One of the most important questions connected with the problem of reactivity of molecules in different environmental conditions is the prediction and interpretation of the preferred direction of a reaction and the product formation [1
]. The study of molecular interactions has been a great challenge from the experimental and theoretical point of view [3
]. There have been a lot of attempts to explain the nature of bonding and reactivity of molecular systems based on some intuitive ideas and empirical rules that are essentially derived from several experimental observations and many chemical facts [4
]. During the development of the quantum chemical methods, many of the empirical chemical concepts were derived rigorously and it has provided a method for the calculation of the properties of chemical systems and the bonding that is involved in the molecular systems [4
]. There also exist different kinds of theoretical approaches in correlating the reactivity of molecular systems based on different quantities, like molecular orbital density, charge on atoms, bond order, etc. [7
]. In particular, the correlation between the frontier molecular orbitals and reactivity was brought out by the seminal works of Fukui and co-workers and it has been widely used to predict the nature of photochemical reactions. In the same period, Pearson had introduced the concept of hardness and softness (η/S) parameters in the context of explaining the reactivity of acids and bases [8
]. Accordingly, he has systematized the reactivity of the acids and bases in terms of softness and hardness indices, based on the experimental observations. This study has eventually led to the celebrated principle, the so-called Pearson's Hard-Soft Acid-Base (HSAB) principle. It says that there is an extra stabilization when the soft acid combines with soft base and hard acid combines with hard base. HSAB principle has been very successful in rationalizing most of the acid-base reactions and it has become popular among the community of chemists because of its wider applicability and simplicity.
The nature of these basic chemical concepts, hardness and softness, called global reactivity descriptors (GRD), has been theoretically justified within the framework of density functional theory (DFT) [9
]. Along with these global descriptors, other important local reactivity descriptors (LRD), such as Fukui function and local softness, were also proposed to rationalize the reactivity of a particular site in a molecule [11
]. In the subsequent years, many groups have attempted to validate and prove the HSAB principle using the global and local reactivity descriptors [12
]. These studies have led to some important insights about the nature of the reactivity and the stability of molecular systems in terms of η/S parameters [13
]. Despite its partial success in describing the reactivity of the chemical systems, such studies have remained primarily qualitative. It should also be noted that the transformation of this qualitative principle into a quantitative form has been one of the challenging and difficult problems. This particular issue has been emphasized by many groups in the context of explaining the relative bond strengths of acid-base complexes or the reaction energies [6
]. Drago and co-workers have given an expression to calculate the stabilization energy of the complexes in terms of the covalent and ionic (C and E) parameters [18a-b
]. However, these are largely dependent on empirical parameters. In a recent study, we have raised some important questions that are pertinent for the establishment of a formal theoretical relationship between the structure and reactivity of molecular systems using the GRD and LRD [20
]. In particular, we have attempted to provide a quantitative approach to calculate the interaction energy (IE) between the molecular systems using the density based descriptors. The quantitative approach is essentially based on the energy density perturbations up to the second order, as a functional of the number of electrons and the external potential and it has been formulated by Gazquez and Mendez [22
] and Li and Evans [24
]. Gazquez has calculated bond energies or IE for several diatomic molecular systems using GRD [16a
]. He has also shown that the activation energy of a chemical reaction depends mainly on the difference between the hardness of the initial state of a reaction and the hardness of the transition state [16b
]. Ghanty and Ghosh have also attempted to calculate the bond energies of diatomic molecular systems [15
]. Their model involves the valence orbital radii, the electron density and the geometric mean of the homonuclear bond energies of the constituent atoms. The calculated bond energies for simple hetero-nuclear diatomic molecules are shown to agree very well with the experimental values. These models are essentially derived from the model proposed by Pauling that determines the bond energies in terms of the electronegativity [4
]. All these models have been formulated to calculate the bond energy for some simple diatomic molecules in terms of the chemical potential and η/S parameters. For the case of poly-atomic molecular systems, the models are not directly applicable and it requires many parameters which are empirical in nature.
The model that is described in the present paper is to calculate the IE of the weak to moderate types of intermolecular interactions is based on local HSAB principle, developed by Gazquez and co-workers [22
]. However, the formula contained an ad hoc parameter λ, which can not be rigorously calculated. In our recent work, we have made a critical study on the applicability of the local and global reactivity descriptors to describe weak interactions using the parameter λ as the charge transfer [20
]. This has been tested for different weak interaction cases, for e.g. adsorption of molecules (N2
and CO) on cation exchanged zeolite surface [20
]. It has also been applied to explain the energetics of nitrogen and oxygen molecules inside the zeolite cage and the results explain the selective sorption of N2
molecule from air by the Na and Ca ion exchanged zeolite-A [25
]. Although the model contains an ad hoc parameter and is thus semi-quantitative in nature, it has been successful in determining the interaction energies of these complexes. In view of this, a further study is yet to be made to understand the effect of the η/S parameters in the molecular interactions.
Accordingly, to study the above factors and to clarify the issues as detailed above, we have considered a wide range of systems that encompasses some of the chemical reactions, for instance, Lewis acid-base interaction, charge transfer interaction and hydrogen bonded (H-bonding) complexes. Another aspect of the present study is to demonstrate that the present model can be considered as a tool to monitor the influence of these descriptors in determining the reactivity of several types of complexes.
The paper is organized as follows: in section II
the theoretical basis of the concepts of GRD and LRD, and the expression for the IE is given. Section III
deals with the methodology and computational details and in Section IV
, we discuss the results of the present study on the description of molecular interactions in terms of the η/S concepts.
III. Methodology and computational details
We have performed Möller-Plesset second order (MP2) [28
] quantum chemical calculations to examine the reactivity of molecular systems. All the monomers and molecular complexes were optimized without any symmetry constraints, using MP2 level of theory through the standard split valence basis set, 6-31G(d,p). The restricted HF method has been used for the energy calculations of neutral and for the corresponding anionic and cationic systems, the restricted open shell HF method has been performed. The condensed Fukui function and local softness for each reactive atom were calculated via eq.10 using Mulliken population analysis [29
]. The ab initio
molecular orbital calculations were carried out using the GAMESS system of programs on an IRIX-6.2 silicon graphics workstation [30
]. The parameter λ was calculated using eq.15 through the Mulliken population scheme. The reactive atoms that we have considered in our study for each type of interactions are, hydrogen, boron and halogen atoms in oxide-HX, BH3
(electrophilic centers), respectively. Similarly, the nucleophilic reactive centers are oxygen atom in case of oxides, nitrogen atom in BH3
complexes. Accordingly, we have evaluated the values of the local softness sk+
for electrophilic or nucleophilic centers in the molecules.