Chemical hardness: Temperature dependent definitions and reactivity principles

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.

Proposal of a Fermi-Dirac-Derived Reactivity Descriptor: Beyond the Frontier MO Model

In this paper, we derive a reactivity descriptor stemming from the Fermi-Dirac population scheme, applied to density functional calculations on molecular systems. Assuming that molecular orbitals only marginally change when temperature is slightly increased from 0 K, we study the response of electron density to a change in temperature. Connection with usual conceptual density functional theory descriptors is made, and the T-variation of electron density for some representative examples is given and discussed.

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.

Ambident Nucleophilic Substitution: Understanding Non-HSAB Behavior through Activation Strain and Conceptual DFT Analyses

The ability to understand and predict ambident reactivity is key to the rational design of organic syntheses. An approach to understand trends in ambident reactivity is the hard and soft acids and bases (HSAB) principle. The recent controversy over the general validity of this principle prompted us to investigate the competing gas-phase SN 2 reaction channels of archetypal ambident nucleophiles CN- , OCN- , and SCN- with CH3 Cl (SN 2@C) and SiH3 Cl (SN 2@Si), using DFT calculations. Our combined analyses highlight the inability of the HSAB principle to correctly predict the reactivity trends of these simple, model reactions. Instead, we have successfully traced reactivity trends to the canonical orbital-interaction mechanism and the resulting nucleophile-substrate interaction energy. The HOMO-LUMO orbital interactions set the trend in both SN 2@C and SN 2@Si reactions. We provide simple rules for predicting the ambident reactivity of nucleophiles based on our Kohn-Sham molecular orbital analysis.

Establishing the Relationship between Quantum Capacitance and Softness of N-Doped Graphene/Electrolyte Interfaces within the Density Functional Theory Grand Canonical Kohn-Sham Formalism

The joint density functional theory (JDFT) is applied in the context of the grand canonical Kohn-Sham theory to calculate the global and local softness of pristine and N-substituted graphene structures. A comparison is established between the different theoretical approaches to evaluate total capacitance, revealing that the JDFT approach presents the closest result of this property with experimental data. A model of series capacitors is used to determine the quantum and nonquantum contributions of total capacitance, which enables us to determine the limitations of the rigid band approximation for the studied systems. It is found that global chemical softness is proportional to the total capacitance measured in the experiments, when the geometry relaxation is neglected. In this context, it is possible to obtain quantum and total capacitance (and consequently softness) from an average number of electrons vs applied potential plots and the model of series capacitors. Likewise, the relation of capacitance and softness gives rise to a new definition of local capacitance within the JDFT formalism. The evaluation of global and local softness paves the way to analyze electrochemical surface reactivity as a function of applied potential for a solid-electrolyte interface.

An electronic temperature definition for the reactive electronic species: Conciliating practical approaches in conceptual chemical reactivity theory with a rigorous ensemble formulation

By working under the framework of the Helmholtz potential as a functional of the equilibrium density matrix, in this contribution, we provide theoretical evidence about a particular thermodynamic situation, where electronic species display their highest susceptibility to exchange electrons to or from surroundings. This situation is denominated as the electronic temperature condition. Neutral chemical species display their lowest possible hardness value at the electronic temperature condition, and remarkably, under this circumstance, the exchange of any amount of electronic charge will necessarily be translated into a net increase in the corresponding chemical hardness. Chemical response functions defined as partial derivatives of the Helmholtz potential with respect to the (average) number of electrons and evaluated at the electronic temperature condition provide comparable results than those obtained from the coarse quadratic approximation to the exact dependence of the electronic energy vs the number of electrons, including composite quantities as the electrophilicity index. In this context, we show that the exact Helmholtz potential dependence with respect to the number of electrons can accurately be approximated by "temperature dependent" polynomial fits (up to fourth order), evaluated at the electronic temperature condition.