#
Ab Initio Approach to the Structure, Vibrational Properties, and Electron Binding Energies of H_{2}S∙∙∙SO_{2}

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}S∙∙∙SO

_{2}. The analysis of vibrational frequencies reveals an intramolecular vibrational energy transfer phenomenon, where energy from the stretching modes of H

_{2}S is transferred to the ν1s mode of SO

_{2}. At the CCSD(T)/aug-cc-pVQZ level, the interaction energy between H

_{2}S and SO

_{2}is predicted to be 2.78 kcal/mol. Electron propagator theory calculations yield a HOMO–LUMO gap of 8.24 eV for H

_{2}S∙∙∙SO

_{2}. Furthermore, by utilizing ab initio results for the adiabatic ionization energy and electron affinity, the electrophilicity of H

_{2}S∙∙∙SO

_{2}is estimated to be 2.01 eV. This value is similar to the electrophilicity of SO

_{2}, suggesting comparable reactivity and chemical behavior. The non-covalent interaction (NCI) analysis of the H

_{2}S∙∙∙SO

_{2}complex emphasizes the significant contribution of non-covalent van der Waals interactions in its energetic stabilization.

## 1. Introduction

_{2}) and other acidic pollutants into the atmosphere, which react with water vapor to form sulfuric acid (H

_{2}SO

_{4}) and other acids [1,2,3,4,5,6,7]. The natural pH of rain is close to 5.5. However, acid rain has a substantially lower pH, reaching 4.4. The low pH of this type of rain can cause structural problems in buildings and severe environmental damage, especially in primarily aquatic ecosystems [8].

_{2}emission [10,11,12,13]. Volcanoes, power plants, smelters, and the oil and gas industry are the primary sources of SO

_{2}[14]. H

_{2}S primary emission comes from organic matter in swamp areas [15,16]. Processes involving desulfurization reactions, such as the Claus reaction, are used to convert sulfur-based gases, such as H

_{2}S and SO

_{2}, into elemental sulfur. The reaction typically proceeds as follows:

_{2}S to SO

_{2}and the second reaction is a gaseous reaction between H

_{2}S and SO

_{2}to form the expected product. However, the second reaction can be processed to form S

_{2}O and H

_{2}O so that two new side reactions can start to occur [17]:

_{2}S∙∙∙SO

_{2}reagents, contrary to what would be expected to move to H

_{2}O∙∙∙S

_{2}O [17].

_{2}S and SO

_{2}as well as the associated energetics involved in forming the H

_{2}S∙∙∙SO

_{2}complex. This understanding is particularly significant due to the influence of H

_{2}S∙∙∙SO

_{2}in atmospheric chemistry and industrial contexts [17].

_{2}S∙∙∙SO

_{2}, there is evidence suggesting that the interactions occurring in this system are primarily associated with S∙∙∙S chalcogen–chalcogen interactions [23,24,25,26]. These interactions play a crucial role in determining the stability and behavior of the H

_{2}S∙∙∙SO

_{2}complex, highlighting the significance of studying these specific intermolecular interactions at a molecular level.

_{2}S∙∙∙H

_{2}S, SO

_{2}∙∙∙SO

_{2}, and H

_{2}S∙∙∙SO

_{2}. These methods allow for determining interaction energies and the distribution of electronic density [21,27]. On the other hand, CCSD(T) (Coupled Cluster with Single and Double excitations and Triple excitations corrections) can be utilized to obtain data related to the transfer of electron density between atoms, as well as the energies involved in the process and the geometry of the system. Notably, a high degree of accuracy is observed in the calculated energies when compared with experimental data [21,23,28]. An example is the recently reported results for H

_{2}S∙∙∙H

_{2}S, where CCSD(T) results agree with the geometry and vibrational frequencies [21]. These computational methods provide valuable insights into the electronic structure, energetics, and geometries of H

_{2}S∙∙∙H

_{2}S, SO

_{2}∙∙∙SO

_{2}, and H

_{2}S∙∙∙SO

_{2}dimers, aiding in the understanding of their properties and behavior.

_{2}S∙∙∙SO

_{2}, particularly the energies of the frontier orbitals. These frontier orbitals play a significant role in ionization and electron attachment processes. By studying the energies of these orbitals, valuable information can be obtained regarding the reactivity and chemical behavior of the H

_{2}S∙∙∙SO

_{2}system. Understanding the electronic properties and the energetics of the frontier orbitals provides insights into the potential for ionization or electron attachment events, which are relevant for various chemical and environmental processes involving H

_{2}S∙∙∙SO

_{2}. In this context, electron propagator theory (EPT) is reliable for obtaining accurate orbital energies. A detailed review on the methodology and applications of EPT was provided by Ortiz [29].

_{2}S∙∙∙SO

_{2}system. This aim is achieved by employing high-level ab initio methods, specifically CCSD(T) and EPT. Some emphasis was placed on the calculation of reactivity indexes such as the chemical potential, hardness, and electrophilicity, which are closely related to the ionization and electron attachment processes [30].

## 2. Results and Discussion

#### 2.1. Structure, Vibrational Frequencies, and Rotational Constants

#### 2.1.1. Structure

_{2}S∙∙∙SO

_{2}is illustrated in Figure 1. The complex is stabilized by SS chalcogen–chalcogen interaction. Additional O∙∙∙H interactions should also be considered. The O∙∙∙H distances observed in H

_{2}S∙∙∙SO

_{2}are in the range of approximately 3.1–3.3 Å, as shown in Table 1. These distances fall on the upper side of the typical hydrogen bond range, which is generally between 2.3–3.3 Å.

_{2}S∙∙∙SO

_{2}relying on different methods and basis sets are gathered in Table 1. Additional data for geometric parameters are reported in the Supplementary Material Tables S1–S3.

_{2}plane and the SS line, while φ represents the angle between the H

_{2}S plane and the SS line. Our calculated values of angle θ are smaller than the experimental values reported by Kukolich et al. [26]. One possible explanation is that their values were obtained through a fitting procedure involving rotational constants and different fittings were proposed in their work [26].

_{2}S and SO

_{2}fragments with those in H

_{2}S∙∙∙SO

_{2}, it is observed that most of the changes in bond lengths and valence angles are primarily associated with the SO

_{2}fragment. The SO

_{2}fragment exhibits more significant changes in distances and angles compared with the relatively smaller changes observed in H

_{2}S.

_{2}S∙∙∙SO

_{2}complex compared to the monomer values are smaller than 0.2%. Similarly, the variations in the HSH angle for H

_{2}S in the complex are less than 0.3%. For the SO

_{2}fragment, the variations in bond lengths are below 0.08% and the angle variation is within 0.6% when comparing the complex to the monomer values. Indeed, the results obtained from MP2 calculations strongly suggest that the structural changes in the H

_{2}S∙∙∙SO

_{2}complex, when compared to the isolated H

_{2}S and SO

_{2}molecules, are minimal. This indicates that the interaction between H

_{2}S and SO

_{2}does not significantly alter the overall geometry of the individual molecules. These findings provide valuable insights into the nature of the H

_{2}S∙∙∙SO

_{2}complex and its molecular behavior.

_{2}S∙∙∙SO

_{2}complex regarding the monomer-optimized geometry. The difference in the interatomic distances is smaller than 0.0021 Å for the distances and 3.5° for the angles. In general, the interatomic distances show the same trend for all methods. The MP2 r(SH) and r(SO) are closer to the CCSD(T) values than CCSD. Both HS and SO distances are slightly increased (almost 0.001 Å) in relation to the monomer distance, except MP2/AVDZ for the SO distance. Therefore, both bonds have weakened.

_{2}S∙∙∙H

_{2}S complex, the H

_{2}S∙∙∙SO

_{2}complex has received much less attention in studies reported in the literature, and the geometry and energies have fewer estimates. Despite the minor variations in bond distances and angles concerning the 1990 experimental data of Kukolich [26], the results of all correlation-consistent basis sets show reliability and are in better accordance than the theoretical results of the literature. Therefore, comparing with the experimental bond distance and angles, the useful geometric data obtained with CCSD(T)/aug-cc-pVTZ and CCSD(T)/aug-cc-pVQZ are suitable estimates for this complex and can be taken as a reference calculation.

#### 2.1.2. Vibrational Frequencies

_{2}S and SO

_{2}have a gap between symmetric (ν$1\mathrm{s})$ and antisymmetric (ν$1\mathrm{a})$ modes. Here, for both HS and SO stretching, we will define a parameter δ as ν1a-ν1s to represent the gap between the antisymmetric (ν1a) and symmetric (ν1s) stretching frequencies.

_{2}S and SO

_{2}. Vibrational frequencies (in cm

^{−1}) for the antisymmetric ${\mathsf{\nu}}_{1\mathrm{a}}$ and symmetric ${\mathsf{\nu}}_{1\mathrm{s}}$ stretching modes in H

_{2}S∙∙∙SO

_{2}are reported in Supplementary Material Table S4.

_{2}S, the deviations from experimental data are positive and relatively small, with values less than 10 cm

^{−1}. The results obtained from the CCSD method show better agreement with the experimental values.

_{2}, the vibrational results obtained from the MP2 method are in good agreement with the experimental data. However, the CCSD and CCSD(T) methods underestimate the gap between the symmetric and antisymmetric stretching frequencies for SO

_{2}. It should be observed that δ for SO

_{2}presents the most significant deviations from the experimental data. Among various other sources to enhance confidence, a possible explanation for the observed differences could be the importance of including additional d functions in the calculation for studying structures and frequencies involving sulfur atoms [32,33]. As reported in the literature, including extra d functions can improve the accuracy of the estimates and better capture the electronic behavior of sulfur-containing molecules [32,33,34,35].

_{2}S∙∙∙SO

_{2}. This agreement supports the accuracy of the currently employed ab initio methods in predicting the properties of these molecules. The impact of spin contamination regarding the formation of the H

_{2}S∙∙∙SO

_{2}complex has been explored. The multireference T1 diagnostic, as defined for the CCSD wave function, is the Frobenius norm [36] and is used to establish the single-reference quality. The T1 diagnostic of CCSD/aug-cc-pVQZ is less than 0.018, which suggests that a single reference is probably enough for this system (values smaller than 0.02). As an alternative, the percentage of the molecular total atomization energy (%TAE

_{e}[(T)]) is of practical use to assess the nondynamic correlation and the reliability of single reference calculation [37,38]. For the aug-cc-pVQZ basis set, %TAE

_{e}[(T)] is less than 4.3%, which leads to confidence in using a single reference [39].

_{2}S and SO

_{2}in H

_{2}S∙∙∙SO

_{2}can be related to the difference between the vibrational frequencies in the complex and monomers. Table 3 reports results for $\u2206\nu \equiv {\nu}_{H2S-SO2}-{\nu}_{X}$, where X = H

_{2}S, SO

_{2}.

_{2}S, both the antisymmetric stretching frequency (ν1a) and symmetric stretching frequency (ν1s) are red-shifted in the complex compared to the monomer. The CCSD method predicts smaller values for these frequencies while MP2 yields larger values. Regarding SO

_{2}, the antisymmetric stretching frequency (ν1a) is also red-shifted in the complex. Interestingly, the symmetric stretching frequency (ν1s) is blue-shifted, meaning it is shifted to higher frequencies compared to the monomer. The observed result suggests that an intramolecular vibrational energy transfer occurs upon complex formation [40,41]. This process involves the transfer of vibrational energy from the stretching modes of H

_{2}S to the ν1s mode of SO

_{2}. Due to this energy transfer, the antisymmetric stretching frequency of H

_{2}S undergoes a red-shift, while the symmetric stretching frequency of SO

_{2}experiences a blue-shift. This phenomenon highlights the dynamic interplay and energy exchange between the vibrational modes of the molecules within the H

_{2}S∙∙∙SO

_{2}complex.

#### 2.2. Interaction Energies and Electronic PropertiesInteraction Energies

_{2}S and SO

_{2}in H

_{2}S∙∙∙SO

_{2}was computed using this minimum geometry and is defined as

_{2}S) and E(SO

_{2}) are calculated at the geometry of the H

_{2}S∙∙∙SO

_{2}complex. Basis set superposition errors (BSSE) due to finite basis set effects were corrected using the counterpoise (CP) method, where the energies of the fragments are calculated with the same basis set of H

_{2}S∙∙∙SO

_{2}. The corrected ${\mathsf{\Delta}E}_{I}\text{}$is represented as ${\mathsf{\Delta}E}_{I}$(CP) in Table 4.

_{2}S∙∙∙SO

_{2}of 1.7 kcal/mol, interaction energy data are apparently not available in the literature. In the absence of precise values for the interaction energy of H

_{2}S∙∙∙SO

_{2}, it is worth noting that a DFT study [42] reported an interaction energy of 5.86 kcal/mol for the H

_{2}O∙∙∙SO

_{2}system. This finding predicts stronger binding energy compared to the H

_{2}S∙∙∙SO

_{2}interaction, which is the expected result.

#### 2.3. Electronic Properties

#### 2.3.1. Electron Binding Energies and Reactivity Parameters

_{2}S, SO

_{2}, and H

_{2}S∙∙∙SO

_{2}. ∆E(CCSD) calculations were performed to account for relaxation effects during ionization or electron attachment processes, predicting adiabatic IEs and EAs. The estimates include zero-point vibrational energy (ZPVE) corrections at the MP2/AVTZ level.

_{2}S from the outer valence Green’s function (OVGF) method, which is 10.448 eV, is in excellent agreement with the experimental value of 10.453 ± 0.008 eV. This IE corresponds to the highest occupied molecular orbital (HOMO) energy in H

_{2}S. Furthermore, based on the results obtained for the electron affinities (EAs) of H

_{2}S, no significant electron attachment is expected to occur for this species.

_{2}were reported by Pawlowski and Ortiz [43]. Our calculations using the outer valence Green’s function (OVGF) method yield very good agreement with their reported values and the experimental value of 12.349 eV [44]. The vertical and adiabatic ionization energies of SO

_{2}are 12.619 eV and 12.537 eV, respectively, which closely match their results of 12.614 eV and 12.427 eV. The electron affinity calculation places the LUMO energy of SO

_{2}at 0.73 eV, resulting in a HOMO–LUMO (HL) gap of 11.9 eV. The adiabatic electron affinity obtained from ∆E[CCSD] calculations is 1.267 eV, which is in good agreement with the experimental value of 1.14 ± 0.05 eV reported by Rothe in 1975 [45] and 1.107 ± 0.008 eV reported by Nimlos in 1986 [46].

_{2}S-SO

_{2}, the OVGF results for the vertical ionization energy and electron affinity are 10.619 eV and 0.609 eV, respectively, leading to a HOMO–LUMO gap of 8.24 eV. The corresponding adiabatic values from ∆E[CCSD] calculations are 9.873 eV and 1.637 eV. Unfortunately, we are not aware of any experimental results for the ionization energy and electron affinity of H

_{2}S∙∙∙SO

_{2}.

**Table 5.**Ionization energies and electron affinities (in brackets). EPT/AVQZ calculations were carried out with CCSD/AVTZ-optimized geometries. Adiabatic values rely on CCSD/AVQZ//MP2/AVTZ calculations. Values in eV.

Vertical | Adiabatic | |||
---|---|---|---|---|

KT | OVGF | P3+ | $\u2206\mathbf{E}$ [CCSD] | |

IE [EA] | IE [EA] | IE [EA] | IE [EA] | |

H_{2}S (a) | 10.487 [−0.682] | 10.448 [−0.507] | 10.328 [−0.485] | 10.343 [−0.468] |

SO_{2} (b) | 13.560 [−0.069] | 12.619 [0.730] | 12.751 [0.792] | 12.537 [1.267] |

H_{2}S-SO_{2} | 10.144 [0.111] | 10.129 [0.979] | 9.929 [1.043] | 9.873 [1.637] |

_{2}S-SO

_{2}. The HOMO exhibits a localized S p-orbital primarily confined to the H

_{2}S fragment. On the other hand, the complex structure of the LUMO demonstrates spatial delocalization and p-d orbital mixing, primarily involving the SO

_{2}moiety.

_{2}electrophilicity, the deviation from experimental results is less than 0.2 eV, indicating good agreement. Additionally, the electrophilicity value for H

_{2}S∙∙∙SO

_{2}(4.227 eV) is quite similar to the one predicted for SO

_{2}, suggesting that the electron flow from the environment to H

_{2}S∙∙∙SO

_{2}is mainly determined by the SO

_{2}fragment. Fukui functions are depicted in Figure S1 and show the same trend of electrophilicity.

#### 2.3.2. Electrostatic Potential and Non-Covalent Interactions (NCI) Analysis

_{2}S∙∙∙SO

_{2}complex (left panel) and the H

_{2}O∙∙∙SO

_{2}complex (right panel). In the case of H

_{2}S∙∙∙SO

_{2}, the polarization effects arising from the difference between positive and negative regions of the electrostatic potential are primarily localized on the SO

_{2}monomer. This indicates that the interactions between H

_{2}S and SO

_{2}predominantly involve the polarization of the SO

_{2}molecule. In contrast, for the H

_{2}O∙∙∙SO

_{2}complex, significant polarization effects are observed on both the H

_{2}O and SO

_{2}monomers.

_{2}S and SO

_{2}within the complex.

_{2}S∙∙∙SO

_{2}complex. These interactions play a crucial role in the overall stability and binding of the complex. Additionally, the analysis reveals a depletion of electronic density between the fragments, indicating a characteristic feature of non-covalent interactions. It is important to note that there is also a presence of strong repulsion in certain regions of the same surface, as indicated by the brown region in Figure 4. This suggests the existence of repulsive forces between specific parts of the H

_{2}S and SO

_{2}molecules within the complex. The interplay between attractive van der Waals interactions and repulsive forces contributes to the overall energetics and structural characteristics of the H

_{2}S∙∙∙SO

_{2}complex. Interestingly, NCI analysis for the H

_{2}O∙∙∙SO

_{2}complex also shows that non-covalent interactions play a significant role in the energetic stabilization of this system. This suggests that the natures of the intermolecular SS and SO interactions exhibit some similarity.

## 3. Materials and Methods

_{2}S, SO

_{2}, and H

_{2}S∙∙∙SO

_{2}were optimized using three different methods: MP2 (Møller–Plesset second-order perturbation theory) [52,53], CCSD (coupled cluster with single and double excitations) [54,55], and CCSD(T) (coupled cluster with single and double excitations, and correction to triple excitations) [56].

_{2}S∙∙∙SO

_{2}) and fragments (H

_{2}S and SO

_{2}). To address this issue, it is necessary to apply the Counterpoise (CP) correction method, which helps estimate the influence of the Basis Set Superposition Error (BSSE) [60]. The nature of the interaction between the H

_{2}S and SO

_{2}monomers in H

_{2}S∙∙∙SO

_{2}was discussed by non-covalent interactions (NCI) analysis [51].

## 4. Conclusions

_{2}S∙∙∙SO

_{2}complex. The analysis of vibrational frequencies reveals an intramolecular vibrational energy transfer phenomenon, where energy from the stretching modes of H

_{2}S is transferred to the ν1s mode of SO

_{2}. At the CCSD(T)/aug-cc-AVQZ level, the interaction energy between H

_{2}S and SO

_{2}is predicted to be 2.78 kcal/mol. This provides insight into the strength of the interaction and the stability of the complex.

_{2}S∙∙∙SO

_{2}. This information sheds light on the electronic properties and the energy required for ionization and electron attachment processes. Furthermore, by utilizing ab initio results for the adiabatic ionization energy and electron affinity, the electrophilicity of H

_{2}S-SO

_{2}is estimated to be 2.01 eV. This value is found to be similar to the electrophilicity of SO

_{2}, suggesting comparable reactivity and chemical behavior.

_{2}S∙∙∙SO

_{2}complex, contributing to a deeper understanding of this system. The non-covalent interactions (NCI) analysis conducted on the H

_{2}S∙∙∙SO

_{2}complex emphasizes the significant contribution of non-covalent van der Waals interactions in its energetic stabilization.

## Supplementary Materials

_{2}S∙∙∙SO

_{2}complex; Table S2: Angles (degrees) in SO

_{2}, H

_{2}S and in the SO

_{2}∙∙∙H

_{2}S complex, where θ and φ are defined as in Ref [10]; Table S3 Difference of bond distances and angles of H

_{2}S and SO

_{2}in relation to the monomer; Table S4: Vibrational frequencies (in cm

^{−1}) for the antisymmetric v

_{1a}and symmetric v

_{1s}stretching modes in H

_{2}S∙∙∙SO

_{2}.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

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**Figure 2.**HOMO (

**left**) and LUMO (

**right**) of H

_{2}S-SO

_{2}. The isodensity is 0.005 ($\mathrm{e}/{\mathrm{a}}_{0}^{3}$).

**Figure 3.**Electrostatic potential over isodensity surfaces. Left: H

_{2}S∙∙∙SO

_{2}; right: H

_{2}O∙∙∙SO

_{2}. The isodensity is 0.004 e/ao

^{3}. Electrostatic potential in a.u.

**Figure 4.**NCI analysis of the H

_{2}S∙∙∙SO

_{2}interactions. Left: H

_{2}S∙∙∙SO

_{2}; right: H

_{2}O∙∙∙SO

_{2}. Color labels: yellow sulfur, red oxygen, and white hydrogen.

S∙∙∙S | H∙∙∙O | OS∙∙∙S | HS∙∙∙S | $\mathit{\theta}$ | $\mathit{\varphi}$ | |
---|---|---|---|---|---|---|

MP2/AVTZ | 3.414 | 3.107 | 89.27 | 76.78 | 88.623 | 70.768 |

MP2/AVQZ | 3.387 | 3.137 | 90.11 | 78.40 | 90.215 | 73.140 |

MP2/AV5Z | 3.382 | 3.156 | 90.33 | 79.24 | 90.615 | 74.288 |

CCSD/AVTZ | 3.499 | 3.315 | 90.48 | 81.83 | 90.619 | 77.391 |

CCSD/AVQZ | 3.481 | 3.335 | 90.70 | 82.37 | 91.324 | 78.983 |

CCSDT/AVTZ | 3.454 | 3.181 | 89.25 | 78.43 | 88.558 | 73.168 |

CCSDT/AVQZ | 3.427 | 3.221 | 90.12 | 80.33 | 90.248 | 75.960 |

Other Values | ||||||

Matsumura (a) | 3.520 | 3.145 | 99.0(13) | 56.8(11) | ||

Kukolich (b) | 3.45(1) | 103(1) | 71(3) | |||

Ford (c) | 3.802 | 72.88 | 67.28 | |||

Plumer (d) | 3.577 | 3.07 |

**Table 2.**Difference between theoretical and experimental data for the antisymmetric–symmetric gap $\delta $ (in cm

^{−1}) for the H

_{2}S and SO

_{2}monomers.

AVTZ | AVQZ | AV5Z | |
---|---|---|---|

H_{2}S | ${\delta}_{th}-{\delta}_{expt}$ | ${\delta}_{th}-{\delta}_{expt}$ | ${\delta}_{th}-{\delta}_{expt}$ |

MP2 | 8.92 | 8.57 | 8.21 |

CCSD | 4.19 | 3.56 | |

CCSD(T) | 5.40 | 5.07 | |

SO_{2} | ${\delta}_{th}-{\delta}_{expt}$ | ${\delta}_{th}-{\delta}_{expt}$ | ${\delta}_{th}-{\delta}_{expt}$ |

MP2 | −4.59 | 2.39 | 8.15 |

CCSD | −17.96 | −10.98 | |

CCSD(T) | −15.13 | −7.40 |

**Table 3.**Difference $\u2206\nu $ for the antisymmetric and symmetric stretching frequencies between H

_{2}S∙∙∙SO

_{2}and monomers.

MP2 | CCSD | CCSD (T) | |||||
---|---|---|---|---|---|---|---|

AVTZ | AVQZ | AV5Z | AVTZ | AVQZ | AVTZ | AVQZ | |

HS | |||||||

${\u2206\mathsf{\nu}}_{1\mathrm{a}}$ | −14.60 | −16.05 | −11.76 | −3.74 | −5.86 | −7.06 | −6.71 |

${\u2206\nu}_{1s}$ | −13.88 | −15.43 | −11.29 | −3.31 | −5.93 | −6.79 | −6.62 |

SO | |||||||

${\u2206\nu}_{1a}$ | −1.60 | −3.02 | −3.76 | −6.12 | −5.83 | −5.50 | −5.86 |

${\u2206\nu}_{1s}$ | 5.80 | 5.20 | 4.47 | 1.34 | 1.68 | 1.34 | 1.68 |

S∙∙∙S | ${\mathsf{\Delta}\mathit{E}}_{\mathbf{I}}$ | BSSE | ${\mathsf{\Delta}\mathit{E}}_{\mathbf{I}}\left(\mathit{C}\mathit{P}\right)$ | |
---|---|---|---|---|

MP2/AVTZ | 3.4142 | 3.2268 | 0.4757 | 2.7600 |

MP2/AVQZ | 3.3866 | 3.1661 | 0.2333 | 2.9500 |

MP2/AV5Z | 3.3822 | 3.1021 | 0.1205 | 3.0000 |

CCSD/AVTZ | 3.4993 | 2.7071 | 0.3788 | 2.3400 |

CCSD/AVQZ | 3.4805 | 2.6006 | 0.1558 | 2.4600 |

CCSD(T)/AVTZ | 3.4543 | 3.0396 | 0.4473 | 2.6000 |

CCSD(T)/AVQZ | 3.4275 | 2.9537 | 0.1831 | 2.7800 |

**Table 6.**Chemical potential ($\mu $), hardness ($\eta $), and electrophilicity ($\omega $). Values in eV. Experimental values in brackets.

$\mathit{\mu}=-\frac{\mathit{I}\mathit{E}+\mathit{E}\mathit{A}}{2}$ | $\mathit{\eta}=\frac{\mathit{I}\mathit{E}-\mathit{E}\mathit{A}}{2}$ | $\mathit{\omega}=\raisebox{1ex}{${\mathit{\mu}}^{2}$}\!\left/ \!\raisebox{-1ex}{$2\mathit{\eta}$}\right.$ | |
---|---|---|---|

H_{2}S | −4.937 | 5.406 | 2.255 |

SO_{2} | −6.902 | 5.635 | 4.227 [4.027] |

H_{2}S-SO_{2} | −5.755 | 4.118 | 4.021 |

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**MDPI and ACS Style**

Magalhães, I.O.M.; Cabral, B.J.C.; Martins, J.B.L.
Ab Initio Approach to the Structure, Vibrational Properties, and Electron Binding Energies of H_{2}S∙∙∙SO_{2}. *Molecules* **2023**, *28*, 6656.
https://doi.org/10.3390/molecules28186656

**AMA Style**

Magalhães IOM, Cabral BJC, Martins JBL.
Ab Initio Approach to the Structure, Vibrational Properties, and Electron Binding Energies of H_{2}S∙∙∙SO_{2}. *Molecules*. 2023; 28(18):6656.
https://doi.org/10.3390/molecules28186656

**Chicago/Turabian Style**

Magalhães, Isaac O. M., Benedito J. C. Cabral, and João B. L. Martins.
2023. "Ab Initio Approach to the Structure, Vibrational Properties, and Electron Binding Energies of H_{2}S∙∙∙SO_{2}" *Molecules* 28, no. 18: 6656.
https://doi.org/10.3390/molecules28186656