Dulal C. Ghosh

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.

Quantum chemical study of the umbrella inversion of the ammonia molecule

The physical event of the umbrella inversion of ammonia has been studied in detail by application of the formalisms of frontier orbital theory, the density functional theory, the localized molecular orbital method, and the energy partitioning analysis. An intuitive structure for the transition state and dynamics of the physical process of structural reorganization prior to inversion have been suggested. The computation starts with the CNDO/2 equilibrium geometry, and thereafter the cycle proceeds through all the conformations of ammonia obtained by varying the ∠HNH angle in steps of 2° from its equilibrium value up to the transition state. The geometry of each conformation is optimized with respect to the length of the N–H bond. The glimpses of the charge density reorganization during the movement of the molecule from equilibrium conformation toward the transition state is computed in terms of dipole moment and the quantum mechanical hybridizations of bond pair and lone pair of N atom through the localized molecular orbitals (LMOs) of all the conformations. Results demonstrate that as the geometry of the molecule begins to evolve through the reorganization of structure, the N–H bond length and the dipole moment begin to decrease, and the trend continues up to the transition state. The dipole moment of the molecule at the suggested transition state is zero. The computed nature of quantum mechanical hybridization of bond pair and lone pair of the N atom as a function of reaction coordinates of the ∠HNH angles reveals that the percentage of s character of the lone pair hybrid decreases and that of the bond pair hybrid forming the σ(N–H) bond increases during the process of geometry reorganization from the equilibrium shape to the transition state. The rationale of the zero dipole moment of the transition state for inversion is not straightforward from its point-group symmetry, but is self-evident from its electronic structure drawn in terms of LMOs. The electronic structure of the transition state, which may be drawn in terms of the LMOs, seems to closely reproduce its suggested intuitive structure. The pattern of variation of dipole moment and nature of the changes of the percentage of the s character in the lone pair hybrid creating dipole with the evolution of geometry during the physical process of structural reorganization for the inversion are found to be nicely correlated according to the suggestion of Coulson. The profiles of the increasing strength of the N–H bond and the increasing percentage of s character of the bond pair hybrid of N atom forming this bond as a function of reaction coordinates are also found to be correlated in accordance with the suggestion of Coulson. The profile of global hardness as a function of reaction coordinate seems to demonstrate that the dynamics of the evolution of the molecular structure from equilibrium shape to the transition state following the course of suggested mode of structural reorganization conforms to the principle of maximum hardness (PMH). The profiles of parameters like the energies of highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO), the gap in energy between HOMO and LUMO, the global hardness, the global softness, and chemical potential as a function of reaction coodinates of a continuous structural evolution from equilibrium shape to the transition state mimic the potential energy diagram of the total energy. Both the frontier orbital parameters and the density functional quantities are found to be equally effective and reliable to monitor the process of necessary structural reorganization prior to the inversion of mofecules. An energy partitioning analysis demonstrates that the origin of barrier has no unique single source rather as many as four mutually exclusive but interacting one- and two-center energy terms within the molecule entail the origin and the height of the barrier. From a close analysis of the results, it seems highly probable that the necessary structural reorganization prior to umbrella inversion of ammonia most realistically occurs following the course of normal modes of vibration of the molecule.

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.

Computation of the atomic radii through the conjoint action of the effective nuclear charge and the ionization energy

A new ansatz for computing the absolute radii (r) of the atoms based upon the conjoint action of two periodic properties namely, ionization energy (I) and effective nuclear charge (Zeff ) is proposed as r = a(1/I) + b(1/Zeff ) + c, where a, b and c are constants, determined by regression analysis. The ansatz is invoked to calculate sizes of atoms of 103 elements of the periodic table. In the absence of any benchmark to perform a validity test of any set of atomic size, reliance is upon the ‘sine qua non’ of a set of atomic size. The express periodicity of periods and groups exhibited by the computed size data, d and f block contraction and the manifest relativistic effect in the sizes of lanthanoids and actinoids, etc. speak volumes for the efficacy of the present method. Furthermore, size data have been linked to compute some physical descriptors of the real world, such as equilibrium internuclear distances of a good number of heteronuclear diatomic molecules as validity test. A comparative study of the theoretical vis-à-vis experimental equilibrium inter-nuclear distances reveals that there is close agreement between the theoretical prediction and experimental determination.

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.

Correlation of the Drug Activities of Some Anti-Tubercular Chalcone Derivatives in Terms of the Quantum Mechanical Reactivity Descriptors

Under the QSPR/QSAR paradigm, a comparative study is made of the known drug activity of as many as 15 anti-tubercular drugs vis-A -vis the computed quantum mechanical global reactivity descriptors like global hardness, global softness and global electrophilicity index. The comparative study reveals that the experimentally determined activity of drug molecules, including its variation with side substitution on the parent moiety, correlate nicely with the theoretical descriptors. The global electrophilicity index of a molecule may be useful in predicting the mechanism of the drug receptor interaction. In addition, the authors predicted the QSAR models to correlate the antitubercular activities with quantum mechanical descriptors like global hardness, electronegativity, global softness, and global electrophilicity index. The multilinear model using all four global descriptors computed through PM3 method, effectively predicts the antitubercular activities for a series of chalcone derivatives. The high value of R2 (0.961) supports the validity of that particular model. A nice correlation between the predicted and experimental activities validates the effort.

A zero differential overlap study of chemical binding in ammonia-borane and carbony l-borane

A cndo/2D study of the charge distribution obtained through Mulliken population analysis in the ground state of the title compounds shows that the features of charge distribution found by severalab initio calculations are fairly well reproduced by this method. The one-particle density, the interference density at the mid-point of the bond axis and the kinetic part of the interference energy calculated through the deorthogonalized density matrices over a wide range of intermolecular separation between the donor and the acceptor show that the one-particle density and the interference density steadily grow with decreasing internuclear separation, while the kinetic interference energy starts with negative value at large distance, then decreases and passes through a minima near but above the equilibrium distance and then increases rapidly below it conforming to the characteristic general behaviour of the kinetic component of Morse curve. The orbital pairwise interference density and the corresponding kinetic energy components reveal that the orbitals involved in the covalent binding are σ2p AO of B and 2S and σ2p AO of N and C atoms in H3B-NH3 and H3B-CO respectively.