Article pubs.acs.org/JPCA
The Role of Spin−Orbit Coupling in the Double-Ionization Photoelectron Spectra of XCN2+ (X = Cl, Br, and I) Soumitra Manna and Sabyashachi Mishra* Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur, India S Supporting Information *
ABSTRACT: The photoelectron spectra of XCN2+ (X = Cl, Br, and I) were calculated employing ab initio electronic structure methods with high-level electron correlation and explicit treatment of spin−orbit coupling. Twelve scalarrelativistic excited states of the dicationic systems, calculated from state-averaged CASSCF/MRCI calculations, were used as the electronic basis to evaluate spin−orbit eigenstates. While the spin−orbit effects in ClCN2+ are found to be negligible, the electronic spectroscopy of BrCN2+ and ICN2+ is significantly influenced by interstate spin−orbit coupling. Several electronic degeneracies are lifted, and many unexpected accidental degeneracies occurred due to the spin−orbit coupling. In particular, the spin−orbit interactions between X̃ 3Σ−−b̃ 1Σ+, Ã 3 Π−c̃ 1Π, B̃ 3Δ−ã 1Δ, and C̃ 3Σ+−d̃ 1Σ− are found to be strong in BrCN2+ and ICN2+. By careful analysis of the effect of spin−orbit coupling parameters and the spin−orbit eigenstate composition, an assignment of the hitherto unidentified experimental photoelectron bands of BrCN2+ and ICN2+ is presented.
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experimental and theoretical studies.26−42 However, theoretical studies of the dications of cyanogen halides that are necessary for an informed interpretation of the corresponding photoelectron spectra are missing. Herein, we employ ab initio electronic structure methods with high-level electron correlation and explicit treatment of spin−orbit coupling to investigate the excited-states electronic structure and spectroscopy of XCN2+ (X = Cl, Br, I). We describe the role of spin−orbit coupling in the electronic spectroscopy of these systems. Finally, by analyzing the spin− orbit eigenstates, we provide an assignment of the photoelectron spectra of ICN2+ and BrCN2+, and predict the same for ClCN2+.
INTRODUCTION Ionization processes involving ejection of at least one electron and formation of ions provide insight into the excited-state structure and dynamics of the formed ions.1 While ionization of a single electron is conventionally analyzed by electron spectroscopy and by ion spectroscopy and spectrometry, the ionization processes involving ejection of more than one electron requires more specialized techniques, such as coincidence spectroscopy.2−4 Depending on the nature of the systems under investigation, different types of coincidence techniques are employed, such as photoelectron−photoion coincidence (PEPICO),5 photoion-photoion coincidence (PIPICO),6−8 photoelectron−photoion−photoion coincidence (PEPIPICO),9,10 and photoelectron-photoelectron coincidence (PEPECO).11−13 In recent years, the coincidence techniques have been applied to explore the excited states of several systems. Using the PEPICO method, ionization processes of rare gases, CF4, CH3, N2, CF3Br, SiCl4, C4F8, and even some clusters have been recently studied.14−21 Several small molecules, for example, H2, Br2, CO2, OCS, have been studied by PIPICO technique,22−25 whereas photoionization of CS2, NO2, SO2, and CH3I has been successfully investigated by PEPIPICO method.10 Using time-of-flight PEPECO method, the photoelectron spectra and dissociation dynamics of ICN2+ and BrCN2+ have been studied by Eland and Feifel.11 The photoelectron spectra of these dications contain interesting and complex structures that have not been interpreted.11 Over the years, the cyanogen halides and their cations have been the subject of several © XXXX American Chemical Society
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COMPUTATIONAL METHOD The XCN molecules with X = Cl, Br, and I are closed-shell linear molecules in the ground electronic state X̃ 1Σ+, with the valence-shell electronic configuration given by 1σ2 2σ2 3σ2 1π4 4σ2 2π4. The double ionization photoelectron spectroscopy of XCN molecules leads to the formation of the dicationic electronic states of XCN2+, which can be obtained by removing two electrons from the frontier occupied molecular orbitals. Simultaneous removal of two electrons from the highest occupied molecular orbital (HOMO), that is, 2π2, gives rise to a half-filled π-shell, which results in the dicationic electronic Received: December 14, 2015 Revised: February 10, 2016
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DOI: 10.1021/acs.jpca.5b12219 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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Table 1. Optimized Geometrya and Harmonic Vibrational Frequency in the Ground State of Neutral and Dicationic XCN
states 3Σ−, 1Δ, and 1Σ+.43 The ionization of one electron each from the HOMO and HOMO−1, that is, 4σ1 2π3, leads to the formation of dicationic electronic states 3Π and 1Π. Similarly, when one electron is removed from the first and second π molecular orbitals, one obtains 1Σ−, 3Δ, 3Σ+, 3Σ−, 1Δ, and 1 + Σ electronic states, of which the latter three are much higher in energy compared to the former three and hence are ignored in the present study. The interplay of the above electronic states of XCN2+ together with spin−orbit coupling is the central focus of this work. For the halogen atoms, we employed the spin−orbit averaged semilocal energy-adjusted pseudopotentials to describe the core, that is, 1s-2p for Cl (10 electrons), 1s-3d for Br (28 electrons), and 1s-4d for I (46 electrons).44 The valence electrons of Br and I are described by basis sets of augmented quadruple-ζ quality, composed of optimized contracted s, p, d, f, and g functions,44 while the valence shell of Cl is described by optimized contracted s and p functions of augmented quadruple-ζ quality.45 The d, f, and g polarization functions are obtained from the augmented correlation-consistent polarized valence quadruple-ζ (aug-cc-pVQZ) basis set of Woon and Dunning.46 The C and N atoms are described by the augmented correlation-consistent polarized valence triple-ζ (aug-cc-pVTZ) basis set of Dunning.47,48 The optimized geometries and vibrational frequencies of the ground state of XCN and XCN2+ have been calculated employing multireference configuration interaction (MRCI) method,49,50 which uses complete-active-space self-consistentfield (CASSCF)51,52 orbitals as N-electron basis. For the CASSCF and MRCI calculations, we correlated 14 electrons in 12 orbitals. For an accurate electron correlation of the excited electronic states of XCN2+, we employed the state-averaged (14,12) CASSCF followed by MRCI method for a scalar relativistic description of the 12 components of the lowest eight electronic states at the reference geometry of the neutral XCN. The CASSCF calculation that accounts for the static electron correlation provides reasonable starting orbitals, which are used during MRCI calculation to obtain the dynamic part of the electron correlation. To account for the size-consistency problem, the MRCI energy with Davidson correction53 is used while calculating the vertical ionization energies. The MRCI wave functions obtained from the abovementioned scalar-relativistic electron correlation calculation are further used to calculate the Breit−Pauli spin−orbit matrix elements, where the most important two-electron contributions of the spin−orbit operator are incorporated by means of an effective one-electron Fock operator.54 In the present calculations, the dimension of the spin−orbit matrix is 24 (from six singlet and six triplet states). The diagonalization of the spin−orbit matrix in the space of all spin−orbit-free electronic states provides information about the spin−orbit eigenstates. While the eigenvalues of the spin−orbit matrix reveal the spin−orbit energy levels, the eigenvectors are used to determine the composition of the spin−orbit eigenstates in terms of the scalar-relativistic states. All calculations were performed using Molpro package.55
states ClCN ClCN2+ BrCN BrCN2+ ICN ICN2+ a
X̃ X̃ X̃ X̃ X̃ X̃
Σ 3 − Σ 1 + Σ 3 − Σ 1 + Σ 3 − Σ 1 +
bond length (Å)
frequency (eV)
X−C
C−N
C−N str
X−C str
X−C−N bend
1.66 1.51 1.80 1.72 2.03 1.94
1.17 1.33 1.16 1.27 1.17 1.23
0.275 0.168 0.280 0.173 0.271 0.213
0.087 0.095 0.076 0.076 0.059 0.065
0.047 0.089 0.055 0.082 0.039 0.063
The optimization in all the systems shows linear geometry.
increases from Cl to I, while the C−N distance remains nearly constant irrespective of the nature of the halogen atom in neutral XCN molecules. A similar trend is also seen in the vibrational frequencies, where the X−C stretching frequency decreases from 704 cm−1 (ClCN) to 480 cm−1 (ICN), whereas the C−N stretching frequency remains in the range of 2185− 2260 cm−1 for the three molecules (Table 1). The ground state of XCN2+(X̃ 3Σ−) shows an increase in the C−N bond distance and a decrease in the X−C bond distance as compared to the neutral XCN molecules in all three systems. This arises from the fact that the HOMO of XCN is described by a π orbital that involves a bonding overlap between C−N and an antibonding overlap between the X−C centers. The calculated harmonic vibrational frequencies for C−N in BrCN2+ and ICN2+ (0.173 and 0.213 eV, respectively) are comparable to the corresponding experimental values (0.175 and 0.183 eV, respectively).11 The discrepancy between the calculated and experimental values of the vibrational frequencies may arise due to anharmonic effects. The calculated value of the Br−C stretching frequency in BrCN2+ (0.076 eV) is in very good agreement with the experimental value of 0.073 eV, whereas the I−C vibrational structures are unresolvable in the experimental photoelectron spectra of ICN2+.11 Additionally, the geometry of the XCN2+ in all the excited states considered in this study were optimized (Table S1 in the Supporting Information), which suggests that the excited states under consideration have stable minima near the equilibrium geometry of the neutral molecules. The dications are found to be linear in all these excited states. The vertical ionization energies of the lowest eight scalarrelativistic electronic states (four nondegenerate and four doubly degenerate states) of XCN2+ with respect to the electronic ground state of the neutral XCN (X̃ 1Σ+), calculated via SA-CASSCF/MRCI (with Davidson correction) method, are reported in Table 2. In all three dicationic systems, the electronic states arising from π2 electronic configuration leads to the X̃ 3Σ− as the ground electronic state, followed by ã 1Δ and b̃ 1Σ+, in accordance to the Hund’s rule. The vertical ionization energy of the ground state is the lowest for ICN2+, followed by BrCN2+ and ClCN2+, which is due to the nature of the valence orbitals of the halogen atoms in the frontier molecular orbitals of the XCN2+. In case of ICN2+, it is easier to remove electrons from the valence molecular orbitals, which are composed of 5s and 5p atomic orbitals of I atom, whereas electron removal requires more energy for BrCN2+ and ClCN2+, due to the involvement of fourth and third shell atomic orbitals of Br and Cl, respectively. The calculated vertical ionization energies of the X̃ 3Σ− state of BrCN2+ and ICN2+ (i.e., 30.785 and 28.609 eV, respectively) agree well with
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RESULTS AND DISCUSSION The optimized geometries and harmonic vibrational frequencies in the ground state X̃ 1Σ+ of the neutral XCN molecules as well as in the ground state X̃ 3Σ− of dicationic XCN2+ systems are given in Table 1. The optimized geometries in all the systems are found to be linear. The X−C bond distance B
DOI: 10.1021/acs.jpca.5b12219 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Table 2. Scalar-Relativistic Vertical Ionization Energiesa (in eV) of the Excited States of XCN2+ from the X̃ 1Σ State of XCN
calculated to be 0.323 and 0.333 eV (ICN2+), 0.151 and 0.165 eV (BrCN2+), and 0.034 and 0.041 eV (ClCN2+), respectively. The spin−orbit splitting of both à 3Π and B̃ 3Δ states increases, as expected, from ClCN2+ to ICN2+ due to the presence of the heavier halogen center. Apart from the spin−orbit splitting of the à 3Π and B̃ 3Δ states, the spin−orbit coupling operator introduces several spin−orbit coupling between the scalar-relativistic states. The magnitude of the spin−orbit coupling values between the scalar-relativistic states are given in Table 3 for the XCN2+ systems. These spin−orbit coupling parameters are the matrix elements of the Breit−Pauli spin−orbit operator in the basis of scalar relativistic electronic states obtained from MRCI calculations. It can be seen that in all three systems, the spin−orbit coupling constants between the states, such as X̃ 3 − Σ −b̃ 1Σ+, X̃ 3Σ−−C̃ 3Σ+, ã 1Δ−B̃ 3Δ, à 3Π−c̃ 1Π, and d̃ 1Σ−− C̃ 3Σ+, are found to be relatively stronger in their respective systems (Table 3). Overall, the spin−orbit coupling between the states of ClCN2+ are rather weak, and these coupling strengths increase from ClCN2+ to ICN2+. Using the spin−orbit couplings given in Table 3 and the scalar relativistic MRCI energies given in Table 2, we report the double photoionization spectra of the XCN in Table 4. The calculated energies of the spin−orbit eigenstates are presented with respect to the energy of the lowest spin−orbit eigenstate, which indicates the origin of the spectrum. ClCN2+. In ClCN2+, the weak spin−orbit splitting in the states à 3Π (0.034 eV) and B̃ 3Δ (0.041 eV) and weaker interstate spin−orbit coupling between all other states suggests that the relativistic effects have a rather insignificant effect on its
vertical ionization energy (eV) state X̃ 3Σ− ã1Δ b̃1Σ+ Ã 3Π c̃1Π d̃1Σ− B̃ 3Δ C̃ 3Σ+
ClCN 32.561 33.065 33.308 33.370 33.929 34.229 34.381 34.445
2+
(0.504) (0.747) (0.809) (1.368) (1.668) (1.820) (1.884)
BrCN2+ 30.785 31.237 31.488 31.660 31.979 32.118 32.254 32.311
(0.452) (0.703) (0.875) (1.195) (1.333) (1.469) (1.526)
ICN2+ 28.609 29.139 29.452 29.712 29.919 29.997 30.125 30.177
(0.530) (0.843) (1.104) (1.310) (1.388) (1.516) (1.568)
a
Computed by the MRCI/SA-CASSCF method. Values in parentheses refer to the MRCI/SA-CASSCF results with the vertical ionization energy of the X̃ 3Σ− adjusted to zero.
the experimental origin of the corresponding photoelectron spectra (31.106 and 28.881 eV, respectively).11 The difference in the vertical ionization energies of the cationic excited states with respect to the ground state of XCN2+ (X̃ 3Σ−) are shown in the parentheses (Table 2). In all three dications, the lowest quintet state appears more than 6 eV above their respective ground states, and hence the quintet states are not considered in further analysis. Among the electronic states considered here, the à 3Π and B̃ 3 Δ states possess zeroth-order spin−orbit splitting due to simultaneous presence of orbital- and spin-angular momenta. The spin−orbit splittings in the à 3Π and B̃ 3Δ states are
Table 3. Matrix Elements of the Breit−Pauli Spin−Orbit Operator in the Basis of Scalar Relativistic Electronic States of XCN2+(in eV) states
X̃ 3Σ−
ã 1Δ
b̃ 1Σ+
c̃ 1Π
d̃ 1Σ−
B̃ 3Δ
C̃ 3Σ+
0.034 0.036 0.002 0.002 0.001 BrCN2+
0 0 0 0.001
0 0 0.041
0.041 0
0
0.151 0.155 0.007 0.006 0.005 ICN2+
0 0 0.001 0.003
0 0 0.165
0.165 0
0
0 0 0.001 0.004
0 0 0.332
0.333 0
0
à 3Π 2+
ClCN
X̃ 3Σ− ã 1Δ b̃ 1Σ+ Ã 3Π c̃ 1Π d̃ 1Σ− B̃ 3Δ C̃ 3Σ+
0 0 0.041 0.004 0.003 0 0 0.035
0 0 0.003 0 0 0.036 0
0 0.003 0 0 0 0
X̃ 3Σ− ã 1Δ b̃ 1Σ+ Ã 3Π c̃ 1Π d̃ 1Σ− B̃ 3Δ C̃ 3Σ+
0 0 0.184 0.019 0.016 0 0 0.137
0 0 0.016 0 0 0.145 0
0 0.013 0 0 0 0
X̃ 3Σ− ã 1Δ b̃ 1Σ+ Ã 3Π c̃ 1Π d̃ 1Σ− B̃ 3Δ C̃ 3Σ+
0 0 0.416 0.054 0.050 0 0 0.249
0 0 0.043 0 0 0.281 0
0 0.033 0 0 0 0
0.323 0.324 0.010 0.010 0.007 C
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The Journal of Physical Chemistry A Table 4. Assignment of the Photoelectron Bandsa of XCN2+ and Composition of the Spin−Orbit Eigenstates in Terms of Spin−Orbit-Free States energy (calcd)
energy (expt)
0 0.002 0.491 0.740 0.830 0.862 0.898 1.417 1.657 1.768 1.810 1.851 1.872 1.879 0 0.031 0.507 0.839 0.881 0.973 1.181 1.443 1.448 1.511 1.695 1.748 1.830 1.842
0 0.073 0.557 1.120 1.190 1.290 1.510 1.750 1.750 1.750 1.870 1.870 1.870 1.870
0 0.125 0.621 1.039 1.125 1.172 1.319 1.367 1.672 1.698 1.777 1.792 1.798 2.009 2.035
0 0.183 0.636 1.060 1.259 1.259 1.469 1.469 1.620 1.620 1.970 1.970 1.970 1.970 1.970
calculated composition (weight in %) ClCN2+ 3 − Σ (99.70); 1Σ+ (0.30) 3 − Σ (100) 1 Δ (100) 1 + Σ (99.60); 3Σ− (0.40) 3 Π (100) 3 Π (100) 3 Π (100) 1 Π (100) 1 − Σ (96); 3Σ+ (4) 3 Δ (100) 3 Δ (100) 3 Δ (100) 3 + Σ (100) 3 + Σ (96); 1Σ− (4) 2+ BrCN 3 − Σ (95); 1Σ+ (5) 3 − Σ (100) 1 Δ (98); 3Δ (2) 1 + Σ (95) ; 3Σ− (5) 3 Π (100); 3 Π (88); 1Π (12) 3 Π (100) 1 − Σ (76); 3Σ+ (24) 1 Π (88); 3Π (12) 3 Δ (100) 3 Δ (98); 1Δ (2) 3 + Σ (100) 1 − Σ (24) ; 3Σ+ (76) 3 Δ (100) ICN2+ 3 − Σ (86); 1Σ+ (14) 3 − Σ (97); 3Σ+(3) 1 Δ (90); 3Δ (6); 3Π (4) 3 Π (96) ; 1Δ (3); 3Δ (1) 3 Π (66); 1Π (34) 1 + Σ (83); 3Σ− (13); 3Π (4) 1 − Σ (63); 3Σ+ (37) 3 Δ (100) 3 Π (100) 3 Π (96); 1Σ+ (4) 3 Δ (93); 1Δ (7) 3 + Σ (94); 3Σ− (2); 3Π (2); 1Π (2) 1 Π (64); 3Π (32); 3Σ+ (4) 3 + Σ (63); 1Σ− (37) 3 Δ (100)
Figure 1. Energy of the spin−orbit states of ClCN2+ with the spin− orbit splitting of the 3Π and 3Δ states (a) and with all interstate spin− orbit interactions (b). The energy at the left-hand side of the graph represents the scalar-relativistic energy.
and 3Δ3,2,1 at 1.768, 1.810, and 1.851 eV, respectively. Each of these energy levels is doubly degenerate representing the orbital degeneracy of the Π and Δ electronic states. The orbital degeneracies of the states ã 1Δ and c̃ 1Π are also preserved. However, the X̃ 3Σ− and C̃ 3Σ+ states show minor splitting of 0.002 and 0.007 eV, respectively, due to the interstate spin− orbit coupling of X̃ 3Σ−−b̃ 1Σ+ and d̃ 1Σ−−C̃ 3Σ+, respectively. This is also reflected in the composition of the spin−orbit eigenstates, where the energy levels at 0 and 0.740 eV are mixture of X̃ 3Σ− and b̃ 1Σ+ states (Table 4), and the energy levels at 1.657 and 1.879 eV arise from the combination of d̃ 1 − Σ and C̃ 3Σ+ states (Table 4). BrCN2+. In BrCN2+, the spin−orbit splitting of the states à 3 Π (0.151 eV) and B̃ 3Δ (0.165 eV) leads to splitting of both the Π and Δ states to three spin−orbit multiplets each. Since the scalar relativistic states d̃ 1Σ− and C̃ 3Σ+ are closely spaced to the B̃ 3Δ state, the spin−orbit splitting of the latter leads to a situation where the spin−orbit multiplets of the B̃ 3Δ state span the two scalar-relativistic states d̃ 1Σ− and C̃ 3Σ+ (Figure 2a). The interstate spin−orbit coupling between X̃ 3Σ− and b̃ 1Σ+ states results in an interaction between the b̃ 1Σ+ state and the 3 − Σ 0 component of the X̃ 3Σ− state, which leads to the splitting of the spin-degeneracy of the X̃ 3Σ− state, yielding an energy difference of 0.031 eV between the 3Σ−0 and 3Σ−±1 components of the X̃ 3Σ− state (Figure 2b). Similar interstate spin−orbit
a
All energies are in electronvolts. The calculated values of the spinorbit energies are with respect to the energy of the lowest spin-orbit state, and the experimental energy values are with respect to the origin of the spectrum (ref 11).
electronic spectroscopy. The scalar relativistic and the spin− orbit coupled energy levels of ClCN2+ are shown in Figure 1. It can be seen that the spin−orbit splitting of the à 3Π and B̃ 3Δ leads to two sets of three closely spaced energy levels corresponding to the 3Π2,1,0 at 0.830, 0.862, and 0.898 eV
Figure 2. Energy of the spin−orbit states of BrCN2+ with the spin− orbit splitting of the 3Π and 3Δ states (a) and with all interstate spin− orbit interactions (b). The energy at the left-hand side of the graph represents the scalar-relativistic energy. D
DOI: 10.1021/acs.jpca.5b12219 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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Figure 3. Energy of the spin−orbit states of ICN2+ with the spin−orbit splitting of the 3Π and 3Δ states (a). (b−f) The energy of the spin−orbit states when the coupling parameters between 3Σ−−1Σ+, 3Σ+−1Σ−, 3Π−1Π, 3Δ−1Δ, and 3Σ−−3Σ+, are switched on sequentially. (g) The energy of the spin−orbit states when all spin−orbit coupling parameters are present.
interaction between the states d̃ 1Σ− and C̃ 3Σ+ lowers the energy of the d̃ 1Σ− state (1.443 eV, Table 4) while increasing the energy of the 3Σ+0 components of the C̃ 3Σ+ state, which leads to the removal of spin degeneracy of the C̃ 3Σ+ state, yielding the 3Σ+±1 and 3Σ+0 components at 1.748 and 1.83 eV, respectively (Table 4). The interstate spin−orbit interaction between the states à 3 Π and c̃ 1Π introduces an interaction between the c̃ 1Π state and the 3Π1 component of the à 3Π state, thus lowering the energy of the 3Π1 component (0.973 eV) and raising the energy of the c̃ 1Π state (1.448 eV). The interstate spin−orbit interaction between the states à 3Π and c̃ 1Π removes the symmetry of the energy spacing between the spin−orbit multiplets of the à 3Π state (Figure 2b). The energy difference between the 3Π2 and 3Π1 spin−orbit components is reduced to 0.092 eV, while the energy difference between the 3Π0 and 3Π1 spin−orbit components is increased to 0.208 eV from the spin−orbit splitting value of 0.151 eV in the isolated à 3Π state. The combined effect of the interstate spin−orbit coupling between d̃ 1Σ−−C̃ 3Σ+ states (where the energy of the former is lowered) and à 3Π−c̃ 1Π states (where the energy of the latter is raised), reduces the gap between the scalar-relativistic states c̃ 1 Π and d̃ 1Σ− (see Figure 2b) from 0.135 to 0.005 eV, causing a near accidental degeneracy (energy levels at 1.443 and 1.448 eV, Table 4). In addition to the above-described interstate spin−orbit couplings, we do observe weak spin−orbit couplings between the states ã 1Δ−B̃ 3Δ and X̃ 3Σ−−C̃ 3Σ+. However, their effect on the electronic spectrum of BrCN2+ is rather limited. ICN2+. Unlike ClCN2+ and BrCN2+ the spin−orbit coupling between the states of ICN2+ are much stronger, and their combined effect makes the electronic spectrum of ICN2+ very complex. To understand the impact of the strong spin−orbit coupling constants on the spin−orbit states, we analyze the spin−orbit states by considering the interstate couplings sequentially, as shown in Figure 3a−g, where the left-hand side represents the scalar-relativistic situation and the righthand side represents the situation where all the interstate spin− orbit interactions are operative. The spin−orbit splitting of the à 3Π (0.323 eV) and B̃ 3Δ (0.333 eV) states causes the 3Π and 3Δ states to split to three spin−orbit multiplets each. Because of the large spin−orbit
splitting in ICN2+, the lowest spin−orbit multiplet of the à 3Π (i.e., 3Π2) becomes accidentally degenerate with the b̃ 1Σ+ (Figure 3a), and the middle spin−orbit multiplet of the à 3Π (i.e., 3Π1) comes very close (0.09 eV) to the lowest spin−orbit multiplet of the B̃ 3Δ state (i.e., 3Δ3) (Figure 3a). The large spin−orbit splitting in ICN2+ renders several scalar-relativistic states (such as c̃ 1Π, d̃ 1Σ−, and C̃ 3Σ+) appear within the spin− orbit multiplets of the à 3Π and B̃ 3Δ states (Figure 3a). Similar to BrCN2+, the interstate spin−orbit coupling between the X̃ 3Σ− and b̃ 1Σ+ states lifts the spin-degeneracy of the X̃ 3Σ− state, yielding an energy difference of 0.125 eV between the states 3Σ−0 and 3Σ−±1 (Figure 3b). A similar, but more pronounced, effect is seen for the interstate spin−orbit coupling between the d̃ 1Σ− and C̃ 3Σ+ states, where the strong interstate coupling leads to a splitting of 0.211 eV between the spin components of the C̃ 3Σ+ state (Figure 3c). The interstate spin−orbit coupling parameter between the states X̃ 3Σ−−b̃ 1Σ+ is stronger (0.416 eV) than that of d̃ 1Σ−−C̃ 3Σ+ coupling (0.332). However, the impact of the former coupling on the spectroscopy is smaller than that of the latter. This is due to the large energy difference between the scalar relativistic states X̃ 3 − Σ and b̃ 1Σ+ (0.843 eV) compared to the smaller energy difference between the states d̃ 1Σ− and C̃ 3Σ+ (0.180 ev). Hence, the impact of the spin−orbit coupling in the electronic spectroscopy of the dicationic systems not only depends on the corresponding coupling constants but also on the relative spacing between the concerned scalar relativistic states. The spin−orbit interaction between the states à 3Π and c̃ 1Π leads to repulsion between the c̃ 1Π state and the 3Π1 component of the à 3Π state, thus lowering the energy of the 3Π1 component significantly. Similar to BrCN2+, this interaction leads to a situation where the gap between two consecutive spin−orbit multiplets of the à 3Π state becomes very unsymmetric, that is, 0.086 and 0.573 eV from the spin− orbit splitting value of 0.332 eV in the isolated à 3Π state (Figure 3d). The interstate spin−orbit interaction between the ã 1Δ−B̃ 3Δ states leads to the lowering of energy of the ã 1Δ state and a rise in the energy of the 3Δ2 component of the B̃ 3Δ. This results in an unsymmetric spacing between the consecutive spin−orbit multiplets of the B̃ 3Δ state (0.406 and 0.262 eV as compared to 0.332 eV in the isolated B̃ 3Δ state); see Figure 3e. E
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The Journal of Physical Chemistry A In ICN2+, a moderately strong coupling between the 3Σ±1 components of the X̃ 3Σ− and C̃ 3Σ+ states is observed (0.249 eV, Table 3), which leads to the lowering of the 3Σ−±1 of the X̃ 3 − Σ and a corresponding rise in the energy of the 3Σ+±1 of the C̃ 3Σ+ state. This interaction, to some extent, mitigates the effect of the interaction between X̃ 3Σ−−b̃ 1Σ+ states and d̃ 1 − Σ −C̃ 3Σ+ states, which leads to the lifting of the spin degeneracy of the X̃ 3Σ− and C̃ 3Σ+ states, as described earlier. The effect of the spin−orbit interaction between states à 3 Π−b̃ 1Σ+ leads to an interesting situation, where the orbital degeneracy of the 3Π0 component of the à 3Π is lifted due to the interaction of the state b̃ 1Σ+ with only one of the two orbital components (corresponding to orbital angular momentum Λ = +1) that constitutes the 3Π0 state. In this case the orbital degeneracy of an electronic state is lifted due to pure electronic (spin−orbit) effect, unlike Jahn−Teller and Renner− Teller effects where nuclear motion plays the driving role for lifting of electronic degeneracies.56 In addition to the above-described interstate spin−orbit couplings, we do observe weak to moderate range of spin−orbit interaction between the states à 3Π−X̃ 3Σ−, à 3Π−ã 1Δ, à 3Π− B̃ 3Δ, à 3Π−d̃ 1Σ−, and b̃ 1Π−X̃ 3Σ−. However, their effect on the electronic spectrum of ICN2+ is rather limited. Comparison with Experimental Photoionization Spectra. The double ionization photoelectron spectra of ICN and BrCN show complex features, some of which have been assigned in the earlier experimental study.11 Several vibrational progressions along both the stretching modes in the X̃ 3Σ− and ã 1Δ electronic states of XCN2+ have been identified in the assignment of the experimental spectra.11 However, the experimental spectra of BrCN2+ and ICN2+ show many unidentified lines, and the assignment of the bands ignores the possible spin−orbit coupling between the electronic states.11 In particular, the spin−orbit interaction between X̃ 3 − Σ and b̃ 1Σ+ states in BrCN2+ and ICN2+ leads to the splitting of the X̃ 3Σ− state that amounts to 0.031 and 0.125 eV, which are very similar in magnitude with the experimentally observed X−C stretching vibrational frequency in BrCN2+ (0.073 eV) and C−N stretching frequency in ICN2+ (0.183 eV), respectively.11 Therefore, a strong overlap of the bands of different vibronic origin is expected. Because of the low resolution of the experimental spectrum, the vibrational structures in the electronic states beyond ã 1Δ are not seen.11 The effect of nuclear dynamics on the electronic states via vibronic coupling mechanisms is important to describe the role of the former on the photoelectron spectra. However, in the present study, our discussion is restricted to the electronic origin of the photoelectron bands with special emphasis on the electronic spin−orbit coupling. In the photoelectron spectrum of BrCN2+ the band at 0.557 eV from the origin of the spectrum is assigned as the ã 1Δ, which agrees well with our calculated value of 0.507 eV (Table 4). At higher energies, the experimental peaks at 1.12 and 1.19 eV (separated by 0.07 eV) can be assigned to origin from the closely spaced b̃ 1Σ+ and the lower spin−orbit component of the à 3Π state, calculated as 0.839 and 0.881 eV (energy separation of 0.04 eV), respectively (Table 4). The photoelectron bands at 1.29 and 1.51 eV can be assigned as the middle and upper spin−orbit components of the à 3Π state, respectively. This assignment agrees well with the calculated value of the effective spin−orbit splitting in the à 3Π state, where the energy difference between the two lower spin−orbit
components of the 3Π state is calculated as 0.092 eV and the energy difference between the two upper spin−orbit components of the 3Π state is calculated as 0.208 eV, which compare well with the experimental splitting values of 3Π state (0.10 and 0.22 eV, respectively). The experimental band between 1.65 and 1.80 eV (centered around 1.75 eV) can be assigned to be originating from the closely spaced electronic states 3Σ−, 1Π, and the lower spin−orbit components of the 3Δ state. The unresolved and low-intensity spectral structure at 1.87 eV from the origin of the photoelectron spectrum of BrCN2+ can be assigned to be originating from the coupled 3Δ and 3Σ+ states (Table 4). The experimental photoelectron spectrum of ICN2+ shows the band associated with the ã 1Δ state at 0.636 eV from the origin of the spectrum. The energy difference between the X̃ 3 − Σ and ã 1Δ electronic states of ICN2+ is calculated as 0.533 eV from the scalar-relativistic MRCI calculations (Table 2), which upon inclusion of the spin−orbit coupling increases to 0.621 eV (due to X̃ 3Σ−−b̃ 1Σ+ coupling), which compares well with the experimental value of 0.636 eV; see Table 4. At higher energies, the photoelectron spectra of ICN2+ show several unidentified peaks. The peak at 1.06 eV from the origin of the spectrum has been assigned as the first overtone of the C−N stretch mode in the ã 1Δ state.11 This peak comes very close to the calculated value of the lower spin−orbit components of the à 3Π state (1.04 eV); see Table 4. At further higher energies, three unresolved broad bands centered at 1.26, 1.47, and 1.97 eV manifest in the experimental photoelectron spectrum.11 The peak at 1.26 eV (spreads between 1.12 to 1.32 eV) can be assigned to originate from the coupled states 1Σ− and the spin− orbit component of 3Π state, whose energy levels are calculated to be 1.172 and 1.25 eV from the lowest spin−orbit state (Table 4). The electronic states 1Σ−and the lower spin−orbit component of 3Δ are calculated to be 1.319 and 1.367 eV (above the ground spin−orbit state), which compare well with the unidentified band at 1.47 eV from the origin of the experimental spectrum.11 The experimental spectrum of ICN2+ exhibits a very low intensity peak at 1.62 eV from the origin of the spectrum, which may originate due to the upper spin−orbit components of the 3Π electronic state, calculated as 1.672 and 1.698 eV (the splitting is due to 3Π−1Σ+ spin−orbit interaction). Finally, a rather broad band centered around 1.97 eV that spans between 1.77 to 2.07 eV can be assigned to originate from the coupled 3Δ, 1Π, and 3Σ+ states, which are calculated between 1.773 and 2.035 eV (Table 4).
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CONCLUSIONS In this work we have explained the complex spectral features of the photoelectron spectra of XCN2+ by employing ab initio electronic structure methods with high-level electron correlation and accurate treatment of spin−orbit coupling. To this end, we have determined the geometries and harmonic vibrational frequencies of the neutral and dicationic XCN (X = Cl, Br, and I) systems at the MRCI level, employing relativistic effective core potentials for the halogens. By simultaneous ionization of two electrons from the frontier molecular orbitals, we have calculated the vertical ionization energies of the lowest eight scalar-relativistic electronic states of XCN2+ employing state-averaged CASSCF/MRCI calculation where 14 electrons were correlated in 12 orbitals. The scalarrelativistic states are further used as the electronic basis to construct spin−orbit Hamiltonian matrix, whose eigenvalues and eigenvectors are used to obtain the energies of the spin− F
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(4) Baer, T.; Booze, J.; Weitzel, K. Photoelectron Photoion Coincidence Studies of Ion Dissociation Dynamics. In Vacuum Ultraviolet Photoionization and Photodissociation of Molecules and Clusters; Ng, C.-Y., Ed.; World Scientific Pub Co Inc, 1991; pp 259−296. (5) Arion, T.; Hergenhahn, U. Coincidence Spectroscopy: Past, Present and Perspectives. J. Electron Spectrosc. Relat. Phenom. 2015, 200, 222−231. (6) Dujardin, G.; Leach, S.; Dutuit, O.; Guyon, P.; Richard-Viard, M. Double Photoionization of SO2 and Fragmentation Spectroscopy of SO++ 2 Studied by a Photoion-photoion Coincidence Method. Chem. Phys. 1984, 88, 339−353. (7) Winkoun, D.; Dujardin, G.; Hellner, L.; Besnard, M. One- and Two-step Double Photoionisation Processes in Valence Shells of H2O. J. Phys. B: At., Mol. Opt. Phys. 1988, 21, 1385−1394. (8) Curtis, D.; Eland, J. Coincidence Studies of Doubly Charged Ions Formed by 30.4 nm Photoionization. Int. J. Mass Spectrom. Ion Processes 1985, 63, 241−264. (9) Frasinski, L.; Stankiewicz, M.; Randall, K.; Hatherly, P.; Codling, K. Dissociative Photoionisation of Molecules Probed by Triple Coincidence Double Time-of-flight Techniques. J. Phys. B: At. Mol. Phys. 1986, 19, 819−824. (10) Eland, J. The Dynamics of Three-body Dissociations of Dications Studied by the Triple Coincidence Technique PEPIPICO. Mol. Phys. 1987, 61, 725−745. (11) Eland, J. H.; Feifel, R. Double Ionization of ICN and BrCN Studied by a New Photoelectron-photoion Coincidence Technique. Chem. Phys. 2006, 327, 85−90. (12) Feifel, R.; Eland, J.; Storchi, L.; Tarantelli, F. Complete Valence Double Photoionization of SF6. J. Chem. Phys. 2005, 122, 144309. (13) Eland, J.; Vieuxmaire, O.; Kinugawa, T.; Lablanquie, P.; Hall, R.; Penent, F. Complete Two-electron Spectra in Double Photoionization: The Rare Gases Ar,Kr and Xe. Phys. Rev. Lett. 2003, 90, 1−4. (14) Hall, R.; Ellis, K.; McConkey, A.; Dawber, G.; Avaldi, L.; MacDonald, M.; King, G. Double and Single Ionization of Neon, Argon and Krypton in the Threshold Region Studied by Photoelectron-ion Coincidence Spectroscopy. J. Phys. B: At., Mol. Opt. Phys. 1992, 25, 377−388. (15) Prümper, G.; Ueda, K.; Tamenori, Y.; Kitajima, M.; Kuze, N.; Tanaka, H.; Makochekanwa, C.; Hoshino, M.; Oura, M. Intramolecular Auger-electron Scattering in the Ultrafast Dissociation of CF4 at the 1s → a1* Excitation. Phys. Rev. A: At., Mol., Opt. Phys. 2005, 71, 052704. (16) Garcia, G.; Soldi-Lose, H.; Nahon, L. A Versatile Electron-ion Coincidence Spectrometer for Photoelectron Momentum Imaging and Threshold Spectroscopy on Mass Selected Ions Using Synchrotron Radiation. Rev. Sci. Instrum. 2009, 80, 023102. (17) Liu, X.; Prümper, G.; Kukk, E.; Sankari, R.; Hoshino, C.; Makochekanwa, M.; Kitajima, M.; Tanaka, H.; Yoshida, H.; Tamenori, Y.; Ueda, K. Site−selective Ion Production of the Core−excited CH3F Molecule Probed by Auger−electron−ion Coincidence Measurements. Phys. Rev. A: At., Mol., Opt. Phys. 2005, 72, 042704. (18) Prümper, G.; Fukuzawa, H.; Lischke, T.; Ueda, K. Combining High Mass Resolution and Velocity Imaging in a Time-of-flight Ion Spectrometer Using Pulsed Fields and an Electrostatic Lens. Rev. Sci. Instrum. 2007, 78, 083104. (19) Hatherly, P.; Smith, D.; Tuckett, R. Non-statistical Effects in the Fragmentation of Electronic States of Gas-phase Polyatomic Molecular Ions. Z. Phys. Chem. 1996, 195, 97. (20) Parkes, M.; Ali, S.; Tuckett, R.; Mikhailov, V.; Mayhew, C. Threshold Photoelectron Photoion Coincidence Spectroscopy and Selected Ion Flow Tube Cation-molecule Reaction Studies of Cyclic− C4F8. Phys. Chem. Chem. Phys. 2006, 8, 3643. (21) Kooser, K.; Ha, D. T.; Itälä, E.; Laksman, J.; Urpelainen, S.; Kukk, E. Size Selective Spectroscopy of Se Micro-clusters. J. Chem. Phys. 2012, 137, 044304.
orbit states and their composition in terms of the scalarrelativistic states. For ClCN2+ the spin−orbit interactions between the electronic states are found to be marginal. Apart from the spin−orbit splitting of the 3Π and 3Δ state (0.034 and 0.041 eV, respectively), the nonrelativistic calculations provide a complete picture of the excited electronic states of ClCN2+. On the contrary, in BrCN2+, the strong spin−orbit interactions, in particular the interactions between 3Σ−−1Σ+, 3Π−1Π, and 3 + 1 − Σ − Σ play a crucial role in the final assignment of the experimental photoelectron spectrum of BrCN2+. In particular, the unsymmetric spin−orbit splitting pattern of the 3Π electronic states (due to 3Π−1Π spin−orbit coupling) where the calculated energy difference between the lower two spin− orbit components and upper two spin−orbit components (0.092 and 0.208 eV, respectively) match well with the experimental results. The strong spin−orbit interactions in ICN2+ make its electronic spectroscopy very complex. To understand the effect of each of the spin−orbit interactions on the electronic spectroscopy of ICN2+, we sequentially analyzed the effect of interstate spin−orbit couplings to the energy spectrum of ICN2+. We report very strong spin−orbit interactions between 3Σ−−1Σ+, 3Π−1Π, 3Σ+−1Σ−, and 3Δ−1Δ, which lead to strong admixing of the scalar-relativistic states via the spin−orbit coupling. Finally, by analyzing the composition of the spin−orbit states, we have explained and assigned the complex experimental photoelectron spectrum of ICN2+. Taken together, in this work we have successfully explained the photoelectron spectra of BrCN2+ and ICN2+ and predicted the photoelectron spectrum of ClCN2+.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b12219. Tabulated data indicating optimized geometry of excited states of XCN2+ with CASSCF level of electron correlation. (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS S. Manna acknowledges the University Grants Commission of India, New Delhi, for research fellowship. S. Mishra acknowledges the financial support from IIT Kharagpur for ISIRD grant and the Department of Science and Technology, India, for the International Year of Chemistry research grant.
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REFERENCES
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(44) Bergner, A.; Dolg, M.; Kuechle, W.; Stoll, H.; Preuss, H. Ab Initio Energy-adjusted Pseudopotentials for Elements of Groups 13− 17. Mol. Phys. 1993, 80, 1431−1441. (45) Dolg, M. Ph. D. Thesis, University of Stuttgart, 1989. (46) Woon, D.; Dunning, T., Jr. Gaussian Basis Sets For Use in Correlated Molecular Calculations. III. The Atoms Aluminum Through Argon. J. Chem. Phys. 1993, 98, 1358. (47) Wilson, A. K.; Woon, D. E.; Peterson, K. A.; Dunning, T. H., Jr. Gaussian Basis Sets for use in Correlated Molecular Calculations. IX. The Atoms Gallium Through Krypton. J. Chem. Phys. 1999, 110, 7667. (48) Dunning, T. H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron Through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007. (49) Werner, H. J.; Knowles, P. J. An Efficient Internally Contracted Multiconfiguration−reference Configuration Interaction Method. J. Chem. Phys. 1988, 89, 5803. (50) Knowles, P. J.; Werner, H. J. An Efficient Method for the Evaluation of Coupling Coefficients in Configuration Interaction Calculations. Chem. Phys. Lett. 1988, 145, 514. (51) Werner, H. J.; Knowles, P. J. A Second Order Multiconfiguration SCF Procedure with Optimum Convergence. J. Chem. Phys. 1985, 82, 5053. (52) Knowles, P. J.; Werner, H. J. An Efficient Second-order MCSCF Method for Long Configuration Expansions. Chem. Phys. Lett. 1985, 115, 259. (53) Langhoff, S. R.; Davidson, E. R. Configuration Interaction Calculations on the Nitrogen Molecule. Int. J. Quantum Chem. 1974, 8, 61. (54) Berning, A.; Schweizer, M.; Werner, H. J.; Knowles, P. J.; Palmieri, P. Spin-orbit Matrix Elements for Internally Contracted Multireference Configuration Interaction Wave Functions. Mol. Phys. 2000, 98, 1823. (55) Werner, H. J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. et al. MOLPRO 2012.1, a package of ab initio programs, see http://www.molpro.net 2012. (56) Domcke, W.; Yarkony, D. R.; Köppel, H. Conical Intersections: Electronic Structure, Dynamics and Spectroscopy; World Scientific: Singapore, 2004.
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The Role of Spin−Orbit Coupling in the Double-Ionization Photoelectron Spectra of XCN2+ (X = Cl, Br, and I) Soumitra Manna and Sabyashachi Mishra* Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur, India S Supporting Information *
ABSTRACT: The photoelectron spectra of XCN2+ (X = Cl, Br, and I) were calculated employing ab initio electronic structure methods with high-level electron correlation and explicit treatment of spin−orbit coupling. Twelve scalarrelativistic excited states of the dicationic systems, calculated from state-averaged CASSCF/MRCI calculations, were used as the electronic basis to evaluate spin−orbit eigenstates. While the spin−orbit effects in ClCN2+ are found to be negligible, the electronic spectroscopy of BrCN2+ and ICN2+ is significantly influenced by interstate spin−orbit coupling. Several electronic degeneracies are lifted, and many unexpected accidental degeneracies occurred due to the spin−orbit coupling. In particular, the spin−orbit interactions between X̃ 3Σ−−b̃ 1Σ+, Ã 3 Π−c̃ 1Π, B̃ 3Δ−ã 1Δ, and C̃ 3Σ+−d̃ 1Σ− are found to be strong in BrCN2+ and ICN2+. By careful analysis of the effect of spin−orbit coupling parameters and the spin−orbit eigenstate composition, an assignment of the hitherto unidentified experimental photoelectron bands of BrCN2+ and ICN2+ is presented.
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experimental and theoretical studies.26−42 However, theoretical studies of the dications of cyanogen halides that are necessary for an informed interpretation of the corresponding photoelectron spectra are missing. Herein, we employ ab initio electronic structure methods with high-level electron correlation and explicit treatment of spin−orbit coupling to investigate the excited-states electronic structure and spectroscopy of XCN2+ (X = Cl, Br, I). We describe the role of spin−orbit coupling in the electronic spectroscopy of these systems. Finally, by analyzing the spin− orbit eigenstates, we provide an assignment of the photoelectron spectra of ICN2+ and BrCN2+, and predict the same for ClCN2+.
INTRODUCTION Ionization processes involving ejection of at least one electron and formation of ions provide insight into the excited-state structure and dynamics of the formed ions.1 While ionization of a single electron is conventionally analyzed by electron spectroscopy and by ion spectroscopy and spectrometry, the ionization processes involving ejection of more than one electron requires more specialized techniques, such as coincidence spectroscopy.2−4 Depending on the nature of the systems under investigation, different types of coincidence techniques are employed, such as photoelectron−photoion coincidence (PEPICO),5 photoion-photoion coincidence (PIPICO),6−8 photoelectron−photoion−photoion coincidence (PEPIPICO),9,10 and photoelectron-photoelectron coincidence (PEPECO).11−13 In recent years, the coincidence techniques have been applied to explore the excited states of several systems. Using the PEPICO method, ionization processes of rare gases, CF4, CH3, N2, CF3Br, SiCl4, C4F8, and even some clusters have been recently studied.14−21 Several small molecules, for example, H2, Br2, CO2, OCS, have been studied by PIPICO technique,22−25 whereas photoionization of CS2, NO2, SO2, and CH3I has been successfully investigated by PEPIPICO method.10 Using time-of-flight PEPECO method, the photoelectron spectra and dissociation dynamics of ICN2+ and BrCN2+ have been studied by Eland and Feifel.11 The photoelectron spectra of these dications contain interesting and complex structures that have not been interpreted.11 Over the years, the cyanogen halides and their cations have been the subject of several © XXXX American Chemical Society
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COMPUTATIONAL METHOD The XCN molecules with X = Cl, Br, and I are closed-shell linear molecules in the ground electronic state X̃ 1Σ+, with the valence-shell electronic configuration given by 1σ2 2σ2 3σ2 1π4 4σ2 2π4. The double ionization photoelectron spectroscopy of XCN molecules leads to the formation of the dicationic electronic states of XCN2+, which can be obtained by removing two electrons from the frontier occupied molecular orbitals. Simultaneous removal of two electrons from the highest occupied molecular orbital (HOMO), that is, 2π2, gives rise to a half-filled π-shell, which results in the dicationic electronic Received: December 14, 2015 Revised: February 10, 2016
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Table 1. Optimized Geometrya and Harmonic Vibrational Frequency in the Ground State of Neutral and Dicationic XCN
states 3Σ−, 1Δ, and 1Σ+.43 The ionization of one electron each from the HOMO and HOMO−1, that is, 4σ1 2π3, leads to the formation of dicationic electronic states 3Π and 1Π. Similarly, when one electron is removed from the first and second π molecular orbitals, one obtains 1Σ−, 3Δ, 3Σ+, 3Σ−, 1Δ, and 1 + Σ electronic states, of which the latter three are much higher in energy compared to the former three and hence are ignored in the present study. The interplay of the above electronic states of XCN2+ together with spin−orbit coupling is the central focus of this work. For the halogen atoms, we employed the spin−orbit averaged semilocal energy-adjusted pseudopotentials to describe the core, that is, 1s-2p for Cl (10 electrons), 1s-3d for Br (28 electrons), and 1s-4d for I (46 electrons).44 The valence electrons of Br and I are described by basis sets of augmented quadruple-ζ quality, composed of optimized contracted s, p, d, f, and g functions,44 while the valence shell of Cl is described by optimized contracted s and p functions of augmented quadruple-ζ quality.45 The d, f, and g polarization functions are obtained from the augmented correlation-consistent polarized valence quadruple-ζ (aug-cc-pVQZ) basis set of Woon and Dunning.46 The C and N atoms are described by the augmented correlation-consistent polarized valence triple-ζ (aug-cc-pVTZ) basis set of Dunning.47,48 The optimized geometries and vibrational frequencies of the ground state of XCN and XCN2+ have been calculated employing multireference configuration interaction (MRCI) method,49,50 which uses complete-active-space self-consistentfield (CASSCF)51,52 orbitals as N-electron basis. For the CASSCF and MRCI calculations, we correlated 14 electrons in 12 orbitals. For an accurate electron correlation of the excited electronic states of XCN2+, we employed the state-averaged (14,12) CASSCF followed by MRCI method for a scalar relativistic description of the 12 components of the lowest eight electronic states at the reference geometry of the neutral XCN. The CASSCF calculation that accounts for the static electron correlation provides reasonable starting orbitals, which are used during MRCI calculation to obtain the dynamic part of the electron correlation. To account for the size-consistency problem, the MRCI energy with Davidson correction53 is used while calculating the vertical ionization energies. The MRCI wave functions obtained from the abovementioned scalar-relativistic electron correlation calculation are further used to calculate the Breit−Pauli spin−orbit matrix elements, where the most important two-electron contributions of the spin−orbit operator are incorporated by means of an effective one-electron Fock operator.54 In the present calculations, the dimension of the spin−orbit matrix is 24 (from six singlet and six triplet states). The diagonalization of the spin−orbit matrix in the space of all spin−orbit-free electronic states provides information about the spin−orbit eigenstates. While the eigenvalues of the spin−orbit matrix reveal the spin−orbit energy levels, the eigenvectors are used to determine the composition of the spin−orbit eigenstates in terms of the scalar-relativistic states. All calculations were performed using Molpro package.55
states ClCN ClCN2+ BrCN BrCN2+ ICN ICN2+ a
X̃ X̃ X̃ X̃ X̃ X̃
Σ 3 − Σ 1 + Σ 3 − Σ 1 + Σ 3 − Σ 1 +
bond length (Å)
frequency (eV)
X−C
C−N
C−N str
X−C str
X−C−N bend
1.66 1.51 1.80 1.72 2.03 1.94
1.17 1.33 1.16 1.27 1.17 1.23
0.275 0.168 0.280 0.173 0.271 0.213
0.087 0.095 0.076 0.076 0.059 0.065
0.047 0.089 0.055 0.082 0.039 0.063
The optimization in all the systems shows linear geometry.
increases from Cl to I, while the C−N distance remains nearly constant irrespective of the nature of the halogen atom in neutral XCN molecules. A similar trend is also seen in the vibrational frequencies, where the X−C stretching frequency decreases from 704 cm−1 (ClCN) to 480 cm−1 (ICN), whereas the C−N stretching frequency remains in the range of 2185− 2260 cm−1 for the three molecules (Table 1). The ground state of XCN2+(X̃ 3Σ−) shows an increase in the C−N bond distance and a decrease in the X−C bond distance as compared to the neutral XCN molecules in all three systems. This arises from the fact that the HOMO of XCN is described by a π orbital that involves a bonding overlap between C−N and an antibonding overlap between the X−C centers. The calculated harmonic vibrational frequencies for C−N in BrCN2+ and ICN2+ (0.173 and 0.213 eV, respectively) are comparable to the corresponding experimental values (0.175 and 0.183 eV, respectively).11 The discrepancy between the calculated and experimental values of the vibrational frequencies may arise due to anharmonic effects. The calculated value of the Br−C stretching frequency in BrCN2+ (0.076 eV) is in very good agreement with the experimental value of 0.073 eV, whereas the I−C vibrational structures are unresolvable in the experimental photoelectron spectra of ICN2+.11 Additionally, the geometry of the XCN2+ in all the excited states considered in this study were optimized (Table S1 in the Supporting Information), which suggests that the excited states under consideration have stable minima near the equilibrium geometry of the neutral molecules. The dications are found to be linear in all these excited states. The vertical ionization energies of the lowest eight scalarrelativistic electronic states (four nondegenerate and four doubly degenerate states) of XCN2+ with respect to the electronic ground state of the neutral XCN (X̃ 1Σ+), calculated via SA-CASSCF/MRCI (with Davidson correction) method, are reported in Table 2. In all three dicationic systems, the electronic states arising from π2 electronic configuration leads to the X̃ 3Σ− as the ground electronic state, followed by ã 1Δ and b̃ 1Σ+, in accordance to the Hund’s rule. The vertical ionization energy of the ground state is the lowest for ICN2+, followed by BrCN2+ and ClCN2+, which is due to the nature of the valence orbitals of the halogen atoms in the frontier molecular orbitals of the XCN2+. In case of ICN2+, it is easier to remove electrons from the valence molecular orbitals, which are composed of 5s and 5p atomic orbitals of I atom, whereas electron removal requires more energy for BrCN2+ and ClCN2+, due to the involvement of fourth and third shell atomic orbitals of Br and Cl, respectively. The calculated vertical ionization energies of the X̃ 3Σ− state of BrCN2+ and ICN2+ (i.e., 30.785 and 28.609 eV, respectively) agree well with
■
RESULTS AND DISCUSSION The optimized geometries and harmonic vibrational frequencies in the ground state X̃ 1Σ+ of the neutral XCN molecules as well as in the ground state X̃ 3Σ− of dicationic XCN2+ systems are given in Table 1. The optimized geometries in all the systems are found to be linear. The X−C bond distance B
DOI: 10.1021/acs.jpca.5b12219 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Table 2. Scalar-Relativistic Vertical Ionization Energiesa (in eV) of the Excited States of XCN2+ from the X̃ 1Σ State of XCN
calculated to be 0.323 and 0.333 eV (ICN2+), 0.151 and 0.165 eV (BrCN2+), and 0.034 and 0.041 eV (ClCN2+), respectively. The spin−orbit splitting of both à 3Π and B̃ 3Δ states increases, as expected, from ClCN2+ to ICN2+ due to the presence of the heavier halogen center. Apart from the spin−orbit splitting of the à 3Π and B̃ 3Δ states, the spin−orbit coupling operator introduces several spin−orbit coupling between the scalar-relativistic states. The magnitude of the spin−orbit coupling values between the scalar-relativistic states are given in Table 3 for the XCN2+ systems. These spin−orbit coupling parameters are the matrix elements of the Breit−Pauli spin−orbit operator in the basis of scalar relativistic electronic states obtained from MRCI calculations. It can be seen that in all three systems, the spin−orbit coupling constants between the states, such as X̃ 3 − Σ −b̃ 1Σ+, X̃ 3Σ−−C̃ 3Σ+, ã 1Δ−B̃ 3Δ, à 3Π−c̃ 1Π, and d̃ 1Σ−− C̃ 3Σ+, are found to be relatively stronger in their respective systems (Table 3). Overall, the spin−orbit coupling between the states of ClCN2+ are rather weak, and these coupling strengths increase from ClCN2+ to ICN2+. Using the spin−orbit couplings given in Table 3 and the scalar relativistic MRCI energies given in Table 2, we report the double photoionization spectra of the XCN in Table 4. The calculated energies of the spin−orbit eigenstates are presented with respect to the energy of the lowest spin−orbit eigenstate, which indicates the origin of the spectrum. ClCN2+. In ClCN2+, the weak spin−orbit splitting in the states à 3Π (0.034 eV) and B̃ 3Δ (0.041 eV) and weaker interstate spin−orbit coupling between all other states suggests that the relativistic effects have a rather insignificant effect on its
vertical ionization energy (eV) state X̃ 3Σ− ã1Δ b̃1Σ+ Ã 3Π c̃1Π d̃1Σ− B̃ 3Δ C̃ 3Σ+
ClCN 32.561 33.065 33.308 33.370 33.929 34.229 34.381 34.445
2+
(0.504) (0.747) (0.809) (1.368) (1.668) (1.820) (1.884)
BrCN2+ 30.785 31.237 31.488 31.660 31.979 32.118 32.254 32.311
(0.452) (0.703) (0.875) (1.195) (1.333) (1.469) (1.526)
ICN2+ 28.609 29.139 29.452 29.712 29.919 29.997 30.125 30.177
(0.530) (0.843) (1.104) (1.310) (1.388) (1.516) (1.568)
a
Computed by the MRCI/SA-CASSCF method. Values in parentheses refer to the MRCI/SA-CASSCF results with the vertical ionization energy of the X̃ 3Σ− adjusted to zero.
the experimental origin of the corresponding photoelectron spectra (31.106 and 28.881 eV, respectively).11 The difference in the vertical ionization energies of the cationic excited states with respect to the ground state of XCN2+ (X̃ 3Σ−) are shown in the parentheses (Table 2). In all three dications, the lowest quintet state appears more than 6 eV above their respective ground states, and hence the quintet states are not considered in further analysis. Among the electronic states considered here, the à 3Π and B̃ 3 Δ states possess zeroth-order spin−orbit splitting due to simultaneous presence of orbital- and spin-angular momenta. The spin−orbit splittings in the à 3Π and B̃ 3Δ states are
Table 3. Matrix Elements of the Breit−Pauli Spin−Orbit Operator in the Basis of Scalar Relativistic Electronic States of XCN2+(in eV) states
X̃ 3Σ−
ã 1Δ
b̃ 1Σ+
c̃ 1Π
d̃ 1Σ−
B̃ 3Δ
C̃ 3Σ+
0.034 0.036 0.002 0.002 0.001 BrCN2+
0 0 0 0.001
0 0 0.041
0.041 0
0
0.151 0.155 0.007 0.006 0.005 ICN2+
0 0 0.001 0.003
0 0 0.165
0.165 0
0
0 0 0.001 0.004
0 0 0.332
0.333 0
0
à 3Π 2+
ClCN
X̃ 3Σ− ã 1Δ b̃ 1Σ+ Ã 3Π c̃ 1Π d̃ 1Σ− B̃ 3Δ C̃ 3Σ+
0 0 0.041 0.004 0.003 0 0 0.035
0 0 0.003 0 0 0.036 0
0 0.003 0 0 0 0
X̃ 3Σ− ã 1Δ b̃ 1Σ+ Ã 3Π c̃ 1Π d̃ 1Σ− B̃ 3Δ C̃ 3Σ+
0 0 0.184 0.019 0.016 0 0 0.137
0 0 0.016 0 0 0.145 0
0 0.013 0 0 0 0
X̃ 3Σ− ã 1Δ b̃ 1Σ+ Ã 3Π c̃ 1Π d̃ 1Σ− B̃ 3Δ C̃ 3Σ+
0 0 0.416 0.054 0.050 0 0 0.249
0 0 0.043 0 0 0.281 0
0 0.033 0 0 0 0
0.323 0.324 0.010 0.010 0.007 C
DOI: 10.1021/acs.jpca.5b12219 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A Table 4. Assignment of the Photoelectron Bandsa of XCN2+ and Composition of the Spin−Orbit Eigenstates in Terms of Spin−Orbit-Free States energy (calcd)
energy (expt)
0 0.002 0.491 0.740 0.830 0.862 0.898 1.417 1.657 1.768 1.810 1.851 1.872 1.879 0 0.031 0.507 0.839 0.881 0.973 1.181 1.443 1.448 1.511 1.695 1.748 1.830 1.842
0 0.073 0.557 1.120 1.190 1.290 1.510 1.750 1.750 1.750 1.870 1.870 1.870 1.870
0 0.125 0.621 1.039 1.125 1.172 1.319 1.367 1.672 1.698 1.777 1.792 1.798 2.009 2.035
0 0.183 0.636 1.060 1.259 1.259 1.469 1.469 1.620 1.620 1.970 1.970 1.970 1.970 1.970
calculated composition (weight in %) ClCN2+ 3 − Σ (99.70); 1Σ+ (0.30) 3 − Σ (100) 1 Δ (100) 1 + Σ (99.60); 3Σ− (0.40) 3 Π (100) 3 Π (100) 3 Π (100) 1 Π (100) 1 − Σ (96); 3Σ+ (4) 3 Δ (100) 3 Δ (100) 3 Δ (100) 3 + Σ (100) 3 + Σ (96); 1Σ− (4) 2+ BrCN 3 − Σ (95); 1Σ+ (5) 3 − Σ (100) 1 Δ (98); 3Δ (2) 1 + Σ (95) ; 3Σ− (5) 3 Π (100); 3 Π (88); 1Π (12) 3 Π (100) 1 − Σ (76); 3Σ+ (24) 1 Π (88); 3Π (12) 3 Δ (100) 3 Δ (98); 1Δ (2) 3 + Σ (100) 1 − Σ (24) ; 3Σ+ (76) 3 Δ (100) ICN2+ 3 − Σ (86); 1Σ+ (14) 3 − Σ (97); 3Σ+(3) 1 Δ (90); 3Δ (6); 3Π (4) 3 Π (96) ; 1Δ (3); 3Δ (1) 3 Π (66); 1Π (34) 1 + Σ (83); 3Σ− (13); 3Π (4) 1 − Σ (63); 3Σ+ (37) 3 Δ (100) 3 Π (100) 3 Π (96); 1Σ+ (4) 3 Δ (93); 1Δ (7) 3 + Σ (94); 3Σ− (2); 3Π (2); 1Π (2) 1 Π (64); 3Π (32); 3Σ+ (4) 3 + Σ (63); 1Σ− (37) 3 Δ (100)
Figure 1. Energy of the spin−orbit states of ClCN2+ with the spin− orbit splitting of the 3Π and 3Δ states (a) and with all interstate spin− orbit interactions (b). The energy at the left-hand side of the graph represents the scalar-relativistic energy.
and 3Δ3,2,1 at 1.768, 1.810, and 1.851 eV, respectively. Each of these energy levels is doubly degenerate representing the orbital degeneracy of the Π and Δ electronic states. The orbital degeneracies of the states ã 1Δ and c̃ 1Π are also preserved. However, the X̃ 3Σ− and C̃ 3Σ+ states show minor splitting of 0.002 and 0.007 eV, respectively, due to the interstate spin− orbit coupling of X̃ 3Σ−−b̃ 1Σ+ and d̃ 1Σ−−C̃ 3Σ+, respectively. This is also reflected in the composition of the spin−orbit eigenstates, where the energy levels at 0 and 0.740 eV are mixture of X̃ 3Σ− and b̃ 1Σ+ states (Table 4), and the energy levels at 1.657 and 1.879 eV arise from the combination of d̃ 1 − Σ and C̃ 3Σ+ states (Table 4). BrCN2+. In BrCN2+, the spin−orbit splitting of the states à 3 Π (0.151 eV) and B̃ 3Δ (0.165 eV) leads to splitting of both the Π and Δ states to three spin−orbit multiplets each. Since the scalar relativistic states d̃ 1Σ− and C̃ 3Σ+ are closely spaced to the B̃ 3Δ state, the spin−orbit splitting of the latter leads to a situation where the spin−orbit multiplets of the B̃ 3Δ state span the two scalar-relativistic states d̃ 1Σ− and C̃ 3Σ+ (Figure 2a). The interstate spin−orbit coupling between X̃ 3Σ− and b̃ 1Σ+ states results in an interaction between the b̃ 1Σ+ state and the 3 − Σ 0 component of the X̃ 3Σ− state, which leads to the splitting of the spin-degeneracy of the X̃ 3Σ− state, yielding an energy difference of 0.031 eV between the 3Σ−0 and 3Σ−±1 components of the X̃ 3Σ− state (Figure 2b). Similar interstate spin−orbit
a
All energies are in electronvolts. The calculated values of the spinorbit energies are with respect to the energy of the lowest spin-orbit state, and the experimental energy values are with respect to the origin of the spectrum (ref 11).
electronic spectroscopy. The scalar relativistic and the spin− orbit coupled energy levels of ClCN2+ are shown in Figure 1. It can be seen that the spin−orbit splitting of the à 3Π and B̃ 3Δ leads to two sets of three closely spaced energy levels corresponding to the 3Π2,1,0 at 0.830, 0.862, and 0.898 eV
Figure 2. Energy of the spin−orbit states of BrCN2+ with the spin− orbit splitting of the 3Π and 3Δ states (a) and with all interstate spin− orbit interactions (b). The energy at the left-hand side of the graph represents the scalar-relativistic energy. D
DOI: 10.1021/acs.jpca.5b12219 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A
Figure 3. Energy of the spin−orbit states of ICN2+ with the spin−orbit splitting of the 3Π and 3Δ states (a). (b−f) The energy of the spin−orbit states when the coupling parameters between 3Σ−−1Σ+, 3Σ+−1Σ−, 3Π−1Π, 3Δ−1Δ, and 3Σ−−3Σ+, are switched on sequentially. (g) The energy of the spin−orbit states when all spin−orbit coupling parameters are present.
interaction between the states d̃ 1Σ− and C̃ 3Σ+ lowers the energy of the d̃ 1Σ− state (1.443 eV, Table 4) while increasing the energy of the 3Σ+0 components of the C̃ 3Σ+ state, which leads to the removal of spin degeneracy of the C̃ 3Σ+ state, yielding the 3Σ+±1 and 3Σ+0 components at 1.748 and 1.83 eV, respectively (Table 4). The interstate spin−orbit interaction between the states à 3 Π and c̃ 1Π introduces an interaction between the c̃ 1Π state and the 3Π1 component of the à 3Π state, thus lowering the energy of the 3Π1 component (0.973 eV) and raising the energy of the c̃ 1Π state (1.448 eV). The interstate spin−orbit interaction between the states à 3Π and c̃ 1Π removes the symmetry of the energy spacing between the spin−orbit multiplets of the à 3Π state (Figure 2b). The energy difference between the 3Π2 and 3Π1 spin−orbit components is reduced to 0.092 eV, while the energy difference between the 3Π0 and 3Π1 spin−orbit components is increased to 0.208 eV from the spin−orbit splitting value of 0.151 eV in the isolated à 3Π state. The combined effect of the interstate spin−orbit coupling between d̃ 1Σ−−C̃ 3Σ+ states (where the energy of the former is lowered) and à 3Π−c̃ 1Π states (where the energy of the latter is raised), reduces the gap between the scalar-relativistic states c̃ 1 Π and d̃ 1Σ− (see Figure 2b) from 0.135 to 0.005 eV, causing a near accidental degeneracy (energy levels at 1.443 and 1.448 eV, Table 4). In addition to the above-described interstate spin−orbit couplings, we do observe weak spin−orbit couplings between the states ã 1Δ−B̃ 3Δ and X̃ 3Σ−−C̃ 3Σ+. However, their effect on the electronic spectrum of BrCN2+ is rather limited. ICN2+. Unlike ClCN2+ and BrCN2+ the spin−orbit coupling between the states of ICN2+ are much stronger, and their combined effect makes the electronic spectrum of ICN2+ very complex. To understand the impact of the strong spin−orbit coupling constants on the spin−orbit states, we analyze the spin−orbit states by considering the interstate couplings sequentially, as shown in Figure 3a−g, where the left-hand side represents the scalar-relativistic situation and the righthand side represents the situation where all the interstate spin− orbit interactions are operative. The spin−orbit splitting of the à 3Π (0.323 eV) and B̃ 3Δ (0.333 eV) states causes the 3Π and 3Δ states to split to three spin−orbit multiplets each. Because of the large spin−orbit
splitting in ICN2+, the lowest spin−orbit multiplet of the à 3Π (i.e., 3Π2) becomes accidentally degenerate with the b̃ 1Σ+ (Figure 3a), and the middle spin−orbit multiplet of the à 3Π (i.e., 3Π1) comes very close (0.09 eV) to the lowest spin−orbit multiplet of the B̃ 3Δ state (i.e., 3Δ3) (Figure 3a). The large spin−orbit splitting in ICN2+ renders several scalar-relativistic states (such as c̃ 1Π, d̃ 1Σ−, and C̃ 3Σ+) appear within the spin− orbit multiplets of the à 3Π and B̃ 3Δ states (Figure 3a). Similar to BrCN2+, the interstate spin−orbit coupling between the X̃ 3Σ− and b̃ 1Σ+ states lifts the spin-degeneracy of the X̃ 3Σ− state, yielding an energy difference of 0.125 eV between the states 3Σ−0 and 3Σ−±1 (Figure 3b). A similar, but more pronounced, effect is seen for the interstate spin−orbit coupling between the d̃ 1Σ− and C̃ 3Σ+ states, where the strong interstate coupling leads to a splitting of 0.211 eV between the spin components of the C̃ 3Σ+ state (Figure 3c). The interstate spin−orbit coupling parameter between the states X̃ 3Σ−−b̃ 1Σ+ is stronger (0.416 eV) than that of d̃ 1Σ−−C̃ 3Σ+ coupling (0.332). However, the impact of the former coupling on the spectroscopy is smaller than that of the latter. This is due to the large energy difference between the scalar relativistic states X̃ 3 − Σ and b̃ 1Σ+ (0.843 eV) compared to the smaller energy difference between the states d̃ 1Σ− and C̃ 3Σ+ (0.180 ev). Hence, the impact of the spin−orbit coupling in the electronic spectroscopy of the dicationic systems not only depends on the corresponding coupling constants but also on the relative spacing between the concerned scalar relativistic states. The spin−orbit interaction between the states à 3Π and c̃ 1Π leads to repulsion between the c̃ 1Π state and the 3Π1 component of the à 3Π state, thus lowering the energy of the 3Π1 component significantly. Similar to BrCN2+, this interaction leads to a situation where the gap between two consecutive spin−orbit multiplets of the à 3Π state becomes very unsymmetric, that is, 0.086 and 0.573 eV from the spin− orbit splitting value of 0.332 eV in the isolated à 3Π state (Figure 3d). The interstate spin−orbit interaction between the ã 1Δ−B̃ 3Δ states leads to the lowering of energy of the ã 1Δ state and a rise in the energy of the 3Δ2 component of the B̃ 3Δ. This results in an unsymmetric spacing between the consecutive spin−orbit multiplets of the B̃ 3Δ state (0.406 and 0.262 eV as compared to 0.332 eV in the isolated B̃ 3Δ state); see Figure 3e. E
DOI: 10.1021/acs.jpca.5b12219 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A In ICN2+, a moderately strong coupling between the 3Σ±1 components of the X̃ 3Σ− and C̃ 3Σ+ states is observed (0.249 eV, Table 3), which leads to the lowering of the 3Σ−±1 of the X̃ 3 − Σ and a corresponding rise in the energy of the 3Σ+±1 of the C̃ 3Σ+ state. This interaction, to some extent, mitigates the effect of the interaction between X̃ 3Σ−−b̃ 1Σ+ states and d̃ 1 − Σ −C̃ 3Σ+ states, which leads to the lifting of the spin degeneracy of the X̃ 3Σ− and C̃ 3Σ+ states, as described earlier. The effect of the spin−orbit interaction between states à 3 Π−b̃ 1Σ+ leads to an interesting situation, where the orbital degeneracy of the 3Π0 component of the à 3Π is lifted due to the interaction of the state b̃ 1Σ+ with only one of the two orbital components (corresponding to orbital angular momentum Λ = +1) that constitutes the 3Π0 state. In this case the orbital degeneracy of an electronic state is lifted due to pure electronic (spin−orbit) effect, unlike Jahn−Teller and Renner− Teller effects where nuclear motion plays the driving role for lifting of electronic degeneracies.56 In addition to the above-described interstate spin−orbit couplings, we do observe weak to moderate range of spin−orbit interaction between the states à 3Π−X̃ 3Σ−, à 3Π−ã 1Δ, à 3Π− B̃ 3Δ, à 3Π−d̃ 1Σ−, and b̃ 1Π−X̃ 3Σ−. However, their effect on the electronic spectrum of ICN2+ is rather limited. Comparison with Experimental Photoionization Spectra. The double ionization photoelectron spectra of ICN and BrCN show complex features, some of which have been assigned in the earlier experimental study.11 Several vibrational progressions along both the stretching modes in the X̃ 3Σ− and ã 1Δ electronic states of XCN2+ have been identified in the assignment of the experimental spectra.11 However, the experimental spectra of BrCN2+ and ICN2+ show many unidentified lines, and the assignment of the bands ignores the possible spin−orbit coupling between the electronic states.11 In particular, the spin−orbit interaction between X̃ 3 − Σ and b̃ 1Σ+ states in BrCN2+ and ICN2+ leads to the splitting of the X̃ 3Σ− state that amounts to 0.031 and 0.125 eV, which are very similar in magnitude with the experimentally observed X−C stretching vibrational frequency in BrCN2+ (0.073 eV) and C−N stretching frequency in ICN2+ (0.183 eV), respectively.11 Therefore, a strong overlap of the bands of different vibronic origin is expected. Because of the low resolution of the experimental spectrum, the vibrational structures in the electronic states beyond ã 1Δ are not seen.11 The effect of nuclear dynamics on the electronic states via vibronic coupling mechanisms is important to describe the role of the former on the photoelectron spectra. However, in the present study, our discussion is restricted to the electronic origin of the photoelectron bands with special emphasis on the electronic spin−orbit coupling. In the photoelectron spectrum of BrCN2+ the band at 0.557 eV from the origin of the spectrum is assigned as the ã 1Δ, which agrees well with our calculated value of 0.507 eV (Table 4). At higher energies, the experimental peaks at 1.12 and 1.19 eV (separated by 0.07 eV) can be assigned to origin from the closely spaced b̃ 1Σ+ and the lower spin−orbit component of the à 3Π state, calculated as 0.839 and 0.881 eV (energy separation of 0.04 eV), respectively (Table 4). The photoelectron bands at 1.29 and 1.51 eV can be assigned as the middle and upper spin−orbit components of the à 3Π state, respectively. This assignment agrees well with the calculated value of the effective spin−orbit splitting in the à 3Π state, where the energy difference between the two lower spin−orbit
components of the 3Π state is calculated as 0.092 eV and the energy difference between the two upper spin−orbit components of the 3Π state is calculated as 0.208 eV, which compare well with the experimental splitting values of 3Π state (0.10 and 0.22 eV, respectively). The experimental band between 1.65 and 1.80 eV (centered around 1.75 eV) can be assigned to be originating from the closely spaced electronic states 3Σ−, 1Π, and the lower spin−orbit components of the 3Δ state. The unresolved and low-intensity spectral structure at 1.87 eV from the origin of the photoelectron spectrum of BrCN2+ can be assigned to be originating from the coupled 3Δ and 3Σ+ states (Table 4). The experimental photoelectron spectrum of ICN2+ shows the band associated with the ã 1Δ state at 0.636 eV from the origin of the spectrum. The energy difference between the X̃ 3 − Σ and ã 1Δ electronic states of ICN2+ is calculated as 0.533 eV from the scalar-relativistic MRCI calculations (Table 2), which upon inclusion of the spin−orbit coupling increases to 0.621 eV (due to X̃ 3Σ−−b̃ 1Σ+ coupling), which compares well with the experimental value of 0.636 eV; see Table 4. At higher energies, the photoelectron spectra of ICN2+ show several unidentified peaks. The peak at 1.06 eV from the origin of the spectrum has been assigned as the first overtone of the C−N stretch mode in the ã 1Δ state.11 This peak comes very close to the calculated value of the lower spin−orbit components of the à 3Π state (1.04 eV); see Table 4. At further higher energies, three unresolved broad bands centered at 1.26, 1.47, and 1.97 eV manifest in the experimental photoelectron spectrum.11 The peak at 1.26 eV (spreads between 1.12 to 1.32 eV) can be assigned to originate from the coupled states 1Σ− and the spin− orbit component of 3Π state, whose energy levels are calculated to be 1.172 and 1.25 eV from the lowest spin−orbit state (Table 4). The electronic states 1Σ−and the lower spin−orbit component of 3Δ are calculated to be 1.319 and 1.367 eV (above the ground spin−orbit state), which compare well with the unidentified band at 1.47 eV from the origin of the experimental spectrum.11 The experimental spectrum of ICN2+ exhibits a very low intensity peak at 1.62 eV from the origin of the spectrum, which may originate due to the upper spin−orbit components of the 3Π electronic state, calculated as 1.672 and 1.698 eV (the splitting is due to 3Π−1Σ+ spin−orbit interaction). Finally, a rather broad band centered around 1.97 eV that spans between 1.77 to 2.07 eV can be assigned to originate from the coupled 3Δ, 1Π, and 3Σ+ states, which are calculated between 1.773 and 2.035 eV (Table 4).
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CONCLUSIONS In this work we have explained the complex spectral features of the photoelectron spectra of XCN2+ by employing ab initio electronic structure methods with high-level electron correlation and accurate treatment of spin−orbit coupling. To this end, we have determined the geometries and harmonic vibrational frequencies of the neutral and dicationic XCN (X = Cl, Br, and I) systems at the MRCI level, employing relativistic effective core potentials for the halogens. By simultaneous ionization of two electrons from the frontier molecular orbitals, we have calculated the vertical ionization energies of the lowest eight scalar-relativistic electronic states of XCN2+ employing state-averaged CASSCF/MRCI calculation where 14 electrons were correlated in 12 orbitals. The scalarrelativistic states are further used as the electronic basis to construct spin−orbit Hamiltonian matrix, whose eigenvalues and eigenvectors are used to obtain the energies of the spin− F
DOI: 10.1021/acs.jpca.5b12219 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry A
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orbit states and their composition in terms of the scalarrelativistic states. For ClCN2+ the spin−orbit interactions between the electronic states are found to be marginal. Apart from the spin−orbit splitting of the 3Π and 3Δ state (0.034 and 0.041 eV, respectively), the nonrelativistic calculations provide a complete picture of the excited electronic states of ClCN2+. On the contrary, in BrCN2+, the strong spin−orbit interactions, in particular the interactions between 3Σ−−1Σ+, 3Π−1Π, and 3 + 1 − Σ − Σ play a crucial role in the final assignment of the experimental photoelectron spectrum of BrCN2+. In particular, the unsymmetric spin−orbit splitting pattern of the 3Π electronic states (due to 3Π−1Π spin−orbit coupling) where the calculated energy difference between the lower two spin− orbit components and upper two spin−orbit components (0.092 and 0.208 eV, respectively) match well with the experimental results. The strong spin−orbit interactions in ICN2+ make its electronic spectroscopy very complex. To understand the effect of each of the spin−orbit interactions on the electronic spectroscopy of ICN2+, we sequentially analyzed the effect of interstate spin−orbit couplings to the energy spectrum of ICN2+. We report very strong spin−orbit interactions between 3Σ−−1Σ+, 3Π−1Π, 3Σ+−1Σ−, and 3Δ−1Δ, which lead to strong admixing of the scalar-relativistic states via the spin−orbit coupling. Finally, by analyzing the composition of the spin−orbit states, we have explained and assigned the complex experimental photoelectron spectrum of ICN2+. Taken together, in this work we have successfully explained the photoelectron spectra of BrCN2+ and ICN2+ and predicted the photoelectron spectrum of ClCN2+.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b12219. Tabulated data indicating optimized geometry of excited states of XCN2+ with CASSCF level of electron correlation. (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS S. Manna acknowledges the University Grants Commission of India, New Delhi, for research fellowship. S. Mishra acknowledges the financial support from IIT Kharagpur for ISIRD grant and the Department of Science and Technology, India, for the International Year of Chemistry research grant.
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REFERENCES
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DOI: 10.1021/acs.jpca.5b12219 J. Phys. Chem. A XXXX, XXX, XXX−XXX
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DOI: 10.1021/acs.jpca.5b12219 J. Phys. Chem. A XXXX, XXX, XXX−XXX
![Double-inversion mechanisms of the X⁻ + CH₃Y [X,Y = F, Cl, Br, I] SN2 reactions.](/assets/img/hold.png)
