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

On the link between the reaction force constant and conceptual DFT

CONTEXT

The reaction force constant ( κ ), introduced by Professor Alejandro Toro-Labbé, plays a pivotal role in characterizing the reaction pathway by assessing the curvature of the potential energy profile along the intrinsic reaction coordinate. This study establishes a novel link between κ and the reactivity descriptors of conceptual density functional theory (c-DFT). Specifically, we derive expressions that relate the reaction force constant to nuclear softness and variations in chemical potential. Our findings indicate that regions of the reaction pathway where κ is negative match with significant electronic structure rearrangements, while positive κ regions match mostly with geometric rearrangements. This correlation between κ and c-DFT reactivity descriptors enhances our understanding of the underlying forces driving chemical reactions and offers new perspectives for analyzing reaction mechanisms.

METHODS

The internal reaction path for the proton transfer in SNOH, chemical potential, and nuclear softness were computed using DFT with B3LYP exchange-correlation functional and 6-311++G(d,2p) basis set.

Spin-Polarized Conceptual Density Functional Theory from the Convex Hull

We present a new, nonarbitrary, internally consistent, and unambiguous framework for spin-polarized conceptual density-functional theory (SP-DFT). We explicitly characterize the convex hull of energy, as a function of the number of electrons and their spin, as the only accessible ground states in spin-polarized density functional theory. Then, we construct continuous linear and quadratic models for the energy. The nondifferentiable linear model exactly captures the simplicial geometry of the complex hull about the point of interest and gives exact representations for the conceptual DFT reactivity indicators. The continuous quadratic energy model is the paraboloid of maximum curvature, which most tightly encloses the point of interest and neighboring vertices. The quadratic model is invariant to the choice of coordinate system (i.e., {N, S} vs {Nα, Nβ}) and reduces to a sensible formulation of spin-free conceptual DFT in the appropriate limit. Using the quadratic model, we generalize the Parr functions {P+(r), P-(r)} (and their derivatives with respect to number of electrons) to this new spin-polarized framework, integrating the Parr function concept into the context of (spin-polarized) conceptual DFT, and extending it to include higher-order effects.

Effect of "magic chlorine" in drug discovery: an in silico approach

The chlorine atom plays a vital role in drug design, yet the benefits of chlorine in 250 FDA-approved chlorine-containing drugs have not been studied properly. To see the "magic chloro" effect, computational studies have been carried out for 35 inhibitors, which are numbered as 12 complexes with (parent (-H), one chlorine, or two chlorine) substituents. The physicochemical properties are studied by conceptual density functional theory (CDFT). The pharmacokinetics, toxicity and metabolic properties of the studied inhibitors are estimated using chemoinformatics tools. SwissTargetPrediction is used to predict the multitarget activities of the studied inhibitors. Four FDA-approved drugs, diazepam, chloroquine, chloramphenicol, and bendamustine, are referenced to validate the studies. A higher HOMO-LUMO gap predicted high stability for the studied one and two chlorine-substituted analogues. Most of the studied inhibitors show "drug likeliness", nontoxicity, and high gastrointestinal (GI) absorption. The addition of one or two chloro substituents has increased the physicochemical properties and stability of most of the inhibitors compared to the parent analogues, whereas the toxicity is not affected. No change in metabolic properties is observed on addition of one or two chlorine substituents. The multi-target activities of all the studied inhibitors are validated by the reference drugs and experimental results.

Molecular interactions from the density functional theory for chemical reactivity: Interaction chemical potential, hardness, and reactivity principles

In the first paper of this series, the authors derived an expression for the interaction energy between two reagents in terms of the chemical reactivity indicators that can be derived from density functional perturbation theory. While negative interaction energies can explain reactivity, reactivity is often more simply explained using the “|dμ| big is good” rule or the maximum hardness principle. Expressions for the change in chemical potential (μ) and hardness when two reagents interact are derived. A partial justification for the maximum hardness principle is that the terms that appear in the interaction energy expression often reappear in the expression for the interaction hardness, but with opposite sign.

Conceptual density functional theory based electronic structure principles

In this review article, we intend to highlight the basic electronic structure principles and various reactivity descriptors as defined within the premise of conceptual density functional theory (CDFT). Over the past several decades, CDFT has proven its worth in providing valuable insights into various static as well as time-dependent physicochemical problems. Herein, having briefly outlined the basics of CDFT, we describe various situations where CDFT based reactivity theory could be employed in order to gain insights into the underlying mechanism of several chemical processes.

Bond stretch isomerism in Be32− driven by the Renner–Teller effect

Illustration of bond stretch isomerization of triangular D_3h Be₃²⁻ moieties via the linear D_∞h intermediate through the Renner–Teller effect. The reactant, intermediate and products are connected schematically by the C_2v transition states; moreover, a connection between the transition states and excited state linear intermediate is depicted.

The generalized maximum hardness principle revisited and applied to solids (Part 2)

Building on Part 1 devoted to atoms and molecules (PCCP, in press 2017), we now focus on the crystal structure and electronic properties of solids as viewed from the Maximum Hardness Principle (MHP), first formulated by Pearson in 1987. The focus is on cases where nuclear potential acting on electrons does not remain constant and where substantial modifications of the nuclear geometry take place (Generalized MHP, GMHP). We present an overview of important manifestations of the (G)MHP for solids such as (i) a tendency of metals and doped-semiconductors to undergo superconducting transition at low temperatures, (ii) propensity of many types of alloys to develop a band gap or a pseudo-gap, (iii) preference for preserving the noble gas (octet, doublet) configuration of main block element ions in the solid state, (iv) preference of Jahn-Teller systems for band-gap-opening vibronic-coupling-related lattice distortions, (v) pressure phenomena leading to localization of the electronic density, (vi) tendency to annihilate the null band gap via phase separation (while preserving the nominal chemical composition), (vii) absence of a large number of families of high-T_C superconductors, (viii) resistance of most stable systems to chemical doping, etc. GMHP turns out to be an important qualitative guide in studies of solid state polymorphism and electronic phenomena. Exceptions from (G)MHP are discussed, and a more restrictive formulation of the principle is proposed.

Hardness maximization or equalization? New insights and quantitative relations between hardness increase and bond dissociation energy

It has been overlooked that the change of hardness, η, upon bonding is intimately connected to thermochemical cycles, which determine whether hardness is increased according to Pearson's "maximum hardness principle" (MHP) or equalized, as expected by Datta's "hardness equalization principle" (HEP). So far the performances of these likely incompatible "structural principles" have not been compared. Computational validations have been inconclusive because the hardness values and even their qualitative trends change drastically and unsystematically at different levels of theory. Here I elucidate the physical basis of both rules, and shed new light on them from an elementary experimental source. The difference, Δη = η _mol - <η _at>, of the molecular hardness, η _mol, and the averaged atomic hardness, <η _at>, is determined by thermochemical cycles involving the bond dissociation energies D of the molecule, D ⁺ of its cation, and D ^- of its anion. Whether the hardness is increased, equalized or even reduced is strongly influenced by ΔD = 2D - D ⁺  - D ^-. Quantitative expressions for Δη are obtained, and the principles are tested on 90 molecules and the association reactions forming them. The Wigner-Witmer symmetry constraints on bonding require the valence state (VS) hardness, η _VS, instead of the conventional ground state (GS) hardness, η _GS. Many intriguingly "unpredictable" failures and systematic shortcomings of said "principles" are understood and overcome for the first time, including failures involving exotic and/or challenging molecules, such as Be_2, B₂, O₃, and transition metal compounds. New linear relationships are discovered between the MHP hardness increase Δη _VS and the intrinsic bond dissociation energy D _i . For bond formations, MHP and HEP are not compatible, and HEP does not qualify as an ordering rule.

The generalized maximum hardness principle revisited and applied to atoms and molecules

Part 1 of this duology is devoted to isolated atoms and molecules, and to chemical reactions between them; we introduce here basic concepts beyond the Generalized Maximum Hardness Principle, and the corresponding Minimum Polarizability Principle, and we illustrate applicability of both principles to a broad range of chemical phenomena and distinct systems in the gas phase.

Computational nanochemistry report on the oxicams--conceptual DFT indices and chemical reactivity

A density functional theory study of eight oxicams was carried out in order to determine their global and local reactivities. These types of reactivities were measured by means of global and local reactivity descriptors coming from the conceptual density functional theory. Net electrophilicity as a global reactivity descriptor and local hypersoftness as a local reactivity descriptor were the used tools to distinguish reactivity and selectivity among these oxicams. Globally, isoxicam presents the highest electron donating capacity; meanwhile, the highest electron accepting capacity is exhibited by droxicam. Locally, two oxicams present neither nucleophilic nor electrophilic relevant reactivity in their peripheral pyridine ring, droxicam and tenoxicam, so that their more reactive zones are found on the respective fused rings. Oxicams have been divided into two subgroups in order to facilitate the local analysis of reactivity. One group is characterized because their most important condensed values for local hypersoftnes are well-separated: 4-meloxicam, lornoxicam, meloxicam, and normeloxicam. Meanwhile, the opposite situation is found in droxicam, isoxicam, piroxicam, and tenoxicam. As a whole, the nucleophilic characteristic noticeably predominates in these eight oxicams instead of an electrophilic behavior, thus meaning a greater tendency to donate electrons rather than withdrawing them; a consequence of this behavior implies a favorable interaction with a hypothetical receptor bearing one or more electron acceptor functional groups rather than electron donor functional groups; this would imply a maximization of this interaction from the covalent point of view.

Do the local softness and hardness indicate the softest and hardest regions of a molecule?

In this work, we will show that the largest values of the local softness and hardness do not necessarily correspond to the softest and hardest regions of the molecule, respectively. Based on our results, we will argue that it is more useful to interpret the local softness and the local hardness as functions that measure the "local abundance" or "concentration" of the corresponding global properties. This new point of view helps reveal how and when these local reactivity indices are most useful.

Critical thoughts on computing atom condensed Fukui functions

Different procedures to obtain atom condensed Fukui functions are described. It is shown how the resulting values may differ depending on the exact approach to atom condensed Fukui functions. The condensed Fukui function can be computed using either the fragment of molecular response approach or the response of molecular fragment approach. The two approaches are nonequivalent; only the latter approach corresponds in general with a population difference expression. The Mulliken approach does not depend on the approach taken but has some computational drawbacks. The different resulting expressions are tested for a wide set of molecules. In practice one must make seemingly arbitrary choices about how to compute condensed Fukui functions, which suggests questioning the role of these indicators in conceptual density-functional theory.

Imaginary Vibrational Modes in Polycyclic Aromatic Hydrocarbons: A Challenging Test for the Hardness Profiles

In a very recent article (J. Am. Chem. Soc. 2006, 128, 9342-9343) Moran et al. found that electron-correlated methodologies using popular Pople basis sets lead to spurious nonplanar polycyclic aromatic hydrocarbon (PAH) equilibrium structures. Furthermore, some of the present authors have shown that the hardness profiles along a reaction path can be a useful tool to find spurious stationary points in the potential energy surface. Herein, we test the performance of the hardness profiles to detect shortcomings in energy profiles for the challenging case of nonplanar PAHs. The results obtained show that in 41 of the 42 imaginary vibrational modes studied, the hardness profiles indicate the wrong number and type of the potential energy surface stationary points.

Aromaticity of Distorted Benzene Rings: Exploring the Validity of Different Indicators of Aromaticity

The effect of three in-plane (bond length alternation, bond length elongation, and clamping) and three out-of-plane deformations (boatlike, chairlike, and pyramidalization) on the aromaticity of the benzene molecule has been analyzed employing seven widely used indicators of aromaticity. It is shown that only the aromatic fluctuation index (FLU) is able to indicate the expected loss of aromaticity because of distortion from the equilibrium geometry in all deformations analyzed. As FLU has been shown previously to fail in other particular situations, we conclude that there is not yet a single indicator of aromaticity that works properly for all cases. Therefore, to reach safer conclusions, aromaticity analyses should be carried out employing a set of aromaticity descriptors on the basis of different physical manifestations of aromaticity.

Woodward-Hoffmann rules in density functional theory: Initial hardness response

The Woodward-Hoffmann rules for pericyclic reactions, a fundamental set of reactivity rules in organic chemistry, are formulated in the language of conceptual density functional theory (DFT). DFT provides an elegant framework to introduce chemical concepts and principles in a quantitative manner, partly because it is formulated without explicit reference to a wave function, on whose symmetry properties the Woodward-Hoffmann [J. Am. Chem. Soc. 87, 395 (1965)] rules are based. We have studied the initial chemical hardness response using a model reaction profile for two prototypical pericyclic reactions, the Diels-Alder cycloaddition of 1,3-butadiene to ethylene and the addition of ethylene to ethylene, both in the singlet ground state and in the first triplet excited state. For the reaction that is thermally allowed but photochemically forbidden, the initial hardness response is positive along the singlet reaction profile. (By contrast, for the triplet reaction profile, a negative hardness response is observed.) For the photochemically allowed, thermally forbidden reaction, the behavior of the chemical hardness along the initial stages of the singlet and triplet reaction profiles is reversed. This constitutes a first step in showing that chemical concepts from DFT can be invoked to explain results that would otherwise require invoking the phase of the wave function.

Local Aromaticity in Natural Nucleobases and Their Size-Expanded Benzo-Fused Derivatives

The influence of the insertion/addition of a benzene ring to the natural nucleic acid bases on the local aromaticity of the so-called size-expanded (xN, with N being adenine, guanine, cytosine, and thymine) bases is examined. To this end, the local aromaticity of the six- and five-membered rings in both the natural bases and their benzoderivatives is determined using HOMA, NICS, aromatic fluctuation index (FLU), and para-delocalization index (PDI) descriptors. In general, there is a good correspondence between the different indices, so that ring moieties with more negative NICS values also have larger HOMA and PDI measures and lower FLU indices. The results also point out notable differences in the aromatic character of the natural and size-expanded bases, which generally are hardly affected upon hydrogen bonding. The differences in the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap determined for the size-expanded nucleobases show an inverse correlation with the aromaticity of the fused benzene ring, so that the larger the HOMO-LUMO gap is, the lower the destabilization experienced by the benzene upon insertion/addition to the natural bases. This finding suggests that the introduction of suitable chemical modifications in the benzene ring might be useful to modulate the HOMO-LUMO gap while enabling the design of modified DNA duplexes that are able to act as molecular wires.

Pseudo-Jahn−Teller Effect as the Origin of the Exalted Frequency of the b2u Kekulé Mode in the 1B2u Excited State of Benzene

In this paper we show that a pseudo-Jahn-Teller (PJT) coupling between the (1)A1g ground state and the (1)B2u excited states along the Kekulé mode of b2u symmetry is responsible for the surprisingly low frequency of this mode in the ground state and its remarkable upward shift of 261 cm(-1) upon excitation to the first (1)B2u excited state.

Pseudo-Jahn-Teller origin of geometry and pseudorotations in second row tetra-atomic clusters X4 (X=Na,Mg,Al,Si,P,S)

Experimentally determined or ab initio calculated molecular geometries carry no information about their origin. Employing the Jahn-Teller (JT) vibronic coupling effects as the only source of instability and consequent distortions of high-symmetry molecular configurations, we have worked out a procedure that allows us to trace the origin of particular geometries and determine the detailed electronic mechanism of their formation. This procedure is illustrated by considering a series of X(4) clusters with X=Na, Mg, Al, Si, P, and S. It shows explicitly why Na(4), Si(4), and Al(4) have a rhombic geometry in the ground state, while Mg(4) and P(4) are tetrahedral, whereas S(4) is a trapezium. Even when the minimum-energy geometries are the same (as in the case of rhombic Na(4), Si(4), and Al(4)), the electronic mechanism of their formation is quite different. In particular, in Na(4) and Si(4) the rhombic minima are produced by a strong pseudo JT coupling between two excited states in the square-planar configuration (different in the two cases) that stabilizes one of them and makes it the ground state by rhombic distortions. The rhombic configuration of Al(4) is due to the pseudo JT effect in its ground-state square-planar configuration, and the trapezium in S(4) is formed by two pseudo JT couplings essentially involving excited states. In several cases this analysis shows also the tunneling paths between equivalent configurations.

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.

Stiffness and Raman Intensity: a Conceptual and Computational DFT Study

A DFT-based reactivity descriptor, the nuclear stiffness, is related to the Raman scattering intensity, which is experimentally accessible. The application of this new relationship obtained within certain approximations has been checked in two different sets of molecules. First, we study a favorable case, where the contribution of the anisotropy to the Raman intensity is zero (symmetric stretching mode in 15 tetrahedral molecules). Second, we consider a "worst" case scenario, where the anisotropy contribution can be expected to be important (stretching mode in 32 diatomic molecules). The numerical results clearly show a relationship between stiffness and Raman intensity reflecting the expected anisotropy influence.

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.

The hardness profile as a tool to detect spurious stationary points in the potential energy surface

In the present work, we have computed the energy and hardness profiles for a series of inter and intramolecular conformational changes at several levels of calculation. All processes studied have in common the fact that the choice of a weak methodology or a poor basis set results in the presence of spurious stationary points in the energy profile. At variance with the energy profiles, the hardness profiles calculated as the difference between the vertical ionization potential and electron affinity always show the correct number of stationary points independently of the basis set and methodology used. For this reason, we have concluded that hardness profiles can be used to check the reliability of the energy profiles for those chemical systems that, because of their size, cannot be treated with high level ab initio methods.