Multiparent configuration interaction calculations of low-lying states of O22+

ChemicalPhysics 147 (1990) 115-119 North-Holland

Multiparent configuration interaction calculations of low-lying states of OS+ Hong Yang, David M. Hanson Department of Chemistry, State University of New York, Stony Brook, NY 11794-3400, USA Florian

V. Trentini

Department of Chemistry, Villanova University, Villanova. PA 19085, USA

and Jerry L. Whitten Department of Chemistry. State University of New York Stony Brook, NY II 794-3400. US4 and Physical and Mathematical Sciences, North Carolina State University, Raleigh, NC 276958201, USA Received 30 April 1990

Multiparent configuration interaction calculations of potential curves are reported for several low-lying electronic states of

.

O:+ The electronic energies, bond lengths, and frequencies of harmonic vibrations are given. The results do not supportthe recent assignment of oxygen luminescence to the OS+, B ‘f&-A ‘Z: transition.

1. Introduction Relatively little is known about the electronic states of doubly charged molecular ions. A recent experiment [ I] has indicated that Auger decay following selective excitation of core electrons in molecules by synchrotron radiation can produce sufficient quantities of the doubly positive molecular ions in excited states to allow luminescence spectra to be observed. Probing the Auger final state by observing its fluorescence decay makes it possible to do Auger spectroscopy with the high resolution of an optical spectrometer, which is sufficient to resolve rotational and vibrational structure. Luminescence spectra with resolved rotational and vibrational structure clearly can provide significant information about the energy spacing between electronic states, about the structure and bonding properties of ions in these states, and about the populations of rotational and vibrational levels, which can characterize the dynamics of core electron excitation and Auger decay. It therefore is of

interest to have available highquality calculations pertaining to the electronic structure of these ions to assist in the identification and assignment of observed transitions. The first observation of dispersed luminescence following core electron excitation by monochromatic synchrotron radiation was for the case of oxygen [ 11. Luminescence spectra obtained with oxygen in a cell at a pressure of around 0.1 Torr and excitation energies in the region of the oxygen K edge consisted of two series of bands. The longer wavelength series matches the known fluorescence of 0,‘. The shorter wavelength series with peaks at 2.97, 2.80, and 2.64 eV do not match any known luminescence of this ion or other possible atomic or molecular species. In spite of some disagreement and large uncertainties, previous experimental results and some theoretical calculations indicated that the B ‘TI, and A ‘Z,+ states of 0;’ were separated by about 3 eV. This conclusion is substantiated by the recent analysis of Sambe and Ramaker [ 21. It therefore was proposed that the

0301-0104/90/S 03.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)

116

H. Yanget al. / CI calculations of lowlying states of a+

shorter wavelength bands are the analog of the wellknown first positive system (B ‘&-*A ‘Z,‘) of NS, which is isoelectronic to 02’. It has been pointed out by Penkina and Rebane [ 3 ] that the whole series of homonuclear doubly positive ions of the type A$+ are not, strictly speaking, stable. The Coulomb repulsion causes the electronic energy of the system to be higher than the dissociation limit. There is, however, a region of internuclear distances where the exchange interaction dominates the Coulomb repulsion and a local minimum is formed in the potential curve. Although this minimum lies above the dissociation energy, the lifetimes of the quasistationary vibrational levels are so large that these levels are not very different from the levels of bound molecules [ 3 1. Hurley [ 4 ] used an empirical scaling procedure to predict some of the low-lying electronic states of 0%’ in terms of N2. His method yielded accurate energies for C02+, Ns+, and NO’+ states [4,5]. Later, Penkina and Rebane [3,6] improved the scaling method, and calculated the potential curves of the ground states for A$+ molecular ions of the first series elements. There are only a few other calculations of OS+ electronic states. Beebe et al. [ 71 predicted the O$+ potential curves in configuration interaction calculations by using a minimum Slater type basis set, which severely limits the description of excited states. Dunlap et al. [ 81 calculated the 0;’ state energies, the Auger transition probabilities, and the Auger line widths by using the Xa method, which is unable to distinguish the various multiplet states arising from an electronic configuration. The results of these previous calculations are not in complete agreement because of the approximations that were employed. The disagreements are not only in the quantitative detail of the potential curves, but sometimes in the shape of these curves as well. Of particular concern is the fact that Beebe et al. found the A ‘Z,+ state to be dissociative, but Hurley [ 41 found this state to be bound. In order to address important questions regarding the electronic. states of @‘, we have undertaken the present ab initio multiparent configuration interao tion study.

2. Calculations The Gaussian type orbital (GTO) basis set was taken from Whitten [ 91. These are [ lOs, Sp] component Gaussian basis functions centered on each oxygen atom, contracted to a [ 5s, 3p] group. In addition, a set of d polarization functions (exponent of 0.8) is added to the basis. Configuration interactions are performed including all electron and the entire set of virtual orbitals. Approximately 1500 on the average, and up to 3000 configurations are generated from an initial set of four to twenty parent configurations describing each state. Single and double excitations from each determinant in the initial description are allowed. All configurations arising from excitations are retained explicitly in the expansion if the second order interaction energy exceeds a threshold of 1 x 10m5hartree, contributions of the excluded configuration are added using second-order perturbation theory. Details of the procedure are given in ref. [ 10 1. The flexible basis and the absence of core constraints allow the description of the low-lying states. In order to test the present basis set, the ground state potential curve for O2 is calculated. The calculated equilibrium distance r,, the frequency of harmonic vibration w,, and the dissociation energy D,, are 1.23 A, 1603 cm-‘, and 4.14 eV, respectively as listed in table 1. The experimental values are 1.2 1 A, 1580cm-‘,and5.21 eV,respectively [ll].Theprevious state-of-the-art ab initio configuration interaction calculations by Schaefer [ 121 gave the values of r,= 1.22 A, co,=1614 cm-‘, and D,=4.72 eV by using a 4s2p Id set of contracted Slater functions. Peyerimhoff and Buenker [ 13 ] obtained r,= 1.23 A, Table 1 Calculated potential minimum of the ground state X ‘xi for Oz ‘IlliS

Exp. a’

Ref. [ 121 b)

Ref. [13] c’

1.21 1580 5.08

1.22 1614 4.12

1.23 1585 4.19

work r,(A) % (cm-‘) 4 (eW

1.23 1603 4.14

l) Ref. ill]. b, Iterative natural orbital CI calculations using Slater type orbitals. Cl Iterative natural orbital CI adculations with basis functions remaining at the midbond position as molecular dissociation.

117

H. Yang et al. / CI calculations of low-lying states of @+

w,= 1585 cm-‘, and &=4.79 eV by performing iterative natural orbital CI calculations using mid-bond Gaussian functions and a double zeta s and p basis. The results indicate that the wavefunctions of oxygen can be fairly well described by the present basis set. The calculated total energy for the ground state of o:+ xiz; at the equilibrium distance is - 148.59277 au. This energy is 35.2 eV above the calculated O2 X 3Eg ground state, which is close to the recent experimental value of 36.3 eV from the electron impact mass spectrum measurement [ 21.

3. Results and discussion The potential curves of the calculated low-lying electronic states of the O$+ molecular ion are shown in fig. 1. The bond lengths, r,, the frequencies of the harmonic vibrations, w,, and energies for each state calculated, along with the experimental results are reported in table 2. Energies are given relative to the 05’ X ‘El ground state. In table 3, the comparisons of the present calculations with the results from Beebee et al. [ 7 ] and Hurley [ 41 are listed.

Our calculations show that the ground state of O$+ is X ‘Zg+, with the electronic configuration (lo,)‘( la,)*(2o,)*(2o,)*(30,)*( lxU)4. The potential minimum occurs at r, = 1.12 A and the calculated o, is 177 1 cm-‘. The present bond length of the X ‘El state is in good agreement with the value of 1.10 A obtained by Penkina and Rebane [ 3 ] using an improved scaling method, which appears to be very successful in calculations of bond lengths for A$+ molecular ions. For comparison we provide the values of r, calculated in earlier works: r, = 1.17 A calculated by Beebe et al. [ 7 ] using ab initio CI method with a minimum Slater basis, r, = 1.03 A calculated by Hopkinson et al. [ 15 ] performing LCAO MO SCF with double zeta Gaussian functions, and r, = 1.O1 A by Hurley [4]. The frequencies of the harmonic vibrations o,, obtained by the scaling methods, are 2363 cm- * from Hurley [ 41 and 1975 cm- ’ from Penkina and Rebane [ 6 1. These values indicate that the potential curve of @+ X ‘El from the scaling method is sharper than that obtained by the present calculations. The present curve gives the effective dissociation energy Des (potential minimum to top of barrier) of 2.6 eV, compared with the values of 6.45 eV

-148.0

h

Ei d

-148.2

V

-148.6 1.5

2.5

3.5

4.5

r ( a.u. ) Fig. 1. Potential curves of the calculated low-lying electronic states of the O$+ molecular ion.

H. Yang et al. f CI cakdationr oflow-iying states ofOj+

11s

Table 2 Calculated potential minima and energies for 0$* State

This work sf re (A)

*q

1.12

33: * Y.47 IF IS ‘4, “Q ‘Z$

1.25 1.47 1.46 1.36 1.26

Ex;. .%I (W

Ref. [7]

&h teW

E b, (W

E =’ ievt

re (A)

0.00

0.00 4.5 6.1

0.00 2.6 5.8

1.174

6.9 7.3 -

5.6 7.3 8.8

1.291 1.458 1.418 1.393 1.271

0.00 5.84 7.73

-5.41

9.12 7.92 9.57 10.11 9.27 17.17

6.92 7.16 7.69 8.33 8.48 -

Ref. [4] .G, CeVt

rs (A)

Emi. fev)

0.00 2.56 5.07

1.010 1.285 -

0.00 4.16

6.10 5.70 7.21 7.97 7.26 12.04

1.163 1.246 1.239 1.212 1.175 -

6.67 7.01 7.37 8.14 8.17

a) I&,, is the vertical excitation energy from the ground state X ‘Zz potential curve minimum. E,, is the energy of an excited state at its equilibrium separation relative to the ground state X ‘xc minimum energy. bt Auger electron spectrum analyzed by Sambe and Ramaker [ 21. ‘) Electron impact rn~~men~ by means of high resolution energy-gain spectroscopy by Hamdan and Brenton [ 141.

Table 3 Calculated molecular spectroscopic constants for O$+ State

Ref. [4]

This work

Ref. [7]

re (A)

0, (cm-‘)

k (ev)

r, (A)

oh (cm-“)

&r (ev)

re (A)

& (ev)

1.12

1771

2.6

1.010 1.285

2363 952

5.1 0.5

1.174

0.9

I1.47 .25 1.36 1.46

1231 638 773 990 820

0.3 0.6 0.9 0.8

1.163 1.246 1.239 1.212

1405 1170 1204 1453

0.7 1.0 1.7 1.2

I.458 1.291 1.393 1.418

0.3 0.2 0.9 0.7

1.26

1123

1.f

1.175

1367

1.6

1.271

I.3

by the improved scaling method [ 3 J, and 5.1 eV from Hurley’s prediction [ 41. On the other hand, Beebe et al.‘s calculations estimated Des of 0.9 eV, but the w, value is not given. In other comparisons, it appears that the scaling methods generaliy overestimate the effective dissociation energy. The reasons for this overestimation and a prooedure to correct for it are described in another publication [ 161. The lowest excited state calculated for C@” is A 3Xz. This state, along with the ‘Z:,’ state, however, has no potential minimum, consistent with the Cal-

culations by Beebe et al, [ 71, but contrary to the prediction by Hurley [ 41 who gives the potential minimum at r,-- 1.285 A. The existence of the “A,, state below the B SI&state is confhmed. The 3& and B “I& as well as 3X;, ‘l&y, ‘Au, ‘II, have potential minima as shown in fig. 1. The bond lengths obtained in the present work are 1.47, 1.25, 1.47, 1.46,1.36,and 1.26Aforthestates 3AD,31TW3P ‘C;, I&, and ‘II, respectively, and thefrequenc~~oftheharmonicvibrationsw,are638, 1231, 773, 820, 990, and 1123 cm-’ for the above

H. Yang et al. / CI calculations of low-lyingstates of Oj+

states, respectively. The calculated effective dissociation energies DefFfor the above states are 0.3,0.6,0.3, Q&0.9, and 1.1 eV, respectively. Except the state ‘A,,, the predicted molecular spectroscopic constants for the states listed above are fairly consistent with the configuration interaction calculations by Beebe et al. [ 7 1. However, there are large gaps between the present work and the predictions from Hurley’s scaling method [ 41 (see table 3 ). The energies of the excited states calculated generally are not far from the experimental values (see table 2 ) . The energies of the triplet states, 3A,, ‘II,, and ‘EC, at their equilibrium position, are calculated to be 5.5, 6.9, and 7.2 eV relative to the ground state X ‘Z:. These energies are very close to the Auger electron spectrum assignments [ 2 ] of 6.1,6.9 and 7.3 eV, respectively. From table 2, it is clear that the energies for each state in the present calculations are consistent with Hurley’s predictions [ 41, however, our calculated vertical excitation energies are quite ditTerent from the results obtained by Beebe et al. [ 71. This difference can be easily understood from the different equilibrium distances calculated for the ground state X ‘El by the minimum Slater basis functions and the present treatment. A recent observation of dispersed luminescence following core electron excitation by monochromatic synchrotron radiation for the case of oxygen suggests that the possible transition energies of B 3&-+ A ‘EC: are 2.64, 2.80, and 2.97 eV [ 11. Our calculations show that the vertical energy separation between the ‘D, and ‘I;: states is about 2.8 eV; however, our calculations indicate that the A 3EC: state is purely repulsive. The transition ‘II, --)3EI;,’therefore should not provide vibrationally resolved luminescence, which has been obtained with 0.8 A linewidths [ 171. It therefore is concluded that the calculations reported here do not support assignment of the observed luminescence to the O$+ , B ‘&+A ‘2,’ transition.

119

Acknowledgement We thank Dr. Kaidee Lee for helpful discussions. Support of this work by the US Department of Energy and the National Science Fundation (CHE 8703340) is acknowledged.

References [ 1 ] K. Tohji, D.M. Hanson and B.X. Yang, J. Chem. Phys. 85 (1986) 7492. [2]H.SambeandD.E.Ramaker,Chem.Phys. 104(1986) 331. [ 31 N.N. Penkina and T.K. Rebane, Opt. Spectry. (USSR) 62 ( 1987) 306. [4] A.C. Hurley, J. Mol. Spectry. 9 ( 1962) 18. [S] A.C. Hurley and V.W. Maslen, J. Chem. Phys. 34 (1961) 1919. [6] N.N. Penkina and T.K. Rebane, Opt. Spectry. (USSR) 46

(1979) 253. [ 71 N.H.F. Beebe., E.W. Thulstrup and A. Andersen, J. Chem. Phys. 64 ( 1976) 2080. [ 81 B.I. Dunlap, P.A. Mills and D.E. Ramaker, J. Chem. Phys. 75 (1981) 300. [9] J.L. Whitten, J. Chem. Phys. 44 (1966) 359. [ 101 P. Madhavan and J.L. Whitten, J. Chem. Phys. 77 (1982) 2673. [ 111 G. Her&erg, Spectraof Diatomic Molecules (Van Nostrand, New York, 1950). [ 121 H.F. Schaefer, J. Chem. Phys. 54 ( 1971) 2207. [ 13 ] S.D. Peyerimhoff and R.J. Buenker, Chem. Phys. Letters 16 (1972) 235. [ 141 M. Hamdan and A.G. Brenton, to be published. [ 151 AC. Hopkinson, K Yates and LG. Csizmadia, Theoret. Chim. Acta 23 (1972) 369. [ 161 K.D. Lee and D.M. Hanson, to be published. 117lL.A. Kelly, E.D. Poliakoff, D.M. Hanson, C.I. Ma, D.A. Lapiano-Smith and K.T. Wu, unpublished results.