Maximum Hardness Principle Research Articles

Electrostatic guidelines and molecular tailoring for density functional investigation of structures and energetics of (Li)n clusters

A molecular electrostatic potential (MESP)-guided method for building metal aggregates is proposed and tested on prototype lithium (Li)(n) clusters from n=4 to 58. The smaller clusters are subsequently subjected to direct density functional theory based geometry optimization, while the larger ones are optimized via molecular tailoring approach (MTA). The calculations are performed using PW91-PW91 as well as B3LYP functionals, and the trends in the interaction energies are found to be similar. The MESP-guided model for building metal clusters is validated by comparing the resulting cluster geometries with the ones reported in the literature up to n=20. A comparison of the ionization potential and polarizability (up to n=22) with their experimental counterparts shows a fairly good agreement. A new MTA-based scheme for calculating the ionization potential and polarizability values of large metal clusters is proposed and tested on Li(40) and Li(58) clusters. Further, the existence of "magic numbered clusters" up to n=22 is justified in terms of "maximum hardness principle" as well based on molecular electron density topography and distance descriptors.

Impact of Lewis Acids on Diels−Alder Reaction Reactivity: A Conceptual Density Functional Theory Study

Density functional theory (DFT) and conceptual/chemical DFT studies are carried out in this work for the normal electron demand Diels-Alder reaction between isoprene and acrolein to compare chemical reactivity and regioselectivity of the reactants in the absence and presence of Lewis acid (LA) catalysts. A cyclic coplanar structure of acrolein-LA complex has been observed and the natural bond orbital analysis has been employed to interpret the interaction between acrolein and LAs. Reactivity indices from frontier molecular orbital energies are proved to be adequate and efficient to evaluate the catalytic property of LAs. Linear relationships have been discovered among the bond order, bond length, catalytic activation, and chemical reactivity for the systems concerned. The validity and applicability of maximum hardness principle, minimum polarizability principle, and minimum electrophilicity principle are examined and discussed in the prediction of the major regioselective isomer and the preferred reaction pathway for the reactions in the present study.

Theoretical Study and Comparasion of Bent's Rule with Hardness and Polarizibility for SF4, SF4O, PCl4F, PCl3F2, PCl2F3, PCl2F4 Molecules

Electronic parameters such as HOMO-LUMO energies, Mulliken charges, dipole moments for different isomers of SF4, SF4O, PCl4F, PCl3F2, PCl2F3, PCl2F4 molecules have been carried out at the MP2 level of theory using 6-31G(d), 6-311G(d,p) basis sets by applying Gaussian 03 Revision B-04. Maximum hardness and minimum polarizability have been calculated to see the consistency with the Bent rule. According to Maximum Hardness Principles (MHP) and Minimum Polarizability Principles (MPP) most stable structure can be predicted if they have different isomers. We have investigated how bond orbitals change for studied molecules by natural bond orbital (NBO) analysis, as well. There is agreement between our results and experimentaql results on the dipole moments and structures of the phosphorus chlorofluorides obtained by IR and Raman vibrational data, NMR measurements and 35Cl pure quadrupole resonance frequencies reported earlier by Holmes aand coworkers.

Na N + (N ⩽ 12) clusters fragmentation channels: A conceptual DFT approach

In this paper we study the small Na$_{N}^{+}$ (N l 12) cationic clusters fragmentation channels, with all electronic calculations performed at the B3LYP/6-311G+(d,p) DFT level of theory. For these cluster sizes, we obtain for all neutral, cationic, bi-cationic and anionic species the optimized geometries, total energies and electronic properties such as the adiabatic ionization potentials, electron affinities and global hardnesses. Furthermore, we propose the novel concept of global hardness change, Δ η, within the conceptual DFT formalism, based on the maximum hardness principle of Chattaraj, Lee, and Parr. Thereafter we compute for all possible fragmentation channels the involved energetics, ΔE, and the global hardness change, Δη, both methods are shown to be in agreement with available experimental findings for all but one case. We show that hardness and the global hardness change are good DFT descriptors to assess the preferred fragmentation channels, where formation of the hardest fragments seems to be the driving force.

Minimum Polarizability Principle Applied to Lowest Energy Isomers of Some Gaseous All-Metal Clusters

In comparison with the minimum energy criterion as an indicator of the most stable state, the minimum polarizability and maximum hardness principles have been examined to describe the relative stability of various isomers of nine gaseous all-metal clusters M4X- (Cu4Na-, Cu4Li-, Al4Cu-, Ag4Li-, Au4Li-, Ag4Na-, Au4Na-, Al4Ag-, Al4Au-) on the basis of MP2 calculations. In these species, there are two lowest energy isomers with near isoenergy that sometimes make it very difficult to determine which of them is more stable when we depend only on the minimum energy criterion. According to the minimum polarizability principle, however, the square-pyramidal structure is always more stable than the planar isomer at various computational levels, which was also confirmed by the results from the minimum energy principle that sometimes requires higher computational precision. Thus, there is an indication that, at least for our present cluster system, the minimum polarizability principle is less dependent on the computational levels compared to the minimum energy principle.

Acidity of meta- and para-substituted aromatic acids: a conceptual DFT study

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.

Is There a Minimum Electrophilicity Principle in Chemical Reactions?

AbstractFor 25 simple reactions, the changes of the hardness (Δη), polarizability (Δα) and electrophilicity index (Δω) and their cube‐roots (Δη1/3, Δα1/3, Δω1/3) were calculated. It is shown that although the Maximum Hardness and Minimum Polarizability Principles are not valid for all reactions, but in most cases Δω1/3<0, whereas we always find Δω<0. Our observation implies to this fact that for those chemical reactions in which the number of moles decreases or at least remains constant, the most stable species (reactants or products) have the lowest sum of electrophilicities. In other words "the natural direction of a chemical reaction is toward a state of minimum electrophilicity". This fact may be called Minimum Electrophilicity Principle (MEP).

Theoretical study on the structure and properties of crenulatin molecule in herb Rhodiola crenulata

Crenulatin (C 25H 20O 10) is a flavonol derivative, which can be isolated from the roots of Rhodiola crenulata (Hook. F. et Thoms.), a widely used medicinal herb due to its nice curative effect. In this study, theoretical analysis on the geometries and electronic properties of its molecular structure (crenulatin-a or crenulatin-b diastereoisomers) in gas phase is reported. As judged by total energy, the frontier orbital energy gap, the maximum hardness principle and 13C chemical shifts, we predict that crenulatin-a structure is the preferable structure of crenulatin molecule. Both diastereoisomers are soluble in water which enhances its biological activity of antioxidant. In order to evaluate the antioxidant activity of the molecule, the best indicators of the antioxidative, the O–H bond dissociation enthalpy (BDE) and adiabatic ionization potential (IP) were computed by density functional theory (DFT). We obtained that the most active site is the 3-OH group and crenulatin is active as an electron donor. All these results suggest that crenulatin is a potential antioxidant similar to kaempferol.

Use of nuclear stiffness in search for a maximum hardness principle and for the softest states along the chemical reaction path: A new formula for the energy third derivative γ

Nuclear stiffness, expressed as a hardness derivative, appears to be a good measure of the slope of global hardness. The authors analyze molecular states for which hardness has a maximum value. Maximum hardness principle (MHP) has been discussed. At the ground state hardness function does not obtain a maximum value versus spatial coordinates within a constant number of electrons (N), but is so within constant chemical potential (mu) constraint. The authors apply this feature to evaluate an energy third derivative (gamma). MHP has been analyzed via symmetry considerations of nuclear stiffness and nuclear reactivity. Nuclear stiffness has been also applied to study the hardness profile for a chemical reaction. In this case, the authors seek molecular states for which hardness is at a minimum. They have examined systems for which they have recently obtained regional chemical potentials [P. Ordon and A. Tachibana, J. Mol. Model. 11, 312 (2005); J. Chem. Sci. 117, 583 (2005)]. The transition state is found not to be the softest along the chemical reaction path. Nuclear stiffness reflects well the softest conformation of a molecule, which has been found independently along the intrinsic reaction coordinate profile. Electronic energy-density [A. Tachibana, J. Mol. Mod. 11, 301 (2005)] has been used to visualize the reactivity difference between the softest state and the transition state.

Chemical reactivity patterns of [ n]paracyclophanes

We present a systematic density functional theory study of the global and local reactivity patterns of [ n]paracyclophanes. Maximum hardness principle (MHP) and minimum electrophilicity principle (MEP) are obeyed in these strained molecules. Linear relationships among strain energy, electrophilicity, aromatic stabilization energy and chemical hardness are established. The Fukui function (FF) values at the carbon atoms of the benzene ring of [ n]paracyclophanes are critically analyzed. The presence of weak C–H…π interactions is evident from the AIM topographical analysis.

Minimum electrophilicity principle in photocycloaddition formation of oxetanes

AbstractThe regio‐ and stereoselectivity of some Paternó–Büchi reactions are studied within a density functional framework with B3LYP exchange‐correlation energy functional and 6‐31G** basis set. It is shown that although in most cases the Minimum Polarizability and the Maximum Hardness Principles (MPP and MHP) successfully predict the major oxetane products of these reactions, but in all of the considered reactions, with no exception, the main products have the lesser electrophilicity values than the minor isomers, and therefore the Minimum Electrophilicity Principle (MEP) correctly predicts the most stable stereoisomer of the reaction. Copyright © 2007 John Wiley & Sons, Ltd.

Structural and Dynamic Properties of (SiO2)6 Silica Nanostructures: A Quantum Molecular Dynamics Study

Structural and dynamic properties of the building block of silica nanowires, (SiO2)6, are investigated by Born-Oppenheimer quantum molecular dynamics simulations. Thirteen conformers have been identified, seven of which have not been reported before. The energy component analysis shows that the lower electrostatic interaction differentiates the global minimum from the other structures. We also observe that the maximum hardness principle can be employed to justify the molecular stability for this system. Time profiles of a few density functional reactivity indices exhibit correlations of dynamic fluctuations between HOMO and LUMO and between chemical potential and hardness. Electrophilicity, nucleaofugality, and electrofugality indices are found to change concurrently and significantly, indicating that the nanostructures sampled during the dynamic process are exceedingly reactive and rich in chemistry.

Size dependence of the structures and energetic and electronic properties of gold clusters

The structures and stabilities of gold clusters with up to 14 atoms have been determined by density-functional theory. The structure optimizations and frequency analysis are performed with the Perdew-Wang 1991 gradient-corrected functional combined with the effective core potential and corresponding valence basis set (LANL2DZ). The turnover point from two-dimensional to three-dimensional geometry for gold clusters occurs at Au12. The energetic and electronic properties of the small gold clusters are strongly dependent on sizes and structures, which are in good agreement with experiment and other theoretical calculations. The even-odd oscillation in cluster stability and electronic properties predicted that the clusters with even numbers of atoms were more stable than the neighboring clusters with odd numbers of atoms. The stability and electronic structure properties of gold clusters are also characterized by the maximum hardness principle of chemical reactivity and minimum polarizability principle.

Post Hartree–Fock and density functional theory studies on Di-Protonated Allopurinol 2+

Post Hartree–Fock and density functional theory (DFT) methods have been employed to study the molecular properties of Di-Protonated Allopurinol 2+ tautomers in gaseous and aqueous phase environments. The tautomers in gaseous phase have been optimized at MP2/6-311G(2d,2p) and B3LYP/6-311G(2d,2p) levels of theory. The self-consistent reaction field theory (SCRF) has been employed to optimize the tautomers in aqueous phase ( ε = 78.5) at B3LYP/6-311G(2d,2p) level of theory and the solvent effect has been studied. The structure, energetics and relative stabilities of the tautomers have been analyzed both in gaseous and aqueous phases. The principle of maximum hardness (MHP) has been tested at B3LYP/6-311G(2d,2p) level of theory. The condensed Fukui functions have been calculated using the atomic charges obtained through Natural population analysis to identify the relative change in the most reactive site of the optimized structures. NMR studies have been carried out, on the basis of Cheeseman coworker’s method, to analyze the molecular environment as well as the delocalization activities of electron clouds.

Further links between the maximum hardness principle and the hard/soft acid/base principle: insights from hard/soft exchange reactions

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.

REGIOSELECTIVITY OF HETERO DIELS–ALDER REACTIONS BETWEEN 1-AZA-1,3-BUTADIENE DERIVATIVES AND DIMETHYLVINYLAMINE: A THEORETICAL INVESTIGATION

The regioselectivity of hetero Diels–Alder reactions between 1-aza-1,3-butadiene derivatives and dimethylvinylamine is elucidated by means of several theoretical approaches, namely, the Gazquez–Mendez rule based on the calculation of local softnesses, barrier activation calculations, maximum hardness principle, and the Houk rule based on the FMO theory. The calculations were performed at the B3LYP/6-31G(d) level of theory, and the obtained results are in agreement with available experimental results. Moreover, the present analysis shows that these inverse electron demand polar cycloadditions present a linear relationship between the activation barriers of the favored ortho regio-isomers and the inverse of electrophilicity differences of the reagents.

Gas-Phase Structures, Rotational Barriers, and Conformational Properties of Hydroxyl and Mercapto Derivatives of Cyclohexa-2,5-dienone and Cyclohexa-2,5-dienthione

The rotational barriers and conformational properties of the hydroxyl and mercapto groups attached to the alpha and beta positions of cyclohexa-2,5-dione and cyclohexa-2,5-dienthione have been studied at the B3LYP/ 6-311++G(d,p) level of theory. The results show that the conformational preferences of these studied systems are the result of a subtle interplay between different competing effects (conjugation, hyperconjugation, and steric repulsions). The applicability of the density functional theory reactivity indices and the maximum hardness principle for the present systems has been analyzed.

AN ANALYSIS OF THE REGIOSELECTIVITY IN HETERO DIELS–ALDER REACTIONS USING DFT-BASED REACTIVITY INDEXES

The regioselectivity of hetero Diels–Alder reactions (HDA) of 2-azabutadiene with aldehydes has been elucidated by means of Gazquez–Mendez rules, which are based on the calculation of local softnesses of the four terminal atoms involved in cyclization. The theoretical results obtained with the B3LYP/6-31G(d) method confirm the regioselectivities observed experimentally for all substituents ( R = H , CH 3, CN ) present in the aldehyde reactant. The regioselectivities of these HDA reactions have been confirmed by the calculation of the activation barriers corresponding to the two cyclization modes, and also by the application of the Houk rule and the maximum hardness principle.

Study of static dipole polarizabilities, dipole moments, and chemical hardness for linear CH 3–(C [tbnd6]C) n–X (X=H, F, Cl, Br, and NO 2 and n=1–4) molecules

Ab initio and density functional theory calculations have been performed to determine the dipole moment and static polarizabilities for CH 3–(C C) n –X (X=H, F, CL, Br, NO 2 and n=1–4) molecules. It is shown that a simple linear relation involving the aggregation number fits the polarizability results well with a correlation coefficient greater than 0.99 at ab initio and dft levels of calculations. The chemical hardness, global softness, and chemical potential have been calculated for the above molecules at HF and B3LYP levels of theory. It has been shown that good linear correlation between the dipole polarizabilities and cube root of static polarizabilities with dipole moments. Similarly, the softness parameters correlate well with the dipole polarizabilities and cube root of static polarizabilities. In addition to the above, we have calculated the cube root of static polarizabilities with the distortion of C–X bonds in CH 3–(C C)–X (X=H, F, CL, Br, and NO 2) molecules and tested the principle of maximum hardness.

Theoretical support for using the Δ f( r) descriptor

The Δ f( r) descriptor characterizes the variations of the absolute hardness when the external potential changes. In this work, the Δ f( r) descriptor is regarded through three different theoretical points of view: its relations with the Fukui functions; its links with the covalent interaction energy; and finally its compliance with the Principle of Maximum Hardness. It appears from the three studies that the sign of the descriptor is able to characterize the electrophilic/nucleophilic behavior of a molecular site.