Disulfides XSSX and their isomers SSX2 (X: H, CH3, F, Cl, Br) have been investigated for their importance in atmospheric chemistry as well as biochemistry. Particularly, sulfur-sulfur bond in the cysteine residue plays a significant role in biological systems as the major stabilizer of the protein's third structure . Many S2X2 systems have been found to have two disulfide isomers (XSSX) with C2 symmetry and a thiosulfoxide isomers (SSX2) with CS symmetry. These two isomers have been separated and verifiable . Based on Greenwood and earnshaw, sulfur and fluorine have produced seven various binary compounds with a wide range of physical and chemical features involving S2F10 and SF6 .
Ball (2003) investigated the heat of formation and vibrational frequency of FSSF, SSF2 with the theory of G2 and G3 and a complete basis set . Disulfide difluoride was known for almost 170 years, but in 1963 the presence of two isomers of S2F2 compound by microwave and IR spectroscopy was proven .
Cao et al.  recently surveyed SSF2→FSSF isomerization reaction at 23 °C and 50 °C. HeI photo-electron spectroscopic technique (PES) was utilized to identify the kinetical parameters, the mechanism of many chemical reactions, and the isomerization reaction.
In 2007, the SSXY → XSSY (X or Y = F, Cl, Br, I) isomerization reaction applying B3LYP/6-311 ++ G (2DF) and MP2/6-311 ++ G (2DF) and B3LYP / 6-311 ++ G (2DF) was studied regarding electron density distribution theory .
Most experimental studies on the IR and Raman spectra of bromine species show that the molecule is transformed into a skew structure belonging to C2 point group . Applying CCSD (T) with a basic set of structural and vibrational spectrum correlations, the relative stability and heat of formation and the isomerization barrier S=SBr2 and BrSSBr have been surveyed . Many interamolecular rearrangements resulting from the reorganization and redistribution of electron density among the atoms of a molecule are generally significant in reactivity and selectivity .
In 2013, the compounds of X2Y2 structure with two isomers XYYX and X2YY (X: Li, Na, F, Br, Cl, I) and (Y: O, S, Se, Te) applying (Density Functional Theory) DFT were studied by ZORA-BP86/QZ4P computational method .
Cattaraj et al., surveyed the impacts of solvents as well as intermolecular rearrangements based on DFT research. They investigated the relative energy and chemical potential of electron and the chemical hardness and polarization for F2S2→ FSSF and Trans-N2H2 → Cis-N2H2 rearrangements in the gaseous and soluble phases, respectively .
X2Y2 systems with C2 conformation were more stable than other forms due to the anomeric impact on noncyclic and heterocyclic systems involving heteroatoms . Due to the anomeric impact in Y-X-X-Y systems (X: O, Y: O, N, halogen) with C2 conformation, X-X bond length is shorter and X-Y bond length is longer . The conversion reaction XSSY→ SSXY (X or Y: F, Cl, Br, I) was studied by B3LYP/6-311++G(2df) and MP2/6-311++G(2df) computational approach in 2007. In this reaction, there are two pathways for the transfer of atoms X and Y .
Due to the importance of the effect of substitution, many studies have been done in this field [16-18]. In this study, the stability of C2 and Cs conformation of S2X2 compounds with X: F, Cl, Br substitution was investigated. Thermodynamic parameters ΔG, ΔH and ΔE0 and structural parameters, hardness, softness, electronegativity parameters and electrophilic index were calculated by LC-ωPBE/Aug-cc-pVTZ and LC-BLYP/Aug-cc-pVTZ methods.
Result and Dissection
Gaussian 09W package and gaussview 5.0  was utilized to compute examine the Perdew-Burke-Ernzerhof (LC-ωPBE) and Becke-Lee- Yang- Parr (LC-BLYP) [20-22]. Aug-cc-pVmZ (m: 3) are basis sets for the C2 and CS conformations of compounds 1 to 3. The whole of electronic and zero-point energies (E0 = Eel + ZPE), electronic and thermal enthalpies (H = E + RT), electronic and thermal free energy (G=H–TS) were explored as thermodynamic parameters. The differences within the thermodynamic information of ΔG, ΔH, and ΔE0 were computed in product state C2 and reactant states CS for compounds 1 to 3. The structural parameters of the compound 1-3 were for the reactant CS and product C2 audit. The highest orbital molecular occupied (HOMO), the lowest unoccupied molecular orbital (LUMO) and gap HOMO and LUMO were recognized by computational strategy LC-BLYP/Aug-cc-pVTZ and LC-ωPBE/Aug-cc-pVTZ. The HOMO-LUMO gap decides the degree of hardness. Figure 1 indicates the intermolecular reearengment process of the reactant (CS) → transition state (TS)→product(C2).
Figure 1: Symmetry variations through conformational change X: F (1), Cl (2), Br (3)
Figure 2 indicates Gibbs free energy difference between reactant S=SX2 and product XSSX for compounds 1- 3.
Figure 2: Diagram of Gibbs free energy changes in the conversion process S=SX2→XSSX [X: F (1), Cl (2), Br (3)]
Structural features of bond length (r), bond angle (θ), and dihedral angle (φ) for compounds 1-3 with C2 and CS conformation applying LC-ωPBE /Aug-cc-pVTZ and LC-BLYP /Aug-cc-pVTZ computational approaches are indicated in Table 1. Comparing bond lengths and angles experimental and computed in C2 and CS conformations for compounds 1 to 3 are performed in Table 1.
The difference between the enthalpy and the free energy Gibbs and the corrected electronic energy between conformations C2 and Cs for compounds 1-3 by LC-ωPBE/Aug-cc-pVTZ and LC-BLYP/Aug-cc-pVTZ computational approaches are mentioned in Table 2. In this research, we apply enthalpy difference and Gibbs free energy and corrected electronic energy to conformation Cs and C2 Δ[H (C2) -H (Cs)], Δ[G (C2) -G (Cs)] and Δ[E0 (C2) -E0 (Cs) ] is calculated according to Table 2. ΔG, ΔH, ΔE0 increasing from compound 1 to 3.
Global hardness and electronegativity
The highest orbital molecular occupied (HOMO) and lowest unoccupied molecular orbital (LUMO) for Compounds 1-3 with C2 and CS conformation by LC-ωPBE/Aug-cc-pVTZ and LC-BLYP/Aug-cc-pVTZ computational approaches are indicated in Tables 3 and 4, respectively. HOMO-LUMO gap is measured by the hardness the chemical compounds. The difference in HOMO- LUMO gap of compounds 1 to 3 in the product (C2) was 0.4321, 0.3836, 0.3588 (a. u) and product (CS) was 0.3966, 0.3443, 0.3135 (a. u) by the LC- ωPBE method, respectively. Also, the difference in HOMO- LUMO gap of compounds 1 to 3 in the product (C2) was 0.4434, 0.3921, 0.3664 (a. u) and reactant (CS) was 0.4064, 0.3509, 0.3185 (a. u) by the LC-BLYP method, respectively. The higher the chemical hardness of compounds, the lower the chemical activity and the greater the stability . The hardness difference from the compounds 1 to 3 was increasing. The relation between the hardness and the electron affinity energy of (A) and the ionization energy (I) of a molecule is mentioned in Equation 1.
Based on Principle Koopmans, theorem  the hardness of chemical compounds is explained by Equation 2.
Based on the findings provided from the approaches LC-ωPBE/Aug-cc-pVTZ and LC-BLYP/Aug-cc-pVTZ for compounds 1-3 with C2 and Cs conformations, the hardness of compounds with C2 conformation is higher than CS.
The relationship between electronegativity (χ) and electron affinity energy (A) and ionization energy (I) is given according to eq 3. Tables 3 and 4 indicate the global electronegativity for compounds 1 to 3 reactant (CS) and product (C2) conformation by LC/ωPBE and LC/BLYP method.
χ =I+A/2 3
The softness (S) of chemical compounds is provided based on the relation S = 1/2η. Regarding Tables 3 and 4, the conformation CS in compounds 1-3 is softer than that of C2. Based on the principle maximum hardness, the hardest compounds of a molecule are the most stable form . Based on the results obtained by LC-BLYP/Aug-cc-pVTZ and LC-ωPBE/Aug-cc-pVTZ computational methods, the difference in hardness among the conformations of C2 and CS for compounds 1-3 Δ [η (C2)-η (CS)] increased from 1 to 3 compounds which corresponds to an increase in ΔG, ΔH, ΔE0. The difference in hardness of compounds 1 to 3 in the reactant (CS) and product (C2) with the LC-ωPBE method was 0.01776, 0.01961, 0.02268 (a.u.), respectively, and for LC-BLYP approach, it was 0.02035, 0.02060, 0.0239 (a.u.), respectively. The hardness difference from the 1 to 3 compounds was increasing.
Index electrophilicity (ω) is the ability of an electrophile to provide electrical charge and system resistance to the exchange of electron charge with the environment . Eq 4 indicates the hardness and electronegativity relationship with index electrophilicity.
ω =χ2/2η 4
The process of increasing the difference hardness was be described by increasing ΔG, ΔE0, ΔH of compounds 1 to 3. There is a linear relationship between ΔG and Δη for compounds 1 to 3 by LC-ωPBE/Aug-cc-pVTZ and LC-BLYP/Aug-cc-pVTZ (Fig3). An increase in Δη of compounds 1 to 3 corresponds to an increase in ΔG.
Figure 3: Relation of ΔG vs. ΔHardness with the LC-ωPBE/aug-cc-pVTZ (◊) and LC-BLYP/aug-cc-pVTZ
In this research, for compounds 1 to 3 for two conformations C2 and CS by LC-BLYP, LC-ωPBE with basis set Aug-pVTZ, the bond length and the bond angle and the dihedral angle were computed. ΔE0, ΔH, ΔG are increasing from compounds 1 to 3. The difference in hardness Δ [η(C2)-η(CS)] of compounds 1 to 3 is increasing. There is a direct relationship between the difference in hardness and Gibbs free energy difference for compounds 1 to 3 with the LC-ωPBE/aug-cc-pVTZ and LC-BLYP/aug-cc-pVTZ approach, which shows C2 conformation stability. Research has shown the chemical hardness of C2 and CS conformations revealed that C2 conformations are more stable.
This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.
All authors contributed toward data analysis, drafting and revising the paper and agreed to be responsible for all the aspects of this work.
Conflict of Interest
We have no conflicts of interest to disclose.
HOW TO CITE THIS ARTICLE
Zahra Mokhayeri. Investigation of Thermodynamic properties and Hardness by DFT Calculations of S2X2 isomers (X: F, Cl, Br), Chem. Methodol., 2022, 6(1) 52-58