Dynamics of Chemical Reactivity Indices for a Many-Electron System in Its Ground and Excited States

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.

Electrophilicity index revisited

This review aims to be a comprehensive, authoritative, critical, and accessible review of general interest to the chemistry community; because the electrophilicity index is a very useful global reactivity descriptor defined within a conceptual density functional theory framework. Our group has also introduced electrophilicity based new global and local reactivity descriptors and also new associated electronic structure principles, which are important indicators of structure, stability, bonding, reactivity, interactions, and dynamics in a wide variety of physico-chemical systems and processes. This index along with its local counterpart augmented by the associated electronic structure principles could properly explain molecular vibrations, internal rotations and various types of chemical reactions. The concept of the electrophilicity index has been extended to dynamical processes, excited states, confined environment, spin-dependent and temperature-dependent situations, biological activity, site selectivity, aromaticity, charge removal and acceptance, presence of external perturbation through solvents, external electric and magnetic fields, and so forth. Although electrophilicity and its local variant can adequately interpret the behavior of a wide variety of systems and different physico-chemical processes involving them, their predictive potential remains to be explored. An exhaustive review on all these aspects will set the tone of the future research in that direction.

The electronic temperature and the effective chemical potential parameters of an atom in a molecule. A Fermi-Dirac semi-local variational approach

We developed a numerical procedure to compute the electronic temperature and the effective (local) chemical potential undergone by electrons belonging to a particular molecular species. Our strategy relies on consider atomic basins as open quantum (sub)systems within the context of the quantum theory of atoms in molecules. Each basin is represented by the two parameters, the electronic temperature and the effective chemical potential, which are determined by distributing electrons (fermions) imbedded in each atomic region, through a Fermi-Dirac semi-local variational procedure. The results obtained for 40 different chemical species show that the effective chemical potential is a useful tool to reveal the most acidic/basic atoms in a molecule while the electronic temperature is closely related to the concept of chemical hardness at the local level. Our numerical data also indicate that the electronic temperature values undergone by electrons imbedded in atomic basins are way beyond the room temperature condition, allowing to fractionally occupy several of the one-particle quantum states. In this context, we developed two new indexes useful to reveal outstanding orbitals involved in the chemical reactivity of atoms in molecules.

Local Temperature as a Chemical Reactivity Descriptor

Using the electron density and its associated quantities in a molecular system to quantify chemical reactivity in density functional theory is of considerable recent interest. Local temperature based on the kinetic energy density is an intrinsic property of a molecular system, which can be employed for this purpose. In this work, we explore such a possibility. To this end, we examine the local behavior of local temperature with a few choices of the kinetic energy density, apply it to determine regioselectivity of nucleophilic and electrophilic compounds, and then investigate its performance in appreciating reactions along the intrinsic reaction pathway for exothermic, endothermic, and thermoneutral transformations. Our results confirm that local temperature can be used as an effective descriptor of molecular reactivity.

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.

Reactivity Dynamics

The chemical reactivity of a molecule as a whole or of an atom in a molecule varies during a chemical reaction. A variation of global and local reactivity descriptors in the course of a physicochemical process was studied within a quantum fluid density functional theory framework. Effects of a physical confinement and the electronic excitation therein were studied. In this Perspective, we also highlight the direction of a spontaneous chemical reaction in the light of the dynamical variants of the conceptual density functional theory-based electronic structure principles. An exhaustive state-of-the-art dynamical study is warranted in order to understand a chemical reaction from a reactivity perspective augmenting the associated molecular reaction dynamics analysis.

A statistical thermodynamics view of electron density polarisation: application to chemical selectivity

A fundamental link between conceptual density functional theory and statistical thermodynamics is herein drawn, showing that intermolecular electrostatic interactions can be understood in terms of effective work and heat exchange. From a more detailed analysis of the heat exchange in a perturbation theory framework, an associated entropy can be subsequently derived, which appears to be a suitable descriptor for the local polarisability of the electron density. A general rule of thumb is evidenced: the more the perturbation can be spread, both through space and among the excited states, the larger the heat exchange and entropy.

Atomic polarizability: A periodic descriptor

Atomic polarizability is an essential theoretical construct to define and correlate many physicochemical properties. It exhibits periodicity and has a relationship with other periodic descriptors. Although a number of scales are available to compute atomic polarizability, the final scale is yet to be designed. In this venture, we have invoked a new empirical approach to compute the atomic polarizability of 103 elements of the periodic table, considering the conjoint action of other periodic descriptors, namely effective nuclear charge (Zeff) and absolute radii (r). The proposed approach is [Formula: see text], where “e” represents the electronic charge, Zeff is the effective nuclear charge, r is the absolute radius, and α is the polarizability. Our computed atomic polarizability follows all sine qua non of the periodicity. Our model significantly exhibits the relativistic effect too. A close agreement between our computed data and other available theoretical and experimental results demonstrates the efficacy of our proposed approach. Furthermore, we have established the polarizability equalization principle in terms of our computed data.

Triphenylamine-Based Fluorescent Styryl Dyes: DFT, TD-DFT and Non-Linear Optical Property Study

The electronic structures and spectroscopic properties of triphenylamine-based monostyryl and bis(styryl) dyes were studied using quantum chemical methods. The ground-state geometries of these dyes were optimized using the density functional theory (DFT) method. The lowest singlet excited state was optimized using time-dependent density functional theory (TD-DFT). The absorption was also calculated using the ground-state geometries. All the calculations were carried out in the gas phase and in solvent. The results indicate that the absorption maxima calculated using the TD-DFT are in good agreement with those obtained experimentally. These dyes possess a large second-order non-linear property and this is mainly due to the strong donor-π-acceptor conjugation which is attributed to the excited state intramolecular charge transfer (ICT). There is a relationship between the hardness and first hyperpolarizability and second hyperpolarizability of mono- and bis(styryl) dyes. The efficiency of the intersystem crossing process can be improved by reducing the energy gap between the singlet and triplet excited states.

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.

Quantitative Structure-Activity/Property/Toxicity Relationships through Conceptual Density Functional Theory-Based Reactivity Descriptors

Developing effective structure-activity/property/toxicity relationships (QSAR/QSPR/QSTR) is very helpful in predicting biological activity, property, and toxicity of a given set of molecules. Regular change in these properties with the structural alteration is the main reason to obtain QSAR/QSPR/QSTR models. The advancement in making different QSAR/QSPR/QSTR models to describe activity, property, and toxicity of various groups of molecules is reviewed in this chapter. The successful implementation of Conceptual Density Functional Theory (CDFT)-based global as well as local reactivity descriptors in modeling effective QSAR/QSPR/QSTR is highlighted.

Orbital free DFT versus single density equation: a perspective through quantum domain behavior of a classically chaotic system

Regular to chaotic transition takes place in a driven van der Pol oscillator in both classical and quantum domains.

HSAB principle applied to the time evolution of chemical reactions

Time evolution of various reactivity parameters such as electronegativity, hardness, and polarizability associated with a collision process between a proton and an X- atom/ion (X = He, Li(+), Be(2+), B(3+), C(4+)) in its ground ((1)S) and excited((1)P,(1)D,(1)F) electronic states as well as various complexions of a two-state ensemble is studied using time-dependent and excited-state density functional theory. This collision process may be considered to be a model mimicking the actual chemical reaction between an X-atom/ion and a proton to give rise to an XH(+) molecule. A favorable dynamical process is characterized by maximum hardness and minimum polarizability values according to the dynamical variants of the principles of maximum hardness and minimum polarizability. An electronic excitation or an increase in the excited-state contribution in a two-state ensemble makes the system softer and more polarizable, and the proton, being a hard acid, gradually prefers less to interact with X as has been discerned through the drop in maximum hardness value and the increase in the minimum polarizability value when the actual chemical process occurs. Among the noble gas elements, Xe is the most reactive. During the reaction: H(2) + H(+) --> H(3)(+) hardness maximizes and polarizability minimizes and H(2) is more reactive in its excited state. Regioselectivity of proton attack in the O-site of CO is clearly delineated wherein HOC(+) may eventually rearrange itself to go to the thermodynamically more stable HCO(+).