Journal of Molecular Graphics and Modelling 120 (2023) 108419 Contents lists available at ScienceDirect Journal of Molecular Graphics and Modelling journal homepage: www.elsevier.com/locate/jmgm Theoretical studies on the reaction mechanisms of the oxidation of tetramethylethylene using MO3Cl (M=Mn, Tc and Re) Emmanuel Adu Fosu a, Collins Obuah a,c,*, Louis Hamenu a, Albert Aniagyei b, Anita Oppong a, Michael Kojo Ainooson a,c, Alfred Muller c a Department of Chemistry, University of Ghana, Legon, Ghana b School of Basic and Biomedical Sciences, University of Health and Allied Sciences. Ho, Ghana c Department of Chemical Sciences, University of Johannesburg, Auckland Park Kingsway Campus, Auckland Park, 2006, Johannesburg, South Africa A R T I C L E I N F O A B S T R A C T Keywords: A theoretical study on the reaction mechanisms of the addition of transition metal oxo complexes of the type Quantum methods MO3Cl (M = Mn, Tc, and Re) to tetramethylethylene (TME) is presented. Theoretical calculations using B3LYP/ Reaction mechanisms LACVP* and M06/LACVP* (LACVP* is a combination of the 6-31G(d) basis set along with LANL2DZ pseudo- Oxidation potentials on the metallic centres) were performed and the results are discussed within the framework of reaction Diols Epoxides energetics. The nature of the stability of the reaction mechanisms was equivalent for both theories. However, the M06/LACVP* simulations generally had slightly lower energies and shorter bond lengths compared to the B3LYP/LACVP* computations. Furthermore, it was observed that the reaction does not proceed via the stepwise reaction mechanism due to kinetic and thermodynamic instabilities. Epoxidation was also found to occur via the [2 + 2] concerted reaction mechanism for the MO3Cl (M = Tc and Re) whereas the permanganyl chloride complex epoxidizes TME via the [2 + 1] concerted reaction mechanism on the singlet potential energy surface (PES). Dioxylation was observed to proceed via the [3 + 2] route for the addition of MO3Cl (M = Tc and Re) and TME. Results indicate that all reaction surfaces were unselective except for the permanganyl chloride catalyzed surface which leads to the formation of epoxides exclusively. Changes in temperatures from 298.15 K to 373.15 K, resulted in kinetically and thermodynamically unstable reaction pathways as the activation and reaction energies increased generally. On the singlet PES, the rate constant calculations showed that the [3 + 2] catalyzed surface reaction mechanism leading to dioxylation was faster than the [2 + 2] mechanism in cases where plausible. Theoretical values from the global reactivity parameters, namely the chemical hardness, chemical potential, electrophilic and nucleophilic indices, are in good correlation with the DFT activation and reaction energies at both levels of theories. Thus, as the electrophilic nature of the metal decreases from Mn to Re, so do the acti- vation and reaction energies increase from Mn to Re, indicating that the higher the electrophilicity of the metal centre, the more spontaneous the oxidation reaction. 1. Introduction and materials science, but the accuracy of KS-DFT depends on the ap- proximations made to the exchange-correlation functional [1,2]. The Nowadays, the use of quantum methods such as density functional M06 and B3LYP models, which are hybrid functionals, have been widely theory (DFT) and Ab Initio techniques have become essential for inves- used due to their broad applicability in studying chemical systems. The tigating the fascinating molecular mechanisms and structural challenges B3LYP functional, a Hartree–Fock DFT model [3,4] is made up of the posed by chemical processes. exchange-correlation energy from the local spin-density approximation The Kohn–Sham density functional theory (KS-DFT) has been widely (LSDA) model, 20% of the difference between the Hartree–Fock ex- utilized for several applications in chemistry, condensed-matter physics, change energy and the LSDA exchange energy, 72% of the Becke * Corresponding author. Department of Chemistry, University of Ghana, Legon, Ghana. E-mail address: cobuah@ug.edu.gh (C. Obuah). https://doi.org/10.1016/j.jmgm.2023.108419 Received 9 November 2022; Received in revised form 3 January 2023; Accepted 17 January 2023 Available online 25 January 2023 1093-3263/© 2023 Elsevier Inc. All rights reserved. E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 exchange potential, 81% of the Lee-Yang–Parr correlation potential [5] TME. Results from this study will be very useful for experimentalists in and 19% of the Vosko–Wilk–Nusair potential [6]. The B3LYP functional the design and use of group 7b oxo complexes as catalysts for the se- is one of the most widely used exchange-correlation functionals in lective oxidation of TME. organometallic chemistry. Furthermore, the M06 functional [7] is a global hybrid meta-generalized gradient approximation (meta-GGA) 1.1. Computational details with 27% of Hartree–Fock exchange energy, leading to a well-balanced functional for overall good performance for studying chemical systems. In this theoretical study, the DFT/HF hybrid functional model [5,6, Over recent years, the M06 functional has thus been recommended 26] B3LYP, and M06 were employed as implemented in Spartan’16 for application in organometallic chemistry [7–9]. To date, the M06 and V.2.0.7 [27] in conjunction with the basis set of LANL2DZ for the B3LYP models are the two most popular DFT tools used in studying transition metals (Mn, Tc, and Re), and the split valence double-ξ (DZ) organometallic transformations [7,9,10]. M06 is currently the first [28] 6-31G (d) for other atoms (C, H, O, Cl). choice of functional for energy calculations of transition metal systems, The MO3Cl (M = Mn, Tc, and Re) and TME systems on the singlet and followed by B3LYP, DFT-D3, and M06L [9] for the computational triplet surfaces were computed as neutral structures. The Spartan’s studies on synthetically relevant homogeneous organometallic catalysis. graphical model builder was used in modeling the molecular systems of Modern-day chemistry demands researchers to design and develop the starting geometries. The modeled geometries were minimized new catalysts for chemical reactions to help achieve high selectivity and interactively using the Sybyl force field [29]. Full optimization of all efficiency [11,12]. Oxidation reactions remain one of the most efficient stationary points on the PES was done without any symmetry con- methods in the synthetic tool kits for chemists due to the widespread straints. The nature of the stationary points was verified by performing a applications of oxidized substrates in the chemical industry. Debates normal mode analysis. All molecular structures on the minima or equi- surrounding the mechanistic details of the formation of vicinal diols librium geometries were characterized by the absence of imaginary from olefinic substrates catalyzed by osmium tetroxide, a typical and frequencies corresponding to any mode of vibration in the system. The well-known oxidation reaction have been resolved by several quantum saddle point structures were located by a series of constrained geometry chemical studies which predicted the [3 + 2] route to be both kinetically optimizations in which the forming – and breaking – of bonds were fixed and thermodynamically stable than the [2 + 2] pathway [11,13,14, at various lengths while the remaining internal coordinates were opti- 14–19]. The use of osmium and its oxo complexes as catalysts is very mized. The approximate stationary points located from such a procedure useful in chemical synthesis. However, factors such as toxicity, its were then fully optimized using the standard transition state optimiza- expensive nature, scarcity, and volatility demerit its use and urge sci- tion procedure in Spartan [27]. All first-order saddle points were shown entists to explore other options. to have a Hessian matrix with a single negative eigenvalue, character- In recent years, theoretical and experimental procedures have ized by an imaginary vibrational frequency along the reaction pathway. focused on rationalizing theories around the electronic and structural In cases where no molecular structures could be optimized from the nature of group VII B elements [17,19–21]. Group VII B transition metal saddle point, a PES scan was performed to verify this observation. This elements (Mn, Tc, and Re) and their oxo complexes continue to be of study reports energies in Gibbs free energy values at a temperature of great asset to chemists due to their ability to oxidize olefinic substrates 298.15 K and pressure of 1 atm using unscaled frequencies unless [12,22,23]. Hence, that was why the oxo complexes of Mn, Tc, and Re otherwise noted. The imaginary frequencies corresponding to the vi- were employed in this study. Although several theoretical and experi- brations along the reaction pathway for each transient structure can be mental works on the reaction of ethylene with metal oxo complexes are found in Tables S1–S3. Also, the cartesian coordinates for all optimized known, the same cannot be said for the reactions involving substituted stationary points can be found in Data S1–S2. ethylene. Some of the few theoretical works on the oxidation of tetramethyl- 2. Results and discussion ethylene (TME) by transition metal oxo complexes were done by Wis- tuba et al. [24] and Aniagyei et al. [25]. Wistuba et al. [24] studied the 2.1. Reaction of ReO3Cl with TME oxidation of ethylene mediated by permanganyl chloride by theoretical and experimental means. Per the DFT results, Wistuba et al. [24] pre- Fig. 1a–e represent the relative Gibbs free energy profile, optimized dicted that the [3 + 2] addition of tetramethylethylene (TME) to the transition state structures located on the singlet PES and a graphical MnO2 moiety of MnO3Cl is thermodynamically favoured over the [2 + representation of the interaction between the frontier molecular orbitals 1] mechanistic route. In addition, Wistuba et al. [24] experimentally of the reactants respectively. investigated the TME/MnO3Cl system through matrix-isolation tech- The ground state DFT/B3LYP and DFT/M06 optimization of the niques and concluded that the selective formation of the epoxidation ReO3Cl molecular system on both singlet and triplet PES yielded a tet- product [ClO2Mn{O[C(CH3)2]2}] was observed. rahedron geometry with C1 symmetry. This indicates the absence of all Aniagyei et al. [25] on the other hand explored the singlet and triplet symmetry elements except the identity operation, thus the rhenium oxo PESs for the same reaction only theoretically at 298.15 K and 0.00001 complex has no symmetry. On the singlet PES, the DFT/B3LYP atm at the B3LYP/LACVP* level of theory. The results also predicted that computed Re=O and Re-Cl bond lengths of the ReO3Cl optimized the pathway leading to the formation of the five-membered dioxylate complex were found to be 1.704 Å and 2.265 Å respectively whereas the intermediate via the concerted [3 + 2] addition was kinetically and optimized ReO3Cl complex on the triplet PES has all three Re=O and Re- thermodynamically stable over the three other possible pathways, thus, Cl bond lengths at 1.701 Å, 1.701 Å, 1.886 Å, and 2.312 Å respectively. the [2 + 2] addition via the transient metallaoxetane intermediate, On the other hand, the DFT/M06 singlet ReO3Cl optimized geometry has epoxidation, and hydrogen transfer pathways. Aniagyei et al. [25] also all Re=O and Re-Cl bonds at 1.693 Å and 2.251 Å respectively whereas noted that kinetically, both the stepwise and the concerted [2 + 1] its counterpart on the triplet surface has all three Re=O and Re-Cl bonds addition pathways leading to the epoxide precursors were very lengths at 1.690 Å, 1.690 Å, 1.691 Å, and 2.291 Å respectively. The competitive with an activation barrier difference of lesser than 0.7 triplet oxo complex showed less stability compared to the singlet kcal/mol. structure by 60.90 kcal/mol and 63.89 kcal/mol at DFT/B3LYP and This work, therefore, employs the hybrid functional DFT models, DFT/M06 respectively. As shown in Fig. 1d and e, calculations of the B3LYP and M06 in conjunction with the basis set LACVP* to extend the frontier molecular orbitals of the reacting species show that electrons works by Wistuba et al. [24] and Aniagyei et al. [25] by investigating all flow from the Highest Occupied Molecular Orbital (HOMO) of the TME the concerted and stepwise mechanistic channels resulting from the into the Lowest Unoccupied Molecular Orbital (LUMO) of the rhenium- addition of MO3Cl (M = Mn, Tc, and Re) across the olefinic bonds of oxo complex at both levels of theories. 2 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 Fig. 1a. Relative Gibbs free energy profile diagram for the reaction between ReO3Cl and TME on the singlet surface at the DFT/M06/LACVP*(red colour) and DFT/ B3LYP/LACVP* (black colour) level of theory. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) On the singlet concerted PES, the direct [3 + 2] insertion of the optimized B3LYP transition state [TS 1Cs in Scheme 1] from the [2 + 2] olefinic bond across the O=Re=O functionality of the ReO3Cl complex pathway has its newly forming C–O and Re-C bonds at 1.963 Å and leads to the formation of [1As] intermediate. The DFT/B3LYP free 2.256 Å respectively. On the singlet PES, the computed M06 saddle point activation and reaction energies associated with this process were 33.64 structure from the [2 + 2] pathway has its newly forming C–O and Re-C kcal/mol and 15.78 kcal/mol respectively. Furthermore, the DFT/M06 bonds at 2.070 Å and 2.367 Å respectively. activation and reaction energies associated with the initial [3 + 2] step The free activation energy computed for the formation of the diox- were found to be 28.62 kcal/mol and 0.85 kcal/mol respectively. Results ylate intermediate [1As] on the singlet surface through the saddle point from both levels of theory suggest that the formation of the dioxylate structure [TS-2Cs in Scheme 1] was 57.75 kcal/mol and 47.19 kcal/ intermediate [1As] is not a spontaneous process due to the endergonic mol at the B3LYP and M06 respectively. There was no transient structure nature of the oxidation process on the singlet PES. The DFT/B3LYP [TS-2Ct in Scheme 1] optimized from the triplet surface at the B3LYP computed triplet dioxylate intermediate [1At] lies 3.62 kcal/mol lower level. This observation was confirmed by the M06 computations. Due to than its singlet counterpart [1As] whereas the DFT/M06 singlet dioxy- the kinetic hindrance of the [2 + 2] route, that is, the high activation late intermediate [1As] was 4.84 kcal/mol more stable than its triplet barrier of the initial [2 + 2] step, and the endergonic nature of the counterpart [1At]. An exhaustive attempt to locate the transition state formation of the [2 + 2] intermediate, the formation of diols favours the linking the reactant to the product on the triplet surface proved futile for [3 + 2] pathway in terms of energetics as shown in Fig. 1a. the [3 + 2] route at both levels of theories. The possibility of epoxidation via the transition state [TS-1Ds in The stepwise [2 + 2] route via the transition state TS1C and a 1C Scheme 1] was explored at both levels of theory and was computed to metallaoxetane intermediate in Scheme 1, which according to Sharpless have free activation and reaction energies of 52.08 kcal/mol and 30.94 et al. [30] re-arranges to the [3 + 2] product was also explored at both kcal/mol at the B3LYP level and 39.24 kcal/mol and 18.25 kcal/mol at levels. the M06 level respectively on the singlet PES. The B3LYP singlet epoxide A DFT/B3LYP computed energy barrier of 42.84 kcal/mol needs to [1Ds] was computed to lie lower than its triplet counterpart [1Dt] by be overcome to form the metallaoxetane intermediate [1Cs] on the 10.07 kcal/mol. On the other hand, the M06 singlet epoxide [1Ds] was singlet surface. At the DFT/M06 level, the activation barrier for the computed to lie lower than its triplet counterpart [1Dt] by 11.50 kcal/ initial [2 + 2] route on the singlet was 33.55 kcal/mol. There was no mol. Similar to the observation on the [3 + 2] and [2 + 2] triplet PES at transition state located for the [2 + 2] mechanism on the triplet PES at both levels of theory, no transition state [TS 1Dt in Scheme 1] was both levels of theory. The computed activation energies at both levels found. After an exhaustive search on the PES, it was observed that suggest that the free energy of activation for the singlet transition state is epoxidation via transients [TS-1B and TS-2A in Scheme 1] was not high for the [2 + 2] route than for the [3 + 2] route. This observation possible on the singlet and triplet surfaces at both levels of theory. This makes the initial [2 + 2] route unstable over the [3 + 2] route. indicates that the formation of an epoxide by the oxidation of TME Furthermore, on the singlet PES, the formation of the singlet metal- mediated by the ReO3Cl catalyst occurs only via the [2 + 2] route. The laoxetane intermediate shows an endergonicity of 19.12 kcal/mol and [2 + 1] route or the re-arrangement of the dioxylate intermediate is not 4.80 kcal/mol at the B3LYP and M06 levels respectively. The B3LYP possible as evident from the computations. triplet metallaoxetane intermediate [1Ct] was located and found to be Efforts to optimize saddle point structures from the stepwise reaction 16.83 kcal/mol less stable than the singlet counterpart [1Cs] whereas mechanism proved futile for all pathways on both singlet and triplet the M06 singlet metallaoxetane intermediate [1Cs] was located and surfaces at both levels of theory. This indicates that the oxidation of TME found to be 22.27 kcal/mol less stable than the triplet counterpart. The catalyzed by the rhenium oxide will proceed via the concerted [3 + 2] 3 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 Fig. 1b. Optimized transition states involved in the reaction between ReO3Cl and TME on the singlet surface at the DFT/M06/LACVP* level of theory. The colour code for atoms; Red = Oxygen, Green = Chlorine, Grey = Carbon, White = Hydrogen, and Blue = Rhenium. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) route in terms of dioxylation and the concerted [2 + 2] route in terms of Å respectively for the optimized triplet geometry. At both levels of epoxidation. It can therefore be said that the formation of diols and theory, the singlet structure was stable over its triplet counterpart epoxides from the oxidation of TME mediated by the rhenium oxide (>46.00 kcal/mol). As evident from Fig. 2d and e, the movement of complex is not a spontaneous process at 298.15 K and 1 atm. electrons from the (HOMO) of the TME into the (LUMO) of the TcO3Cl is favoured at all levels of theory compared to vice versa. Hence, in the oxidation of TME assisted by TcO3Cl, electrons will flow from the TME 2.2. Reaction of TcO3Cl with TME into the d orbitals of the technetium complex. From the stepwise reaction mechanism (blue coloured in Scheme The relative energy profiles, saddle point structures optimized from 1), the formation of the organometallic intermediate (1Xs intermediate the singlet PES and HOMO-LUMO energy gaps are shown in Fig. 2a–e in Scheme 1) is an endergonic process per the B3LYP results and exer- respectively. gonic per M06 calculations with Gibbs free energies at 13.64 kcal/mol The M06 and B3LYP optimized technetium oxide complex on the and − 2.14 kcal/mol respectively. The computed B3LYP and M06 acti- single PES was found to be chiral since ground state optimization at both vation energies for the formation of the intermediate 1Xs in Scheme 1 levels of theories yielded a C1 point group. The B3LYP geometry opti- were found to be 25.58 kcal/mol and 17.59 kcal/mol respectively on the mization of the TcO3Cl molecular system yielded Tc=O and Tc-Cl bond singlet surface. As illustrated in Fig. 2a, the formation of the singlet distances of 1.698 Å and 2.262 Å respectively. On the other hand, the dioxylate intermediate, 1As [Scheme 1] via the rearrangement of the triplet optimized TcO3Cl complex had geometry with all three Tc=O and intermediate, 1Xs through the transient TS-[2Xs] has to overcome free Tc-Cl bond distances at 1.693 Å, 1.726 Å, 1.873 Å, and 2.280 Å activation energy of 33.23 kcal/mol and 23.19 kcal/mol at the B3LYP respectively. Furthermore, the M06 optimized TcO3Cl complex had its and M06 level respectively. No transition state [ TS3X and TS-4X] could Tc=O and Tc-Cl bond distances at 1.687 Å and 2.249 Å respectively, and be located on both singlet and triplet surfaces for the formation of an Tc=O and Tc-Cl bond distances at 1.699 Å, 1.683 Å, 1.895 Å, and 2.269 4 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 Fig. 1c. Optimized transition states involved in the reaction between ReO3Cl and TME on the singlet surface at the DFT/B3LYP/LACVP* level of theory. The colour code for atoms; Red = Oxygen, Green = Chlorine, Grey = Carbon, White = Hydrogen, and Blue = Rhenium. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) epoxide and the metallaoxetane intermediate respectively at both levels of theory. From the B3LYP computations on the singlet surface, the of theory. metallaoxetane formation was 20.70 kcal/mol endergonic and was Dioxylation resulting from the concerted reaction mechanism on the computed to have an activation barrier of 47.73 kcal/mol. The ener- singlet surface ([3 þ 2] route in Scheme 1) needs to overcome an getics computed at the M06 agrees with that at the B3LYP with activa- activation barrier of 18.25 kcal/mol and 13.02 kcal/mol at the B3LYP tion and Gibbs free energies of 4.46 kcal/mol and 35.38 kcal/mol and M06 levels of theories respectively. The Gibbs free energies respectively on the singlet PES. The nature of the energetics computed computed at the M06 and B3LYP levels for the [3 + 2] (route in Scheme for the metallaoxetane formation route on the singlet PES rules out its 1) are − 27.03 kcal/mol and − 13.14 kcal/mol respectively on the singlet formation on the singlet surface due to the thermodynamic and kinetic PES. instability as compared to the [3 + 2] pathway. On the triplet surface, no As compared to the dioxylation abilities of ReO3Cl (discussed in transition state is located for the [2 + 2] reaction mechanism at both section 3.1), the dioxylation process catalyzed by TcO3Cl is spontaneous levels of theory. Geometry optimization of the metallaoxetane inter- at 298.15 K as evident from the calculations and illustrated in Fig. 2a. It mediate [1C] at the B3LYP level of theory showed that the singlet was found that the B3LYP computed triplet dioxylate intermediate metallaoxetane intermediate was stable over its triplet structure by [1At] lies 1.53 kcal/mol lower than its singlet structure [1As]. This 33.10 kcal/mol whereas the M06 triplet metallaoxetane intermediate story did not differ from that of the M06 level where the singlet dioxylate lay 23.46 kcal/mol below its counterpart on the singlet PES. intermediate [1As] was also 1.75 kcal/mol more stable than its triplet The computations at the B3LYP and M06 levels of theory showed counterpart [1At]. Efforts to explore the reaction surface to optimize that dioxylation via the [2 + 2] route through the rearrangement of the the triplet saddle point structure for the [3 + 2] route proved futile at metallaoxetane intermediate via the saddle point geometry [TS-2Cs in both levels of theory. Scheme 1] needed to overcome an activation barrier of 37.22 kcal/mol A competing reaction process; that is the formation of metal- and 23.09 kcal/mol respectively. Efforts to optimize a transient [TS-2Ct laoxetane intermediate via the transition state TS1C in Scheme 1, was in Scheme 1] from the triplet PES at both levels of theory proved futile. explored on both singlet and triplet surfaces at the B3LYP and M06 levels Based on the energetics computed at both levels for all routes leading to 5 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 at the B3LYP level, the computed free activation and reaction energies of the barrier were 29.16 kcal/mol and 4.82 kcal/mol whereas an activa- tion barrier and Gibbs free energy of 16.66 kcal/mol and − 6.12 kcal/ mol respectively were computed at the M06 level. Again as observed in section 3.1, the B3LYP optimized singlet epoxide [1Ds] was computed to be more stable than its triplet structure[1Dt] at all levels of theory (>6.0 kcal/mol). Furthermore, on the singlet and triplet surfaces, it was observed at both levels of the theory that epoxidation via the saddle point geometries [TS-1B and TS-2A in Scheme 1] were not possible. Hence, it can be inferred that epoxidation of TME will proceed via the [2 + 2] reaction mechanism on the singlet surface. Results from the oxidation of TME catalyzed by TcO3Cl at both levels of the theory sug- gest that hydroxylation [3 þ 2] and epoxidation [2 þ 2] will likely proceed via the concerted route and not stepwise. 2.3. Reaction of MnO3Cl with TME Illustrated in Fig. 3a–e respectively are the relative free energy profiles, optimized transients optimized from the singlet PES and the HOMO-LUMO energies between the reactants. Optimization of the singlet permanganyl chloride complex at both levels of theory yielded a tetrahedron geometry with C1 symmetry. Similar to the observations in sections 3.1 and 3.2, the permanganyl chloride was found to be chiral due to the absence of all symmetry el- ements except the identity operation (E). As shown in Fig. 3d (B3LYP calculations) and 3e (M06 calculations), the movement of electrons from Fig. 1d. Graphical representation of the interaction between the frontier mo- the TME molecular system into the d orbitals of the manganese metal of lecular orbitals between the ReO3Cl complex and TME on the singlet surface at the permanganyl chloride complex on the singlet PES is favoured the DFT/B3LYP/LACVP* level of theory. energetically over vice versa. The B3LYP optimized permanganyl chloride geometry has all Mn=O and Mn–Cl bond lengths equal to 1.558 Å and 2.127 Å respectively whereas the triplet MnO3Cl complex on the triplet PES has all the three Mn=O and Mn–Cl bond lengths at 1.723 Å, 1.552 Å, 1.556 Å, and 2.124 Å respectively. Furthermore, the MnO3Cl complex has all Mn=O and Mn–Cl bond lengths equal to 1.550 Å and 2.106 Å respectively whereas the triplet MnO3Cl complex on the triplet PES has all the three Mn=O and Mn–Cl bond lengths at 1.744 Å, 1.550 Å, 1.549 Å, and 2.103 Å respectively at the M06 level of theory. As observed in sections 3.1 and 3.2, the triplet oxo complex showed less stability compared to the singlet structure (<20.00 kcal/mol) at both levels of theory. The formation of epoxides on the singlet PES from the manganox- etane and dioxomangana-2,5-dioxolane intermediate precursors was explored at both levels of theory on the singlet and triplet surfaces. However, no transient structure [TS-2A and TS-1D in Scheme 1] could be optimized from both the singlet and triplet PES at both levels. Moreover, it was observed that epoxidation via the transition state [TS- 1Bs in Scheme 1] is an exergonic process (− 27.38 kcal/mol, B3LYP) (− 30.40 kcal/mol, M06). The free activation barrier was computed to be 6.06 kcal/mol and 0.67 kcal/mol at the B3LYP level and M06 level respectively on the singlet PES. On the singlet surface, it was observed that the B3LYP epoxide [1Ds] was found to lie lower than its triplet structure [1Dt] by 5.50 kcal/mol. On the other hand, the M06 triplet epoxide [1Ds] was also found to lie lower than its singlet counterpart [1Dt] by 15.67 kcal/mol. The nature of stability of stationary points as discussed in sections 3.1 and 3.2 was similar to this observation. This tells us that this oxidation of TME mediated by permanganyl chloride will likely occur on the singlet surface. No saddle point structure be optimized for all other concerted reaction mechanisms ([3 + 2] and Fig. 1e. Graphical representation of the interaction between the frontier mo- [2+]) at both levels of theory on the singlet and triplet surface. This tells lecular orbitals between the ReO3Cl complex and TME on the singlet surface at us that permanganyl chloride will exclusively epoxide TME at 298.15 K the DFT/M06/LACVP* level of theory. and 1atm. A similar observation was made by Fosu et al. [31] who predicted the manganese oxo complex of the type, MnO3L (L = F-) to dioxylation, the [2 + 2] route is not favoured for dioxylation due to the exclusively epoxide on the singlet surface at 298.15 K and 1 atm. kinetic and thermodynamic factors. Along the stepwise pathway, one of the C=C π bonds of TME attacks Epoxidation via the transient [TS-1Ds in Scheme 1] was explored at an oxo-ligand of the permaganyl chloride complex to form the organo- both levels of theory on the singlet and triplet PES. On the singlet surface metallic intermediate [1Xs] in Scheme 1. As shown in the Gibbs free 6 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 Scheme 1. A proposed mechanistic pathway for the addition of MO3Cl [M = Mn, Tc, and Re] to tetramethylethylene (TME). Fig. 2a. Relative Gibbs free energy profile diagram for the reaction between TcO3Cl and TME on the singlet surface at the DFT/M06/LACVP*(red colour) and DFT/ B3LYP/LACVP* (black colour) level of theory. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) energy profile (Fig. 3a), the formation of the intermediate 1Xs in manganoxetane, and dioxomangana-2,5-dioxolane at both levels of Scheme 1 is highly spontaneous, however, the organometallic interme- theory on the singlet and triplet PES. The nature of the energetics on the diate [1Xs] could not act as a precursor for the formation of epoxide, PES of the oxidation of TME by permanganyl chloride points out that the 7 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 Fig. 2b. Optimized transition states involved in the reaction between TcO3Cl and TME on the singlet surface at the DFT/M06/LACVP* level of theory. The colour code for atoms; Red = Oxygen, Green = Chlorine, Grey = Carbon, White = Hydrogen, and Green = Technetium. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) manganese oxide complex will predominantly lead to epoxidation at and maximum electronic charge (ΔNmax) of the metal oxo complexes 298.15 K confirming the experimental study by Wistuba et al. [24]. and the TME molecular system on the singlet PES were calculated using equations (1) and (2) respectively. 2.4. Global and local reactivity indices calculations on the singlet PES ω= μ2/2η (1) In this quantum chemical study, the global electrophilicity index (ω) 8 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 Fig. 2c. Optimized transition states involved in the reaction between TcO3Cl and TME on the singlet surface at the DFT/B3LYP/LACVP* level of theory. The colour code for atoms; Red = Oxygen, Green = Chlorine, Grey = Carbon, White = Hydrogen, and Green = Technetium. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) ΔNmax μ (2) shown in equation (1), it is dependent on electronic properties such as = − /η the electronic chemical potential μ [Eq. (3)], and chemical hardness The electrophilicity indexes quantitatively predict the electron- [33], η [Eq. (4)] accepting nature of reacting species on reaction surfaces [32]. As 9 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 Fig. 3a. Relative Gibbs free energy profile diagram for the reaction between MnO3Cl and TME on the singlet surface at the DFT/MO6/LACVP*(red colour) and DFT/B3LYP/LACVP* (black colour) level of theory. (For interpretation of Fig. 2d. Graphical representation of the interaction between the frontier mo- the references to colour in this figure legend, the reader is referred to the Web lecular orbitals between the TcO3Cl complex and TME on the singlet surface at version of this article.) the DFT/B3LYP/LACVP* level of theory. μ HOMO + LUMO= (3) 2 η = [LUMO] – [HOMO] (4) Hence, molecular structures that have large electrophilicity values will tend to be more reactive toward nucleophilic centres on the reaction surface in a given set of reagents. These equations are based on the Koopmans theory [34] originally established for calculating ionization energies from closed-shell Hartree–Fock wavefunction but have since been adopted as acceptable approximations for computing electronic chemical potential and chemical hardness. Furthermore, the maximum electronic charge transfer (ΔNmax) estimates the maximum electronic charge that an electrophile may accept. This means that molecular systems with large ΔNmax index would be the best electrophile for a given series of compounds. The ΔNmax values for all transition metal oxo complexes are greater than that of the TME system on the singlet PES. This indicates that on the reaction surfaces the transition metal oxo complexes will be electrophiles as shown in Table 1 at both levels of theories. As evident from Table 1, all the transition metal oxo complexes have a lower chemical potential (μ) compared to the TME molecular system on the singlet PES at both levels of theories. This suggests that electrons will tend to easily move from the olefinic systems to the metal complexes on the singlet PES. At both levels of theories, it is evident that the TME geometry has the largest chemical potential value indicating that it will be easy to liberate electrons from the TME system to the metal oxo complexes on the singlet PES. This indicates that TME is the nucleophile and the metal oxo complexes are the electrophiles. These results support Fig. 2e. Graphical representation of the interaction between the frontier mo- the observation made with the frontier molecular orbital calculations. lecular orbitals between the TcO3Cl complex and TME on the singlet surface at Furthermore, the permanganyl chloride has the highest electrophi- the DFT/M06/LACVP* level of theory. licity index value followed by the technetium and rhenium oxide com- plexes. This electronic nature indicates that the permanganyl complex will be the likely complex to easily accept electrons from the olefins with the rhenium oxide complex being the least. 10 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 Fig. 3b. Optimized transition states involved in the reaction between MnO3Cl and TME on the singlet surface at the DFT/M06/LACVP* level of theory. The colour code for atoms; Red = Oxygen, Green = Chlorine, Grey = Carbon, White = Hydrogen, and Voilet = Manganese. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) Fig. 3c. Optimized transition states involved in the reaction between MnO3Cl and TME on the singlet surface at the DFT/B3LYP/LACVP* level of theory. The colour code for atoms; Red = Oxygen, Green = Chlorine, Grey = Carbon, White = Hydrogen, and Voilet = Manganese. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) This observation can also be related to the activation and reaction was done to study the effects of temperature changes on the reaction energies on the reaction surface with the most electrophilic system being properties (kinetics and thermodynamics) of the addition of MO3Cl (M the most reactive and thus having the lowest activation and reaction = Mn, Tc, and Re) to tetramethylethylene on both singlet and triplet PES energies. This further explains why the rhenium oxide addition route has at both levels of theories (M06 and B3LYP). the highest activation and reaction energies and the permanganyl At both levels of theory (M06 and B3LYP), it was observed that in chloride catalyzed route has the lowest activation and reaction energies cases where no stationary points could be optimized from both singlet on the singlet PES. and triplet PES at 298.15 K, the observation was the same when the temperatures were elevated to 323.15 K and 373.15 K. For example, as seen in Table S4, there are no activation energy barriers observed for the 2.5. Temperature changes effects on the oxidation strengths of MO3Cl (M concerted [2 + 1] and the stepwise mechanistic route [TS-1X] at all = Mn, Tc, and Re) temperatures. Generally, it was observed that the free activation and reaction en- The reaction temperature was varied to 323.15 K (50 ◦C) and 373.15 ergies increased when the temperature was changed from 298.15 K to K (100 ◦C) after the reaction was studied at room temperature (298.15 K, 373.15 K on the singlet PES as shown in Tables S4–S9. This observation, 25 ◦C). The reaction and activation energies along the reaction pathway therefore, tends to suggest that at elevated temperatures the oxidation for each catalyzed route structure can be found in Tables S4–S9. This 11 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 This could be attributed to the fact that at elevated temperatures, the catalyst deactivates or decomposes hence affecting the fate of the re- action. As evident from Tables S4–S9, the oxidation reaction will be suitable to perform at 298.15 K and 1 atm for maximum yield of prod- ucts. Moreover, the stabilities of the reaction pathways did not change as all mechanistic channels were still not favoured thermodynamically and kinetically at varying temperatures for all catalyzed surfaces. Further- more, from the computations at both levels of theories, the reaction mechanism favoured the concerted reaction mechanism over the step- wise reaction pathways at elevated temperatures. As shown in Tables S4–S9, the preferred reaction mechanism in terms of dioxylation was via the [3 + 2] mechanistic channel respec- tively where plausible. Similar to what was observed in sections 3.1-3.3, all singlet stationary points were computed to be stable over their triplet counterparts at the elevated temperatures except with the formation of dioxomangana-2,5-dioxolane intermediate where the vice versa occurs at both levels of theories. It was observed that the temperature changes did not affect the na- ture of the bonding of the reacting species between 298.15 K and 373.15 K as electrons still flowed from the HOMO of the tetramethylethylene (TME) molecule into the LUMO of the metal oxo complexes in all cases. 2.6. Rate constants (k) calculations of the main mechanistic pathways The rate constants of all considered reaction pathways at 298.15 K were calculated for all catalyzed singlet reaction surfaces at both levels Fig. 3d. Graphical representation of the interaction between the frontier mo- of theories using equation (5) [35,35,36]. lecular orbitals between the MnO3Cl complex and TME on the singlet surface at the DFT/B3LYP/LACVP* level of theory. KᵦT k T e− ΔG ◦ [ ] = RT (5) h◦C where KB = 1.380662 × 10− 23 J/K is Boltzmann’s constant, T = 298.15 K is the reaction temperature, h = 6.62617 × 10− 34 Js is Planck’s con- stant, R = 1.987 cal/mol.K is the molar gas constant, ΔG◦ is the Gibbs free energy of activation, and ◦C is the concentration of the reacting species which is taken as 1 M. In Tables 2–4, the [3 + 2] rate constant values represent k values for the initial [3 + 2] route, the [2 + 2]a values represent the rate constants for the initial [2 + 2] route and the [2 + 1] values give the rate constant for the direct addition leading to epoxidation. Furthermore, the [2 + 2]b and [2 + 2]c values show the rate constant values for the mechanistic channels for the conversion of the metallaoxetane intermediate into dioxylate intermediate and epoxides respectively on the singlet PES. The rate constant values for the formation of the organometallic interme- diate [1Xs] are also shown in Tables 2–4 From Tables 2 and 3, it is clear that the fastest reaction mechanism among all pathways studied is the [3 + 2] mechanistic route leading to dioxylation on the singlet PES since the rate constant in both cases is the highest compared to other competing routes. Furthermore, the [2 + 2] route is a relatively slow reaction process due to low reaction rate constant values for both the rhenium and technetium-catalyzed surfaces. The stepwise process leading to the formation of the 1X intermediate from the technetium oxide catalyzed surface as shown in Table 3 is a moderately fast reaction. This makes it a competing process kinetically with the [3 + 2] route. The rhenium oxide catalyzed surface [3 + 2] route is 5.58 × 106 (B3LYP) or 4.11 × 103 (M06) faster than the [2 + 2] route whereas the [3 + 2] reaction mechanism is 4.09 × 1021 (B3LYP) or 2.46 × 1016 (M06) faster than the [2 + 2] route on the technetium oxide catalyzed singlet PES. For the epoxidation process seen in the case of the oxidation TME by the permanganyl chloride (results in Table 4), the reaction mechanism is Fig. 3e. Graphical representation of the interaction between the frontier mo- very fast due to the high-rate constant value at 298.15 K. In all cases, the lecular orbitals between the MnO3Cl complex and TME on the singlet surface at rate constants from the M06 simulations were higher than that of B3LYP DFT/M06/LACVP* level of theory. computations on the singlet PES. reaction becomes more kinetically and thermodynamically unstable. 12 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 Table 1 Quantum chemical parameters of all reacting species presented in this study at the B3LYP/LACVP* and M06/LACVP* level of theory in the gas phase. Reactants B3LYP/LACVP* M06/LACVP* μ (eV) η (eV) ω ΔNmax μ (eV) η (eV) ω ΔNmax TME 3.47 6.94 0.87 − 0.50 3.69 7.38 0.92 − 0.50 MnO3Cl − 7.63 3.85 7.55 1.98 − 7.73 4.36 6.85 1.77 TcO3Cl − 7.31 5.07 5.27 1.44 − 7.43 5.56 4.96 1.34 ReO3Cl − 6.90 5.85 4.07 1.18 − 7.04 6.50 3.81 1.08 DFT/B3LYP/LACVP* and DFT/M06/LACVP* computations. It was also Table 2 observed that the reaction and activation energies computed at DFT/ Rate constants (s− 1) for the formation of the various products in the oxidation of M06/LACVP* were lower compared to the DFT/B3LYP/LACVP* en- TME mediated by ReO3Cl on the singlet PES in the gas phase. ergies in all cases. From the computations, it is evident that MO3Cl (M = ReO3Cl [3 + 2] [2 + 2]a [2 + 2]b [2 + 2]c Mn and Tc) is a good oxidation catalyst for olefinic substrates. B3LYP 1.36 × 10− 12 2.44 × 10− 19 2.87 × 10− 30 4.12 × 10− 26 Furthermore, frontier molecular orbital (FMO) analysis showed that the M06 6.49 × 10− 9 1.58 × 10− 12 1.58 × 10− 22 1.06 × 10− 16 HOMO of the TME molecule couples with the LUMO of the MO3Cl (Mn, Tc, and Re) complex on the singlet PES at both levels of theory. Also, it was observed that the dioxylation and epoxidation reaction mechanisms Table 3 on the concerted reaction surface were stable over their formation on the Rate constants (s− 1) for the formation of the various products in the oxidation of stepwise reaction surface at all temperatures. TME mediated by TcO3Cl on the singlet PES in the gas phase. Moreover, from the quantum simulations, it can be predicted that the TcO3Cl [3 + 2] [2 + 2]a [2 + 2]b [2 + 2]c 1X oxidation reaction at elevated temperatures tends to become more B3LYP 2.60 6.36 3.22 2.61 1.10 kinetically and thermodynamically unstable due to increasing free × × × × × 10− 1 10− 23 10− 15 10− 9 10− 6 activation and reaction energies. Hence, the best condition to consider M06 1.77 × 103 7.19 × 7.35 × 10− 5 3.80 × 10◦ 7.91 × for the oxidation reaction studied will be at a temperature and pressure 10− 14 10− 1 of 298.15 K and 1 atm respectively. Furthermore, the rate constant calculations suggested that the epoxidation process via the permanganyl chloride catalyzed surface was the fastest process of all catalyzed sur- Table 4 faces studied with the highest rate constant values at both levels of Rate constants (s− 1) for the formation of the various products in the oxidation of theories. Also, the [3 + 2] route was found to be faster than the TME mediated by MnO3Cl on the singlet PES in the gas phase. competing [2 + 2] route in all cases on the singlet PES. MnO3Cl [2 + 1] 1X Conclusively, the theoretical results point out that the reaction B3LYP 6.15 1012 1.83 108 mechanisms of the addition of TME to MO3Cl complexes proceed simi-× × M06 9.87 × 1011 1.07 × 1012 larly as seen in the oxidation of ethylene by MO3Cl (M = Mn, Tc, and Re) complexes. From the reactivity indices, the metal oxo complexes will act as the 2.7. B3LYP results versus M06 results electrophiles whiles TME acts as the nucleophile with the permanganyl chloride being the best electrophile as observed from both levels of From the theoretical results as discussed in the early result sections theories. It was also found that the electrophilic nature among the group (all figures and tables), it is clear that the results (reaction energies, bond VII B group decreases down the group, thus Mn > Tc > Re, which is in lengths, angles, and dipole moments) obtained from the M06 simula- good correlation with the activation and reaction energies. tions are better than the B3LYP theoretical results on both singlet and triplet PESs. Ethical approval The M06 functional is a global hybrid metageneralized gradient approximation (meta-GGA) with 27% of Hartree–Fock exchange, lead- Not applicable. ing to a well-balanced functional for overall good performance for chemistry. For main group, organometallics, kinetics, and non-covalent Authors’ contributions bonds, M06 suite has a very good response under dispersion forces, improving one of the biggest deficiencies in DFT methods [7]. The s6 All authors (E.A.F, C.O, L.H, A.A, A.O, MKA, and A.M) have made a scaling factor on Grimme’s long range dispersion correction is 0.25. This substantial, direct, and intellectual contribution to the work and accounts for why M06/LACVP* simulations generally have slightly approved it for publication. lower energies and shorter bond lengths compared to the B3LYP/LACVP. Funding 3. Conclusion We acknowledge The University of Ghana for financial support, The University of Johannesburg for using the Spartan cluster, and the Centre The results from this theoretical study show that the [3 + 2] mech- for High-Performance Computing (CHPC-South Africa) for using the anistic pathway is both kinetically and thermodynamically favorable for cluster. the formation of diols for the oxidation of MO3Cl (M = Tc and Re) by TME upon hydrolysis. Availability of data and materials On the MnMnO3Cl-catalyzedinglet PES, there are no side reactions that competed with the formation of the epoxides. Furthermore, for the Electronic supporting information data file is submitted. All data are MO3Cl (M = Tc and Re) catalyzed surfaces, epoxide formation if plau- included in this article and its supplementary material file. sible will form via the [2 + 2] mechanistic channel on the singlet PES, but not via the [3 + 2] or [2 + 1] direct pathway as evident from the 13 E.A. Fosu et al. J o u r n a l o f M o l e c u l a r G r a p h i c s a n d M o d e l l i n g 120 (2023) 108419 Declaration of competing interest accelerated osmylations, J. Am. Chem. Soc. 119 (8) (1997) 1840–1858, https:// doi.org/10.1021/ja961464t. [16] R. Tia, E. Adei, [3+2] versus [2+2] addition of metal oxides across CC bonds: a The authors declare that they have no known competing financial theoretical study of the mechanisms of oxidation of ethylene by osmium oxide interests or personal relationships that could have appeared to influence complexes, Comput. Theor. 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