Investigations of several infrared bands of 12C2H2 and studies of the effects of vibrational rotational interactions

JOURNAL

OF

MOLECULAR

SPECTROSCOPY

44, 131-144 (1972)

Investigations of Several Infrared Bands and Studies of the Effects of Vibrational Interactions KENT

F. PALMER,

Department

MICHAEL

of Physics,

E.

MICKELSON,

AND R.

The Ohio State University

of ‘*C2H2 Rotational

NARAHARI

Columbus,

RAO

Ohio 48810

Twenty seven infrared bands of acetylene (12CsH2) in seven selected regions have been measured with high resolution vacuum spectrographs. Some of these have been studied for the first time under high resolution, several molecular constants have been determined with improved accuracy and the rotational assignments have been corrected in a few instances. The need to determine the relative orientations of the A states from experimental studies has become evident in recent work related to CzDz and CZHD spectra. In the present investigation, for the two A states 0000°22 and (00011)2 the c component has been found to be higher than the corresponding d component. For the first time, a H state has also been established to have the same feature; normally, in the case of II states the TIdcomponent is higher than the II, I. INTRODUCTION

This article presents the results of observation, measurement and interpretation of the rotational structure of infrared bands of the “CzHz molecule occurring in several selected regions between 1.5 and 15 P. The bands centered around 1.9 and 2.6 p have been studied here for the first time using high resolution vacuum spectrographs. For the other bands, considerable improvement has been achieved in the quality of the basic observational data as compared to earlier work. This is primarily due to advances in technology in recent years. The present work includes a comprehensive investigation of the bands of acetylene in the region of the v5fundamental. As emphasized by Baldacci, Ghersetti, Hurlock and Rao (I) for the case of C&D%, such a study is essential in providing information not only for the OOOO”l’level (the upper state of the vg band), which cannot be determined indirectly from studies of “hot” bands, but also for many other levels. Knowledge of these other levels allows a clearer elucidation of the effects of vibrational rotational interactions in acetylene spectra. II. A FEW

OBSERVATIONAL

DETAILS

13.7 I.LRegion Use of a liquid helium cooled Ge: Cu detector enhanced the available spectral resolution at these long wavelengths to nearly 0.04 cm-’ as compared to 0.15 131 Copyright

@ 1972 by Academic

All rights of reproduction

Press, Inc.

in any form reserved.

13”

PALMER,

MICKE:LHON

ANJ)

I:AO

cm -’ obt’ainrd by Scott and I&o (2) by employing a t’hcrmocouplc as a detector. In the present study, for the first timcl, a transition to a ZP &ate has brcn iden Cfied. Six transitions account for nearly all the structure observed irl this sp(>ctral region. They are: band ~v:“-v; bands vg

( v4 + v5)0’2-vr1 bands

( ‘u1vyv32~4’“~‘)‘( u1’ll~v3v~zv59 ooOO”l”-ooooooo oooo”20-ooooo1’ oooo”22-ooooo 1’ (oooll);+-0001’0” (00011);--0001’0” (oooll)‘L-oool’ou

N

(lLJ”‘) (z,+-IL) ( A,-IL,) (ZU+-Il,) (X-&J 1 (A,+,)

The present study has established that the previous assignments (2) involving A-II bands need to be modified. The lines which had been assigned to the P branch of the ( vq + vg)‘-v,’ band (A,-&) belong to the P,, branch of this band, whereas lines which had been considered as making up the R branch of this band, Finally, the rotational belong to the R,, branch of the 2vl-v b1band (A,-&). assignments which were ascribed to the 2vb2-vb1band are now assigned to the (&--I&,) band ( v4+ vr,)&-vqr. As a result of these reassignments the vibrational band origin of 2vs2-v51has been shifted by about +0.3 cm-’ as compared to previous work, and the origin of (~4 + v~)‘-Y~ is shifted by about -0.1 cm-‘. The revised assignments led to rotational constants which are more consistent with those derived from other bands where there were no ambiguities in the assignments. Figure 1 shows a small portion of the 13.7 p region of the acetylene spectrum identifying the different Q branches of the bands observed. The Q branch was resolved only in the case of the ~51 band; the structure was measurable between J = 5 and J = 43. No other Q branch showed rotational structure. 7.5 P Region The strongest feature of this region is the ( v4 + I+,)’ band which is a zl,+-2,’ transition between the levels (OOO1l)” and OOOO”Oo. The Ad,’ “forbidden”

FIG. 1. Acetylene spectrum Path length: 13 meters.

at the center of the YOregion. Pressure: less than 0.2 mm Hg.

;

INFRARED

SPECTRUM

OF ‘2CzHz

133

band ( va + va)’ has also been observed (S) because of the strong vibrationalrotational interactions between the (OOOll)~+ and (00011),2 levels (4, 5). a-

vll

Band

The J numbering of the & branch of this “difference” band xas increased by one unit as compared to previous work (6). The present numbering allowed the determination of qz in agreement with other evaluations for this constant and the alternation of intensities are now in agreement with what one would expect from theory. In the above, special attention has been drawn to a few details of the acetylene spectra. Other results, especially those related to the effects of perturbations taking place, will become evident when the molecular constants derived from observational data are critically examined. III. MOLECULAR

CONSTANTS

Tables I-III present the effective molecular constants from the measurement,s which are included in Table IV appearing at the end of this article. The calculations were made by employing Palmer’s (7) computer program which allows the processing of several bands having a common vibrational state. The following vibrational term values which became available during the present evaluations are of interest: Go(OOO1’OO)= 612.870 f 0.002 cm-’ Go(lOOO”Oo) = 3372.851 f 0.003 Go(O1OOOOO) = 1974.317 zt 0.003 IV. VIBRATIONAL

ROTATIONAL

INTERACTIONS

The present investigation considerably augments the large amount of experimental data which has recently become available for the acetylene molecule and its isotopic species. These data are now both extensive and detailed enough, so that definite patterns are emerging as far as vibrational rotational interactions consisting of l-type doubling and l-type resonance are concerned. Anomalously large rotational distortion has been observed for the level (OOOll)“,+ in all cases. The effect has been accounted for as a strong interaction between the Z+ and A, states of the v4 = us = 1 levels (4, 5). The c and c2notation refers to labeling the + ( -) components for even(odd) J rotational levels by c and the - (+) component by d. As in the case of the CzDz bands, for the A states 0000°22 and (00011)’ of C,Ht it has been possible to establish experimentally that the c component is higher than the d component for a particular J. The method involves the determination of the t’erm value difference (Tb, - TA.,) . For instance, the following relations are easily verified:

($

(Ku)+

(::) + u

(O0112)lc

(00112)1,

1, 5289.1085

5289.1057

5260.0221

5260.0221 : 21

5230.2828 ' 26

5230.2327

5230.2327 f 17

:

4

3

3

2

2

1.17425

16

1.177OG + 15

4

1.16754 5 1.16496 1

3

2

2

2

2

2

1.17551 A

1.17065 ?

1.17065 -

1.17236 t

1.17248

1.1748G

1.17017 -. 2

1.18821 i

1.17860 t

1.17974 i

I.18046

B'

’ 3

2

1

4.4

4.9

1.77

2.96 +

2.35

2.58 L

18

5-

-3.85

4

1

27

1.65 i 11

+ Indicatesband was not used in determinationof ground state rotational constants.

* Indicates that this level was highly perturbed and constantswcrc not meaningful.

14, Do = (l.GlO

5

4

14

2

5

3

3

9

9

9

1.15 L 12

1.17 3.15 +

: 2

13

-1.4 k

7) x.10-G

7.7

5.0

6.4

6.6

6.1

5.7

5.6

6.1

4.8

7.0

11.0

6

1 12

1.2 2

-3.16

7.3

-

St. Dev. Y lo3 of SimultaneousFit

5

2.94 -

H' x lOlo

’ 2

2.25 +

3.13

2.38

1.650

1.617 ? 14

2.84 = 11

2.51 .r 8

-0.30

3.59

u' x 106

ksults of the SimultaneousAnalysis for the Ground State: So = 1.176608

(ZJ

(02011)0&

(Zu'

(01021,1,

0110000 -~

3897.1649

3898.3356 I 17

cr,,

(O1021)lc 3897.1600

3881.2354

17

3882.4060

(::) u

(oollo)lc

,I

3294.8424

3294.8424 ! 18

(r"+)

oolo"oO

2701.9054 3281.9048

(ZJ

(01011)0,+

II

3281.9048 5 18

(XJ

2701.9101

(01001&

2560.5971

2703.0802 I 15

(EJ

(zu+)*t 2560.5971 i 17

0 (00031)>Jt

(olool)lc

(JJ

(00003)1, 2169.1505

2169.1601

(..J II

1342.8097

1347.5286 + 40

'170.;387 2 20

('SU)

1328.0735

_ B'&" + BUa*2

(oooo3~1c

vO

1328.0735I 17

12 = G ' - G a 0 0 0

(00011)0,+

Species

(oooll,'c

Upper state

TABLE I

12 C211,Molecular Constants (cm-l) of Bands OriginatingFrom the Ground Stata

(ii,)

(;>u)

(E”)

(CJ

cn,)

cn”)

(ooo11)2c

(00011)2,

(ooo21)lc(II)*

(00021)1,(II)*

(ooo21)lc(I) *

(00021)1,(I) *

(CJ

cn”)

(01021)lc

(01021)1,

oolo"oo

cc”+) q+)

(I:“-)

(00011)0,_

(ololl)"~+

715.2045 i 25

Ku,+)

(00011)0~

3285.4708

5

4

3

4

1.17636 -L 5

1.17065 i

2 3

1.17231 i

7

1.17252 t

1.17990 i

1.18308 i 11

1.18572 i

1.17800 i

1.17984 i

4

3

1.18010 I 1.17985 i

4

1.18054 i

x

lo6

’ 2

5

+ 4

2.49 I 4

2.39 i 3

2.77 i 4

2.30 ? 4

3.112

5.3

3.13 i 5

2.88 t 4

1.62

-0.20

1.69 i 2

3.65 ! 4

D’

-6 Dd = (1.654 ? 17) x 10

= 1.180558 T 25

and (II) to the laver of these states.

quantum numbers. The designation (I) refers to the higher

* These levels are characterized by the same vibrational

Bd

-6 Dc = (1.640 ? 15) x 10

Bc = 1.175339 1 24

Results of the Simultaneous Analysis for the OOO1lO" Level:

,I

3285.4713

2683.1483

3285.4666 t 17

2670.2080

2681.9729 i 24

1347.9945

1347.9862

1328.3049

1328.3074

731.1100

731.1048

728.8574

716.3799

dl2 ) 12 + B/, v. - B 1

2669.0326 * 24

1347.9939 i 38

1328.3102 - 19

11

734.6488 ? 19

727.6760 + 22

v. = Go' - GO'

Species

upper state

TABLE II

3

0.3

0.4

5

31

0.5

k

i

i2

i

i

2

2

5

1

1.62 ?-15

-2.7 i

3.22 + 18

H' x lOlO

12 C2H2 Molecular Constants (cm-l) of Bands Originating from the OOOllOo Level

7.6

10.0

8.3

13.0

8.6

9.3

10.0

9.7

Std. Dev. x 10' of Simultaneous Fit

a,+)

(.E, (i\S,

(rg+)

(n&J

oooo"20

oooo"22 oooo022c d

oloo"oo

(OO012)lc (00012)1,

(n&j

(01012)lc (01012)1,

(Z,)

(rg+)

1000000

(ilg)

'i (K", (;L) *

oooo"ll 0000011=

d

Species

upper state

TABLE III

3286.3867 3286.3846

2643.6956

1318.7263 1318.7214

1245.1620

729.1342 729.1388

719.9658

729.1503

729.1550

, 82 + B*a,,2 v. - B .f.

1.17068 * 3 1.17752 + 4

1.16980 : 2

1.17783 + 4 1.18749 i 3

1.17040 i 3

1.18074 +_3 1.18077 ? 3

1.18110 i 3

B'

7 +

1

4 4

3

4 1

1.89 t 2 1.46 t12

1.60 i

2.35 2.66

1.65 f

-1.07 + 1.67 k

4.105 I 19

D' x 106

*

= (1.610 i Y) x 10-6 ~~ = (1.655 + 10) x 10-6

nc

-4

other transitions are from OOOO"ll.

0.9 1.0

tl

+1 i 2

f 2

4.91 -i5

H' x 1O1'

-6.7

Transitions to these levels are from the ground state. All

Bd = 1.181112 : 19

B = 1.176412 - 18 c

Results of the Simultaneous Analysis for the OOOO"ll Level:

3286.3810 a 18 8,

2642.5192 ? 18

1318.7278 ? 19 I,

1243.9856 i 18

732.6808 ? 23 1,

718.7893 i 22

II

730.3314 + 16

v. = GO' - Go*

12 C2H2 Molecular Constants (cm-') of Bands Involving the OOOO"ll Level

5.2

8.1

9.6

A.9

9.1

14.0

5.2

Std. Dev. x lo3 of Simultaneous Fit

INFRARED

R(J)

4 5 6 7 8 9 10 11 12 13 14 15 16

P(J)

SPECTRUM

F.(J)

137

OF WzH2

Q(J)

P(J)

R(J)

P(J)

5282.265 5284.359 5286.430 5288.482 5290.500 5292.501 5265.289 5267.307 5269.292 5271.268

5331.175

5280.691 25 26 27

5284.273 5287.733

P(J)

R(J)

P(J)

O(J)

R(J)

P(J)

Q(J)

138

c-c

d-4

0-r

-

d-d

INFRARED SPECTRUM OF “C&

TABLE Iv mnrinuea)

139

140

PALMER,

S(J)

I’(J)

K(J)

MICKELSON

i’(J)

AND

RAO

d-d

c-c

_---R(J)

P(J)

R(J)

P(J)

INFRARED SPECTRUM OF W$i~

E.(J)

R(J)

Q(J)

PO)

141

Q(J)

P(J)

2161.460 2162.088 2159.77, 2151.43,

2169.5M) 2169.668 2169.796 2169.982 2170.164 2170.412 2110.658 2110.931 2111.224 2171.862 2172.212 2172.584 2112.976 .?1,3.3,, 2174.235 2174.689 2175.162

:: 34 35 36 37

2753.656

J

“1 -

3

1

R(J)

P(J)

2648.370

2601.332 2638.972

2652.968 2655.262 2657.538 2659.190 2662.038 2664.256 2666.196 2668.706 2670.882 26,3.051 2675.213 2677.373 2681.620 2683. ,32 2685,834 2687.908 2692.036 2694,067 2696.088 2698.094 2702.078 2,06.020 2707.94, 2709.869 2711.793

(3V& Q(J)

2687.828 2690.lbS 2692.484

:“6::: Ei 2631.798 2629.,,6 2626.939 2626.519 2612.059 2619.586 2614.608 2612.095 2609.574 2607.031 2601.490 2601.919 2599.355 2596.765 2594.173 2591.563 2588.939 2586.306 2583.65, 2580.994 2578.324 25X.636 2572.943 2570.242 2567.523 2564.794 2562.049

R(J)

2697.120 2699.428 2,01.,30

2640.98, 2640.612 2640.225 2639.390 2638.414 2637.980 2631.148 2636.909 2636.355 2635.714

2706.306 2708.579 2710.851 2,13.102 2715.361 2,1,.598 2719.826 2122.05‘ 2720.156 2726.469 2728.641 2730.813 2732.96, 2735.10, 2,,,.244 2741.460 2743.548 2745.614 2,4,.6,5 2749.719 2751.75, 2753.758

P(J)

2678.932 2676.068 2673.715 2611.336 2668.94, 2666.56, 2664.181 2661.775 2659.366 2656.962 2654.543 2652.113 2669.681 2644.,,9 2602.314 2639.829 2637.363 2634.666 2632.38, 2629.859 2627.332 26X.799 2622.260 2619.698

Q(J)

2683.052 2682.984 2682.69, 2682.799 2682.548 2682.395 2682.221 2682.042 2681.839

2677.323 26,6.810 2675.724

2611.942 2609.328 2606.690

2673.881

2631.055 2556.526 2719.289 2721.105

2628.696

2598.67, 2596.008 2593.235 2590.511

2671.796

R(J) 2562.966 2565.342 256,.,,9 2510.14, 2572.572 25E.016 2577.478 2579.960 2582.471 2584.995 2587.547 2590.138 2592.742 2595.386 2598.051 2600.752 2603.484 2606.236 2609.024 2611.845

+ Y5P9 PO)

2558.242 2555.904 2553.578 2551.272 2548.96, 2546.688 2546.423 2542.181 2539.959 25,,.,61 2535.591 2533.445 2531.331 2529.243 2527.18, 2525.158 2523.159 2521.19* 2519.249 2517.338 2515.458 2513.606 2511.174 2509.965 2508.176 .?506.41, Z504.681

INFRARED

SPECTRUM

143

OF YXsHz J

+

d

ooo0°2~t= -t-

R,

3 7)

37

;= +=

=:’

<

+0 0 o”0”-B,(f

FIG. 2. Illustrating

38

-< -d

-d -c -d -r

3 8)

0

-d

39)

4

+-00004’

39

(3 9)

39 38 37

)9)

-< -<

39

-c

37

38

(4 0)

B,(3

-Lb(38)‘(39)’

(4 OY

+

-c

_

the relations

given in Eqs.

0

(1) and (2) for the J = 38 level of the

OOW22 state of WzH2. T&(J)

=

[B(J

+

l)(J

+

2)

-

D(J +

T*,(J)

=

[BJ(J

+

1)

-

D(J)‘(J

+

l)‘(J

+

2)’

“‘]groundstato

l)lq + P&J +

[&(J

+

+

1)”

+

[P(J)]“,

* ’ ‘]ground +

(1) 1)1(2+“51)

,

1)1(2”,~-“,9

.

state [Rcc(J

-

(2)

These relations are illustrated for J = 38 in the energy level diagram in Fig. 2. In all cases where this type of calculation was possible the TA, - To, came out to be negative. In the case of the (00011)2 such calculations are not possible because the OOO1’O”-OOOO”Oo transition is not allowed. Nevertheless, if the molecular constants of the (00011) 2 c and d sublevels are used, one can make calculations of the term values needed. Finally, mention should be made of a II, vibrational state, tentatively identified as (00112) ‘, which has been found to have the c components of the rotational levels higher in energy than the corresponding d components. From the P, &, and R transitions of the (00112) l-OOOO”Oo band the energy difference between the d and c components Tn,( J) - Tn,( J) , was found for many J values, in a manner similar to the case of the 0000°22 state. These differences were found to be negative for all J values.

144

PALMER, MICKELSON +0.1 c

AND RAO

J(J+l)

l

FIG. 3. Plot of !&,(J)

-

Tn, (J) versus J(J + 1) for the (00112)’ state of

‘2GHz .

For an unperturbed II state, the differences can be expressed as G,(J)

-

T&(J)

LX --Q + nJ(J

+ l),

(3)

for low J. Thus, it is clear from Eq. (3) that the plot of the energy differences, Tn,( J) - Tn,( J) , of an unperturbed II state, versus J( J + 1) should be linear with positive slope equal to 4. However, for the case of the (00112)’ level such a plot does not show a positive trend (see Fig. 3). ACKNOWLEDGMENTS Support extended by the National Science Foundation and the Office of Naval Research is gratefully acknowledged. Thanks are due to Professor J. Pliva and Dr. S. C. Hurlock for helpful discussions. RECEIVED: January

l&l972 REFERENCES

1. A. BALDACCI,S. GHERSITTI, S. C. HURLOCK,AND K. NARAHARI RAO, J. fifol. Spectrosc. 43, 327 (1972). 8. J. F. SCOTTANDK. NARAHARIRAO, J. Mol. Spectrosc. 16,15 (1965). S. J. PLIVA, S. GHERSETTI,M. E. MICHELSON,AND K. NARAHARI RAO, The Twenty-fifth

4. 6. 6. 7.

Symposium on Molecular Structure and Spectroscopy, Columbus, Ohio, 1970, Paper N3. G. AMAT AND H. H. NIELSEN, J. Mol. Spectrosc. 2, 152 (1958). G. AMAT AND H. H. NIELSEN, J. Mol. Spectrosc. 2, 163 (1958). T. A. WIGGINS, E. K. PLYLER, ANDE. D. TIDWELL, J. Opt. Sot. Amer. 61.1219 (1961). K. F. PALMER,Ph.D. Dissertation, The Ohio State University, 1972.