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Electronic and Vibrational Spectroscopy of CsS Published as part of The Journal of Physical Chemistry virtual special issue “William M. Jackson Festschrift”. Karim Elhadj Merabti,† Sihem Azizi,† Roberto Linguerri,‡ Gilberte Chambaud,‡ Muneerah Mogren Al-Mogren,§ and Majdi Hochlaf*,‡ †

Laboratoire de Physique Théorique, Université Abou Bekr Belkaid Tlemcen, Algeria Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, 5 bd Descartes, 77454 Marne-la-Vallée, France § Chemistry Department, Faculty of Science, King Saud University, PO Box 2455, Riyadh 11451, Kingdom of Saudi Arabia

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‡

S Supporting Information *

ABSTRACT: Using multi configurational ab initio methodologies, we compute the potential energy curves (PECs) of the lowest electronic states of the diatomic CsS. These computations are performed using internally contracted multireference interaction configuration including Davidson correction (MRCI+Q) with and without considering spin−orbit effects. The shapes of the PECs are governed by the interactions between the two ionic states, 2Σ+ and 2Π, correlating at large internuclear separations (RCsS) to the first ionic dissociation limit and the other electronic states correlating to the three lowest neutral dissociation limits. Computations show the importance of considering a large amount of electron correlation for the accurate description of the PECs and spectroscopy of this molecular system. As expected, these PECs are also strongly affected by the spin−orbit interaction. For the bound states, we report a set of spectroscopic parameters including equilibrium distances, dissociation energies, and vibrational and rotational constants. The effects of spin−orbit-induced changes on these parameters are also discussed. Moreover, we show that the 22Π state presents a “bowl” potential with a rather flat region extending to large RCsS distances. After being promoted to this state, wavepackets should undergo strong oscillations, similar to those observed by Zewail and co-workers for the NaI molecule. These should provide information on the shape of the PEC for the 22Π state and also on the couplings between this and the neighboring states.

I. INTRODUCTION Cesium, Cs, being the alkali element with the lowest (albeit non-negligible) ionization energy (3.89 eV), can be regarded as a good source material for electrons in plasma heating modules. Such media have complex chemical compositions inducing a variety of physical and chemical processes, where cesium chalcogenides may act as impurities. For instance, CsO is listed as a possible impurity in Tokamaks using Cs grids, due to the presence of oxygen traces in the heating chamber.1,2 Traces of sulfur and sulfur bearing species can also exist there. After reaction with cesium compounds, they probably result in the formation, for example, of CsS or Cs2S. Moreover, it is known that cesium nitride, Cs3N, can be readily attacked by sulfur.3 Upon heating CsO (for T > 150−200 °C) in the presence of dry sulfur dioxide, incandescence is observed.3 Again, molecular species such as CsS or Cs2S may be produced during these reactions and contribute to the observed effects. To understand the phenomena taking place during these reactions and in plasma, one needs a full characterization of the involved atomic and molecular species. Since alkali-metal monoxides are commonly found in many high-temperature systems, they have been the subject of many studies, both experimental and theoretical.4−16 However, their sulfur © 2018 American Chemical Society

isovalent analogues, i.e., alkali-metal monosulfides (MS), were investigated,17,18 but not to the same extent; consequently, there is a lack of information on these molecules. For instance, spectroscopic data on CsS, of interest in the present study, are limited to the determination of the nature of its lowest lying electronic states by Partridge et al.17 and by Lee and Wright.18 They deduced spectroscopic constants for the ground state, of 2 Π symmetry, and for the first close-lying excited state of 2Σ+ symmetry. Both states are coupled by spin−orbit interactions. Nevertheless, no information is available on the upper excited electronic states. To date, no experimental studies have been performed on the spectroscopy of gas phase CsS. However, accurate data can be provided by pure theoretical treatments. The goal of this work is to characterize the electronic ground and low-lying excited states of CsS using high-level ab initio calculations. Here we investigate the CsS molecule using multireference post Hartree−Fock methods and large basis sets. We first compute the CsS potential energy curves (PECs) with and without Received: March 15, 2018 Revised: May 28, 2018 Published: May 29, 2018 5354

DOI: 10.1021/acs.jpca.8b02543 J. Phys. Chem. A 2018, 122, 5354−5360

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The Journal of Physical Chemistry A taking into account the spin−orbit interaction. In addition to the X2Π and 12Σ+ states, we found another bound electronic excited state, the 22Π state. The shapes of all these potentials are strongly affected by considering the spin−orbit interaction and electron correlation. Then, we derived a set of spectroscopic constants that may be used for the identification of CsS in plasma or in the laboratory.

Table 1. Dissociation Channels for CsS and Molecular States That Correlate to These Asymptotesa for the Lowest Fine Structure Levels

dissociation fragments 2

3

Cs( S) + S( P2) Cs(2S) + S(1D) Cs(2P01/2) + S(3P2) Cs+(1S) + S−(2P3/2)

II. COMPUTATIONAL METHODS In this work we study the low-lying doublet and quartet electronic states of CsS. The Cs atom is described using the ECP46MDF relativistic pseudopotential, where the nine external electrons are described by [13s,11p,9d,10f,5g] functions.8 For S, after carefully checking the performance of the aug-cc-pVXZ (X = Q, 5, 6) basis sets,19,20 it was decided to use the aug-cc-pV5Z one. The electronic computations are performed using the MOLPRO program suite.21 Since MOLPRO does not consider infinite point groups, these calculations are done in the C2v point group where the B1 and B2 representations were equivalently described. Through benchmark calculations, we found that the shapes and relative positions of the CsS PECs are very sensitive to the level of accuracy of the electron correlation description (see below). Thus, one needs to use strongly correlated postHartree−Fock methods for a correct characterization of the CsS electronic states. Also, we found that several of these electronic states exhibit a pronounced multiconfigurational character. Hence, this invalidates the use of single reference electronic structure methods for their investigation. Here, we used the state-averaged complete active space self-consistent field (CASSCF)22,23 followed by multireference configuration interaction (MRCI) techniques.24−26 The Davidson correction (MRCI+Q) was also added to the MRCI energies.27 The CASSCF active space employed in this study is composed of the 3s, 3p atomic orbitals of S and 6s, 6p orbitals of Cs. This ansatz leads to seven valence electrons distributed in eight valence orbitals. In the CASSCF computations we averaged the doublets and quartets together using the default averaging procedure of MOLPRO. In the MRCI step, the complete CASSCF wave functions were used as a reference. For the treatment of spin−orbit interactions, the effective Breit−Pauli SO operator, HSO, as implemented in MOLPRO was used.28 The PECs were later incorporated into variational treatments of the nuclear motions. The spectroscopic parameters were obtained by variational computations using the Numerov package29 where the nuclear motion problem is solved with the method of Cooley.30

experimental relative energies (eV)b 0.00 1.14 1.38 1.82

d

calculated relative energies (eV)c 0.00 1.16 1.37 2.00

d

molecular states (Σ−,Π) (Σ+,Π,Δ) 2,4 (Σ+,Σ−(2),Π(2),Δ) 2 + (Σ ,Π) 2,4 2

a

We give also the energy positions (eV) of the asymptotes. bReference 41. cMRCI+Q-SO/aug-cc-pV5Z level of theory. dUsed as reference.

Figure 1. Potential energy curves of the X2Π, 22Π (solid lines), and 12Σ+ (dashed lines) states of CsS as computed at the CASSCF/aug-ccpV5Z (red lines), MRCI/aug-cc-pV5Z (black lines), and MRCI+Q/ aug-cc-pV5Z (blue lines) levels. The reference energy is chosen to be the energy of CsS (X2Π) at equilibrium.

the importance of considering dynamical electron correlation (within MRCI) for the accurate description of the electronic states of CsS. Since there is an interplay between covalent (Cs···S) and ionic (Cs+···S−) bonding character for the formation of these electronic states, we assume that the Cs+··· S− interaction is poorly described at the CASSCF level and only MRCI+Q computations recover such effects. The nature of the bonding and of the ground electronic state of alkali chalcogenides (MX) was subject to several studies. Indeed, the lowest 2Σ+ and 2Π states are close-lying and their relative ordering, and hence the nature of the electronic ground state of MX, depend on the balance between long-range attractive electrostatic terms that favor the 2Π state, and Pauli repulsion terms that tend to favor the 2Σ+ state at shorter ranges. For instance, alkali-metal monoxides exhibit a change in the electronic ground state as they descend the alkali column: LiO,31,32 NaO,33 and KO34 have a 2Π ground state, while RbO35 and CsO12 possess a 2Σ+ ground state. For alkali-metal monosulfides, Lee and Wright established a 2Π ground state whatever the nature of the alkali.18 Our results on the two lowest 2Σ+ and 2Π states of CsS confirm these findings, as shown in Figure 2 by the MRCI+Q/aug-cc-pV5Z potential energy curves along the Cs−S bond length (RCsS). In addition to those of the X2Π and 12Σ+ states, Figure 2 displays the PECs of the other electronic states correlating at large internuclear distances to [Cs(2S) + S(3P)], [Cs(2S) + S(1D)], and [Cs(2P) + S(3P)] asymptotes (Table 1). An

III. NATURE OF THE ELECTRONIC STATES OF CsS The electronic states investigated in the present contribution are correlated at large internuclear distances to [Cs(2S) + S(3P)], [Cs(2S) + S(1D)], [Cs(2P) + S(3P)], and [Cs+(1S) + S−(2P)] dissociation limits (see Table 1). Figure 1 presents the CASSCF, MRCI, and MRCI+Q PECs of the three lowest electronic states of CsS, X2Π, 22Π, and 12Σ+, computed with the aug-cc-pV5Z basis set. These electronic states correlate adiabatically to the [Cs(2S) + S(3P)] and [Cs(2S) + S(1D)] dissociation limits at large internuclear separations (Table 1). While the three sets of PECs have smooth shapes and gently reach their limits, we observe drastic differences between the PECs computed using CASSCF and those derived at the MRCI and MRCI+Q levels. This shows 5355

DOI: 10.1021/acs.jpca.8b02543 J. Phys. Chem. A 2018, 122, 5354−5360

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take place. Since 12Σ− leads directly to the first dissociation limit, the ro-vibrational levels of 12Σ+ located above this limit are expected to be predissociated by this state, resulting in a shortening of their lifetimes. Additional mutual interactions can be found after inspection of Figure 2. For energies >3 eV, the situation is even more complicated because of the high density of states correlating to the [Cs(2S) + S(1D)] and [Cs(2P) + S(3P)] dissociation limits. In these series, only 12Σ+ and 22Π states present potential wells greater than 1 eV. The other states present either shallow potentials or repulsive ones. It is worth noting the existence of several avoided crossings between the states of the same space and spin multiplicities. For states with the same spin multiplicity, we also observe crossings between Σ−Π and Π−Δ doublets where vibronic and also spin−orbit couplings may take place as discussed above for 12Σ+ and 12Σ−. It is worth noting that we have previously computed similar patterns and shapes for the isovalent NaS diatomic.36 Table 2 shows the calculated vertical transition energies for the lowest electronic states of CsS together with the dissociation energies for the bound states, obtained at the CASSCF/aug-cc-pV5Z and MRCI+Q/aug-cc-pV5Z levels. We again refer to the in-depth analysis done by Lee and Wright18 for the 2Σ+−2Π energy ordering. Table 2 lists also the dominant electron configurations of CsS states as quoted at the equilibrium geometry of CsS (X2Π). In the molecular region, the dominant electron configurations of the two lowest electronic states (X2Π and 12Σ+) correspond to occupation of the outermost 7σ or 3π molecular orbitals (MOs), which are mainly located on the sulfur atom, giving a Cs+S− character to these states. For the other states, the dominant configurations correspond mostly to the promotion of one electron from the 7σ or 3π MOs into the vacant 8σ or 9σ or 4π MOs, which have more Cs character, resulting in quasi covalent bonds. At medium and large internuclear distances, the wave functions of these electronic states are strongly mixed because of their mutual interactions. For instance, one can identify several avoided crossings between the states presenting the

Figure 2. MRCI+Q/aug-cc-pV5Z potential energy curves of CsS along the internuclear separation (RCsS). The reference energy is chosen to be the energy of CsS (X2Π) at equilibrium.

interesting pattern in this figure is the behavior of the 2Π and 2 + Σ states that are intercepted at long distance by the 2Π and 2 + Σ ionic states correlating to the [Cs+(1S) + S−(2P)] limit, which is the fourth dissociation limit (given in Table 1 but not shown in Figure 2). Figure 2 shows that among the electronic states correlating to the [Cs(2S) + S(3P)] lowest limit, only the ground state presents a deep potential well whereas we compute a repulsive potential (for 14Π) or small potential wells for the other states (i.e., 12Σ− and 14Σ−). For RCsS ∼ 5.75 Å, the 12Σ− state is crossed by the 12Σ+, where further interaction may

Table 2. CASSCF and MRCI+Q/aug-cc-pV5Z Vertical Excitation Energies (Tv, eV) and Dissociation Energies (De, eV) of the Lowest Electronic States of CsSa Tv

a

De

electronic state

CASSCF

MRCI+Q

CASSCF

MRCI+Q

X2Π 12Σ+ 14Σ− 14Π 12Σ− 22Π 12Δ 24Π 32Π 24Σ− 22Δ 22Σ+ 22Σ− 34Π 32Σ− 34Σ− 42Π

0.00 0.19 1.22 1.26 1.27 1.44 2.33 2.23 2.32 2.31 2.65 2.47 2.36 2.39 2.39 2.36 2.50

0.00 0.15 3.05 3.09 3.10 3.17 4.22 4.27 4.30 4.31 4.33 4.36 4.36 4.38 4.37 4.40 4.42

0.72 1.69

2.72 3.79

0.65

0.99

dominant electronic configuration (0.88)7σ2 (0.92)7σ1 (0.99)7σ2 (0.99)7σ1 (0.99)7σ2 (0.92)7σ1 (0.99)7σ1 (0.99)7σ2 (0.85)7σ2 (0.94)7σ2 (0.99)7σ2 (0.86)7σ1 (0.65)7σ1 (0.99)7σ1 (0.35)7σ1 (0.94)7σ1 (0.85)7σ1

3π3 3π4 3π2 8σ1 3π3 8σ1 3π2 8σ1 3π3 8σ1 3π3 4π1 3π2 4π1 3π2 4π1 3π2 9σ1 3π2 8σ1 3π3 4π1 3π3 4π1 & (0.35)7σ2 3π2 9σ1 3π3 9σ1 3π3 4π1 & (0.65)7σ2 3π2 9σ1 3π3 4π1 3π39σ1

In parentheses, we give the weight of the corresponding dominant configurations as quoted at the equilibrium distance of CsS (X2Π). 5356

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The Journal of Physical Chemistry A same spin and space symmetry, such as the one between the X2Π and 22Π for RCsS ∼ 6 Å and between 22Π and 32Π for RCsS ∼ 8 Å (Figure 3). These avoided crossings result in an

Figure 4. Potential energy curves of the lowest 2Σ+ states of CsS along the internuclear separation (RCsS) and their dipole moments. The reference energy is chosen to be the energy of CsS (X2Π) at equilibrium. Figure 3. Potential energy curves of the lowest 2Π states of CsS along the internuclear separation (RCsS) and their dipole moments. The reference energy is chosen to be the energy of CsS (X2Π) at equilibrium.

7.2 Å). Again, this avoided crossing is responsible for an unusual shape of the upper state. Close to equilibrium geometry of the X2Π state, examination of the dipole moment of CsS (X2Π) (Figure 3) shows that the Cs−S bond is polarized, corresponding to Csq+−Sq− polarization with a value of q close to unity. Indeed, a Mulliken population analysis shows that q = 0.75 at the MRCI level. On the contrary, for the 22Π state the bond is mostly covalent between Cs and S for this geometry. As in the X2Π state, a large dipole moment is computed for 12Σ+ (Figure 4) signature of the ionic character of the C−S bond in this electronic state. The calculation of the energies of the spin−orbit states has been performed at the MRCI+Q level, where all the vectors correlating to the three lowest dissociation asymptotes from a previous state-averaged CASSCF computation have been used for the multireference configuration interaction treatment. The MRCI+Q energies have been taken as diagonal terms in the HSO matrices instead of the MRCI energies. This ansatz accounts for 19 Λ−Σ electronic states resulting in 82 Kramers doublets corresponding to 41 fine structure states (with Ω = 1/2, 3/2, 5/2, and 7/2). Figure 5 presents the Ω PECs of CsS, in the 0−4 eV energy domain, after considering the spin−orbit interaction. Mostly, this figure displays the Ω (=1/2(5), 3/2(3), and 5/2) components arising from the X2Π, 14Σ−, 12Σ−, and

unconventional shape for the 22Π state. Instead of the usual Morse-like shape, it has a “bowl” profile with a flat region extending from RCsS ∼ 3.5 up to ∼6 Å. This potential shape is interesting from an applicative point of view. For instance, Zewail and co-workers showed that there are two limiting possibilities when a wavepacket is promoted into a potential of this kind: (i) either it is trapped on the adiabatic potential without crossing (resonance) as for NaI,37 or (ii) it jumps on the diabatic potential as for ICN.38−40 These two limiting cases give rise to different temporal evolutions. The observation of oscillations gives access to the shape of the potentials of the states and to their mutual couplings. CsS (22Π) falls in case (i) so we expect wavepacket oscillations (resonance) during the dissociation reactions. This can be confirmed experimentally using femtosecond spectroscopy. Since the X2Π-22Π excitation energy is about 3 eV, this transition occurs in the visible range for which femtosecond lasers are available in laboratories. Figure 4 shows that an avoided crossing takes place between the 12Σ+ and 22Σ+ state at large internuclear distance (RCsS ∼ 5357

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Table 3. Spectroscopic Parameters of 133Cs32S (X2Π and 12Σ+) States Calculated at the MRCI+Q/aug-cc-pV5Z Level, before and after Considering the Spin−Orbit Interactions −1

Te (cm ) T0 (cm−1) ωe (cm−1) ωeχe (cm−1) Re (Å)

X2Π

12Σ+

XΩ3/2

1Ω1/2

2Ω1/2

0 0 202.4 195.8a 1.95 0.639a 3.082 3.092a

599 608 213.2 201.9a −12.4 0.698a 2.906 2.905a

0 0 202.3 195.7a 1.84 0.595a 3.081 3.091a

307 303 200.4 197.7a 5.89 6.12a 3.077 3.088a

892 968 b 281.3a b 6.60a 2.941 2.955a

a Reference 18. bStrongly anharmonic. See Table 4 for the pattern of the vibrational levels.

Figure 5. MRCI+Q/aug-cc-pV5Z potential energy curves of the Ω states of CsS calculated after considering the spin−orbit interactions along the internuclear distance (RCsS).

14Π states, which correlate to the [Cs(2S1/2) + S(3P2,1,0)] dissociation limit, and the Ω (=1/2(2) and 3/2) components arising from the 12Σ+ and 22Π states, which correlate to the [Cs(2S1/2) + S(1D2)] one. For clarity, we have not reported in this figure the Ω (=3/2 and 5/2) components arising from the 2 Δ state, also correlated to the second asymptote, since their shapes are very regular. The most interesting feature is the avoided crossing, due to spin−orbit coupling, between the Ω = 1/2 states at ∼6 Å. This interaction results in the correlation of the Ω = 1/2 component arising from the 12Σ+ state to the lowest dissociation limit. To have a further insight into the effect of the spin−orbit interaction on the investigated states, we give as Supporting Information (Tables S1 and S2) the composition of the spin−orbit states in terms of the 82 Kramers’ doublets originating from the manifold of 19 Λ−Σ states, at RCS = 3 Å, i.e., close to the ground-state equilibrium geometry, and RCS = 6 Å. Using MRCI+Q/aug-cc-pV5Z calculations, we compute the following splittings for S(3Pj) states, S(3P2) = 0 eV, S(3P1) = 0.0495 eV, and S(3P0) = 0.0720 eV, which compare very well with the experimental splittings (i.e., S(3P2) = 0 eV, S(3P1) = 0.0491 eV, and S(3P0) = 0.0711 eV, respectively41). For the S−(2P) state, the 2P3/2−2P1/2 splitting is calculated to be 0.0609 eV (491 cm−1) with a similar approach. At low energies, Figure 2 shows that the X2Π and 12Σ+ states cross mutually in the repulsive parts of their potentials and close to the minimum of the 12Σ+ state. The spin−orbit interaction between them results in a significant modification of the Ω = 1/2 potential components, whereas the Ω = 3/2 is just pushed down with respect to the unperturbed X2Π potential. In Table 3, we can see that the splitting of the two components of the X2Π state is calculated to be 307 cm−1 at equilibrium geometry, which is coherent with the ionic character [Cs+S−] of the X2Π state and the interaction between the two Ω = 1/2 states which pushes down the 1Ω1/2 state. Figure 6 shows that

Figure 6. Enlargement of the PECs displayed in Figure 5 in the 0−1 eV energy range.

the 1Ω1/2 PEC presents an inflection point at RCsS ∼ 2.9 Å and that the 2Ω1/2 PEC exhibits a steep repulsive wall for RCsS < 2.8 Å. These spin−orbit-induced changes have an influence on the spectroscopic terms and on the vibrational energy pattern of these states. For instance, the MRCI+Q/aug-cc-pV5Z X2Π data are Re = 3.082 Å, ωe = 202.4 cm−1, and ωexe = 1.95 cm−1 (Table 3). These values are close to those derived for XΩ3/2, Re = 3.081 Å, ωe = 202.3 cm−1, and ωexe = 1.84 cm−1, whereas, large deviations between X2Π and 12Σ+ spectroscopic parameters and those of 1Ω1/2 and 2Ω1/2 are observed. This is more remarkable for the 12Σ+/2Ω1/2 sets of data. For instance, the harmonic frequency of 12Σ+ jumps from ωe ∼ 213 cm−1 up to an unreasonable value for 2Ω1/2 (of ωe ∼ 406 cm−1, not shown in Table 3), which is associated with an unphysical very large value of the anharmonic term (ωexe ∼ 57 cm−1, not shown in Table 3). These findings are in line with the analysis of Lee and Wright.18 Since there are no experimental measurements for these states, we list in Table 4 the pattern of vibrational levels for v ≤ 12 deduced from variational calculations. For 1Ω1/2 and 2Ω1/2, the spacing between adjacent vibrational levels is not regular where one can see that ΔG(1Ω1/2) decreases by ∼15 cm−1 for v ≤ 3 and then it remains unusually constant at ∼160 cm−1. For 2Ω1/2, perturbations in the pattern can be seen for the lowest levels as low as v equals 2−3. For the Ω states correlating to the [Cs(2S1/2) + S(3P2,1,0)] asymptotes, the situation is extremely complicated. Indeed, 5358

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The Journal of Physical Chemistry A Table 4. Pattern of the Vibrational Levels (E, cm−1) of XΩ3/2, 1Ω1/2, and 2Ω1/2 States of X2Π

12Σ+

XΩ3/2

Cs32Sa

133

1Ω1/2

2Ω1/2

v

E

ΔG

E

ΔG

E

ΔG

E

ΔG

E

ΔG

0 1 2 3 4 5 6 7 8 9 10 11 12

101.3 300.9 499.8 700.0 899.1 1096.7 1293.8 1490.1 1685.6 1880.5 2074.9 2268.7 2461.4

101.3 199.6 198.9 200.2 199.1 197.7 197.0 196.3 195.5 194.9 194.4 193.7 192.8

110.3 338.9 566.2 774.9 984.9 1192.1 1396.1 1599.3 1800.6 2000.4 2199.2 2396.4 2592.6

110.3 228.5 227.3 208.7 209.9 207.3 204.0 203.1 201.4 199.8 198.7 197.2 196.2

101.3 300.9 499.9 700.2 899.2 1096.9 1294.0 1490.4 1685.9 1880.9 2075.4 2269.2 2461.9

101.3 199.7 198.9 200.2 199.1 197.7 197.1 196.4 195.6 194.9 194.5 193.8 192.8

98.0 284.9 455.2 605.7 755.5 915.0 1075.0 1237.4 1401.0 1564.9 1729.8 1895.2 2060.8

98.0 186.9 170.2 150.5 149.8 159.5 160.0 162.4 163.6 163.9 164.9 165.3 165.6

178.0 494.1 762.0 1026.3 1277.9 1525.7 1768.4 2006.2 2239.7 2469.0 2694.2 2915.7 3134.0

178.0 316.1 267.9 264.3 251.6 247.8 242.7 237.8 233.5 229.3 225.1 221.5 218.3

a ΔG (cm−1) is the energy difference between two successive levels. These energies are given with respect to the energy of the corresponding minimum of each state. The calculated (MRCI+Q/aug-cc-pV5Z) absolute energies at the equilibrium geometry of each state are E(X2Π) = −417.774729 au, E(12Σ+) = −417.771998 au, E(XΩ3/2) = −417.775498 au, E(1Ω1/2) = −417.774100 au, and E(2Ω1/2) = −417.771435 au.

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several avoided crossings exist between the Ω = 1/2 components for 5.5 ≤ RCsS ≤ 6.5 Å. This results in local shallow minima. It is unlikely that these minima support rovibrational levels, but they may play a crucial role during the photodissociation of CsS. One can see also that the Ω = 3/2 PECs exhibit an avoided crossing, resulting in a flat potential well for the 2Ω3/2 state. The 1Ω5/2 PEC is repulsive. The dynamics of wavepackets promoted into these potentials should be rather complicated.

Corresponding Author

*E-mail: [email protected] (M.H.). ORCID

Gilberte Chambaud: 0000-0002-8031-2746 Majdi Hochlaf: 0000-0002-4737-7978 Notes

The authors declare no competing financial interest.

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IV. CONCLUSIONS We used post-Hartree−Fock approaches to compute the PECs of the lowest electronic states of CsS with and without considering the spin−orbit interaction. In addition to the already known X2Π and 12Σ+ states, we give for the first time reliable information on the excited states of this cesium chalcogenide including their spectroscopic parameters, excitation energies, and vibrational level patterns. We showed that these quantities are affected by spin−orbit interactions; especially we showed that additional avoided crossings and couplings between Ω states are in action. We also identified odd shapes for the upper electronic states of CsS. Wavepackets promoted into these potentials should show complex dynamics as observed earlier by Zewail and co-workers for other molecular systems.37 Finally, the present data and findings should help in the experimental identification of the CsS molecule in its ground and electronically excited states. The comparison of highly resolved spectra to our theoretical data should represent a critical test for the ab initio methodologies we used for studying this cesium chalcogenide.

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AUTHOR INFORMATION

ACKNOWLEDGMENTS The authors extend their appreciation to the International Scientific Partnership Program (ISPP) at King Saud University for funding this research work through ISPP# 0045. We gratefully acknowledge the support of the COST Action CM1405 entitled MOLIM: Molecules in Motion.

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REFERENCES

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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.8b02543. Composition of the 12 lowest spin−orbit eigenstates in terms of the 82 Kramers’ doublets arising from the 19 Λ−Σ electronic states and an input and output file of MOLPRO (PDF) 5359

DOI: 10.1021/acs.jpca.8b02543 J. Phys. Chem. A 2018, 122, 5354−5360

Article

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