Minimum Polarizability Principle Research Articles

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.

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.

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).

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.

Relative stabilities of all-metal clusters [formula omitted] (M = Li +, Na +, K +, Rb +, Cs +, Cu +, Ag +, Au +)

Upon having made use of relative energy, relative polarizability and relative harness as three descriptors of relative stability, we test their behaviors in the description of the lowest energy isomers of all-metal clusters MAl 4 - (M = Li +, Na +, K +, Rb +, Cs +, Cu +, Ag +, Au +). It has been shown that the stability of the pyramidal isomer decreases with the addition of atomic number. Due to this reason, finally the planar isomer of the AuAl 4 - cluster is more stable than its pyramidal isomer. Compared to the minimum energy principle, the minimum polarizability principle is worth recommendation in assessing relative stabilities of isomers.

A theoretical study on the regioselectivity of Diels–Alder reactions using electrophilicity index

The regioselectivity for a series of Diels–Alder reactions (67 reactions) has been studied using hardness, polarizability and electrophilicity of the corresponding products as global reactivity indexes. It is shown that in many cases, the maximum hardness and minimum polarizability principles (MHP and MPP) cannot predict the major regioisomer of a Diels–Alder reaction; whereas the analysis of global electrophilicities of the products shows that at least in those cases, which diffuse basis sets are used, the major product of the reaction has always the less electrophilicity values. It seems that there is a tendency in atoms to arrange themselves so that the obtained molecule reaches the minimum electrophilicity. This rule may be called the minimum electrophilicity principle (MEP).

The Breakdown of the Minimum Polarizability Principle in Vibrational Motions as an Indicator of the Most Aromatic Center

The vibrational motions that disobey the minimum polarizability principle (MPP) in pi-conjugated molecules are distortions of the equilibrium geometry that produce a reduction in the polarizability due to the localization of pi electrons. For aromatic species, this electronic localization is responsible for the subsequent reduction in the aromaticity of the system. In the present work, we diagonalize the Hessian matrix of the polarizability with respect to the vibrational nontotally symmetric normal coordinates, to calculate the nontotally symmetric distortions that produce the maximum breakdown of the MPP in a series of twenty polycyclic aromatic hydrocarbons. It is shown that the nuclear displacements that break the MPP have larger components in those rings that possess the highest local aromaticity. Thus, these vibrational motions can be used as an indicator of local aromaticity.

Generalizing the Breakdown of the Maximum Hardness and Minimum Polarizabilities Principles for Nontotally Symmetric Vibrations to Non-π-Conjugated Organic Molecules

In previous works we have shown that certain pi-conjugated organic molecules possess nontotally symmetric vibrations that break the maximum hardness (MHP) and minimum polarizability principles (MPP). We have also derived a set of simple rules to determine a priori without calculations whether a particular pi-conjugated organic molecule violates these two principles. In the present work, we generalize these results, and we show that not only pi-conjugated organic molecules but also other molecules without pi-conjugated structure or even pi-bonds can exhibit nontotally symmetric molecular distortions that do not follow these two principles. We have also found that the breakdowns of the MHP and the MPP are not necessarily connected, since the polarizability is not always proportional to the softness. Finally, we also introduced a methodology based on the diagonalization of the hardness Hessian matrix with respect to the vibrational normal coordinates to determine the nontotally symmetric molecular displacements that do not follow the MHP.

Non-planarity and solvent effects on structural and polarizability properties of cytosine tautomers

We report equilibrium geometries, relative stabilities, electronic and vibrational polarizabilities of cytosine tautomers and of reference compounds phenol, aniline and pyrimidine, in the gas phase and in solution, calculated by conventional correlated ab initio (CCSD, CCSD(T) and MP2) and density functional (B97-1) methods, using a variety of basis sets. Gas phase ionization potentials, electron affinities and torsional potentials for the internal rotation of the –OH and –NH2 groups, were obtained at MP2 and B97-1 levels of theory. The results show that the structures of the tautomers are non-planar in the gas phase and become planar as the polarity of the solvent increases, in contrast with aniline where the amino group remains non-planar also in the polar CH3CN solvent, what has a correspondence in the NH2 inversion barrier and NH2 wagging vibration lower in cytosine than in aniline. To constrain NH2 to be planar does not produce important changes in the relative energies, polarizabilities, ionization potential and electron affinities of the tautomers in vacuo. Polarizabilities are consistently influenced by solvent effects. The –OH and –NH2 groups show much higher π interaction with the heterocyclic ring than with the phenyl ring, what determines barriers for internal rotation of the groups much higher in cytosine than in phenol and aniline. Hardness and polarizability profiles for the –OH and –NH2 rotation do not follow, however, the maximum hardness and the minimum polarizability principles, respectively.

The maximum hardness and minimum polarizability principles in accordance with the Bent rule

Abstract Energies, hardness values and polarizabilities for different isomers of SF4, SF4O molecules and a family of PClxF5−x, (x=1,2,3,4) compounds are calculated at the density functional level of theory (B3LYP) using different basis sets (6-31G**, 6-311G**, 6-31++G and 6-311++G). For all molecules and in all cases the Bent rule is confirmed with the stability orders, which is obtained from the calculated energies. It is also found that for each molecule the isomer in which the more electronegative atom occupies the axial position has maximum hardness; and therefore according to the Maximum Hardness Principle (MHP), it must be the most stable isomer. This result is consistent with the Bent rule, but for some cases in which there are more than two isomers, the obtained trends for the stability are not in accordance with this rule. On the other hand, since the calculation of dipole polarizability is very sensitive to the quality of the selected basis set, only for those calculations in which diffuse basis sets are used the obtained trends of stability from the Minimum Polarizability Principle (MPP) are the same as those which are predicted from the Bent rule. It seems that when there are more than two isomers for a molecule both the MHP and MPP can only predict the most stable isomer and cannot predict the correct trend for the stability of the isomers.

Static dipole polarizability and binding energy of sodium clusters Nan (n=1-10): A critical assessment of all-electron based post Hartree-Fock and density functional methods.

A systematic all electron post Hartree-Fock as well as density functional theory (DFT) based calculations for the polarizability and binding energy of sodium metal clusters have been performed and an in-depth analysis of the discrepancy between the experimental and theoretical results is presented. A systematic investigation for the assessment of different DFT exchange-correlation functionals in predicting the polarizability values has also been reported. All the pure DFT functionals have been found to considerably underestimate the calculated polarizability values as compared to the MP2 results. DFT calculations using the full Hartree-Fock exchange along with one-parameter progressive correlation functional have, however, been shown to yield results in good agreement with the MP2 and experimental results. The possible sources of error present in the experimental measurements as well as in the different theoretical methods have also been analyzed. One of the most important conclusions of the present study is that the effect of electron correlation plays a significant role in determining the polarizability of the clusters and the MP2 method can be considered to be one of the most reliable methods for their prediction. It has also been noted that the polarizability value of the lower member clusters (Na2 and Na4) calculated by highly sophisticated methods such as, CCSD and CCSD(T) are found to be very close to the corresponding MP2 values. The polarizability and the binding energy of the clusters are found to be inversely related to each other and their correlation is rationalized by invoking the minimum polarizability principle. A good linear correlation between the polarizability and volume of the cluster has also been found to exist.

The maximum hardness and minimum polarizability principles as the basis for the study of reaction profiles

New and useful aspects of chemical reactivity as described by reactivity indexes and used in connection with the maximum hardness and minimum polarizability principles (MHP and MPP, respectively) are discussed and illustrated for two classical reactions in organic chemistry. They include the Beckmann rearrangement and the condensation reactions of α-amino acids. The MPP appears as a more general rule than the MHP. Another relevant result is related to the usefulness of both empirical reactivity rules to predict the most probable reaction mechanism among two different pathways displaying very close values in activation energy (competitive pathways). This is illustrated for the condensation reaction of a series of α-amino acids: while the accepted stepwise route follows both the MHP and MPP rules, the alternative concerted channel does not, yet its associated activation energy is slightly lower than that corresponding to the nonconcerted reaction mechanism.

Towards understanding the molecular internal rotations and vibrations and chemical reactions through the profiles of reactivity and selectivity indices: an ab initio SCF and DFT study

Ab initio SCF and DFT(B3LYP) calculations are performed with 6–311G** basis sets for obtaining insights into molecular internal rotations in HXNX (X = O,S), different vibrational modes in water and double proton transfer reaction in (HONO)2. While chemical reactivity is analyzed in terms of the profile of the global reactivity parameters, such as energy, chemical potential, hardness, polarizability, molecular valency and electrophilicity indices, the site selectivity is understood through the variations in local descriptors, such as the Fukui function and atomic valency. Principles of maximum hardness and molecular valency and the minimum polarizability principle are found to be valid in almost all cases. Rotational isomerization reactions can be better characterized by making use of the maximum hardness principle along with Hammond's postulate. Extremum points in electrophilicity during internal rotations, vibrations and chemical reaction can be located from those of chemical potential and hardness. The Fukui function and atomic valency show inverse behaviour in most cases.

Ground‐ and excited‐states reactivity dynamics of hydrogen and helium atoms

AbstractDynamic profiles of various reactivity parameters like hardness, chemical potential, polarizability, phase volume, and electrophilicity index are studied in gaining insights into the ground‐ (n = 1) and excited‐ (n = 15) states dynamics of hydrogen and helium atoms. Pertinent time‐dependent Schrödinger equations are solved for the ground and excited states of hydrogen atom and the Rydberg state of the helium atom while a generalized nonlinear Schrödinger equation is solved for the ground state of the helium atom, all interacting with external electric fields of different frequencies and intensities. For both the atoms ground states are more stable than the corresponding excited states. Hardness and phase volume can be used as diagnostics for the chaotic ionization from the Rydberg states of those atoms. Other quantities like higher‐order harmonics also lend additional support. Dynamic variants of the maximum hardness and minimum polarizability principles are found to be operative. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

In a recent paper [J. Am. Chem. Soc. 123, 7951 (2001)] we have shown for the first time the existence of molecules with nontotally symmetric vibrational modes that break the maximum hardness (MHP) and minimum polarizability (MPP) principles. We present here an extension of this previous work by devising a mathematical procedure that helps to determine the nontotally symmetric molecular distortions of a given molecule that do not follow the MPP or the MHP. This methodology is based on the diagonalization of the Hessian matrix of the polarizability or the hardness with respect to the vibrational normal coordinates. For a relatively large series of molecules, we have carried out diagonalizations of the Hessian matrix of the polarizability to determine the molecular distortions with a more marked MPP or anti-MPP character. From the results obtained, we have derived a set of simple rules that allow to predict a priori without calculations the existence of vibrational modes that break the MPP. With respect to the MHP, the results strongly depend on the method of calculation, but the same rules are useful to predict the existence of vibrational modes that disobey the MHP when the Koopmans’ approximation is used to calculate the hardness.

Theoretical study of the trans-N 2H 2→ cis-N 2H 2 and F 2S 2→FSSF reactions in gas and solution phases.

We present a density functional theory (DFT) study of the solvent effects on two intramolecular rearrangements. We have used relative values of energy, electronic chemical potential, chemical hardness and dipole polarizability as global descriptors to analyze the trans-N 2H 2→ cis-N 2H 2 and F 2S 2→FSSF rearrangements in gas and solution phases. Our results agree well with the maximum hardness principle and the minimum polarizability principle. Both reactions become thermodynamically and kinetically more favorable, in the condensed phase. All the species associated with these reactions become less electrophilic in the presence of a polarizable environment. The lowering in the electrophilicity of the species upon solvation may be partitioned into two contributions. The first one contains the variations in electronic chemical potential for the change of phase; whereas the second one indirectly encompasses the variations in chemical hardness through the changes in the maximum charge transfer to the environment. For both reactions, the electronic chemical potential and chemical hardness variations cooperatively contribute to the loss in the electrophilicity power from the gas to solution phase.

Ab Initio Study of the Structure and Polarizability of Sulfur Clusters, Sn (n = 2−12)

The structure and the dipole polarizabilities of Sn clusters (n = 2−12) have been calculated using density functional theory within the B3LYP approximation and conventional ab initio Hartree−Fock (HF) and coupled-cluster with single and double and perturbative triple excitations (CCSD(T)) methods. The results show that the binding energy per atom increases with the size of the cluster and reaches the asymptotic limit for a relatively small n value. There is an excellent agreement between B3LYP and CCSD(T) data in predicting the energy of the disproportionation reaction 2Sn → Sn-1 + Sn+1, which indicates that S2, S6, and S8 are especially stable, in agreement with the experiment. 〈α〉 increases with n and linearly correlates with the molecular volume. 〈α〉/n increases with n and reaches the asymptotic limit per n → ∞ from below, contrary to what happens in small semiconductor and metallic clusters. A well-defined correlation between 〈α〉 and hardness is not found, while the 〈αn〉 − n〈α1〉 difference value linearly correlates with the atomization energy. In the sulfur clusters, the minimum polarizability principle does not hold, the lone-pair electron polarizability being more diffuse, hence more polarizable, in the cluster than in the free atom. Pure vibrational effects on 〈α〉 are negligible.

On the validity of the maximum hardness and minimum polarizability principles for nontotally symmetric vibrations.

ADVERTISEMENT RETURN TO ISSUEPREVCommunicationNEXTOn the Validity of the Maximum Hardness and Minimum Polarizability Principles for Nontotally Symmetric VibrationsMiquel Torrent-Sucarrat, Josep M. Luis, Miquel Duran, and Miquel SolàView Author Information Institut de Química Computacional Universitat de Girona, E-17071 Girona Catalonia, Spain Cite this: J. Am. Chem. Soc. 2001, 123, 32, 7951–7952Publication Date (Web):July 20, 2001Publication History Received1 March 2001Revised26 June 2001Published online20 July 2001Published inissue 1 August 2001https://doi.org/10.1021/ja015737iCopyright © 2001 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views201Altmetric-Citations94LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit Read OnlinePDF (35 KB) Get e-AlertsSupporting Info (4)»Supporting Information Supporting Information SUBJECTS:Equilibrium,Hardness,Mathematical methods,Oscillation,Polarizability Get e-Alerts

Theoretical analysis of some substituted imine-enamine tautomerism

We present a theoretical study of the CH3CXNH⇌CH2CXNH2 tautomerism. The analysis is performed in terms of global descriptors of reactivity, such as electronic chemical potential, chemical hardness and chemical softness. Chemical hardness is used to study the relative stability in the frame of the maximum hardness principle. Chemical softness appears to be related to the molecular polarizability, and it is used to discuss relative stability in the context of the minimum polarizability principle. Both empirical rules are simultaneously satisfied for this equilibrium. Transition states, in which the transferred proton is found about midway between the donor and acceptor atoms, are rationalized in terms of the Bronsted coefficient for the relative position along the reaction coordinate and the Marcus equation for the energy barriers. Substituent effects on the activation properties are analyzed in a partitioned form that probes the effect of the substituent group on the molecular properties at the ground-state and transition-state structures.