 13CD3OH was revisited in this way, and we were able to establish a number of high-K a n d / o r high-n IR assignments with assistance from the FIR laser observations. It is clear that for the trial-and-error assignment procedures described above, a data base of predicted Q-branch origins in the excited vibrational states, (n", r", K + 1)v ' ~ (n', r', K) v' ( w h e r e ' and " denote the upper and lower states of a transition involved), is extremely valuable. For this purpose, we added our observed IR subband origins from Refs. [ 16,18,19,23] to groundstate J-independent energies calculated with the molecular constants from Ref. [21] in order to obtain torsion-K-rotation energies for the in-plane 13CD3-rocking, the ~3COstretching, and the ~3CD3-deformation vibrational states. These excited-state energies were then grouped according to ~- and fitted to a cosine function with an appropriate phase ce for each r column of the form

E(K) = a o + a ,

cos(a2K+cr ) -l-a3 K2,

(7)

where the coefficients a o, aj, a2, a 3 and a all depend on the (n, ~.)v state. Most of the ~- curves were well represented by this simple cosine function and the fitted coefficients and phase shifts were consistent with our expectations from the known constants. The curves could then be interpolated and extrapolated to determine any missing K points (assuming the absence of perturbations), and a data base of excited-state b-type Q-branch origins calculated to serve as a foundation for the trial FIR laser assignment schemes discussed above. Note that in our data base we included not only the origins for transitions within each specific vibrational state, but also for the first time we calculated the wavenumbers for Q-branch transitions between different vibrational modes. This turned out to be particularly useful in detecting several system assignments in Table 1 in which the FIR laser transitions cross over between excited vibrational states.

369

4. New FIR laser line assignments and review of current data Table 1 tabulates all previously available information from the literature as well as our new assignments for 13CD3OH FIR laser lines. The first ten columns describe the IR-pump/FIR-laser measurements, then the last five columns give the spectroscopic assignments. The IR-pump/FIR-laser information is subdivided into CO 2 pump and FIR laser sections. The CO 2 pump line, wavenumber and offset are listed first, then the FIR laser data on frequency, wavelength and wavenumber (calculated either from frequency measurements as V[cm '1 = UiMml/29979.2458 or wavelength measurements as P[cm '] = 104/A[~m] )' polarization, sample pressure, relative intensity and references are presented. The right half of Table 1 gives the spectroscopic assignments with successive columns listing the IR pump assignment, upper and lower state FIR laser quantum numbers, FIR laser polarization, predicted wavenumber from loop calculations, and literature references. By use of the FIR laser assignment techniques discussed above together with our extensive IR and FIR data sets for 13CD3OH, we have been able in this work to determine new (n, "r, K, j ) v quantum number assignments for 44 FIR laser lines, and J-assignments for 7 further FIR laser lines. These results are all indicated by " n e w " in the last reference column of Table 1. This brings the total of FIR laser line assigned for ~3CD3OH to 100, representing just over 50% of all of the observed FIR laser lines. As well, we have also corrected a significant number of mistaken FIR laser line assignments existing in the literature. Comments on these corrections and on some of the new FIR laser assignments are given below.

4.1. 10P(24) + 99 MHz pump and FIR laser lines at 35.6785 em - 1 (11) and43.8835 cm z (11) In Ref. [9], Moraes et al. assigned FIR laser lines at 35.6785 c m - l (ID and 43.8835 cm-J (][) to the (0, 2, 1, 28) c° ~ (0, 2, 1, 27) c° and (0, 2, 1, 28) c° -~ (0, 3, 0, 27) ~° transitions, respectively, with pump assignment P(0, 2, I, 29). In earlier reports [17,20], we showed using closed loops that the correct transi-

370

L.-H. Xu, D. Hurtmans / lnfrared Physics & Technology 38 (1997) 357-372

tion assignments for the 35.6785 c m - 1 (11) and 43.8835 c m - l (11) FIR lines are (0, 1, 5, 28) ~° ~ (0, 1, 5, 27) c°, and (0, 1, 5, 28) c° ~ (0, 2, 4, 27) c°. It was pointed out that the (0, 3, 0) ° and (0, 1, 2) ° levels are accidentally near-coincident, and that the corresponding ~3CO-stretching states are also in Fermi interaction with the fourth excited torsional state (n = 4) of the ground vibrational state [17,19,21]. Calculated energy values for these two states will thus have large errors if special treatment has not been implemented and FIR laser line assignments based only on such calculated energies will most likely be mistaken. 4.2. 1 0 P ( 2 2 ) - 98 M H z CO 2 pump and FIR laser line at 29.68 c m - ~ (11)

Moraes et al. proposed an assignment for the 29.68 cm -1 FIR laser line as (1, 2, 1, 26) c° ---)(1, 3, 0, 25) c° with a P(1, 2, 1, 27) pump in Ref. [9]. Our high-resolution F r assignment of P(1, 2, 1, 27) at 942.5290 cm-~ does not agree with the 10P(22)-98 M H z CO 2 laser wavenumber of 942.3800 cm -1, suggesting the above FIR laser line assignment is wrong. For the same pump offset, Telles et al. [11] recently observed a new FIR laser line at 31.95 cm-1 which we assign as an a-type transition from J = 25 ~ 24. It is very likely that the IR coincidence involves the first or second excited torsional state, which is consistent with a weak absorption feature at 942.3800 cm-1 observed in the spectrum. A P(26) pump assignment also matches with observed downshifts for the excited torsional states relative to n = 0 levels for the 13CO-stretch mode. Further evidence from Eq. (6) supporting this partial FIR laser assignment is that 31.95/25 = 1.278 cm -1, which is a typical value of 2B' for the torsionally excited 13CO-stretch vibration. Unfortunately, only wavelengths of limited accuracy have been measured for the FIR laser lines observed with the 10P(22) pump. Thus, we can not rely on these to assist us with the spectroscopy and the assignments of the other quantum numbers still remain open. 4.3. 10R(24) + 100 M H z CO 2 pump and FIR laser lines at 34.89 c m - ] (11) and 65.40 c m - 1 (_1_)

Moraes et al. in Ref. [8] gave the pump assignment as Q(1, 3, 6, 24) for this system and assigned

the 34.89 cm - l (11) and 65.40 cm -1 ( ± ) FIR laser lines to the (1, 3, 6, 24) ~° ~ (1, 2, 7, 24) ~° transition and (1, 3, 6, 24)c°-> (1, 2, 7, 23) ~° transitions, respectively. However, our Q(1, 3, 6, 24) wavenumber of 976.2388 cm-~ calculated from the observed R(23) and P(25) wavenumbers does not agree with the CO 2 10R(24) + 100 M H z wavenumber of 978.4756 cm -~. We propose here a new assignment scheme for the two FIR laser lines, with 34.89 c m - 1 (11) as (0, 3, 13, 24) ~° ~ (0, 1, 12, 24) ~° and 65.40 cm -1 ( ± ) as (0, 3, 13, 24) ~° ~ (0, 1, 12, 23) ~°. The J assignments in our scheme agree with those in Ref. [8], but our proposed Q(0, 3, 13, 24) pump is now consistent with the observed n = 0 Q-branch wavenumbers for other K-subbands. We hope to confirm this assignment scheme by locating weak IR transitions, which might be possible if the FIR laser frequencies are accurately measured. 4.4. 10R(26) + 184 M H z C O 2 pump and FIR lasers at 17.85 ( L ) , 22.37 (ll) and 40.23 ( ± ) c m - 1

Moraes et al. in Ref. [8] gave the pump assignment as Q(0, 1, 8, 14) and the FIR laser assignments for 17.85 cm - l ( ± ) as (0, I, 8, 14) c°---) (0, 1, 8, 13) c°, for 22.37 c m - 1 (11) as (0, 1, 8, 14) c° ~ (0, 2, 7, 14) c° and for 40.23 cm -1 ( ± ) as (0, 1, 8, 14) c° ~ (0, 2, 7, 13) ~°. We showed in Ref. [17] that the corrected assignment scheme should be Q(0, 2, 5, 14) pump with the two orthogonally polarized FIR laser lines going to the (0, 2, 5, 13) c° and (0, 3, 4, 13) ~° states, respectively, and the parallel polarized line to the (0, 3, 4, 14) c° state. In general, our experience with the four corrected FIR laser assignment schemes above teaches us that FIR laser assignment based solely on energy level calculations is not the right approach to take and will lead to incorrect assignments in many cases. Of course, with the help from observation of a triad, one should sometimes be able to get the J-assignment right. 4.5. 9P(48) CO 2 pump system

It is possible that the most important of the new FIR laser lines, spectroscopically speaking, will tum out to be those pumped by 9P(48) CO 2. Early on we assigned the FIR laser line at 75.19 cm -1 pumped

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L.-H. Xu, D. Hurtmans / lnfrared Physics & Technology 38 (1997) 357-372

Table 2 Assigned A ± labels to the HR laser lines according to the allowed A ± selection rules Pump R(0, 2, 8 +, 32) R(0, 2, 8 +, 32) R(0, 2, 8-, 32) R(0, 2, 8-, 32)

Frequency ( M H z ) 999676.2 1258774.6 999657.8 1258766.4

Wavenumber (cm- i ) 33.3456 41.9882 33.3450 41.9879

by 9P(48) to the (0, 2, 8, 3 3 ) c ° ~ ( 0 , 3, 7, 32) c° transition [20]. Our assignment scheme allowed us to predict wavenumbers for two more FIR laser lines not yet observed at that time. Recently, Zink et al. [10] reported frequency measurements of FIR laser lines associated with this system, and the two predicted FIR laser lines were indeed observed. More interestingly, the frequency measurements showed that the FIR laser lines at 33.345 c m - l and 41.988 c m - i are each close doublets with the splitting for the first being 18.4 MHz and that for the second being 8.2 MHz. This observed doublet structure is consistent with our assignment scheme of A torsional symmetry. It is difficult for us to provide spectroscopic data to form loops for more rigorous checking as the splitting is small and not resolved in our FT spectra. However, we can assign the A -+ labels to the FIR laser lines according to the allowed A -+ selection rules as presented in Table 2. Our proposed full quantum number assignments are consistent with the allowed selection rules, the relative FIR laser intensities observed, and the reported pump offset pattern in which the 99676.2 MHz and 1258774.6 MHz lines were stated to be pumped at the same offset which was different from that for the 999657.8 MHz and 1258766.4 MHz lines. The simplest excited-state doublet energy pattern suggested by these observations has the 18.4 MHz splitting for the (0,2,8,33) c° levels only with very little splitting, if any, for the (0,3,7,33) c° levels. The 8.2 MHz splitting of the a-type FIR laser lines would then subtract from the 18.4 MHz to give a splitting of 10.2 MHz for the (0,2,8,32) c° levels. If this were true, then the difference in pump offsets for the two pairs of FIR laser lines should also be 18.4 MHz, since there is negligible K = 8 splitting in the ground state. Unfortunately, the offsets were not measured, hence it would be interesting to investigate these to see if they agreed with our idea. In any event, this system appears to show clear splitting for

Int. 75 80 65 70

FIR laser assignment (0, 2, 8 +, 33)c° ~ (0, 3, 7-, 33)c° (0, 2, 8 +, 33)c° ~ (0, 2, 8 +, 32)c° (0, 2, 8-, 33)c° ~ (0, 3, 7 +, 33)c° (0, 2, 8-, 33)c° ---,(0, 2, 8 , 32)c°

the K = 8 levels in the J3CO-stretching state, which are the highest K energy level of methanol for which resolved asymmetry splitting has ever been observed. The source of this splitting must almost certainly be a perturbation involving widely-split doublet levels in another vibrational state, hence this system carries information which is potentially very valuable for understanding the vibrational energy manifold. So far, we have not identified a possible perturber.

5. Conclusion The present work describes the results of a reexamination of the IR spectra of the in-plane rocking, 13CO-stretching, and symmetric formation fundamental bands of 13CD3OH in order to deduce new assignments of optically pumped FIR laser transition systems. We have proposed new line assignments with full quantum numbers for 44 FIR laser lines, and partial J-assignments for 7 further lines, including a number of transitions crossing between different vibrational states. The assignments are based on a variety of spectroscopic clues, notable the comparison of observed or predicted Q-branch FIR laser wavenumbers with a new data base of approximate wavenumbers for Q-branch transitions within and between the three excited vibrational states which was calculated by fitting our spectral data for the three modes to a simple model for the torsion-K-rotation energies. In conjunction with the new results we have reviewed all known results on IR-pump/FIR-laser observations and assignments for 13CD3OH, and have compiled a table synthesizing and updating this information. Significant corrections have been made in this work to some of the previous FIR laser transition identifications proposed in the literature.

13CD3~ 13CD3-de-

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L.-H. Xu, D. Hurtmans / lnfrared Physics & Technology 38 (1997) 357-372

A reported system of particular spectroscopic interest is that in which the 9P(48) CO 2 line pumps two pairs of very close FIR laser doublets whose splittings were determined accurately by heterodyne measurements. Our assignment for this system suggests that the splittings arise in K = 8 A levels of the excited 13CO-stretching mode. This represents the highest K-state so far for which asymmetry splitting has been seen for methanol, and probably arises through a potentially very interesting interaction with an as-yet unknown perturbing state.

Acknowledgements This research was supported by the Natural Sciences and Engineering Research Council of Canada, and the University of New Brunswick Research Fund. The authors thank R.M. Lees for useful comments on the manuscript.

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