Nazmul Islam

A new algorithm for the evaluation of the global hardness of polyatomic molecules

Relying upon the commonality of the basic philosophy of the origin and development of electronegativity and hardness, we have attempted to explore whether a hardness equalization principle can be conceived for polyatomic molecules analogous to the electronegativity equalization principle. Starting from the new radial-dependent electrostatic definition of hardness of atoms suggested by the present authors and assuming that the hardness equalization principle is operative and valid, we have derived a formula for evaluating the hardness of polyatomic molecule, , where n is the number of ligands, ri is the atomic radius of the ith atom and C is a constant. The formula has been used to calculate the hardness values of 380 polyatomic molecules with widely divergent physico-chemical properties. The computed hardness data of a set of representative molecules are in good agreement with the corresponding hardness data evaluated quantum mechanically. The hardness data of the present work are found to be quite efficacious in explaining the known reaction surfaces of some well-known hard–soft acid–base exchange reactions in the real world. However, the hardness data evaluated through the ansatz and operational and approximate formula of Parr and Pearson poorly correlate the same reaction surface. This study reveals that the new definition of hardness and the assumed model of hardness equalization are scientifically acceptable valid propositions.

On the electrophilic character of molecules through its relation with electronegativity and chemical hardness.

Electrophilicity is an intrinsic property of atoms and molecules. It probably originates logistically with the involvement in the physical process of electrostatics of soaked charge in electronic shells and the screened nuclear charge of atoms. Motivated by the existing view of conceptual density functional theory that similar to electronegativity and hardness equalization, there should be a physical process of equalization of electrophilicity during the chemical process of formation of hetero nuclear molecules, we have developed a new theoretical scheme and formula for evaluating the electrophilicity of hetero nuclear molecules. A comparative study with available bench marking reveals that the hypothesis of electrophilicity and equalization, and the present method of evaluating equalized electrophilicity, are scientifically promising.

Modeling of the Chemico-Physical Process of Protonation of Molecules Entailing Some Quantum Chemical Descriptors

Relying upon the basic tenets of scientific modeling, an ansatz for the evaluation of proton affinity of mole-cules are evolved in terms of a four component model. The components of the model chosen are global de-scriptors like ionization energies, global softness, electronegativity and electrophilicity index. These akin quantum mechanical descriptors of atoms and molecules are linked with the charge rearrangement and polarization that occur during the physico-chemical process of protonation of molecules. The suggested ansatz is invoked to compute the protonation energy of as many as 43 compounds of diverse physico-chemical nature viz, hydrocarbons, alcohols, carbonyls, carboxylic acids, esters, aliphatic amines and aromatic amines. A detailed comparative study of theoretically evaluated protonation energies of the above mentioned molecules vis-a-vis their corresponding experimental counterparts reveals that there is a close agreement between the theory and experiment. Thus the results strongly suggest that the proposed modeling and the ansatz for computing PA, the proton affinity, of molecules for studying the physico-chemical process of protonation may be valid proposition.

SPECTROSCOPIC EVALUATION OF THE GLOBAL HARDNESS OF THE ATOMS

This study explored a new route for calculating the global hardness of atoms using spectroscopy. Working on a new definition of global hardness and relying on the Bohr model of the hydrogenic atom, a new formula for the global hardness of atoms was derived in terms of the wave number, reflecting the electron transition from the ground state to infinity. Since the spectral lines emitted from an atom bear the signature of all complex and complicated energetic effects, including relativity, in the internal constitution of the atom, it is expected that all such effects are automatically subsumed in the hardness data computed in terms of spectral lines. The hardness of the atoms of the 103 elements of the periodic table have been computed using spectral data and in terms of the new formula suggested in this work. The effect of relativity in pre- and post-lanthanoid elements is distinctly manifest. The express periodic behaviour and correlation of the most important physico-chemical properties of elements suggest that the present approach is an alternative scientifically meaningful method for evaluating the global hardness of atoms.

Editorial: Conceptual Density Functional Theory: Its Grand Application to Atomic and Molecular Domain

The usage of physical information in quantum mechanics is important for the ramification of the theoretical models dealing with the micro-domain of the nature. Some key components of conceptual constructs of chemistry and physics are atomic radius, electronegativity, the global hardness and the global electrophilicity index. These ingredients are fundamentally atomic descriptors and are carrying physical or quantum information of physical or quantum systems –the atoms into the molecules. The descriptors of conceptual constructs of chemistry and physics find application in the real world of chemistry and physics. Their importance can be assessed by simply noting that without the concept and operational significance of radius, hardness and electronegativity the chemistry and many aspects of condensed matter physics become chaotic and the long established unique order in chemico-physical world would be disturbed. But when their fundamental status in science is enquired it is transparent that, in spite of their manifold applications in the chemico-physical world, none of the descriptors-the radius, the electronegativity, the hardness and electrophilicity index has ever been measured experimentally as because none of them is physical observable. Thus they may be considered as mythical saga or Kant’s Neumann ie they exist in mind not in the real world. Moreover, since the descriptors are not observables, according to the rules of quantum mechanics, no operator can be suggested for their quantum mechanical evaluation. Hence these important and indispensible descriptors are basically qualitative per se. However, the conceptual density functional theory has developed theoretical algorithms to evaluate such descriptors and when these numerical values are applied to study chemico physical phenomena we get encouraging results.

Modeling of the Chemico-Physical Process of Protonation of Carbon Compounds

We have suggested a model for the evaluation of proton affinity of molecules in terms of so\me akin quantum mechanical descriptors that follow closely the physico-chemical process of protonation. Method relies upon the basic tenets of scientific modeling having four akin descriptors – the ionization energy (I), the global softness(S), the electronegativity (χ), and the global electrophilicity index (ω) as the components. These akin theoretical descriptors can be entailed in following and describing the alteration in geometrical parameters, the charge rearrangement and polarization in molecules as a result of protonation. The modeling has evolved an ansatz for the evaluation of gas phase proton affinity, PA, of molecules as PA = C + C1 (−I) + C2 S + C3 (1/χ) + C4(1/ω), where C, C1, C2, C3, and C4 are the constants. The suggested ansatz is invoked to compute the protonation energy of as many as 88 carbon compounds of diverse physico-chemical nature viz, hydrocarbons, alcohols, carbonyls, carboxylic acids, esters, aliphatic amines, aromatic amines, pyridine derivatives and amino acids. A detailed comparative study of theoretically evaluated protonation energies of the above mentioned molecules vis-a-vis their corresponding experimental counterparts strongly suggest that the proposed modeling and the ansatz for computing the proton affinity of molecules are efficacious for studying the physico-chemical process of protonation and the hypothesis is scientifically acceptable 14.

Hardness Equalization in the Formation Poly Atomic Carbon Compounds

In this work we have basically launched a search whether there is a physical process of hardness equalization for molecules similar to the electronegativity equalization. We are tempted by the fact that the electronegativity equalization principle is widely accepted and theoretically justified and there is much communality in the basic philosophy of the origin and operational mechanism of the two fundamental descriptors– the electronegativity and the hardness of atoms. We have analyzed the origin and development in terms of the shell structure of atoms and molecules and classical theorems of electrostatics and put forward an alternative new definition of hardness. In the next venture, we have posited and logistically proved the occurrence of the physical process of hardness equalization principle at the event of molecule formation. Starting from our new definition of hardness and the new radial dependent formula of computing hardness of atoms and relying upon our newly introduced model of hardness equalization principle, we have derived an algorithm for the evaluation of the hardness of the hetero nuclear poly-atomic molecules. The algorithm is invoked to compute the hardness of as many as 22 poly atomic carbon containing molecules. In absence of any experimental benchmark, we have compared the computed hardness data of such molecules with the hardness data computed by an ab- initio quantum chemical method. From comparative study we find that there is close correlation between the two sets hardness data one set evaluated through the algorithm suggested by us, and the other set evaluated through the ab- initio quantum chemical method.