Fourier transform spectroscopy of 13CD3OH: Assignment of far-infrared laser lines

JOURNAL OF MOLECULAR SPECTROSCOPY 153, i81-196

(1992)

Fourier Transform Spectroscopy of ‘%D30H: Assignment of Far-Infrared Laser Lines LbHONG

Xu AND R. M. LEES’

CEMAID and Department of Physics, University ofNew Brunswick. Fredericton. New Brunswick, Canada E3B 5A3

I. MU~OPADHYAY Laser P~ogra~~e,

Cenire for Advanced T~h~olo~,

CAT Raj~dranagar,

Indore 452012, India

AND J. W. C. JOHNS Herzberg Institute OfAstrophysics, National Research Council Canada, Ottawa, Canada

KIA

OR6

High-resolution infrared(IR) and far-infrared (FIR) Fourier transform spectroscopic studies of r3CD30H have been applied to the identification of the IR-pump/FIR-laser transition systems associated with optically pumped FIR Iaser emission. Assignments are considered for 13 reported or proposed pump systems and are supported for most of these by rigorous closed-loop frequency ~mbi~tion relations. Three of the systems originate from Fermi resonances between C-O stretch levels and high-lying excited torsional levels of the vibrational ground state. Spectral positions have been obtained for the majority of the FIR laser lines to an estimated accuracy of ~0.001 cm-’ from spectroscopic combination differences. Q 1992Academic PESS, IW. I. INTRODUCTION

Although a somewhat unusual isotopic species of methyl alcohol, 13CD30H shares the characteristic of all its relatives of being an excellent source for optically pumped far-infrared (FIR) laser lines. On the one hand, the fundamental band of the C-O stretch mode overlaps well with the IO-pm CO, laser bands to give numerous suitable coincidences between CO? laser lines and 13CD30H infrared (IR) absorptions for efficient pumping. On the other, the presence of both parallel and ~~ndicular dipole moment com~nen~ coupled with the complex to~ion-ro~tion energy level structure in the excited state gives the possibility for FIR laser emission over a wide range of transition types and frequencies. Furthermore, 13CD30H has the distinction of yielding the second most efficient FIR laser line known, the 127-pm transition pumped by the lOP(8) CO;! laser line (1-3) and assigned earlier as the (~TK,J)~ = ( 116,17)co + ( 125,16 )‘O torsionally excited transition (4). Our ( ~TK,J)” energy level designation in this paper is the Dennison notation (5) commonly used in the FIR laser literature (6, 7). The quantum number n denotes the torsional state, T is an index labeling the A, E, , or EZ torsional symmetry of the level, K is the projection along the near-symmetry u-axis of the rotational angular ’ To whom correspondence should be addressed. 181

0022”2852/92 $5.00 Copyright 0 1992by Academic All rights of reproduction

Press, Inc.

in any form reserved.

182

XU ET AL.

momentum J, and li denotes the vibrational state. Here, we will employ v = 0 to indicate the ground state, v = CO the C-O stretch mode, and TV= R the in-plane CD3rocking mode. Levels of A torsional symmetry with K > 0 are split by the effects of molecular asymmetry, so they are given an additional + or - superscript to indicate the specific doublet component (5). Since the initial report of the strong 127-pm FIR laser line along with several others (1-J), further investigations carried out notably by the group of Sealabtin and Pereira in Brazil with Strumia in Pisa have yielded many new FTR laser transitions and some line assignments (8-10). Simultaneously, we have been investigating the high-resolution IR and FIR spectroscopy of 13CD30H in order first to identify IR coincidences with CO1 pump lines to deduce possible assignment schemes, and then to apply the powerful combination-loop technique ( 7) to their rigorous confirmation. In this paper, we present the assignments for the IR-pump/FIR-laser transition systems that we have determined so far, together with the IR and FIR spectroscopic data utilized to form confirmatory closed transition loops. We also report, as valuable by-products of the loops, combination-difference values for the FIR laser wavenumbers to the spectroscopic accuracy of +O.OOl cm-‘, which is generally substantially better than that obtained from wavelength measurements. II. THE C-O STRETCH SPECTRUM

OF 13CD30H

The Fourier transform infrared (FTIR) spectrum of ’ 3CD30H from 8 1.5 1030 cm-’ was obtained at 0.002 cm-’ resolution on the modified DA3.002 Bomem spectrometer at the Herzberg Institute of Astrophysics in Ottawa. The spectrum was recorded at room temperature at a pressure of 100 mTorr in 4 transits of a 0.5-m White cell, with a total of 16 scans coadded. A low resolution trace is shown in Fig. 1, juxtaposed with the same band for normal CH30H for comparison. The J-numbering for the individual n = 0 multiplets in the P and R branches is quite clear and was recently reported by Moraes et al. ( I I ) from a similar spectrum recorded at 0.004 cm-’ resolution. However,

(a)

(b)

WD30H

P

Q

R

CHBOH

FIG. 1. Low-resolution spectra ofthe IR C-O stretch fundamental bands for (a) 13CD30H, and (b) normal CH30H, showing the differences in width of the P(J) and R(J) multiplets.

FIR LASER ASSIGNMENT FOR “CD30H

183

it can be seen in Fig. 1 that the P(J) and R(J) multiplets are much narrower for 13CD30H than for normal CH30H. This means that there is a great deal of blending in the former and the detailed (nrK) assignment of the high-resolution structure is much more difficult for 13CD30H than for CH30H. The full 0.002 cm-’ resolution is very necessary to minimize line overlap in the centers of the multiplets for the n = 0 ground torsional transitions, and the identification of a number of heavily blended n = 0 series required painstaking detective work. Nevertheless, we feel that we now have the C-O stretch band fairly firmly under control, and will report the detailed analysis shortly in a separate communication. Of our large set of assigned IR frequencies, we utilize here only those which are directly relevant to the FIR laser assignments. The list is given in Table I. As with other isotopic species of methanol, most of the series in the n = 1 first excited torsional state are shifted downwards in J by one or more units relative to the n = 0 multiplets, so they tend to be better resolved with consequent greater ease and confidence to the assignments. Again in common with other species, certain prominent series are shifted into clear regions of the spectrum by strong Fermi resonances with high torsional levels of the vibrational ground state (12, 13). Figure 2 shows the torsion-rotation energy level diagram for i3CD30H in the region of the C-O stretch state, with the Fermi resonances highlighted. As found for CD30H (13), resonances occur for the (~TK)” = (039)‘O and (0310)co levels which appear particularly beautifully in the Q branch of the band, illustrated by Moraes et al. ( I1 ) and shown here in Fig. 3 with the assignments indicated. Some of the perturbations turn out to lead to coincidences with CO2 laser lines and thus to FIR laser pump systems, which are discussed in Section IV. III. FIR SPECTRUM OF 13CD30H

Our assignment approach for the C-O stretching band relied extensively on [R(J) differences to link the P- and R-branch series for given ( n 7K). These were obtained from two other major spectral studies conducted in parallel with this one, namely, an investigation of the 13CD3-rocking band (14), which gave reliable combination differences for the low-K n = 0 series, and a study of the FIR ground state spectrum, which gave good values for higher-K n = 0 series and for n = 1 and n = 2 series. The FIR assignments were essential in order to close the 4-member transition loops used to tie down the FIR laser line identifications discussed in the next section. The FIR spectrum was recorded at the Herzberg Institute at 0.002 cm-’ resolution in the range from 20-220 cm-‘. It consists largely of b-type & branches with their associated strong ‘R or pP branches, distributed more or less randomly throughout the entire range. The problem of line overlap is less severe than for the IR C-O stretch band, except for the origins of low-K An = 0 Q branches, and the assignments presented little problem apart from the considerable time required to organize and catalog the thousands of frequencies involved. The detailed FIR spectral analysis will also be presented elsewhere, so again we have included in Table I just those wavenumbers important to the FIR laser assignments. - P( J + 2)] ground-state combination

IV. FIR LASER ASSIGNMENTS FOR “CD,OH

To date, we have applied our spectroscopic data to the identification and confirmation of 13 reported or proposed IR-pump/ FIR-laser transition schemes. The results

184

XU

ET AL.

TABLE Infrared and Far-Infrared System lOP(26)+84MHz

(#l!

lOP(24)+

20.5 MHz

1x21

lOP(24)+99MHz

w31

Label

Spectroscopic

Data

IR Transition

I

(in cm-’ ) for uobs

Label

FIR Transition

58.16482 95.19018

P

(l16,28)co -

(l16,291°

938.69390

a

A

(ll6,28)=' +

(116,27j"

1011.56799

b

(116,29)0 -

B

(116,27)CO-

(116,28)O

940.16560

c

(l16,27)co -

(116,26)O

1010.49006

d

D

(125,28)CO+

(125,29)0

939.38441

e

E

(125,28jco -

(125,271°

1012.16427

F

(125,27)c0 -

(126,28)O

940.85899

G

(125,27)CO -

(125,26)0

1011.09836

9

1671

(125,28)O

58.11546

(116,28)0 +

(125,27)O

93.87046

(116,27)0 .- (125,27)O

58.07097

(116,27)0 +

(125,26)"

92.55508

(116,26)0 +

(125,26)O

58.03026

46.45000

(l18,27)co +

(ll8,28)O

940.54743

a

(II 8,28)O +

(127,28)0

(ll8,27)CO +

(118,26)O

1010.96770

b

(118,28)0 +

(127,27)O

82.19431

B

(ll8,26y=' +

(118,27)O

942.02422

(118,27)0 +

(127,27)0

46.34390

c

(118,26)C'J+- (118,25)"

1009.88400

d

(118,27)0 -

(127,26)0

80.81600

D

(127,27)co +

(127,28)O

940.78010

e

(118,26)0 +- (127,26)O

46.24607

E

(127,27)CO -

(127,26)0

1010.99519

(118,26)'J .- (127,25)0

79.44690

F

(127,26)co -

(127927)"

942.26188

9

(118,25)0 -

(127,25)0

46.15675

G

(127,26)co +

(127,251°

1009.93624

P

(Olf1,28)~O-

(015,29)O

940.55166

(015,30)0 *

(024,29)0

46.64000

A

(O15,28)co +

(Ol5,27)O

1013.54869

(015,29)0 +. (024,28)O

45.34977

B

(015.27)CO -

(015.28)0

942.00954

(015,28)0 +

(024,27)O

44.06079

c

(O15,27)co -

(016,26)"

1012.45650

(015,27)O +

(024,26)"

42.77295

D

(024,27)CO -

(024,28)"

942.01820

(124,30)0 -

(015,30)0

167.99563

E

(024,27)CO -

(024,26)0

1012.43982

(124,30)0 .- (O15,291°

206.40719

(024,28)CO .- (024,27)O

1013.52600

9

(124,29)0 +

(015,29)0

168.11003

940.55700

h

(124,29)0 -

(015,28)0

205.24600

w51

lOR(24)+126MHz

(116,28)0 -

P

:7MHz

WI

(125,28)"

uobs

A

(024.28Jco -

(024,29)O

k

lOP(8)

FIR Laser Systems

(116,29)0 .- (125,29)“

G

lOP(l6)-

“CDjOH

(124,28)0 -

(015.29)o

131.08232

(124,28)0 t

(015,28)O

188.21869

(124,28)0 +- (015,27)0

204.07976

(124,27)" t

(015,28)O

132.46204

(124,27)" -

(015,27)"

168.32261

(124,27)0 +- (315,26)0

202.90846

(O13+,23)co +

(013+,24)"

947.74104

(013+,24)"

+

(022+,23)"

31.48549

(O13+,23)C0 -

(013+,22)O

1008.03247

(013+,23)0

+

(022+,22)0

30.20457

(013+,22)C" +

(Ol3+,23)"

949.16859

(013+,22)0

-

(022+,21)0

28.92230

(O13+,22)co +

(013+,21)O

1006.90105

(013+.24)0 +

(013+,23)"

30.78500

(022+,22)co +

(022+,23)0

949.22004

(013+,23)0

-

(013+,22)O

29.50000

(022+.22p

(022+,2l)o

1006.94831

(013+,22)0

-

(013+,21)0

28.22620

(022+,23)0

.- (022+,22)0

29.50387

(022+,22)0

+- (022+,21)0

28.22401

+

P

(116,17)CO *

(116,18)O

A

(l16,17)C" +

(116,16)O

B

(116,16)C~+

(116,17)0

954.54559 999.33595 955.94809

c

(116,16)Co+

(116,15)O

998.18185

(116,17)" -

(125,18)O

79.56249

D

(125~16)~~ -

(125,17)O

956.67074

(116,16)0 +- (125,16)0

57.80635

E

(125,18)co -

(125,15)O

998.88370

F

(125,17)C'J+

(125,181"

955.26712

G

(125,17)co +- (125,16)O

1000.03338

P

(019,24)CO +

(019,24)0

A

(019,23)Co+

(019,24)"

(116,18)" *

(125,18)"

(116,18)~ +

(125,17)0

57.83095 80.85205

(116.17)'J +. (125,17)0

57.81774

(116,16)“ +- (125,15)O

78.27458

(116,15)0 -

(125,15)0

57.79685

978.47849

(019,25)0 +

947.90215

(019,24)0 (019,23)” (028,23)0 (028,24)0

(028,24)‘J (028,23)0 (028,22)0 (028,22)” (028,23)‘J

59.23488 57.96975 56.70373 29.46821 30.74525

B

(ol9,24)CO -

(019,23)O

1009.20953

C

(019,24)CO+

(019,25)O

946.46642

D

(019,23)CO +

(019,23)0

978.63600

E

(028,24)CO +- (028,23)0

1009.19301

F

(028,23)co +

(028,24)O

947.86572

G

(028,23)CO t

(028,221"

1008.07760

9

+ + +-

FIR LASER ASSIGNMENT

FOR

‘3CDPH

185

TABLE I-Continued system

Label

10R(26)+ 184,MHz

P

we1

A 0 c 0 E F G n

lOR(26)-20 MHz I#91

P A 0 c D E F G H

10R(26)+182MHz WOI

I#121

997.64585 998.46468 961.84579 960.47108

(025,14)Co c (025,13)O (025,13)=+ (025,121"

997.67093 996.48331

(038,12)CO+ (038,12)" (03e ll)Co* (038,12)0 (03e:tt)CO * (036,ll)O (038,12)Co .- (038,13)" (038,12)'= - (038,11)* (017,12)C* +. (01?,11)* (017,32)cO - (017,12)O (017,il)C~ * (017,ll)~ (017,tl)co * (017,12)* (017,ll)C~ - (017.10)*

979.70428 964.39493 979.78516

FlRTranstHon

a b c d

(025,15)0- (034,15)0 (025,14)0.- (034,14)0 (025.13)O.- (034,13)" (025,12)0t (034.12)O (025,16)O+ (034,14)O (025,14)0+- (034,13)"

U0b-s

g

22.32913 22.33967 22.34817 22.35484 41.57990 40.30742 (025,13)0+ (034,12)O 39.03274

a b c

(038,13)0+ (017,12)0 38.19813 (038,12)*+- (017,11)" 36.91824 (038,lt)Q.- (O17,10)" 35.63827

8

t

963.03208 995.09645 995.29939 979.90758 979.96600 964.59423 994.09731 a b c

(0310,12)~.- (019,12)0 26.04192 (0310,12)Qt (019,11)~ 4t.43074 (0310,tt)~* (0l9,ll)Q 26.04510

c

(0310:10)c~ +- (0310,11)~ (0310,1l)C~ +- (0310,12)" (019,lO)C~ + (019,ll)~ (019,1t)~* * (019,ll)~ (019,ll)~~ 4- (019,lOf~ (01!3,11)c* * (019,12)0 (OlS,iO)~~ + (019,10~~ (ot9,io)co c (019,9)~

966.89528 965.53411 966.01438 960.04724 994.15532 964.65875 980.12203 992.94785

d

(0310,ti)~+ (O19,10)" 40.15262 (0310.10)~+- (019,10)* 26.04606 (0310,lO)~* (019,9)~ 38.87401

967.70928

a b

P A 6

E F

v131

(034,13]cO+ (034,12)0 (025 13)Co+ (025,14)* (025:14)=' .- (025,15)0

979.71156 960.42702 981.80239

Label

(0310 t1p + (0310,tt)o 980.92006 (03to:ttp +- (0310,10)~ 995.02449 (0310 top +- (0310,~O)~ 98O.SSSSS

c D

10R(46)+17MHz

(025,14)Co +..(025,lrl)O (034,¶4)C* + (034,15)~ (034,13)CO +- (034,14)0 (034,14)CO c (034,13)0

uobs

P A B D E F G H

lOR(8)+61 MHz

IR TransItIon

P A 3 c D E F G H

(039,S)"O + (039,101~ (039,9)CO +- (039,9)0 (018,8)c* + (018,8)C" + (018,8p + (Ote,s)C* -

(Ot8.W (018,91° (Of8,8)~ (018,S)Q

(018,S)CO +- (Ot8,tO)0

980.53438 968.67267 991.70250 980.21820

8 f

23.67415 36.50180 23.67695 35.22187

c d

(039,tO)~.- (018,tO)o (039,tO)O+ (018,9)" (039,s)~+ (OlS,S)Q (039,S)Q+- (Oi8,8)"

9 h

(125,10)*+- (Ot6,tt)" 150.65715 (125,lO)o+- (Ot6,tO)" 164.76987 (125,lO)Q- (Ot6,9)O 177.60024 (125,9)*+ (Ot6,tO)* 151.97113 (125,SfO.- (Ot6,9)* 164.80107 (125,8)"+ (Ot6,S)O 153.28089 (125,8)*- (Ot6,8)" 164.82900 (125,7)Oc (016,8)0 154.68846

980.15737 967.32948

(125,S)c" +. (12.C1,9)~ 990.62020 (125,B)Co +- (125,7)O 989.40889 (t25,9)COc (125,tO)" ~6.30099 (1256)Co+ (125,9)O 967.64812 (016,~O)C~ * (016,9)0 992.86516 (016,lO)Co + (016,11)9 965.92260 (016,lO)C" +- (016,lO)~ 980.03515 (016,S)Co - (O16,tO)" 967.27191 (016,S)Co +- (016.9)" 980.10267 (016,9)cO+ (Ot6,81° 991.65050

-

are collected in Table II, with IR pump and FIR laser line assignments given along with our best values for the wavenumbers of both observed and predicted FIR lines. The confi~ato~ evidence and loop combination relations on which the assignments are based are discussed for each of the systems individually, as follows.

186

XU

ET AL.

1150

V=O,rl=4

V,,=l,n=O k 0 c ;; $ & I:

1050

V=O,n=3

s .3 L g

6 .2 e

V,=l,n=O

9%

0

4

2

6

a

10

K Values

FIG. 2. Torsion-vibration energy levels for “CD,OH, levels and n = 4 levels of the vibrational ground state.

1. lOP(26)

highlighting

-

T’I

-

i=2

-

r-3

12

Fermi resonances

between C-O stretch

+ 84 MHz

A small peak appears in our FTIR spectrum offset by 169 MHz from the lOP( 26) CO* laser line, somewhat higher than reported for the FIR laser pump transition (8). We have assigned this as the P( 116,29) transition and believe that it is the pump absorption for the 35.5 cm-’ laser line L,, although this is still somewhat tentative. With our (116) and (125) IR assignments plus the ground state (116)O + (125)O FIR series, we can construct the loop diagram of Fig. 4a. The wavenumber of line L, is given from three independent loop relations as

I 97850

I I 978.70 97890

I I 979.10 97930

I 97950

I 97970

I 97990

I 98010

FIG. 3. Upper part of the Q-branch of the C-O stretch fundamental labeling for the Fermi-shifted (nsK) = (039) and (03 10) series.

I 98030

I I 980.50 98070

I 98090

band of 13CD30H, showing

I 981LO the J-

187

FIR LASER ASSIGNMENT FOR ‘3CD3CWI TABLE II Assignments of FIR Laser Lines in ‘3CD30H OpticaIIy Pumped by a CO2 Laser -I me System CO2+Offs@ IRAbs0fplioii FtR LaserTmmtttaP Ret %tJs [u in cm-‘]

Pa 11

1% in cm-l]

lOP(26)+54MHt

P(116,29)

Lab@

(116,26)'= --t (lt6,27)=

938.69390

938.69106

Cal

(nYK’.J’)’ -+ (~“x%“,J”)~

La

-+ [(125.28)=']

lOP(24)+ 20.5 MHz

[l,4,8]

X3 181

940.54878

lOP(24)+SS

940.54743

MHz

34.37368

(127,27)=

Lb

46.16938

I

46.21796

-_) (127,26)m

Lc

60.45052

II

80.47911

k

35.53029

II

35.67631

21

43.75027

II

43.88253

(118.26)Co

(OlS,ZB)CO -_) (015,27)w

940.55166

940.55140

-_) (024.27)C"

w [Ill

f4

--f t(o24.28m #4

tOp~~.~~MHz

ISI #S fl.41

?o~(t6)-17

MHz

t1:4,

X7 [Q]

18 [Ql

#9

fW

954.54509

lOR(24)+126

/I

35.65818

(013+,23)" -_) COl3+,22)=

b

29.367656b

I/

29.35753

-+ (022+,22)=

Lb

~.006484b

I\

30.00649

(116,17)CO --t (116,18)"~

b

21.60761

[II]

21.63182

--t (125,16)‘=

Lb

7";7';;;gb

It

78.72686

+

Lc

P(Ot3+,24)

954.54559

MHz

978.47649

lOR(26)+ 164MH.z 979.71156

iOR(26)-2UMHz 979.70475

(125,17)c"

978.47649

CI(025.14)

0(038.12)

1

Lb

27.22570

II

27.25264

+

(02823)Co

Lc

57.67013

1

57.83552

L,

17.64756

1

17.86575

Lb

40.22528

I

40.24874

22.37136

II

22.37319 [15.309821

21.s?%‘ob

I4 [II]

+

(034,13)~

+

(034,14)co

Lc

(038,12)CO -+ (038,ll)CO

lbl

979.704284

A

#II

ft.81

#I2

lOR~28)+182M~ 980.91928

lOP(42)+5MHz 922.91446

+

b Lc

(017,12)m

lOR(8)+61

MHz

967.70928 X13

lOR(48)+17MHr 990.62020

36.52301

ff(O310,lt) 980.92006

I: 4

P(l21.14)

(121,13)R +

922.91466

P(O39,lO)

(121.12)R

990.62020

36.63619

w

[14.02464]

Ill1 .L

40.950612

16.53ltl

II

67.43086

i

(n"t"K",t3fAWD

+

(n"r"K",12)Aelm.D k

83.96306

I[

+

(n"r"K".t3)"'

Ld

53.43308

1

+

(012,14)Co

L0

132.18771

(125,9)C" --t [(t25,W'] --* f(016,lo)y --)

K01a,91mI

21.32288

I

+

--f rcOt8,8w

R(125.6)

La Lb

40.89980

[26.91748]

t6.54881

II

;z

f4 Ill1

P-al lb1

Ill1 fill

[151.03584]

Kc1

[I]

[t 61.79866)

(039,ll)C~ -_) [(ot8,9)y

967.70928

57.10866

(028,24)='

-_) (017,ll)~ X10

30.53435

+

(025,14)CO --f (025.13)C"

979.71156

b

W

30.57393

(019.24)CO -_) (Ot9,23)co

0(019,24)

LE.222741

35.62903

(023.28)=' -_) (023.27)"

P(ll6.16)

lOP(8)

[93.02490]

b

Pt023.29) 940.54271

947.74104

947.74141

35.60289 [57.47450]

1)

+

P(O15,29)

If

Wats pm-?]

34.36426

(116.27)=' +

P(118,26)

35.50380

PO1

[bl s-cl h

-+ [(125.27)"] t2

[cm-‘1

[24.05364] 135.538371 [11.45194]

n Transitions in brackets are predicted. b Precise heterodyne frequency measurement from Ref. f I ). L, =

P + b - c - B = 35.60302 cm-’

=A-t-e-d-B=35.60290cm-’ = A + f - g - C = 35.60275 cm-‘. The system assignment could be solidified by observation of the other two potential F?R laser lines, [I+( _I_)] and [ I,,( II)], at wavenumbers given from the foilowing loops: [Lb] = P + a - D = 57.47431 cm-’ = A + e - E = 57.47469 cm-’

[LJ = P + b - F = 93.02509 cm-’ = A + f-

G = 93.02471 cm-‘.

188

XU ET AL.

(a)

(b) 26 27

27 26

J 27 26

V,,=l C 10 P(26)

10 P(24) + 20.5 MHz

64ilHz

.29

-

26

_-

27

26

-

26

27

-25

-

:l1 6) 26

(12 5)

(n7 K)

,26

vo=o

-

26

-27

(1 1 6)

25

(12 7)

(nT K)

FIG. 4. Energy level and transition diagram for the ‘%ZD30H FIR laser system optically pumped by (a) the lOP(26) + 84 MHz, and (b) the lOP(24) + 20.5 MHz COz laser lines.

We should note that the internal consistency of the FIR laser wavenumbers calculated from independent loops, to within the loop accuracy of about kO.00 1 cm-‘, is strong confirmation of the correctness of the IR and FIR spectroscopic assignments in Fig. 4a. However, with just a single reported AK = 0 u-type FIR laser line for this system, one cannot be absolutely sure if the P( 116,29) IR transition is indeed the right pump for line L,,because the frequencies of a-type transitions are not strong functions of the ( n TK) quantum numbers. 2. lOP(24) + 20.5 MHz The FIR laser lines L, and L, were initially reported as belonging to the lOP( 22) CO2 pump (I), but this was revised to the 10P( 24) line in a careful reinvestigation of the 10P(22) and lOP( 24) systems (8). In this later study, one new FIR laser line was observed with the lOP( 22) pump, while five lines were observed with lOP( 24), including the two previously attributed to the 10 P( 22) pump. One of the new FIR laser lines, Lb, was observed at the same offset as L, and L,, and satisfied the frequency and polarization rules for a triad of emission lines, namely, L, + Lb a L,, with L, and L, having the same polarization and Lb the opposite ( 15). The triad was assigned by Pereira et al. with the pump being the P( 1 l&28) torsionally excited transition (8)) so that the partial J-numbering proposed earlier (4) was correct. The assignments are now confirmed with well-determined spectroscopic information. Some discrepancy again exists in the offset, as our FTIR data give - 17 MHz rather than the reported +20.5 MHz. However, the polarizations and wavenumbers agree well with the scheme in Fig. 4b, and the numerous loops that can be formed leave no doubt about the line identifications, as shown in the following examples:

FIR LASER ~SI~NMENT

L,=

P+b-c-B=34.37362cm-’

189

FOR 13CD30H

Lb = P-i- a -D

= 46.21733 cm-’

= A + f - g - C = 34.37385 cm-’

= A + e - E = 46.21858 cm-’

= A + e - d - B = 34.37355 cm-’

L, = P + b - F = 80.47986 cm-’ = A + f - G = 80.47836 cm-‘.

It should be noted that although the lOP( 24) frequency lies right in the middle of the n = 0 P( 29) multiplet, the assigned pump coincidence is actually with the P( 118,28 ) absorption. This iliustrates the general downward shift observed for the TV= I levels in the C-O stretch state, and underlines the caution needed when dete~ining the Jnumbering for torsionally excited transitions. 3. lOP(24) + 99 &!UY.z From the FTIR assignments, the lOP( 24) CO2 line turns out to be in coincidence with the (015 ) series also, in this case the P( 0 15,29) transition at an observed offset of 106 MHz. The wavenumbers of the two FIR laser lines L, and Lb identified in Table II indicate that the third AJ = 0 emission line of the triad should be around 8.22 cm-‘, in good agreement with our calculated (0 15)O + (024)O ground state Qbranch origin. Within our FIR spectral range, we could only obtain the R branch for this tmnsition, so needed the extra data from our ( 124)O + (0 15)O a~gnmen~, as shown in Fig. 5, to construct combination loops for confirmation. More precise FIR laser wavenumbers for L, and Lb can be obtained from the following loops:

‘27

J 2827vco=

1

i 0 P(24) 99+MHz

30 29 26 27

-26 (0 1 5) (n 7 K)

FIG. 5. Energy level and transition diagram for the ‘%DsOH FIR laser system optically pumped by the lOP( 24) + 99 MHz COz laser line.

190

XU

ET AL.

L, = P - g + h - B = 35.67809

cm-’

= P-i+j-B=35.67849cm-’ =A-k+j-B=35.67808cm-’ = A - m + I-

B = 35.67858

= A - m + n - C = 35.67804 Lb = P + b - D = 43.88323

cm-’ cm-‘.

cm-’

=A+d-E=43.88182cm-’ = P - i + k + d - E = 43.88223

cm-’

= A - k + i + b - D = 43.88282

cm-’

The residuals between the observed FIR laser wavenumbers obtained from the measured wavelengths and those calculated from the FTIR loop combination differences are about 0.14 cm-‘. This is consistent with the typical FIR laser wavelength measurement accuracy of a few tenths of a percent. With our extensive loop diagram, we can predict the third FIR laser wavenumber associated with this system from the following five loops, [L,] = P - g + h + c - F = 8.22242 cm-’

= P + e - f+

a - G = 8.22310 cm-’

= P-i+j+c-F=8.22282cmp’ =A-k+j+c-F=8.22241cm-’ = A-m+/+c-F=8.22291cm-‘,

which give an average wavenumber of 8.22273 cm-‘. 4.lOP(24)

- 141 MHz

A third coincidence with the 10 P( 24) CO2 line is the P( 023-,29 ) absorption, at an observed offset of about - 155 MHz. For pumping at this offset, one FIR laser line was reported. We assign it as the (023-,28 )‘O + (023-,27)” a-type emission, which is consistent with both the FIR laser wavenumber and its polarization. 5. lOP(16)

- 17 MHz

This is one of the systems assigned speculatively by Mukhopadhyay et al. (4). With our FTIR information, we confirm their identification of the P( 013+,24) absorption at 947.74104 cm-’ as the pump line, at an observed offset of -28 MHz. The wavenumbers of the two FIR laser lines that have been reported (1) were both measured precisely, so provide good checks of the combination loops. In our FIR spectrum, the R branch of the (013’)O + (022’)O transition has been assigned, as well as the atype (013’, J+ 1 f .J)O and (022’, J+ 1 + J)O transitions all listed in Table II. The loop defects including the accurate FIR laser wavenumbers from Table I are 6, = L,-P-d+B=0.00021 d2 = L, -A

- f+

cm-’

C = 0.00004 cm-’

I& = Lb - P - a + D = -0.00001

cm-’

& = Lb - A - c + E = 0.00002 cm-’

FIR LASER ASSIGNMENT

FOR

t3CD,0H

191

~S=Lb-L,-L3-b-h+E=-0.00003cm-‘. These very small loop defects not only support the FIR laser assignments, but also confirm the IR and FTR assignments associated with this rather complicated system. 6. lOP(8) The famous 127”pm FIR laser line, the second most efficient known (1, .3), is produced under 10P( 8 ) CO2 pumping. The ( 116,17 )‘O * ( 12516 )co assignment for this line was initially proposed by Mukhopadbyay et al. (4). Both the ( 116) and (125)IR~~esandthe~R~l16)co + ( 125 )O ~signments related with this system are clearcut, so that we can construct the loops needed for definitive confirmation of this important FIR laser system. The accurate wavenum~r measurement for the 127pm FIR laser line agrees with our small loop defects shown below, &r = L~-~-b+~=O.~O6cm-’

lj2 = Lb -A

- S-l- E = 0.00013 cm-“.

The u-type emission L, here should have parallel polarization, as indicated in brackets in Table II, while the third line L, in the triad has perpendicular polarization (3). Loop-improved wavenumbers for L, and L, are given by L,=P+b-c-B=21.63181cm-* = Aff-g-C=21.63183cm-’

L, = P + a - F = 57.10942 cm-’ = A + E - G = 57.10892 cm-‘.

The self-consistency of the assignment scheme is demonstrated by the small defects of the loops above, which include the precise laser wavenumber Lb, and also of a number of closed loops inde~ndent of the FIR laser line: 6,= P-A-e+G-F+a=O.O0050cm&= P-A-~+E-D+b=O.~OO7cm-’ 2j3= B-C-g+E-D+c=O.O0009cm-‘. The ofBet of the P( 116,18) pump absorption from the 10 P( 8) CO2 laser wavenumber is given spectroscopically from our Bomem peak-finder output as 15 MHz, compared to the zero offset reported f I ).

The lOR( 24) CO, line lies in the Q-branch region of the C-O stretch band, suggesting that the pump very likely belongs to a Q-branch transition. A triad of FTR laser lines at the same offset was indeed reported having polarizations consistent with a Q-branch pump, namely L, and L, being perpendicular and Lb parallel. The J-numbering for this pump could be inferred from the ratio L,/2Bco, taking Bco M 0.638 cm-‘, which is close to an integral value of 24. Next, the 27.22 cm-’ wavenumber for Lb agreed well with our calculated FIR Q-branch origin for the (0 19)O + (028)O transition of 27.33 cm-‘, thus giving the complete system assignment in Table II. We reexamined the condensed Q-branch region of our spectrum and were able to find the coincidence between the lOR( 24) CO2 pump and the Q( 0 19,24 ) absorption. The fR measurements are quite extensive for both the (0 19 ) and the (028 ) series. The ground state values a, b, and c in Table I are from direct FIR observations, while d and e are obtained as differences from the ‘3CD3-rocking band measurements. Loop relations determine the three FIR laser wavenumbers as

192

XU ET AL.

L, = P - A = 30.57434 cm-’

= B - D = 30.57353 cm-’

Lb = P + b - E = 27.25323 cm-’

= B + c - d - E = 27.25204 cm-’

and L, = B + c - G = 57.83576 cm-’

= P+b-e-F=57.83527cm-‘. As seen in Table II, the loop wavenumbers for L, and Lb are reasonably close to those calculated from their wavelength measurements. However, the discrepancy in L, is significantly larger at 0.17 cm-’ , for which we have no explanation for the time being. 8. 10R(26)

+ 184 MHz

This is another system in which the pump overlaps with the Q branch of the C-O stretch band. The reported triad in Table II for the pumping at 184 MHz offset has perpendicular polarization for lines L, and Lb and parallel for L,, proving that the pump indeed is a Q-branch transition. The L,/2Bco ratio gave the upper pumping level as J = 14, and the wavenumber of LC suggested the (025)‘O + (034)‘O transition as the Q-branch FIR laser line. Our IR and FIR assignments in Table I confirm this energy scheme, with four different combination loops for laser line L,: L, = P - E = 17.86577 cm-’

= F + e - b - E = 17.86552 cm-’ = G + c - f - E = 17.86589 cm-’ = G + g - d - H = 17.86552 cm-‘. For each of Lb and L,, three independent loops can be formed: Lb = P + b - B = 40.24884 cm-’

L, = P +

f - C = 22.37313 cm-’

= F + e - B = 40.24859 cm-’

= F + a - A = 22.37319 cm-’

= G + g - D = 40.24879 cm-’

= G + c - C = 22.37325 cm-‘.

9. 1OR (26) - 20 MHz One of the interesting features of the FIR laser emission in methanol is the contribution of Fermi resonances to the production of the FIR laser lines. In the case of the closely related CD30H isotopic species, no less than six of the IR-pump/FIR-laser transition systems were found to involve Fermi-shifted levels (12, 13, 16). We have observed similar behavior for 13CD30H with three of the Fermi-perturbed states highlighted in Fig. 2, namely (038)“, (039)“, and (0310)co, all participating in FIR lasing systems. In the first of these, Fermi interaction between the (038)‘O and (438)O states shifts the former appreciably downwards by about -0.166 cm-‘. This makes the FIR laser wavenumber Lb, 2 1.32357 cm-‘, quite consistent with the calculated Q-branch origin of 2 1.53574 cm-’ for the (038)O + (017)O transition, in the scheme of Table II. This Q-branch assignment would give parallel polarization for Lb, which has not been reported previously. Another piece of supporting evidence is the newly observed FIR

FlR LASER ASSIGNMENT FOR “CD30H

193

laser line at 36.52301 cm-’ with perpendicular polarization at about the same pump off&et ( 9). The assignment of the accurately-rne~u~d FIR laser line Lb can be confirmed by the small defects for loops including the iaser wavenumber itself: 6’ = Lb - P - b -t E = 0.00044 cm-’

J2 = Lb - C - a + F = 0.00094 cm-’

A better wavenumber for L, is given from three independent loops as L, = P + b - G = 36.63652 cm-’ = C + a - H = 36.63598 cm-’ = D + c - I = 36.63641 cm-‘. A third FIR laser line associated with this pump would be [La], with perpendicular polarization. Its wavenum~r is predicted to be [L,] = P-

A = 15.30935 cm-’

= D -B

= 15.31029 cm-‘.

This is one of the pumping systems which have been reported very recently ( 9). The IR pump transition is assigned as Q( 0310,11), the second line in the Fermishifted 10 A Q-branch shown in Fig. 3. The pump coincidence with Q(03 10,ll) and the reported perpendicular polarization of the FIR laser line L, suggest that the Qbranch laser emission in the excited state should be around 26.9 cm-‘, about 0.9 cm-’ higher than the calculated ground state Q-branch origin for the (03 1O)O f- (019)’ transition. This is consistent with the upward Fermi shift seen in Fig. 3, further supporting our FIR laser assignment scheme in Table II. For this system, both the 10 A and 9 A IR series and the FIR (0310)’ + (019)’ transitions are spectroscopically well determined, so we have extensive loops to confirm the FIR laser line L, and to predict the wavenum~rs for the other two potential FIR laser lines in the triad. Line [LJ should occur at 14.02464 cm‘.’ with perpendicular polarization and [Lb] at 26.9 1748 cm-’ with parallel polarization. Sample loops are [La] = P - C = 14.02478 cm-’ = A - B = 14.02450 cm-’ and [Lb] = P + c - F = 26.91792 cm-’

L, = P + c - E = 40.95078 cm-’

= P+d-G=26.91736cm-’

= P + d - I = 40.95065 cm-’

= A + e - G = 26.91723 cm-’

= A + e - I = 40.95052 cm-”

= L) + a - H = 26.91728 cm-’

= A + f-

= D+b-F=26,91761cm-’

= D + b - E = 40.95047 cm-‘.

J = 40.95065 cm-’

II. Tentative Ass~~ments for the IOPf42) + 5 MHz System The 10 P( 42) CO, laser line is located in between the ‘3CD3-rocking band and the C-O stretch band. With evidence from other n = 1 series in the ‘3CD3-rocking band

194

XU ET AL.

( 14)) we assign the coincident IR absorption as the P( 12 1, 14)R transition from the ground state to the 13CD3-rocking state. Our observed frequency is offset by 12 MHz from the COZ laser pump. This assignment is consistent with the observed triad of FIR laser lines I;,, Lb, and L,, both as to the a-type frequency L, and the polarizations of L,, Lb, and I;,, so that the ~-numbe~ng is pretty certain. However, it seems that the only possibfe lasing levels for Lb and L, to reach belong to the asymmetric i3CD3deformation state. Unfortunately, we do not yet have enough assignments for that IR band to provide any confirmation of this possible scheme, so it remains distinctly tentative. In analyzing the C-O stretch band, we found a local shift around the (0 12,14)” level, which seems likely to have introduced the chance for the FIR laser line L, observed in this system, according to our approximate calculated energies. We have di~culty in checking this assignment too, because the ( 12 1)O +- (Of2)0 FIR series is calculated to be very weak and its origin is located in a very crowded spectral region. Thus, this FIR assignment is still missing from our list. Furthermore, the (012)O state is accidentally nearly degenerate with the (030)’ state, leading to large level perturbations, and we do not have any FIR assignments which link to the (012)O state in order to form combination loops. 12. Predicted 1ORf??) -I-61 MHz System One of the advantages of detailed spectroscopic analysis in the C-O stretch band is the discovery of more possible coincidences between IR absorptions and COZ laser pump lines (11). We can propose two such potential pumping systems from our present spectroscopic information. In the FTIR spectrum, there is a clear absorption peak at about 6 1 MHz offset from the 10R( 8) COZ laser frequency, as was also noted by Moraes et al. ( 11) . We assign it as the P(O39,lO) transition, which has its upper level in Fermi resonance with the n = 4 excited torsional state of the ground vibrational state. Therefore, it would be a very good candidate for pumping new FIR laser lines. According to our energy scheme, the 10 R( 8) CO* laser line should pump two such lines, [L,] and [Lb]. The poIarization of [L,] would be perpendicular and that of [Lb] parallel, and their wavenumbers are given by the loops below, [Lo] = P + a - F = 24.05395 cm-’

[Lb] = P -I-b - B = 35.53841 cm-’

= P + h - E = 24.05371 cm-’

= A -t c - B = 35.53866 cm-’

= A -b c - E = 24.05396 cm-’

= A + d - L3 = 35.53805 cm-i

= A t- d - C = 24.05375 cm-‘. The mean predicted wavenumbers are 24.05384 cm-’ and 35.53837 cm-’ for [Ln] and [Lb], respectively. 13. Predicted 1OR(46) f 17 MHz System The lOR( 46) CO2 laser Iine is in coincidence with a line appearing at 990.62020 cm-’ in our spectrum and at 990.62068 cm-’ in the spectrum of Moraes et al. (II ): which we assign as the torsionally excited transition R( 125,8). The potential FIR lasing routes are through a-type emission to the ( 125,S)” level and b-type to the (016,9)” and (01610) Co levels. There will be no AK = ~1 b-type lasing to other n = 1 excited torsional levels since the ( 125)O state is at a local energy minimum. The

195

FIR LASER ASSIGNMENT FOR “CD30H

proposed pumping scheme in Table II predicts three potential FIR laser lines at wavenumbers each derived from four independent frequency loops: [La]=

P+g-h-A= = P+ f-

e-

= B+b-d-C=

11.45185cm-’ C= 11.45190cm-’

[Lb] = P + f-

D = 151.03593 cm-’

= B + a - E = 151.03554 cm-’

11.45161 cm-’

= B + b - F = 151.03571 cm-’

= B + c - e - C = 11.45204 cm-’

= B + c - D = 151.03607 cm-’

[L,] = P + f - H = 163.79842 cm-’ = B + b - G = 163.79895 cm-’

[L,] = P + g - Z = 163.79870 cm-’ = B + c - H = 163.79856 cm-‘.

From the above loops, the average wavenumbers for [I,,] and [Lb] are 11.45 185 cm-’ and 15 1.0358 1 cm-‘, respectively, both with parallel polarizations. The wavenumber of [LJ would be 163.79866 cm-’ with perpendicular polarization. V. DISCUSSION AND CONCLUSIONS

In this work, our spectroscopic assignments in the 13C-0 stretch and in-plane “CD3rocking IR bands together with those in the FIR ground state spectrum have been applied to the identification and confirmation of optically pumped FIR laser transitions for 13CD30H. All of the assignments proposed previously (4,8) have been rigorously confirmed through the formation of closed frequency combination loops ( 7)) including that of the important 127qm FIR laser line of particularly high efficiency (3). In addition, new assignments have been deduced and tested with combination loops for seven further IR-pump/FIR-laser transition systems. As well, three tentative system assignments are put forward. The first is for a new system involving pumping to the in-plane 13CD3-rocking mode and possible lasing down to the asymmetric 13CD3-deformation state. The last two are for additional 13C0 stretch systems for which we predict an assigned IR absorption to be in coincidence with a COZ laser pump line. The closed transition combination loops, which have been established for all systems but two, give calculated wavenumbers for the FIR laser lines which are reliable to the spectroscopic accuracy of approximately +-0.00 1 cm-’ , This represents a significant advance over the customary precision obtainable from wavelength measurements. Furthermore, these loops serve not only to confirm the FIR laser line assignments, but also those of the other IR and FIR transitions in the loops. This is extremely valuable for transitions which are weak or are strongly overlapped in the spectrum. Having the data from both the 13CD3-rocking and 13C-0 stretch bands, we have been able to form very extensive networks of interlocking IR and FIR transitions to test the spectroscopic assignments against comprehensive sets of combination relations. Although 13 systems have assignments proposed here, there are still many reported FIR laser systems for which the transition identifications remain completely open. We believe that several of those systems may involve pumping or lasing to the methyl deformation modes, which we plan to study in the near future. ACKNOWLEDGMENTS This research was made possible in part by a grant to the Centres of Excellence in Molecular and Interfacial Dynamics (CEMAID), funded by the Network of Centres of Excellence Programme in association with the Natural Sciences and Engineering Research Council of Canada. One of us (R.M.L.) also gratefully acknowl-

196

XU ET AL.

edges direct operating support from NSERC and the University of New Brunswick Research Fund. We thank Mr. Mario Noel of the He&erg Institute of Astrophysics for his expert technical assistance in recording the spectra, and Dr. Giovanni Moruzzi of the University of Pisa for the use of his microcomputer analysis program in plotting the spectra for the figures. Finally, it is a great pleasure and privilege to acknowledge the continued encouragement, advice, and stimulation given by our friend and colleague, Dr. Takeshi Oka, for so many years. RECEIVED:

November 26, 199 1 REFERENCES

1. M. 2. N.

INGUSCIO,K. M. EVENSON, F. R. PETERSEN,F. Millimeter Waves 5, 1289-1296 ( 1984).

STRUMIA, AND E. VASCONCELLOS,Int.

10~1, A. MORETTI, F. STRUMIA, AND F. D’AMATO,

J. Infrared

Int. J. Infrared Millimeter Waves 7, 459-486

(1986). 3. N. 10~1, A. MORETTI, AND F. STRUMIA, Appl. Phys. B 48, 305-309 ( 1989). 4. I. MUKHOPADHYAY, R. M. LEES, AND W. LEWIS-BEVAN, ht. J. Infrared Millimeter Waves 9, 54% 553 (1988). 5. E. V. IVASH AND D. M. DENNISON, J. Chem. Phys. 21, 1804-1816 (1953). 6. M. INGUSCIO, F. STRUMIA, AND J. 0. HENNINGSEN, in “Reviews of Infrared and Millimeter Waves” (K. J. Button, M. Inguscio, and F. Strumia, Eds.), Vol. 2, pp. 105-150, Plenum, New York, 1984. 7. G. MORUZZI, F. STRUMIA, R. M. LEES, AND I. MUKHOPADHYAY, Infrared Phys. 32,333-347 ( 1991). 8. D. PEREIRA, J. C. S. MORAES, A. SCALABRIN, A. MORETTI, AND F. STRUMIA, in “Proceedings, 15th International Conference on Infrared and Millimeter Waves” (R. J. Temkin, Ed.), Proc. SPIE Vol. 1514, pp. 735-737, 1990. 9. A. SCALABRIN, D. PEREIRA,G. CARELLI, N. 10~1, J. C. S. MORAES, A. MORETTI, AND F. STRUMIA, in “Proceedings, 16th International Conference on Infrared and Millimeter Waves, Lausanne, Switzerland, 199 I,” pp. 254-255. 10. A. SCALABRIN,D. PEREIRA,G. P. GALVAO, AND K. M. EVENSON, in “Proceedings, 16th International Conference on Infrared and Millimeter Waves, Lausanne, Switzerland, 1991,” pp. 252-253. 11. J. C. S. MORAES, A. SCALABRIN, D. PEREIRA, G. DI LONARDO, AND L. F~SINA, Infrared Phys. 31, 365-372 (1991). 12. W. H. WEBER AND P. D. MAKER, J. Mol. Spectrosc. 93, 131-153 (1982). 13. I. MUKHOPADHYAY, M. MOLLABASHI, AND R. M. LEES, J. Mol. Spectrosc. 138, 521-540 (1989). 14. R. M. LEES, L. H. Xv, K. J. KING, J. W. C. JOHNS, C. YOUNG, AND T. J. LEES, in “Proceedings, 15th International Conference on Infrared and Millimeter Waves” (R. J. Temkin, Ed.), Proc. SPIE Vol. 1514, pp. 726-728, 1990. 15. J. 0. HENNINGSEN, in “Infrared and Millimeter Waves” (K. J. Button, Ed.), Vol. 5, Chap. 2. pp. 29128, Academic Press, New York, 1982. 16. T. KACHI AND S. KON, Int. J. Infrared Millimeter Waves 4, 767-777 ( 1983).