Charge-transfer energy through the dipole moment.

The charge-transfer energy contribution is one of the most controversial components of the total interaction energy. Commonly, the energy associate to a charge-transfer process depends on population analysis. Therefore, the results further depend on how the population analysis is defined, and certainly, the results may be arbitrary.

Temperature and external fields in conceptual density functional theory.

Until quite recently, Conceptual DFT (CDFT) was mainly based on the energy functional, [,], where the number of electrons and the external potential are state variables. One of the strengths of CDFT, however, is the ease with which additional and/or different state variables can be incorporated. Here, the incorporation of new variables-namely temperature and external fields-is discussed, outlining the motivation for these extensions, sketching their theoretical/computational context, and presenting some elucidative examples.

ADCHα-I population analysis and constrained dipole moment density functional theory in force fields for molecular simulations.

A new population analysis, ADCHα-I, based on the interpolation between the Hirshfeld (H) and the iterative Hirshfeld (H-I) methods through a parameter α and on the atomic dipole moment corrected Hirshfeld (ADCH) methodology is proposed, in combination with the constrained dipole moment density functional theory (CD-DFT) previously developed, to determine the charge distributions of force fields. Following this approach, the electronic density of the isolated molecule is determined for the value of the dipole moment that reproduces the experimental dielectric constant, in order to incorporate through this property the effects of the surrounding molecules in the liquid, and to carry on this information to the molecular simulation, the new population analysis is built to obtain the set of charges that reproduces this dipole moment. By selecting α = 1/2, one is led to charges that are larger than the ones obtained through H and ADCH and smaller than those of H-I and that incorporate, at the local level, information about the response of isolated atoms to donate or to accept charge, which is not considered in ADCH.

Can we predict ambident regioselectivity using the chemical hardness?

The hard/soft acid/base (HSAB) principle is a cornerstone in our understanding of chemical reactivity preferences. Motivated by the success of the original ("global") version of this rule, a "local" counterpart was readily proposed to account for regioselectivity preferences, in particular, in ambident reactions. However, ample experimental evidence indicates that the local HSAB principle often fails to provide meaningful predictions.

Hardness of molecules and bandgap of solids from a generalized gradient approximation exchange energy functional.

The deviations from linearity of the energy as a function of the number of electrons that arise with current approximations to the exchange-correlation (XC) energy functional have important consequences for the frontier eigenvalues of molecules and the corresponding valence-band maxima for solids. In this work, we present an analysis of the exact theory that allows one to infer the effects of such approximations on the highest occupied and lowest unoccupied molecular orbital eigenvalues. Then, we show the importance of the asymptotic behavior of the XC potential in the generalized gradient approximation (GGA) in the case of the NCAPR functional (nearly correct asymptotic potential revised) for determining the shift of the frontier orbital eigenvalues toward the exact values.

Analysis of the kinetic energy functional in the generalized gradient approximation.

A new density functional for the total kinetic energy in the generalized gradient approximation is developed through an enhancement factor that leads to the correct behavior in the limits when the reduced density gradient tends to 0 and to infinity and by making use of the conjoint conjecture for the interpolation between these two limits, through the incorporation, in the intermediate region of constraints that are associated with the exchange energy functional. The resulting functional leads to a reasonable description of the kinetic energies of atoms and molecules when it is used in combination with Hartree-Fock densities. Additionally, in order to improve the behavior of the kinetic energy density, a new enhancement factor for the Pauli kinetic energy is proposed by incorporating the correct behavior into the limits when the reduced density gradient tends to 0 and to infinity, together with the positivity condition, and imposing through the interpolation function that the sum of its integral over the whole space and the Weiszacker energy must be equal to the value obtained with the enhancement factor developed for the total kinetic energy.

Temperature-Dependent Approach to Electronic Charge Transfer.

A charge transfer model is developed within the framework of the grand canonical ensemble through the analysis of the behavior of the fractional charge as a function of the chemical potential of the bath when the temperature and the external chemical potential are kept fixed. Departing from the fact that, before the interaction between two species, each one has a zero fractional charge, one can identify two situations after the interaction occurs where the fractional charge of at least one of the species is different from zero, indicating that there has been charge transference. One of them corresponds to the case when one of the species is immersed in a bath conformed by the other one, while the other is related to the case in which both species are present in equal amounts (stoichiometric proportion).

Constrained dipole moment density functional theory for charge distributions in force fields for the study of molecular fluids.

A new procedure, based on electronic structure calculations that only requires a dipole moment value for a given molecule as input and, from which the charges for all the atoms in it are uniquely determined, is developed and applied to the study of molecular fluids with classical dynamics. The dipole moment value considered for the isolated molecule is the one that reproduces the dielectric constant of its corresponding fluid. Following previous work, the Lennard-Jones parameters are determined to reproduce the liquid density and the surface tension at the liquid-vapor interface.

Negative Electron Affinities and Derivative Discontinuity Contribution from a Generalized Gradient Approximation Exchange Functional.

Two methods to calculate negative electron affinities systematically from ground-state density functional methods are presented. One makes use of the lowest unoccupied molecular orbital energy shift provided by approximate inclusion of derivative discontinuity in the nearly correct asymptotic potential (NCAP) nonempirical, constraint-based generalized gradient approximation exchange functional. The other uses a second-order perturbation calculation of the derivative discontinuity based on the NCAP exchange-correlation potential.

Electronegativities of Pauling and Mulliken in Density Functional Theory.

Electronegativity is a fundamental concept in chemistry that allows one to infer important aspects about the interactions between chemical species. In the present work we make use of the framework provided by the density functional theory of chemical reactivity, to discuss in a unified way the approaches to the concept of electronegativity developed by Pauling and by Mulliken. Our analysis starts by making use of the identification of the electronegativity of Mulliken with the chemical potential of density functional theory, and continues to show that the ionic correction proposed by Pauling can be derived, with certain approximations, from the quadratic smooth interpolation of the energy as a function of the number of electrons in terms of the chemical potentials and the hardnesses of the interacting species, from which one can infer the close qualitative relationship between Pauling's electronegativity and the electrophilicity concept.

Generalized Gradient Approximation Exchange Energy Functional with Near-Best Semilocal Performance.

We develop and validate a nonempirical generalized gradient approximation (GGA) exchange (X) density functional that performs as well as the SCAN (strongly constrained and appropriately normed) meta-GGA on standard thermochemistry tests. Additionally, the new functional (NCAP, nearly correct asymptotic potential) yields Kohn-Sham eigenvalues that are useful approximations of the density functional theory (DFT) ionization potential theorem values by inclusion of a systematic derivative discontinuity shift of the X potential. NCAP also enables time-dependent DFT (TD-DFT) calculations of good-quality polarizabilities, hyper-polarizabilities, and one-Fermion excited states without modification (calculated or ad hoc) of the long-range behavior of the exchange potential or other patches.

Chemical hardness: Temperature dependent definitions and reactivity principles.

In this brief report, we show that the three different chemical hardness definitions developed in the framework of the temperature-dependent density functional theory-namely, the electronic, the thermodynamic, and the Helmholtz hardnesses-imply both the hard and soft acids and bases (HSAB) principle and the maximum hardness (MH) principle. These hardnesses are identified as the second derivative of a thermodynamic state function and avoid the somewhat arbitrary approach, based on the parabolic interpolation of the energy versus electron number, that is normally used to justify these principles. This not only leads to a more mathematically sound justification of the HSAB and MH principles in the low-temperature limit but also establishes that the HSAB and the MH principles hold at any temperature of chemical relevance.

Local and nonlocal counterparts of global descriptors: the cases of chemical softness and hardness.

A new strategy, recently reported by us to develop local and linear (nonlocal) counterparts of global response functions, is applied to study the local behavior of the global softness and hardness reactivity descriptors. Within this approach a local counterpart is designed to identify the most important molecular fragments for a given chemical response. The local counterpart of the global softness obtained through our methodology corresponds to the well-known definition of local softness and, in agreement with what standard conceptual chemical reactivity in density functional theory dictates, it simply reveals the softest sites in a molecule.

Global and local charge transfer in electron donor-acceptor complexes.

The formation of electron donor-acceptor complexes is studied with global and local charge transfer partitionings. The 1-parabola model is applied to the bromination reaction of alkenes and the correlations found between the global and local charge transferred with the transition energy of the charge transfer bands and the kinetic rate constants indicate that the nucleophilic attack of alkenes to bromine is the electronic process controlling the reactivity in the formation of the electron donor-acceptor complexes in this reaction. The 2-parabolas model is used in studying the nitrosation of aromatic compounds where colorful electron donor-acceptor complexes are formed.

Local electrophilicity.

In this work some possibilities for deriving a local electrophilicity are studied. First, we consider the original definition proposed by Chattaraj, Maiti, and Sarkar (J Phys Chem A 107:4973, 2003), in which the local electrophilicity is given by the product of the global electrophilicity, and the Fukui function for charge acceptance is derived by two different approaches, making use of the chain rule for functional derivatives. We also modify the proposals based on the electron density so as to have a definition with the same units of the original definition, which also introduces a dependence in the Fukui function for charge donation.

Reply to the 'Comment on "Revisiting the definition of local hardness and hardness kernel"' by C. Morell, F. Guégan, W. Lamine, and H. Chermette, Phys. Chem. Chem. Phys., 2018, 20, DOI.

This reply complements the comment of Guégan et al. about our recent work on the revision of the local hardness and the hardness kernel concepts. Guegan et al.

Role of Reaction Conditions in the Global and Local Two Parabolas Charge Transfer Model.

The local and global charge transfer approach based on the two parabolas model is applied to several problems aiming to show the importance of incorporating the reaction conditions to evaluate the global and local chemical descriptors. It is shown that, by preparation of the reactants, the chemical potentials of the reacting species determined by the two parabolas model satisfy the condition for the transfer of electrons in the direction dictated by the chemical potential difference. The model is applied to the hydration of alkenes, showing that it recovers Markovnikov's rule, to aromatic nitration, and to the interaction of nitrobenzenes with 1,3-diethylurea, an electrochemically controlled hydrogen-bonding problem.

Thermodynamic Justification for the Parabolic Model for Reactivity Indicators with Respect to Electron Number and a Rigorous Definition for the Electrophilicity: The Essential Role Played by the Electronic Entropy.

The temperature-dependence of the Helmholtz free energy with respect to the number of electrons is analyzed within the framework of the Grand Canonical Ensemble. At the zero-temperature limit, the Helmholtz free energy behaves as a Heaviside function of the number of electrons; however, as the temperature increases, the profile smoothens and exhibits a minimum value at noninteger positive values of the fractional electronic charge. We show that the exact average electronic energy as a function of the number of electrons does not display this feature at any temperature, since this behavior is solely due to the electronic entropy.

Thermodynamic responses of electronic systems.

We present how the framework of the temperature-dependent chemical reactivity theory can describe the panorama of different types of interactions between an electronic system and external reagents. The key reactivity indicators are responses of an appropriate state function (like the energy or grand potential) to the variables that determine the state of the system (like the number of electrons/chemical potential, external potential, and temperature). We also consider the response of the average electron density to appropriate perturbations.

Thermodynamic hardness and the maximum hardness principle.

An alternative definition of hardness (called the thermodynamic hardness) within the grand canonical ensemble formalism is proposed in terms of the partial derivative of the electronic chemical potential with respect to the thermodynamic chemical potential of the reservoir, keeping the temperature and the external potential constant. This temperature dependent definition may be interpreted as a measure of the propensity of a system to go through a charge transfer process when it interacts with other species, and thus it keeps the philosophy of the original definition. When the derivative is expressed in terms of the three-state ensemble model, in the regime of low temperatures and up to temperatures of chemical interest, one finds that for zero fractional charge, the thermodynamic hardness is proportional to T(I-A), where I is the first ionization potential, A is the electron affinity, and T is the temperature.

Donation and back-donation analyzed through a charge transfer model based on density functional theory.

The net charge transfer process that occurs between two species, A and B, interacting with each other, may be decomposed into two processes: one in which A receives charge from B, which can be identified as the electrophilic channel for A or the nucleophilic channel for B, and a second in which A donates charge to B, which can be identified as the nucleophilic channel for A or the electrophilic channel for B. By determining the amount of charge associated with both processes through the minimization of the interaction energy associated with each case, the expressions for the amount of charge involved in each case can be expressed in terms of the directional chemical potentials and the hardnesses of the interacting species. The correlation between the charges obtained for the interaction between phosphine ligands of the type PRR'R'' and Ni, and the A carbonyl stretching frequency provides support for their interpretation as measures of the electrophilicity and nucleophilicity of a chemical species, and, at the same time, allows one to describe the donation and back-donation processes in terms of the density functional theory of chemical reactivity.

New Fukui, dual and hyper-dual kernels as bond reactivity descriptors.

We define three new linear response indices with promising applications for bond reactivity using the mathematical framework of τ-CRT (finite temperature chemical reactivity theory). The τ-Fukui kernel is defined as the ratio between the fluctuations of the average electron density at two different points in the space and the fluctuations in the average electron number and is designed to integrate to the finite-temperature definition of the electronic Fukui function. When this kernel is condensed, it can be interpreted as a site-reactivity descriptor of the boundary region between two atoms.

Local chemical potential, local hardness, and dual descriptors in temperature dependent chemical reactivity theory.

In this work we establish a new temperature dependent procedure within the grand canonical ensemble, to avoid the Dirac delta function exhibited by some of the second order chemical reactivity descriptors based on density functional theory, at a temperature of 0 K. Through the definition of a local chemical potential designed to integrate to the global temperature dependent electronic chemical potential, the local chemical hardness is expressed in terms of the derivative of this local chemical potential with respect to the average number of electrons. For the three-ground-states ensemble model, this local hardness contains a term that is equal to the one intuitively proposed by Meneses, Tiznado, Contreras and Fuentealba, which integrates to the global hardness given by the difference in the first ionization potential, I, and the electron affinity, A, at any temperature.

Revisiting the definition of local hardness and hardness kernel.

An analysis of the hardness kernel and local hardness is performed to propose new definitions for these quantities that follow a similar pattern to the one that characterizes the quantities associated with softness, that is, we have derived new definitions for which the integral of the hardness kernel over the whole space of one of the variables leads to local hardness, and the integral of local hardness over the whole space leads to global hardness. A basic aspect of the present approach is that global hardness keeps its identity as the second derivative of energy with respect to the number of electrons. Local hardness thus obtained depends on the first and second derivatives of energy and electron density with respect to the number of electrons.