Accurate ab initio potential energy curves and spectroscopic properties of the low-lying electronic states of OH− and SH− molecular anions

ABSTRACT Multireference configuration interaction method was used in order to generate accurate potential energy curves of the OH, SH, OH− and SH− electronic states correlating to the three lowest dissociation limits. These curves were used in addition with core–valence correlation and scalar relativistic corrections for the calculations of accurate spectroscopic constants of bound states, which generally are found in excellent agreement with best available experimental and theoretical values in the literature. The spin–orbit interactions between electronic states have been calculated for the cases in which the couplings were assumed to be responsible for perturbations and used to explain the predissociation of A2Σ+ state of OH and SH by dissociative states 14Σ−, 12Σ− and 1 4Π. Dipole moment functions were also computed along internuclear distances and used to explain polarity of these molecules in different calculated electronic states. In addition, stability and metastability of electronic states (X 1Σ+, A1Π and a3Π) of OH− and SH− molecular anions have been studied relatively to curves of neutral parent electronic states. Finally, we have computed adiabatic electron affinity of OH and SH and these values have been found in very good agreement with the best experimental values and resort as among the best achieved values.


Introduction
Many diatomic molecules are involved in the construction of larger molecular systems, such as triatomics or tetratomics. As such, their understanding permits better descriptions of certain physico-chemical properties of the larger molecules in which they are involved. In fact, many benchmark studies performed on diatomics, have been focused particularly on the determination of spectroscopic constants and have permitted to reach chemical accuracy, D e ∼ 1 kcal/mol, for major parts of neutral species [1]. CONTACT  However, negatively charged systems present more challenge and remain a problem to date, even for simplest diatomic anions [2], and require further computational efforts. It is important to precise that increasing interest about molecular anions go back to the last decade, where based on laboratory spectroscopic investigations, several molecular anions were detected in the interstellar and circumstellar media [3]. The discovery of these anions have accentuated theoretical and experimental investigations for a better understanding of chemical and physical properties of anions aiming at identifying other anions in these harshest environments.
As a matter of fact, many anions have been studied among which the hydroxyl anion OH − is one of the most important anions for several reasons. It is of great interest in astrophysics, atmospheric and laser chemistry [4], and has a beneficial impact on human health [5]. This anion was identified by Lee and Dateo [4] as probably the best experimentally characterised anion with high resolution of three isotopologues ( 16 OH − , 18 OH − , 16 OD − ) and therefore was an excellent candidate for theoretical investigations.
The first experimental investigation on OH − was performed in 1966 by Branscomb [6] and followed later by many other researchers [7][8][9][10][11][12]. On the theoretical side, the first relevant study was performed by Werner et al. [13] using multireference configuration interaction (MRCI) level of theory for determination of the ground state's spectroscopic constants. Later on, Lee and Dateo [4] used the coupled-cluster singles and doubles combined with a perturbative correction of triple excitations (CCSD(T)) method for a convergence study of spectroscopic constants and established accurate rovibrational data for OH − ground state. Martin [14] in a similar convergence study established that CCSD(T) has a systematic tendency to overestimate harmonic frequencies because of the neglect of quadruple excitations and scalar relativistic effects, then has used the ACPF (average coupledpair functional) method for more accurate spectroscopic constants. Very recently, Srivastava and Sathyamurthy [15] have used MRCI and have determined spectroscopic constants of the low-lying states of OH − . Nevertheless, for the ground state, their calculated value of harmonic frequency (ω e ) deviate from 97 cm −1 with respect to the recommended value (3741 cm −1 ) as proposed by Lee and Dateo [4].
Contrary to OH − molecular anion, the isovalent molecular anion SH − with a similar importance has received a poor attention. Very few investigations on this system have been registered in spite of abundant studies on sulphur containing components. This rarity could be explained by the lateness astronomical detection of the neutral parent SH [16] in 2000. To the best of our knowledge, the scarce experimental [17][18][19][20] and theoretical [21][22][23][24] studies about SH − available in the literature are limited to the ground state and performed with low level of accuracy.
In the present work, we have used MRCI+Q including Davidson correction, thanks to its size consistency, and also because it approximatively accounts for the effect of quadruple excitations, added to core-valence correlation and scalar relativistic corrections to predict accurate spectroscopic parameters of low-lying excited states of OH − and SH − molecular anions. We also intend with this ab initio investigation, to discuss the stability and metastability of these electronic states and finally to evaluate spin-orbit integrals in order to find out different pathways of conversion through spin-orbit coupling.

Computational details
Theoretical study on OH, SH, OH − and SH − diatomics consists of ab initio calculations of the adiabatic potential energy curves (PECs) of the electronic states correlating at the lowest dissociation limits. These calculations were done in C2v symmetry, and were performed using the complete active space self-consistent field (CASSCF) approach [25,26], followed by the internally contracted MRCI [27,28] and MRCI+Q [29] techniques, as implemented in the MOLPRO 2002 suite of programs [30]. In the CASSCF calculations, all electronic states having the same spin multiplicity and symmetry were averaged together using CASSCF averaging procedure. To keep the symmetry equivalence between the π x and π y molecular orbitals, states of B 1 and B 2 symmetries were averaged together. The core orbitals were frozen in all the calculations and fixed to (1, 0, 0, 0) for OH/OH − and to (2, 0, 0, 0 ) for SH/SH − . Active spaces of CASSCF wavefunctions have consisted of (5, 2, 2, 0) for OH/OH − and (7, 2, 2, 0) for SH/SH − . All configurations state functions obtained from the CASSCF wavefunctions were taken as reference for MRCI calculations.
The CASSCF wavefunctions were also used to evaluate the spin-orbit coupling matrix elements in cartesian coordinates. The CASSCF wavefunctions were used as the multi-electron basis for the two-step spin-orbit coupling calculation [31,32] at the level of Breit-Pauli Hamiltonian [33]. All the basis sets used belong to the correlation consistent Dunning and coworkers basis sets family [34] , both regular cc-pVXZ (correlation consistent polarised X-tuple zeta), and diffuse functions [35] augmented aug-cc-pVXZ (X=D(2), T(3), Q(4), 5, 6) basis sets, denoted respectively in short VXZ and AVXZ.
In addition to valence calculations, a composite approach including core-valence correlations and scalar relativistic corrections has been used. In fact, effects of inner-shell correlations or core-valence correlations, E CV were assessed by MRCI+Q calculations using non diffuse basis of Woon and Dunning [36], cc-pCVQZ (or CVQZ for short) and calculated as difference between the total energy obtained in the frozen core approximation and the total energy obtained with all electrons correlated. The scalar relativistic effects, SR have been calculated using the spin-free, one-electron Douglas-Kroll-Hess Hamiltonian (DKH) [37,38] at the second order with recontracted cc-pVQZ-DK [39] basis sets. The contribution of core-valence correlation ( E CV ) and scalar relativistic ( SR ) were used to produce corrected potential energies (E tot ) given by: (1)

Results and discussion
Till date, theoretical PECs that predict ro-vibrational energy levels and spectroscopic parameters with respective accuracies of (ν ∼ 1 cm −1 ) and (ω e ∼ 10 cm −1 ) as compared to experimental values are considered as highly accurate. It is well known that correct description of PECs is needed for a good description of spectroscopic properties (determination of predissociative and radiative lifetimes) of molecular systems. All PECs depicted in this work are obtained using MRCI+Q potential-energy values calculated as a function of the internuclear distance (R), ranging from 1.0 a 0 to 8.0 a 0 (1 bohr=1 a 0 =0.5291171 × 10 −10 m ) using VXZ and AVXZ basis sets.

Potential energy curves of OH and SH neutral species
The comparison of theoretical and experimental data for neutral species is useful for judging the accuracy of the present computational approach for the so-far unknown states of their ionic counterparts. The neutral radicals SH (mercapto radical) and OH (hydroxyl radical) are isovalent radical species and are of similar importance with their anionic counterparts. Electronic structure calculations reveal equivalent electronic structure for OH [40][41][42][43][44] and SH [45][46][47][48][49][50]. For these neutral species, we have restricted our investigations to five lowest electronic states : the bound electronic states, X 2 and A 2 + and the repulsive states 1 4 − , 1 2 − and 1 4 , correlating all to the two lowest dissociation limits of OH and SH. Roughly, no particular difference is observed between PECs calculated with the AV6Z and V6Z basis sets for neutral species (see  in Supporting information (SI)). Nevertheless, for 1 4 , 1 2 electronic sates of OH calculated at the MRCI+Q/AV6Z level of theory, we observe a small hump around of 2.0 a 0 similarly to PECs obtained by Ref. [42], for which the authors postulated that this hump is due to avoided crossing with higher ionic states. This irregularity is corrected for PECs calculated at the MRCI+Q/V6Z level of theory similarly to Ref. [44], which illustrated that this hump is due to the computational procedure, hence led us to use VXZ basis kind for OH investigations. In the same way, the small hump observed (around 2.4 a 0 ) for 1 2 and 1 4 of SH in Refs. [45], [47] and [48] is absent in our work. As illustrated by this work (see  in SI) and previous

Species
Dissociative atomic/ionic states Electronic states theoretical works, electronic ground states of OH and SH do not cross any upper electronic states and consequently have not perturbed rovibrationals levels. In contrast, the A 2 + electronic states are predissociated by 1 4 − , 1 2 − and 1 4 .

Potential energy curves of OH − and SH − molecular anions
PECs of low-lying states correlating to the three lowest dissociation limits of OH − and SH − molecular anions as presented in Table 1 are computed in the same computational approach applied to neutral species. Contrary to PECs obtained for OH and SH, the nature of OH − and SH − PECs is strongly dependent on the basis sets used. For the sake of clarity of the figures, we choose not to represent electronic states correlating to the second and third dissociation limits of OH − and SH − anions, because of strong mixing between them due to couplings (spinorbit and vibronic) and avoided crossings which complicate their study. In the following lines, calculations were restricted to spectroscopic constants of electronic states, X 1 + , A 1 and a 3 correlating to the first dissociative limit of OH − and SH − anions. Use of VXZ and AVXZ basis sets for A 1 and a 3 electronic states of OH − leads to the same shape of curves as presented in Figures 1 and 2. However, deeper wells are observed for augmented basis sets. For SH − , the nature of PECs of A 1 and a 3 is strongly affected by basis sets used as depicted in Figures 3 and 4.   In fact, for non-augmented basis sets, the PECs of a 3 and A 1 electronic states have a very shallow minima which cannot support any vibrational levels and become weakly bound for augmented basis sets.
Regarding basis sets dependence of electronic states of OH − and SH − molecular anions, the polar nature of anions and to respect of electronic equivalence between OH − and SH − , using of largely augmented basis sets appears to be the most indicated for investigations of these anions. Thus, a convergence study has been carried out using AVXZ (X=D, T, Q, 5, 6) and have established AV5Z as the more adapted basis sets, giving correct dissociation limits and accurate spectroscopic constants.

Spectroscopic constants of OH and SH
Spectroscopic parameters of bound states presented in this work were computed from the derivatives of the potential at their respective minima. Equilibrium bond distance (R e ), harmonic wave numbers (w e ), anharmonic terms (w e x e and w e y e ), rotational constants (B e and α e ), vibrational quanta ν = G(1) − G(0) and the adiabatic excitation energy (T e ) are calculated using the Numerov method [51]. The dissociation energy (D 0 ) have been calculated in the supermolecular approach from vibrational level (ν = 0) to the adiabatic dissociation limit within the internuclear distance fixed at 10.0 a 0 . The classical dissociation energy (D e ) have been calculated using the approximation : Despite the large number of experimental and theoretical studies on X 2 and A 2 + electronic states of OH and SH, accurate data are rather limited, and achieving accuracies of the order ν ∼ 1 cm −1 and ω e ∼ 10 cm −1 are scarce, particularly for A 2 + , due principally to predissociation process of lowest vibrational levels [48]. Computed molecular parameters of these electronic states are collected in Tables 2-5 including also experimental and theoretical values available in the literature for comparison.
In the previous section, it was established that nonaugmented basis sets (VXZ) are recommended for OH and by extrapolation to SH PECs. Thus, we have used MRCI+Q/V6Z level of theory for the determination of their molecular parameters. Both core-valence correlations and relativistic corrections are used for SH case and only the relativistic correction is used for OH.
The spectroscopic constants of OH ground state X 2 are reported in Table 2 and attest of excellent quality of our results. As presented in this table, available experimental results have existing differences and to assess the accuracy of our computational approach, the best experimental results have to be fixed. Here, reference experimental results (R e =1.8516 a 0 , w e =3737.7024 cm −1 , w e x e =84.8245 cm −1 , w e y e =0.51862 cm −1 ) are taken from Ref. [52] and matched to our best computed values obtained with inclusion of scalar relativistic effects. The deviation of the calculated equilibrium distance (R e =1.8339 a 0 ) from experimental ones is less than 1%. The calculated value of harmonic wave numbers (w e =3737.564 cm −1 ) is perfectly achieved within 0.14 cm −1 (3.7 x 10 −3 %) of fixed experimental value. For the rest of computed spectroscopic parameters, a similar order of precision is observed, w e x e (1.05%), B e and    α e (0.37%) [62]. It is important to note that, inclusion of scalar relativistic corrections weakly affect R e (0.0003 a 0 ), w e (3.6 cm −1 ) and w e x e (0.015 cm −1 ) and is necessary for accurate spectroscopic constants of OH's ground state.
In the same way, the calculated spectroscopic parameters of A 2 + state of OH are also accurately described and reported in Table 3. The relative differences between our calculated values using only MRCI+Q/V6Z level of theory and experimental results are 0.26%, 0.02% and 9.82%, respectively, for R e , w e and w e x e [53,65]. Comparison of these weak relative difference to other theoretical works erects our values to the best available theoretical result. Contrary to the ground state, inclusion of scalar relativistic effect slightly increase deviation compared to reference experimental values. It is, therefore, not necessary to include scalar relativistic correction for this excited state.
For the mercapto radical, the paper of Resende and Ornellas [48] is recommended for detailed discussion on spectroscopic parameters of X 2 and A 2 + electronic states. As reported in Table 4, our computed constants of X 2 (SH) including scalar relativistic and core-valence corrections appear as the best achieved till date. In fact, for w e our value differ to the best experimental value (w e =2696.  [47] of other theoretical works, we note the best agreement for this work. The same agreement is observed for the first anharmonic term, w e x e =48.74cm −1 [70] within 2.67 cm −1 of discrepancy. The other theoretical works as presented in Table 4 have greater discrepancies. The experimental equilibrium bond length (R e =2.5336 a 0 ) [70] is reproduced within 0.001a 0 of deviation and is also to our knowledge the best accurate theoretical value till date.
As also pointed out by Ref. [48] and  [47] for (w e , w e x e ). In spite of worst result for w e x e in the same order of precision that of Ref. [46], we obtain the best agreement for w e . The inclusion of scalar relativistic and core-valence corrections increases the deviation for SH (A 2 + ) spectroscopic constants (approximately 64.6 cm −1 of difference for ω e ) comparatively to OH (A 2 + ).
To conclude, one can say from a general point of view that all computed constants for OH and SH are well described. The registered deviations are very weak ( < 1 % ) and this attest of the high quality of our results. In addition, it is important to note that inclusion of additional corrections do not improve spectroscopic constants of excited states and will not be used for investigations of the excited states of anions.

Spectroscopic constants of OH − and SH −
Spectroscopic constants of electronic bound states of OH − and SH − , X 1 + , A 1 and a 3 presented in this section are computed in the same computational approach used for neutral counterparts. For the OH − ground state, reference experimental values (R e =1.8225 a 0 , w e =3741.0 cm −1 , w e x e =93.81 cm −1 , ν=3555.6057 cm −1 ) presented in Table 6 are taken from Refs. [4,14] and may be considered as the most reliable up to now. We also observe for OH − that inclusion of scalar relativistic correction gives the best agreement with experimental values. The deviations from experimental values are of 0.0004 a 0 , 0.290 cm −1 , 0.364 cm −1 and 1.269 cm −1 , respectively, for R e , w e , w e x e and ν, and attest also of the high accuracy of our computational approach. These accurate data obtained led us to hope the same order of precision for spectroscopic constants of OH − excited states, A 1 and a 3 collected in Table 7. As experimental values of A 1 and a 3 excited states are not available yet, we compare our values to scarce theoretical values and expect the more accurate values for this work.
The comparison of SH − computed spectroscopic constants with the available experimental molecular constants [19] is presented in Table 8. A very good agreement is observed, especially if we include uncertainties. Our values computed at the MRCI+Q/AV5Z level of theory are in error by 0.0072 a 0 , 17.142 cm −1 and 0.091 cm −1 , respectively, for R e , w e and B e . The calculated values with inclusion of core-valence and scalar relativistic corrections differ by 0.0272 a 0 , 28.29 cm −1 and 0.208 cm −1 ,  respectively, for R e , w e and B e . The rarely available theoretical values in the scientific literature show equally a good agreement with our values. Concerning the excited states of SH − anion, we have performed for the first time the computations of spectroscopic constants and the values are presented in Table 9.
Touching comparison of electronic structure of SH (X 2 )/SH − (X 1 + ) and OH (X 2 )/OH − (X 1 + ) systems, we observe the same behaviour for both systems. In fact, the difference between both harmonic frequencies (w e ) of SH and SH − ground states is about 3.8 cm −1 in the same magnitude with 3.3 cm −1 obtained between OH and OH − ground states.

Spin-orbit couplings and dissociation process
It is known that the fast nonradiative decay processes operating in A 2 + electronic states of OH and SH neutral species complicates the experimental studies and justifies the abundant and discordant results obtained either theoretically or experimentally. To respond to the need of further theoretical and experimental investigations on A 2 + of OH and SH, we discuss in this section on crossing between A 2 + and 1 4 − , 1 2 − and 1 4 through spinorbit coupling, which is one of the main mechanisms of predissociation.
From Figure 1, one can see that our A 2 + (OH) curve crosses the 1 4 − curve at R= 2.809 a 0 and at 5.443 eV, above the ground state minimum. The A 2 + crosses also the 1 2 − and 1 4 at 2.975 a 0 and 3.078 a 0 , respectively, at 5.698 eV and 5.832 eV above the minimum of the ground state. A very good agreement is observed with theoretical values (2.773 a 0 , 2.962 a 0 and 3.045) of Yarkony [75].
For SH molecule as depicted in Figure 3, the crossing between A 2 + and 1 4 − is produced at R=3.3357 a 0 and at 4.207 eV above of the ground state minimum. For 1 2 − and 1 4 , the crossings occur at R=3.6687 a 0 and at 4.452 eV for the doublet state and at 3.938 a 0 with weakly higher relative energy equal to 4.571 eV for the quartet state. Our crossing points agree very well with the most recent work of Resende and Ornellas [48] who has predicted crossing points at, respectively, 3.319 a 0 , 3.683 a 0 and 3.931 a 0 . The older results (computed with lower computational levels) by Manaa (3.24 a 0 , 3.59 a 0 and 3.86 a 0 ) [47], Bruna and Hirsch (3.10 a 0 , 3.50 a 0 and 3.80 a 0 ) [46] and Senekowitsch (3.10 a 0 ) [22] have predicted shorter values compared with this work.
To establish the effectiveness of several predissociations listed above, the spin-orbit couplings between these electronic states must have non-zero values. We have computed values of spin-orbit couplings at the respective crossing points for OH and SH molecular systems. These spin-orbit couplings have been performed throughout this work at the CI/VQZ level of theory. To assess the accuracy of our computational approach, the spin-orbit splitting (A e ) of X 2 electronic state for OH and SH have been computed and presented, respectively, in Tables 3 and 5, together with their comparisons with previous theoretical and [70]. Compared with other theoretical values, −390.8 cm −1 [46], −331.6 cm −1 [47] and −340.7 cm −1 [48], we have the best achieved value to date. In the same way, we have computed A e =−153.25 cm −1 for OH (X 2 ) and expect the same precision.
To compare and assess the accuracy of OH (X 2 ) spin-orbit splitting, we have also computed this value at R=10.0 a 0 and found it equal to 98.81 cm −1 in very good agreement with previous works which established its asymptotic limit to 100 cm −1 [15,76,77]. With regard to spin-orbit couplings, we note for OH that the spin-orbit coupling between A 2 + and 1 4 − at crossing point has an absolute value around of 31.32 cm −1 , sufficiently large to allow predissociation of A 2 + by 1 4 − . Similarly, crossing between A 2 + and 1 2 − on one side and A 2 + and 1 4 on the other hand gives values of spin-orbit couplings equal, respectively, to 26.34 cm −1 and 46.70 cm −1 . These values are large enough to allow predissociation. For the SH case, the spin-orbit couplings between the A 2 + and the three repulsive states 1 4 − , 1 2 − and 1 4 are, respectively, given by 51.66 cm −1 , 56.13 cm −1 and 127.13 cm −1 at their crossing points. One can see that spin-orbit couplings between A 2 + and 1 4 − or 1 2 − and 1 4 are high enough to allow these predissociations. Thus, one can say similarly to previous studies [75,76] that, the predissociation by spin-orbit couplings of higher vibrationnal levels of A 2 + (OH and SH) is more faster for them than lower vibrationnal levels.

Stability, metastability and dipole moment functions
To obtain electronic states of anionic systems, an electron should be attached on one orbital of neutral parent state. The molecular configuration orbital for the ground state, X 1 + of the both OH − and SH − molecular anions are obtained by attachment of an electron on the (1π) orbital of the neutral's ground state X 2 . The states of different spin-multiplicity A 1 and a 3 for OH − and SH − have the same molecular configuration obtained by electron attachment either on (4σ ) or (8σ ) molecular orbital of the neutral parent state X 2 , respectively, of OH and SH. These configurations and their respective weights are collected in Table 10.
Stability and metastability of anionic electronic states are evaluated according to some criteria. (1) The electron affinity with respect to the neutral parent state should be positive. (2) The radiative depletion by spin forbidden autodetachment for at least one of the fine structure components should be very slow. (3) The interaction between electron continuum wave and the wave function should be weak. In respect to enumerated criteria, only the X 1 + electronic states of OH − and SH − are stable. In the molecular region (Franck-Condon region), PECs of A 1 and a 3 of the both OH − and SH − molecular anions lie above their neutral parent states and therefore cannot be metastable. However, at long-range part, these PECs lie below their neutral parent states and so they exist at these long-distances. In addition, due to  Breit-Wigner resonances where anion excited states are buried in the continuum of neutral molecule plus free electron (NMFE) system, the OH − and SH − molecular anions in their excited electronic states could be qualified as NMFE [2,15]. The dipole moment functions of the studied electronic states of neutral species (OH and SH) and their ionic counterparts (OH − and SH − ) are calculated along the internuclear distances and drawn, respectively, in Figures 5 and 6. The dipole moment functions are very important tools to study polarity of molecules in its electronic states and to evaluate the intensities of electronic transitions. From Figure 5, we note similar curves between the both isovalent neutral species, with larger values around 0.9 Debye for OH. We also observe similar shape of curves with the previous work of Yoshimine and Liu [62] concerning the OH radical. The calculated and positive values of Figure 5 are represented in the direction O − − H + and S − − H + . Thus, for X 2 and A 2 + of OH and SH, we note a covalent character for bond length greater than to 5.0 a 0 with dipole moment values close to zero. For bond length fixed between 1.0 a 0 and 5.0 a 0 , we note positive fluctuations of calculated dipole moments values due to crossings with higher electronic states. These fluctuations with maximum fixed around of 3.0 a 0 characterise an ionic nature for these electronic states and a large electronic density on oxygen atom (O).
In the case of ions, it is well known that the choice of the origin has an impact on the accuracy of the computed values of the dipole moment. So, one should carefully fix this origin. In a benchmark study on a series of 17 hydride cations, Cheng et al. [78] have shown that taking the origin at the centre of mass of the molecular ion leads to accurate dipole moments, and the obtained values may be positive or negative depending on the molecular ion of interest. In the present calculations, the origin has been fixed at the centre of mass. For the electronic states of OH − and SH − under investigation, we note a fluctuation of the computed dipole moment functions with internuclear distance as depicted in Figure 6. In the bound region, all these anionic electronic states have negative values of the dipole moment, which show that negative charge is located on hydrogen atom for these electronic states in this region. With increasing R, the supplemental charge is progressively shifted towards the oxygen (O) (or sulfur (S)) atom, except for the a 3 state of OH − which have large negative values at the long-range parts.
Furthermore, the absolute values of calculated dipole moments of anionic electronic states are larger than those of the neutral electronic states. These larger dipole moment values confirm that anionic electronic states have more pronounced polar nature as compared with neutral electronic states.

Adiabatic electron affinity of OH and SH
The adiabatic electron affinity (AEA) is obtained by subtracting the energies of neutral and its corresponding anion at their respective equilibrium geometries, including the zero-point vibrational energy correction. To obtain more accurate values of electron affinity, we  also included spin-orbit energy correction calculated as the half of spin-orbit splitting and the correction on computational approach, obtained by the difference between calculated and experimental values of the electron affinity of oxygen (O) and sulfur (S) atoms, respectively, for OH and SH. The final values of the AEA obtained for OH and SH are collected in Table 11 and compared with previous experimental and theoretical works. For OH, the obtained direct calculation of electron affinity at the MRCI+Q/AV5Z level of theory gives 1.783 eV. If we compute the electron affinity of O at the same level of theory, we obtain a value of 1.443 eV, which is in error by 0.018 eV compared to the experimental value 1.4610 eV [57]. The half of spin-orbit splitting 153.25 cm −1 (76.3 cm −1 ) increase the AEA's energy by 0.00946 eV. Considering these two corrections, we obtain the final value of electron affinity around of 1.811 eV in very good agreement with the best experimental value 1.82765 eV [12]. The dispcepancy is about 1.646 x 10 −2 eV, a very weak deviation corresponding to 0.91 %. Compared with previous computed AEAs, our value turn out to be among the best achieved theoretical work.
Concerning SH, the calculated AEA using MRCI+Q/AV5Z level of theory is 2.175 eV. The computed electron affinity of S atom at the same level of theory deviates by 0.06 eV as compared with experimental value 2.017 eV [57]. Adding the spin-orbit energy correction equal to 0.023 eV to the two previous computed values gives the final calculated value of 2.26 eV. This value is in very good agreement with the only one experimental value 2.33 eV [20] known to be the best value to our knowledge. The absolute error is of 0.07 eV or 3.1% of relative error. In addition, comparison with previous theoretical works, establish clearly our value as the best achieved up to date.
Moreover, the weak discrepancies of the AEAs of OH (and perhaps of SH), observed between experimental values on one hand and theoretical ones on the other hand, may be due to the non-consideration of the rotational zero-point energy (RZPE) as mentioned in Stanton and coworkers' work [88].

Conclusions
Highly correlated ab initio methods completed with large basis sets have been used to compute accurate PECs for the low-lying states of OH, SH, OH − and SH − correlating at the first three (03) dissociation limits. These computed PECs corrected by core-valence correlation energies and scalar-relativistic energies have been used to determine accurate spectroscopic constants of bound states. Spinorbit coupling functions have also been computed and used to explain predissociation of first excited states of neutral species. Our calculations permitted us to test the accuracy of some selected basis sets on OH, SH, OH − and SH − . It turns out from the calculations performed on neutral species OH and SH that non-augmented basis sets are recommended, while basis sets supplemented with diffuse functions are necessary for accurate description of OH − and SH − thanks to their strong polar nature. In addition, the computed positive electron affinities of OH and SH, which are found in very good agreement with experimental values, confirm the stability of the ground states of OH − and SH − anions. The metastability of excited states was discussed based on the configurations and the relative positions of the PECs of OH − and SH − with respect to those of the corresponding neutral parent states. This work reveals also that the anionic isovalent molecules OH − and SH − have similar behaviour and the same magnitude of electronic states.