ELSEVIER International Journal of Mass Spectrometry and Ion Processes 159 (1996) 37-48

Bend-stretch Fermi resonance in NO; observed by delayed pulsed-field ionization zero-electron kinetic energy photoelectron spectroscopy

Hiroshi Matsui*, Jane M. Behm, Edward R. Grant

Department of Chemistry, Purdue Universiv, West Lafayette, IN 47907, USA

Received 3 April 1996; accepted 26 June 1996

Abstract

By means of zero-electron kinetic energy (ZEKE) threshold photoelectron spectroscopy, we examine bend-stretch Fermi resonance in NO;. Accurate fundamental frequencies are obtained by using the (000) 3~0 Rydberg state as a reference state for all ionic vibrational ZEKE spectra. The degree of (100)-(02°0) Fermi resonance observed in NO; is comparable to that found in the NO* 3pu Rydberg state, and results for both systems agree well with recent CCSD(T) and MRD-CI a6 ink calculations. Comparison of the vibrational frequencies of the 3pa Rydberg state and the cation suggests that the presence of the Rydberg electron slightly perturbs the harmonic potential and its second-order anharmonicities, but has little effect on the cubic coupling term associated with core Fermi resonance.

Keywords: Fermi resonance; Pulsed-field ionization; Photoelectron spectroscopy

1. Introduction

In recent work, we have investigated Fermi resonance in NO; by extensively studying the vibrational structure of the 3pa 2Cc Rydberg state of the neutral molecule. Comparative vibra- tional frequencies, as well as intensity patterns in vibrational autoionization, suggest that potential energy surfaces in the Rydberg core and the free cation are substantially parallel, and thus lead to the expectation that vibrational coupling will be the same. This supposition, however, neglects the effect of the Rydberg electron, which autoioniza- tion lineshapes show, couples strongly with vibrational motion in certain modes. One mani- festation of this coupling can be detected in the

* Present address: Department of Chemistry, Columbia Univer- sity, New York, NY 10027, USA.

symmetric stretching vibration, where the funda- mental frequency in the Rydberg state differs from that of the cation by approximately 14 cm-‘. Data comparing cation versus Rydberg fre- quencies for the overtone of the bend have been unavailable, which has left open the question of whether the interaction between symmetric stretching and the 3pa Rydberg electron orbital motion alters vibrational coupling in the core. We have now returned to the cation, and, in high-resolution threshold photoionization experi- ments, determined precise frequencies of the bending overtones in NO; for comparison to those of the Rydberg state. The results complete the picture of mode-dependent quantum defects for the low-lying vibrational levels in the 3pa *Ci Rydberg state of NO2 and establish the extent to which the extravalent electron plays a role in vibrational coupling.

016%1176/96/$15.00 Copyright 0 1996 Elsevier Science B.V. All rights reserved PII SO168-1176(96)04440-O

38 H. Matsui et al./lnternational Journal of Mass Spectrometry and Ion Processes 159 (1996) 37-48

By analysis of the 3pa *C: Rydberg state of N02, we have characterized Fermi resonance associated with the coupling between the symmetric stretch fundamental (100) and the symmetric overtone of the bend (02’0), as well as higher vibrational interactions such as those between the states (llO)-(03’0) (0420)-(1220), and (0400)-(1200)-(200). The experimental vibrational energy levels yield anharmonic con- stants, harmonic frequencies, the force constant krz2, energy shifts due to Fermi resonance, and Fermi matrix elements [l]. Though we find a cubic anharmonicity, k122, comparable to that of C02, observed splitting due to Fermi reso- nance in the 3pa Rydberg state of NO2 is smaller because the zeroth-order bend-stretch frequency mismatch, Ao, is larger. Wavefunc- tions derived from these coupling parameters produce a (02’0) state that includes ca. 12% symmetric stretch.

For the present study we apply three-color, triple-resonant absorption with zero-electron kinetic energy (ZEKE) detection to examine directly bend-stretch Fermi resonance in NO;. From rotational assignments of the ZEKE spec- tra, we determine thresholds for (010) (02’0) (0220), and (100). To check assignments and con- firm positions of cation bands (Y~v&, we com- pare spectra obtained in vertical transitions from matching (Y~v& 3pa intermediate states with off-diagonal threshold photoionization scans from a common level of 3pa (000). We find excellent agreement between the threshold ener- gies obtained by these two methods. This proce- dure has produced improved estimates for all of the fundamental frequencies of NO; [2,3]. From an analysis of the threshold photoionization spec- tra, we find that the degree of (lOO)-(02*0) Fermi resonance in NO3 compares closely with that of the 3pa Rydberg state, and that frequencies in both cases agree well with new CCSD(T) ab initio calculations [4]. From these results, we conclude that core-Rydberg electron coupling in the 3pa 2C,+ state has relatively little affect on higher-order anharmonic features of the

potential that couple bending with stretching vibrational states in the NO; core.

2. Experiment

Our newly constructed apparatus uses standard methods of ZEKE photoelectron spectroscopy [5]. The sample gas, NO*, seeded 1:1:20 in 02:He is cooled by expansion through a differ- entially pumped pulsed-jet source (General Valve, IOTA 1). The skimmed molecular beam enters a magnetically shield longitudinally oriented ZEKE spectrometer through the first plate (repeller) of a three-gridded plate ion-optics assembly. Three superimposed laser beams cross the molecular beam between the repeller and second (extractor) plates, which are spaced by about 2.5 cm. The distance between the beam valve and the point of excitation is about 7.5 cm. For the present experiments, intermediate rotational levels of the (000), (010) (020), and (100) vibrational modes of the 3pu 2CU+ Rydberg state are selected by double resonance. The third laser then promotes excited molecules to succes- sive ionization thresholds, where we scan over the rovibronic structure of the (000), (OlO),

0 3.7 4.0 4.3 4.6 4.9 5.2 5.5

Time Ws)

Fig. 1. Shape of the stairway extraction pulse used for delayed pulsed-field ionization.

H. Maisui et al.linternational Journal of Mass Spectrometly and Ion Processes 159 (1996) 37-48 39

(OZO), and (100) states of NO;. Near-threshold high Rydberg electrons are released and extracted by delayed pulsed-field ionization (2-5 ps) and detected by a two-plate multi- channel electron detector. The extractor is held at ground. For some experiments, to maximize the threshold photoionization signal, we apply a simple square pulsed field from 800 mV to 2.4 V to the repeller. To optimize resolution, we use a Tektronix AWG-2020 arbitrary waveform gen- erator to produce a stepped-pulsed field, as shown in Fig. 1 [6]. The ZEKE signal is amplified and collected by a LeCroy 9450 digital oscilloscope.

Tunable radiation for the first and the second excitation steps are provided by Lambda Physik 3002 and 2002 dye lasers pumped by a Lambda Physik EMG 201 MSC XeCl excimer laser. A single-mode optical parametric oscillator (Con- tinuum Mirage 500) pumped by a seeded Con- tinuum Powerlite 8100 Nd:Yag laser is used for the third step. The bandwidths of the dye lasers are 0.2 cm-’ and that of the OPO is 0.01 cm-‘. The wavelengths of the lasers are calibrated by a Burleigh W-4500 pulsed wavemeter.

Scheme I

3. Results

3.1. State selection via the 3pa ‘C: Rydberg state

For the present study we apply three-color, triple-resonant absorption with ZEKE detection to examine bend-stretch Fermi resonance in NO;. We use two different excitation schemes as shown in Fig. 2. In Scheme I, we add w3 from 3pa (yIy2v3) to reach the same set of ionic vibrational quantum numbers (v 1~2~3) at thresh- old. In Scheme II, we start in all cases from 3pa (000), adding w3 to reach ionic (Y~Y&. Scheme II is made possible by discrete-continuum coupling which distributes (000) character and thus off-diagonal Frank-Condon intensity to those otherwise forbidden transitions that pro- ceed from 3pa (000) to high-Rydberg states built on (OlO), (020), and (100) states of the core. Although at the cost of signal intensity, this method has the advantage of directly giving the relative positions of band origins from a com- mon rovibrational reference point. From rota- tional assignments of the ZEKE spectra obtained via Scheme I, we determine thresholds

w+

NO2 3~0 Rydberg state

Scheme II

(1W WV (010) NW

Fig. 2. An energy level diagram for the excitation of NO2 from its 3~0 Rydberg state to various photoionization thresholds. Scheme I: excitation to ionic (YIY~Y~) vibrational states from (Y,Y~Y~) 3p (T Rydberg states. Scheme II: excitation to ionic (Y~Y~Y~) vibrational states from the (000) 3~0 Rydberg state.

40 H. Matsui et al./Internuttonal Journal of Mass Spectrometty and Ion Processes 159 (1996) 37-48

for (010) (02’0) (0220), and (100). Assignments are checked and positions confirmed by the ZEKE spectra obtained in Scheme II.

We achieve rotational and vibrational selec- tion in the 3pa *C: Rydberg state as follows. The first laser (wr), tuned in the visible around 20 800 cm-‘, excites ground-state NO2 to its mixed Bi, Bz, A2 system of long-lived, low- lying excited electronic states. The originating states depicted in excitation Scheme I are popu- lated using a second laser (w2) to excite the mole- cule to a selected rotational level in the (000) (02’0), (0220) or (100) band of the 3pa 2C: Ryd- berg state, using an ultraviolet photon energy between 34 740 and 36 190 cm-‘. The intermedi- ate state for this two-color transition is adjusted for maximum double-resonant intensity by syn- chronously tuning w i to the red and w2 to the blue at fixed total transition energy. The third laser promotes the system to the corresponding (V I v2y3) ionization threshold with photon ener- gies around 21670 cm-‘. In excitation Scheme II, the second laser in every case excites the molecule to the (000) level of the 3pa “C: Ryd- berg state, using an ultraviolet photon energy at 34747.9 cm-‘. Third laser scans promote transi- tions to ionization thresholds for (000), (010) (020), and (100) with energies between 21600 and 23100 cm-‘. By fixing the energies of the second and the third color on a specific transition and scanning the first laser, we obtain spectra of the rotational levels of the NOz *Ai ground state and select a specific rotational state for the triple- resonant ZEKE experiment.

For all vibronic states of N1602, nuclear-spin statistics allow only states symmetric in the exchange of the nuclei. Thus, all vibrational states have permutation-inversion symmetry either ( + , S) or ( - , S) [7]. This symmetry is determined by the electronic symmetry of the u, Rydberg electron combined with the rovibronic symmetry of the cation core. For the cation ground state, the vibronic symmetry of the core is C,. For states which are vibronically C, the effect of nuclear-spin statistics is to exclude cer-

tain rotational quantum numbers. Thus, only odd rotational quantum numbers, N’, are present for 3pu (000), (02’0), (100) vibronic states. All values of N’ greater than two are found for (02*0) and all values of N’ greater than one are found for (010). We select first- and second- photon frequencies that excite transitions to 3pu *C,’ Rydberg N’ = 3 from ground states IV’ = 1 for (000) and V = 3 for (02’0) (0220), and (100). Two-photon selection rules allow transitions strictly from - to - , or from + to + . This has the effect of constraining the ground-state prolate-top K substates from which transitions to various Rydberg vibrational levels can origi- nate. Thus, two-photon selection rules allow tran- sitions to (000), (02’0) and (100) only when x’ is odd. In the present work, scans over these bands and (02*0) originate from K” = 1 (prolate sym- metric top states with ZC’ = 3 and higher are neg- ligibly populated in our molecular beam).

3.2. Rotational structure in vibrationally excited states of NO;

Third-photon threshold photoionizing transi- tions from individual 3pu rotational states are governed by selection rules and propensities for Rydberg-Rydberg transitions. Within a vibra- tional band, zeroth-order intensities are deter- mined by rotational line strengths for Hund’s case (b) to case (d) transitions. A correlation dia- gram for tracing the evolution from case (b) to (d) for 3pu (000) is summarized in Ref. [3]. The cation cores of (000), (OlO), (02’0), (0220), and (100) are vibronically C,, nU, C,, Ag, and C,. To the extent that Rydberg orbital angular momen- tum L is a good quantum number both in the originating 3pu (L = 1) and final near-threshold (ZEKE) high-Rydberg states, g - u selection rules require the final L to be an even number for vertical transitions from 3pu (vrv2v~) to ionic (yrv2v3) in all cases, and from (000) to all (V r V& for which the final state has g vibrational symmetry. In general, from an initial Rydberg state of L = 1 in a rotational state N’, we should

H. Matsui et al.llnternational Journal of Mass Spectrometry and Ion Processes 159 (1996) X-48 41

expect N’ = N’ i 3 by Hund’s case (b) to case (d) rotational selection rules governing total angular momentum less spin [3]. Because the present spectra originate in each case from 3pa (zJ~v~v~) Rydberg N’ = 3, we can expect N+ = 0,2,4,6 for ionic states of C, vibrational symmetry. For AE ionic (02’0), transitions originating from the L =Upa (02*0) Rydberg N’ = 3 state access N + = 2, 3, 4, 5 and 6. For transitions from 3pa (000) to ionic (010) vibrational states, g - u selection rules require the final L to be odd. Inten- sity for these transitions is transferred by vibronic coupling between L = 1 high-Rydberg states of NO; (010) and L = 0 and 2 states of the NO; (000) cation plus free-electron continuum. Such coupling paths, conserving parity and total angu- lar momentum, can be constructed for all NO;

(010) core rotational quantum numbers, N’ = 1, 2, 3...

3.3. Vibrational positions: findamental frequencies of NO;

Figs 3 and 4 show vertical threshold photo- ionization spectra of NO; vibrational states (000) and (100) obtained in transitions from 3pa Rydberg levels (000) N’ = 3 and (100) N’ = 3 respectively. Fig. 5 displays a composite of three scans consisting of vertical spectra of the C and A components of the bending overtone, (02’0) and (02*0), observed from corresponding levels in the 3pa Rydberg state, accompanied by a spectrum of the structure observed in this region by scanning from the vibrationless intermediate

I 77320

Three-Photon Frequency (cm-‘)

Fig. 3. ZEKE threshold photoionization spectrum of NO; (000) via the 3pa (0OO)N’ = 3 intermediate Rydberg state. The frequency is referenced to the ground A”’ = 0, K’ = 0 state.

42 H. Matsui et al.ilnternational Journal of Mass Spectromety and Ion Processes 159 (1996) 37-48

3pa (000) state. Similar off-diagonal scans from 3pa (000) to NO; (100) and (010) are shown in Fig. 6. Frequencies of spectra are corrected for extraction fields and referenced to the lowest rotational level of the neutral ground state, K” = 0, w = 0.

Non-vertical transitions directly confirm the positions of vibrationally excited states com- pared with (000). As a result, we obtain improved estimates of the fundamental vibrational frequen- cies of NO; as shown in Table 1. Also listed for reference in Table 1 are frequencies for higher vibrational states, (110) and (200), determined by earlier measurements on the cation [2,3] and 3~0 Rydberg state [l].

3.4. Rotational assignments of ZEKE spectra

Totally symmetric states (Figs 3-5(b) and Fig. 6(b)) show the structure expected from 3pa intermediate N’ = 3, consisting of transitions to even N’ = 0, 2, 4 and 6. Adiabatic ionization potential and threshold energies derived from ZEKE spectra agree well with earlier observa- tions based on autoionizing Rydberg series extra- polations [3]. Both (02’0) spectra observed in vertical transitions from 3pa (02’0) (Fig. 5(b)) and in off-diagonal transitions from 3pa (000) (Fig. 5(a)) show the same rotational states. Weak structure on the blue side of the non-ver- tical spectrum in Fig. 5(a) is assigned to the

I ’ ’ 1 t 1

N+ 0 2 4

I I I , I

78690 78700 78710 78720

Three-Photon Frequency (cm-‘)

Fig. 4. ZEKE threshold photoionization spectrum of NO; (100) via the 3pu (100) N’ = 3 intermediate Rydberg state. The frequency is referenced to the ground N” - 0, x*’ = 0 state.

H. Matsui et al.lIntemational Journal of Mass Spectrometry and Ion Processes 159 (1996) 37-48 43

(02’0) state by comparison with the vertical spectrum from 3pa (02’0) pictured in Fig. 5(c). Although weak coupling obscures rotational structure in the (010) off-diagonal transition from 3pa (000) we mark rotational states N+ = 1, 2, 3, 4, 5 for reference as shown in Fig. 6(a).

4. Discussion

4.1. Bending and symmetric stretching frequencies of NO;

To obtain band positions, we extrapolate the cation rotational structure observed for each band

to its origin according to

T, = w, + BJv(N + 1)

and adjust transition energies to reference a common originating state of neutral NOz. Funda- mental frequencies of NO; are summarized in Table 1, together with fundamental frequencies of the NOz 3pa ‘C: Rydberg state, frequencies calculated by MRD-CI ab initio calculations [8], and frequencies calculated by CCSD(T) ab initio calculations that include the effect of Fermi resonance [4], the best results for which are obtained by combining CCSD(T)l[4s3p2dlfl an- harmonic constants with CCSD(T)/[Ss4p3d2flg] harmonic frequencies [9]. Fundamental frequen- ties derived from individual vertical spectra are

I I I I

(4 N+ = 02 4 6

(b)

(cl NC= 234 5 6

I I I /

78520 76540 78560 76560

Three-Photon Frequency (cnC1)

Fig. 5. ZEKE threshold photoionization spectrum of NO; (020): (a) through 3~0 (000) N’ = 3 (Scheme II), (b) through 3~0 (02’0) N’ = 3 (Scheme I), (c) through 3po (02’0) N’ = 3 (Scheme 1). All frequencies are referenced to the ground K’ = 0, K’ = 0 state.

44 H. Maisui et al.linternational Journal of Mass Spectromeq and ion Processes 159 (1996) 37-48

confirmed by a set of scans over vibrationally excited thresholds originating from the 3pa (000) state, which yield relative spacings from a common reference point.

In the limit where the 3pa Rydberg electron is separable from the core, one expects a close match of vibrational frequencies between the 3pa 2C: Rydberg state and the cation. However, for the bending fundamental, (OlO), the vibra- tional frequency of the cation is 6 cm-’ higher than that of the 3pa Rydberg state. For the sym- metric stretch the frequency of the cation is 14 cm-’ lower than that of the 3pa Rydberg state. Similarly, shifts to lower frequency are seen for the overtones of the bend. From relative shifts in the vibrational positions, we can conclude that

the binding of a 3pa Rydberg electron apparently affects both the harmonic potential and the anhar- manic coupling terms. We shall be interested to compare these apparent lower-order shifts upon electron binding to the comparative effect of Fermi resonance on positions in the (02’0)- (100) dyad. Shifts can be expected to be small because they relate to Fermi matrix elements by:

;( JiiGzzG-Ao)

in which for NO; [l], A0 (the unperturbed energy separation E” 000j-E~2 is much larger than the Fermi matrix element, W~r~)-$), and thus dominates the expression. This large A0 diminishes the effect of Fermi resonance and

77940

Three-Photon Frequency for (010) (cm-‘)

77950 77960 77970 I I I 1 f ’

6- (a)

(b)

I , I , I I , , , , , , , , , , , , , I , , , 1

78670 78680 78690 78700 78710 78720

Three-Photon Frequency for (100) (cm-‘)

Fig. 6. (a) ZEKE threshold photoionization spectrum of NO; (010) through 3~0 (000) N’ = 3 (Scheme II). (b) ZEKE threshold photoionization spectrum of NO; (100) through 3~0 (000) N’ = 3 (Scheme II). All frequencies are referenced to the ground N’ J 0, K’ = 0 state.

Table 1

H. Matsui et al.JInternational Journal of Mass Spectrometry and Ion Processes 159 (1996) 37-48 45

Experimental fundamental frequencies and overtone bands for the NOr cation and 3~0 ‘Z: Rydberg state, as well as CCSD(T) and MRD-CI ab inifio results. All values are in cm-‘. Values for (110) and (200) are from Ref. [2]

Experimental

NO2 3pu ‘Z: [l] NO; ‘Z’ cation B

Theoretical

CCSD(T) [4] MRD-CI [8]

(000) 0.0 0.00 0 0.00 (010) 621.2 626.90 625 634 (02”O) 1238.0 1234.44 1238 1250 (02 ‘0) 1250.7 1242.47 1251 -

VW 1401.1 1386.84 1384 1385 (110) a 2039.5 2031.90 - - (200) a 2801.2 2775.00 -

a See Refs. [2,3].

any difference in anharmonic coupling between state ( - 1.658 cm-‘)[l]. Because transitions from the ion core and the 3pa Rydberg state. The the (Y~Y& 3pa ‘Ci Rydberg state to the ionic (V evaluation of Fermi resonance coefficients is r v~Y~) state are observed to be strongly vertical, it important because it reveals information about is reasonable to assume that this local bending vibrational state mixing, and the role in this pro- anharmonicity in the ion and Rydberg state are cess, if any, played by the 3~0 Rydberg electron. similar. A similar value of g22 for the isoelectro- To sort out the magnitudes of these various effects nic molecule, C02, ( - 1.046 cm-‘) [lo] supports we now analyze the ZEKE spectrum to extract this assumption. Subtracting eqn (2) from eqn (3) the strength of Fermi coupling in the bare cation. yields eqn (5):

4.2. Fermi resonance in the cation (5)

Including Fermi resonance, the energy levels of the (010) (02’0) (0220) and (100) states of the ion can be expressed in terms of fundamental frequencies and anharmonic corrections,

E(,oo) = 01 +2x11 +x21 + 1/2X31 + w (1)

E(02’0) = 202 + 8x22 + 4g22 + x21 + x32 (2)

E (02”O) = 2w2 + 8x22 + x21 + x32 - w (3)

E(Ol0) = ~2 + 3x22 + g22 + ]/2X21 + 1/2Xj2 (4)

where xll, ~22, xzlr x3?, gzz are anharmonic con- stants, w t and w2 are harmonic frequencies and W is the energy shift due to Fermi resonance.

Substituting our estimated value for g22 gives an energy shift, W, due to (100)-(02°0) Fermi reso- nance of 14.86 cm-‘.

Next, we consider the Fermi resonance matrix element WAHOO)-& which can be expressed as,

@-A; w(ltlO)-(02”O) =

klz =- 2

fi

Table 2

We compute the (100)-(02°0) Fermi resonance matrix and cubic anharmonicity con- stant, krz2, using the experimental fundamental frequencies in Table 1 and the anharmonic con- stant, g2?, determined for the 3pa ‘C: Rydberg

Comparison of the unperturbed separation (A,,), the Fermi reso- nance matrix element, W&-(“2, and cubic anharmonicity, k,Zz, determined for the (lOO-(02”O) Fermi resonance in NO;, in the 3~0 Rydberg state of NO?, and CCSD(T)/[4s3p2dlfl ab initio cal- culations for NO;. Quantities determined experimentally for NO; use gL: = -1.658 cm-’ as obtained for the 3pa Rydberg state. All values are in cm-’

NO; ‘C; 121.96 45.69 -64.62 NO: 3~0 ‘E; [I] 124.44 52.72 -74.56 Ah initio [4] 117.94 48.0 1 -67.90

46 H. Matsui et ai.!lnternational Journal of Mass Spectrometry and ion Processes 159 (1996) 37-48

where A represents the separation of the two perturbed energy levels, E~tooj - Eh2, and A0 denotes the unperturbed separation, E&a, - $12. The unperturbed energy levels can be obtained from eqns (7) and (8):

Et:OO) = E( loo) - w (7)

qo,oo) = -qo,oo) + w (8)

where E~looj and E~,,o,) are the experimentally observed energy levels of NO; at 1386.84 and 1234.44 cm-’ respectively. Then E&,, is calcu- lated as 1371.98 cm-’ and E& as 1249.30 cm-‘. These unperturbed energies are then substituted into eqn (6) to obtain the Fermi resonance matrix element, @jj00-(02, as 45.21 cm-’ and the cubic anharmonicity constant, krZ2 as - 63.94 cm-‘. A comparison of the Fermi resonance matrix ele- ment and k122 determined experimentally in NO; with the experimental quantities in the NO* 3pa ‘C: Rydberg state and the CCSD(T)/[4s3p2dlfl ab ini& calculation for NO; [4] are summarized in Table 2. We find good agreement for the k122 and Fermi resonance matrices among ionic and 3~0 Rydberg state observations, and CCSD(T)/ [4s3p2dlfl ab in& calculations. Upon rearran- gement, eqn (6) yields

Az=A~+41W~loo,~~o~~~o~~z (9)

The small difference observed in We,,,) _ (02~10J (and thus k122) between the 3pa ‘Ci Rydberg state and the ion apparently arises from the fact that both the ionic A and Aa values shift by about the same amount between the 3pa ‘C: Rydberg state and the cation, and this effect cancels in eqn (9).

The close agreement in the Fermi resonance terms for the 3pa ‘C,+ Rydberg state and the ion suggests that the core-electron coupling does not significantly alter the degree of Fermi resonance in the Rydberg states of N02. Thus, even though the presence of the electron alters the harmonic potential and quadratic anharmonic coupling, it has only a small effect on the third-order term, km

4.3. Comparison of harmonic and anharmonic coefjicients in the 3pa “C: Rydberg state and the cation

When we subtract eqn (4) from eqn (2), we obtain

x22 + gzz = l/=,0220, - Qolo) (10)

Substituting experimental frequencies for the 3pa ‘Ci Rydberg state and the ion from Table 1 into eqn (10) yields:

x22 + g22 = 4.15 (3pa ‘Cu+ Rydberg state)

x22 +gzZ = -5.57 (the cation)

If we assume g22 to be similar for the 3pa 2Cl Rydberg state and the cation, we calculate ~22 to be - 3.91 cm-’ in the cation, and, by contrast, 5.81 cm-’ in the 3pa Rydberg state.

This difference has a substantial effect on the harmonic frequencies predicted for bending in the cation and 3pa Rydberg state. Off-diagonal bending anharmonicities computed for NO; [9], x21 = - 5.766 cm-’ and x32 = - 16.447 cm-‘, can be combined with x22 = - 3.91 cm-’ to estimate a bend harmonic frequency, w2, of 651.39 cm-‘. Combining the same off-diagonal anharmonici- ties with x22 = 5.81 cm-‘, we obtain harmonic wZ =616.70 cm-’ for the 3pa Rydberg state. Thus, anharmonicity substantially raises the fre- quency observed for v2 in the Rydberg state while lowering it in the cation. The net effect is a small apparent red shift of 6 cm-’ upon comparing the neutral to the cation. In the (0220) overtone, displacements due to ~22 anhar- monicity are larger in each case, and the observed frequency difference appears as a 8 cm-’ blue shift on electron binding.

Frequencies listed in Table 1 for (100) and (200) show that the effects of anharmonicity are smaller in symmetric stretch and appear more concordant in the cation and neutral Rydberg state. Thus, electron binding blue shifts sym- metric stretch 14 cm-’ in the fundamental and 26 cm-’ in the overtone. The combination state

H. Matsui et al.llnternational Journal of Mass Spectrometrv and Ion Processes 159 (1996) 37-48 47

(110) confirms displacements observed individu- ally for (010) and (100). The frequency shift observed in v1 + v2 upon 3pa electron coordina- tion is a net 8 cm-’ to the blue.

4.4. Eigenfinctions for mixed vibrational states in the 3pa Rydberg state and in the cation

From standard perturbation theory, eigenfunc- tions of pairs of states that result from vibrational mixing can be expressed as linear combinations of the unperturbed eigenfunctions:

$(lOO) = a@lOO) -w&0, (11)

Combining these equations with the solution of the secular determinant (eqn (9)) allows the coef- ficients to be written explicitly as:

1

b =

Based on the Fermi matrix elements, W~loo)-(02~o),

and A0 values listed in Table 2, coefficients a and b are calculated to be 0.949 and 0.316 respectively. The squares of the coefficients give the zeroth-order composition of the per- turbed wavefunctions. Thus, we find that the perturbed ionic (02’0) state has 90% (02’0) character and 10% (100) character. By compar- ison, the perturbed (02’0) level in the 3pa Ryd- berg state has 88% (02’0) character and 12% (100) character [l]. Thus the mixing is almost identical in the 3pa Rydberg state and in the cation, and the presence of the 3pa Rydberg electron does not seem to affect Fermi reso- nance in the NO; core.

5. Conclusions

We have examined bend-stretch Fermi reso- nance in NO; by means of three-color, zero-elec- tron kinetic energy (ZEISE) threshold photoelectron spectroscopy. According to the spectra, we have determined threshold energies for the (010) (02’0) (02*0), and (100) vibra- tional states of the cation. We have obtained accurate fundamental frequencies using the (000) 3pa Rydberg state as a reference state for all of the ionic vibrational ZEKE spectra, revis- ing some values of fundamental frequencies reported before. The degree of (100)-(02°0) Fermi resonance observed in NO; is comparable to that found in the NOz 3pa Rydberg state, and results for both systems agree well with recent CCSD(T) and MRD-CI ab initio calculations. Comparison of the vibrational energies of the 3pa Rydberg state and the cation suggests that the presence of the Rydberg electron slightly per- turbs the harmonic potential and its second-order anharmonicities, but has little effect on the cubic coupling term associated with core Fermi resonance.

Acknowledgements

HM gratefully acknowledges a fellowship from the Purdue Research Foundation. This work was supported by the National Science Foundation under grant No. CHE-9307131. We thank Dr. T.J. Lee and Dr. G. Theodorakopoulos for helpful discussions and for comunicating results in advance of publication.

References

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