Comparison between the frozen core and finite differences approximations for the generalized spin-dependent global and local reactivity descriptors in small molecules

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.

Chiral Jahn-Teller Distortion in Quasi-Planar Boron Clusters

In this work, we have observed that some chiral boron clusters (B16-, B20-, B24-, and B28-) can simultaneously have helical molecular orbitals and helical spin densities; these seem to be the first compounds discovered to have this intriguing property. We show that chiral Jahn-Teller distortion of quasi-planar boron clusters drives the formation of the helical molecular spin densities in these clusters and show that elongation/enhancement in helical molecular orbitals can be achieved by simply adding more building blocks via a linker. Aromaticity of these boron clusters is discussed. Chiral boron clusters may find potential applications in spintronics, such as molecular magnets.

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.

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.

Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents

Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.

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.

Site-Specific Description of the Enhanced Recognition Between Electrogenerated Nitrobenzene Anions and Dihomooxacalix[4]arene Bidentate Ureas

Electron transfer controlled hydrogen bonding was studied for a series of nitrobenzene derivative radical anions, working as large guest anions, and substituted ureas, including dihomooxacalix[4]arene bidentate urea derivatives, in order to estimate binding constants (Kb) for the hydrogen-bonding process. Results showed enhanced Kb values for the interaction with phenyl-substituted bidentate urea, which is significantly larger than for the remaining compounds, e.g., in the case of 4-methoxynitrobenzene a 28-fold larger Kb value was obtained for the urea bearing a phenyl (Kb ∼ 6888) vs tert-butyl (Kb ∼ 247) moieties. The respective nucleophilic and electrophilic characters of the participant anion radical and urea hosts were parametrized with global and local electrodonating (ω(-)) and electroaccepting (ω(+)) powers, derived from DFT calculations. ω(-) data were useful for describing trends in structure–activity relationships when comparing nitrobenzene radical anions. However, ω(+) for the host urea structures lead to unreliable explanations of the experimental data. For the latter case, local descriptors ωk(+)(r) were estimated for the atoms within the urea region in the hosts [∑kωk(+)(r)]. By compiling all the theoretical and experimental data, a Kb-predictive contour plot was built considering ω(-) for the studied anion radicals and ∑kωk(+)(r) which affords good estimations.

Nature of electrogenerated intermediates in nitro-substituted nor-β-lapachones: the structure of radical species during successive electron transfer in multiredox centers

Electrochemical, spectroelectrochemical, and theoretical studies of the reduction reactions in nor-β-lapachone derivatives including a nitro redox center showed that reduction of the compounds involves the formation of several radical intermediates, including a biradical dianion resultant from the separate reduction of the quinone and nitro groups in the molecules. Theoretical descriptions of the corresponding Fukui functions f(αα)⁺ and f(ββ)⁺(r) and LUMO densities considering finite differences and frozen core approximations for describing the changes in electron and spin densities of the system allowed us to confirm these results. A description of the potential relationship with the obtained results and biological activity selectivity indexes suggests that both the formation of stable biradical dianion species and the stability of the semiquinone intermediates during further reduction are determining factors in the description of their biological activity.

Koopmans’ multiconfigurational self-consistent field (MCSCF) Fukui functions and MCSCF perturbation theory

Prediction of chemical reactivity has become one of the highest priority tasks of computational chemistry since the development of the methods of modeling electronic structure. Despite the general simplicity of the physical concept of reactivity and the rapid development of modern density functional theory (DFT) methods, this task remains state-of-the-art for systems with wavefunctions that have a multiconfigurational character. In such cases, for the accurate description of reactivity one needs to use multiconfigurational approaches that are much heavier computationally then ordinary single-determinant DFT methods. Moreover, the complexity of the calculation of reactivity is increased by the necessity to calculate ionic and transition states. These computational challenges can be addressed by employing the concepts of Koopmans’ theorem and its extension to a multiconfigurational case. We present a simplified methodology for the calculation of Fukui functions, based on Koopmans’ approximation for multiconfigurational Green’s functions developed in our previous works. Also, an extension of this methodology based on perturbation theory has been developed to improve accuracy.

Substituent effect on a family of quinones in aprotic solvents: an experimental and theoretical approach

In this work a comparison between redox potentials, obtained by constructing current-potential plots from chronoamperometric measurements, and the parameter sigma(x), as proposed by Zuman in terms of the Hammett substituent parameters, was performed for several quinone compounds. This study shows the limitations of this approach and proves that methods based on quantum chemistry can be used to study the substituent effect in quinone systems. By using the Density Functional Theory, in the Kohn-Sham context with three exchange-correlation functionals, BLYP, B3LYP, and BHLYP, it was found that the electron affinity is good enough to give a useful relationship with experimental redox potentials of quinone systems. This conclusion is reached when the basis set functions involve diffuse functions, and also when the Hartree-Fock exchange energy is included in the exchange-correlation functional. The Fukui function, to describe preferential sites involved at initial stages of a system that bind an electron, is analyzed when electron donor and electron acceptor groups are present as substituents in quinone systems. The methods applied in this work are valid for any kind of quinone compound and will be used in further analysis of the electron reorganization in semiquinone species.

Accurate Calculation of Absolute One-Electron Redox Potentials of Somepara-Quinone Derivatives in Acetonitrile

Standard ab initio molecular orbital theory and density functional theory calculations have been used to calculate absolute one-electron reduction potentials of several para-quinones in acetonitrile. The high-level composite method of G3(MP2)-RAD is used for the gas-phase calculations and a continuum model of solvation, CPCM, has been employed to calculate solvation energies. To compare the theoretical reduction potentials with experiment, the reduction potentials relative to a standard calomel electrode (SCE) have also been calculated and compared to experimental values. The average error of the calculated reduction potentials using the proposed method is 0.07 V without any additional approximation. An ONIOM method in which the core is studied at G3(MP2)-RAD and the substituent effect of the rest of the molecule is studied at R(O)MP2/6-311+G(3df,2p) provides an accurate low-cost alternative to G3(MP2)-RAD for larger molecules.

Spin-Polarized Conceptual Density Functional Theory Study of the Regioselectivity in Ring Closures of Radicals

The regioselectivity of ring-forming radical reactions is investigated within the framework of the so-called spin-polarized conceptual density functional theory. Two different types of cyclizations were studied. First, a series of model reactions of alkyl- and acyl-substituted radicals were investigated. Next, attention was focused on the radical cascade cyclizations of N-alkenyl-2-aziridinylmethyl radicals (a three-step mechanism). In both of these reactions, the approaching radical (carbon or nitrogen centered) adds to a carbon-carbon double bond within the same molecule to form a radical ring compound. In this process, the number of electrons is changing from a local point of view (a charge transfer occurs from one part of the molecule to another one) at constant global spin number Ns (both the reactant and the product ring compound are in the doublet state). It is shown that the experimentally observed regioselectivities for these ring-closure steps can be predicted using the spin-polarized Fukui functions for radical attack, f0NN(r).