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The stability, reactivity and aromaticity of clusters of various noble gas atoms trapped in aromatic H3+ and Li3+ rings are studied at the B3LYP/6-311+G(d) and MP2/6-311+G(d) levels of theory. Electrophilicity, a gain in energy and nucleus-independent chemical shift values lend additional insights into the overall behavior of these clusters.

Using a kinetic-energy-density functional with a modified ``first-gradient'' correction, Dirac exchange functional, and a parametrized Wigner-type local correlation functional, a simple quadratic equation is solved for the ground-state electronic densities and properties of atoms and ions, including alkaline-earth-metal singly charged negative ions. The results for various expectation values and the electrostatic potential compare quite favorably with near-Hartree-Fock and relativistic density-functional results, respectively.

Conceptual density functional theory provides a method for analyzing the chemical reactivity in terms of different global reactivity descriptors including electrophilicity and their local counterparts like philicity. These concepts’ definitions and various applications that demonstrate their interpretive power are discussed. Global and local electrophilicities are able to account for a wide variety of chemical phenomena.

A quantum-fluid density-functional theory (QF DFT) is proposed, yielding a time-dependent (TD) generalized nonlinear Schr\"odinger equation (GNLSE) as the equation of motion (EOM) for dealing with proton--helium-atom collisions from ``start'' to ``finish.'' The EOM contains the Weizs\"acker term as the kinetic-energy functional, apart from local exchange and correlation functionals. The GNLSE is numerically solved in cylindrical polar coordinates by a leapfrog-type finite-difference algorithm. Various TD quantities such as difference density (DD), induced-dipole moment (IDM), dipole polarizability tensor component, reaction probability, etc., have been studied to obtain physical insights into the mechanism of the TD collision process. In particular, the DD and the oscillating IDM permit a natural partitioning of the p-He collision process into approach, encounter, and departure regimes. The TD DD profiles reveal that, as a result of the interaction, p\ensuremath{\sigma} densities mix substantially into the 1s density of the He atom. Critical comments are made on the usefulness of the QF DFT approach for understanding TD processes.

Softness and polarizability are calculated for different complexions of two-state ensembles of various helium isoelectronic systems (He, Li+, Be2+, B3+, C4+). It is shown for the first time for the systems studied that an increase in the excited-state contribution in a two-state ensemble makes the system softer and more polarizable, as expected from the principles of maximum hardness and minimum polarizability.

A simple descriptor, viz the number of carbon (N C )/non-hydrogenic (N NH ) atoms present in a molecule, is proposed for the development of useful Quantitative Structure-Property-Relationship (QSPR) models. This work is prompted by that of Randic and Basak (J. Chem. Inf. Comput. Sci.2001, 41, 614-618) who have shown that this descriptor is superior to the simple connectivity index and is marginally worse than the variable connectivity index for analyzing the toxicity of aliphatic ethers. It is tested in the present work in models pertaining to the estimation of boiling point of alcohols, enthalpy of vaporization of Polychlorinated Biphenyls (PCBs), n-octanol/water partition coefficient of PCBs and chloroanisoles, pK a values of carboxylic acids, phenols, alcohols, etc. High values of various regression coefficients (R 2 , R 2 CV , R 2 AD ) suggest the significance of this descriptor which further improves in the resulting two-parameter QSPR models with electrophilicity or its local variant as an additional descriptor. Other statistical quantities are also analyzed for gaining additional insights into the proposed models. Although the atom number is not the best possible descriptor in a QSPR model in all cases, its simplicity provides it a special place in the development of those models. The present analysis extends the work of Randic and Basak by delineating the situations when N C /N NH performs well vis-a-vis the other descriptors.

Quantum chemical computations with full geometry optimization at the B3LYP/6-31G(d) level in aqueous phase at 298 K are performed to calculate a set of molecular properties for 45 aromatic organic acids such as benzoic acid, phenol, cinnamic acid, benzohydroxamic acid, anilinium ion and their meta- and para-substituted derivatives. In a separate set of calculations the 6-31+G(d) basis set is employed for substituted benzoic and cinnamic acids as representative test cases, to test the effect of diffuse functions. Molecular descriptors such as ionization potential, electron affinity, hardness, chemical potential, global electrophilicity and free energy of deprotonation of these acids are computed. The local descriptors such as Fukui functions and group philicity (ω+g) are calculated with Mulliken Population Analysis (MPA) and Hirschfeld Population Analysis (HPA) schemes. These aromatic acids are reacted with a strong base, OH−. The computed Gibbs free energy of deprotonation, the fractional number of electrons transferred, ΔN and electrophilicity based charge transfer index (ECT) in acid–base reaction with a strong base, OH−, ω+g and group charges are correlated with the experimental pKa values of these acids. It is found that this approach is particularly effective in discussing trends of changes in acidity of intimately related molecules. The effect of substituents on these descriptors is also studied. These parameters are correlated with experimental Hammett substituent constants (σ). The ECT, fractional number of electron transfer (ΔN) and group charge correlate strongly with pKa and σ in separate groups of aromatic acids. Minimum energy, maximum hardness and minimum electrophilicity principles are tested for the acid–base reactions.

Modifications of the first-gradient correction to the Thomas-Fermi kinetic-energy (KE) functional have been proposed based on its global correlation with the Weizs\"acker energy functional. The self-consistent solution of the Thomas-Fermi-Dirac equation containing the modified first-gradient KE functional and a Wigner-type local-correlation-energy functional leads to acceptable energy values when one considers the computational simplicity.

This article reviews three different interesting nonlinear chemical dynamical problems tackled by us. It includes scattering from rough surfaces, topological equivalence of pseudorotation in cyclopentane with soliton in a ring and quantum fluid density functional theory of time-dependent phenomena, e.g., ion-atom collisions or atom-field interactions.

Principles of minimum energy, minimum polarizability, minimum electrophilicity, and maximum hardness dictate that the aromatic molecules are associated with low energy, low polarizability, low electrophilicity, and high hardness values. The antiaromatic molecules should possess high energy, high polarizability, high electrophilicity, and low hardness values. This fact is demonstrated through the B3LYP/6-311G** calculations on benzene and cyclobutadiene. Aromaticity in aluminum clusters is also analyzed.

Ayers, Parr, and Pearson recently showed that insight into the hard/soft acid/base (HSAB) principle could be obtained by analyzing the energy of reactions in hard/soft exchange reactions, i.e., reactions in which a soft acid replaces a hard acid or a soft base replaces a hard base [J. Chem. Phys., 2006, 124, 194107]. We show, in accord with the maximum hardness principle, that the hardness increases for favorable hard/soft exchange reactions and decreases when the HSAB principle indicates that hard/soft exchange reactions are unfavorable. This extends the previous work of the authors, which treated only the "double hard/soft exchange" reaction [P. K. Chattaraj and P. W. Ayers, J. Chem. Phys., 2005, 123, 086101]. We also discuss two different approaches to computing the hardness of molecules from the hardness of the composing fragments, and explain how the results differ. In the present context, it seems that the arithmetic mean of fragment softnesses is the preferable definition.

A recent paper [P. W. Ayers, J. Chem. Phys122, 141102 (2005)] considered the hard/soft acid/base exchange reaction, showing that the products associated with the hard/soft acid/base rule (in which the hard acid and hard base are bound, as are the soft acid and soft base) have lower energy than the alternative (in which the hard acid and soft base would have been bound and similarly the soft acid and hard base). Here we show that the maximum hardness principle also predicts this result. Unlike the previous derivation, we do not need to make any assumptions about the relative strength of the acids and bases.

Hardness and polarizability are associated with easily discernible atomic shell structures across the periodic table. In a given period the noble gas atom is the hardest and the least polarizable, as expected from its exceptional stability vis-a-vis the principles of maximum hardness and minimum polarizability. The electrophilicity index also exhibits periodicity.

The specific selection rules for both pure and Raman rotational transitions using simple group theoretical arguments.

Threesimulated expressions are suggested regarding the Z-dependence of groundstate energies of neutral atoms at the Hartree-Fock, exact nonrelativistic and relativistic levels. The Hartree-Fock-level Z−1/3-expansion contains three previously derivedplus two newly derived terms, the latter signifying exchange corrections from the ‘inner core’ and the ‘core mantle’ of the Lieb atom. This leads to better agreement than any previous expression, with every coefficient being physically transparent. The Z-dependence of the correlation energy is obtained from a semiempirical Wigner-type correlation potential while the relativistic correction is taken to be in between the values suggested separately by Scott and Schwinger. Agreement with reference values is again better than before. It appears, however, that the atomic Z−1/3-expansion should not proceed beyond terms O(Z).

This paper proposes a quantum-fluid density-functional theory (an interlinking of quantum-fluid dynamics and density-functional theory) for dealing with molecular collisions, in order to incorporate both time dependence and excited states. Using a new kinetic energy density functional for ion-atom collisions, we have derived a single-particle time-dependent single density equation for many-electron systems. The equation is a new generalized nonlinear Schr\"odinger equation whose solution directly yields the time-dependent charge density, current density, and a pulsating effective potential surface on which the process occurs. The new equation is also derived through Nelson's stochastic interpretation of the single-particle Schr\"odinger equation. A ``thermodynamics'' of the entire time-evolving system is suggested in terms of space- and time-dependent quantities. New algorithms have been devised for solving the above equation in one and two spatial dimensions, in a succession of time steps. Results have been obtained and analyzed in the approach regime for proton-neon high-energy (25-keV) collisions, which permit excitation but not ionization. These results show distinct nonlinear features.

For a pdf involving both space and time variables, stability criteria are presently shown to change drastically when the equation contains i, as in the quantum-mechanical equations of motion. It is further noted that the stability of finite difference schemes for quantum-mechanical equations of motion depends on both spatial and temporal zoning. It is possible to compare a free particle Green's function to the solution of a simple diffusion equation, and the quantum-mechanical motion of a free particle to Fresnel diffraction in optics.

Density functional theory (DFT) has not been applied on a large scale to time-dependent problems and problems involving excited states. Atomic and molecular collisions involving both these types of phenomena remain outside the purview of DFT. An amalgamation of quantum fluid dynamics (QFD) with DFT considerably broadens the range of applicability of traditional (ground-state) DFT. Ion-atom collisions have been studied by jointly using DFT and QFD.

Using a recently proposed kinetic energy density functional and an amalgamation of density functional theory with quantum fluid dynamics, a time-dependent Kohn-Sham-type equation in three-dimensional space, which is a new non-linear Schrodinger equation, has been derived. The equation is also derived through the stochastic interpretation of quantum mechanics. A molecular “thermodynamic” viewpoint is suggested in terms of space-time-dependent quantities. Numerical solution of the above equation yields the time-dependent charge density, current density, effective potential and chemical potential. Perspective plots of these quantities for the proton-neon 25 keV head-on collision are presented.

Using the double-zeta wavefunctions of Snyder and Basch [5], the Weizsacker correction \(T_w = \tfrac{1}{8}\int d \vec r(\nabla \rho \cdot \nabla \rho )\rho ^{ - 1} \) has been evaluated for the molecules H2, HF, BF, N2 and CO. There was no linear correlation between Tw and the binding energy for these molecules.

Two simple uncertainty corrections to the Thomas-Fermi theory are suggested. The first is derived according to statistical-mechanical considerations, and the second is obtained by a semi-empirical extension to many-electron systems of a spherical one-electron-system result. For both corrections results are quite good; in particular, most of the results from the second correction are probably the best reported so far.

Scattering cross sections are obtained for scattering of waves from one-dimensional lattices chosen as simplistic models of Cantor-like sets. The self-similar geometry is described in terms of a fractal dimension. A parametric dependence of the cross-section on the fractal dimension is proposed. The average wavefunction method is used to calculate the differential scattering cross section. The integrated cross section shows a fractional power-law dependence on the wave-vector of the incoming wave. Results are presented for a wide range of energies and two different regimes exhibiting different fractal behaviour are observed.

A new simple form for the atomic kinetic energy-density functional ( t ) is proposed as a sum of the Thomas-Fermi term and a radial correction term, namely, t [ p ] = (3/10) (3π 2 ) 2/3 p 5/3 - ( 1/40 )( r ·▽ p )/ r 2 , where the first term is the Thomas-Fermi term and p ( r ) is the Hartree-Fock atomic density. The correction term is part of the -(1/4)▽ 2 p term which occurs in the kinetic energy density; it adds mainly terms of O( Z 2 ) and O( Z 5/3 ) to the Z 7/3 atomic Thomas-Fermi energy. The above form generally displays improved local and global behaviour for atomic kinetic energies. Besides satisfying the virial theorem, it gives rise to chemical binding in molecules.

The Euler-Lagrange equation in density functional theory is generally a differential (or integro-differential) equation. An integral equation for direct calculations has been obtained from the Euler-Lagrange equation. It is easier to solve the new equation numerically than the original differential equation.

This review article discusses several interesting generalized nonlinear Schrodinger equations (GNLSE) occurring in quantum fluid dynamics for both time-independent and time-dependent situations as well as the possibility of soliton or solitary wave solutions for such equations. It concludes with a brie f report on a new GNLSE derived by the authors recently.

Recently, an assessment regarding the validity of maximum hardness principle has been done taking 34 exothermic chemical reactions (Poater, J.; Swart, M.; Solà, M. J. Mex. Chem. Soc. 2012, 56, 311) in which only 46% and 53% of the total reactions have greater hardness for the products and the reactants than those for the reactants and the transition states, respectively. They have also mentioned that a larger set of reactions should be studied to draw a general conclusion regarding the validity of maximum hardness principle. We have noticed that the reactions having fewer number of reactants than that of products and / or very hard atoms like H, N, O, F or very hard molecules like H2, N2, HF, HCN, CH4, etc. appearing in the reactant side, are more likely to disobey maximum hardness principle. In addition, dependence of hardness values on level of theory, basis sets, definitions, formulas, approximations should be kept in mind before criticising the validity of maximum hardness principle. Since these electronic structure principles are qualitative in nature, one should not expect them to be valid in all cases.

Molecular vibrations in ammonia (NH3) and hydrogen sulfide (H2S), and internal rotations in hydrogen peroxide (HOOH), hydrogen thioperoxide (HSOH), hydrogen persulfide (HSSH), and ethylene (C2H4) are studied using ab initio SCF methods at the Hartree−Fock level using a standard Pople 6-311G** basis set. Polarizability values are calculated using both Pople's and Sadlej's basis sets. Any nontotally symmetric distortion in bond length or bond angle along the vibrational symmetry coordinates of a molecule around its equilibrium geometry decreases the equilibrium hardness value and increases the equilibrium polarizability value. During rotational isomerization the minimum energy conformation corresponds to the maximum hardness and minimum polarizability values and the maximum energy conformation corresponds to the minimum hardness and maximum polarizability values. Density functional calculations confirm these observed trends. In general we have found that the conditions of maximum hardness and minimum polari...

Hydrogen storage potential of two sets of lithium containing systems, viz., Li-doped borazine derivatives and various bondstretch isomers of Li3Al4 - is studied at the B3LYP/6-311+G(d) level of theory occasionally supplemented by the results from the associated MP2/6-31+G(d) calculations. Negative values of interaction energy, reaction enthalpy, reaction electrophilicity, and desorption energies for the gradual hydrogen-trapping processes justify the efficacy of these systems as the hydrogen storage material. Presence of Li as well as aromaticity improves the situation. Various conceptual density functional theory based reactivity descriptors like electronegativity, hardness, and electrophilicity and the associated electronic structure principles such as the principles of maximum hardness and minimum electrophilicity lend additional support

The chemical reactivity descriptors, such as electronegativity, hardness and electrophilicity of major oxides computed from density functional theory are reported in this paper. These parameters are plotted within a fitness landscape diagram, showing that the principles of minimum electrophilicity (MEP) and maximum hardness (MHP) act as guides towards the region of higher stability. The diagrams indicate the trends and the parameters that control the evolution of natural rocks. Application of the principle S-bearing copper compounds shows the possible and preferred combinations of elements, that give rise to compounds observed during ore formation.

Department of Chemistry and Centre for Theoretical Studies, Indian Institute of Technology, Kharagpur-721 302, West Bengal, India E-mail : pkc@chem. iitkgp.ernet. in Manuscript received 23 May 2011, accepted 30 May 2011 Starting from aromatic polynitrogen systems like N42- and N64-, several potential molecular materials have been generated, with suitable linkers. Necessary optimization and frequency analysis have been performed at the 83LYP/ 6-31 + G(d) and B3L YP/6-31G(d) levels of theory. Conceptual density functional theory based reactivity descriptors and the nucleus independent chemical shift values lend additional insights into their stability, reactivity and aromaticity. They may be considered to be suitable candidates for hydrogen storage material.&nbsp

Gas-surface scattering is speculated as a meaningful problem for understanding the physics of fractals. Fractal behaviour can be associated with a self-similar geometry on a solid surface. The interaction potential for a gas atom or molecule approaching the lattice depends primarily on local factors but a parametric dependence of the cross-section data on the fractal dimension can be conceived. Such a dependence on the self-similar character of a multi-centred target is more explicit when multiple scattering is included. Application of approximation schemes like the previously developed average wavefunction method to this problem is suggested.

We review the Bethe-Salpeter equation (BSE) approach to the calculation of electronic excitation energies of molecular systems. We recall the general Green's function many-theory formalism and give the working equations of the BSE approach within the static GW approximation with and without spin adaptation in an orbital basis. We apply the method to the pedagogical example of the H2 molecule in a minimal basis, testing the effects of the choice of the starting one-particle Green's function. Using the non-interacting one-particle Green's function leads to incorrect energy curves for the first singlet and triplet excited states in the dissociation limit. Starting from the exact one-particle Green's function leads to a qualitatively correct energy curve for the first singlet excited state, but still an incorrect energy curve for the triplet excited state. Using the exact one-particle Green's function in the BSE approach within the static GW approximation also leads to a number of additional excitations, all of them being spurious except for one which can be identified as a double excitation corresponding to the second singlet excited state.