Kaya's composite descriptor and Maximum Composite Hardness Rule for chemical reactions

doi:10.1016/j.jics.2022.100364

Journal of the Indian Chemical Society

Volume 99, Issue 3, March 2022, 100364

https://doi.org/10.1016/j.jics.2022.100364 Get rights and content

Highlights

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Different electronic structure principles are compared.
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Kaya's composite descriptor.
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Maximum Composite hardness rule in chemical reactions.

Abstract

Within the framework of Maximum Hardness and Minimum Polarizability Principles and as compatible with Jenkins Volume Based Thermodynamics approach, Kaya and coworkers calculated the lattice energies of inorganic ionic crystals using their η_M/V_m^1/3 ratio (here η_M and V_m represent the chemical hardness and molar volume of any molecule, respectively). This ratio is called as Kaya's composite descriptor. It is apparent that Kaya's composite descriptor can be considered in the analysis of the chemical stability of compounds and the directions of chemical reactions. In a recent paper, Szentpaly, Kaya and Karakuş proposed Maximum Composite Hardness Rule for solid state double exchange reactions. To see the validity in other reaction types also of Kaya's composite descriptor and Maximum Composite Hardness Rule, twenty-eight chemical reactions including especially organic molecules were investigated. Reactivity descriptors such as chemical hardness, molar volume, polarizability regarding reactants and products putting in an appearance were calculated at B3LYP/6-31++g (d, p) calculation level with the help of computational chemistry tools. The result showed that instead of using separately the chemical hardness, polarizability and molar volume concepts, the use of Kaya chemical reactivity approach will be more useful to predict whether the reactions are exothermic or endothermic. It can be concluded from here that new composite descriptors should be derived and used for the accurate prediction of the reactivities of the chemical systems.

Graphical abstract

Introduction

One of the main objectives of theoretical and computational chemists is to find new approaches, theories and equations that can be used in the explanations of reactivity or stability of chemical species [1]. Maximum Hardness [2], Minimum Polarizability [3] and Minimum Electrophilicity [4]. Principles are some of the approaches proposed for this purpose. First approach about chemical hardness concept is Hard and Soft Acids- Bases (HSAB) [5] Principle states that “Hard acids prefer to coordinate to hard bases and soft acids prefer to coordinate to soft bases.” After HSAB Principle proposed in the light of observations about Lewis acid-base reactions of R.G. Pearson, Maximum Hardness Principle based on the idea of “at a given temperature, a chemical system tends to arrange itself so as to achieve the maximum hardness and the chemical hardness can be considered as a measure of stability.” was proposed. It is apparent that there is an inverse relation between hardness and polarizability concepts because chemical hardness is reported as the resistance of any chemical compound opposite the polarization. In a paper investigating the correlation between hardness, polarizability and size of atoms, molecules and clusters, the inverse relation between hardness and polarizability was firstly emphasized by Ghanty and Ghosh [6] with the explanation of “softness is proportional to the cube root of the polarizability.” A few years later, same authors [7] observed that for isomerization reactions, the states with minimum polarizability can be closely associated with higher stability or maximum hardness. So, it can be noted that the first evidences of minimization of polarizability at steady states were reported by Ghanty and Ghosh.

By taking inspiration from this inverse relationship between hardness and polarizability, Chattaraj and Sengupta [3] published important papers regarding to the justification of the Minimum Polarizability Principle states that “the natural evolution of any system is toward a state of minimum polarizability.” It should not be forgotten that the aforementioned electronic structure principles successfully have been applied to many issues regarding to reactivity and stability analysis like aromaticity [8], molecular vibrations [9], different reaction types [10,11]. One of the most important developments supported the validity of Maximum Hardness and Minimum Polarizability Principles was introduced in the literature with a useful lattice energy equation by one of the authors of this article [12]. The lattice energy (U) equation mentioned is given as: $U (k j / m o l) = 2 I [(a η_{M} / ({V_{m}}^{1 / 3})) + b]$

In the equation given above, η_M and V_m are molecular hardness and molar volume of an inorganic ionic crystal, respectively. a and b are the constants, which take different numerical values for different stoichiometries in terms of the charge of anion and cation in inorganic ionic crystals. I is ionic strength of the lattice and is calculated based on the number (n) and type of ions with charge z_i in a crystal using formula $I = 1 / 2 \sum n_{i} z_{i}^{2}$ . Normally, as indicated below, the parameter associated with chemical stability is polarizability, not molar volume. But, in the light of Volume Based Thermodynamic (VBT) Approach of Jenkins and Glasser [13,14], we also preferred to use the molar volume instead of the polarizability. The advantage of the use of molar volume is that it can be easily determined via formula mass and density data. In this methodology, to calculate the molecular hardness values of inorganic compounds, the following molecular hardness (η_M) equation derived by us [15] is used. The hardness equation mentioned is useful for simple molecular structures and is derived with the help of Hardness Equalization Principle proposed by D. Datta [16]. $η_{M} = [(2 \sum_{i =}^{N} (b_{i} / a_{i}) + q_{M}] / [\sum_{i = 1}^{N} 1 / a_{i}]$ wherein, a_i and b_i are the parameters based on first ionization energy (IE) and first electron affinity (EA) of the atoms forming any molecule and are mathematically described as: $a_{i} = (I E + E A) / 2$ and $b_{i} = (I E - E A) / 2$ . N and q_M stand for the number of atoms in the molecule and charge of molecule, respectively.

It is well-known that lattice energy is an important parameter in terms of its thermochemical analysis and in the prediction of stability of any inorganic ionic crystal and this parameter has been calculated using η_M/V_m^1/3 ratios of inorganic compounds via our lattice energy methodology. If so, one can say that this ratio closely related to the stability of chemical species. The aim of this article is to support the validity of our new approach in the analysis of chemical stability of molecules and the prediction of directions of chemical reactions including many organic molecules and a few inorganic molecules.

Section snippets

Computational details, equations and theorems used

In the part regarding to DFT, all calculations performed using Gaussian 09 software [17]. The molecular structures of investigated compounds were optimized using DFT with B3LYP [18] using 6-31++G (d, p) basis set. The geometry optimizations were considered to be complete when the stationary point was located. The optimized structures were confirmed to be true minima by frequency analysis (no imaginary frequencies). Reactivity descriptors such as chemical hardness, polarizability, molar volume

Results and discussion

In the thermochemical analysis of various reactions, thermochemical parameters like enthalpy, entropy and Gibbs free energy regarding to products and reactants are considered. The changes in Gibbs free energy for a chemical reaction is related with the change in enthalpy and entropy via $Δ G = Δ H - T Δ S$ formula. In the formula, T represents the absolute temperature in Kelvin unit. In Table 1, for studied chemical reactions, calculated and reference enthalpy, entropy and Gibbs free energy values are

Conclusion

Methodologies regarding the analysis of the directions of chemical reactions and the reactivity of products and reactants in a chemical reaction are very important for chemists. In the present report, taking inspiration from Kaya's composite descriptor and Maximum Composite Hardness Rule, we introduced a simple way providing information about exothermic or endothermic nature of the chemical reactions. The calculation and analyses made showed that Alone using of single descriptors like hardness,

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

References (41)

S. Kaya et al.
A new equation based on ionization energies and electron affinities of atoms for calculating of group electronegativity
Comput. Theor. Chem.
(2015)
R. Pal et al.
Chemical reactivity from a conceptual density functional theory perspective
J. Indian Chem. Soc.
(2021)
T. Koopmans
Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den einzelnen Elektronen eines Atoms
Physica
(1934)
S.A. Blair et al.
How often is the minimum polarizability principle violated?
Chem. Phys. Lett.
(2013)
P.K. Chattaraj et al.
A connection between softness and magnetizability
J. Mol. Struct.: THEOCHEM
(2007)
S. Kaya et al.
Two empirical formulae for estimating standard entropy of inorganic ionic solids and a possible connection between two associated electronic structure principles
Polyhedron
(2021)
R.G. Pearson
The principle of maximum hardness
Acc. Chem. Res.
(1993)
P.K. Chattaraj et al.
Popular electronic structure principles in a dynamical context
J. Phys. Chem.
(1996)
E. Chamorro et al.
Variation of the electrophilicity index along the reaction path
J. Phys. Chem.
(2003)
R.G. Pearson
Hard and soft acids and bases
J. Am. Chem. Soc.
(1963)

T.K. Ghanty et al.

Correlation between hardness, polarizability, and size of atoms, molecules, and clusters

J. Phys. Chem.

(1993)

T.K. Ghanty et al.

A density functional approach to hardness, polarizability, and valency of molecules in chemical reactions

J. Phys. Chem.

(1996)

P.K. Chattaraj et al.

Electronic structure principles and aromaticity

J. Chem. Educ.

(2007)

P.K. Chattaraj et al.

Validity of the minimum polarizability principle in molecular vibrations and internal rotations: an ab initio SCF study

J. Phys. Chem.

(1999)

T.K. Ghanty et al.

Hardness and polarizability profiles for intramolecular proton transfer in water dimer radical cation

J. Phys. Chem.

(2002)

S. Pan et al.

On the validity of the maximum hardness principle and the minimum electrophilicity principle during chemical reactions

J. Phys. Chem.

(2013)

S. Kaya et al.

A simple method for the calculation of lattice energies of inorganic ionic crystals based on the chemical hardness

Inorg. Chem.

(2015)

H.D.B. Jenkins et al.

Relationships among ionic lattice energies, molecular (formula unit) volumes, and thermochemical radii

Inorg. Chem.

(1999)

H.D.B. Jenkins et al.

Lattice potential energy estimation for complex ionic salts from density measurements

Inorg. Chem.

(2002)

S. Kaya et al.

A new equation for calculation of chemical hardness of groups and molecules

Mol. Phys.

(2015)

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View full text

Kaya's composite descriptor and Maximum Composite Hardness Rule for chemical reactions

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Computational details, equations and theorems used

Results and discussion

Conclusion

Declaration of competing interest

Comput. Theor. Chem.

J. Indian Chem. Soc.

Physica

Chem. Phys. Lett.

J. Mol. Struct.: THEOCHEM

Polyhedron

The principle of maximum hardness

Acc. Chem. Res.

Popular electronic structure principles in a dynamical context

J. Phys. Chem.

Variation of the electrophilicity index along the reaction path

J. Phys. Chem.

Hard and soft acids and bases

J. Am. Chem. Soc.

Correlation between hardness, polarizability, and size of atoms, molecules, and clusters

J. Phys. Chem.

A density functional approach to hardness, polarizability, and valency of molecules in chemical reactions

J. Phys. Chem.

Electronic structure principles and aromaticity

J. Chem. Educ.

Validity of the minimum polarizability principle in molecular vibrations and internal rotations: an ab initio SCF study

J. Phys. Chem.

Hardness and polarizability profiles for intramolecular proton transfer in water dimer radical cation

J. Phys. Chem.

On the validity of the maximum hardness principle and the minimum electrophilicity principle during chemical reactions

J. Phys. Chem.

A simple method for the calculation of lattice energies of inorganic ionic crystals based on the chemical hardness

Inorg. Chem.

Relationships among ionic lattice energies, molecular (formula unit) volumes, and thermochemical radii

Inorg. Chem.

Lattice potential energy estimation for complex ionic salts from density measurements

Inorg. Chem.

A new equation for calculation of chemical hardness of groups and molecules

Mol. Phys.