Chemical Physics 70 (1982) 291-298 North-I{olland Publishing Company

ELECTRON ENERGY-LOSS SPECTROSCOPY OF FORBIDDEN TRANSITIONS TO

VALENCE AND RYDBERG STATES OF FORMALDEHYDE

Steven TAYLOR, David G. WILDEN and John COMER Physics Deparhnen?. Schuster Luboratory, l7re Univem&y, Mancitester Mi3 9PL, UK

Received 29 March 1982

The electronic spectrum of formaIdehyde has been studied by the technique of electron scattering covering the range of ener_gy loss from 0 to 12 eV with a range of incident energies of the electrons from 10 to 100 eV, the scattered electrons being detected over a range of angles up to 60”. Peaks in the spectra whose intensities change with incident energy and with angle relative to the electric dipole allowed peaks are identified as either singbt-triplet (spin-forbidden) transitions or as

electric quadrupole transitions. The most prominent of the valence states ax the n + Al* and 7 -+ z* triplet features where, for the fist time, the detailed vibrational structure is well resolved. In the case of the triplet rr - K* transition WC estimate the C-O bond length of the excited state to be 1.423 k 0.005 A. In the region of the spectrum covering the Rydberg states we observe spin-forbidden transitions to 12s. and np Rydberg states for the first time. In addition ou observation of electric quadn?pole transitions to singlet Rydberg states suggests a reassignment of the 3dbl ‘A2 and 3pbl IA2 states.

1. Introduction

The formaldehyde molecule is usually taken as the

prototype for organic molecules containing the dipolar C=O functional group, and accordingly holds an irn- portant position in spectroscopy and molecular phys- ics. The smallness of the molecule makes it amenable to theoretical study and in recent years numerous ab initio and empirical calculations of the energy levels of the molecule have been published jl-71. The dis- covery of formaldehyde in the intersteilar medivm has led to renewed interest in the photochemistry and excited states of the mole&e. In spite of this, a num- ber of low-lying electronic states of formaldehyde have been predicted in theoretical stu&es, but not reported experimentally.

The electronic configuration of formaldehyde in its ground state is (3a1)2(lb1)2(2b2)2(2b1)0(4a1)0, which can be written more concisely as (u)‘(li)’ (q)2 (n*)O(o*)O. High-resolution optical spectroscopical techniques have resulted in a detailed understanding of the n + z* lA2 state [S-lo] and many of the Rydberg states [ 1 l-151, while more recently, efec-

tron impact techniTJes have been used to study the optically forbidden n -+ a* and n + B* transitions to

triplet states [16]. With the exception of these transi- ?ions, no experimental assignments have been made of states arising from the n + u*, o--f Al* or si --f u* tran- sitions which are all expected to lie within 40 eV of the ground state. Calculated excitation energies for the low-lying states of formaldehyde are summarized in table 1. Additionally, unlike its triplet counterpart, the ?I + n* IA, state, which is electric dipole allowed and is cdculated to have a very large osciUator strength 1171 has never been conclusively identified.

For these reasons, we present here the results of a re-examination of the formaldehyde spectrum up to the first iolrization limit, using the technique of elec- tron energy-loss spectroscopy, at low impact energies and variable scattering angles, in order to attempt to identify additional electric dipole forbidden transi- tiOll%

2. Experimental

The electron spectrometer used in this study em- ploys electron and molecule beams crossed at right

angles and conventional hemispherical electron anal- ysers. The instrument has been described in more

0301-0ol04/82(0000-0000/$02.75 0 1982 North-H&and

Table ? Summary of calculated esdtaiion encr$cs for singkt and triplet stzfes of formaldehyde

Tnnsition state CaIcula:ed excitation enerees (eV)

ref. [Is] ref. [I] r-f. 131 rei. [2! ref. [ 71 ref. [5] ref. 1171 ref. [4]

z-z* ’ Xl 11.18 12.13 _ 9.80 10.10 6.04-8.17 9.92 15.6 3x1 5.66 4.99 4.17 - 5.29 2.80-5.65 6.17 -

n--of I B2 10.14 - _ - - - 5.44-6.18 8.12 3B2 _ 9.95 - - - 4.64-5.80 - -

a--_’ ‘BI 9.1s 8.6 1 7.86 8.43 9.19 5.66-6.94 10.29 8.32 3B* _ 7.62 6.95 - - - 9.48 -

n - 3s ‘Ez 7.48 6.07 7.09 7.28 - - - 3B, - _ 6.03 - _ _

z-0* ‘Bl _ - - - - - - 7.16 3% - - _ - _ _ -

n-77' l .A2 3.80 3.43 1.62 - 4.04 2.41-3.37 4.41 3.83 j& 3.3a 3.01 2.25 - 3.46 1.98-3.37 3.90 3.46

~________.._.

detail by Wilden et al. [ 1 S] _ The electron monochro- mator can be rotated through a range of scattering angles from Cl to 60”. During each experimental run, the residual energy of the detected electrons was fLved wflik the energy of the incident electrons was repeti- tively scanned to sweep through the energy-loss spec- trum. Electrons which have undergone inelastic colli- sions with target gas molecules were detected after passing through the hemispherical analyser and into the entrance of a channel electron multiplier.

The formaldehyde was obtained by gently warming solid paraformaldehyde to =SO°C. The pipeline lead- ing from the source to the target region was alsb held at +30°C to reduce the possibility of condensation in the spectrometer. Despite this precaution, accumula- tion of solid paraformnldehyde inside the hypodermic needle used to define the molecular beam restricted the duration of experimental runs to typically 2-3 h. Inside the vacuum chamber the background pressure [uncorrected ionization gauge reading) was maintained at ===5 X 10-j Torr, the pressure at the scattering centre being higher by a factor or’=103_

3. Results

Fig. 1 shows spectra covering the energy-loss range 2-5 eV. In spectrum la two bands of optical absorp-

tion features involving transitions to the n + TT* ‘A1 states are identified [S]. Our energy-loss measure- ments of the features shown in the spectrum (table 2) are in excellent agreement with the optically observed series. Spectrum lb shows the vibrarionaily resolved n * z* 3A2 state which was shown by Chutjian [ 161 to have an angular intensity variation typical of a singlet to triplet transition. Our measurements and assignments of this band are shown in table 3 and are discussed in section 4.2.

Fig. 2 shows a valence band first observed as an un- resolved feature by Chutjian [16] who assigned it as a transition to the TI + n* 3A, state. The measured ener- gy losses of these peaks are summarized in table 4. On fig. 2a we have indicated a sharp feature at 4.72 eV which we believe to be due to scattering from a low background pressure of mercury vapour in the vacuum

chamber. The presence of this contaminant was sus- pected because a mercury diffusion pump was em- ployed to evacuate the spectrometer. After careful comparison of our spectra with published mercury spectra [ 191 we are confident that no other features

observed in our spectra can be assigned to this im- purity_

Fig. 3 shows the ener,T-loss region 6.5-l 1 .O eV.

The Rydberg progressions marked on spectrum 3a are optically allowed (e.g. ref. [23) and have been ob- served using energy-loss spectroscopy by Weiss et al.

S. Taylor et al. 1 Energy-loss spectroscopy of forntaIdehyde 293

[20] with a resolution of30 meV. Weiss’s results were taken only at high impact energies (250 eV) and at a scattering angle of0”. We have studied the region for the frost time at low impact energies. Figs. 3b, 3:: and 3d show spectra at J 0 eV scattered ener,v and at scattering angles of 3,30 and 60’ respectively. Fea- tures whose energy and angular intensity variations

are typical of symmetry-forbidden and spin-forbidden transitions are identifkd by the letters Q (quadrupole) and T (triplet) respectively. Tentative assignments of the features are shown in table 5.

4. Discussion of results

4.1. Angular and energy vacfatfons in energy-loss intensities

A powerful advantage of electron-impact spectro- scopy over optical techniques is the ability to study the energy/angular dependences of the intensities of spectral features. By this means electric dipole allowed transitions may be distinguished from spin- or symme- try-forbidden transitions (see refs. [21,22]). In this study, spectra were accumulated at two values of rcsi- dual energy (10 and 100 eV) and several scattering angles. In order to increase the signal stren@h and to allow a c!ear spectrum to be accumulated in the short collection times mentioned in section 2, the resolution employed was typically 40 meV (fwhm). In general, the features seen in the spectra are characterised in three different ways.

(1) At relatively high impact energies (e.g. 100 eV) and near zero scattering ulgles, electric dipole trznsi- tions are expected to dominate the spectrum and the energy-loss spectrum closely resembles a photoabsorp-

tion spectrum. (2) At lower residual energies (e.g. 10 ev) and at

small scattering angles (o-10”) electric quadrupole transitions become strongly enhanced compared with optical spectra.

(3) At low scattered energy and hi&her scattering

angles @30”) singlet to triplet transitions become pronounced.

4.2; The n +- JT* transition

The n + n* transition is the lowest-energy transi-

Fig. 1. Energy-loss spectra of formaldehyde vapour covering the range 2.6-5.2 eY Bi a residual energy of 10 eY and scatter- ing angles of 3 and 30”. The assignments indicated are taken from ref. [ 81.

tion in formaldehyde and gives rise to a singlet and a triplet state of A2 symmetry. Both states appear in the energy-loss region 3.0-4.5 eV which is shown in fig. 1.

Transitions to the IA2 state are expected to be optically forbidden from the ground state but in fact are weakly allowed due to distortion of the molecule from planarity. The state is observed in photoabsorp- tion studies [8-10,121 as a well-resolved band involv-

ing excitation of quanta of vl (C-H stretch), 9 (C-O stretch), and v4 (the out-of-plane bend) [23]. In electron-impact spectroscopy [16,20], the band has been observed as a broad unresolved feature. In the present spectra (fig. la) we can distinguish 12 levels, of which three have not been reported previously and

for the remaining nine our measured excitation ener- gies (table 2) are in excellent agreement with those of Brand [Xl.

Transitions to the 3A2 state are forbidden in opti- cal spectra by the spin selection rule although very weak absorption, to low vibrational levels of the state,

Table 2 Summary of excitation energies and assignment of levels of then - _ a* I.%-, state of form~dehyde, shown in fig. la

Measured excitation ener@rs Assi_gnment 0

encgv loss 2) optiai “I spectm b)

u2 w

3.506 3.511 0 0 1 3.652 3.657 0 1 1 3SO2 3.801 a z 1 3.86 1 3.867 I 0 1 3.943 3.943 0 3 1 4.007 4.013 1 i 1 4.089 4.083 0 4 1 -1.11; 4.161 1 2 1

J.ZZ 1 at00 0 5 1

4.298 - 1 d 3 3) 1 31

4.361 _ 0 a) 6 a) 1 3)

4.425 - 1 a) 4 a) 1 a)

3) Present rcsults. b, Ref. [S]. c) Ref. 1231.

Table 5 Sunm;lry of excitation cncr+ and crssifnment of levels of then - _ ir* 3.A1 stxc of CII:_O shown in iig. lb

Measured excitation energy Assignment”)

energy energy optical ioss n) loss b)

u2 u4 spectn c)

3 Present work. b, Ref. 1161. c, R-f. [IO].

was observed by Robinson and Egiorgio [IO] whose excitation energies are indicated on spectrum lb. The higher vibrational levels overiap the spectral region in which the more intense IA2 band occurs and could not be detected in optical work. In the ener&oss spectrum of Chutjian [I 61, a broad envelope extend- ing to =:4.5 eV was observed and from measurements of the angular variation of the intensity, the band was shown to be spin forbidden. Within the limltatiors of the statistical accuracy of the spectra ~5 vibrational features could be resolved. In the present spectrum of fig. lb we observe at least 19 levels as shown in table 3. From the observed intensities we identify two long progressions in the ZJ? mode, one consisting of weak peaks corresponding to us = 0, and the other consist- ing of more intense peaks (u4 = 1). From the observed excitation energies, the average vibrational spacing of the v4 mode is measured to be 0.065 eV, and the pro- gression in zz2 is well described by the spectroscopic corxtants 5ire = 0.152 eV and wpc = 0.8 meV.

4.3. 7r + II * states

Excitation of the outermost ?; electron to the ii* orbital produces 3A, and !A1 states. In theoretical studies (table 1) the 3A, state has been well charac- terised and calculations of the vertical excitation ener- gy are generally in good agreement with one another. The assignment of the long band shown in fig. 2 to this state appears certain. In contrast, the IA2 state is dififcult to treat theoretically with calculated excita- tion energies being as diverse as 6 and 12 eV (see table 1). Despite the large cross section expected for this optically allowed transition [ 171, no firm assign- ment of the state has been made experimentally.

The HAM3 calcuIations of Lindholm and co- workers have been shown to yield reliable excitation energies for x electron excitations in a number of small molecules. Their excitation ener,v for the n-t IT* state of CH,O (10.2 eV) places the transition in the part of the spectmm dominated by intense Rydberg transitions (fig. 3). While we have no deftite evidence that the transition is present OF. our spectra, it may take the form of a broad, undetected feature, underlying the Rydberg transitions, in the same way that the Ridberg transitions of ethylene are superim- posed on the broad l(~i + n*) transition. Indeed in- spection of spectrum a in fig. 3 shows that the spec-

S. Taylor dt al. /Energy-loss spectroscopy of formaldehyde 295

1 . & , I 1 I ,

5 0 !S

'A, I i I I I II II I I I I I II Ii 1

F& 2. Enerzy-loss spectra of CH,O covering the range 4.6- 7.0 eV ai a residuai energy of 10 eV. The feature marked “Hs” is believed to be an atomic mercury transition arising from the mercury diffusion pump used to evacuate the spec- trometer.

tral peaks above ~8 eV energy loss do appear to be positioned on a non-zero background.

In a previous electron-impact study [16] the ‘Al state was observed as a broad, unresolved feature; in the present study vibrational structure of the transi- tion has been observed for the frost time. From-a least- squares fit to the observed excitation energies the vibrational frequency, we = 0.106 eV, and the anhar- monicity, c+xe = 0.9 meV, have been calculated. The symmetry-allowed vibrations which may accompany the electronic transition comprise u2 (C=O stretch, vibrational spacing 0.15 eV in the’ground state), v3 (in-plane bend, spacing 0.19 eV) and v4 (out-of-plane bend, spacing 0.08 eV). v4 can be discounted since the depth of the potential-energy well as a function of out-of-plane angle is not expected to be sufficiently deep to produce the 2 eV width of the band on our energy-ioss spectrum [l] _ On the basis of the observed vibrational interval, we conclude that the band present in our spectra probably consists of a progression in the vz mode.

In the C=O stretching mode, the dominant terms in the potential energy variarion come from the mo- tion of the C and 0 atoms. A Franck-Condon calcu- lation has been performed in order to estimate the C-O bond length in the 3A, state. In this calculation the approximation has been made that if the HCH bond angle does not change during the vibration the molecule may be treated as a diatomic molecule which resembles NO, the potential-energy variation being simply a function of C-O bond length. The potential- energy curve parameters (we, ~exe and re) of the ground state of formaldehyde were taken from Herzberg [24] and for the excited state, the values of w, and wex, discussed above were used. The excited- state C-O bond length which gave the best agreement between the calculated Franck-Condon factors and the intensities measured from fig. 2 was found to be

Tab!e 4 Summary of vibrational levels of the ;7 -IT* 3Ar state of CH20. The measured excitation energies and intensities of the vibrational levels shown in fig. 2 are compared with calcw hted Franck-Condon intensities based on the simp!e diatomic molecule NO

” b, Mcasurcd energy Measured e, Calculated a) loss (ev) intensity intensity

0 - cl 2

1 4.83 11 8 2 4.94 23 21 3 5.07 45 39 4 5.19 56 59 5 5.30 68 71 6 5.42 82 90 7 5.53 100 98

8 5.65 97 100 9 5.75 90 97

10 5.86 93 91 11 5.96 83 83 12 6.06 71 74 13 6.16 59 64 14 6.26 51 55 I5 6.35 54 47 16 6.45 42 40 17 6.55 d) 33 18 6.63 21 28 19 6.73 15 23

a) Calculated intensities based on the diatomic molecule NO with re = 1.423 A for the excited state.

b, Quanta of c=6 stretching mode (yz)_ c) Noi observed. d) Obscured. e, Typical uncertainty ?5%.

296 S. Taylor et al. j Energy-10;s specnoscopy offormaldehyde

1.423 IO.005 A. The good agreement between the calculated sod measured intensities can be judged from table 4. Our value for re is also in good agree- ment with the value of 1.49 A which we estimate to be the minimum of the theoretical potential-energy curve of the 3-4, state &c&ted by Buenker and Peyerimhoff [ 1 ] _

4.4. Rydberg states in the regiin 7-11 eV

Rydberg states of formaldehyde, converging on the first ionizarion limit were first observed optically by Price f 151 and the series involving excitation of the outermost 7bl electron to s, p and d Rydberg levels were first identified by Allison and Walsh [25]. The assignments marked on fig. 3a are taken from the re- su!ts of Mental1 et al. [?I _ Since these results were ob-

_ _._~~‘.-_-__-_-I- r .-~r-i

I;is. 3. Energy-loss spectra ofCH20 showing Rydbcr: series conveging on the first ionization limit. The scattering angle and elccrron snergics used xc shown against each spectrum.

Thrcz opticAly observed saries [?I are indicated on spectrum

(a). The peaks mxked T, ?o Ts dnd CJ, to Qa are believed to bc spin forbidden, and eiuctric qoadrupolc allowed transitions respectively.

tained using photoabsorption techniques, they may be compared directly against our 100 eV, 0’ spec- trum. On fig. 3a good agreement can be seen beiween the assignments of Mentall et al. and the peaks in the present spectra. The 3sa, IB, state is accompanied by vibrational structure which takes the form of at least three inversion doub!ets [2] _ This doublet separa- tion is = 50 meV and is detected in the 100 eV spec-

trum as shoulders on the high-ccergy side of the main peak. Also the peaks corresponding to u2 = 1, and u’, = 2 [ 183 are seen at 7.40 and 7.65 eV.

The 3p Rydberg e!ectron in formaldehyde has

three different possible symmetries, aI, b3 and b,. The former two orbitals give rise to B, a& A, states respectively which are allowed by electric dipole selec- tion rules, while the latter gives A2 states which can be populated only by electric qrtadrupole transitions. The analysis of the structure of the 3p Rydberg state has been discussed by Mentall et al. [I] _

In addition to the electric dipole allowed transi- tions to Rydberg states, a number of features in fig. 3 have angular and energy intensity variations typical of forbidden transitions. Using the criteria discussed in section 4.1 we have assigned features Q1 to Q: as singlet electric quadrupole transitions and features T, to Tq as spin-forbidden transitions. The measured ex- citation energies are summarized in table 5, together with our assignments which are discussed below.

Q1 and Q, are identified with the two features ob- served in photoabsorption by Lessard and Moule [la], and assigned by them as vibrational levels of the for-

Table 5 Summary of measurements and assignments ofoptically for- bidden Rydbeg transitions studied in the present work

Feature Energy loss a) Qttantum Tentative (Cv) defect b, assignmeni

Tt 6.827 ~1.18 353, 3 Ba

T2 7.790 zo.90 3pbz 3A,

T3 7.955 50.74 3par 3 Bz

T‘I 9.589 ==O.SO or 4pbz 3A,

4pal 3B2

Ql 8.374 =O.65 3pbr ‘AZ

QZ 8.568 =0.55 3pb, ‘A2 + u3 Q3 9.220 ==0.12 3db, IA,

a) Present work. b, Calculated from energies in column 2.

S. Taylor et al. / Emrgv-loss spec!rorcop_v of formaldehyde 297

bidden 3pb, lA, Rydberg state. One mechanism by which the state could appear in the optical spectra is by vibronic mixing of the state via quanta of a non- totally symmetric vibrational mode. In this way the state could be observed as a weak electric dipole tran- sition. In the assignment of Lessard and Moule the two levels observed are due to mixing via single quanta of

~5 and v6 modes respectively, while the fully forbidden vibrational ground state was not detected. We are forced to reject this assignment on two grounds.

(1) Both features have intensity variations which label them as electric quadrupole in character rather

than as electric dipole. (This behaviour is well shown if the intensities of QI and Qz are compared with the small electric dipole ahowed feature at 28.3 eV.)

(2) The vibrational band or@ which should appear as a quadrupole transition in our technique, cannot be detected in our spectra.

Instead we conclude that Q1 itself is the band cjri- gin and Q2 must be an excited vibrational level of 2

totally symmetric mode, that is, either ZJI, u2, or vj. The separation of the two features which we designate Q1 and QZ has been measured for 2 number of iso- topically substituted forms of formaldehyde in the

optical study of Lessard and Moule [ 12 J. From their

measurements, we calculate that the ratio of the sep- aration for CD,0 to the separation for CH,O is 0.73 + 0.02, which is close to the value of 6.74 for vl and y3 based on the ground-state vibrational data tabulated by Shimanouchi [26] but is quite different

from the value of 0.97 expected for mode v2. The magnitude of the Q1 -Q2 separation for CH,O (=O.i98 ev) favours the assignment to the v3 mode rather than ~1~.

Q3 exhibits energy/angular behaviour indicating that the transition is electric quadrupole in character. On the 3” spectrum at 10 eV, Q3 is approximateIy half the height of its two neighbours to lower energy. On the 60” spectrum its intensity increases to become comparable with the two lowerenergy peaks. The position of Q3 (~9.30 eV) compares well with the position of the 3dXz lA2 orbital (9.24 eV) as predicted by the calculations of Harding and Goddard [27] _ This assignment is also supported by the calculated quantum defect of %0.12. We conclude that Qs rep- resents the transition to the 3d,, ‘A2 state observed for the first time.

Feature T, appears ~250 meV below the 3sal 1Bt

state 2s 2 broad peak. Its intensity rises from about one fortieth of the intensity of the lB2 state on the 100 eV spectrum, to about one quarter of its intensity on the IO eV, 60’ spectrum. On the basis of this in- tensity variation, it is clear that feature T, corresponds to 2 spin-forbidden transition. Its quantum defect (1.17) sugests that it is the triplet 3s Rydbeg state. Our observed singlet-triplet splitting is in poor agree- ment with the theoretically predicted spiitting of 0.04 eV by ref. [3]. In a similar way, T2 lies slightly lower in energy loss than the singlet 3p Rydberg levels, and shows the same increase in intensity as the scatter-

ing angle increases; its assignment 2s the triplet 3p state seems certain. Feature T, is coincident with the lowest level of the singlet 3p Rydberg state. However the notable increase in the intensity of the peak, as compared with the nearby peak at ~8.2 eV, indicates that a triplet transition underlies the singlet feature. The separation of.T, and T, (0.165 eV) is identical to the separation of the two main peaks of the singlet 3p state, and we have therefore assigned T, as a vibra- tionally excited level of T2. The final triplet feature, T4 lies close to the singlet 4p transition. However, after careful calibration of the energy scale, the corre- sponding peak on fig. 3d was found to be displaced slightly to lower ener,v loss. We conclude that on the 60” spectrum, peak T4 contains a significant contri- bution from the triplet 4p Rydberg state.

5. Conclusion

The energy-loss spectrum of formaldehyde from O-12 eV has been studied with high resolution by the techniqtte of electron scattering. For the first time

detailed vibrational structure of the n + a* and IT + n* triplet states has been observed. in the region of the Rydberg states, transitions to ns, np and nd states have been identified on the basis of their quantum defects. Four previously unobserved triplet transitions have been assigned 2s involving 3s, 3p and 4p Rydberg orbit&. Also, three electric quadrupole excited states involving excitation of the b, electrons to 3p and 3d Rydberg orbitals have been identified and their assign- ments are discussed in the light of previous optical results. In our spectra we see no evidence for additional valence states in the spectral region up to the first ioni- zation limit; it is, however, possible that such transitions may underlie the sharp structure in the Rydberg region.

298 S Taylor er al. /Energy-loss spectroscopy of fonnuidehyde

Ac!inowledgement

We gratefully acknowledge the fmancial support of the Science and En$neering Research Councn and would iike to thank them for a research studentship held by one of us {ST).

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