The direct observation, assignment, and partial deperturbation of the ν4and ν6 vibrational fundamentals in 1Au acetylene (C2H2)A. L. Utz, J. D. Tobiason, E. Carrasquillo M., L. J. Sanders, and F. F. Crim Citation: J. Chem. Phys. 98, 2742 (1993); doi: 10.1063/1.464156 View online: http://dx.doi.org/10.1063/1.464156 View Table of Contents: http://jcp.aip.org/resource/1/JCPSA6/v98/i4 Published by the American Institute of Physics. Additional information on J. Chem. Phys.Journal Homepage: http://jcp.aip.org/ Journal Information: http://jcp.aip.org/about/about_the_journal Top downloads: http://jcp.aip.org/features/most_downloaded Information for Authors: http://jcp.aip.org/authors

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The direct observation, assignment, and partial deperturbation of the V4 and Vs vibrational fundamentals in A 1Au acetylene (C2H2)

A. L. Utz,a) J. D. Tobiason, E. Carrasquillo M}) L. J. Sanders,c) and F. F. Crim Department of Chemistry, University of Wisconsin-.Madison, Madison, Wisconsin 53706

(Received 6 October 1992; accepted 10 November 1992)

A pulsed-laser double resonance ~~hnique provides previously un~vailable spectrQsc~pic data on the rovibrayonal structure of A Au acetylene (C2H:2). Our assignment and analysis oftran­sitions to the A state V4 (torsion) and v;' (antisymmetric in-plane bend) vibrationaLfunda­mentals uncovers a strong Coriolis interaction between these two neaLly degenerate modes and weaker Coriolis interactions between the v4lv;' pair and remote A state rovibrationallev­els. We deperturb the direct Coriolis interaction between V4 and v;' to obtain vibrational fre­quencies, Coriolis coupling constants and partially deperturbed rotational and centrifugal dis­tortion constants for these previously unobserved fundamentals. Parity selection rules for the A<-X band permit an unambiguous as!;ignment of the vibrations (v4=764.9±0.1 ,£m- 1 and v;' = 768.3 ± 0.2. cm -1). We use these new expeLimental values to reassign several A state vi­brations and to assign previously unidentified A state levels. We also identify two vi,!?rational resonances that seem to be important in determining the rovibrational structure of A 1Au

C2H2•

I. INTRODUCTION

The A 1Au<-X 12,: electronic band system of acetylene is one of the most thoroughly studied electronic bands in a polyatomic m..9lecule.l-11 Previous investigations have es­tablished the A state equilibrium geometry to be trans-bent and planar with an equilibrium _C-C bond length about 15% greater than in the linear X state. As a result, long progressions in the trans-bending and C-C stretching vi­brations appear. The rotational structure of the vibronic bands is characteristic of a perpendicUlar transition from the linear ground state to a strongly prolate asymmetric top. Additional rotational transitions appear due to axis switching and the rotational asymmetry of th~ excited elec­tronic state. Many vibrational levels in the A state are as­signed and analyzed with full rotational resolution, and several of these levels show sptztroscopic perturbations.

Prior investigations of the A state in acetylene (C2H 2 )

provide only a partial picture of its vibrational struc~re in spite of intense study. Of the six singly-degenerate A state normal modes, which Fig. 1 shows, previous experiments have firmly established fundamental frequencies for only two (V2 and V3)' The frequency for vi arises from the assignment and analysis of a vibrational progression that does not include the fundamental and is therefore less cer­tain. Fundamentals of the remaining three modes (V4' vs, and v;') are unobserved, and assignments of the few iso­lated vibrational combinations involving these modes are uncertain. Two factors contribute to the scarcity of infor­mation on the V4, vs,_ancL v;' vibrational levels. First, the previously assigned A <-X vibronic transitions originate

a) Present address: Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139.

b)Present address: Department of Chemistry, University of Houston, Houston, TX 77004.

c)Pre~ent address: Department of Chemistry, Wittenberg University, Springfield, OH 45501.

from the ground vibrational level or thermally populated fundamental and overtone levels of the trans-bending vi­bration, v4', all of which have gerade symmetry. The rig­orous g+-+u symmetry selection rule for the centrosymmet­ric acetylene molecule forbids single-photon transitions from these gerade X state vibrations to gerade vibronic levels, such as the A state V4' vs, and v;' fundamentals. Second, the elongation of the G-·C bond and bending of th~ molecule upon electronic excitation fav<?rs transitions to A state vibrations having significant C-C stretching (V2) or trans-bending (V3) excitation and makes transitions to vi­brationallevels involving the V4 . (torsion), Vs (antisymmet­ric C-H stretch), and v;' (in-plane antisymmetric bend) modes relatively weak.

We use a pulsed-laser double resonanse technique to obtain previously unavailable data on the A ~ate ungerade vibrational levels. Our scheme excites an X state vibra­tional overtone level in the first step and transfers some of the vibrationally excited molecules to the electronically ex­cited A state in the second step. The selection rules for this two-photon process requi~ that we access only ungerade vibrational levels in the A state. Thus, our double reso­nance studies complement single photon absorptio~mea­surements by observing a completely different set of A state vibrational levels. We have used this technique to detect and assign electron transitions to the A state V4' vs, and v;' fundamentals and several combination vibrations.

Here, we describe our detection and assignment of electronic transitions to the A state V4 and v;' vibrational fundamentals. We observe a strong Coriolis interaction be­tween these two nearly degenerate bending ~odes as well . as weaker Coriolis interactions with remote A state vibra­tiona1levels. We deperturb the direct interaction between V4 and v;' to obtain vibrational frequencies, Coriolis inter­actioIlc:onstants, and"'partially deperturbed rotational con­stants. Our room temperature double resonance experi­ment accesses· rotational levels with J' <,27, and the

2742 J. Chern. Phys. 98 (4), 15 February 1993 0021-9606/93/042742-12$06.00 © 1993 American Institute of Physics

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Utz et al.: V4 and Vs fundamentals in A 1Au acetylene 2743

A lAu (C2h ) Normal Modes

Mode Nuclear Motion Vibronic Vibrational Synunetry Synunetry

V'

* A ag 1 u

V' A ag 2 u V' ~ A ag 3 u V' ~ A au 4 g

v'

~ B bu 5 g

v' B bu 6 g

FIG. 1. Normal mode vibrations for A lAu C2H2• The six singlydegener­ate normal modes are the symmetric C-H stretch (vD, C-C stretch (vz), trans-bend (vD, torsion (V4), antisymmetric C-H stretch (vs), and in­plane antisymmetric bend (vi,). The vibronic (upper case) and vibra­tional (lower case) wave function symmetries are classified within the C2h

point group.

combination of i-mixing in the intermediate level with axis switching, asym~etry mixing, and b-axis Coriolis-induced K mixing in the A state results in our electronic transitions reaching an unusually wide range of v';' and v;' asymmetric rotor levels (nominal Ka ranging from 0 to 7). We limit our fitting procedure to the six lowest subbands to mini­mize both the influence of remote a-axis Coriolis perturb­ers on v';' and V6 and the possible effects of torsional split­ting on the rotational structure of v';'.

Neglecting the effects of remote Coriolis perturbers and torsional splitting significantly alters the rotational and centrifugal distortion constants that we obtain from our fit but not the v'!pra!!onal frequencies. The parity selection rules for the A.-X band permit an unambiguous assign­ment of the V4 and v;' frequencies. We evaluate prior as­signments.s>f v';' in A ~D2 and C2HD, reassign previously reported A state corgbination vibrations in C2H2, assign several unidentified A state vibrations, and identify vibra­tional resonances that form the basis for two important vibrational coupling mechanisms in A IAu C2H 2 with these newly assigned frequencies.

II. EXPERIMENTAL APPROACH

The energy level diagram in Fig. 2 illustrates our ex­perimental approach. Excitation of the second overtone of the antisymmetric C-H stretching vibration (3v3', EVib ;:::: 9640 cm -I) via a P- or R -branch transition from v" = 0 prepares an intermediate level with ~;; vibronic symmetry, rotational quantum number J", vibrational angular mo­mentum l" =0, and parity e. We then record laser induced fluorescence excitation (LIF) spectra from this single quantum state by fixing the vibrational overtone excitation wavelength, scanning the wavelength of a second, ultravi­olet laser, and detecting fluorescence from the electroni­cally excited acetylene molecules. We repeat this procedure using each of the 3v3' rotational levels J" =0-20,22,24,26

A A u

---L.----v"=O

FIG. 2. Energy level diagram for the double resonance studies of A lAu

~H2' Near infrared light (AIR::::: 1 /-Lm) excites a fraction of the molecules in v" =0 to a specific rotational level of 3v3', or some other intermediate vibrational level in the ground electronic state. Ultraviolet light (AUV :::::300 nm) then excites the vibrationally energized molecules, but not molecules in thermally populated i state rovibrational levels, to an A state rovibronic level. We detect the undispersed fluorescence signal from the electronically exci~d mo!!;cules. Primed and double-primed quantum numbers refer to the A and X electronic states, respectively.

as well as the J" = 4 and 6 levels of the nearby combination band vi' +vz +v3' +2v4'°( 1112°0), as intermediate levels. The double resonance reduces the complexity of the fluo­rescence excitation spectra and simplifies their assignment. Unlike single photon absorption measurements, which de­tect transitions arising from a Boltzmann distribution of vibrational and rotational levels, the electronic transitions we observe in a particular fluorescence excitation spectrum originate from a single rovibrational eigenstate. Our ability to specify the intermediate level effectively presorts the electronic transitions and guides our assignment of them. We extract vibrational frequencies and rotational constants for v4 and vI; by using previously reported term values for the intermediate state and optimizing a model of the A state's rovibrational structure in the region of v';' and V6 to fit the data.

The apparatus is similar to that used for our double­resonance measurements of collisional relaxation in highly vibrationally excited acetylene. 12,13 A room temperature glass cell, which has Brewster's angle windows, internal baffles and Wood's horns to reduce scattered laser light, holds a static sample of acetylene (Matheson, Purified grade) at a low pressure (0.020 Torr). A 7 ns, 5 mJ pulse of infrared light (AIR;:::: 1 /Lm) from a Nd:YAG excited, Raman-shifted (second Stokes in H2) rhodamine-590 dye laser passes through the cell and excites a small fraction of the acetylene molecules to the desired rotational level of 3v3'y,14 An intracavity etalon in the dye laser reduces the bandwidth of the infrared light to 0.10 cm -1.15 About 10% of this laser pulse enters an independent photoacoustic spectroscopy cdl where we verify resonance of the infrared laser with the desired acetylene transition. AWns, 0.1-1.0

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2744 Utz et al.: V4 and Vs fundamentals in A 1Au acetylene

mJ pulse of ultraviolet light (Auv:::::3OO nm, .iv:::::0.14 cm -1) from an excimer laser pumped, frequency doubled dye laser operatiI~g with a mixture of rhodamine-590 and coumarin-540 A laser dyes counterpropagates through the fluorescence cell and excites the vibrationally energized molecules to an A state rovibrational level. We delay the ultraviolet laser pulse by 10 ± 2 ns relative to the infrared laser pulse. A photomultiplier tube mounted at a right angle to the laser propagation direction views the undis­persed A state fluorescence through an f /2 optical system and adjustable slit assembly. The polarization of the ultra­violet light is perpendicular to that of the infrared light. Using the dye laser fundamental, we calibrate the ultravi­olet photon energy to an absolute accuracy <;0.10 cm- 1

with a solid monitor etalon (nommal FSR=0.6667 cm- 1) and atomic neon transitions detected via the optogalvanic effect (OGE).16,17 The neon transitions calibrate the free spectral range of our monitor etalon and provide an abso­lute photon energy reference. Fluorescence from an iodine cell provides an independent check of the wavelength cal­ibration procedure and verifies our estimate of the uncer­tainty in the ultraviolet photon energy. Computer­controlled data acquisition electronics set the wavelengths of both laser systems and record the integrated acetylene fluorescence signal, IR and UV laser pulse energies, the photoacoustically detected IR absorption signal, and aGE, etalon, and iodine fluorescence signals on a shot-to-shot basis.

Several features of the experiment ensure that the LIF transitions arise from direct electronic excitation of the desired intermediate level. Our LIF spectra are free of hot band contributions because the UV photons have insuffi­cient energy to e~cite molecules electronic8;lly from ther­mally populated X state vibrational levels. Performing the experiment under essentially collisionless conditions en­sures that transitions from collisionally populated levels do not appear in these LIF spectra. 18 We reject LIF transi­tions arising from spurious intermediate levels by analyz­ing only those electronic transitions that appear for both P­and R-branch excitation of the selected intermediate level.

III. THEORY AND DATA ANALYSIS

A. Vibrational overtone spectroscopy and characterization of the intermediate 3vg and v;' + vi + Va + 2v:;o levels

Several groups ha\'e performed high-resolution absorp­tion measurements on the 3v3' and (1112°0) bands in C2H2.19-21 We use their results to compute term values for the intermediate levels in our vibrational overtone-UV double resonance scheme. The molecular constants21 and Eq. (1),

Tv"=vo + B~J" (J" + 1) - D~ [J"(J" + 1) ]2, (1)

yield the term values (Tv") for these states. Results from our laboratory demonstrate that the

nominally 3v3' molecular eigenstates prepared via vibra­tional overtone excitation are actually admixtures of the zeroth-order C-H stretching state and other vibrational

levels containing significant bending excitation.22,23 Be­cause the couplmg between 3v3' and these background states is weak, it does not perturb the 3v3' rovibrational term values by more than 0.015 cm- 1. However, the very poor Franck-Condon factors for excitation from a highly excited zeroth-order C-H stretching state to a trans-bent electronic state cause these perturbations to have a dra­matic, rotational-level-dependent effect on the probability for electronic excitation out of the 3v3' intermediate levels. In fact, we do not observe any electronic transitions from 3v3' rotational levels with J" < 8 to the v4Iv6 pair.24 In­stead, we use (1112°0) as an intermediate level for excita­tion of low-J' levels.

B. Electronic spectroscopy and preliminary analysis of the A state rovibrational levels

Following excitation of a single intermediate rovibra­tionallevel, we scan the ultraviolet laser wavelength from 3011 A to 2940 A in 0.0042 A steps to generate LIF spec­tra for this study.25 Figure 3 shows portions of these spec­tra obtained after preparation of selected rotational levels of 3v3'. The data are the integrated fluorescence signals linearly normalized to the pulse energies of both the vibra­tional overtone excitation and LIF probe lasers, as well as the fluorescence cell pressure, on a shot-to-shot basis. We obtain these spectra under nearly collisionless conditions (Z:::::0.006).

We convert the calibrated ultraviolet vacuum wave­lengths, Auv,vac' to A state term values, Tv" by adding the term value of the intermediate level, Tv"; to the calibrated ~ photon energy of each transition and subtracting the A .... X electronic origin,4 T o=42 197.57 cm-I,

he Tv,=Tv"+-1--·~To·

/l,UV,vac (2)

Subtracting a J-dependent term, Bavg[J' (J' + 1 )], froEl Tv' yields reduced term values (Tred ) for levels with an A state rotational quantum number J'. The choice of Bavg= 1.074 cm -1::::: B makes most of the rotational subbands appear as horizontal lines when the T red are plotted versus [J' (J' + I)] in a reduced term value plot. Since P-, Q-, or R-branch transitions may originate from the single inter­mediate rotational level, we initially compute T red for these three possible assignments of each LIF transition and plot all of the T red vs the appropriate [J' (J' + 1)]. We inspect the reduced term value plot and identify nearly horizontal lines that correspond to rotational subbands. The appear­ance of a reduced term value on one of these lines identifies which of the three possible assignments is correct. We then remove the other two T red from the plot. Figure 4 is a reduced term value plot for our 316 observed electronic transitions, all of which appear as assigned points. The plot shows that the transitions belong to vibronic bands and subbands whose origins range from about 750 to 1400 cm -1 above the A state origin. A complete listing of these transitions is available from the authors.

Electronic transitions in the A .... X band system have nonvanishing intensity only when the integrand of the Franck-Condon overlap integral is symmetric with respect

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Utz et al.: V4 and V6 fundamentals in Ii 1Au acetylene 2745

• 3v3";J"=20 •

10 x1 • •

01 • 0

0 0 • 10

~ 0 0 ~ 0 0 0 1

•

I 3v3";J"=18

0 ·0 '" 0

0 x90 0 0 • 0

• 0

•

I 3v3";J"=16

0

po • 0 • 0 • I o. 0>1 0 .0 0 x9 I

• 3v3";J"=14 0

I ~ •

x6S 1

• 00 • ~ 0

0 0 0

0 0 3v3";J"=12 0 • 0 oj • J x6S J 0 10

01 0 •

0 L 0

0 3v3";J"=10

I I 0

• 0 x6S 0 • 0 10 J

0 0

• . 3v3";J"=8

. ~ J.t 0 0

,[ 0 0 n o.\. 0 0 x 300

.1. o oP

J 0 J • J

I I

3010 3005 3000 2995 2990

LlF Excitation Wavelength, AUV' (A)

FIG. 3. Portions of the fluorescence excitation spectra originating from selected rotationalleve1s (1") of 3v3'. The transitions are labeled with their P­(diamond), Q- (circle), or R- (square) branch assignments. Unlabeled transitions arise from spurious intermediate levels. The variation in scale factors for spectra originating in different 1" levels of 3v3' is evidence for the zeroth-order state mixing described in the text.

to all symmetry operations common to the two electronic states.26 This requirement gives the vibrational selection rules for the A ..... X band system, which are a++a, b++b, g++g, and u++u when expressed in the reduced symmetry C21z point group of the A state.27 Because the ~: symmetry of both 3v3' and (1112°0) correlates to bu sym,Eletry in C21z,

our electronic transitions may only access A state levels with bu vibrational symmetry. The normal mode analysis of Chaturvedi and Rao yielded a complete set of vibra­tional frequencies for the C2H2 A state,28 and several ab initio calculations have also predicted values for the A 1Au vibrational fundamentals. 8

,29 Table I summarizes the re­sults of these studies, which indicate that v;' is the only bu-symmetry vibrational level in the o~erved energy range. Because Coriolis interactions in the A state mix lev­els of a and b symmetry, the other ungerade vibration in this region, the au symmetry V4 level, can mix with v;'.

Previous studies clearly establish the r.Qtat!gnal struc­ture of unperturbed vibronic bands in the A ..... X band sys­tem. I- 7 Acetyh::ne is a strongly prolate asymmetric top in the A state with Ae'iJ>Be-;:::,Ce and an asymmetry parameter K= -0.9845 (v=O). The a axis lies in the plane of the molecule 10.130 off the internuclear axis of the C-C bond, the c axis contains the C2 symmetry axis, and the b axis lies in the molecular plane perpendicular to both the a and c axes.7 The projection of the total angular momentum on the molecule-fixed symmetry axis (K~) is a useful label for unperturbed rotational levels but is not a rigorous quantum

number. The rotational selection rules for this perpendic­ular electronic band26 are LlJ=O, ± 1 and LlKa= (K~-l") = ± 1. Additional transitions with LlKa=O, ±2 and I:l.Ka = ± 3 (due to axis-switchinll an~ the asymmetry of the upper state) appear in the A ..... X band system.3,7 These additional bands are generally much weaker than the prin­cipal LlKa= ± 1 bands except in the case of high J(J-;:::,20). Since both of the intermediate levels we prepare have /" =0, we expect a principle I:l.Ka= + 1 band and weaker I:l.Ka=0,+2 and I:l.Ka=+3 bands whose intensities in­crease approximately as J2 and .1', respectively. . A comparison of the reduced term value plo.,! in Fig. 4

with that of an unperturbed vibrational level of A 1Au acet­ylene4 shows that the rotational structure we observe is far too dense to arise from a principal I:l.Ka= + 1 ban~ with additional LlKa=O, 2, and 3 transitions to a single A state vibrational level, as we would expect in the absence of perturbations. In addition, the highly irregular J depen­dence of the asymmetric rotor levels suggests a strong per­fErbation. We conclude that the term value plot shows two A state vibrational levels, which we assign as the Coriolis­coupled v4lv;' pair on the basis of their vibrational symme­tries and predicted frequencies.

Selection rules for the parity quantum number allow us to determine the energy ordering and approximate vibra­tional frequencies of the nearly degenerate zeroth-order V4 and v;' vibrations. The parity of the total molecular wave function with respect to inversion of the electronic and

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2746 Utz et al.: V4 and Vs fundamentals in A 1Au acetylene

1400rr---.,--.--'.----,.r------,

1300 ~

1200 I-

a> 1100 -::::I ctI > E ..... Q)

r- 1000 -"0

~ ::::I "0 Q)

a:: 900~

(a) 0._1110. 0 o. 0 •

o • · -

-

• o 0

-

01110 0 0 0 O. 0

-• 0 •

o .-1!l00.0 0 •

-<8«ljI.o+ .... ijI. • 0 • • • 0

()t(!IJ 00000 0 o· 0

~01il0.0. • • 800~0e~1iI1i10. o· _

r4-r-----~-----r----~----~

-----

w--eEl"O-_ E1- ___ _

~--iJ

1--

P R - <>- -0 - e-parity

<JJ<l8):O ~ ·~I!IO· 0 • 0 • 0 ~ 0 ~.OO 740 ~ •• ". 0.: g • B ; 0 : 0

Q •

~ ____ ~~ ____ -L~ __ ~~~£-~~ ~ ____ ~ ______ -L ______ L-____ ~

o 200 400 600 800 0 800

J'(J'+ 1)

FIG. 4. Reduced term value plots of the data. Panel (a) shows reduced term values for all of the transitions we detect, and Panel (b) shows only those transitions that we include in our fit. The solid circles identify the e-parity states that Q-branch transitions access, and the open symbols label the f-parity levels that P- (diamonds) and R- (squares) branch transitions access:The solid and dashed lines passing through the data show the results of our fit for the e- and f-parity levels, respectively. Zeroth-order rotational and vibrational quantum numbers for the six lowest rotational subbands appear in Table V.

nuclear space-fixed coordinates is a rigorous quantum number in the absence of an external electric field. Table II summarizes the relevant +1- parity classifications of acetylene in its linear X state and its planar A state. 30 We also classify parity in acetylene with the equivalent ell parity labeling scheme, which specifies that a rovibronic level with a parity of ( _l)J or - ( _l)J has e or j parity, respectively.31 Table I!.shows that all rotational levels of ~+ vibrations in the X state, such as 3v3' and (1112°0), have a parity of e. Since the singly degenerate K~=O asym­metric rotor levels in the A state have K~=J', the parities of these levels for v4(au ) and v6(bu ), are e and j, respec­tively. Figure 5 illustrates our assignment of ell parity labels to higher energy asymmetric rotor levels of V4 and vI;.

The parity selection rule~ for dipole-allowed transi­tions from the intermediate X state ~ + vibrational lev­els4,31 (Q-branches: e+-+j; P- or R-branches: e+-+e,j+-+/)

permit only Q-branch transitions to access the K~=O level of V6 and only P- or R-branch transitions to access the

TABLE I. Calculated and observed vibrational frequencies for ~H2 AIAu'"

Ab initio

Mode Obs. Calc.f Calc.g Calc.h Calc.i

vi (ag ) 3040.6b 3018 3320 3299 2975 vz(ag) 1386.90(2)C 1385 1503 1538 1444 vJ(ag ) 1047.55(2)C 1052 1134 1171 1101 v4(au ) 764.90(6)d 642 960 971 572 vs(bu ) 2857.4(2)e 3026 3308 3286 2947 v;'(bu ) 768.26(9)d 948 747 728 765

'Observed values are mechanical frequencies (v); calculated values are harmonized frequencies (6)). Units are cm- I

. Error limits for observed frequencies refer to the last decimal given.

bReference 5 (assuming X I3 =-60.5 cm- I , X 33 ::::;-9 cm- I , X 23 ::::;0 cm- I ).

cReference 4. dThis work. "Recent value from_our laboratory (Ref. 46). fNormal modes calculation (Ref. 28). gReference 8 and citations therein. Double zeta. hReference 8 and citations therein. Double zeta plus polarization. iRe[erence 29. Double zeta.

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Utz et al.: V4 and Vs fundamentals in A 1Au acetylene 2747

TABLE II. Parity classifications in C2H2•

Electronic Vibrational Electronic Vibrational Rotational Rovibronic state symmetry parity parity parity +/- parity

Xll:+ l:+ +1 +1 (-1)J (-1)J - g u AlAu ag -I +1 ( _1)Kc _(_1)Kc

AlAu au -I -I ( _1)Kc +(_1)Kc

AlAu bg -I -I ( _1)Kc +(_1)Kc

AlAu bu -I +1 (_1) Kc _(_1)Kc

K~=O levels of V4' These selection rules, which are de­picted in Fig. 5, allow us to assign vibrational quantum numbers to the observed states. The lowest energy rota­tional subband in the reduced term value plot (Fig. 4) has a subband origin of about 760 cm -1, is doubly degenerate, and therefore has K~>O. We discuss its assignment later. The next two higher subbands are nondegenerate levels with zeroth-order K~=O and subband origins between 765 and 770 cm- I . Because the lower energy (low-J' limit) subband comprises solely P- and R-branch transitions while the higher energy singly degenerate level is composed of only Q-branch transitions, we assign the lower frequency vibration as V4 and the higher frequency vibration as v;'. A

K~

4

K' c

A

3 -..:::---...::::..... J'-3 (e)

2 -..:::---...::::..... J'-2 (f)

-..:::---..::::::.....J·-1 (e)

o ----,,-..;::::- J' (f)

Q

K~

4

K' c

3 -..:::---...::::.....J·-3 (f)

2 -..:::::-----"~J·-2 (e)

-..:::---...::::.....J·-1 (f)

o ----,,-..;::::-J. (e)

P&R

(e)

FIG. 5. Parity labels for the X and A state rovibronic levels in our experiment and selection rules for electronic transitions originating in X state vibrational levels with l:;; symmetry. Asymmetric rotor correlation diagrams represent the rotational levels of A state vibrations with ag or bu vibrational symmetry (on the left) or with au or bg symmetry (on the right). Because the parity ofasymmetric.I0tor rotational wave functions depends only on their limiting K~ value, A state levels with a common K~ label share !!Ie same e//parity. The arrows show that Q-branch transi­tions from X .§tate vibrations with l:;; rovibronic parity access /-parit.Y levels in the A state, but P- and R-branch transitions from the same X state levels access e-parity levels in the A state.

TABLE III. Coriolis interactions in A IAu C2H2•

C2h ag bg au bu

ag Jc Ja,Jb

bg Ja,Jb Jc au Jc Ja,Jb

bu Ja,Jb Jc

crude extrapolation of the K~=O levels to J' =0 yields vi­brational frequencies for V4 and v;' of about 765 and 768 cm -1, respectively.

C. Rovibrational state mixing in A 1Au acetylene (C2H2)

We can identify terms in the Hamiltonian that directly couple the nearly degenerate V4 and vi; vibrations and lead to the perturbations we observe in the reduced term value plot. Bunker's trea.!ment of N2H2,32 which is isomorphic with C2H2 in its A state, is particularly re.levant to our analysis. Symmetry restrictions prohibit anharmonic cou­pling and centrifugal distortion terms from mixing v4(au) and v6(bu), but the Coriolis term, T eor' does couple them. Coriolis mixing arises from cross terms between the total angular momentum, J wand the vibrational angular mo-mentum, ITa. The term has the form ..

'" e af-£aa T Cor = ~ £..- f-£aaIT~a+ aQ QrIT~a+"',

a,r r (3)

where a refers to a particular molecular axis (a=a,b,c), f-£~a is a diagonal component of the equilibrium inverse inertial tensor, f-£aa is the inverse inertial tensor, and the Qr are normal coordinates. The higher order terms in the sum, which result from an expansion of f-£aa about f-£~a are sum­marized by Dai et al. 33 For V4 and V6' all terms but the first vanish due to symmetry. The vibrational angular momenta are

(4) rs

where rand s label the normal coordinates, their conjugate momenta (P), and the Coriolis constants ;~S' which couple modes rand s via rotation about the ath axis. Permutation of rand s changes the sign of the Coriolis coupling con­stant. Expressing the normal coordinates and momenta in terms of the harmonic oscillator raising and lowering op­erators reveals the origin of vibrational mode mixing and simplifies the evaluation of matrix elements.33

Symmetry restricts the states that may interact via a particular Coriolis resonance, and Jahn first summarized a convenient set of rules for identifying the nonzero ;~ con­stants.34 Table III summarizes the resulting vibrational symmetry restrictions on Coriolis mixing in the C2h point group of A IAu C2H2• While Jahn's rules do not ensure a nonzero ;~, they are a necessary condition for a nonvan­ishing Coriolis coupling constant. Table III indicates that both a- and b-axis rotations may couple v4(au ) and v;'(bu ),

but that a c-axis rotation does not couple the two bending

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2748 Utz et al.: V4 and Vs fundamentals in A 1Au acetylene

fundamentals (~6=0). Thus, the nonvanishing matrix el­ements of ITa that couple V4 and v6 are

(1,01 ITa I 0,1) =S16(1,0 I Q4P6-q6P4 I 0,1),

(0,11 ITa I 1,0) =S16(0,11 Q4P6-Q6P4 I 1,0),

a=a,b,

a=a,b, (5)

where I V4,V6) are A 1Au rovibrational wave functions. Sub­stituting these expressions into Eq. (3) and incorporating all constants that come from expressing the matrix ele­ments in wave number units yields

(1,01 T cor IO,l) = - (1,01 T cor IO,l)

= -~~e[ ~+ ~] (l,OIJaIO,l)

-s~6Be[ ~+~] (1,OIJbl~,l). (6)

Ae and Be are the equilibrium rotational constants of A 1Au C2H2, which we approximate with Ao and Bo from Ref. 4, the {J)r are harmonic normal mode frequencies, which we approximate with the observed mechanical frequencies, v,., and the Ja are rotational matrices written in units of ft. Since the magnitude of the coupling matrix element is di­rectly proportional to_the appropriate equilibrium rota­tional constant, C2H 2 A state Coriolis interactions induced by a-axis rotations are roughly an order of magnitude larger than those induced by b- or c-axis rotations.

Symmetry arguments also give relationships between the Coriolis coupling constants. Meal and Polo first pre­sented the form of these sum rules for a general polyatomic molecule.35,36 Watson expanded their original treatment, 37 and Watson et al. 4 reported the result of applying these sum rules to the eight nonzero Coriolis coupling constants for A 1Au acetylene. One of these rules,

(7)

applies to the ;.46 constants we use in our model. We treat A 1Au acetylene as a rigid asymmetric rotor

(F prolate top limit) with symmetric top centrifugal dis­tortion terms. A normal mode basis describes the vibra­tions, and we explicitly include vibration-rotation interac­tion terms in T Cor that directly couple V4 and v;'. Since the Hamiltonian is block diagonal in J, we treat each J level independently. The form of our Hamiltonian is

H=~(Bv+Cv) [J~+J~] +A~~+~ L (~+Ar(f,) r

- L .u~aIT""a' (8) a=a,b

where Av, Bv, and Cv are the eqUilibrium rotational con­stants for vibrational state v and n;, n;K, and ffv are qua­dratic centrifugal distortion constants. The Hamiltonian is block diagonal in v except for the last term, which gives

rise to Coriolis-induced rovibrational state mixing. The ap­pearance of terms linear in Ja motivates our use of a sym­metrized rotational basis, such as the one described by Huber,38 that gives all real matrix elements. We omit a detailed discussion of this rotational basis, but note that the matrix elements of Ja determine the rotational selection rules for Coriolis mixing inA 1Au C2H 2• Figure 4 of Ref. 33 illustrates the rotational coupling pathways for Coriolis interactions in nearly prolate asymmetric rotor and shows that a-axis Coriolis coupling does not mix levels with dif­ferent zeroth-order Ka, unlike b- and c-axis Coriolis inter­actions, which do mix zeroth-order levels differing in Ka. Thus, a-axis coupling preserves the identity of Ka while b­and c-axis interactions degrade or destroy the validity of Ka as a label for the asymmetric rotor levels of acetylene. Both J and the elf parity remain rigorous quantum numbers.

D. Fitting the data

Our analysis focuses on 150 electronic transitions to the six lowest rotational subbands of the v4lv6 pair. We extract deperturbed vibrational frequencies, partially dep­erturbed rotational constants, and Coriolis c~pling con­stants from our data by fitting the observed A state term values to a model Hamiltonian using a nonlinear least­squares procedure. Since all LIF transitions il!9luded in our analysis originate from well characterized X state vi­brational levels, we constrain the molecular constants to those of the lower levels.21 This constraint is implicit in our computation of the A state term values in Eq. (2). Numer­ical diagonalization of the effective Hamiltonian matrix in Eq. (8), which exactly treats both the a- and b-axis Cori­olis coupling of V4 and v;', yields energy eigenvalues for the v4lv;' Coriolis coupled pair. We label states by their energy rank within each J' manifold and employ an iterative, Levenberg-Marquadt nonlinear least squares procedure39

to minimize X2• Since we include only the six lowest sub­

bands of the v4lv6 pair in our fit, we restrict the basis set to the lesser of I K~ I =J' or I K~<5 and verify that expansion of the basis set does not affect the resulting eigenvalues. We obtain initial guesses for the S~ from a normal mode anal­ysis of A 1Au C2H2,40 starting values for the rotational and centrifugal distortion constants from previously observed vibrational levels of A 1Au C2H 2, and estimates for V4 and v;' from the extrapolation described previously. Figure 4 depicts the results of the fit, and Table IV gives the numer­ical results along with literature values for the rotational

-I constants of A Au v' =0.

IV. DISCUSSION

We have assigned all 316 q!:>seryed transitions in the long wavelength region of the A <--X band system to sub­bands of the Coriolis coupled v4lv6 pair. The intensities of these transitions depend strongly on the rovibrational iden­tity of the intermediate level in our double resonance scheme. We observe many unexpected transitions, with nominal IK~-l" I as large as seven, while some of the expected llKa = ± I transitions are missing. These anoma­lies very likely come from weak, zeroth-order mixing of the

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Utz et al.: V4 and Vs fundamentals in A 1Au acetylene 2749

TABLE IV. Vibrational term values and rotational constants determined from fits to the coriolis coupled two-state model".

Spectroscopic constant (cm -I)

Vo

A. B. Co D~X103 D'.,KXlOs

.o:x 106

~ ~6

# of transitions Ufit

r"

o 13.057(5)

1.123 82(9) 1.0307(1)

3.7(4) -8(2) 2.3(1)

764.90(6) 768.26(9) 11.36(8) 14.59(13)

1.1425(15) 1.1031(15) 1.0323(15) 1.0274(15)

96± 13 -354±52 -18±11 200±34

0.61±0.53 -0.838±0.7 0.7074(13) 0.6999(28)

150 0.104 cm- I

1.09

BError limits (± u) refer to the last decimal place.

intermediate X state level with background states having significant bending excitation.22,23

Extensive Coriolis perturbations are evident in the low­energy region of the reduced term value plot (Fig. 4). The J-dependence of the subbands is strongly perturbed, with several asymmetry doublets crossing themselves at inter­mediate values of J'. We identify the zeroth-order K~ level of a particular subband from the lowest J' level, since J:nin =K~, and we use the energy ordering of the e and I levels within each asymmetry doublet to assign z~oth­order vibrational quantum numbers to the levels with zeroth-order K~> I (Fig. 5). Table V lists zeroth-order K~ labels and vibrational quantum numbers for the subbands included in our fit, and shows that the energy ordering of the subbands differs from that of an unperturbed near­prolate top.

Although we can identify zeroth-order rotational and vibrational quantum numbers for the subbands, Coriolis interactions thoroughly mix the zeroth-order states and destroy the validity of these labels. As an example, we use the eigenvectors of our effective Hamiltonian matrix to compute the basis state composition of eigenstates belong­ing to the I-parity component of subband 5.41 Figure 6 shows that even in the low-J' limit, a-axis Coriolis cou­pling, with its tJ(~=O selection rule, leads to a nearly complete mixing of vibrational character in this nominally v;',K~= 1 level. As J' increases, b-axis Coriolis perturba­tions begin to mix levels with different zeroth-order K~

TABLE V. Zeroth-order identity of the subbands used in the fit.

Energy Tree! of Vibrational K' a

rank band origin" parentage parentage

1 759.6 V4 1 2 764.9 V4 0 3 768.3 v' 6 0 4 777.6 V6 2 5 797.5 V6 1 6 819.0 V6 3

'Units are in cm- I •

20 25

Rotational Quantum Number, J'

'=4

1)' 4

1)' 6

FIG. 6. Zeroth-order state mixing in the v4/v (, Coriolis coupled pair. The figure shows the basis state composition of eigenstates belonging to the i-parity compound of subband 5 as a function of J'. The basis states are labeled on the right side of the figure with their zeroth-order vibrational quantum number and the unsigned K~ quantum number for the I-parity component of the asymmetry doublet. The figure shows that the eigen­states are strongly mixed, and that their zeroth-order character changes dramatically as a function of J'.

character. At J' =27, nine different zeroth-order rovibra­tional states with K~ ranging from 0 to. 4: contribute to the eigenstate.

A. Rotational constants

The reduced X2 of our fit, X;, is nearly one, which implies a satisfactory modeling of the data,42 but the rota­tional constants for V4 and v;', and particularly their cen­trifugal distortion constants, differ significantly from those of other A state vibrations (Table IV)4,5 and suggest the further perturbation of V4 and v;'. Both Coriolis and cen­trifugal distortion terms in the Hamiltonian couple V4 and v;' to a number of remote perturbers,22,32 the nearest of which lies 1000 cm- 1 above the v4Jv;' pair. Despite the large energy difference between states, these perturbations shift the observed V4 and v;' levels by a measurable amount, particularly in the limit of high J' and K~. Applying the Van Vleck transformation41 to an effective Hamiltonian that includes interactions between the v4Jv;' pair and other remote" states reveals that, up to fourth order, the remote states perturb only the rotational and centrifugal distortion constants of V4 and v;'. Thus, the anomalous rotational and centrifugal distortion constants for V4 and v;' most likel,¥. reflect their further perturbation by a host of remote A state vibrational levels.

A second anomaly in the rotational structure of these vibrational bands is apparent only for a larger subset of the data. We observe that including successively higher asym­metric rotor levels degrades the X~ of our fit. Examining

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2750 ~ Utz et al.: V4 and V6 fundamentals in A 1Au acetylene

the residuals of the fit shows that severlJ,! of the observed subbands appear to be Jilternately higher and lower than the calculated levels. This staggerjng of levels is qualita­tively consistent with the influence" of torsional tunneling on the asymmetric rotor levelsY We suspect that such effects may be particularly importantc jn describing the rovibrational structure of the torsio~al morle, '1'4' We are currently attempting to confirm the ;role of torsional tun­neling in the eigenstate spectrum of the '1'4/'1'6 pair and plan to present a complete deperturbation 'of these two vibra­tions, including the effects of remote perturbers and tor­sional tunneling, in the future.

B. Vibrational frequencies and Coriolis constants

The vibrational frequencies we obtain for the '1'4 and '1'6 fundamentals, v4=764.9±O.1 cm- I and v6=768.3±0.2 cm -I, are relatively undistorted,' 'in contrast to the rota­tional constants discussed above.43 The sparse vibrational structure in the A state at these low levels of vibrational excitation precludes significant anharmonic coupling with other A state vibrational levels, and our data for the nom­inally K~=O levels in the low-J' limit, which are the most useful for determining the vibrational frequencies of these two bending fundamentals, ar~ least affected by Coriolis perturbations whose magnitude scales with increasing J' and K~.

We obtain approximate Coriolis coupling constants for a- and b-axis mixing of '1'4 and '1'6 from our fit. Because we use mechanical rather than harmonized frequencies in Eq. ( 6), our fitting parameters differ from the trueCoriolis constants. We expect the difference to be small, and we find that our fitting parameters very nearly obey the sum~rule [(~6)2+(S~6)2=0.9903::::::1]. We also find, in agreement with Dai et al. 33 thatthe Coriolis constants calculated from our normal mode analysis40 are accurate to better than 10%.

C. Comparison with other isotopes

The Teller-Redlich product rules 1 1 for polyatomic molecules establish relationships between the normal mode frequencies of a mQlecule's various isotopomers. Applying these rules to the A electronic state of acetylene permits a direct comparison of the '1'4 frequencies in C2H2, C2D2, and C2HD.44 We find that our assignment ofv4=764.9±0.1 cm -I in C2H 2 confirms the "very tentative" assignment of '1'4::::::526 cm- I in C2D2,45 but casts doubt on the "tenta­tive" assignment ofv4::::::586 cm- I in C2HD.44 Because the :product rules do not permit a direct comparison of other A-state normal modes, we use a different approach to eval­uate the tentative assignments of '1'6 in other acetylene iso­topomers., We plan to present that approach, expand our comparison ofthe '1'4 assignments in different isotopomers, and evaluate previous assignments of '1'5 and '1'6 in C2D 2 and C2HD in the future. 40

D. The reassignment of previously observed A 1Au C2H2 vibrations

Previously reported assignments of bands involving the '1'4, '1'5, and '1'6 normal modes used the best available theo­retical estimates of their frequencies. Our experimentally determined vibrational frequencies for the '1'4 and '1'6 fun­damentals differ from these prior estimates and permit a reevaluation of the assignments. We use our newly ob­tained frequencies for '1'4 and '1'6' which we report here, as well as a preliminary value for the '1'5 fundamental, whose assign!!lent we describe elsewhere,46 to reassign several of these A state ,£ombinations and to assign several previously unidentified A state levels.

In 1986, Scherer et al. 8 reported a previously unob­served A ~ate vibration that interacts with the K~= 1 level of C2H2 A 1Au3v3' An elegant analysis of the perturber's nature established that the new vibrational state had V3 < 3, K~= 1, a vibrational frequency of 3091.5 cm- I and that the perturbation satisfied a AK~ = 0 selection rule. These re­strictions limit the perturbation mechanism to either a-axis Coriolis or Fermi mixing. Since there were no obvious can­didates for an a-axis Coriolis interaction with 3'1'3' the au­thors concluded that they were observing a Fermi interac­tion with a previously unobserved ag vibrational state. The parity of the observed perturber clearly establishes its vi­brational symmetry" as ag arid, thus, unambiguously iden­tifies the perturbation as a Fermi resonance with an ag

vibrational level, not an a-axis Coriolis interaction with a bg level. . ,

The 'authors also found that a third vibrational state apparently perturbs the e-Ievel of the K~= 1 doublet in the new vibration. They inferred that this additional perturba­tion Was a b-axis Coriolis interaction between the Fermi pertilrber and a nearby A state vibration with bg vibrational symmetry and K~=O. The lack of experimental informa­tion dn the frequencies of ungerade vibrational fundamen­tals in acetylene forced them to make vibrational assign­"ments for these new states using the best available ab initio frequencies. They assigned the 3'1'] Fermi perturber as ( '1'2 + 2'1'4) and the Coriolis perturber of ('1'2 + 2'1'4) as ('1'4+ 3'1'6)'

Table VI lists our estimates for the vibrational frequen­cies of all states within ± 200 cm -I of 3'1'3 as well as the vibrational symmetries of these states. We calculate vibra­tional frequeEcies using a harmonic approximation since most of the A state anharmonicities are unknown. Within this limit, we predict the frequency of '1'2 + 2'1'4 to be 2916.7 cm-I, over 170 cm- I below the observed Fermi perturber. In contrast, all of the levels in the pentad containing a total of four quanta of '1'4 and/or '1'(;, which {4Vb} denotes, lie within 30 cm -I of 3'1'). Thus, we propose that one of the three {4vb} levels with ag symmetry (4'1'4' 2'1'4+2'1'(;, or 4'1'6) is the Fermi perturber. Our harmonic state count places the nearest of these levels less than 18 cm- 1 below the observed perturber, and a small, positive, diagonal an­harmonicity of 2-3 cm - 1 would easily shift any of the {4vb} levels into near resonance with 3'1'3' Since the diag­onal and off-diagonal anharmonicities of '1'4 or '1'6 are pres­ently unknown., we are unable to predict which member of

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Utz et al.: V4 and Vs fundamentals in A 1Au acetyler:te 2751

TABLE VI. Estimated frequencies and vibrational symmetries of C2H2 A state vibrational levels in the region of 3v).

Vibrational Vibrational Vibrational mode frequency (em -I) symmetry

v2+2v.i 2916.7 ag

V2+VH V6 2920.1 bg , ~'2+2V6 2923.4 ag

vi 3040.8 ag

4v.i 3059.6 ag

3V4+V6 3063.0 __ ~_bg .-:-.

2vH2v6 3066.3 ag

V';+ 3V6 3069.7 bg

4V6 3073.0 ag

3v) 3088.14" ag

vi+V) + v'; 3199.4 au Vi+v3+ v6 3202.7 bu

'Experimental value from Ref. 8.

the ag symmetry triad is the Fermi perturber. The third vibrational state reported by Scherer et al. 8 provides fur­ther support for our assignment of the Fermi perturber. Each member of the triad of ag levels with four quanta of vibration has two b-axis Coriolis partners in the nearby 3V4+V6 and v4+3v6 vibrational levels of bgsymmetry. One of these two levels is likely to be the unseen Coriolis per­turber of the observed Fermi perturber. The mixing of 3v) with {4vb}, all of .Fhose members correlate with die cis­bend (vs) in the X state, may also explain the recent re­sults of Yamanouchi et al.;47 who report a difference in Franck-Condon overlap between the 2v} and 3V3 levels and highly vibrationally excited X state levels containing excitation in vs.

Van Craen et al. 5 reported their observation of an un­identified A state vibronic level with ag vibrational s~mme­try and a band origin of 5156.89 cm- I above the A state origin. They reported a· separation of nearly 35 cm - I be­tween the Ka=O and 1 subband origins of the level and suggested that the two Ka sublevels may belong to different vibronic bands whose origins differ by 15-20 cm- I

. 'Since these sub~nds appear in direct absorption measurements from the X state, the transitions must have relatively large Franck-Condon factors. We calculate twelve ag vibrational levels to lie within 200 cm -I of the observed levels and list them in Table VII. The most likely candidates are the three ag symmetry members of the 2V3 +{ 4vb} pentad (2v3+4v4' 2V3+2v4+2v/;, and 2v3+4v6)' The nearest of these levels lies within 2 cm - I of the observed band origin. The V3 excitation in these levels provides favorable Franck-Condon overlap with the X state, and it is likely that two of the three ag levels are separated by about 15 cm-I, which explains the observation of two nearby, but separate, vibronic bands. Thus, we assign the observed Ka=O level with a band origin at' 5156.89 cm- I to one member of the 2v}+{4vb} pentad, and the Ka=l level with a subband origin of 5191.44 cm -I to a higher-lying member of the pentad. Once again, we are unable to assign these levels unambiguously to specific members of the pen­tad because we do not know anharmonicities for v4 and v6'

TABLE VII. Estimated frequencies of ag symmetry C2H2 A state vibra­tions in the region of state X.

Vibrational Vibrational mode frequency (em-I)

v2+2vJ+2v'; 5011.8

VHVJ+ V6 5012.6

v2+ 2v)+2v6 5018.5 5v) 5039.62"

Vi+ 2v3 5135.94.1 2v)+4v'; 5154.7 2vH vs+v6 5155.5

Vx 5156.89"

2vJ+ 2v4+ 2v6 5161.4

VS+ 3V6 5162.2 2v)+4v6 5168.1 3v2+v) .5208.2 2v2+vJ+2v'; 5351.2

"Experimental values from Ref. 5.

E. Vibrational resonances in A 1Au C2H2

Our reinterpretation of the perturbations observed by Scherer et al. suggests that the near-degeneracy of 3V3 and the {4vi,t levels is the basis for an anharmonic resonance between A state vibrational levels. Our assignment of other previously reported perturbers, which Table VIII summa­rizes, reinforces this interpretation and suggests that this resonance is a pervasive feature in the rovibrational struc­ture of A IAu C2H2• As a result, we propose that for states with three or more quanta of v}, one must consider the role of an anharmonic resonance with the correspondingAv} =~3, Avi,=+4 mode. Since v} is the~ominant Franck­Condon-a£.tive vibrational mode in theA state, many of the observed A state vibronic levels contain multiple quanta of v} and are candidates for this anharmonic resonance.

The strong Coriolis interaction between V4' and vI; is one example of another important vibrational resonance in A IAu C2H2• The near-degeneracy of these two modes and their sizable interaction matrix elements make the exten­sive Coriolis perturbation of other A state vibrational levels containing excitation in either V4 or vI; likely. We expect the AV4= ±1, Av/;= =F 1 resonance to alter the rotational structure of the affected states dramatically, as we observe in our reduced term value plots for the v4/v6 pair, and to allow transitions to additional vibronic bands whose zeroth-order symmetry would ordinarily prevent their de-

TABLE VIII. Proposed assignments of previously observed C2H2 A state perturbers,

Perturbed level

3v)" 4V3b vi+3v)b Vi+ 4v3b

"Reference 8. bReference 5.

Vvib (em-I)

3088.16 4072.95 4489.40 5461.02

Proposed Veale C

perturber (em-I)

{4v;,} . 3060-3073 vJ+{4v;,} ·4107-4120 vi + {4Vb} 4447-4460

v2+ v3+ { 4v;,} 5494:-5507

cCalculated for the perturbing states within the harmonic approximation.

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2752 Utz et al.: 114 and 116 fundamentals in A 1Au acetylene

tection. At higher J', Coriolis mixing of the K~ basis func­tions may permit transitions to additional rotational sub­bands of the perturbed levels.

The v4Jv;, Coriolis resonance may also alter the behav­ior of A state anharmonic perturbers containing excitation in either V4 or v;'. Since these perturbers are likely to have irregular rotational structure, their interaction with an­other A state vibrational level might result in an unusual pattern of anharmonic perturbation. The number of per­turbing eigenstates may also increase. For example, in the V3 + { 4v/,} /4V3 anharmonic resonance assigned in Table VIII, Coriolis interactions among the members of V3 + {4v/,} may distribute the character of a single anhar­monic perturber over all eigenstates in the pentad.

V. CONCLUSIONS

A vibrational overtone-UV double resonance tech­nique allows us to excite and detect transitions to theyre­viously unobserved ungerade vibrational levels in the A lAu electronic state of acetylene (C2H 2). This Jwo-photon technique complements conventional direct UV absorption and single-photon UV-LIF studi~s of acetylene by provid­ing access to a different set of A state vibrational levels. Using this approach, we have observed and assigned 316 transitions to subbands of the V4 and v;' vibrational funda­mentals. A reduced term value plot shows these two bend­ing fundamentals to be nearly degenerate and very strongly perturbed by the a- and b-axis Coriolis interactions that couple them. Analysis of the six lowest subbands yields deperturbed vibrational frequencies for V4 and v;'. Coriolis interactions with remote perturbers and the possible effects of torsional tunneling on the asymmetric rotor levels of V4 prevent our complete deperturbation of rotational and Co­riolis coupling constants for these two states. The rigorous e/ f parity selection rules for the electronic transitions per­mit our unambiguous assignment of vibrational frequencies as v4=764.9±O.1 cm- l and v;'=768.3±O.2 cm- l .

Our experimental measurements of the V4 and v;' fun­damental frequencies which are significantly different fro~ previous estimates, allow us to calculate the location of A state combinations and overtones involving V4 or v;' with much greater accuracy than was previously possible. We use the~ calculated frequencies to reassign previou~y ob­served A state vibrations and to assign unidentified A state vibrations whose presence was directly observed or was inferred from the perturbation of an observed level. Our ability to !!.ssign virtually all of the previously unidentified levels as A state vibrations suggests that additional elec­tronic states are, in general, unnecessary in explaining our observations and other data. The one exception is the per­turber of K~ = 3 of V2 + V3 reported by Watson et aI., 4

which we are unable to assign. The new frequencies for the V4 or v;' fundamentals al­

low us to identify two vibrational resonances that seem to be important in determining the rovibrational structure of A lAu C2H 2• The first of these is based on the direct Cori­olis interaction between V4 and v;'. We expect the near­degeneracy of these two fundamentals to cause analogous interactions among higher-lying combination'and overtone

levels involving V4 and v;'. The perturbations of 3V3 re­ported by Scherer et al. suggest a second type of vi!Jra­tional resonance based on the near-resonance of 3V3' and the pentad of states containing four quanta of V4 or v;', which we designate as {'!Y/,}. We show that the 3v3++{4v/,} resonance affects other A state vibrations as well and sug­gest that this anharmonic resonance is important for states containing three or more quanta of V3.

ACKNOWLEDGMENTS

We thank Professor E. L. Sibert of the University of Wisconsin-Madison and Professor R. W. Field of MIT for their helpful suggestions and Anne McCoy for provid­ing a portion of the computer code. The Air Force Office of Scientific Research supports this work.

1 C. K. Ingold and G. W. King, J. Chern. Soc. 1953, 2702. 2K. K. Innes, J. Chern. Phys. 22, 863 (1954). 3J. T. Hougen and J. K. G. Watson, Can. J. Phys. 43, 298 (1965). 4J. K. G. Watson, M. Herman, J. C. Van Craen, and R. Colin, J. Mol. Spectrosc.95, 101 (1982).

5J. C. Van Craen, M. Herman, R. Colin, and J. K. G. Watson, J. Mol. Spectrosc. 111, 185 (1985).

6J. C. Van Craen, M. Herman, R. Colin, and J. K. G. Watson, J. Mol. Spectrosc. 119, 137 (1986).

'T. R Huet, M. Godefroid, and M. Herman, J. Mol. Spectrosc. 144, 32 (1990).

8G. J. Scherer, Y. Chen, R. L. Redington, J. L. Kinsey, and R. W. Field, J. Chern. Phys. 85, 6315 (1986).

9p. D. Foo and K. K. Innes, Chern. Phys. Lett. 22, 439 (1973). 1OL. E: Brus, J. Mol. Spectrosc. 75, 245 (1979). 11 G. Herzberg, Molecular Spectra and Molecular Structure IL Infrared

and Raman Spectra of Polyatomic Molecules (Van Nostrand Reinhold, New York, 1945).

12 A. L. Utz, J. D. Tobiason, E. Carrasquillo M., M. D. Fritz, and F. F. Crlm, J. Chern. Phys. 97, 389 (1992).

13 J. D. Tobiason, A. L. Utz, and F. F. Crim, J. Chern. Phys. 97, 7437 (1992).

14We estimate that we excite about 10-3 or 2X 10-4 of the molecules to the selected rotational level of 3113' or (1112°0), respectively.

15The infrared laser bandwidth for measurements using (1112°0) as the intermediate level is about 0.2 em-I. .

16D. S. King, P. K. Schenck, K. C. Smyth, and J. C. Travis, Appl. Opt. 16,2617 (1977).

I'K. C. Smyth and P. K. Schenck, Chern. Phys. Leu. 55, 466 (1978). 18We estimate that fewer than 6 in 1000 of the vibrationally excited

acetylene molecules have suffered an inelastic collision during the ex­periment (Z < 0.006). See Ref. 12.

19S. Ghersetti, J. E. Adams, and K. N. Rao, J. Mol. Spectrosc. 64, 157 (1977). '

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Utz et al.: V4 and V6 fundamentals in Ii 1Au acetylene 2753

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43 The reported vibrational frequency error limits are ± 20" limits from our fit.

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