Basicity and Nucleophilicity Effect in Charge Transfer of ALH3-Base Adducts

This study permits to explore the interactions involved in Lewis acid (AlH 3 ) and Lewis bases: CO; H 2 O; NH 3 ; PH 3 ; PC1 3 ; H 2 S; CN - ; OH-; O 2-2 ; F-; N (CH 3 ) 3 ; N 2 ; N 2 H 4 ; N 2 H 2 ; pyridine; aniline. By means of DFT theory calculations with B3LYP functional using 6-31G(d,p) basis set and in order to check the effects of both the donor and the acceptor in the establishment of the different adducts we focused mainly on the calculation of the energetic gap ∆E HOMO-LUMO, Gibbs energies ∆ G, the angle (𝜃) in AlH 3 -Base and the interaction energy values E int . The several parameters of the reactivity (electrophilicity index (𝜔) , nucleophilicity (𝑁), chemical potential ( μ ), hardness ( η ) and polarizability ( α ) are also calculated to defined the weak interaction as well as to distinguish between the nucleophilicity and basicity of the different Lewis basis. Our results showed that the electronic charge transfer is estimated to be important in the systems where the interaction is established between Al and anionic bases, and the electron donor power is predictable for O -2 , F - , OH - and CN-. The pseudo-tetrahedral adduct arrangements depend on the parameter geometries (bond length interaction and 𝜃 angle) and Gibbs energies ∆G characterizing the main stability.


INTRODUCTION
Lewis acid-base interaction adducts include a partially formed dative bond that provide several new and intriguing viewpoints on molecular structure and bonding [1]. The adducts are characterized by the interaction between the electron rich sites of basis and featuring electron hole of acids, and thus, are in the considerable interest for understanding chemical bonding [2,3]. This concept is the broadest, and it may be used to classify a large range of events as acid-base reactions. It is therefore not surprising that discussions of Lewis acidity and basicity appears in almost every textbook of general, organic and inorganic chemistry [4].
Much effort has gone into developing a fundamental measure for estimating Lewis acidity in solids [5,6], which has proven to be problematic. The majority of the frequent metric is the strength of a basic molecules binding to an acidic site. The most used explanation for this interaction is represented by the electron density in a frontier orbital, resulting from a modest change in the overall number of electrons [7].
In addition, a number of theoretical efforts have been made to provide qualitative and quantitative insights into these basic notions. From a theoretical standpoint, it has been noted that density functional theory (DFT) offers an effective framework for the creation and investigation of a chemical reactivity theory [8,9]. A rising number of gas-phase and theoretical research molecular structure [10] is not an unchanging aspect of a molecule in this context, but rather demonstrates a remarkable phase dependency [11].
In this study, and following to our previous work [12] we will explore more detail about the interactions established between molecules or between molecules and ions. So, in the investigation below, our interest is the Lewis acid-base interactions which is realized among AlH 3 and a series of neutral and anionic bases (CO; H 2 O; NH 3 ; PH 3 ; PC1 3 ; H 2 S; CN-; OH-; O 2 -2 ; F-; N (CH 3 ) 3 ; N2; N 2 H 4 ; N 2 H 2 ; pyridine; aniline) are stems from the fact that they are quite strong and pseudo-tetrahedral in the coordination chemistry [13]. We have examined the nature of the interaction, the strength bonding, and the stability of adducts. Moreover, the concepts of HOMO and LUMO orbitals in describing electron-donor (Lewis-Base) and electron-acceptor (Lewis-Acid) interactions are introduced to estimate and to classify the bases according to their nucleophilicity [14]. Thus, the dipolar moment is used as an important property for donor-acceptor adducts as a fundamental measure of charge distribution.
The big request that occurs when a Lewis acid-base reaction takes place, and leads to the creation of a covalent bond between the acid and the base [15,16] according to the literature: This bond does not necessarily comprise the entire electronic doublet originating from the base. but rather a fraction of it, which may be clarified using various charge transfer methods [17].
This study aims to present quantitative answers: -How do the Lewis donor-acceptor interactions influence the occupancies of the involved bonds?
-This interaction causes complete transfer of the electronic doublets or just a partially dative bond?
-What factors influence the quality of the resulting bond and the adducts stability?

HSAB (Hard and Soft Acids and Bases) PRINCIPLE
Pearson established the HSAB hypothesis, or acid-base concept, in 1963 [18], and it is commonly used in chemistry to describe compound stability and reaction rate. The concept was introduced in relation to the behavior of Lewis acids (A) and bases (B).
A + :B → A:B………………(1) Since the complex molecules or ions, A: B, were considered to be formed from an acceptor electrons A and an electron donor B, since the acid-base complex, A: B, can be an organic molecule, an inorganic molecule or a complex ion.
The stability of A:B It is the result of the acid-base interaction between the two parts. Any insight into the properties of A and B that leads to the formation of a forte binding, would be very helpful. It was well known that there is no one order of acidic force, or of basic strength, which would be vigorous in any case. The "force" here is used in the sense of connection strength formation: that is, a strong acid and a strong base will form the same strong bond.
Based on this classification, Pearson [19] formulated his HSAB principle (hard and soft acids and bases main HSAB) as follows: "Hard acids prefer to react with hard bases and soft acids prefer to react with soft bases".

IONIZATION POTENTIAL I [20]
Pearson et al showed that the Mulliken electronegativity (χ) and the hardness (η), analogous to the first-and second-derivatives of energy with respect to number of electrons, respectively, can be used to measure Lewis acidity with more accuracy. Applying a finite difference approximation for the first derivative and three-point finite difference approximation for the second derivative leads to operational definitions in terms of ionization potential (I) and electron affinity (A) as follows: The ionization potential and electron affinity can be replaced by the HOMO and LUMO energies, respectively, using Koopmans' theorem [21] within a Hartree-Fock scheme yielding Parr and co-workers [22] interpreted that chemical potential (μ) could be written as the partial Parr and al [22] have introduced the global electrophilicity index ( ) as a measure of energy lowering due to maximal electron flow between a donor and an acceptor in terms of the chemical potential and the hardness as: Hardness [23,24] is one of the most significant global reactivity descriptors. Hardness is described as one of the key global reactivity descriptors, and has the definition in equation (7) The vertical ionization energy and electron affinity, respectively, are I and A. The reciprocal of hardness is softness (S) [25] which is defined as In 2007, Gázquez introduced the concepts of the electroaccepting, + , and electrodonating, − , powers as [26]: … … … … … … … … . . (12) where + represents a measure of the propensity of a given system to accept electron density, while − represents the propensity of this system to donate electron density.
In 2008, we proposed an empirical (relative) nucleophilicity N index for closed-shell organic molecules based on the HOMO energies, E HOMO , obtained within the Kohn-Sham scheme as an approach to the gas phase, and defined as [27]: The nucleophilicity N index is referred to tetracyanoethylene (TCE) , which is the most electrophilic neutral species, the expected least nucleophilic neutral species. This choice allowed convenient handling of a nucleophilicity scale of positive values. An analysis of a series of common nucleophilic species participating in polar organic reactions allowed a further classification of organic molecules as strong nucleophiles with N > 3.0 eV, moderate nucleophiles with 2.0 ≤ N ≤ 3.0 eV and marginal nucleophiles with N < 2.0 eV [28] In our calculations we have found the E HOMO (TCE) = −9.121eV at B3LYP/6-31G(d,p) level.
Besides, the maximum number of electrons ∆ that an electrophile can acquire is given by the expression [29] The maximum charge that each species may accept from the environment which is measured by ∆ , is almost parallel to the variation in electrophilicity for whole series of Lewis acidbase adducts. Since the nucleophilicity index obtained as 1 − was below, we can define the nucleophilicity as ′′ = 10 − Following methods [30] were adopted for the present study. This suggests that Lewis acid-base is a complicated interaction that is influenced by the entire system rather than just the isolated acids and bases.
When two systems, B and A, are combined, electrons move from the lower to the higher until the chemical potentials are equal. For generalized acid-base reactions, the fractional number of electrons transferred.
A + :B → A:B, (up to first order) is provided by The global interactions between AlH 3 and the selected bases of systems have been determined using the parameter ∆N, which represents the fractional number of electrons, transferred from a system A to a system B. Charge transfer data are presented in Table- x 10 -8 ).
The reduction in energy caused by this electron transfer from a greater chemical potential (base) to a lower chemical potential (acid) is provided by [33].

COMPUTATIONAL DETAILS
Geometry optimizations and frequency calculations of all the molecules and adducts were carried out using density functional theory along with three-parameter hybrid model (DFT/B3LYP) [34][35][36] in conjunction with 6-31G(d,p) basis function. All quantum chemical calculations were performed using the Gaussian 09 program [37]. All the optimized geometries have no negative vibrational modes showing that all structures are minima on the potential energy surface. generally adopt a pseudo-tetrahedral configuration at the Aluminium centre [41].

STRUCTURE OF AlH 3 LEWIS ACID
In our results of geometry optimization presented in  Table 1.
The interactions of AlH 3 with a variety of Lewis-basis suggests that the aluminium center has direct contact with the various atoms X of the Lewis-basis (Fig.2.) and that leads to a pseudotetrahedral configuration adducts.    The nucleophilicity estimated theoretically and listed in Table 3. for some anionic and neutral bases (Fig.3.). The low ionization energy I shows that the molecule is highly reactive. according to Table 2.

NUCLEOPHILICITY CARACTER IN CHOSEN BASES
According to the Lewis definition, Lewis bases have high electron density centers, while

MEASUREMENT OF LEWIS BASICITY
The term "basicity" refers to a thermodynamic concept. The location of an equilibrium is determined by the respective stabilities of the entities included in the two members of the acido-basic eq. (20) (associated): this may be expressed using the formula ∆G = -RTLogK, where ∆G" is the free standard variation of enthalpy of the reaction.
According to the glossary of terms used in physical organic chemistry published by the International Union of Pure and Applied Chemistry [42], Lewis basicity is defined as follows: The thermodynamic tendency of a substance to act as a Lewis base. Comparative measures of this property are provided by the equilibrium constants for Lewis adduct formation for a series of Lewis bases with a common reference Lewis acid.

Interaction Lewis acid-base
in the Lewis acid-base interaction, the Lewis acid intervenes through its orbital LUMO to receive the electron doublet. On the other hand, the Lewis base intervenes by orbital HOMO which includes an electronic doublet to give it.
In the Lewis acid-base interaction diagram, the energy gap ∆E1 between LUMO ALH3 and HOMO O -2 is estimated at 19.618 eV. Depending on the results obtained from the deviations, this value appears to be the highest, which reflects the difficulty of O -2 in giving their electronic doublet to the aluminum center. The HOMO of O -2 is more energetic than the LUMO of ALH 3 , allowing laborious interaction to place the non-binding doublets of O -2 in a lower energy orbital. The energy gap (Fig.4.) indicates that the electron donor power which is estimated in the following increasing order: CN -< N 2 H 4 <N (CH 3 ) 3 < N2H2 < aniline < NH3 < Pyridine < H2S < PH3 < H2O < PCl3 < OH-< F-< CO < N2 < O -2 .
The above classification makes it possible to give the order of the nucleophilicity of the cited bases, therefore CNappears as the most nucleophilic while O -2 is the least nucleophilic.
The lower interaction energy is according to the more stable supermolecule or complex. In our case, the interaction energy for anionic adducts appears as a lower in the case of AlH 3 ---O 2 -2 (-20.524 au), wile for neutral adducts

FRONTIER MOLECULAR ORBITALS (FMO)
Molecular orbitals and their properties such as energy are useful for chemists in frontier electron density for predicting the most reactive systems [20] and also explains several types of reactions in conjugated systems. FMO analysis is widely employed to explain the optical and electronic properties of organic compounds [52].
The DFT method predicts that the HOMO -LUMO energy gap of obtained adducts which is found to be very low in the case of AlH 3 -N 2 H 2 (3.78eV) and it leads to less stability (high chemical reactivity) of the complex and it is more polarizable (43.133 a.u).

The angle and Al-O bond
In regular tetrahedral geometry (AlX 4 )the angle is estimated at 109.64°. When the base interacts with AlH 3 a pseudo-tetrahedral geometry (AlH 3 B) is appeared and the angle value may reflect a good parameter stability. On the other hand, Al-O bond length is between 1.64 to 1.69 in many compounds with four-coordinate aluminium [53]. The value that is most similar to regular is indicated in AlH 3 -Fadduct (109.52°) and the distance Al-Fis equal to  Table 4. Except for AlH 3 -pyridine and AlH 3 -aniline, the remaining structures present an angle less than 100°.
Optimized structures of all adducts with Mullikan atomic charge and the main bond lengths are shown in Fig.5. AlH 3 ----base bond length (Å) and the corresponding IR stretching frequency ( −1 ), dipolar moment and induced dipolar moment in (Deby), the fractional charge transfer (Δ ), the interaction energy , the polarizability ( ), the enthalpy in (Kcal/mol) and the free Gibbs energies Δ in (Kcal/mol) calculated at the same level and at T = 298.15 °K are listed in Table 5. The order of stability in the considered adducts is AlH 3 -O -2 > AlH 3 -PCl 3 > AlH 3 -CN -> AlH 3 -H 2 S > AlH 3 -OH -> AlH 3 -PH 3 > AlH 3 - AlH3-CO > AlH 3 -N 2 . Table 4. energetic parameters of ALH 3 ... base adducts Table 5. Dipolar Moment ( ), Polarizability ( ), ∆G Adduct , ∆H Adduct , , Δ and Δ .  The electrostatic potential of the molecule (MEP) is still a helpful guide determining a molecules reactivity toward positively or negatively charged structures. The MEP is usually displayed by projecting its values onto a surface that reflects the boundaries of the molecules.
In the electrostatic potential map Table 6. The total density depicts the localization of charges surrounding the atoms; it should be noticed that the richness of electrons is concentrated in the red and yellow color regions, the blue region of EP relates to the positive charge.
The largest interval of electron density has been found for AlH 3 -H 2 O structure, and it tends to be between ∓ 9.548 −2 . While the restraint interval of electron density characterizes AlH 3 -N 2 H 2 adduct and it tends toward ∓0.101 e0. (eV) and the electrostatic surface potential map (ESP).

INDUCED DIPOLAR MOMENT
Dipolar moment [54] is an important property for donor-acceptor complexes as a fundamental measure of charge distribution in gas phase [55] or in solution [56].
In this work, we present the calculated values of dipolar moment, at B3LYP/6-31G ( Δμ ind = μ AB − μ A − μ B……………………. (25) The Mulliken charge analysis and the Natural bond orbital (NBO) are important tools for studying intermolecular and intramolecular interactions, as well as a good starting point for investigating net charge transference in molecular systems.

The NBO theory
NBO analysis has already proved to be an effective tool for the chemical interpretation of hyperconjugative interactions and electron density transfer from the filled lone-pair electron [58]. The orbital natural binding (NBO) method of Weinhold et al [59] provides a suitable scheme for the analysis of Lewis acid-base interactions [60] because it emphasizes the computation of the delocalization of the electron density in vacant orbitals.
An interesting example is provided by the NBO analysis of the water dimer H 2 O…H-O-H, where the left and right molecules act like the Lewis base and Lewis acid, respectively.
Interaction energy is broken down into charge transfer (CT) and no charge transfer (NCT) as follows: For each donor NBO(i) and acceptor NBO(j), the stabilization energy (E 2 ) associated with the delocalization i → j is given by [61] In our case, the significant interaction in the calculate adduct structures are listed in Table 7. In the major cases, the partial charge transfer from the formed Al-base goes to the non- transfer. π → π* interactions occur between the bonding πN5-C10 and antibonding orbitals π*C6-C7 as well as the bonding πC2-C3 and antibonding orbitals π*C1-C6, with a strong stabilization energy 91.09 and 244.39 kcal/mol respectively.
In comparison, σ → σ* interactions have the lowest delocalization energy compared with π → π* interactions. As a result, the σ bonds have higher electron density occupancy than the π bonds.

CONCLUSION
In this investigation, using at DFT/B3LYP/6-31G(d,p) level of theory, we have described the concept of the partial dative bond which can be established in the Lewis acid-base interaction.
Besides, this work provides detailed insights into the electronic structure properties using the conceptual DFT to determine the major factors that control the formation of this bond and the stability of the produced adducts.
The charge transfer plays a crucial role in describing dative bond formation, ∆N, ∆N max and the energy following the charge transfer ∆E, the electrodonating ω − , and the potential ionization permit to quantify and classify O -2 as the best nucleophilic system.
The interactions that take place revealed to be capable of explaining the activity of the lone pairs to participate in the new bonding that appear in the Lewis acid-base interaction.
Calculating of energetic gap between HOMO of the bases and the LUMO of AlH 3 indict that    Estimation of the nucleophilicity via the energetic gap ∆E between HOMO Basis and LUMO AlH3 Figure 5 Optimized adducts at B3LYP/6-31G(d,p) level.

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