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An experimental and theoretical investigation of the valence double photoionisation of the iodine molecule
Chemical Physics 324 (2006) 674–678 www.elsevier.com/locate/chemphys
An experimental and theoretical investigation of the valence double photoionisation of the iodine molecule D. Edvardsson a, A. Danielsson a, L. Karlsson a, J.H.D. Eland b
b,*
a Department of Physics, Uppsala University, Box 530, SE-751 21 Uppsala, Sweden Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom
Received 5 October 2005; accepted 9 December 2005 Available online 10 January 2006
Abstract The double photoionisation spectrum of molecular iodine has been measured at three wavelengths by the TOF-PEPECO technique and is interpreted using relativistic molecular structure COSCI calculations of potential curves for a large number of electronic states connected to the three lowest groups of dissociation limits. The lowest double ionisation energy is 24.85 ± 0.02 eV (adiabatic) or 2þ 24.95 ± 0.02 eV (vertical). It is associated with the 3 R g;0 electronic state of I2 . The double ionisation process is mainly direct, and positions and widths of the bands are well reproduced by the calculations. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Double photoionisation; I2; Coincidence technique
1. Introduction Double ionisation of iodine is easily observed in its mass spectrum, as the cross-section for the photon or electron induced process is large. Although the mass to charge ratio + for I2þ 2 is identical to that of I , the existence of long-lived 2þ I2 ions is shown by the shape of the I+ peak in time-offlight (TOF) mass spectra, where a sharp I2þ 2 peak is seen on top of a broad I+ peak. In coincidence experiments I+ + I+ ion pairs are also prominent and their kinetic energy suggests an ionisation energy of 29 eV for the dissociative precursor state [1]. No recent measurement of iodine’s double ionisation threshold or spectrum appear to have been made, however, although multiple ionisation has been studied in strong laser fields [2]. This paper reports a study of the full valence double photoionisation spectrum up to 40 eV by the TOF-PEPECO method [3]. The double ionisation energy of I2 was first calculated by Hurley and Maslen [4] as 25.74 eV, which is less than
*
Corresponding author. Fax: +44 0 1865 275410. E-mail address: [email protected] (J.H.D. Eland).
0301-0104/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.12.004
1 eV higher than the experimental energy obtained in the present investigation. In this work, we have carried out calculations of the potential curves for all dicationic states associated with the three lowest groups of dissociation limits into I+ + I+. They correspond to various combinations of the 3P2,1,0 and 1D2 states of the atomic ions and include all states relevant to the present experimental data. For the interpretation of the experimental spectrum we refer to the electron configuration of the neutral ground state as . . . ð10ru Þ2 ð11rg Þ2 ð6pu Þ4 ð6pg Þ4 This configuration has been confirmed by many spectroscopic investigations, and most recently in a study using both multiphoton ionisation and photoelectron spectroscopy [5], but it must be considered as an approximation since both relativistic and correlation effects are found to be important [6]. ZEKE-PFI spectroscopy has been used to study the cationic valence states at very high resolution, and has revealed extensive vibrational fine structure in great detail in the outermost bands [7]. Moreover, a quartet electronic state was observed in the energy region of the A 2 P3/2,u ionic state.
D. Edvardsson et al. / Chemical Physics 324 (2006) 674–678
Other studies of interest for comparison with the present results are photo-double ionisation spectra of the HI [8,9] and Br2 [10] molecules. The spectra have been recorded using the present method [9] and by threshold photoelectrons coincidence (TPEsCO) spectroscopy [8,10], and the HI work also included ab initio calculations incorporating spin–orbit interaction [8]. 2. Experimental apparatus and procedure In the TOF-PEPECO technique [3] molecules are ionised by wavelength-selected light from a pulsed atomic gas discharge. Ionisation occurs in the divergent magnetic field of a shaped permanent magnet, which forces almost all photoelectrons to follow the field lines of a long solenoid to a 5.5-m distant detector. Energies of all the emitted electrons can be deduced from their arrival times relative to the light pulse. In this study, the atomic lines used were at wavelengths 30.4 nm (40.81 eV, HeII), 37.9 nm (32.69 eV, NeIII) and 46.1 nm (26.91 eV, NeII). The spectra have been calibrated by measuring the normal photoelectron spectrum of O2, which gives many resolved lines of known energy, before and after each iodine run. At the time of this work, the lamp produced double pulses rather than single ones when working on the 30.4-nm HeII line. As the pulse shape (in time) is recorded at the same time as the spectrum, its effect could be largely removed from the spectra during the data treatment by a mild deconvolution using the Siska iterative procedure [11]. 3. Computational details We have carried out relativistic electronic structure calculations on the neutral iodine molecule as well as the doubly charged system using the MOLFDIR program package [12,13]. This program has been used previously by de Jong et al. [14] to derive potential curves of both neutral and ionised states of the molecule. The four-component electronic wavefunctions (spinors) of open-shell systems are optimized using the so-called average of configuration Dirac–Hartree–Fock Hamiltonian (DHF) [15]. Since the number of electronic states in the energy region under consideration is high we have performed full configuration interaction (CI) calculations within the space of the open-shell spinors to project out all the different states that arise from the open-shell manifold. This active space is constructed from the molecular orbitals formed out of the six atomic 5p orbitals. Thus, for the doubly charged molecule, all electronic states obtained by distributing eight electrons in 12 active spinors are calculated. The method is called Complete Open Shell Configuration Interaction (COSCI) [14] and is a procedure that gives a good balanced description of the states in the dicationic manifold at a reasonable computational cost. We do not expect the COSCI method to give accurate values of the vertical ionisation energies, since effects due to dynamical correlation and relaxation are not accounted
675
for. To incorporate these effects would require, e.g., a multireference CI method, which was not considered necessary for the present investigation. A Gaussian charge distribution with an exponential value of 1.845238916E + 09 is used in the relativistic calculations and the value of the speed of light is 137.0359895 atomic units. All calculations are performed in the D4h point group and its double group. The basis set used is the contracted pVDZ basis taken from [15]. The radial nuclear Schro¨dinger equation is solved using the program Level 7.5 [16] and spectroscopic constants are obtained from the calculated vibrational energies by a curve fitting procedure. 4. Results and discussion The spectra recorded for doubly ionised iodine at the three wavelengths, 30.4, 37.9 and 46.1 nm are displayed in Fig. 1. They are essentially similar to each other but with small variations in relative intensity and linewidth of the peaks. The energies and, to facilitate identification in the figure, relative peak count rates of the prominent peaks, are listed in Table 1. The onset of the lowest line is readily identified at 24.85 ± 0.02 eV (adiabatic double ionisation energy) whereas the peak maximum is observed at 24.95 ± 0.02 eV (vertical double ionisation energy). Following Hund’s rules this line is associated with the X 3 R g;0 electronic ground state (case a) or 0g (case c). The calculated energy difference between the potential energy minima of the neutral and dicationic ground states is a bit lower, 23.54 eV. As explained in the previous section, the theoretical method used is not expected to give a very accurate value for this energy. At higher energies extensive structures with many individual peaks are observed. The first few are well defined and comparatively narrow, whereas in the region above
Fig. 1. Double ionisation spectra of the iodine molecule at the wavelengths shown. The two error bars reflect only the statistical uncertainty of the intensities.
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Table 1 Experimental and calculated binding energiesa (in eV) and assignments for the doubly ionised cationic states of the I2 molecule Experimental binding energy (eV)
Relative intensityb
Comment
Calculated energya,c (eV)
Calculated equilibrium ˚) distance (A
Assignment of dicationic stated using leading configuration and term
24.95 25.4 25.74 26.02 26.02 26.46 26.82 27.42 27.92 28.88 29.94
0.32 0.26 0.82 0.26 0.26 0.50 0.43 0.47 0.76 1.00 0.79
Line Line Line Broad Broad Line Broad Broad Broad Broad Broad
24.95 25.31 25.69 26.00 26.02 26.30 26.72 27.29 + 27.38 27.43–28.09e 28.2–29.2e
2.71 2.695 2.76
ð6pg Þ2 X 3 R g;0 ð6pg Þ2 X 3 R g;1 (6pg)2 a 1Dg,2 1 1 0 1 ð6pu Þ ð6pg Þ b Ru;0 ð6pu Þ1 ð6pg Þ1 A 3 Rþ u;1 ð6pg Þ2 b1 Rþ g;0 (6pu)1 (6pg)1 B 3Du
a b c d e
int. int. line line peak peak peak
(0g) (1g) (2g) (0u) (1g) (0g)
˚ [17]. The calculated energies are given at the centre of the Franck–Condon region corresponding to an equilibrium internuclear distance of 2.666 A Determined at peak maximum from the 40.8-eV spectrum. The absolute energies have been adjusted to the experimental line at 24.95 eV. Relativistic notation is given in parentheses. Outer limits for a range of energies.
27 eV, the structure is complex and not easily interpreted. The peaks below 27 eV can be associated primarily with terms of the dication having a leading configuration 6p2 g , and, to less extent, a mixed two holes configuration (6pu)1 (6pg)1. The 6pu orbital is chemically bonding, and vacancies in this orbital should be revealed in the spectra by broader peaks than observed for pure 6pg vacancies. Fig. 2 shows the potential energy curves computed for some of the valence states up to about 28 eV and associated with the three lowest groups of dissociation limits of I2þ 2 at about 22.5 eV [I+(3P2) + I+(3P2)], 23.3 eV [I+(3P1,0) + I+(3P2)] and 24.2 eV [I+(3P1,0) + I+(3P1,0)], [I+(3P2) + I+ (1D2)] [17,18]. The potential curves are derived from the COSCI calculations at about 10 different bond distances. As can be seen, a large number of states are predicted. In the Franck–Condon region for direct ionisation, which is indicated in the figure, the potential curves form a dense pattern at energies above 27.3 eV. At lower energies, on the other hand, the curves are well separated, and the correspondence with the experimental spectrum is more obvious. Energies of the potential curves at the centre of the Franck–Condon region are given in Table 1, where the energy of the first peak in the experimental spectrum, 24.95 eV, has been used as the reference energy for the computed energies. A close inspection shows that there is a very good agreement between the experimental and theoretical energies, which allows detailed assignments to be proposed for the lower energy part of the experimental spectrum on this basis. They are given in Table 1. The states associated with a leading (6pg)2 configura3 tion are, in order of increasing energy, X 3 R g;0 , X Rg;1 , a 1 1 þ Dg, and b Rg . We use here the same notation as used in ref [10] for Br2þ in order to facilitate comparisons. For 2 the spin–orbit split components of the X state, 3 R g;0 , and 3 Rg;1 , potential energy minima with a depth of about 0.2 eV are predicted at very nearly the same equilibrium internuclear distance as of the neutral ground state, whilst
the potential energy curve of the a 1Dg state has a minimum that is shifted to a somewhat larger internuclear distance (cf. Table 1). The b 1 Rþ g state is repulsive but with only a
Fig. 2. Computed potential curves of the I2þ 2 dication for the electronic states associated with the three lowest dissociation limits into I+ + I+.
D. Edvardsson et al. / Chemical Physics 324 (2006) 674–678
weak slope inside the Franck–Condon region. These predictions are fully consistent with the experimental spectrum, which shows four narrow lines in the outermost energy region. If even higher accuracy could be achieved in the calculations, the potential minima would probably tend to become deeper, as has been found in many previous investigations, and, possibly, states which do not show a definite minimum in the present data could prove to contain one, even if only very shallow. 3 The X 3 R g;0 and X Rg;1 components are separated by 0.45 eV and very well resolved in the spectrum. In the case of HI2+ the corresponding splitting is only about half of this value, 0.22 eV [8,9]. In both cases, the orbital is located on iodine and the comparison thus gives evidence of a larger effective nuclear charge experienced by the electrons in 2+ I2þ 2 than in HI . The expected vibrational energy level sep2þ aration of I2 , as obtained from the present calculations, is far too small to allow observation of vibrational fine structure at the present level of resolution. Indications of such excitations have been found in the threshold photoelectrons coincidence (TPEsCO) spectrum for the corresponding states of Br2þ [10] and, possibly, highly resolved 2 (TPEsCO) spectra could reveal similar structure of I2þ 2 . The calculated vibrational constants are given in Table 2. In the region between the a 1Dg and b 1 Rþ g states two strongly repulsive states, which we label b0 1 R u , and A 3 Rþ , appear in the Franck–Condon region. They are u;1 separated by only 20 meV and are indicated in Fig. 2 by one single potential energy curve. These states are expected to give rise to a broad band in the spectrum and probably correspond to the rounded weak feature that can be inferred with maximum intensity at 26.02 eV, particularly in the 37.9 eV spectrum. At 26.82 eV another broad structure can be observed. It is most likely associated with the B 3 Du state which, like the b0 1 R u state, is connected to a leading (6pu)1 (6pg)1 configuration, (cf. also Table 1). Further detailed assignments of the spectral structures at higher energies are not readily made on the basis of the present data due to both the complexity of the experimental spectrum and the strong overlap between the calculated states. However, some correspondence between groups of potential curves and broad peaks in the spectra may be present as can be seen by comparing the experimental and theoretical figures. For this reason an overview of the potential curves between 23.0 and 30.0 eV for internu˚ is shown in Fig. 3, where clear distances between 2 and 7 A the dissociation products are also indicated [19].
Table 2 Calculated vibrational constants (in the unit cm1) for bound states of I2þ 2 Electronic state
xe
xexe
X R g;0 X3 R g;1 a 1Dg,2
175.9 185.6 111.9a
3.076 3.843
3
a
The a 1Dg,2 state is found to support only two vibrational levels.
677
Fig. 3. An overview of the computed potential curves and the various associated dissociation products.
In addition to the spectra, the TOF-PEPECO technique gives complete energy distributions of the electron pairs emitted in double photoionisation. The distribution found for iodine at 30.4 nm is shown in Fig. 4 as a greyscale map of intensity as a function of ionisation energy (hm E1 E2) and of the lower electron energy E2. Such maps often reveal indirect ionisation pathways as concentrations of intensity for selected one-electron energies, as seen in extreme form, for example, in O2 [20]. With I2, the map shows a broad concentration of intensity for ionisation energies between 27 and 31 eV and electron energies of 0.8 eV and below. This probably represents an indirect ionisation pathway involving rapid molecular dissociation with autoionisation of the I atom, as suggested in the related HI double photoionisation [9]. Single ionisation photoelectron spectra measured at 30.4 and 37.9 nm show a weak band, presumably a ‘‘configuration interaction satellite’’ extending from the double ionisation onset up to about 30 eV. The autoionisation may involve this intermediate state of Iþ 2 , interacting with Rydberg states related to the many I2þ states at this energy, shown in Fig. 3. The 2 dissociative Rydbergs could decay to atomic I+ + I*, fol-
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biguous identification of the lowest energy states. It further confirms that the lowest states in the experimental spectrum are generated primarily by direct photoionisation processes, because the observed peak widths are in line with simple prediction from the intersection of the Franck–Condon zone with the computed potential energy surfaces. Acknowledgements Prof. A.J. Yencha is gratefully acknowledged for providing us with the manuscript on Br2þ 2 to be presented at the ICPEAC conference 2005, and for helpful discussions. We acknowledge financial support from the EPSRC for the experimental part of the work. References Fig. 4. Greyscale map of the electron pair intensity distribution in double photoionisation of I2 at 30.4 nm (40.81 eV).
lowed by autoionisation of the superexcited iodine. Formation of the lowest states of I2þ 2 seems to be mainly direct, because the horizontal lines in the map representing these processes are of essentially uniform intensity. 5. Conclusions Double photoionisation spectra have been recorded for the I2 molecule using a TOF-PEPECO technique at three different wavelengths of the ionising radiation. The potential energy curves of the corresponding electronic dicationic states have been computed using a high level relativistic CI program. The spectra show a rich structure of which the outermost part between 25 and 27 eV can be associated 3 with the six lowest states, which are X 3 R g;0 , X Rg;1 , a 0 1 1 3 þ 1 þ Dg, b Ru , A Ru;1 and b Rg; . The splitting of the X = 0 and X = 1 components of the X 3 R g ground state term is found to be 0.45 eV, and the two lines are well resolved in the spectra. This splitting is slightly underestimated by the calculations, which give a value of 0.36 eV. The X 3 R g states are found to be quasi-bound with potential curves supporting several vibrational levels. Due to very small energy level separations, the vibrational fine structure cannot be resolved in the present experiment but should be observable in more highly resolved spectra. The good agreement between the experimental and computed double ionisation energies indicates that the COSCI method is sufficiently accurate to allow an unam-
[1] D.M. Curtis, J.H.D. Eland, Int. J. Mass Spectrom. Ion Processes 63 (1985) 241. [2] D. Normand, M. Schmidt, Phys. Rev. A 53 (1996) R1958. [3] J.H.D. Eland, O. Vieuxmaire, T. Kinugawa, P. Lablanquie, R.I. Hall, F. Penent, Phys. Rev. Lett. 90 (2003) 053003. [4] A.C. Hurley, V.W. Maslen, J. Chem. Phys. 34 (1961) 1919. [5] Y.-Y. Gu, A.M. Chojnacki, C.J. Zietkiewcs, A.A. Senin, J.G. Eden, J. Chem. Phys. 119 (2003) 12342. [6] L. Visscher, K.G. Dyall, J. Chem. Phys. 104 (1995) 9040. [7] M.C.R. Cockett, R.J. Donovan, K.P. Lawley, J. Chem. Phys. 105 (1996) 3347. [8] A.J. Yencha, A.M. Juarez, S.P. Lee, G.C. King, F.r. Bennett, F. Kemp, I.R. McNab, Chem. Phys. 303 (2004) 179. [9] A. Pilcher-Clayton, J.H.D. Eland, J. Electron, Spectrosc. Related Phenom. 142 (2005) 313. [10] A.J. Yencha, S.P. Lee, G.C. King, in press. [11] P.E. Siska, J. Chem. Phys. 59 (1973) 6052. [12] P.J. Aerts, O. Visser, L. Visscher, H. Merenga, W.A. de Jong, W.C. Nieuwport, Relativistic Quantum Chemistry: The MOLFDIR Program Package, University of Groningen, The Netherlands, 1995. [13] L. Visscher, O. Visser, P.J. Aerts, H. Merenga, W.C. Nieuwport, Comput. Phys. Commun. 81 (1994) 120. [14] W.A. de Jong, L. Visscher, W.C. Nieuwport, J. Chem. Phys. 107 (1997) 9046. [15] O. Visser, L. Visscher, P.J. Aerts, W.C. Nieuwport, J. Chem. Phys. 96 (1992) 2910. [16] R.J. Le Roy, Level 7.5: A Computer Program for Solving the Radial Schro¨dinger Equation for Bound and Quasibound Levels, University of Waterloo, Chemical Physics Research Report CP-655, 2002. [17] K.P. Huber, G. Herzberg, Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules, Van Nostrand, New York, 1979. [18] C.E. Moore, Atomic Energy Levels, Atomic Energy Levels, Natl. Bur. Stand. (US) Circ. No. 467, US GPO, Washington, DC, 1949. [19] The calculated potential energies for the various states can be obtained from the authors by request. [20] R. Feifel, J.H.D. Eland, Phys. Rev. A 71 (2005) 034501.
An experimental and theoretical investigation of the valence double photoionisation of the iodine molecule D. Edvardsson a, A. Danielsson a, L. Karlsson a, J.H.D. Eland b
b,*
a Department of Physics, Uppsala University, Box 530, SE-751 21 Uppsala, Sweden Physical and Theoretical Chemistry Laboratory, Oxford University, South Parks Road, Oxford OX1 3QZ, United Kingdom
Received 5 October 2005; accepted 9 December 2005 Available online 10 January 2006
Abstract The double photoionisation spectrum of molecular iodine has been measured at three wavelengths by the TOF-PEPECO technique and is interpreted using relativistic molecular structure COSCI calculations of potential curves for a large number of electronic states connected to the three lowest groups of dissociation limits. The lowest double ionisation energy is 24.85 ± 0.02 eV (adiabatic) or 2þ 24.95 ± 0.02 eV (vertical). It is associated with the 3 R g;0 electronic state of I2 . The double ionisation process is mainly direct, and positions and widths of the bands are well reproduced by the calculations. Ó 2005 Elsevier B.V. All rights reserved. Keywords: Double photoionisation; I2; Coincidence technique
1. Introduction Double ionisation of iodine is easily observed in its mass spectrum, as the cross-section for the photon or electron induced process is large. Although the mass to charge ratio + for I2þ 2 is identical to that of I , the existence of long-lived 2þ I2 ions is shown by the shape of the I+ peak in time-offlight (TOF) mass spectra, where a sharp I2þ 2 peak is seen on top of a broad I+ peak. In coincidence experiments I+ + I+ ion pairs are also prominent and their kinetic energy suggests an ionisation energy of 29 eV for the dissociative precursor state [1]. No recent measurement of iodine’s double ionisation threshold or spectrum appear to have been made, however, although multiple ionisation has been studied in strong laser fields [2]. This paper reports a study of the full valence double photoionisation spectrum up to 40 eV by the TOF-PEPECO method [3]. The double ionisation energy of I2 was first calculated by Hurley and Maslen [4] as 25.74 eV, which is less than
*
Corresponding author. Fax: +44 0 1865 275410. E-mail address: [email protected] (J.H.D. Eland).
0301-0104/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.12.004
1 eV higher than the experimental energy obtained in the present investigation. In this work, we have carried out calculations of the potential curves for all dicationic states associated with the three lowest groups of dissociation limits into I+ + I+. They correspond to various combinations of the 3P2,1,0 and 1D2 states of the atomic ions and include all states relevant to the present experimental data. For the interpretation of the experimental spectrum we refer to the electron configuration of the neutral ground state as . . . ð10ru Þ2 ð11rg Þ2 ð6pu Þ4 ð6pg Þ4 This configuration has been confirmed by many spectroscopic investigations, and most recently in a study using both multiphoton ionisation and photoelectron spectroscopy [5], but it must be considered as an approximation since both relativistic and correlation effects are found to be important [6]. ZEKE-PFI spectroscopy has been used to study the cationic valence states at very high resolution, and has revealed extensive vibrational fine structure in great detail in the outermost bands [7]. Moreover, a quartet electronic state was observed in the energy region of the A 2 P3/2,u ionic state.
D. Edvardsson et al. / Chemical Physics 324 (2006) 674–678
Other studies of interest for comparison with the present results are photo-double ionisation spectra of the HI [8,9] and Br2 [10] molecules. The spectra have been recorded using the present method [9] and by threshold photoelectrons coincidence (TPEsCO) spectroscopy [8,10], and the HI work also included ab initio calculations incorporating spin–orbit interaction [8]. 2. Experimental apparatus and procedure In the TOF-PEPECO technique [3] molecules are ionised by wavelength-selected light from a pulsed atomic gas discharge. Ionisation occurs in the divergent magnetic field of a shaped permanent magnet, which forces almost all photoelectrons to follow the field lines of a long solenoid to a 5.5-m distant detector. Energies of all the emitted electrons can be deduced from their arrival times relative to the light pulse. In this study, the atomic lines used were at wavelengths 30.4 nm (40.81 eV, HeII), 37.9 nm (32.69 eV, NeIII) and 46.1 nm (26.91 eV, NeII). The spectra have been calibrated by measuring the normal photoelectron spectrum of O2, which gives many resolved lines of known energy, before and after each iodine run. At the time of this work, the lamp produced double pulses rather than single ones when working on the 30.4-nm HeII line. As the pulse shape (in time) is recorded at the same time as the spectrum, its effect could be largely removed from the spectra during the data treatment by a mild deconvolution using the Siska iterative procedure [11]. 3. Computational details We have carried out relativistic electronic structure calculations on the neutral iodine molecule as well as the doubly charged system using the MOLFDIR program package [12,13]. This program has been used previously by de Jong et al. [14] to derive potential curves of both neutral and ionised states of the molecule. The four-component electronic wavefunctions (spinors) of open-shell systems are optimized using the so-called average of configuration Dirac–Hartree–Fock Hamiltonian (DHF) [15]. Since the number of electronic states in the energy region under consideration is high we have performed full configuration interaction (CI) calculations within the space of the open-shell spinors to project out all the different states that arise from the open-shell manifold. This active space is constructed from the molecular orbitals formed out of the six atomic 5p orbitals. Thus, for the doubly charged molecule, all electronic states obtained by distributing eight electrons in 12 active spinors are calculated. The method is called Complete Open Shell Configuration Interaction (COSCI) [14] and is a procedure that gives a good balanced description of the states in the dicationic manifold at a reasonable computational cost. We do not expect the COSCI method to give accurate values of the vertical ionisation energies, since effects due to dynamical correlation and relaxation are not accounted
675
for. To incorporate these effects would require, e.g., a multireference CI method, which was not considered necessary for the present investigation. A Gaussian charge distribution with an exponential value of 1.845238916E + 09 is used in the relativistic calculations and the value of the speed of light is 137.0359895 atomic units. All calculations are performed in the D4h point group and its double group. The basis set used is the contracted pVDZ basis taken from [15]. The radial nuclear Schro¨dinger equation is solved using the program Level 7.5 [16] and spectroscopic constants are obtained from the calculated vibrational energies by a curve fitting procedure. 4. Results and discussion The spectra recorded for doubly ionised iodine at the three wavelengths, 30.4, 37.9 and 46.1 nm are displayed in Fig. 1. They are essentially similar to each other but with small variations in relative intensity and linewidth of the peaks. The energies and, to facilitate identification in the figure, relative peak count rates of the prominent peaks, are listed in Table 1. The onset of the lowest line is readily identified at 24.85 ± 0.02 eV (adiabatic double ionisation energy) whereas the peak maximum is observed at 24.95 ± 0.02 eV (vertical double ionisation energy). Following Hund’s rules this line is associated with the X 3 R g;0 electronic ground state (case a) or 0g (case c). The calculated energy difference between the potential energy minima of the neutral and dicationic ground states is a bit lower, 23.54 eV. As explained in the previous section, the theoretical method used is not expected to give a very accurate value for this energy. At higher energies extensive structures with many individual peaks are observed. The first few are well defined and comparatively narrow, whereas in the region above
Fig. 1. Double ionisation spectra of the iodine molecule at the wavelengths shown. The two error bars reflect only the statistical uncertainty of the intensities.
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D. Edvardsson et al. / Chemical Physics 324 (2006) 674–678
Table 1 Experimental and calculated binding energiesa (in eV) and assignments for the doubly ionised cationic states of the I2 molecule Experimental binding energy (eV)
Relative intensityb
Comment
Calculated energya,c (eV)
Calculated equilibrium ˚) distance (A
Assignment of dicationic stated using leading configuration and term
24.95 25.4 25.74 26.02 26.02 26.46 26.82 27.42 27.92 28.88 29.94
0.32 0.26 0.82 0.26 0.26 0.50 0.43 0.47 0.76 1.00 0.79
Line Line Line Broad Broad Line Broad Broad Broad Broad Broad
24.95 25.31 25.69 26.00 26.02 26.30 26.72 27.29 + 27.38 27.43–28.09e 28.2–29.2e
2.71 2.695 2.76
ð6pg Þ2 X 3 R g;0 ð6pg Þ2 X 3 R g;1 (6pg)2 a 1Dg,2 1 1 0 1 ð6pu Þ ð6pg Þ b Ru;0 ð6pu Þ1 ð6pg Þ1 A 3 Rþ u;1 ð6pg Þ2 b1 Rþ g;0 (6pu)1 (6pg)1 B 3Du
a b c d e
int. int. line line peak peak peak
(0g) (1g) (2g) (0u) (1g) (0g)
˚ [17]. The calculated energies are given at the centre of the Franck–Condon region corresponding to an equilibrium internuclear distance of 2.666 A Determined at peak maximum from the 40.8-eV spectrum. The absolute energies have been adjusted to the experimental line at 24.95 eV. Relativistic notation is given in parentheses. Outer limits for a range of energies.
27 eV, the structure is complex and not easily interpreted. The peaks below 27 eV can be associated primarily with terms of the dication having a leading configuration 6p2 g , and, to less extent, a mixed two holes configuration (6pu)1 (6pg)1. The 6pu orbital is chemically bonding, and vacancies in this orbital should be revealed in the spectra by broader peaks than observed for pure 6pg vacancies. Fig. 2 shows the potential energy curves computed for some of the valence states up to about 28 eV and associated with the three lowest groups of dissociation limits of I2þ 2 at about 22.5 eV [I+(3P2) + I+(3P2)], 23.3 eV [I+(3P1,0) + I+(3P2)] and 24.2 eV [I+(3P1,0) + I+(3P1,0)], [I+(3P2) + I+ (1D2)] [17,18]. The potential curves are derived from the COSCI calculations at about 10 different bond distances. As can be seen, a large number of states are predicted. In the Franck–Condon region for direct ionisation, which is indicated in the figure, the potential curves form a dense pattern at energies above 27.3 eV. At lower energies, on the other hand, the curves are well separated, and the correspondence with the experimental spectrum is more obvious. Energies of the potential curves at the centre of the Franck–Condon region are given in Table 1, where the energy of the first peak in the experimental spectrum, 24.95 eV, has been used as the reference energy for the computed energies. A close inspection shows that there is a very good agreement between the experimental and theoretical energies, which allows detailed assignments to be proposed for the lower energy part of the experimental spectrum on this basis. They are given in Table 1. The states associated with a leading (6pg)2 configura3 tion are, in order of increasing energy, X 3 R g;0 , X Rg;1 , a 1 1 þ Dg, and b Rg . We use here the same notation as used in ref [10] for Br2þ in order to facilitate comparisons. For 2 the spin–orbit split components of the X state, 3 R g;0 , and 3 Rg;1 , potential energy minima with a depth of about 0.2 eV are predicted at very nearly the same equilibrium internuclear distance as of the neutral ground state, whilst
the potential energy curve of the a 1Dg state has a minimum that is shifted to a somewhat larger internuclear distance (cf. Table 1). The b 1 Rþ g state is repulsive but with only a
Fig. 2. Computed potential curves of the I2þ 2 dication for the electronic states associated with the three lowest dissociation limits into I+ + I+.
D. Edvardsson et al. / Chemical Physics 324 (2006) 674–678
weak slope inside the Franck–Condon region. These predictions are fully consistent with the experimental spectrum, which shows four narrow lines in the outermost energy region. If even higher accuracy could be achieved in the calculations, the potential minima would probably tend to become deeper, as has been found in many previous investigations, and, possibly, states which do not show a definite minimum in the present data could prove to contain one, even if only very shallow. 3 The X 3 R g;0 and X Rg;1 components are separated by 0.45 eV and very well resolved in the spectrum. In the case of HI2+ the corresponding splitting is only about half of this value, 0.22 eV [8,9]. In both cases, the orbital is located on iodine and the comparison thus gives evidence of a larger effective nuclear charge experienced by the electrons in 2+ I2þ 2 than in HI . The expected vibrational energy level sep2þ aration of I2 , as obtained from the present calculations, is far too small to allow observation of vibrational fine structure at the present level of resolution. Indications of such excitations have been found in the threshold photoelectrons coincidence (TPEsCO) spectrum for the corresponding states of Br2þ [10] and, possibly, highly resolved 2 (TPEsCO) spectra could reveal similar structure of I2þ 2 . The calculated vibrational constants are given in Table 2. In the region between the a 1Dg and b 1 Rþ g states two strongly repulsive states, which we label b0 1 R u , and A 3 Rþ , appear in the Franck–Condon region. They are u;1 separated by only 20 meV and are indicated in Fig. 2 by one single potential energy curve. These states are expected to give rise to a broad band in the spectrum and probably correspond to the rounded weak feature that can be inferred with maximum intensity at 26.02 eV, particularly in the 37.9 eV spectrum. At 26.82 eV another broad structure can be observed. It is most likely associated with the B 3 Du state which, like the b0 1 R u state, is connected to a leading (6pu)1 (6pg)1 configuration, (cf. also Table 1). Further detailed assignments of the spectral structures at higher energies are not readily made on the basis of the present data due to both the complexity of the experimental spectrum and the strong overlap between the calculated states. However, some correspondence between groups of potential curves and broad peaks in the spectra may be present as can be seen by comparing the experimental and theoretical figures. For this reason an overview of the potential curves between 23.0 and 30.0 eV for internu˚ is shown in Fig. 3, where clear distances between 2 and 7 A the dissociation products are also indicated [19].
Table 2 Calculated vibrational constants (in the unit cm1) for bound states of I2þ 2 Electronic state
xe
xexe
X R g;0 X3 R g;1 a 1Dg,2
175.9 185.6 111.9a
3.076 3.843
3
a
The a 1Dg,2 state is found to support only two vibrational levels.
677
Fig. 3. An overview of the computed potential curves and the various associated dissociation products.
In addition to the spectra, the TOF-PEPECO technique gives complete energy distributions of the electron pairs emitted in double photoionisation. The distribution found for iodine at 30.4 nm is shown in Fig. 4 as a greyscale map of intensity as a function of ionisation energy (hm E1 E2) and of the lower electron energy E2. Such maps often reveal indirect ionisation pathways as concentrations of intensity for selected one-electron energies, as seen in extreme form, for example, in O2 [20]. With I2, the map shows a broad concentration of intensity for ionisation energies between 27 and 31 eV and electron energies of 0.8 eV and below. This probably represents an indirect ionisation pathway involving rapid molecular dissociation with autoionisation of the I atom, as suggested in the related HI double photoionisation [9]. Single ionisation photoelectron spectra measured at 30.4 and 37.9 nm show a weak band, presumably a ‘‘configuration interaction satellite’’ extending from the double ionisation onset up to about 30 eV. The autoionisation may involve this intermediate state of Iþ 2 , interacting with Rydberg states related to the many I2þ states at this energy, shown in Fig. 3. The 2 dissociative Rydbergs could decay to atomic I+ + I*, fol-
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D. Edvardsson et al. / Chemical Physics 324 (2006) 674–678
biguous identification of the lowest energy states. It further confirms that the lowest states in the experimental spectrum are generated primarily by direct photoionisation processes, because the observed peak widths are in line with simple prediction from the intersection of the Franck–Condon zone with the computed potential energy surfaces. Acknowledgements Prof. A.J. Yencha is gratefully acknowledged for providing us with the manuscript on Br2þ 2 to be presented at the ICPEAC conference 2005, and for helpful discussions. We acknowledge financial support from the EPSRC for the experimental part of the work. References Fig. 4. Greyscale map of the electron pair intensity distribution in double photoionisation of I2 at 30.4 nm (40.81 eV).
lowed by autoionisation of the superexcited iodine. Formation of the lowest states of I2þ 2 seems to be mainly direct, because the horizontal lines in the map representing these processes are of essentially uniform intensity. 5. Conclusions Double photoionisation spectra have been recorded for the I2 molecule using a TOF-PEPECO technique at three different wavelengths of the ionising radiation. The potential energy curves of the corresponding electronic dicationic states have been computed using a high level relativistic CI program. The spectra show a rich structure of which the outermost part between 25 and 27 eV can be associated 3 with the six lowest states, which are X 3 R g;0 , X Rg;1 , a 0 1 1 3 þ 1 þ Dg, b Ru , A Ru;1 and b Rg; . The splitting of the X = 0 and X = 1 components of the X 3 R g ground state term is found to be 0.45 eV, and the two lines are well resolved in the spectra. This splitting is slightly underestimated by the calculations, which give a value of 0.36 eV. The X 3 R g states are found to be quasi-bound with potential curves supporting several vibrational levels. Due to very small energy level separations, the vibrational fine structure cannot be resolved in the present experiment but should be observable in more highly resolved spectra. The good agreement between the experimental and computed double ionisation energies indicates that the COSCI method is sufficiently accurate to allow an unam-
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