An experimental and theoretical study of the doubly charged ion … · 2018-05-17 · after the completion of our theoretical study4 reports the energies of 12 electronic states 0:

An experimental and theoretical study of the doubly charged ion Oz+ J. Fournier, P. G. Fournier, M. L. Langford,@ and M. Mousselmal Laboratoire de Spectroscopic de Translation, UPS Biit 478, URA C.N.R.S. 1234, 91405 Orsay, France

J. M. Robbe and G. Gandara UFR de Physique, USTL Bfit. P5, URA C.N.R.S. 779 F-59655 Villeneuve D’Ascq, France

(Received 14 October 199 1; accepted 18 November 199 1)

The energy levels of triplet states of doubly charge oxygen, obtained using double charge transfer spectroscopy, have been examined in the light of ab initio calculations. Four peaks were found in the double charge transfer spectrum with energies of 41.1 + 0.2,43.2 f 0.2, 48.2 f 0.3, and 51.3 + 0.3 eV, respectively. The first and third peaks have been assigned to the ‘Z,C and the 311U excited states, respectively. The second peak has been assigned to the population of the 3Hs states. The configuration of the state at 5 1.3 eV is unknown. The effect of the symmetry rule Z’+,Z- is discussed and the validity of the spin conservation rule is demonstrated when a proton is used as a projectile in this experimental technique.

INTRODUCTION

The study of doubly charged species is currently the subject of growing theoretical and experimental interest, even in the case of simple molecules. In this paper, we report on double charge transfer (DCT) experiments using the molecule 0, as the target and on calculations on the elec-

2 + tronic structure of O2 . We have chosen to study this ion, not only because of its importance in radiation, plasma physics and oxidation phenomena, but also in order to verify the selection rules which govern DCT. In the following experiments, protons react with ground state 0,, a triplet state with the configuration ‘2;. The translational energy of the resultant H - ions formed by capture of two electrons from the target in a single collision is examined. If spin is conserved during the reaction, then both the incident and product systems will possess the same total electronic spin. As both ground states H - and H + possess no resultant spin, only the triplet states of 0: + will be formed. The interest in studying these ions is also justified because of the controver- sy surrounding the first excited state of the oxygen dication, the stability of which was invoked in an assignment of luminescence spectra emitted by 0,.

A number of theoretical investigations on the structure of the dication 0: + have already been performed. Hurley and Maslen’ calculated the potential energy curve of the ground state using a scaling procedure based on the isoelec- tronic molecule N, . This study was later extended by Hur- ley’ to include the excited states of 0: + and provided the first comprehensive description of the dication. The calculations concluded that the ground state of 0: + , X ‘Z;8’, would be found to be a bound state with a well depth of 4.7 eV with an equilibrium radius re of 1.010 A and reached by vertical ionization of 0, with an energy of 35.5 eV. The first excited state of 0: + , A ‘XC,+, was computed to lie 4.16 eV above the ground state, at the geometry of the oxygen molecule, and to be bound with an r, of 1.285 A. Beebe et aL3 carried out ab

D) Present address: The Chemical Laboratory, The University of Kent at Canterbury, Canterbury, Kent CT2 2NH, United Kingdom.

initio calculations with a minimal Slater-type orbital (STO) basis and full valence configuration interaction (CI) calculations. The major difference between these calculations is the depth of the potential well of the ‘2: state, which was calculated to be 4.7 eV by Hurley, but only 0.8 eV by Beebe. In addition, Beebe found that the A ‘E,’ and C311, states were repulsive.

In this publication we present our theoretical calculations on the electronic states of 02 + . An article published after the completion of our theoretical study4 reports the energies of 12 electronic states of 0: + , using complete active space self-consistent field multireference configuration inter-action (CASSCF/MRCI) calculations. These calculations were used to enable the assignment of photon and electron excited KW Auger electron spectra which were obtained in the same investigation. Subsequently, the calculations were improved’ in order to definitely establish the character of the ‘2: state; it was concluded that this state does not have a minimum in agreement with the CASSCF calculation.6 In addition, the improved calculations found that the 0: + ground state, ‘Xl, has a deeper potential well (3.59 eV) than had been previously calculated, with the potential barrier located at an increased internuclear distance. A further theoretical study, using multiparent CI calculations, reported ten low-lying electronic states of 0: + .’

Auger emission spectra of 0, were measured first by Seigbahn et ai.’ and then by Moddeman et a1.9 In both cases, limited assignments were made to the states of 0: + using Hurley’s2 theoretical calculations. Moddeman admits to a tentative assignment of these states as the effect of spin COU- pling of the k electron with unfilled shells in the intermediate singly ionized molecule makes firm identification difficult. These spectra have been interpreted by Dunlap et al.,” where 0: + state energies, Auger transition probabilities, and the Auger linewidths were calculated using the Xa method. However, a deficiency in the Xa model prevents the effect of differing spin states in the initial 1s state of 0, being modeled satisfactorily. As a result, calculated and experimentally determined energies differ by as much as 6 eV. A

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reassignment of the 0, Auger emission spectrum was pro- posed by Sambe and Ramaker” using arguments based on spin and symmetry selection rules. It was shown that if only spin and symmetry allowed transitions are observed, then only triplet states of 0: + can be formed in the Auger emission spectrum and that the first excited state A ‘Z,+ will not be observed due to the symmetry selection rule B - 42 + . The first state, formed by Auger transition following the removal of two electrons, located at 42.9 eV at an internuclear distance of 1.27 A, was therefore attributed to the triplet state W ‘A, with the other emission features being attributed to higher triplet states of 0: + . These assignments were supported by Auger linewidth estimates based on the character of the orbital involved in the Auger ground and final states.

A study of the luminescence spectrum of 0, was carried out by Tohji et ~l.,‘~ where selective excitation of core electrons using synchrotron radiation was followed by Auger decay into excited ions. A blue band with peaks at 2.99,2.80, and 2.64 eV was attributed to transitions from Oi+ B 311g (0” = 0) to vibrational states of 0: + A “Z,+ , where the band frequency of 1350 cm - ’ was assumed to be due to the vibrational frequency of the lower ‘Z,+ state. This attribu- tion has not, however, been confirmed.

Six long-lived electronic states of 0: + were identified in a high resolution investigation.i3 The translational energy lost or gained in single electron capture reactions by 0: + from noble gases was measured and assigned using the calculations reported in Ref. 3. The assignment included the identification of the first triplet state,4 ‘2: as a bound state. The energy of the 0: + ground state was measured as 36.6 f 0.1 eV. However, five independent ab initio calculations3-’ have shown that the “2,+ state does not support any vibrational levels.

The first experimental determination of the ground state of 0: + l4 measured a double ionization energy of 50 eV. Better agreement with the calculated data was obtained when an electron ionization efficiency curve was reported by Dorman and Morrison’5 leading to a value of 36.3 f 0.5 eV for the vertical double ionization energy of 0,. In that study, the energy scale was calibrated using an energy of 12.2 eV for the single ionization energy of 0,. If a more recent value of 12.07 eV16 is used, then the first ionization energy of 0: + is reduced to 36.17 eV. Extrapolation of the double ionization cross sections of 0, as a function of the ionizing electron energy” gave a double ionization energy of 35.6 f 0.3 eV. Averaging these results gives a value of 36.1 eV for the ground electronic state of 0: + . This state, observed through electron ionization experiments, must have a lifetime of at least several microseconds.

Daly and Powell” measured an energy of 37.2 f 0.2 eV for the appearence potential of 0: + in charge exchange reactions. This is higher than the values found using electron ionization, but the formation mechanisms are not the same in the two kinds of experiment, in particular, the rovibronic internal energy. In addition, the authors located an excited state at 5.0 f. 0.3 eV above the ground state. A similar investigation by Agee etal.” yields an adiabatic double ionization

Fournier &al.: The doubly charged ion Oz+ 3595

energy of 36.1 + 1.0 eV, where the relatively large error margin is necessary because calculated Franck-Condon transition factors show small transition probabilities to low vibrational levels of 0: + (X ‘1: ) .

The states of 0: + have been determined experimentally by Appell et aL2’ using double charge transfer spectroscopy with the H + ion as the projectile. Two peaks in the spectrum were ascribed to the population of states of 0: + and were assigned using Hurley’s2 calculations. The lowest energy peak was measured at 43.0 + 0.5 eV and was attributed to the population of the two triplet states B 311s and B 38;, the higher energy peak was measured as 48.0 f 1 .O eV and was attributed to the population of the C 311,, state. Neither the ground state of 0: + nor the first excited state were observed in these experiments. This was attributed to the conservation of the Wigner spin conservation rule as the formation of the singlet ground state from ground state 0, , which has a triplet configuration, is forbidden in spin conserved collisions with protons. The nonappearance oftheA ‘Z,+ was attributed to the symmetry transition rule Z ++,4Z - which would have been violated by the population of this state.

There have been a number of studies on the kinetic energy released following fragmentation of 0: + . Beynon et aL21 measured a kinetic energy release of 8.03 eV following the dissociation of 0: + ions with an estimated lifetime of 2-4ys. Using Hurley’s2 calculations, this was attributed to the fragmentation of the “XC,+ state into the ground state ion pair 0 + ( 4S) + 0 + ( 4S). Curtis and Boyd2* also examined the fragmentation reactions of 0: + in a study of unimolecular and collision-induced dissociations. Three energy releases of 6.7, 7.9, and 8.4 eV were measured following unimolecular dissociation from metastable states of 0: + . Two additional kinetic energy releases of 9.2 and 10.9 eV, produced by fragmentation of states of 0: + with an estimated lifetime of 0.2 ps, were found when a collision gas was introduced. The energy release of 6.7 eV was assigned using Beebe’s3 calculations to the fragmentation of the 311s state into o+(4s) +o+(2D).

Brehm and Fr&nes23 used an ion-coincidence technique to investigate ion-pair production following the fast dissociation of 0: + . The ions were formed by electron ionization using electrons with an impact energy of 150 eV. The appearence potential for 0: + from 0, was determined as 40.2 eV and a broad kinetic energy distribution curve was measured with peaks at approximately 7, 11, and 17 eV. The most intense peak, at 11 eV, was attributed to the fast dissociation of the C 311u state into the fragments 0 + ( 4S) + 0 + (‘0). Curtis and Eland24 used He (II) light to study ion pairs resulting from fast dissociation processes following double photoionization of 0,. Although the main component of the incident radiation was the He (II) a line, with an energy of 40.8 eV, an estimated 20% of the beam consisted of the /3 and y lines at 48 and 5 1 eV, respectively. Four kinetic energy releases were measured with the values 2.5 f 0.5,4.5 f 0.3, 7.0 f 0.4, and 11.5 f 1.0 eV. The most intense release of 7 eV was attributed to the production of two 0 + (4S) ions indicating a dissociative state at 39.4 eV, possibly the A ‘X,+ state. A similar study was conducted by Eland et aL2’ using

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3596 Fournier et al.: The doubly charged ion Oz+

selected He (II) wavelengths. Three peaks in the kinetic energy release distribution were measured at 4.5 f 0.2, 7.2 f 0.5, and approximately 9.5 eV following the excitation of molecular oxygen by 48 eV photons. Reduction of the incident photon energy to 40.8 eV resulted in the absence of the energy release at 9.5 eV. A further reduction in photon energy to 38 eV resulted in the production of only the lowest energy release at 4.5 eV. This was attributed to the dissociation of ground state 0: + to two 0 + ( 4S) fragments, whereas the energy release of 7.2 eV was assigned to the dissociation of the ‘X,’ state into two 0 + (45’) ions. The formation of both of these states is allowed by the dipole selection rulez6 which restricts the population of some states in the doubly charged ion by double photoionization. In particular, the formation of the ‘2; , ‘A,, and the ‘II, states of 0: + are forbidden by this selection rule.

The proton beam is angularly defined by two circular aper- tures 0.1 mm in diameter and 26 cm apart before entering an electrically isolated collision chamber 10 cm in length, where the target gas is introduced. The product ions H - are energy selected by a 127” electrostatic analyzer with a resolv- ing power of 4000 and detected by a tubular multiplier. A voltage of 100 V was applied to the collision chamber to remove any background signal due to double charge transfer reactions with residual gas outside the cell.

II. DOUBLE CHARGE TRANSFER SPECTROSCOPY- EXPERIMENTAL DATA AND RESULTS

An accurate energy scale is defined using three different procedures: (i) the application of a potential of value + u to the collision chamber which reduces the energy of the H - ions formed inside by 2~; (ii) variation of the collision energy of the primary beam by 10 eV which shifts the spectrum by the same amount; and (iii) the application of a calibrated sweeping voltage to the electrostatic sector. An accurate energy reference is obtained by calibration experiments on argon which has single and double ionization energies compar- able with those expected for 0,.

The double charge transfer experiment, initiated by one of us,” has already been described in detail elsewhere.” It involves measurement of the translational energy of H - ions arising from the reaction

H+ +M+H- +M*+, (1) where two electrons are transferred from a target molecule M creating a doubly charged ion M* + . In this reaction, the double ionization energy I * + is determined by the relation

I*+ = - (E-E,,) - T,,, - E(H-), where E, is the initial kinetic energy of the protons, E is the measured kinetic energy of the H - ions, and E( H - ) is the energy (14.3 eV) required to form H- in its ground state from H + . The recoil energy of the target T,,, is negligible at the almost-zero scattering angle used in the experiment. For- mation of the H - ion can also occur in two successive single charge exchanges

H+ +M+M+(x) +H (Ha) and

If spin is conserved during a reaction, then both the incident and product systems will possess the same total electronic spin. The ground state of the target molecule 0, has a triplet configuration. Both the ground state ions H + and H - possess no resultant spin. Therefore, if spin is conserved, only the triplet states of 0: + will be formed. Double charge transfer spectroscopy has been applied recently to the NO,, N,O, and CO molecules29-3’ where spin was shown to be conserved in collision with H + ions.

H+M-M+(y)+H-, WI where the singly ionized target molecule M + can be produced in the electronic states x or y. The sum of the two single ionization energies I + (x) and I + (y) required to produce M + in the electronic states x and y is given by

I+(X) +I+(y) = - (E-Eo) -T,(x)

Figure l(a) shows the translational energy loss spectrum of H - ions following double electron capture by 9 keV protons in collisions with O2 at a target gas pressure of 10 - 6 Torr. Figure 1 (b) shows the spectrum obtained at the higher pressure of 10 - 5 Torr. Seven peaks are observed. The peaks labeled a to c, which have measured energy losses ranging from 20-35 eV, vary quadratically in intensity with the target gas pressure. They therefore arise from double collision processes resulting in the formation of singly ionized oxygen molecules (process II). As discussed in previous publica- tions,29-3 ’ the energies of the first five states of o*+, *II&‘= l), d411,(u’=5), ATI,(u’=7), b 42; (u’ = 0), and B *XL (u’ = 1) (determined using photoelectron spectroscopy’6 ) are considered in the assignment of peaks a to c. These peaks are not formed in the reactions of interest in this investigation, but their assignment allows the accuracy of the energy scale to be assessed.

-T,(Y) -EW-1, where T,,, (x) and T,,, (y) are the recoil energies of the two targets involved in processes ( IIa) and ( IIb). As two successive single-electron exchanges involve two collisions, processes ( IIa) and ( IIb) can be distinguished easily from the formation of doubly charged ions by a quadratic dependence on the target gas pressure.

The apparatus is a double mass spectrometer with a Co- lutron ion source in which H + ions are formed by electron ionization of H,. Primary ions of 5 keV energy are mass analyzed by a Wien filter having a mass resolution of 300.

The intensities of the peaks A-D, observed, respectively, at 41.1 f 0.2, 43.2 f 0.2, 48.2 f 0.3, and 51.3 f 0.5 eV vary linearly with the sample pressure and can be attributed to transitions leading to the formation of 0: + . Figures 2 (a) and 2(b) show part of the spectrum obtained at a pressure of 10 - 6 Torr when the energy of the incident protons was lowered to 5 keV. To exclude any effects due to drift during the runs, a mixture of argon and oxygen was used in the collision chamber. Figure 2 (a) shows the spectrum obtained when such a mixture of target gases was used. Figure 2(b) shows the spectrum obtained when only 0, gas is present in the collision cell. The additional peak present in Fig. 2(a), peak E, is caused by the population of Ar* + ( ‘02 ). This

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Fournier eta/.: The doubly charged ion O$+ 3597

DC BA c b a I I I I I I I

f---cl-- I I !

60 50 40 30 20 I 2+ or I’(x) t I+(y) (4

FIG. 1. Double charge transfer spectra of H - ions from 9 keV H + projec- tiles impinging on 0, at target gas pressures of (a) 10e6 and (b) lo-’ Torr.

reaction requires an exactly known energy of 45.112 eV (Ref. 32) and enables an accurate definition of the energy scale. In this way, the energy scale of the charge transfer spectra can be determined experimentally to within 0.2 eV. The full width at half-maximum (FWHM) of peak E is 1.5 eV and allows the broadening of spectrum features due to apparatus effects to be estimated. Peaks A-D are wider by 1 eV than peak E. This is caused by the additional effects of molecular broadening. Measurements performed at a 5 keV collision energy show that peaks A and B are well resolved and are energy separated by 2.2 f 0.2 eV.

Ill. A6 /N/T/O CALCULATIONS-POTENTIAL ENERGY SURFACES AND ELECTRONIC STRUCTURE

Our basis set of Slater-type functions consists of the (5s/4p) atomic basis of Clementi and Roetti33 for the ion 0 + (3P) augmented by the 3d polarization functions with exponents 2.35 and 1.25 on each atom. The self-consistent field (SCF) molecular orbitals which serve as basis orbitals for the configuration interaction (CI) calculations have been determined by minimizing the energy of the lowest

FIG. 2. Double charge transfer spectra of H - ions from 5 keV H + projec- tiles impinging on a mixture of Ar and 0, at target gas pressures of (a) 10 - 6 Torr and (b) on 0, at target gas pressures of 10 - 6 Torr.

state of each calculated symmetry. These orbitals are parti- tioned into three sets consisting of (i) frozen orbitals ( lag,, ) of fixed occupation in all configurations; (ii) valence orbi- t& (20g,,, 3a,,, lag,, ) which correlate at infinity to the 2.s and 2p atomic orbitals; and (iii) virtual orbitals (4ag>u + 6ag.u 9 277g.u + 37rg,, ) selected by an energy threshold.

The CI basis was formed primarily by the full-valence CI, which includes all the valence configuration state functions (CSFs) of the appropriate symmetry generated by dis- tributing ten valence electrons among the valence orbitals. This full valence configuration interaction (FVCI) wave function included all internal correlation effects which would arise from the reallocation of electrons among active orbitals. The CI basis was then augmented by all CSFs in which one valence electron is excited into the virtual orbitals with the constraint that each CSF so obtained must be relat- ed to a limited set of reference determinants by, at most, diexcitations. When the total number of CSFs is typically lower than 500, exact diagonalization of the CI matrix is

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35 1 3 5 7 9

Internuclear distance (au.)

FIG. 3. Potential energy curves for the low-lying singlet states of 0: + . The three vertical lines on the abscissa correspond to the internuclear distances of the ground state of 0, and the ‘Z - and *Z - core-hole states.

performed directly. In other cases, we used the method of the “nearly empty CI matrix” developed by Raseev34 which consists of diagonalizing a matrix filled only on its diagonal and on a number of lines equal to the number of reference determinants and in keeping all CSFs whose coefficients in the wave function are greater than a threshold (here 1 x 10e4). A complete diagonalization of the matrix built on these selected determinants was finally performed. All computations used the ALCHEMY program package35 (345 implemented on the IBM3090 computer at CIRCE (Or- say).

The potential energy curves of 12 electronic states of 0: + were calculated. The calculations were performed over a range of values ( 1.75-l 5 a.u) of the internuclear distance r. From 1.75-4.00 a.u., the calculation was performed in steps of 0.1 a.u. and for values of r ranging from 4-l 5 a.u. in steps of 2 a.u. Figure 3 shows the singlet potential curves and Fig. 4 shows the potential curves of interest in the following dis-

55’ ‘iii’ I I I I I I I

3 5 7 9 Internuclear distance (au.)

FIG. 4. Calculated potential energy curves for the ground state ‘Xl of 0: + together with the low-lying triplet states. The three vertical lines on the abscissa correspond to the internuclear distances of ground state O2 and the ‘L - and ‘2 - corchole states.

3596 Fournier eta/.: The doubly charged ion Oz+

TABLE I. Molecular occupations in 0: + .

Contiguration 20, 3a, 20, 3u, lr, lff, State

Cl 2 2 2 0 4 0 ‘2: (ground) c2 2 2 2 0 2 2 ‘m&i+ c3 222031 I,-&+, I.32 - L3A UP Y

2 2 2 0 1 3 c4 2 1 2 1 4 0 1.38 + Y c5 2 0 2 0 4 2 ‘2; C6 212041 x C7 221041 I*qj

C8 2 1 2 0 3 2 q” Y

cussion: these curves were obtained by fitting the calculated energy values with a cubic spline interpolation technique.

In the energy range O-15 eV above the ground state ‘Xc, it is striking to note that only the lowest state of a given symmetry is stable. Table I gives dominant electronic configurations for these states in the range 1.5-3 a.u. For intemu- clear separations ranging from 1.8 to 2.7 a.u., the ground state ‘2: is dominated by the C 1 configuration, slightly contaminated by the C2 configuration, while the two first excited ‘8: states come almost exclusively from the C 2 configuration. The lowest 38,+ and ‘2: appear flat, while 3A,, ‘A,, ‘8;) and 3H; present a slight m inimum at large internuclear separations. This is because ‘22 and ‘8,+, although dominated by the C 3 configuration which is stable, interact with ‘22 (II) or ‘2: (II ) , whose dominant C 4 configuration appears quite repulsive. No such m ixing can occur for ‘A,,, ‘A,,, ‘2;) and 32; states. The situation for the 311U is complicated due to strong m ixing between the C 7 and C 8 configurations. Finally, 311s is clearly dominated by the C 6 configuration and is quite stable.

The calculated energy for the ground state of Of + at the equilibrium distance is - 148.578 05 a.u. To compare experimental and theoretical results, we have calibrated the energy of the ground ‘X8+ state extrapolated at infinity ( - 148.709 60 a.u.) to the dissociation lim it for the produc-

TABLE II. Energies and spectroscopic constants of the lowest states of 0++ z .

State Vertical energf

X’Z#+ 36.8 2490 1.078 AsI:+ u 40.6 ‘A” 42.2 785 1.438 B'll, 44.1 1800 1.195 B"Y I) 44.1 821 1.358 5; 900 1.342 ‘A” 1045 1.316

‘Energies in electron-volts calculated at the internuclear separation of the ground neutral 0,.

bin cm-‘. c In Angstroms.

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Fournier eta/.: The doubly charged ion O$+ 3599

TABLE III. Energy of the ‘Zz ground state and vertical excitation energies ofexcited states with respect to the 0: * ( ‘2; ) at R = 1.21 A. All values are in electron-volts.

state This work Reference 5* Reference 6 Reference 7b Reference 4’ Reference 3d Reference 2

‘2; 36.8 37.2 37.0 35.2 0 0 35.5 ‘z”+ + 3.8 $4.1 +4.1 + 3.9 + 3.8 + 3.91 + 4.16 ‘A. + 5.4 + 5.7 + 5.5 + 6.2 ‘“I + 7.3 + 6.4 + 6.3 + 6.3 + 6.7 ‘P; + 7.3 +7.15 + 6.7 +7.1 + 7.0

’ Values deduced from Fig. 1. b Values deduced from Fig. 1. ‘Values deduced from Fig. 5. d Values deduced from Figs. 19-26.

tion of two ground state 0 + ions (32.34 eV), assuming that beyond R = 15 au., the potential curve behaves as l/r. Us- ing this procedure, we found a value of 36.8 eV for the ground vertical double ionization energy of 0,. The energy of each state, at the optimized internuclear distance for the ground state of the neutral molecule (r, = 1.207 A), can be estimated and is reported in Table II together with some spectroscopic constants.

IV. DISCUSSION

Figures 3 and 4 show, respectively, the singlet states of 0: + and the singlet ground state together with the low-lying triplet states of O:+ calculated in this investigation. The equilibium distance of the 0, molecule ( 1.207 A) is marked on these figures together with the equilibrium distances of the core hole states 48 - and ‘2 at which the double ionizing Auger transitions occur ( 1.276 and 1.331 A, respectively). The internuclear equilibrium separation for the ground state of the doubly charged ion ( 1.078 A> is lower than that of the neutral molecule ( 1.112 A) since the two ejected electrons come from the antibonding 7r orbital.36

Our calculations for 0: + differ in some respects from previous investigations. 2.3 Vertical double ionization to the ground state of0: + is calculated to require an energy of 36.8 eV, somewhat higher than Hurley’s calculation of 33.6 eV.’ Beebe obtains a value of 36.7 eV. All authors show the ground state to be a bound state, although the depth of the potential well varies between a value of 0.8 eV found by Bee- be and 5 eV by Hurley. We estimate a potential well depth of 3.8 eV. Similar CASSCF/6-31 lG(d) calculations,6 giving an adiabatic ionization energy of 35.8 and 37.0 eV for the vertical ionization energy, agree with our data. Potential curves were also reported for several low-lying electronic states.5-7 Curve shapes are identical to results presented in Fig. 4. Multiparent configuration interaction calculations’ give a calculated total energy for the ground state, at the equilibrium distance of - 148.592 77, i.e., 0.4 eV lower than our value. The values of the double ionization energies calculated by Larsson et aL4 agree with the present theoretical study to within 0.4 eV except for 311s which is energy shifted by 1 eV (see Table III); another difference between the two investigations is the ordering of the three states 3A,,, 311g,

and ‘2; at the internuclear distance where Auger transitions occur.

Vertical energy differences (measured at the internuclear distance 1.212 A) between the ground singlet and the first triplet states, which are correlated to the same dissociation limit, is calculated to be 3.8 eV. The theoretical investigation by Yang et al7 shows an energy difference of 3.9 eV between these two states, while Ref. 6 obtains 4.1 eV. The most reliable investigation of the relative energies between the two lowest electronic states’ concentrated on a calculation of only these two states gives a value of 4.1 eV. When these potential curves are normalized to the dissociation lim- its of the two ground state fragment ions O+ (4S) + O+ (4S), energies of 37.25 and 41.35 eV for the ‘2: and ‘Z,+ states are obtained, giving an energy defect of 4.1 eV. In conclusion, there is general agreement on the difference in potential energy between the ground and the first excited states as most of the calculations performed to date indicate this to be about 4 eV as one can see on Table III.

The present calculations find the first excited state of the oxygen dication, the 3H,f state, to be a repulsive curve in agreement with five theoretical investigations.3-7 The following three states 3A,, 38;, and 311p were all found to be bound, although the 38; state is dissociative in the Franck- Condon region. In addition, we calculate the 311u state to be a repulsive curve. Before assigning the observed peaks, it is necessary to estimate the precision of the calculated potential curves. Since restricted CI spaces have been used, they have been optimized in the valence region. Therefore, the degree of precision will not be quite the same at all internuclear separations. We believe that the energy difference between the states is obtained with a precision of 0.5 eV, but in the Franck-Condon region, the potentials vary rapidly; this must be taken into account.

The lowest double ionization energy observed in the present DCT investigation was measured as 41.1 + 0.2 eV from the low intensity peak A [see Fig. 2(b) 1. As shown in Table IV, this measurement is too high to be attributed to the population of the ‘2: state of 0: + . Therefore, it must be concluded that the ground singlet state is not populated in this DCT experiment, even though the energy defect for this reaction is more favorable than for the reactions which are


3600 Fournier eta/: The doubly charged ion O:+

TABLE IV. Electronic energy levels of 0: + (eV).

State

DCT spectroscopy

1 b

Electron Charge ionization exchange

experiments experiments

Auger spectroscopyC

1.27 A 1.30 A

‘x8+ . . . . . . 36.3 f 0.5d 37.2 f 0.2’ *. . . . .

35.6 f: 0.3’ 36.1 f 1.W ‘2,+ 41.1 f 0.2 ... . . . . . . . . . . . .

3AU . . . . . . . . . . . . 42.9 42.8

‘% 43.2 f 0.2 43.0 f 0.5 . . . . . . 43.6 ... “8; . . . . . . . . . . . . 44.0 ‘.’ “IL 48.2 f 0.3 48.0 f 1.0 . . . . . . 47.6 47.7

51.3 f 0.5 ... . . . . . .

“Present study. b Taken from Ref. 20. “Taken from Ref. 4. Both 1.27, and 1.30 8, correspond to the equilibrium bond distances of the 42- and ‘Z;

core states, respectively. d’Taken from Refs. 15-18 and 17-19.

observed and involve excited states. This is due to the spin conservation rule which has frequently been observed to hold in DCT investigations. 2a31 This rule, in the case of proton projectile ions incident on 0, (31;; ), restricts the population of 0: + states to triplet configurations only. The state measured from peak A at 41.1 eV is exactly 5.5 + 0.5 eV higher than the double ionization energy to the 0: + ground state (35.6 f 0.3 eV), which was obtained using the electron ionization technique.” This differs by 1.5 eV from the calculated energy separation between the first two states ofO:+, which most investigations agree is in the region of 4 eV. At first, it seems likely to assign the first peak seen in double charge transfer experiment to an excitation of the excited state 3A, that almost all calculations show to be at 5.5 eV above the singlet ground state (Table III), but this interpretation is in contradiction to the Auger results4’” which found this state located at 42.9 eV for an internuclear distance of 1.27 A and subsequently -43.4 eV for the 0, internuclear distance (see Fig. 4). The energy separation of 4 eV is calculated, in the theoretical investigations, at the internuclear equilibrium distance of the 0, molecule. In electron ionization experiments, threshold energies are measured and this leads to an underestimate of the vertical ionization energy of 0, as the threshold energy records the population of the zeroth vibrational level which is still inside the Franck-Condon region. This reasoning is supported by examination of the ground state potential curve,’ where an energy of 36.4 eV is calculated at the curve minimum. This value lies 0.8 eV lower than the vertical energy; our calculations give 0.9 eV. Adding this value to the calculated energy separation in the Franck-Condon region gives an energy separation of approximately 4.9 eV. Since the margin of error in theoretical calculations is -0.1-0.3 eV, the two results agree if the above assumptions are admitted. It is likely that 5.5 f 0.5 eV is the experimental energy separation between the adiabatic and nonadiabatic ionization energies of o:+ (‘X&l+, u = 0) and O”, + (‘Zz ) states. The energy of the

3X + state in the Franck-Condon region is calculated to be 40.“6 in this work and 41.4 eV in Ref. 5, so the state measured at 41.1 f 0.2 eV (peak A) can be assigned to the population of the ‘Z + state.

The intensity of peak A appearing as a shoulder in a previous DTC experiment performed with a lower resolution” is much lower than that observed for peak B even though the energy defect for this reaction is more favorable. This may be due to the effect of the selection rules bearing on the symmetry of the involved states Z + +,4Z - established by Appell et al. in Ref. 20. In that paper, it is shown that in the case of homonuclear diatomic molecules, two orientations of the molecule with respect to the H + ion trajectory will pre- serve a symmetry plane:

(i) if the ion trajectory is in the same plane as the internuclear axis of the molecule, this plane will be a symmetry plane for the collision system (orientation 1);

(ii) if the ion trajectory is in the symmetry plane of the diatomic molecule perpendicular to its internuclear axis, this plane will be a symmetry plane for the collision system (orientation 2).

The allowed transitions determined with the help of group theory are represented in Table V for orientation 1 and in Table VI for orientation 2. For other orientations, the selection rules can only indicate the most favorable transitions. In fact, transition to the four lower triplet states “XT, 3Au, 38,, and 311s are forbidden by the selection rule concerning the plane perpendicular to the internuclear axis (see Table V), while transition to the ‘2: is also forbidden by the selection rule concerning the plane containing the intemu- clear axis (see Table VI). This explains why the experimental intensity of the signal is small. Nevertheless, the doubly forbidden O2 ‘2; %O, 2 + 38,f transition can be observed, since it is favored by the lowest amount of energy needed for the transition.

Examination of Table III shows that the energy separation between the 38T and the ‘A, states has been calculated

J. Chem. Phys., Vol. 96, No. 5,l March 1992

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TABLE V. Symmetry selection rules for a diatomic homonuclear molecule.’

States &+ 2; II* As 2.’ I; II, A,

=r+ + + + + + + 2; + + + + + + “4 + + + + + + + + A, + + + + + + + + x + + + + f + T- + + + + + + IL + + + + + + + + A” + + + + + + + +

* -I- indicates allowed transitions when the ion trajectory is in the same plane as the internuclear axis of the molecule (orientation 1).

as 1.6 eV in the present investigation. In Ref. 5, the energy separation between the 32,+ and the 3A, states is 1.8 eV and the 3A,, 38;, and 311p triplet states are all grouped within an energy of 1 eV. Using the present calculated energies, it is possible that peak Bat 43.2 eV can be attributed to the population of the 3AU, 32;, and 311a states since we measure an energy separation of 2.2 eV between peaks A and B. The full width at half-maximum (FWHM) of the present DCT experiments has been estimated as 1 eV from peak B of Fig. 2. Calculated Franck-Condon (FC) factors show that excitation to the 311g state is preponderant, as the potential minimum is in the FC region from ground state oxygen. Thus peak B has been assigned to the population of this state. The asymmetry of the low energy side of this peak is propably due to the contribution of the 3A, state measured at 42.9 eV in Auger spectroscopy and, since the potential curve is flat in the 1.2-I .4 A internuclear distance, we expect identical results in Auger and DCT experiments. The Auger value for the 311s state is given as 43.6 eV and agrees well with our measurement of 43.2 eV, since in double charge transfer, we observetheo, [‘8,+,v=0)-0~+(‘8,+,u=O)]transition and in Auger experiments transition from core states implies excitation of higher vibrational levels of this state (see Fig. 4).

Peak C is a low intensity peak exhibiting a broadening of

TABLE VI. Symmetry selection rules for a diatomic homonuclear molecule.’

states 2; Z; I-I, Ag 2.’ 2; II, Ah,

=c+ + + + + =s- + f + + 5 + + + + A* + + + + k+ + + +’ + x- -I- + + + k + + + + A” + + + +

’ + indicates allowed transitions when the ion trajectory is in the symmetry planeof the diatomic molecule perpendicular to its internuclear axis (orientation 2).

2.8 eV and allows the measurement of an electronic state at 48.2 eV. Comparison with Fig. 4 permits an assignment of this peak to the population of the 311tl state in agreement with Auger results.

The theoretical data presented in this study can be used to interpret the existing Auger emission spectra.4*9-” Al- though the core-hole states of 0: + can have the symmetries ‘A , 22 + , 42 + , and ‘X -, there are only two possible symmetry allowed transitions from the ground state of the oxygen molecule 0, ( 3ZZg ); these are the 42 - and the 22 - states which have core energies of 543.39 and 544.47 eV, respectively. 37 The energy difference of 1.08 eV between the two states and the population of the 42 - state relative to the ‘I: - state gives rise to distinctive pairs of strong and weak peaks in the resultant Auger spectrum for transitions involving the ejection of two electrons. Using these criteria, we evaluate the expected position of the Auger line pairs using experimentally obtained values and then compare these with the Auger spectra in order to assign the emission spectra features to corresponding states of 0: + . The data presented in this study, communicated prior to publication, were already compared with the data of Larsson et ~1.~ at the equilibrium internuclear distances of the relevant core-hole states. It is clear that our data and the energies calculated by Larsson et aL4 agree perfectly in the case of the three lowest energy electronic states. However, there is a slight discrepancy in the calculated energies of the 32; and the 311p states, both of which are associated with the second dissociation limit to the fragment ions 0 + ( 4S) + 0 + (‘0). This difference may be due to rapidly varying potentials in the Franck-Condon region. Despite this discrepancy, the present calculations con- firm the assignment of lines 8-15 of the Auger spectrum measured by Larsson et al4

Using the above assignments, the kinetic energy releases associated with the dissociation of these states have been calculated. The dissociation limit of the repulsive “2,+ state is to the ground state fragment ions 0 + ( 4,S> + 0 + (4S) which have the dissociation energy 32.346 eV. Thus a kinetic energy release of 8.8 eV is predicted. The 311, state is associated with the second dissociation limit to the fragment ions 0 + (4S) + 0 + ( 20) with an energy of 35.67 eV. The 3I;; state is associated to the third dissociation limit to the fragments 0 + (4S) + 0 + (2P) with an energy of 37.36 eV. Therefore two kinetic energy releases of 7.5 and 5.8 eV can be expected.

Observations of an energy release of 4.5 eV using 38 eV photoionization24s25 suggested the existence of a low-lying dissociative state of 0: + at 36.8 eV in contradiction with previous results. Very recent photoelectron-photoelectron coincidence experiments3* have shown, however, that the double photoionization process in 0, is not a one-step vertical transition, but involves intermediate states of O,+ . Some O,+ states dissociate to 0 + + 0* after which the oxygen atoms can autoionize producing 0 + + 0 + pairs with low kinetic energy.

Eland et aL2’ increased the energy of incident photons to 40.8 eV and measured an additional energy release of 7.2 &- 0.5 eV. The dissociation limit for this state is calculat-

Fournier eta/: The doubly charged ion O:+ 3601


3602 Fournier et&: The doubly charged ion O$+

ed to be the ground state ion pair 0 + ( 4S) + 0 + ( 4S). Add- ing the kinetic energy release to the dissociation energy (32.34 eV) indicates a dissociative curve at 39.6 eV. Brehm and De FrGnes23 obtained an appearance potential for 0 + ion pairs from 0, at 40.2 f 0.5 eV. However, since the present study measures a triplet state of 0: + at 41.1 f 0.2 eV, which has been assigned to the population of the ‘Z,t , and since all calculations predict a vertical ionization energy of approximately 41 eV to the first excited state of 0: + , only the ground state of the dication can be involved. As seen in Fig. 4, the potential barrier of the ground ‘I;: doubly charged state is - 40 eV and consequently the dissociation of high vibrational levels occurring by tunneling through this barrier explains these experimental results.23’25 Tunneling lifetimes in the order of nanoseconds from the 13th level were calculated in this work using the Le Roy program.39

Peak C has been assigned to the population of the dissociative 311U state and has calculated kinetic energy releases of 10.8-12.5 eV. Translational energy spectroscopy experiments have been shown to give rise to the kinetic energy releases 10.9 (Ref. 19), 11.0 (Ref. 20), and 11.5 eV (Ref. 21). These may be associated with the dissociation of this state. The position of peak C on the translational energy scale led to the measurement of a state at 48.2 + 0.3 eV. This was in good agreement with a previous measurement of 48.0 + 1 eV which was obtained in a similar investigation.*’ In the present study, we have measured triplet states of 0: + at 43.2 -& 0.2 instead of 43.2 + 0.5 eV*’ confirming the reli- ability of double charge transfer spectroscopy.

The highest energy peak D measured in the DCT spectrum was found to have an energy of 5 1.3 + 0.5 eV. This lies above the region covered in the present calculations, but allows the determination of a triplet state at this energy.

Since the 48 - and the *8 - core-hole states have equilibrium internuclear distances that differ by 0.06 and 0.09 A, respectively, from the ground state of the molecule, we expect, in line with Ref. 4, that the Auger transition takes place at an internuclear distance that is relaxed. This is also re- ferred to as the interference effect in Auger electron spectroscopy. The above comparison of DCT and Auger data are thus made taking into account the whole molecular potential curves of the doubly ionized states in the two experiments, respectively. The present results support the fact that the Auger transitions take place at a relaxed internuclear distance.

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An experimental and theoretical study of the doubly charged ion … · 2018-05-17 · after the completion of our theoretical study4 reports the energies of 12 electronic states 0: