Spin–orbit interaction mediated molecular dissociation E. Kokkonen, T. Löytynoja, K. Jänkälä, J. A. Kettunen, S. Heinäsmäki, A. Karpenko, and M. Huttula Citation: The Journal of Chemical Physics 140, 184304 (2014); doi: 10.1063/1.4873718 View online: http://dx.doi.org/10.1063/1.4873718 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/140/18?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Analytic second derivatives in closed-shell coupled-cluster theory with spin-orbit coupling J. Chem. Phys. 131, 164113 (2009); 10.1063/1.3245954 Spin–orbit ab initio study of alkyl halide dissociation via electronic curve crossing J. Chem. Phys. 121, 5761 (2004); 10.1063/1.1784411 Spin–orbit branching in the photodissociation of HF and DF. II. A time-dependent wave packet study of vibrationally mediated photodissociation J. Chem. Phys. 113, 1879 (2000); 10.1063/1.481991 Photodissociation of CH stretch overtone excited CH 3 Cl and CHD 2 Cl (v CH =5): Cl spin–orbit branching and atomic fragment yields J. Chem. Phys. 109, 7810 (1998); 10.1063/1.477427 Ab initio spin-free-state-shifted spin-orbit configuration interaction calculations on singly ionized iridium J. Chem. Phys. 108, 7980 (1998); 10.1063/1.476233
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THE JOURNAL OF CHEMICAL PHYSICS 140, 184304 (2014)
Spin–orbit interaction mediated molecular dissociation E. Kokkonen,1,a) T. Löytynoja,1,2 K. Jänkälä,1 J. A. Kettunen,1 S. Heinäsmäki,1 A. Karpenko,1 and M. Huttula1 1
Department of Physics, University of Oulu, Box 3000, 90014 Oulu, Finland Division of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, S-106 91 Stockholm, Sweden 2
(Received 14 February 2014; accepted 17 April 2014; published online 8 May 2014) The effect of the spin–orbit interaction to photofragmentation is investigated in the mercury(II) bromide (HgBr2 ) molecule. Changes in the fragmentation between the two spin–orbit components of Hg 5d photoionization, as well as within the molecular-field-splitted levels of these components are observed. Dissociation subsequent to photoionization is studied with synchrotron radiation and photoelectron-photoion coincidence spectroscopy. The experimental results are accompanied by relativistic ab initio analysis of the photoelectron spectrum. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873718] I. INTRODUCTION
Molecular photodissociation following selective excitation has been a fruitful tool to study the link between the electronic structure and dissociation mechanisms. Prominent examples include, for example, site-selective dissociation,1, 2 where a core hole is created and the dissociation pathways are monitored in the vicinity of the absorption edge. These systems generally show a clear interrelation between the electronic excitation and fragmentation pattern. For larger molecules the conventional way to analyze photoinduced molecular dissociation is to focus on the internal energy balance, especially in the valence states. The excited molecular state energy is assumed to be distributed to internal degrees of freedom prior to dissociation, which leads to fragment distributions where the identity of the initial excited electronic state is lost.3 This has led to a common practice where the details of the electronic structure in the photoionized state have been deemed unimportant and the focus has been on the ion specific rate constants, such as dissociation rates as a function of the ion internal energy.4 The spin–orbit effect on the photoionization process has been investigated theoretically in the past for diatomic and polyatomic molecules.5, 6 These studies show the importance of spin–orbit effects on the photodissociation dynamics of various molecules. The interaction between different spin– orbit states clearly affects the final states of the photodissociation processes.7, 8 This exemplifies the importance of knowing the effect of the spin–orbit interaction on the photoexcitation process and on the resulting photofragments. Here we report photoelectron–photoion coincidence (PEPICO) study of HgBr2 dissociation following photoexcitation using synchrotron radiation at 40.2 eV energy. This gives rise to ionization of the valence molecular orbital region as well as the more atomic-like Hg 5d orbitals. The results of the PEPICO procedure provide direct information on the electronic state dependence of the fragmentation a) Electronic mail: [email protected]
0021-9606/2014/140(18)/184304/5/$30.00
process. The HgBr2 molecule on the other hand allows to study relativistic effects in the dissociation process, as spin– orbit splitting in Hg is prominent even in the valence region below double ionization threshold. Strong electronic state dependence is seen in the fragmentation products associated with the Hg 5d orbitals. This dependence on the electronic structure can be seen to be sensitive to the strong spin–orbit and molecular field effects in the 5d region. The spin–orbit split orbitals share the same spatial symmetry but differ in the angular momentum coupling, which in turn affects the molecular field splitting. II. EXPERIMENT
The experiments were conducted at the I411 beamline at the MAX IV-laboratory (Lund, Sweden)9, 10 using a photon energy of 40.2 eV, and a resistively heated oven to evaporate the sample material. The PEPICO setup11 consists of a modified Scienta SES-100 hemispherical deflection analyzer (HDA)11, 12 and a Wiley-McLaren type13 time-of-flight mass spectrometer (TOFMS). In the PEPICO experiments the HDA was operated with a curved entrance slit of 0.8 mm and pass energy of 50 eV. All electron measurements were done using the “magic angle” of 54.7◦ with respect to the electric field vector of the linearly polarized radiation. For the electron measurements, analyzer line broadening of approximately 0.2 eV was produced. To better resolve the electronic states and verify the linewidths, a separate photoelectron spectrum (PES) measurement, without the detection of the final ions, was done on the beamline endstation setup consisting of a Scienta R4000 type HDA.9 The analyzer was operated with a curved entrance slit of 0.5 mm and at a pass energy of 20 eV, providing analyzer broadening of approximately 25 meV. III. CALCULATIONS
Theoretical predictions for the electronic states were carried out with the relativistic DIRAC code.14 The 140, 184304-1
© 2014 AIP Publishing LLC
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Dirac-Coulomb Hamiltonian was used in a form where the two-electron integrals over the small components of the wavefunction were neglected and replaced by simple Coulombic correlation.15 The basis used in the calculations was Dyall triple-zeta basis with core correlating functions for Hg and Br atoms.16, 17 The symmetry of the HgBr2 molecule was linear and represented with the D2h point group. The ground state geometry of the molecule was optimized with the Dirac–Hartree–Fock (DHF) method. This resulted in 2.41 Å bond length between the Hg and Br atoms. The ionization potentials and corresponding pole strengths were computed with the RELADC module,18 which utilizes the four-component extension of the one-particle propagator in the non-Dyson version of the algebraic diagrammatic construction (ADC).19 In this work the calculations were run with the third-order extension of the DHF-ADC method. Additionally, the fragment energies according to energy conservation were calculated. The total energies were obtained by optimizing the geometries of the HgBr2 molecule and the fragments with density functional theory (DFT) calculations using B3LYP(VWN5)20–22 hybrid functional under the unrestricted spin formalism. The calculations were performed with the GAMESS program23, 24 using the Def2TZVPPD basis with effective core potential (ECP) for Hg and Br atoms.25 The bases were obtained from the EMSL Basis Set Library.26, 27 All the single atom calculations were run in D2h symmetry, calculations involving HgBr molecule in C4v symmetry and rest of the molecular calculations in D4h symmetry. Finally, the appearance energies (AEs) were calculated by subtracting the total energy of the ground state of HgBr2 molecule from the total energy of its fragments. The effect of temperature to the total energy of the molecules was neglected in the calculations. We note that a detailed calculation of the dissociation potential energy surfaces was omitted. This was due to difficulties in keeping the spin–orbit dependent core-ionized
wavefunctions stable at the level of theory that is required for reliable theoretical analysis at internuclear distances far from the ground state geometry. IV. DISCUSSION
The recorded PES is presented in Fig. 1 together with the predicted bar spectrum. The PES is divided into two regions: the valence and the mercury 5d orbitals. The valence spectrum in the binding energy region of 10.5–13.5 eV contains six bands corresponding to hybridized molecular orbitals (MOs) of two Br 4p5 atoms and a Hg 6s2 . The bands in the region of 16–19 eV are composed of spin–orbit and molecular field splitted levels of Hg 5d orbital. The spin–orbit splitting of the 5d orbital causes two bands to appear: 2 D5/2 and 2 D3/2 . These bands are further split by the interaction with the intramolecular electric field, dividing 2 D5/2 into three components and 2 D3/2 into two, characterized by the projection quantum number of the total angular momentum onto the molecular axis. The binding energies of the valence and Hg 5d orbitals extracted from the spectrum are presented in Table I together with previously reported values.28, 29 Due to the photoionization cross section differences30 between 40 eV (the present case) and He Iα excitation, the Hg 5d orbitals are more emphasized in our experiment with respect to Eland in Ref. 28. For the 2 D3/2 band, Eland does not observe the splitting. Here we can confirm and determine values for the components of the band. Furthermore, Eland points out the sharpness of the first peak in the 2 D5/2 band, a feature which in our spectrum is exceptionally prominent. In the valence region, vibrational effects cause some bands to have larger Full Widths at Half Maxima (FWHM), but taking this into account, the integrated areas of the bands are of the same magnitude. The measured binding energy values for the valence are almost identical to the previously reported values.28
100 2
Intensity [arb. units]
80
2
2 2
2
2
60 2
2
D3/2
40
D5/2
13.5
13.0
12.5
12.0
11.5
11.0
10.5
20 N2 (
2
0
19
18
17
16
15 14 Binding energy [eV]
13
12
11
10
FIG. 1. Experimental valence photoelectron spectrum of HgBr2 recorded at photon energy of 40 eV (red curve) and the peaks calculated with RELADC (straight, black lines). The calculated peaks were shifted by a constant of +0.14 eV matching 2 3/2g state binding energy to the experimental value.
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TABLE I. The experimental and calculated Hg 5d and valence electronic state binding energies of HgBr2 (in eV).
2
3/2g
2
1/2g
2
3/2u
2
1/2u 2 u 2 g ± 25 3 2D 5/2 ± 2 ± 21 3 2D 3/2 ± 2 ± 21
Eb
Eb
(calc.)a
Eb
(expt.)b
10.59 ± 0.08 10.93 ± 0.09 11.18 ± 0.09 11.48 ± 0.10 12.07 ± 0.09 13.39 ± 0.09 16.41 ± 0.09
10.45 10.80 11.01 11.27 11.75 13.15 16.65
10.62 10.96 11.20 11.54 12.09 13.39 16.40
16.67 ± 0.09
16.89
16.69
16.87 ± 0.24 18.32 ± 0.13
16.97 18.67
16.83
18.47 ± 0.25
18.83
Eb
2
(expt.)c
D3/2
2
D5/2
26
10.560 10.8846
+
HgBr2
24 22 16.397
18.34
Ion time-of-flight [µs]
Term
(expt.)a
+
HgBr
20 Hg
+
18 100
16 14
a
This work. Eland.28 c Linn et al.29
50
b
+
Br
12 0
10
Table I also includes the calculated binding energies. The listed values belong to the states with the highest pole strengths. In Fig. 1 prediction also suggests smaller structures in the 16–19 eV binding energy range, which acquire intensity from the main lines. Mulliken population analysis of the states reveals that some of their charge arises from configurations which have two holes in the valence orbitals and one excitation to a virtual orbital. Some small features in the same area are also seen in the experimental spectrum. Spin–orbit splitting between the 2 D3/2 and 2 D5/2 bands, obtained from the intensity weighted average of the levels, is 1.75 eV. The split from calculated binding energies provide a reasonably good prediction of 1.94 eV. In surprising contrast to the work done by Linn et al.29 we do not detect any Br+ 2 cation fragments in the mass spectrum. The exact reason for the discrepancy is unclear. 2500 Intensity [arb. units]
Br
2000 1500
+
19 18 17 16 Electron binding energy [eV]
FIG. 2. A 2D PEPICO map of the Hg 5d ionization region showing the spin– orbit split components 2 D5/2 and 2 D3/2 and the ions coinciding with these states. hν = 40.2.
A. HgBr2 PEPICO of the 5d region
A visual overview of the PEPICO results in the Hg 5d region is shown as a 2D map in Fig. 2. The electron binding energy is on the horizontal axis and the ion time of flight on the vertical axis. The resolution in the PEPICO data differs from the recorded electron spectra, due to different experimental conditions. In the present case, the structures of the 2 D5/2 band are partially overlapping making intensity and width variations between the individual states less visible.
2
D3/2
2
+
Hg + ±3/2 HgBr + ±1/2 HgBr2
1000 500
20
±1/2
D5/2
±3/2 ±5/2
(a)
0
Relative yield
1.0
(b)
0.5
0.0 19.0
18.5
18.0 17.5 17.0 Electron binding energy [eV]
16.5
16.0
FIG. 3. CIY spectra of the Hg 5d region for all four detected HgBr2 ionization products (panel (a)) and relative CIY spectra of Hg+ and Br+ with respect to + the sum of all four cations (panel (b)). Relative CIYs of HgBr+ 2 and HgBr cations have been neglected in this region.
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However, the data allow us to identify the final ionic products coinciding with the electrons originating from ionization to these particular states. The data show that the very sharp peak at 16.41 eV is heavily coinciding with the Hg+ cation, whereas in the rest of the substates of the 2 D5/2 band the amount of Hg+ diminishes and Br+ increases. On the other hand, the states of the 2 D3/2 band are strongly coinciding with Br+ cation and only a negligible amount of Hg+ cation is seen. Panel (a) of Fig. 3 shows the Coincident Ion Yield (CIY) spectra of all four detected HgBr2 ionization products. The CIY spectra are generated by counting the number of coincident ions per particular electron energy. The same behaviour as in Fig. 2 is seen in the CIY spectra, but in a more convenient and quantitative manner. Panel (b) of Fig. 3 depicts the relative CIY spectra of Hg+ and Br+ , respectively. The relative CIY curves are calculated from the CIY data by Iirel (E) = Ii (E)/j Ij (E), where Ii (E) is the coincident ion yield for ion i at energy channel E and Ij (E) runs over all coincident ion yields within the same energy channel E. The error bars have been calculated using total differential method from the expression of the relative ion yield, and the absolute errors in the √ total differential have been taken as Ii (E) = 2σ (Ii (E)) = 2 Ii (E), assuming Poissonian statistics.31–33 Both panels (a) and (b) of Fig. 3 quantitatively depict the branching rations of Hg+ and Br+ produced with specific energy channel. The amount (in percentages) is also tabulated in Table II for the specific Hg 5d orbitals. The CIY curves and the tabulated values for each electronic state suggest a change in fragmentation in the 2 D5/2 band of the molecule, since the ionic products in different substates in this orbital change. Hg+ is the dominant ion in 2 D5/2 ± 52 , but its yield decreases drastically when moving higher in binding energy— becoming first slightly lower in intensity than Br+ in states 2 D5/2 ± 32 and 2 D5/2 ± 12 and finally decreasing to negligible amounts in the 2 D3/2 band. This indicates that the molecular reactions involving production of Hg+ would have higher yield at the 2 D5/2 ± 52 state, after which the probability of reactions producing Br+ would increase. Moreover, the effect seen here is, in fact, not caused by a fortuitous appearance energy, as all the appearance energies of the fragments are well below the ionization potential of the Hg 5d components. The appearance energies have been reported by Linn et al.29 and are included in Table III together with our calculated fragment energy values which offer a reasonably good prediction with the appearance energies.
TABLE II. Amount of produced cations in specific electronic states with respect to the sum of all coincident ions. Hg+ (%)
Br+ (%)
± 25
61 ± 3
21 ± 4
±
34 ± 4
56 ± 4
33 ± 5
65 ± 4
8±9
85 ± 3
9±6
85 ± 4
State
3 2 ± 21 3 2D 3/2 ± 2 ± 21 2D 5/2
TABLE III. Fragment energies from B3LYP calculations and experimental appearance energies (AE) in eV. Fragments Hg+ + Br2 HgBr+ + Br Hg + Br+ 2 Hg+ + Br + Br HgBr + Br+ Hg + Br + Br+ a b
E (calc.)a
AE (expt.)b
11.88 12.08 12.28 13.99 14.79 15.53
11.85 11.83 12.59 15.08
This work. Linn et al.29
Eland28 points out that the state 2 D5/2 ± 52 lies in a plane perpendicular to the internuclear axis of the molecule and therefore has little or no interaction with the valence molecular orbitals. This also suggests that the state is non-bonding and the lifetime of the final ionic state is very long, making the observed FWHM of the peak small. Moreover, the non-bonding nature of the state leads also to the lack of observed vibrational structure, whereas the other states in the 2 D5/2 band clearly contain vibrational features. Upon consideration of the two energetically very close bands, 2 D5/2 and 2 D3/2 , it is apparent that the fragmentation pathway preferences are very contrasting. We propose that this is due to the effect of the spin–orbit and molecularfield splitting on the respective potential energy surfaces. This is an effective reminder that the properties of specific electronic substates may lead to large differences in the final fragmentation. Our calculations support the theory of orthogonal orbitals, as the study of the Mulliken population analysis shows that the 2 D5/2 ± 52 states have most of their partial charge laying perpendicular to the internuclear axis whereas all the other MOs of the Hg 5d orbitals have significant charge also along the quantization axis. Therefore, the other components in the 2 D5/2 band corresponding to the momentum projection ± 32 and ± 12 , do experience some interaction with the Br valence electrons of the molecule. The amount of mixing between the Hg and Br orbitals should be thus reflected on the amount of Br+ observed in Hg 5d ionization. Interestingly, we see that, in fact, the 2 D3/2 band produces almost solely Br+ , despite it having a larger binding energy, and despite the fact that the charge distributions of states belonging to the projection quantum numbers ± 32 and ± 12 in the 2 D5/2 and 2 D3/2 bands appear similar.
V. CONCLUSIONS
In the present experiment we directly demonstrate strong electronic state dependency of molecular fragmentation upon ionization of highly atomic-like orbitals. The dependence is shown using electron-ion coincidence study of the Hg 5d and valence regions of HgBr2 . To support the PEPICO results, a high resolution photoelectron spectrum in the valence and Hg 5d orbitals is presented, together with calculated interpretation. The fragmentation pathways in the Hg 5d orbitals are discussed based on the PEPICO results.
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The spin–orbit split components of the atomic-like Hg 5d orbitals show large difference in the fragmentation pathways so that the dominant ionic product changes from one spin–orbit component to the other. The first component shows enhanced production of Hg+ whereas the second favors fragmentation in the Br+ channel. These results indicate that the actual dynamics of the fragmentation involves an interplay between the spin–orbit and molecular field split components. The results show conclusively that localized properties, such as the spin–orbit interaction of the atomic-like mercury 5d orbitals in HgBr2 can have large influence on the fragmentation process. We note that the charge distribution of the final products appears to correlate with the MO nature of the initial, neutral configuration, however this does not imply causation. This indicates that the spin–orbit and molecular field splitting effects are important in determining the dissociation pathways and should be given consideration, although much of the conventional work focuses on the energy balance analysis of the fragmentation processes. To fully explain the mechanisms of the dissociation, challenging calculations reproducing the dynamics on the spin-dependent potential energy surfaces of the excited molecule are needed.
ACKNOWLEDGMENTS
This work was financially supported by the Research Council for Natural Sciences and Technology of the Academy of Finland, National Doctoral Program in Material Physics and Vilho, Yrjö and Kalle Väisälä foundation. The research is also supported by the European Community’s Seventh Framework Programme (FP7/2007-2013) CALIPSO under Grant Agreement No. 312284. The staff at the MAX IV-laboratory are acknowledged for their assistance during the experiments. The authors are grateful to J. Niskanen for his constructive comments and advices and S. Urpelainen for assistance during experiments. 1 W.
Eberhardt, T. K. Sham, R. Carr, S. Krummacher, M. Strongin, S. L. Weng, and D. Wesner, Phys. Rev. Lett. 50, 1038 (1983). 2 K. Ueda, H. Chiba, Y. Sato, T. Hayaishi, E. Shigemasa, and A. Yagishita, Phys. Rev. A 46, R5 (1992).
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A. Hatherly, D. M. Smith, and R. P. Tuckett, Z. Phys. Chem. 195, 97 (1996). 4 T. Baer, Int. J. Mass Spectrom. 200, 443 (2000). 5 H. Katagiri and S. Kato, J. Chem. Phys. 99, 8805 (1993). 6 A. B. Alekseyev, H.-P. Liebermann, R. J. Buenker, N. Balakrishnan, H. R. Sadeghpour, S. T. Cornett, and M. J. Cavagnero, J. Chem. Phys. 113, 1514 (2000). 7 H. Haberland, A. Hofmann, and B. v. Issendorff, J. Chem. Phys. 103, 3450 (1995). 8 W. R. Wadt, J. Chem. Phys. 68, 402–414 (1978). 9 M. Bässler et al., J. Electron. Spectrosc. Relat. Phenom. 101–103, 953 (1999). 10 M. Bässler et al., Nucl. Instrum. Methods Phys. Res. A 469, 382 (2001). 11 E. Kukk, R. Sankari, M. Huttula, A. Sankari, H. Aksela, and S. Aksela, J. Electron. Spectrosc. Relat. Phenom. 155, 141 (2007). 12 M. Huttula, S. Heinäsmäki, H. Aksela, E. Kukk, and S. Aksela, J. Electron Spectrosc. Relat. Phenom. 156–158, 270 (2007). 13 W. C. Wiley and I. H. McLaren, Rev. Sci. Instrum. 26, 1150 (1955). 14 DIRAC, a relativistic ab initio electronic structure program, Release DIRAC12, 2012, written by H. J. Aa. Jensen et al., see http://www.diracprogram.org. 15 L. Visscher, Theor. Chem. Acc. 98, 68 (1997). 16 K. Dyall and A. Gomes, Theor. Chem. Acc. 125, 97 (2010). 17 K. Dyall, Theor. Chem. Acc. 115, 441 (2006). 18 M. Pernpointner, J. Chem. Phys. 121, 8782 (2004). 19 J. Schirmer, L. S. Cederbaum, and O. Walter, Phys. Rev. A 28, 1237 (1983). 20 A. D. Becke, J. Chem. Phys. 98, 5648 (1993). 21 P. J. Stephens, F. J. Devlin, C. F. Chabalowski, and M. J. Frisch, J. Phys. Chem. 98, 11623 (1994). 22 R. H. Hertwig and W. Koch, Chem. Phys. Lett. 268, 345 (1997). 23 M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis, and J. A. Montgomery, J. Comput. Chem. 14, 1347 (1993). 24 M. S. Gordon, and M. W. Schmidt, “Advances in electronic structure theory: GAMESS a decade later,” in Theory and Applications of Computational Chemistry: The First Forty Years, edited by C. E. Dykstra, G. Frenking, K. S. Kim, and G. E. Scuseria (Elsevier, Amsterdam, 2005), pp. 1167– 1189. 25 D. Rappoport and F. Furche, J. Chem. Phys. 133, 134105 (2010). 26 K. L. Schuchardt, B. T. Didier, T. Elsethagen, L. Sun, V. Gurumoorthi, J. Chase, J. Li, and T. L. Windus, J. Chem. Inf. Model. 47, 1045 (2007). 27 D. Feller, J. Comput. Chem. 17, 1571 (1996). 28 J. H. D. Eland, Int. J. Mass Spectrom. Ion Phys. 4, 37 (1970). 29 S. H. Linn, W. B. Tzeng, J. M. Brom, and C. Y. Ng, J. Chem. Phys. 78, 50 (1983). 30 J. Yeh and I. Lindau, At. Data Nucl. Data Tables 32, 1 (1985). 31 J. A. Kettunen, A. Sankari, L. Partanen, S. Urpelainen, A. Kivimäki, and M. Huttula, Phys. Rev. A 85, 062703 (2012). 32 J. A. Kettunen, S. Urpelainen, S. Heinäsmäki, and M. Huttula, Phys. Rev. A 86, 023201 (2012). 33 J. A. Kettunen, J. Niskanen, M. Huttula, M. Vapa, S. Urpelainen, and H. Aksela, J. Mass Spectrom. 46, 901 (2011).
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This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 80.254.214.138 On: Mon, 12 May 2014 10:33:59
THE JOURNAL OF CHEMICAL PHYSICS 140, 184304 (2014)
Spin–orbit interaction mediated molecular dissociation E. Kokkonen,1,a) T. Löytynoja,1,2 K. Jänkälä,1 J. A. Kettunen,1 S. Heinäsmäki,1 A. Karpenko,1 and M. Huttula1 1
Department of Physics, University of Oulu, Box 3000, 90014 Oulu, Finland Division of Theoretical Chemistry and Biology, School of Biotechnology, Royal Institute of Technology, S-106 91 Stockholm, Sweden 2
(Received 14 February 2014; accepted 17 April 2014; published online 8 May 2014) The effect of the spin–orbit interaction to photofragmentation is investigated in the mercury(II) bromide (HgBr2 ) molecule. Changes in the fragmentation between the two spin–orbit components of Hg 5d photoionization, as well as within the molecular-field-splitted levels of these components are observed. Dissociation subsequent to photoionization is studied with synchrotron radiation and photoelectron-photoion coincidence spectroscopy. The experimental results are accompanied by relativistic ab initio analysis of the photoelectron spectrum. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4873718] I. INTRODUCTION
Molecular photodissociation following selective excitation has been a fruitful tool to study the link between the electronic structure and dissociation mechanisms. Prominent examples include, for example, site-selective dissociation,1, 2 where a core hole is created and the dissociation pathways are monitored in the vicinity of the absorption edge. These systems generally show a clear interrelation between the electronic excitation and fragmentation pattern. For larger molecules the conventional way to analyze photoinduced molecular dissociation is to focus on the internal energy balance, especially in the valence states. The excited molecular state energy is assumed to be distributed to internal degrees of freedom prior to dissociation, which leads to fragment distributions where the identity of the initial excited electronic state is lost.3 This has led to a common practice where the details of the electronic structure in the photoionized state have been deemed unimportant and the focus has been on the ion specific rate constants, such as dissociation rates as a function of the ion internal energy.4 The spin–orbit effect on the photoionization process has been investigated theoretically in the past for diatomic and polyatomic molecules.5, 6 These studies show the importance of spin–orbit effects on the photodissociation dynamics of various molecules. The interaction between different spin– orbit states clearly affects the final states of the photodissociation processes.7, 8 This exemplifies the importance of knowing the effect of the spin–orbit interaction on the photoexcitation process and on the resulting photofragments. Here we report photoelectron–photoion coincidence (PEPICO) study of HgBr2 dissociation following photoexcitation using synchrotron radiation at 40.2 eV energy. This gives rise to ionization of the valence molecular orbital region as well as the more atomic-like Hg 5d orbitals. The results of the PEPICO procedure provide direct information on the electronic state dependence of the fragmentation a) Electronic mail: [email protected]
0021-9606/2014/140(18)/184304/5/$30.00
process. The HgBr2 molecule on the other hand allows to study relativistic effects in the dissociation process, as spin– orbit splitting in Hg is prominent even in the valence region below double ionization threshold. Strong electronic state dependence is seen in the fragmentation products associated with the Hg 5d orbitals. This dependence on the electronic structure can be seen to be sensitive to the strong spin–orbit and molecular field effects in the 5d region. The spin–orbit split orbitals share the same spatial symmetry but differ in the angular momentum coupling, which in turn affects the molecular field splitting. II. EXPERIMENT
The experiments were conducted at the I411 beamline at the MAX IV-laboratory (Lund, Sweden)9, 10 using a photon energy of 40.2 eV, and a resistively heated oven to evaporate the sample material. The PEPICO setup11 consists of a modified Scienta SES-100 hemispherical deflection analyzer (HDA)11, 12 and a Wiley-McLaren type13 time-of-flight mass spectrometer (TOFMS). In the PEPICO experiments the HDA was operated with a curved entrance slit of 0.8 mm and pass energy of 50 eV. All electron measurements were done using the “magic angle” of 54.7◦ with respect to the electric field vector of the linearly polarized radiation. For the electron measurements, analyzer line broadening of approximately 0.2 eV was produced. To better resolve the electronic states and verify the linewidths, a separate photoelectron spectrum (PES) measurement, without the detection of the final ions, was done on the beamline endstation setup consisting of a Scienta R4000 type HDA.9 The analyzer was operated with a curved entrance slit of 0.5 mm and at a pass energy of 20 eV, providing analyzer broadening of approximately 25 meV. III. CALCULATIONS
Theoretical predictions for the electronic states were carried out with the relativistic DIRAC code.14 The 140, 184304-1
© 2014 AIP Publishing LLC
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Dirac-Coulomb Hamiltonian was used in a form where the two-electron integrals over the small components of the wavefunction were neglected and replaced by simple Coulombic correlation.15 The basis used in the calculations was Dyall triple-zeta basis with core correlating functions for Hg and Br atoms.16, 17 The symmetry of the HgBr2 molecule was linear and represented with the D2h point group. The ground state geometry of the molecule was optimized with the Dirac–Hartree–Fock (DHF) method. This resulted in 2.41 Å bond length between the Hg and Br atoms. The ionization potentials and corresponding pole strengths were computed with the RELADC module,18 which utilizes the four-component extension of the one-particle propagator in the non-Dyson version of the algebraic diagrammatic construction (ADC).19 In this work the calculations were run with the third-order extension of the DHF-ADC method. Additionally, the fragment energies according to energy conservation were calculated. The total energies were obtained by optimizing the geometries of the HgBr2 molecule and the fragments with density functional theory (DFT) calculations using B3LYP(VWN5)20–22 hybrid functional under the unrestricted spin formalism. The calculations were performed with the GAMESS program23, 24 using the Def2TZVPPD basis with effective core potential (ECP) for Hg and Br atoms.25 The bases were obtained from the EMSL Basis Set Library.26, 27 All the single atom calculations were run in D2h symmetry, calculations involving HgBr molecule in C4v symmetry and rest of the molecular calculations in D4h symmetry. Finally, the appearance energies (AEs) were calculated by subtracting the total energy of the ground state of HgBr2 molecule from the total energy of its fragments. The effect of temperature to the total energy of the molecules was neglected in the calculations. We note that a detailed calculation of the dissociation potential energy surfaces was omitted. This was due to difficulties in keeping the spin–orbit dependent core-ionized
wavefunctions stable at the level of theory that is required for reliable theoretical analysis at internuclear distances far from the ground state geometry. IV. DISCUSSION
The recorded PES is presented in Fig. 1 together with the predicted bar spectrum. The PES is divided into two regions: the valence and the mercury 5d orbitals. The valence spectrum in the binding energy region of 10.5–13.5 eV contains six bands corresponding to hybridized molecular orbitals (MOs) of two Br 4p5 atoms and a Hg 6s2 . The bands in the region of 16–19 eV are composed of spin–orbit and molecular field splitted levels of Hg 5d orbital. The spin–orbit splitting of the 5d orbital causes two bands to appear: 2 D5/2 and 2 D3/2 . These bands are further split by the interaction with the intramolecular electric field, dividing 2 D5/2 into three components and 2 D3/2 into two, characterized by the projection quantum number of the total angular momentum onto the molecular axis. The binding energies of the valence and Hg 5d orbitals extracted from the spectrum are presented in Table I together with previously reported values.28, 29 Due to the photoionization cross section differences30 between 40 eV (the present case) and He Iα excitation, the Hg 5d orbitals are more emphasized in our experiment with respect to Eland in Ref. 28. For the 2 D3/2 band, Eland does not observe the splitting. Here we can confirm and determine values for the components of the band. Furthermore, Eland points out the sharpness of the first peak in the 2 D5/2 band, a feature which in our spectrum is exceptionally prominent. In the valence region, vibrational effects cause some bands to have larger Full Widths at Half Maxima (FWHM), but taking this into account, the integrated areas of the bands are of the same magnitude. The measured binding energy values for the valence are almost identical to the previously reported values.28
100 2
Intensity [arb. units]
80
2
2 2
2
2
60 2
2
D3/2
40
D5/2
13.5
13.0
12.5
12.0
11.5
11.0
10.5
20 N2 (
2
0
19
18
17
16
15 14 Binding energy [eV]
13
12
11
10
FIG. 1. Experimental valence photoelectron spectrum of HgBr2 recorded at photon energy of 40 eV (red curve) and the peaks calculated with RELADC (straight, black lines). The calculated peaks were shifted by a constant of +0.14 eV matching 2 3/2g state binding energy to the experimental value.
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TABLE I. The experimental and calculated Hg 5d and valence electronic state binding energies of HgBr2 (in eV).
2
3/2g
2
1/2g
2
3/2u
2
1/2u 2 u 2 g ± 25 3 2D 5/2 ± 2 ± 21 3 2D 3/2 ± 2 ± 21
Eb
Eb
(calc.)a
Eb
(expt.)b
10.59 ± 0.08 10.93 ± 0.09 11.18 ± 0.09 11.48 ± 0.10 12.07 ± 0.09 13.39 ± 0.09 16.41 ± 0.09
10.45 10.80 11.01 11.27 11.75 13.15 16.65
10.62 10.96 11.20 11.54 12.09 13.39 16.40
16.67 ± 0.09
16.89
16.69
16.87 ± 0.24 18.32 ± 0.13
16.97 18.67
16.83
18.47 ± 0.25
18.83
Eb
2
(expt.)c
D3/2
2
D5/2
26
10.560 10.8846
+
HgBr2
24 22 16.397
18.34
Ion time-of-flight [µs]
Term
(expt.)a
+
HgBr
20 Hg
+
18 100
16 14
a
This work. Eland.28 c Linn et al.29
50
b
+
Br
12 0
10
Table I also includes the calculated binding energies. The listed values belong to the states with the highest pole strengths. In Fig. 1 prediction also suggests smaller structures in the 16–19 eV binding energy range, which acquire intensity from the main lines. Mulliken population analysis of the states reveals that some of their charge arises from configurations which have two holes in the valence orbitals and one excitation to a virtual orbital. Some small features in the same area are also seen in the experimental spectrum. Spin–orbit splitting between the 2 D3/2 and 2 D5/2 bands, obtained from the intensity weighted average of the levels, is 1.75 eV. The split from calculated binding energies provide a reasonably good prediction of 1.94 eV. In surprising contrast to the work done by Linn et al.29 we do not detect any Br+ 2 cation fragments in the mass spectrum. The exact reason for the discrepancy is unclear. 2500 Intensity [arb. units]
Br
2000 1500
+
19 18 17 16 Electron binding energy [eV]
FIG. 2. A 2D PEPICO map of the Hg 5d ionization region showing the spin– orbit split components 2 D5/2 and 2 D3/2 and the ions coinciding with these states. hν = 40.2.
A. HgBr2 PEPICO of the 5d region
A visual overview of the PEPICO results in the Hg 5d region is shown as a 2D map in Fig. 2. The electron binding energy is on the horizontal axis and the ion time of flight on the vertical axis. The resolution in the PEPICO data differs from the recorded electron spectra, due to different experimental conditions. In the present case, the structures of the 2 D5/2 band are partially overlapping making intensity and width variations between the individual states less visible.
2
D3/2
2
+
Hg + ±3/2 HgBr + ±1/2 HgBr2
1000 500
20
±1/2
D5/2
±3/2 ±5/2
(a)
0
Relative yield
1.0
(b)
0.5
0.0 19.0
18.5
18.0 17.5 17.0 Electron binding energy [eV]
16.5
16.0
FIG. 3. CIY spectra of the Hg 5d region for all four detected HgBr2 ionization products (panel (a)) and relative CIY spectra of Hg+ and Br+ with respect to + the sum of all four cations (panel (b)). Relative CIYs of HgBr+ 2 and HgBr cations have been neglected in this region.
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However, the data allow us to identify the final ionic products coinciding with the electrons originating from ionization to these particular states. The data show that the very sharp peak at 16.41 eV is heavily coinciding with the Hg+ cation, whereas in the rest of the substates of the 2 D5/2 band the amount of Hg+ diminishes and Br+ increases. On the other hand, the states of the 2 D3/2 band are strongly coinciding with Br+ cation and only a negligible amount of Hg+ cation is seen. Panel (a) of Fig. 3 shows the Coincident Ion Yield (CIY) spectra of all four detected HgBr2 ionization products. The CIY spectra are generated by counting the number of coincident ions per particular electron energy. The same behaviour as in Fig. 2 is seen in the CIY spectra, but in a more convenient and quantitative manner. Panel (b) of Fig. 3 depicts the relative CIY spectra of Hg+ and Br+ , respectively. The relative CIY curves are calculated from the CIY data by Iirel (E) = Ii (E)/j Ij (E), where Ii (E) is the coincident ion yield for ion i at energy channel E and Ij (E) runs over all coincident ion yields within the same energy channel E. The error bars have been calculated using total differential method from the expression of the relative ion yield, and the absolute errors in the √ total differential have been taken as Ii (E) = 2σ (Ii (E)) = 2 Ii (E), assuming Poissonian statistics.31–33 Both panels (a) and (b) of Fig. 3 quantitatively depict the branching rations of Hg+ and Br+ produced with specific energy channel. The amount (in percentages) is also tabulated in Table II for the specific Hg 5d orbitals. The CIY curves and the tabulated values for each electronic state suggest a change in fragmentation in the 2 D5/2 band of the molecule, since the ionic products in different substates in this orbital change. Hg+ is the dominant ion in 2 D5/2 ± 52 , but its yield decreases drastically when moving higher in binding energy— becoming first slightly lower in intensity than Br+ in states 2 D5/2 ± 32 and 2 D5/2 ± 12 and finally decreasing to negligible amounts in the 2 D3/2 band. This indicates that the molecular reactions involving production of Hg+ would have higher yield at the 2 D5/2 ± 52 state, after which the probability of reactions producing Br+ would increase. Moreover, the effect seen here is, in fact, not caused by a fortuitous appearance energy, as all the appearance energies of the fragments are well below the ionization potential of the Hg 5d components. The appearance energies have been reported by Linn et al.29 and are included in Table III together with our calculated fragment energy values which offer a reasonably good prediction with the appearance energies.
TABLE II. Amount of produced cations in specific electronic states with respect to the sum of all coincident ions. Hg+ (%)
Br+ (%)
± 25
61 ± 3
21 ± 4
±
34 ± 4
56 ± 4
33 ± 5
65 ± 4
8±9
85 ± 3
9±6
85 ± 4
State
3 2 ± 21 3 2D 3/2 ± 2 ± 21 2D 5/2
TABLE III. Fragment energies from B3LYP calculations and experimental appearance energies (AE) in eV. Fragments Hg+ + Br2 HgBr+ + Br Hg + Br+ 2 Hg+ + Br + Br HgBr + Br+ Hg + Br + Br+ a b
E (calc.)a
AE (expt.)b
11.88 12.08 12.28 13.99 14.79 15.53
11.85 11.83 12.59 15.08
This work. Linn et al.29
Eland28 points out that the state 2 D5/2 ± 52 lies in a plane perpendicular to the internuclear axis of the molecule and therefore has little or no interaction with the valence molecular orbitals. This also suggests that the state is non-bonding and the lifetime of the final ionic state is very long, making the observed FWHM of the peak small. Moreover, the non-bonding nature of the state leads also to the lack of observed vibrational structure, whereas the other states in the 2 D5/2 band clearly contain vibrational features. Upon consideration of the two energetically very close bands, 2 D5/2 and 2 D3/2 , it is apparent that the fragmentation pathway preferences are very contrasting. We propose that this is due to the effect of the spin–orbit and molecularfield splitting on the respective potential energy surfaces. This is an effective reminder that the properties of specific electronic substates may lead to large differences in the final fragmentation. Our calculations support the theory of orthogonal orbitals, as the study of the Mulliken population analysis shows that the 2 D5/2 ± 52 states have most of their partial charge laying perpendicular to the internuclear axis whereas all the other MOs of the Hg 5d orbitals have significant charge also along the quantization axis. Therefore, the other components in the 2 D5/2 band corresponding to the momentum projection ± 32 and ± 12 , do experience some interaction with the Br valence electrons of the molecule. The amount of mixing between the Hg and Br orbitals should be thus reflected on the amount of Br+ observed in Hg 5d ionization. Interestingly, we see that, in fact, the 2 D3/2 band produces almost solely Br+ , despite it having a larger binding energy, and despite the fact that the charge distributions of states belonging to the projection quantum numbers ± 32 and ± 12 in the 2 D5/2 and 2 D3/2 bands appear similar.
V. CONCLUSIONS
In the present experiment we directly demonstrate strong electronic state dependency of molecular fragmentation upon ionization of highly atomic-like orbitals. The dependence is shown using electron-ion coincidence study of the Hg 5d and valence regions of HgBr2 . To support the PEPICO results, a high resolution photoelectron spectrum in the valence and Hg 5d orbitals is presented, together with calculated interpretation. The fragmentation pathways in the Hg 5d orbitals are discussed based on the PEPICO results.
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The spin–orbit split components of the atomic-like Hg 5d orbitals show large difference in the fragmentation pathways so that the dominant ionic product changes from one spin–orbit component to the other. The first component shows enhanced production of Hg+ whereas the second favors fragmentation in the Br+ channel. These results indicate that the actual dynamics of the fragmentation involves an interplay between the spin–orbit and molecular field split components. The results show conclusively that localized properties, such as the spin–orbit interaction of the atomic-like mercury 5d orbitals in HgBr2 can have large influence on the fragmentation process. We note that the charge distribution of the final products appears to correlate with the MO nature of the initial, neutral configuration, however this does not imply causation. This indicates that the spin–orbit and molecular field splitting effects are important in determining the dissociation pathways and should be given consideration, although much of the conventional work focuses on the energy balance analysis of the fragmentation processes. To fully explain the mechanisms of the dissociation, challenging calculations reproducing the dynamics on the spin-dependent potential energy surfaces of the excited molecule are needed.
ACKNOWLEDGMENTS
This work was financially supported by the Research Council for Natural Sciences and Technology of the Academy of Finland, National Doctoral Program in Material Physics and Vilho, Yrjö and Kalle Väisälä foundation. The research is also supported by the European Community’s Seventh Framework Programme (FP7/2007-2013) CALIPSO under Grant Agreement No. 312284. The staff at the MAX IV-laboratory are acknowledged for their assistance during the experiments. The authors are grateful to J. Niskanen for his constructive comments and advices and S. Urpelainen for assistance during experiments. 1 W.
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