A DFT Study on the Molecular Mechanism of Additions of Electrophilic and Nucleophilic Carbenes to Non-Enolizable Cycloaliphatic Thioketones

The molecular mechanisms of addition of dihalocarbenes and dimethoxycarbene to thioketones derived from 2,2,4,4-tetrmethylcyclobutane-1,3-dione were examined on the basis of the DFT wb97xd/6-311g(d,p)(PCM) calculations. Obtained results demonstrated that the examined processes exhibit polar nature and in the case of electrophilic dichloro-, and dibromocarbenes are initiated by the attack of carbene species onto the sulfur atom of the C=S group. Remarkably, reactions involving more electrophilic carbenes (dichloro-, and dibromocarbene) proceeds via stepwise mechanism involving thiocarbonyl ylide as a transient intermediate. In contrast, analogous reactions with nucleophilic dimethoxycarbene occur via a single step reaction, which can be considered as the [2 + 1] cycloaddition reaction initiated by the attack onto the C=S bond. A computational study showed that difluorocarbene tends to react as a nucleophilic species and resembles rather dimethoxycarbene and not typical dihalocarbene species. Significantly higher reactivity of the thioketone unit in comparison to the ketone group, both present in 3-thioxo-2,2,4,4-tetramthylcyclobutanone molecule, was rationalized in the light of DFT computational study.


Introduction
Carbenes form a group of reactive intermediates in which the central the two-valent carbon atom plays the most important role, determining their structure and chemical behavior [1][2][3][4]. In the last 25 years, along with better known 'classic' electrophilic carbenes, the chemistry of nucleophilic analogues, and especially 'nucleophilic heterocycloc carbenes' (NHCs), has been under rapid development [5][6][7]. Great importance of both electrophilic and nucleophilic carbenes, in the current organic and organometallic chemistry, is demonstrated by a large number of original publications and reviews, which have appeared in the last five years [8][9][10][11][12]. Very recently, new reactions within situ generated carbenes, using non-conventional techniques, such as mechanochemical synthesis [13] or flow-technique [14], have also been reported.
Whereas theoretical studies on mechanisms of [2 + 1] cycloadditions of carbenes with ethylenic compounds are widely discussed in numerous publications [1][2][3][26][27][28], there is a lack of similar works focused on reactions with thiocarbonyl compounds. Appearance of 1,3-dipoles such as azomethine ylides, carbonyl ylides, or thiocarbonyl ylides as reactive intermediates in reactions of carbenes/carbenoiods with imines [29,30], carbonyl [31], and thiocarbonyl compounds [32,33], respectively, has been discussed in numerous publications but the details of postulated mechanisms have never been elucidated using theoretical methods. Due to our continuous interest in the chemistry of thiocarbonyl compounds on one side and in nucleophilic as well as electrophilic carbenes on the other one, we decided to study reactions of some, synthetically significant thioketones with both types of carbenes in detail, and the DFT method was selected as an appropriate tool to solve this problem. Whereas theoretical studies on mechanisms of [2 + 1] cycloadditions of carbenes with ethylenic compounds are widely discussed in numerous publications [1][2][3][26][27][28], there is a lack of similar works focused on reactions with thiocarbonyl compounds. Appearance of 1,3-dipoles such as azomethine ylides, carbonyl ylides, or thiocarbonyl ylides as reactive intermediates in reactions of carbenes/carbenoiods with imines [29,30], carbonyl [31], and thiocarbonyl compounds [32,33], respectively, has been discussed in numerous publications but the details of postulated mechanisms have never been elucidated using theoretical methods. Due to our continuous interest in the chemistry of thiocarbonyl compounds on one side and in nucleophilic as well as electrophilic carbenes on the other one, we decided to study reactions of some, synthetically significant thioketones with both types of carbenes in detail, and the DFT method was selected as an appropriate tool to solve this problem.
The goal of the present computational study was elucidation of the nature of reactive intermediates, which appear in the course of reactions of non-enolizable, sterically crowded thioketones 2a-c, derived from 2,2,4,4-tetramethylcyclobutanone, as well as 2,2,5,5-tetramethylcyclopentanethione (2d) and disclosure of differences between reactions pathways observed in its reactions with differently substituted, electrophilic and nucleophilic carbenes (1a-b versus 1c-d).

Results and Discussion
The presented study is divided into three parts: (i) firstly, the analysis of the electronic properties of addends and their intermolecular interactions according to Conceptual Density Functional Theory (CDFT) reactivity indices is carried out; (ii) in the next paragraph, a full mechanistic consideration of the reaction of dichlorocarbene (1a) with 2,2,4,4-tetramethylcyclobutane-1,3-dithione (2a) is explored, characterized, and discussed; (iii) finally, selected aspects of reactions of carbenes 1a and 1c-d with thiones 2ab are studied.

Global Reactivity
The CDFT is considered a powerful tool for understanding the reactivity of substrates involved in a polar cycloaddition reaction. The CDFT indices were calculated at the B3LYP/6-31G(d) computational level in the gas phase, because it was used to define the universal electrophilicity and nucleophilicity scales [34,35]. The global reactivity indices, namely, electronic chemical potential μ, chemical hardness η, global electrophilicity ω, and global nucleophilicity N, for the reagents involved in reactions are given in Table 1. The goal of the present computational study was elucidation of the nature of reactive intermediates, which appear in the course of reactions of non-enolizable, sterically crowded thioketones 2a-c, derived from 2,2,4,4-tetramethylcyclobutanone, as well as 2,2,5,5-tetramethylcyclopentanethione (2d) and disclosure of differences between reactions pathways observed in its reactions with differently substituted, electrophilic and nucleophilic carbenes (1a-b versus 1c-d).

Results and Discussion
The presented study is divided into three parts: (i) firstly, the analysis of the electronic properties of addends and their intermolecular interactions according to Conceptual Density Functional Theory (CDFT) reactivity indices is carried out; (ii) in the next paragraph, a full mechanistic consideration of the reaction of dichlorocarbene (1a) with 2,2,4,4-tetramethylcyclobutane-1,3-dithione (2a) is explored, characterized, and discussed; (iii) finally, selected aspects of reactions of carbenes 1a and 1c-d with thiones 2a-b are studied. The CDFT is considered a powerful tool for understanding the reactivity of substrates involved in a polar cycloaddition reaction. The CDFT indices were calculated at the B3LYP/6-31G(d) computational level in the gas phase, because it was used to define the universal electrophilicity and nucleophilicity scales [34,35]. The global reactivity indices, namely, electronic chemical potential µ, chemical hardness η, global electrophilicity ω, and global nucleophilicity N, for the reagents involved in reactions are given in Table 1. Firstly, we analyzed interaction between addents reagarding the reaction of 2a with 1a. The electronic chemical potential [35,36] µ of 2a, −4.24 eV, is significantly higher than this of 1a, −5.45 eV (Table 1). It means that, in the course of reaction 1a + 2a, the flux of the electron density will take place from thione 2a to carbene 1a. A similar situation is observed for reactions between thioketones 2b-d and carbene 1a (Table 1). Moreover, the electronic chemical potential µ of dibromocarbene (1b), −5.33 eV, is significantly lower than these of 2a-d (Table 1). It means that, in the course of reaction of 1b with 2a-d the flux of the electron density will be directed also from thioketones 2a-d to carbene 1b. On the other hand, electronic chemical potential µ of difluorocarbene (1c) and dimethoxycarbene (1d), −3.00 and −2.90 eV, respectively, is significantly higher than in analyzed thiones 2a-d (Table 1). It means that, for the reaction 1c + 2a-d, and also 1d + 2a-d, the flux of electron density will be directed from carbenes 1c and 1d to thioketones 2a-d.
The electrophilicity ω indexes of dichlorocarbene (1a) and dibromocarbene (1b) were calculated to 3.91 and 4.11 eV, respectively. It means that both carbenes 1a and 1b can be classified as superelectrophilic species. On the other hand, the nucleophilicity N indexes of 1a and 1b were calculated to 1.76 and 2.06 eV, respectively (Table 1). Therefore, they can be classified as a marginal nucleophiles.
In turn, the electrophilicity ω indexes of difluorocarbene (1c) and dimethoxycarbene (1d) were calculated to 0.81 and 0.75 eV, respectively, and these values are drastically lower in comparrison to electrophilicity ω index of 1a and 1b. On the other hand, the nucleophilicity N indexes of 1c and 1d were calculated to 2.94 and 3.42 eV, respectively, and these values are relatively higher when compared with the nucleophilicity N index of 1a and 1b (Table 1). In consequence, carbenes 1c and 1d can be classified as marginal electrophiles but strong nucleophile at the same time.

Local Reactivity
The regioselectivity of polar processes of non-symmetric reagents can be specified through interaction between the most electrophilic center of the electrophile and the most nucleophilic ones of the nucleophile. In this context, the electrophilic P k + and nucleophilic P k − Parr functions were shown to be the most accurate and insightful tools for the study of local reactivity [38]. In order to characterize the most nucleophilic and the most electrophilic center of the species involved in the analyzed reactions, the electrophilic P k + and nucleophilic P k − Parr functions of carbenes 1a-d and thioketones 2a-d were studied ( Figure 2).
Analysis of the nucleophilic P k − Parr functions of thioketones 2a and 2c-d indicates that the sulfur atom of >C=S fragment constitutes the most nucleophilic center of these species presenting the maximum values at P k − = 0.49 (2a), 0.85 (2c), and 0.91 (2d) eV, respectively ( Figure 2). On the other hand, analysis of the electrophilic P k + Parr functions of thiones 2a and 2c-d indicates that the carbon atom of >C=S fragment is the most electrophilic center of these species presenting the maximum values at P k + = 0.33 (2a), 0.65 (2c) and 0.67 (2d) eV, respectively ( Figure 2). Moreover, the presence of two thiocarbonyl groups in 2a results in a significant reduction of values for both local nucleophilicity and local electrophilicity. On the other hand, 3-thioxocyclobutanone 2b possesses two significant reactive centers, namely >C=S and >C=O groups. Therefore, the nucleophilic P k − Parr functions of thioketone 2b indicates that the sulfur atom constitutes the most nucleophilic center, presenting the maximum value at P k − = 0.66 eV. In turn, the electrophilic P k + Parr functions of 2b indicates that the carbon atom of >C=S fragment is the most electrophilic center, presenting the maximum value at P k − = 0.54 eV ( Figure 2). Notably, in comparison to 2c and 2d, the presence of >C=S and >C=O moieties in the structure of 2b does not result in significant changes in values of local nucleophilicity and local electrophilicity, as well. It is worth mentioning that all of analyzed thioketones 2a-d display a similar reactivity.

Local Reactivity
The regioselectivity of polar processes of non-symmetric reagents can be spe through interaction between the most electrophilic center of the electrophile and the nucleophilic ones of the nucleophile. In this context, the electrophilic Pk + and nucleo Pk − Parr functions were shown to be the most accurate and insightful tools for the of local reactivity [38]. In order to characterize the most nucleophilic and the most el philic center of the species involved in the analyzed reactions, the electrophilic Pk nucleophilic Pk − Parr functions of carbenes 1a-d and thioketones 2a-d were studied ure 2).  Figure 2). On the other hand, analysis of the electrophilic Pk + Parr functio thiones 2a and 2c-d indicates that the carbon atom of >C=S fragment is the most el philic center of these species presenting the maximum values at Pk + = 0.33 (2a), 0.6 and 0.67 (2d) eV, respectively ( Figure 2). Moreover, the presence of two thiocar groups in 2a results in a significant reduction of values for both local nucleophilicit local electrophilicity. On the other hand, 3-thioxocyclobutanone 2b possesses two si cant reactive centers, namely >C=S and >C=O groups. Therefore, the nucleophilic Pk functions of thioketone 2b indicates that the sulfur atom constitutes the most nucleo center, presenting the maximum value at Pk − = 0.66 eV. In turn, the electrophilic Pk functions of 2b indicates that the carbon atom of >C=S fragment is the most electro center, presenting the maximum value at Pk − = 0.54 eV (Figure 2). Notably, in compa to 2c and 2d, the presence of >C=S and >C=O moieties in the structure of 2b does not in significant changes in values of local nucleophilicity and local electrophilicity, as It is worth mentioning that all of analyzed thioketones 2a-d display a similar reactiv According to CDFT theory [34,39], the described interactions show that the reac of thioketones 2a-d with dichlorocarbene (1a) and dibromocarbene (1b) in the i phase will be realized through the interaction of sulfur atom of 2a-d with the two-v carbon atom of carbenes 1a-b. In turn, reactions of 2a-d with difluorocarbene (1c dimethoxycarbene (1d) are initiated by the interaction of carbon atom of the C=S g with reactive C-center of respective carbene. According to CDFT theory [34,39], the described interactions show that the reactions of thioketones 2a-d with dichlorocarbene (1a) and dibromocarbene (1b) in the initial phase will be realized through the interaction of sulfur atom of 2a-d with the two-valent carbon atom of carbenes 1a-b. In turn, reactions of 2a-d with difluorocarbene (1c) and dimethoxycarbene (1d) are initiated by the interaction of carbon atom of the C=S group with reactive C-center of respective carbene.
In the first step, the reaction occurs via TS1A transition state, and its formation is accompanied by an increase of the Gibbs free energy of the reaction system of ca. In contrast to transformation involving carbene 1a, this reaction proceeds via single transition state (TSB). This process is accompanied by the overcome of the activation barrier of 23.1 kcal/mol and 16.5 kcal/mol, respectively, for reactions involving less nucleophilic difluorocarbene (1c), and more nucleophilic dimethoxycarbene (1d). The kinetic aspects of considered additions correlate perfectly with the nature of global interaction between addents. Within the discussed TS, two new ϭ bonda are formed; firstly, between C(1) and S(2) and secondly, between C(1) and C(3) atoms. Thus, formally, this process can be interpreted as the [2 + 1] cycloaddition reaction. The IRC analysis confirms that the localized TS can directly connect with respective valleys of reagents and heterocyclic adducts.
bond is formed between C(1) and S(2) reaction sites. At the same time, the C(1)-C(3) distance remains beyond of the range that is typical for C-C bonds in the transition state [43]. Subsequently, the IRC analysis connects the energetic maximum of TS, with the valleys of individual reagents 1a + 2a and 7aa intermediate. So, the localized TS should be connected with the A-type reaction mechanism (Scheme 3). The further movement from the TS area along the reaction coordinate leads to the minimum connected with the existence of thiocarbonyl ylide 7aa. Evidently, the reaction is determined by an attack of carbene species onto the sulfur atom of the >C=S moiety, which correlates excellently with the nature of local interactions analyzed within the previous paragraph.

A Full Mechanistic Considerations Reaction of Dichlorocarbene (1a) with 2,2 Tetramethylcyclobutane-1,3-dithione (2a)
For reactions of thioketone and with carbene species, two competitive mec can be considered (Scheme 3). In the first case (route A), the formation of the thiir occurs via stepwise mechanism, with the intervention of thiocarbonyl ylide as a intermediate [40]. Alternatively (route B), the thiirane ring can be formed accordin one-step [2 + 1] cycloaddition scheme [26,41]. The computational wb97xd/6-311g(d,p)(PCM) study was performed based model reaction of dichlorocarbene (1a) with 2,2,4,4-tetramethylcyclobutane-1,3-d (2a). Obtained results demonstrated that this transformation, carried out in the chl solution, occurs via stepwise mechanism [42], with the participation of two tr states and a single intermediate (Figure 3). In the first step, the reaction occurs via TS1A transition state, and its form accompanied by an increase of the Gibbs free energy of the reaction system 10kcal/mol. Within this TS, a single new ϭ bond is formed between C(1) and S(2) occurs via stepwise mechanism, with the intervention of thiocarbonyl ylide as a reactive intermediate [40]. Alternatively (route B), the thiirane ring can be formed according to the one-step [2 + 1] cycloaddition scheme [26,41]. The computational wb97xd/6-311g(d,p)(PCM) study was performed based on the model reaction of dichlorocarbene (1a) with 2,2,4,4-tetramethylcyclobutane-1,3-dithione (2a). Obtained results demonstrated that this transformation, carried out in the chloroform solution, occurs via stepwise mechanism [42], with the participation of two transition states and a single intermediate (Figure 3). In the first step, the reaction occurs via TS1A transition state, and its formation is accompanied by an increase of the Gibbs free energy of the reaction system of ca. 10kcal/mol. Within this TS, a single new ϭ bond is formed between C(1) and S(2) reaction From an energetic point of view, addition of 1a to 2a is favorable from thermodynamic point of view, because the Gibbs free energy of thiocarbonyl ylide 7aa is substantially lower than individual addents 1a and 2a. Within the molecule of transient thiocarbonyl ylide, the central >C=S=C< fragment displays the planar structure, and it is located coplanar to four-membered cyclobutane ring. The transformation of 7aa into 8aa is realized via single TS (TS2A) and this process is accompanied by the overcoming of the activation barrier calculated to ca. 12 kcal/mol. Within TS2A, the interatomic distance C(1)-C(3) is shortened when compared with analogous distance in transient ylide 7aa. Subsequently, the dihedral angle between the >C=S=C< fragment and the cyclobutane ring is increased to 48 • . The IRC calculations connect this TS with valleys of 8aa and 9aa. The 8aa→ 9aa is fully irreversible, because the Gibbs free energy of the transformation is equal to −49kcal/mol. Within the 9aa structure, the three-membered ring is fully formed, and it is perpendicularly located to the plane of cyclobutane ring.
The existence of the second >C=S bond in the starting molecule determines two-fold addition of carbene, which finally leads to the formation of a mixture of stereoisomeric bis-adducts, i.e., cis-3aa and trans-3aa. The computational study demonstrated that both transformations: 8aa + 1a → cis-3aa and 8aa + 1a → trans-3aa are realized via analogous mechanism as in the case of already discussed reaction 1a + 2a → 8aa (Figures 4 and 5).
At this point, it should be underlined that the more favored kinetical channels of the cyclisation of 9aa proceed via TS2A2 cis transition state and lead to formation of bis-spiro-adducts with cis configuration of heterocyclic rings in the target molecule. General, mechanistic scheme of addition of dichlorocarbene (1a) with 2,2,4,4-tetramethylcyclobutane-1,3-dithione (2a) is presented in Scheme 4.

Further Aspects of Reactions between Carbenes 1a-d and Thioketones 2a-d
According to a similar scheme proceed analogous reactions involving other thioketone 2 (Tables S1-S5 in Supplementary Materials). It is worth underscoring that in the case of monothioketone 2b, reaction theoretically can proceed upon involvement of >C=S, and/or >C=O bond. The analysis of the local reactivity suggests substantially higher reactivity of the first unit. Indeed, full exploration of reaction channels with the localization, optimization, and verification of all critical structures confirmed this hypothesis. In particular, the wb97xd/6-311g(d,p)(PCM) calculations show that the reaction on the >C=S bond requires the Gibbs free energy of the activation step of ca. 10kcal/mol, whereas the competitive process involving >C=O bond-more than 18kcal/mol ( Figure 6). sites. At the same time, the C(1)-C(3) distance remains beyond of the range that is typical for C-C bonds in the transition state [43]. Subsequently, the IRC analysis connects the energetic maximum of TS, with the valleys of individual reagents 1a + 2a and 7aa intermediate. So, the localized TS should be connected with the A-type reaction mechanism (Scheme 3). The further movement from the TS area along the reaction coordinate leads to the minimum connected with the existence of thiocarbonyl ylide 7aa. Evidently, the reaction is determined by an attack of carbene species onto the sulfur atom of the >C=S moiety, which correlates excellently with the nature of local interactions analyzed within the previous paragraph.
From an energetic point of view, addition of 1a to 2a is favorable from thermodynamic point of view, because the Gibbs free energy of thiocarbonyl ylide 7aa is substantially lower than individual addents 1a and 2a. Within the molecule of transient thiocarbonyl ylide, the central >C=S=C< fragment displays the planar structure, and it is located coplanar to four-membered cyclobutane ring. The transformation of 7aa into 8aa is realized via single TS (TS2A) and this process is accompanied by the overcoming of the activation barrier calculated to ca. 12 kcal/mol. Within TS2A, the interatomic distance C(1)-C(3) is shortened when compared with analogous distance in transient ylide 7aa. Subsequently, the dihedral angle between the >C=S=C< fragment and the cyclobutane ring is increased to 48°. The IRC calculations connect this TS with valleys of 8aa and 9aa. The 8aa→ 9aa is fully irreversible, because the Gibbs free energy of the transformation is equal to −49kcal/mol. Within the 9aa structure, the three-membered ring is fully formed, and it is perpendicularly located to the plane of cyclobutane ring.
The existence of the second >C=S bond in the starting molecule determines two-fold addition of carbene, which finally leads to the formation of a mixture of stereoisomeric bis-adducts, i.e., cis-3aa and trans-3aa. The computational study demonstrated that both transformations: 8aa + 1a → cis-3aa and 8aa + 1a → trans-3aa are realized via analogous mechanism as in the case of already discussed reaction 1a + 2a → 8aa (Figures 4 and 5).   At this point, it should be underlined that the more favored kinetical channels of the cyclisation of 9aa proceed via TS2A2 cis transition state and lead to formation of bis-spiroadducts with cis configuration of heterocyclic rings in the target molecule. General, mechanistic scheme of addition of dichlorocarbene (1a) with 2,2,4,4-tetramethyl-cyclobutane-1,3-dithione (2a) is presented in Scheme 4.

Further Aspects of Reactions between Carbenes 1a-d and Thioketones 2a-d
According to a similar scheme proceed analogous reactions involving other thioketone 2 (Tables S1-S5 in Supplementary Materials). It is worth underscoring that in the case of monothioketone 2b, reaction theoretically can proceed upon involvement of >C=S, case of monothioketone 2b, reaction theoretically can proceed upon involvement of >C=S, and/or >C=O bond. The analysis of the local reactivity suggests substantially higher reactivity of the first unit. Indeed, full exploration of reaction channels with the localization, optimization, and verification of all critical structures confirmed this hypothesis. In particular, the wb97xd/6-311g(d,p)(PCM) calculations show that the reaction on the >C=S bond requires the Gibbs free energy of the activation step of ca. 10kcal/mol, whereas the competitive process involving >C=O bond-more than 18kcal/mol ( Figure 6). Consequently, from a kinetic point of view, within the analyzed reaction system, the addition of 1a to the >C=O moiety, leading to an intermediate carbonyl ylide, should be considered as a forbidden process. From a mechanistic point of view, thus, the reaction leading to 2,2-dichlorooxirane derivative 10ab, proceeds via a completely different scheme as in the case of thiirane formation. In particular, the addition occurs via single transition state. Within this TS, two new ϭ bonds are formed simultaneously and formally, Figure 6. Gibbs free energy profile for reaction of dichlorocarbene (1a) with 3-thioxo-2,2,4,4-tetramethylcyclobutanone (2b) with in the light of wb97xd/6-311g(d,p)(PCM) computational study.
Consequently, from a kinetic point of view, within the analyzed reaction system, the addition of 1a to the >C=O moiety, leading to an intermediate carbonyl ylide, should be considered as a forbidden process. From a mechanistic point of view, thus, the reaction leading to 2,2-dichlorooxirane derivative 10ab, proceeds via a completely different scheme as in the case of thiirane formation. In particular, the addition occurs via single transition state. Within this TS, two new In contrast to transformation involving carbene 1a, this reaction proceeds via single transition state (TSB). This process is accompanied by the overcome of the activation barrier of 23.1 kcal/mol and 16.5 kcal/mol, respectively, for reactions involving less nucleophilic difluorocarbene (1c), and more nucleophilic dimethoxycarbene (1d). The kinetic aspects of considered additions correlate perfectly with the nature of global interaction between addents. Within the discussed TS, two new ϭ bonda are formed; firstly, between C(1) and S(2) and secondly, between C(1) and C(3) atoms. Thus, formally, this process can be interpreted as the [2 + 1] cycloaddition reaction. The IRC analysis confirms that the localized TS can directly connect with respective valleys of reagents and heterocyclic adducts.

Computational Details
All quantumchemical calculations were performed using 'Prometheus' cluster (CYFRONET regional computational center).
The global reactivity indices of the reactants, namely electronic potential μ, chemical hardness η, global electrophilicity ω, and global nucleophilicity N, were estimated in pursuance of the equations defined on the basis of conceptual density functional theory (CDFT) according to the equations recommended by Parr [35] and Domingo [34,45]. In the calculation are used the correlation-exchange functional B3LYP together with the basis 6-31G(d) level set in the gas phase. In this section, the B3LYP/6-31g(d) approach was applied because the electrophilicity and nucleophilicity scales that allow classification of molecules based on their electrophilic and nucleophilic character were established at that level [34,39,45,46].
Molecules 2021, 26, x FOR PEER REVIEW 1 this process can be considered as the [2 + 1] cycloaddition reaction (Figure 7). Gene the mechanistic scheme of addition of dichlorocarbene (1a) to 3-thioxo-2,2,4,4methylcyclobutanone (2b) is presented in Scheme 5.  Finally, additions of nucleophilic carbenes 1c and 1d to thioketone 2a were also lyzed (Scheme 6).  this process can be considered as the [2 + 1] cycloaddition reaction (Figure 7). Generally, the mechanistic scheme of addition of dichlorocarbene (1a) to 3-thioxo-2,2,4,4-tetramethylcyclobutanone (2b) is presented in Scheme 5.  Finally, additions of nucleophilic carbenes 1c and 1d to thioketone 2a were also analyzed (Scheme 6). Finally, additions of nucleophilic carbenes 1c and 1d to thioketone 2a were also analyzed (Scheme 6). In contrast to transformation involving carbene 1a, this reaction proceeds via singl transition state (TSB). This process is accompanied by the overcome of the activation bar rier of 23.1 kcal/mol and 16.5 kcal/mol, respectively, for reactions involving less nucleo philic difluorocarbene (1c), and more nucleophilic dimethoxycarbene (1d). The kinetic as pects of considered additions correlate perfectly with the nature of global interaction be tween addents. Within the discussed TS, two new ϭ bonda are formed; firstly, between C(1) and S(2) and secondly, between C(1) and C(3) atoms. Thus, formally, this process can be interpreted as the [2 + 1] cycloaddition reaction. The IRC analysis confirms that th localized TS can directly connect with respective valleys of reagents and heterocyclic ad ducts.
Earlier, experimental studies demonstrated that thiirane 8cd is efficiently formed from 1c and 2d (generated from Seyerth's regaent) [23]. However, in the case of 2a and 1d expected thiirane 8da was a minor product, only, and nucleophilic 1d preferentially at tacked congested cyclobutane ring yielding five-membered, ring-expanded products [25] Nevertheless, reaction of in situ generated 1d with non-congested adamantenthion yielded corresponding 2,2-dimethoxythiirane as final product, isolated in high yield (83% [44]. In contrast to transformation involving carbene 1a, this reaction proceeds via single transition state (TSB). This process is accompanied by the overcome of the activation barrier of 23.1 kcal/mol and 16.5 kcal/mol, respectively, for reactions involving less nucleophilic difluorocarbene (1c), and more nucleophilic dimethoxycarbene (1d). The kinetic aspects of considered additions correlate perfectly with the nature of global interaction between addents. Within the discussed TS, two new In contrast to transformation involving carbene 1a, this reaction proceeds via single transition state (TSB). This process is accompanied by the overcome of the activation barrier of 23.1 kcal/mol and 16.5 kcal/mol, respectively, for reactions involving less nucleophilic difluorocarbene (1c), and more nucleophilic dimethoxycarbene (1d). The kinetic aspects of considered additions correlate perfectly with the nature of global interaction between addents. Within the discussed TS, two new ϭ bonda are formed; firstly, between C(1) and S(2) and secondly, between C(1) and C(3) atoms. Thus, formally, this process can be interpreted as the [2 + 1] cycloaddition reaction. The IRC analysis confirms that the localized TS can directly connect with respective valleys of reagents and heterocyclic adducts.

Computational Details
bonda are formed; firstly, between C(1) and S(2) and secondly, between C(1) and C(3) atoms. Thus, formally, this process can be interpreted as the [2 + 1] cycloaddition reaction. The IRC analysis confirms that the localized TS can directly connect with respective valleys of reagents and heterocyclic adducts.

Computational Details
All quantumchemical calculations were performed using 'Prometheus' cluster (CYFRONET regional computational center).
The global reactivity indices of the reactants, namely electronic potential µ, chemical hardness η, global electrophilicity ω, and global nucleophilicity N, were estimated in pursuance of the equations defined on the basis of conceptual density functional theory (CDFT) according to the equations recommended by Parr [35] and Domingo [34,45]. In the calculation are used the correlation-exchange functional B3LYP together with the basis 6-31G(d) level set in the gas phase. In this section, the B3LYP/6-31g(d) approach was applied because the electrophilicity and nucleophilicity scales that allow classification of molecules based on their electrophilic and nucleophilic character were established at that level [34,39,45,46].
The electronic chemical potentials (µ) and chemical hardness (η) were evaluated in terms of one-electron energies of FMO (E HOMO and E LUMO ) using the following equations [35,46]: where E HOMO and E LUMO may be approached in terms of the one-electron energies of the frontier MOs respectively HOMO and LUMO.
The values of chemical potentials (µ) and chemical hardness (η) were then used to calculate a global electrophilicity (ω) according to the formula [34,35,47]: In turn, the global nucleophilicity (N) can be expressed as [45]: where E HOMO (TCE) is the HOMO energy for tetracyanoethylene (TCE); is the reference, because it presents the lowest HOMO (E HOMO (TCE) = -9.368 eV). The local electrophilicity (ω k ) and the local nucleophilicity (N k ) concentrated on atom k was calculated based on global properties and the Parr function (P k + or P k − ), according to the formulas [38]: ω k = P + k ·ω N k = P − k ·N For the simulation of the reactions paths, the wb97xd functional included in the GAUSSIAN 09 package [48] and the 6-311g(d,p) basis set [49,50] including both diffuse and polarization functions for all relevant atoms was used. A similar theory level has been commonly used for the mechanistic research aspects of cycloaddition reactions [28,39,[51][52][53][54][55]. All localised stationary points have been characterized using vibrational analysis. It was found that starting molecules as well as products had positive Hessian matrices. On the other hand, all transition states (TS) showed only one negative eigenvalue in their Hessian matrices. For all optimized transition states, intrinsic reaction coordinate (IRC) calculations have been performed. The solvent effect has been included using PCM algorithm [56].

Conclusions
The presented computational study demonstrated that additions of dihalocarbenes to non-enolisable, cycloaliphatic thioketones proceed differently and depend on the type of carbene species involved in the reaction. Whereas electrophilic dichlorocarbene (1a) and dibromocarbene (1b) attack the sulfur atom forming thiocarbonyl ylides as reactive intermediates, less electrophilic difluorocarbene (1c) tend to undergo one-step (but asyn-chronous) [2 + 1] cycloaddition leading to respective 2,2-difluorothiirane. In analogy to 1c, reaction pathway, without formation of an intermediate thiocarbonyl ylide, is observed in the reaction of dimethoxycarbene (1d), which is considered as a typical representative of non-heterocyclic, nucleophilic carbenes.
Obtained results allow us to better understand mechanisms of reactions of carbenes with thiocarbonyl compounds leading to thiiranes or products of their secondary conversions [40]. In addition, they nicely complement experimental observations on appearance of reactive thiocarbonyl S-methanides (thiocarbonyl ylides) in reactions of nonenolizable thioketones with electrophilic methylene [:CH 2 ] carried out in low-temperature Ar-matrices [59].

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.