JOURNAL OF CHEMICAL PHYSICS

VOLUME 114, NUMBER 1

1 JANUARY 2001

Coulomb and centrifugal barrier bound dianion resonances of NO2 L. H. Andersen,a) R. Bilodeau,b) M. J. Jensen, S. B. Nielsen, C. P. Safvan,c) and K. Seiersen Institute of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark

共Received 2 August 2000; accepted 4 October 2000兲 have been studied by bombarding NO⫺ New short-lived resonance states of NO2⫺ 2 2 anions by low-energy, mono-energetic electrons at the ASTRID heavy-ion storage ring. Storage for several seconds before the measurement ensures full vibrational relaxation of NO⫺ 2 target anions. The dianion resonances were identified by the detection of resonances in the cross section for formation of neutral NO2 . Two resonances were observed: The one of lowest energy is assigned to be the ground state of NO2⫺ 2 based on an ab initio calculation. This state may be held by a Coulomb barrier alone. A second state of significantly higher energy is argued to be held by a combined Coulomb and centrifugal barrier. Finally, a new scheme in which electron recombination may create stable dianions is proposed. © 2001 American Institute of Physics. 关DOI: 10.1063/1.1328380兴

I. INTRODUCTION

sphere. It is thus no surprise that large molecular systems may exist as dianions in the gas phase. Large stable dianions may conveniently be formed by the electrospray method.11,12 Experimentally, small dianions are difficult to tackle. First of all, the binding energy becomes small and even negative when the two extra electrons are confined within a small volume. The mere identification of such species is not trivial and in particular in early experiments higherharmonics in the various mass spectrometers led to false signals at the frequence of the dianions.13 Low-energy electron–molecule scattering has been studied for many years.14 The many degrees of freedom of the target molecule makes the interaction rather complex. It is well established that the incoming electron may excite the internal degrees of freedom and become bound in a negativeion complex. When electrons are scattered on negative ions as in the present work, the dominating long-range interaction is the repulsive Coulomb interaction and at first sight it may seem very unlikely that the electron will have a chance to enter the core of the molecule and become a part of a new dianion. Nevertheless, according to quantum mechanics an incoming electron is allowed to tunnel through the repulsive barrier through the classically forbidden region. We present evidence that this may in fact happen when low-energy electrons are scattered on a small negative molecular ion. Specifically, we have studied the scattering of electrons on nitrite:

It was discovered already in 1925 by Auger that atoms of sufficiently high internal energy decay by electron ejection 共Auger effect兲. Later Madden and Codling1 beautifully demonstrated this in the case of the He atom which in addition to the bound states was shown to have doubly excited states of positive energy which decay by this effect, also called autoionization. Molecules are known to posses similar states, and they play a crucial role, e.g., in absorption spectra, and in processes where a continuum electron is captured onto a positively charged molecular ion by inverse autoionization.2 In the present paper we report on molecular states of positive energy of a completely different nature: Positive energy states of the doubly charged negative molecular ion NO2⫺ 2 . The concern here is properties like the binding energy, the process of formation and the stability of the dianion which we prepare by bombarding the singlycharged negative ion by electrons of well defined energy. Thus, not only the existence, but also the process of formation is addressed. It is well known that multiply charged negative ions like 2⫺ and PO3⫺ exist in solutions. However, these SO2⫺ 4 , CO3 4 ions are not stable as isolated entities, i.e., in the gas phase, because of the lack of polarization interactions with the surrounding media. Much recent work has been concerned with the stability of free dianions both from a theoretical3–5 and an experimental point of view.6–10 Theoretically, the problem is difficult because of the strong Coulomb interaction, which in particular for small molecular systems causes strong electron correlation. For large molecules, the additional electrons may be attached on sites far apart, and as a consequence, the interaction energy is low. Also, the electronic states may be delocalized and spread over a large

2⫺ ⫺ ⫺ NO⫺ 2 ⫹e → 兵 NO2 其 resonance→neutral products⫹2e . 共1兲

The presence of positive-energy states is reflected in the occurrence of resonances in the cross section for the formation of the neutral products. We have earlier reported on such states for selected diatomic molecules.10,15,16 In the present work with a larger tri-atomic molecule we see two dianion resonances and provide energies and lifetimes of both states 共the ground state and an excited state兲. The dianion states of the molecule studied here do not live long enough for a study

a兲

Electronic mail: [email protected] Present address: Departments of Physics and Astronomy, McMaster University, Hamilton, Ontario, L8S 4M1, Canada. c兲 Present address: Nuclear Science Center, P.O. Box 10502, Aruna Asaf Ali Marg, New Delhi 110067, India. b兲

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© 2001 American Institute of Physics

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involving the formation, trapping and, e.g., exposure to light, and alternative means of studying such systems may be difficult to find. When dianions are created in collisions involving electrons and negative ions, the incoming electron plays an active role in the dynamics of the process, and it is useful to describe the collision dynamics and the dianion formation in terms of the electron–negative ion distance r. The interaction potential is at large distances given by the repulsive Coulomb potential 1/r. At short distances within the core of the molecule, attraction from the nuclei is experienced. When solving the radial equation for the scattering problem, the repulsive centrifugal barrier also needs consideration, so in total the three different contributions are responsible for the effective interaction potential. The existence of a barrier has been inferred by Compton and co-workers4,7 and was recently seen in photo-electron spectroscopy studies of a series of larger molecular dianions. Wang et al.17 showed that the superposition of short-range electronic binding and long-range Coulomb repulsion gives rise to a repulsive Coulomb barrier, which may cause the trapping of excess electrons. The same group also demonstrated that the Coulomb barrier may trap electrons even in states with positive energy, i.e., resonances. Due to a positive energy of only 0.9 eV 共for a large poly-atomic tetra-anion兲, the barrier was relatively thick and the tunneling escape rate low.18 In essence, we investigate the inverse of the electronescape reactions studied by Wang et al. We form positive energy states of the dianion by transmitting free electrons through the repulsive effective barrier which is not too thick, and hence permeable, near the top. II. EXPERIMENT

The NO⫺ 2 ions were formed from air in a cold-cathode source;19 a discharge current of 60 mA produced a beam current of 190 nA. The ions were accelerated to 150 keV and mass and energy selected before being injected into ASTRID, the Aarhus Storage Ring Denmark.20 They were further accelerated to 2.8 MeV in ⬃5 s. The fast ion beam was then merged with a magnetically confined, adiabatically expanded electron beam21 in one of the arms of the storage ring — see Fig. 1. To obtain zero relative energy between the two beams 共equal velocity兲, the electrons were accelerated to 34 eV. Other relative collision energies were obtained by varying the electron energy while maintaining the ion energy at 2.8 MeV. The experimental arrangement is being used in studies of electron collisions with negative16 as well as positive molecular ions.22 Neutral particles produced in reactions between free electrons and the negative ions continued undeflected through the dipole bending magnets after the interaction region and were detected outside the ring. In order to measure the absolute cross sections for the reaction 共1兲, the neutral particles were counted with a large 共4 cm diameter兲 solid state surface barrier detector placed immediately after the bending magnets. The signal was determined by measuring the neutral particle flux with and without the electron beam. Cross sections were put on an absolute scale by measuring

Andersen et al.

FIG. 1. The ASTRID storage ring and the position of the particle detector shown schematically.

the electron-impact induced yield of neutrals at a specific energy where also electron and ion densities were determined. The detector counted single particles, or groups of particles when arriving within ⬃1 ␮s. It gave signals which were proportional to the total kinetic energy of all particles hitting the detector simultaneously 共i.e., within the ⬃1 ␮ s time interval兲. Destructive collisions with the background gas in the ring 共pressure ⬃10⫺11 mbar兲 led to electron detachment and fragmentation of the stored molecular ions. This caused signal on the particle detector even without the electron beam being on and limited the storage time to seconds. Figure 2 shows the pulse height spectra of the detector. Without the electron beam being on 共dashed curve兲 there is fragmentation as well as electron detachment. When the

FIG. 2. The pulse-height distribution from the solid state detector showing peaks corresponding to the detection of one atom 共N or O兲, two atoms 共a di-atomic molecule or two free atoms NO/N⫹O or O2 /O⫹O) or all three atoms of the molecule. The solid curve is recorded with electrons and the dashed curve without electrons.

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J. Chem. Phys., Vol. 114, No. 1, 1 January 2001

Bound dianion resonances of NO2

149

electrons are turned on at a sufficiently high energy, additional signal is observed corresponding to the reactions ⫺ NO⫺ 2 ⫹e →

再

NO2 ⫹2e ⫺ NO ⫹ O⫹2e

共 a兲 , ⫺

N ⫹ O ⫹ O⫹2e

or O2 ⫹ N⫹2e ⫺

⫺

共 b兲 , 共 c兲 . 共2兲

Given the energy resolution of the detector, it was not possible to resolve NO from O2 — see Fig. 2. Since neutral products of a specific detachment reaction reach the detector essentially simultaneously 共within nano seconds兲, the signals from the above reactions all appear in the full-energy peak 共at 2.8 MeV兲 corresponding to the deposition of the total kinetic energy of all the neutral particles of the molecule. If charged particles had been produced 共e.g., N⫹O⫺ 2 or ), we would see a signal in the low-energy peaks N⫹O⫹ 2 corresponding to the detection of all remaining neutral particles 共the charged particles will not reach the detector because of the magnetic bending field兲. We detected only events in the peak at 2.8 MeV 共see Fig. 2兲 and conclude that the production of charged 共negative/positive兲 fragments is negligible.

FIG. 3. The total detachment cross section as a function of the electron energy. A smooth function 关Eq. 共9兲兴 is fitted to the data in the region of no resonances. After subtraction 共open points兲 the two resonances clearly appear.

characteristic for processes in which a reaction takes place once the interacting particles are inside a certain reaction radius R: 26

冉

␴ NR⫽ pR 2 1⫺ III. RESULTS AND DISCUSSION

To determine the branching ratios of the reactions 共a兲, 共b兲 and 共c兲 we used a well established technique where a grid with known transmission (T) is inserted in front of the detector.15,23,24 The probability for three particles being transmitted through the grid is T 3 , for two out of three particles T 2 (1-T) and so on. Let R 1 , R 2 and R 3 denote the rates for the three peaks, where R 3 corresponds to the full-energy peak. These rates can be expressed as follows: R 1 ⫽ 关 bT 共 1⫺T 兲 ⫹3cT 共 1⫺T 兲 2 兴 R 0 ,

共3兲

R 2 ⫽ 关 bT 共 1⫺T 兲 ⫹3cT 2 共 1⫺T 兲兴 R 0 ,

共4兲

R 3 ⫽ 关 aT⫹bT 2 ⫹cT 3 兴 R 0 ,

共5兲

where R 0 is the total rate of events. The branching ratios a, b and c are normalized according to a⫹b⫹c⫽1. The equations above may be solved to yield a⫽

R3 ⫺bT⫺cT 2 , T

共6兲

b⫽

R1 R2 ⫹ , T 共 1⫺2T 兲 共 2T⫺1 兲共 1⫺T 兲

共7兲

c⫽

R 2 ⫺R 1 . 3T 共 1⫺T 兲共 2T⫺1 兲

共8兲

Experimentally, we observed that R 1 ⬃R 2 and hence channel 共c兲 was neglected. The branching ratios for the remaining two channels were found to be a⫽75%⫾15% and b⫽25% ⫾15% over a large energy range 共10–40 eV兲. Electron-impact detachment of several atomic anions (H⫺ , B⫺ , O⫺ ) has been studied earlier.25–27 It was established that in the absence of resonances the detachment cross section near the threshold is well described by a formula

冊

E th ␲ a 20 . E

共9兲

p is a factor which is close to one, E th is the effective threshold energy, E is the electron energy in atomic units and a 0 is the Bohr radius. The reaction radius R is 1/E th in a.u.25,26 Note that the shape of the cross section only depends on E th . Because electron-impact detachment involves two free but interacting electrons in the final state, E th is larger than the electronic binding energy by typically a factor of 3 共energy must be provided for release and for kinetic energy of the escaping electrons16,26兲. As seen in Fig. 3, which shows the measured total cross sections 关the sum of all the reactions in Eq. 共2兲兴 as a function of the electron energy in the ion reference frame, the NO⫺ 2 data are found to follow the functional form, Eq. 共9兲, with p⫽1.25 and E th⫽7.9 eV. The electronbinding energy of NO⫺ 2 共the electron affinity of NO2 ) is 2.273⫾0.005 eV28 and, as expected, the effective threshold is significantly higher than this value. There are two structures superimposed on the smooth nonresonant part of the cross section. These structures are clearly revealed when the smooth cross section, Eq. 共9兲, is subtracted from the measured total cross section as is seen in Fig. 3. The resonant part of the cross section has been fitted by the sum of two Gaussian functions:

␴ R⫽

兺 i⫽1,2

␴i ⌬ i 冑2 ␲

e ⫺(E⫺E i )

2 /2⌬ 2 i

.

共10兲

The observed resonance energies (E i ) are 7.2 eV 共0.26 a.u.兲 and 16.5 eV 共0.61 a.u.兲. Both are located above the electronbinding energy of NO⫺ 2 , but most of the low-energy resonance is below the effective threshold E th . The widths (⌬ i ) are slightly increasing with energy 共1.0 eV for the lowenergy resonance and 1.5 eV for the high-energy resonance兲. We associate the resonances with positive energy states 29 of the NO2⫺ 2 dianion. At long range the interaction between

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J. Chem. Phys., Vol. 114, No. 1, 1 January 2001

FIG. 4. The scattering problem shown schematically. The potential energy of the scattering electron is shown as a function of the electron–anion distance.

FIG. 5. Schematic presentation of dianion formation. A state of positive energy (E 1 ) is first formed by tunneling through the barrier. Subsequent stabilization by radiation yields a stable dianion in the bound state of negative energy E 0 .

the electron and the anion is dominated by the repulsive 1/r Coulomb potential. In addition there is a repulsive centrifugal term l(l⫹1兲/2r 2 (l is the angular momentum of the free electron兲 and at a short distance within the core region some effective attraction. The resonance energies for the NO2⫺ 2 dianion are indicated in Fig. 4 where the situation is sketched for s (l⫽0兲 and p (l⫽1兲 wave scattering.30 If both resonances belonged to the same partial wave we would expect a significant difference in the lifetime since the low-energy resonance then is associated with a much smaller tunneling probability than the high-energy resonance. Moreover, the Coulomb barrier alone is only 13.6 eV at 2 a.u. (⬃1 Å兲 which is not enough to provide a barrier for the high-energy resonance at 16.5 eV. However, the combined Coulomb and centrifugal barrier, also at 2 a.u., is 20.4 eV for l⫽1 共p wave兲, which is enough to hold the observed high-energy resonance 共see Fig. 4兲. We used the WKB approximation to estimate the tunneling probability and found it to be on the order of 20%–80% for both resonances 共assuming l⫽0 and 1, respectively兲 for the binding part of the potential extending to 2 a.u. If we assume an internal energy of 0.5 a.u. 共13.6 eV兲 共roughly the energy of the resonances兲 the hit rate of the electron on the barrier is about 1016 s⫺1 , which with a 50% transmission probability yields a lifetime of 2⫻10⫺16 s. This is of the same order of magnitude as the lifetimes estimated from the widths of the resonances 关3–4 eV 共FWHM兲 equivalent to 2 – 3⫻10⫺16 s兴. Calculations with the GAUSSIAN-98 program package31 at the B3LYP/6-311⫹G共2d兲 level of theory were performed, and we obtained a ground state energy of NO2⫺ 2 which is ⬃7 共after correction for the eV above the ground state of NO⫺ 2 zero-point motion兲.32 This compares very well with the observed resonance energy of 7.2 eV for the low-energy resonance. The calculated electron affinity of NO2 agrees with the experimental value28 within less than 0.1 eV. The calcu2 lated ground state of NO2⫺ 2 has B 1 symmetry, and the highenergy resonance is most likely associated with electronic and/or vibrational excitation corresponding to an excited state of NO2⫺ 2 . Once a dianion is formed by trapping the electron behind

the barrier, we expect that the applied single-particle picture breaks down due to electron correlations. The system will most likely stabilize by ejecting electrons. However, the dianion may also stabilize by the emission of radiation if formed in an excited state, as shown in Fig. 5. This may either be electronically induced, or the relaxation may be due to a non-Born–Oppenheimer coupling between the electronic and the nuclear degrees of freedom causing infrared emission. If the system in this way stabilizes to a negative energy state 共in the case of a larger molecule兲, a stable dianion is formed. This would be a new energy-resonant type of recombination akin to dielectronic recombination with atomic ions33 where an electron is first captured by inverse autoionization and then, with a small probability, the system is stabilized by a radiative transition. The continuumelectron energy must in both cases match the energy of a resonance state of positive energy, emphasizing the importance of the presence of such positive energy states. IV. CONCLUSION

To summarize, we have measured two positive energy dianion by bombarding NO⫺ states of the NO2⫺ 2 2 anions by free electrons. The lowest lying resonance is assigned to be the ground state of NO2⫺ 2 , which is supported by ab initio calculations. The other resonance is believed to be associated with the excitation of the dianion and may be held by a combined Coulomb and centrifugal barrier. ACKNOWLEDGMENT

This work has been supported by the Danish National Research Foundation through the Aarhus Center for Atomic Physics 共ACAP兲. R. P. Madden and K. Codling, Phys. Rev. Lett. 10, 516 共1963兲. D. R. Bates, Phys. Rev. 78, 492 共1950兲. 3 M. K. Scheller and L. S. Cederbaum, J. Chem. Phys. 99, 441 共1993兲. 4 M. K. Scheller, R. N. Compton, and L. S. Cederbaum, Science 270, 1160 共1995兲. 5 A. I. Boldyrev and J. Simons, J. Chem. Phys. 98, 4745 共1993兲. 6 P. A. Limbach et al., J. Am. Chem. Soc. 113, 6795 共1991兲. 1 2

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J. Chem. Phys., Vol. 114, No. 1, 1 January 2001 7

R. L. Hettich, R. N. Compton, and R. H. Ritchie, Phys. Rev. Lett. 67, 1242 共1991兲. 8 C. Jin et al., Phys. Rev. Lett. 73, 2821 共1994兲. 9 L. S. Wang et al., Phys. Rev. Lett. 81, 2667 共1998兲. 10 H. B. Pedersen et al., Phys. Rev. Lett. 81, 5302 共1998兲. 11 See, e.g., J. B. Fenn et al., Science 246, 64 共1989兲. 12 A. T. Blades and P. Kebarle, J. Am. Chem. Soc. 116, 10761 共1994兲. 13 J. H. Fremlin, Nature 共London兲 211, 1453 共1960兲. 14 G. J. Schulz, Rev. Mod. Phys. 45, 423 共1973兲. 15 L. H. Andersen et al., J. Phys. B 29, L643 共1996兲. 16 H. B. Pedersen et al., Phys. Rev. A 60, 2882 共1999兲. 17 See, e.g., L-S. Wang and X-B. Wang, J. Phys. Chem. A 104, 1978 共2000兲. 18 L-S. Wang and X-B. Wang, Nature 共London兲 400, 245 共1999兲. 19 More details about the ion source will appear in a future paper. 20 S. P. Møller, in the Conference Record of the 1991 IEEE Particle Accelerator Conference, edited by K. Berkner, San Francisco, 1991, p. 2811. 21 L. H. Andersen, J. Bolko, and P. Kvistgaard, Phys. Rev. A 41, 1293 共1990兲. 22 D. Kella et al., Science 276, 1530 共1997兲. 23 O. Heber et al., J. Phys. B 18, L201 共1985兲. 24 S. Datz et al., Phys. Rev. Lett. 74, 896 共1995兲. 25 L. H. Andersen, D. Mathur, H. T. Schmidt, and L. Vejby-Christensen, Phys. Rev. Lett. 74, 892 共1995兲. 26 L. Vejby-Christensen et al., Phys. Rev. A 53, 2371 共1996兲. 27 L. H. Andersen et al., Phys. Rev. A 58, 2819 共1998兲.

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28

K. M. Ervin, J. Ho, and W. C. Lineberger, J. Phys. Chem. 92, 5405 共1988兲. 29 Similar resonances are found for NO3 and O3 and will be published separately. 30 We do not exclude that higher partial waves may be involved. 31 GAUSSIAN98, Revision A.7, M. J. Frisch et al., Gaussian, Inc., Pittsburg, PA, 1998. 32 To test for a basis set dependence, we carried out B3LYP calculations with four different basis sets: 6-31⫹G共d兲, 6-311⫹G共2d兲, 6-311⫹G共2df兲, and 6-311⫹⫹G共3df兲. Essentially the same value was obtained: ⫺6.76 eV, ⫺6.83 eV, ⫺6.86 eV, and ⫺ 6.88 eV, respectively. Furthermore, the methods B3LYP/6-311⫹G共2d兲, MP2/6-311⫹G共2d兲, and CCSD/6-311 ⫹G共2d兲//B3LYP/6-311⫹G共2d兲 all result in a value of approximately ⫺7 eV 共⫺6.86 eV, ⫺7.35 eV and ⫺7.20 eV, respectively兲. All model calculations predict the NO distance in NO2⫺ 2 to increase by 0.1 Å compared to NO⫺ 2 , and the ONO angle to decrease with 3°, both observations in accordance with the occupation of an antibonding orbital by the excess electron. A corresponding decrease in the NO vibrational frequencies were observed due to the weakening of the NO bond. Finally, when geometry optimizations are carried out at the Hartree–Fock level of theory 共no electron correlation兲, the NO bonds break, and the convergence criteria were not met. 33 See, e.g., W. G. Graham et al., in Recombination of Atomic Ions 共NATO ASI兲 Series, Series B: Physics 共Plenum, New York, 1992兲, Vol. 296.

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