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On the electron flow sequence driving the hydrometallation of acetylene by lithium hydride

  • Eduardo ChamorroEmail author
  • Mario Duque-Noreña
  • Savaş Kaya
  • Elizabeth Rincón
  • Patricia Pérez
Original Paper
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Part of the following topical collections:
  1. International Conference on Systems and Processes in Physics, Chemistry and Biology (ICSPPCB-2018) in honor of Professor Pratim K. Chattaraj on his sixtieth birthday

Abstract

The sequence of the electronic flow driving the hydrometallation of acetylene by lithium hydride (and that of the opposite β-hydride elimination reaction from the alkenyl metal intermediate), was examined within the perspective provided by the bonding evolution theory (BET). The analysis was based on the application of catastrophe theory to the changes of the electron localization function topology along the intrinsic reaction coordinate. The description of the electronic processes occurring on the process was represented in terms of topological structural stability domains (SSDs) and the associated elementary bifurcation catastrophes. Within such a framework of representation, the “evolution” of the system through the different SSDs reveals the key chemical events driving the transformation, including the large polarization effect as a consequence of Pauli repulsion between ions of the positive cationic metal on the hydride domain, the activation of the CC triple bond to attack the cationic center, and the agostic stabilizing interactions involving the hardest cationic metal, followed by the attack of the hydride center. These results contribute to emphasizing the intrinsic value and usefulness of using topological-based approaches and associated tools to increase our knowledge and understanding of the subtleties underlying the electronic flow as nuclei evolve along the reaction coordinate, providing detailed and complementary insights in comparison to other interpretative tool such those based on orbital-based representations, concerning the intimate nature of the electronic rearrangement of key mechanistic processes in chemistry.

Graphical abstract

The sequence of the electron flow (indicated by letters a and b) along the intrinsic reaction path for the hydrometallation of acetylene by lithium hydride to yield ethenyl lithium via a four-membered transition structure (TS), as determined within the bonding evolution theory to provide the key chemical events driven the changes in the key bonding patterns. Blue arrow Main event on the side HC ≡ CH + LiH → TS, red arrow the TS → HLiC=CH2 pathway, green arrows relative motion of nuclei along the imaginary frequency at the position of TS on the intrinsic reaction coordinate.

Keywords

Bonding evolution theory (BET) Electron localization function (ELF) Catastrophe theory Hydrometallation β-hydride elimination Ethenyl Lithium LiH 

Introduction

Hydrometallation reactions and β-hydride eliminations in alkyl or alkenyl intermediates constitute key processes in several pivotal synthetic and mechanistic approaches in organometallic chemistry [1, 2, 3]. Although it is commonly accepted that direct (uncatalyzed) processes proceed through a four-centered transition state (TS) [4, 5, 6, 7, 8], the detailed knowledge about the nature of the intimate electronic rearrangement have remained a subject of open interest [9, 10, 11, 12]. In such a context, vinyl metalloid intermediates selectively synthetized remains a highly active field of research [13, 14], driving in fact the richness of synthetic strategies within the interest of several useful applications [15, 16, 17].

Following ongoing efforts [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29] oriented to further explore the usefulness of topological approaches for representing chemical bonding concepts within a position-space representation of molecular systems, here we focus on the variation of the electronic pattern driving the reaction mechanism. Within this context, we applied the so-called bonding evolution theory (BET) to characterize chemical transformations [30, 31, 32]. Our aim was to elucidate the sequence of the electronic flow driving such a key hydrometallation processes by examining the reaction of acetylene by lithium hydride taken as one of simplest models for the general interconversion process (i.e., Fig. 1) [11, 33, 34, 35, 36, 37, 38, 39].
Fig. 1

Reaction processes for the direct hydrometallation of alkynes 1 (path A) and the associated β-hydride elimination from alkenyl intermediates 2 (path B) via a concerted four-membered transition structure (TS). The simplest system (R = R’ = H, M = Li) is taken to be examined within a bonding evolution theory (BET) perspective as a representative example for the electronic rearrangement driven such a key processes. The main focus is directed to uncover the precise nature of the sequence of electronic flux driven bond formation/bond breaking processes along the transformation

Within the BET framework, Thom’s catastrophe theory (CT) [40, 41, 42, 43] concepts are applied to identify and characterize changes in topological patterns associated with the evolution of the gradient field of the electron localization function (ELF) [44, 45, 46, 47], along a chosen reaction path [18, 31, 32, 48, 49, 50, 51]. ELF is a local function describing the relative electron pair (de)localization associated to a given electron density [45, 46, 52]. Within the current DFT level of approximation, ELF can be interpreted as the relative local excess of kinetic energy density arising from the Pauli principle [44, 45, 46, 47, 52, 53, 54]. Basin-dependent electron populations as well as variance-related descriptors, useful for rationalizing electron delocalization have been obtained by integrating the one-electron and two-electron density probabilities in the volume of ELF basins [44, 45, 46, 47, 52, 53, 55, 56, 57]. In this way, BET provides a unique understanding of the behavior of any dynamic system in terms of bifurcations related to the changes of the gradient field of a well characterized local function along the chosen reaction coordinate (see recent examples [18, 32, 49, 58, 59]). The system evolution is sketched into a sequential series of structural stability domains (SSDs) defined in terms of the number and type of critical points [18, 30, 59, 60, 61, 62]. SSDs enclose in fact all sequential configurations of the evolving reacting system having the same number and type of critical points of the gradient field of ELF. The turning points separating each pair of SSDs can be therefore identified and characterized in terms of discontinuities or elemental bifurcation catastrophes [30, 42]. In the context of representation that ELF provides for chemical bond and associated concepts (i.e., the basins of attractors derived from the topological analysis of ELF can be identified to bonding concepts of the Lewis theory [23, 44, 54, 63, 64, 65]), the reaction mechanism become rationalized in terms of an ordered sequence of events corresponding to electronic rearrangements driving the creation and/or annihilation of chemical meaningfully entities associated to both non-bonding or bonding regions (e.g., “lone pairs”, “bond pairs”, etc.).

Computational details

Geometry optimization using analytical gradients [66, 67, 68, 69] and the associated characterization (via frequency calculations) of all stationary points involved in the hydrometallation of acetylene by lithium hydride depicted in Fig. 1 were obtained at the B3LYP functional [70, 71] with the 6–31++G(d,p) basis set by using the Gaussian 09 package of programs [72]. The chosen level of theory is adequate for characterizing all relevant electronic effects expected for the reaction path evolution of the target system that includes only Li, C, and H atoms. Given that the ELF topology (i.e., the position of the critical points associated to its gradient field) is invariant to the level of theory calculation [73], it seems reasonable to expect that this good property be transferable to the BET analysis and characterization of such an electronic rearrangement [74, 75]. The intrinsic reaction coordinate (IRC) [76, 77], which corresponds to the minimum energy reaction pathway in mass-weighted Cartesian coordinates connecting the TS and its reactants and products, has been calculated using a standard integration method [68, 69]. The topological analysis of ELF along the IRC [76, 77] has been performed using Topmod [78] and Multiwfn [79]. Elemental catastrophe theory concepts are then applied in order to identify the sequential SSD and corresponding bifurcation catastrophes [30, 48, 50, 51, 60, 61, 62, 80, 81].

Results and discussion

Within the realm of BET, the reaction of hydrometallation of acetylene by lithium hydride emerges as one process characterized by fold (F), cusp (C and C) and elliptic umbilic (U) elementary catastrophes. It is convenient to recall at this point that the fold F singularity is associated with the transformation of a non-critical point into an attractor and a saddle point, increasing by one the total number of basins in the system. The cusp C catastrophe corresponds to the transformation of an attractor into two attractors and a saddle point, also increasing by one the total number of basins, whereas the cusp C bifurcation merges two attractors and a saddle point into an attractor, decreasing by one the total number of basins in the system. Finally, the elliptic umbilic U catastrophe can be simply associated to changes in the synaptic order of a given basin without changing the total number of basins in the system [18, 30, 42, 60].

The energy profile for the hydrometallation of acetylene by lithium hydride process along the IRC is presented in Fig. 2, revealing the nine structural stability domains that have been identified (SSDs, labelled from I to IX) on the basis of changes in the number and type of valence basins arising from the topological analysis of the electron localization function (ELF) for each examined configuration of system evolving along the chosen IRC pathway. Note that the TS configuration is found to be located within the SSD-V.
Fig. 2

Relative energy (kcal mol−1) along the intrinsic reaction coordinate (IRC) for the hydrometallation of acetylene by lithium hydride 1 resulting in ethenyl lithium 2 via a four-membered TS. The structural stability domains (SSDs) are labelled from I to IX, separated by blue (acetylene + lithium hydride side) and red (alkenyl metalloid intermediate side) vertical lines. The positions of the specific configurations separating the different SSDs are indicated on the top axis by the labels p1p8. The corresponding positions of the intrinsic reaction coordinate are: p1 −1.98693, p2 −0.99450, p3 −0.33149, p4 −0.11051, p5 +0.44199, p6 +0.77350, p7 +2.76074, p8 +3.3599

Figure 3 reports the variation of the electron populations associated to the ELF valence basins of selected points of the IRC for the hydrometallation reaction of acetylene by lithium hydride 1 to yield ethenyl lithium 2. The populations of most relevant valence basins for selected points of the IRC including those separating the different SSDs are reported in Table 1.
Fig. 3

Electron populations integrated in the valence basins arising from the topological analysis of the electron localization function for selected points along the IRC associated to the hydrometallation reaction of acetylene by lithium hydride 1 to yield ethenyl lithium 2. The positions of the specific configurations separating the different SSDs are indicated on the top axis by the labels p1p8. The SSDs are separated by blue (acetylene + lithium hydride side) and red (alkenyl metalloid intermediate side) vertical lines. The small population associated to the asynaptic basin appearing in the SSD-VI is interpreted as being part of the V(H3,Li) valence basin in the process that turns it into a trisynaptic one, i.e., V(H3,C2,Li) in the SSD-VII

Table 1

Variation in valence electron localization function (ELF) basin populations (number of electrons) for selected points along the intrinsic reaction coordinate (IRC; in units of amu1/2 .Bohr) for the hydrometallation of acetylene by lithium hydride 1 to yield ethenyl lithium 2 via a four-membered transition structure (TS)

 

IRC

V(H1.C1)

V(H2.C2)

V(H2.C2.Li)

V(C1.Li)

V(H3)

V(H3.Li)

V(Asyn)

V(H3.C2.Li)

V(H3.C2)

V1.2(C1.C2.Li)

V1.2(C1.C2)

1

−3.080

2.24

2.29

  

1.95

    

5.29

 

−2.095

2.23

2.30

  

1.93

    

5.32

 

p1

−1.987

2.23

 

2.30

 

1.93

    

5.32

 

−1.878

2.22

 

2.30

 

1.93

    

5.33

 

−1.105

2.19

 

2.30

 

1.89

    

5.40

 

p2

−0.994

2.18

 

2.29

0.47

1.88

    

4.95

 

−0.884

2.17

 

2.30

0.59

1.87

    

4.84

 

−0.442

2.14

 

2.30

0.92

1.82

    

4.60

 

P3

−0.331

2.12

 

2.29

0.99

1.8

    

4.57

 

−0.221

2.12

 

2.29

1.06

1.78

    

4.53

 

p4

−0.110

2.11

 

2.28

1.11

 

1.77

   

4.50

 

TS

0.000

2.10

 

2.28

1.17

 

1.75

   

4.48

 

0.331

2.07

 

2.27

1.37

 

1.69

   

4.37

 

p5

0.442

2.06

 

2.26

1.42

 

1.68

0.05

  

4.30

 

0.552

2.07

 

2.25

1.48

 

1.66

0.09

  

4.24

 

0.663

2.06

2.23

 

1.55

 

1.64

0.16

  

4.14

 

p6

0.774

2.06

2.22

 

1.6

   

1.82

 

4.08

 

0.884

2.06

2.21

 

1.65

   

1.84

 

4.02

 

1.658

2.06

2.12

 

2.01

   

1.95

 

3.64

 

2.650

2.02

2.09

 

2.29

   

2.07

  

3.30

p7

2.761

2.01

2.09

 

2.31

   

2.07

  

3.30

2.868

2.01

2.09

 

2.32

   

2.07

  

3.28

3.276

2.01

2.09

 

2.36

   

2.07

  

3.24

p8

3.360

2.01

2.09

 

2.36

    

2.08

 

3.24

2

3.489

2.01

2.09

 

2.37

    

2.08

 

3.24

The bold entries are associated to the configuration points 1, p1, p2, p3, p4, TS, p5, p6, p7, p8 and 2.

Along the hydrometallation path, i.e., 1 → TS→2, the first structural stability domain (SSD-I) is characterized by structures with seven attractors, providing three core basins C(C1), C(C2), C(Li), two disynaptic valence basins V(H1,C1), V(H2,C2), one monosynaptic valence protonated basin V(H3), and one trisynaptic valence basin V(C1,C2, Li). SSD-I reveals itself as the initial stage of interaction of the metallic center and the C1C2 triple bond. The existence of a trisynaptic signature for the C1C2 region and the cationic metal is clearly present along this domain, where indeed the metal hydride is properly represented as an ionic structure with the explicit charge separation Li+H. The electron population at the V(H3) monosynaptic valence basin decreases only slightly from 1.95e to 1.93e along SSD-I. The first catastrophe, at the turning point p1, corresponds to an elliptic umbilic U bifurcation identified with the change of the synaptic order of the V(H2,C2) valence basin. In the second structural stability domain (SSD-II), also with seven basins, a trisynaptic basin V(H2,C2,Li) identifies the interaction of the C2–H2 single bond region (which localize 2.30e) with the cationic metallic center. In this domain, the V(H3) continues to decrease up to 1.89e. The third structural stability domain (SSD-III) is characterized by the appearance of a new disynaptic valence basin V(C1,Li), increasing to eight the total of basins in the system. Henceforth, the turning point at p2 has been identified with a fold F catastrophe. The electron population at V(C1,Li) increases along SSD-III from 0.47e to 0.92e starting the initial formation of the C1–Li bonding interaction, which will continuously grow up until the end of the path.

The fourth structural stability domain (SSD-IV) starts with a split of the trisynaptic V(C1,C2,Li) valence basin becoming here represented as V1,2(C1,C2,Li), increasing to nine the total number of basins. The turning point at p3 is therefore identified with a cusp C catastrophe. The electron population at the V(H3) basin reaches 1.78e. The fourth catastrophe, at the turning point p4, starting the fifth structural stability domain (SSD-V), corresponds to a new elliptic umbilic U bifurcation identified with the transformation of the monosynaptic V(H3) valence basin into the disynaptic V(H3,Li) one. The electron population integrated at this basin decrease in SSD-V from 1.77e to 1.69e. The transition structure belongs to this SSD-V. In the TS, the V(H3,Li) basin integrating 1.75e is associated to the LiH-bond-forming interaction, two trisynaptic basins V1,2(C1,C2,Li) integrating to 4.48e, are associated to C1C2 bonding region, which remains in interaction with the metallic center. A V(H2,C2,Li) basin integrating 2.28e is also observed to associated with the interaction of the C2H2 bonding region with the metallic center. These results indicate that, along the process from 1 to TS, the sequence of the electronic rearrangement is essentially associated to the formation of a new bonding interaction between the Li and C1 centers [82, 83]. This is revealed by a clear disynaptic basin V(C1,Li). On progressing in such a pathway, agostic interactions of the cationic metal center with the C1C2 and C2H2 bonding regions is also evidenced.

The sixth structural stability domain (SSD-VI) is characterized by the creation of a new attractor in the vicinity of C1, increasing to ten the number of basins. The turning point at p5 is therefore identified with a fold F catastrophe. This basin (formally identified as asynaptic) is related to the very initial stage of formation of the C1–H3 bonding interaction. Note that the very small population associated with such an asynaptic basin (i.e., which varies from 0.05e to 0.16e) can be straightforwardly related as part of the V(H3,Li) valence basin in the process that turns it into a trisynaptic one, i.e., V(H3,C2,Li), in the next SSD. The seventh structural stability domain (SSD-VII) is reached after two simultaneous cusp C and elliptic umbilic U catastrophes at the turning point p6, providing the trisynaptic V(H3,C2,Li) and the change of synaptic order associated to the now disynaptic V(H2,C2) valence basins, respectively, while reducing to nine the total number of basins in the system. This domain ends the agostic interaction between the Li and H2 centers. The eighth structural stability domain (SSD-VIII) is reached after an elliptic umbilic catastrophe U at the turning point p7, which changes the synaptic order of the two valence disynaptic basins associated to the now C1 = C2 double bound. This domain remarks the end of any interaction of the unsaturated C1C2 bond region and the metallic center. The next bifurcation catastrophe corresponds to a new elliptic umbilic U at the turning point p8, which is associated to the change of the synaptic order of the newly formed C2-H3 bond, providing the ninth structural stability domain (SSD-IX) in which further stabilization of the ethenyl lithium product will provide the final alkenyl metal configuration 2.

A simple representation for the sequence of SSDs characterizing the hydrometallation of acetylene by lithium hydride yielding ethenyl lithium is depicted in Fig. 4a, where the number of attractors of ELF and associated synaptic order is sketched [30, 48, 50, 51, 60, 61, 62, 80, 81]. The synaptic order in each case is represented by the number of lines (continuous or dashed) connecting them to the associated core attractors C1, C2 and Li. The activation region from 1 to TS (i.e., SSD I to SSD IV) is characterized by the fast (given the small calculated activation energy) interaction driving the formation of the Li–C1 bond. In the process, the lithium center is observed to coordinate as a cationic species that is stabilized by electron rearrangement from the C1C2 triple bond to form the V(C1,Li) attractor and associated basin. An agostic interaction between the metallic center and the C2–H2 bonding region is also present. In the domain of SSD IV, the C1C2 triple bond associated until that point with a single attractor begins to evolve into a double bond characterized by two attractors. The deactivation path, i.e., SSD VII to SSD IX, is essentially identified with the formation of the H3–C2 bond and the structural stabilization of the ethenyl lithium intermediate. Note that, in such a representation, the “migrating” center H exists as a monosynaptic basin V(H3) along the SSDs I to IV. The new bond H3–C2 is formed after the TS is reached, and the process is always “assisted” by the lithium center, as revealed by the nature of a trisynaptic valence basin V(H3,C2,Li) along the structural stability domains VI–VIII. Such an interpretation given in terms of the sequence of topologically defined structural stability domains, emphasizing a visually appealing picture for rationalizing the rearrangement that complements and expands the arguments invoked from within the traditional molecular orbital paradigm [4, 5, 11, 33, 34, 35, 36, 37, 38, 39].
Fig. 4

a BET representation of the electron localization function (ELF) attractors along the sequence of SSDs characterizing the B3LYP/6–31 + G(d,p) IRC associated to the hydrometallation of acetylene by lithium hydride 1 to yield ethenyl lithium 2. The corresponding bifurcation catastrophes separating each SSD are identified over the arrows. The fold catastrophe F splits a non-critical point into an attractor and a saddle point, increasing by one the total number of basins. The cusp catastrophe C merges two attractors and a saddle point into an attractor, decreasing by one the total number of basins, whereas the C splits an attractor into two attractors and a saddle point, increasing by one the total number of basins. The elliptic umbilic catastrophe U is identified with changes in the synaptic order without changing the total number of basins. Attractors for the core basins, C(Li), C(C1), and C(C2), are represented by single labels Li, C1, and C2, respectively. The attractors associated to disynaptic and trisynaptic basins are represented by black circles. The synaptic order of a given basin is associated to the number of lines connecting such a valence attractors with the core ones. Note that the attack of the hydride center is represented by the evolution of a purely monosynaptic V(H3) basin into the disynaptic protonated V(H3,C2) one, including the formation of both disynaptic V(H3,Li) and trisynaptic V(H3,C2,Li) basins in the process (see the text for details). b Sequence of molecular configurations associated to the SSDs for the hydrometallation of acetylene by lithium hydride 1 to yield ethenyl lithium 2. The value of the energy change (in kcal mol−1) associated to the evolution of the reacting system along each SSD is also reported. Note that the greatest energy change is located on the deactivation path (i.e., SSD-VII, −34.97 kcal mol−1) and corresponds to the process of formation of the new H3–C2 bond

In order to provide a complementary insight about the progress of the reaction, geometrical parameters as well as energy differences associated to the evolution of the reacting system along each SSD is provided in Fig. 4b. Note indeed that at the current level of theory this process is predicted to be a favored exergonic reaction with free energy changes for activation and reaction of \( {\varDelta G}_{298}^{\ddagger 0}=6.99 \) kcal mol−1 and \( {\varDelta G}_{298}^0=\kern0.5em -28.79 \) kcal mol−1. The activation entropy is valued in \( {\varDelta S}_{298}^{\ddagger 0}=-7.45 \) cal mol−1 K−1, in agreement with a process via a cyclic TS. Although the enthalpy difference between the reactant complex formed by lithium hydride and acetylene and isolated reactants is evaluated in \( {\varDelta H}_{298}^0=-8.23 \) kcal mol−1, there are no essential differences in terms of free energies, i.e., \( {\varDelta G}_{298}^0=\kern0.5em -0.11 \) kcal mol−1 within the DFT framework. These findings agrees with the experimental available evidence pointing out that hydrometallation to alkynes is fast and indeed accounts for the lack of studies associated to alkenyl β-hydride eliminations from the corresponding metal complexes [82, 83]. The planar four-membered TS is characterized by only one imaginary frequency, i.e., 577.8i cm−1. The motion along such a frequency reveals that most of nuclei displacement at the position of TS are associated primarily with the displacement of the migrating H center and the change of hybridization at the carbon atoms. The DFT geometrical parameters of TS, namely, dC1-C2 = 1.237 Å, dC1-Li = 2.080 Å, dLi-H3 = 1.623 Å, dC2-H3 = 2.114 Å, dC1-H1 = 1.072 Å, and dC2-H2 = 1.067 Å; AH3-C2-C1 = 114.6°, ALi-C1-C2 = 76.2°, ALi-C1-H1 = 128.9°, AH3-C2-H2 = 81.3°, DH3-Li-C1-C2 = 0.000°, DH3-C2-C1-H2 = 180.000°, are close to the already known for this system at the Hartree Fock level of theory [4, 5].

The reaction mechanism can henceforth be described using the suggested notation [18, 30] in terms of bifurcation catastrophes associated with the key chemical events along the IRC pathway as: C2H3Li: 9-UFCUF[CU]UU-0: C2H3Li [18, 30, 42, 60]. The evolution of the ELF topology plotted in the planar reaction center at representative points of each SSD is depicted in Fig. 5. The ELF representation at the chosen DFT level of theory reveals the nature of the electron density rearrangement featuring key characteristics driving the hydrometallation process [1, 2, 3]: (1) a large polarization effect of the positive cationic metal on the anionic V(H3) domain which appears strongly “deformed” as a result of the Pauli repulsion between ions [44, 45, 46, 47, 52, 53, 54, 55, 56, 57] (e.g., Fig. 5a), (2) the activation of the C1C2 triple bond to attack the cationic center (e.g., Fig. 5b–e), and (3) the attack of the hydride center on C2 (e.g. Fig. 5g–h) and the final configurational evolution towards the alkenylmetal intermediate (e.g., Fig. 5i–j).
Fig. 5

Color-filled maps of the ELF in the molecular plane defined by the C1–C2–Li centers for selected points within the different SSDs along the IRC for the hydrometallation of acetylene by lithium hydride 1, resulting in ethenyl lithium 2 via a four-membered TS. The values of the ELF are mapped on a red-green-blue color scale indicated on the left of each representation. In these maps. The contour lines for the values 0.50 (outer) and 0.80 (inner) are represented in bold. The ELF representation at the chosen level clearly reveals the nature of the electron density rearrangement driven by the motion of the cationic lithium center

Conclusions

Hydrometallation of HC≡CH by Li+H and the reverse process associated with the β-hydride elimination in the alkenyl system H2Cβ = CαHLi was characterized in terms of the sequence of SSDs arising from the topological analysis of ELF theory. The bifurcation catastrophes separating the sequential SSDs were identified and characterized within the language of Thom’s catastrophe theory framework. The results provide evidence that, on the metallation pathway (i.e., the fast—energetically favorable—hydrometallation of an alkyne), activation of the CC triple bond is the key factor enabling bond formation of the Li–Cα bonding. This is then followed by the formation of the Cβ–H single bond as a result of the attack on the hydride center. The agostic stabilizing interactions between the cationic center and the CC and C–H bonding regions along the path are identified as key processes along the reaction path. Within such a framework of interpretation, the lithium cation plays a key role by driving the direction of the electron flow rearrangement. These results further exemplify [18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29] the usefulness of BET methodology, providing detailed mechanistic insights beyond the representation of a given chemical reaction (as described by a chosen coordinate) in terms of useful but frequently oversimplified curly arrows [4, 5, 6, 7, 8, 84, 85], a conclusion that, concerning purely electronic effects and density rearrangements, is proposed to extend also to related organometallic systems [13, 14, 15, 16, 17].

Notes

Acknowledgments

We acknowledge the continuous support provided by Fondo Nacional de Ciencia y Tecnología (FONDECYT - Chile) through Projects 1181582 (EC) and 1180348 (PP).

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Facultad de Ciencias Exactas, Departamento de Ciencias QuímicasUniversidad Andres BelloSantiagoChile
  2. 2.Faculty of Science, Department of ChemistryCumhuriyet UniversitySivasTurkey
  3. 3.Facultad de Ciencias, Instituto de Ciencias QuímicasUniversidad Austral de ChileValdiviaChile

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