Theoretical Elucidation of the Formation of γ-Butyrolactone from Haloacetate †

: γ-butyrolactone is a chemical intermediate used in many organic reactions. It is also used in phytochemistry and biology for the production of growth hormones. Experimentally; the obtaining of γ-butyrolactone is done by several chemical routes; the addition of halooacétates to alkenes is an example. In this study; we will be interested on the theoretical elucidation of the addition reaction of Bromoacetate; Chloroacetate and Iodoacetate on alkene to form γ-butyrolactone. The different reactivity indices resulting from the conceptual DFT were calculated; in the first time; in order to identify the different reactional sites. A good agreement was found between the different theoretical approaches used in this study. The transition state theory approach was used; in the second time; and the different stationary states were optimized at the DFT (B3LYP) level with the basis 6-31G +(d, p). The transition states have been well located; optimized and successfully confirmed.


Introduction
Intra or intermolecular reactions of alkenes with nucleophiles are the most common approaches to building backbones [1].Lactones are structural building blocks in many natural products and are mainly used in agrochemicals; pharmaceuticals and organics [2].Experimentally; the production of γ-butyrolactone is done by several chemical routes [3,4]; the addition of haloacetate to alkenes is an example We shall compare experimental work [5]; with theoretical work  In this study; we will focus on the theoretical elucidation of the addition reaction of Bromoacetate; Chloroacetate and Iodoacetate to an alkene to form γ-butyrolactone.We have calculated at the level of the density functional theory with the pseudo potential the different global and local descriptors to target the sites of electrophilic attacks.

Calculation Details
The reactivity descriptors can be classified according to the degree of locality to which they correspond.Thus; the chemical potential (μ) [6]; the hardness (η) [7]; the global electrophilic index (ω) [8] and the global nucleophilicity indices N [9,10] are quantities independent of space.They take the same value at every point of the system to which they relate.They are therefore qualified as global descriptors.Alternatively; local descriptors; such as Fukui functions and local philicity are magnitudes which depend on position in space.Their values differ at each point of the system they characterize.They are therefore suitable descriptors to describe the reactivity.It is interesting to see to what extent they identify the reaction sites of alkene and haloacetates vis-à-vis electrophilic and nucleophilic attacks.To do this; the geometries of the neutral molecules were optimized at the DFT calculation level with the B3LYP functional using the pseudo potential for the iodine atom; the base LanL2dz and for the other atoms; the base 6-31G + (d, p).These geometries are held constant; for cationic and anionic systems used for the calculation of local indices of reactivity using electron populations with Mulliken population analysis (MPA).

Global Reactivity
In Table 1; we have given the values of the HOMO; LUMO and gap energies as well as the values of the hardness, the chemical potential and the electrophilic power of the alkene; bromoacetate (1); chloroacetate (2) and iodoacetate (3).  1 show that the chemical potential μ of haloacetate 1; 2 and 3 is at an energy level higher than that of the alkene; which implies that the transfer of electrons takes place from the haloacetate to the alkene.
The nucleophilicity index of alkene is significantly higher than that of haloacetate, which means that the alkene is a nucleophile while haloacetate is an electrophile.The same conclusion can be drawn from the electrophile index values.

Local Reactivity
If the study of the reactivity of molecules is based on global indices deduced from electronic properties; the study of selectivity must be based on local indices.The different atoms of alkene (A); bromoacetate (1); chloroacetate (2) and iodoacetate (3) are characterized according to the numbering given in Figure 2.

Net Charges on the Various Sites
In order to explain the reactivity of γ -butyrolactone, it was necessary to study the charge distribution on the different sites.Table 2 summarizes the distribution of net charges on the different sites corresponding to the alkene (A); bromoacetate (1); chloroacetate (2) and iodoacetate (3).Calculations were performed using Mulliken population analysis (MPA).Compound A: Both C3 and C6 sites of the C = C bond are rich in electrons (net negative charge).However, the C1 site is deficient in electrons (positive charge).This suggests that the C3 and C6 sites (the carbons of the double bond) are more favored for electrophilic attack.And the C1 site for nucleophilic attack Compounds 1; 2 and 3: the O1 site is rich in electrons (net negative charge).However; the C3 site is deficient in electrons (positive charge).This suggests that the O1 site is more favored for an electrophilic attack.And the C3 site for nucleophilic attack.

Local and Dual Reactivity Descriptors
The function of Fukui  is a measure of the reactivity when the molecule is attacked by a nucleophilic reagent;  when the molecule is attacked by an electrophilic reagent.Thus; the most responsive site is the one with the highest Fukui function value.
From the condensed indices of Fukui; it is obviously possible to construct the condensed indices corresponding to the other local descriptors of reactivity (local electrophilic powers, dual descriptors).Note that the condensed index  provides information on the capacity of a site to receive electron density by nucleophilic attack.At the same time;  provides information on the ability of a site to give up electron density by electrophilic attack.
A site with a very positive value of the dual descriptor corresponds to a site more able to receive electron density than to give up; or even more electrophilic than nucleophilic.Conversely; a site with a very negative value of the dual descriptor must correspond to a site more able to give up electron density than to receive it (more nucleophilic than electrophilic).Finally; a site with a value of the dual descriptor close to zero corresponds to a site whose capacity to receive and that to yield of the electron density are equivalent.
The function of Fukui fk − and ω − provides information on the electrophilic attack.The highest value of the Fukui function is assigned to the most responsive site.Table 3 indicates the C3 site (in compound A) and O1 (in compounds 1, 2 and 3) are more nucleophilic and active towards electrophiles.
The function of Fukui fk + and ω + provides information on nucleophilic attack.The highest value of the Fukui function is assigned to the most responsive site.The C1 site (in compound A) and C3 (in compounds 1; 2 and 3) are more nucleophilic and active with respect to nucleophiles.
The descriptors Δfk and Δωk are capable of simultaneously explaining the electrophilia and the nucleophilia of the given atomic sites.The dual descriptors are found to be particularly able to distinctly identify the strongest nucleophilic sites in haloacetates and the more electrophilic site in the alkene.Indeed, the C1 is more nucleophilic; it will react preferentially with the electrophilic site O1.It is interesting to note that the values of the local reactivity indices and the dual descriptors are strongly dependent on the choice of atomic bases and on the population analysis used to obtain the partial charges.

Prediction of the Reaction Mechanism
We have reported in Table 8 the energies of the reactants (haloacetate), the energies (Ets) of the transition states TS1; TS2 and TS3 as well as the activation energy (Ea) corresponding to the formation of each reactant.The energy profile corresponding to the condensation of the alkene with the haloacetate is shown schematically in Figures 3-5.The activation energy associated with the formation of gamma-butyrolactone from iodoacetate slightly higher than those associated with the formation of gamma-butyrolactone from bromoacetate and chloroacetate.

Conclusions
Theoretical calculation by the DFT B3LYP method of the electron density of certain atoms of the reactants; electrophilic and nucleophilic character; electrophilic and local nucleophilicity indices; the Fukui indices of the addition reaction of alkene with haloacetates; the localization of the transition states, the atomic electronic populations and the reactivity indices calculated by means of natural population (NPA) and the analysis of the Potential energy surface allowed us to conclude that: a good match between theoretical work and experimental work Good agreement was found between the different theoretical approaches used.An ionic bond forms between the O1 atom of haloacetate and the C1 atom of the alkene.The formation of γ-butyrolactone from haloacetate is easily done by iodoacetate.

Table 1 .
Global properties of reactivity.

Table 3 .
The functions of Fukui fk − and fk +.

Table 4 .
Dual descriptors of reactivity in compound A.

Table 4 .
Dual descriptors of reactivity in compound 1.

Table 4 .
Dual descriptors of reactivity in compound 2.

Table 4 .
Dual descriptors of reactivity in compound 3.

Table 8 .
The energies of the transition (Ets), activation (Ea) states.