Ramón Alain Miranda-Quintana

Interpolation of property-values between electron numbers is inconsistent with ensemble averaging

In this work we explore the physical foundations of models that study the variation of the ground state energy with respect to the number of electrons (E vs. N models), in terms of general grand-canonical (GC) ensemble formulations. In particular, we focus on E vs. N models that interpolate the energy between states with integer number of electrons. We show that if the interpolation of the energy corresponds to a GC ensemble, it is not differentiable. Conversely, if the interpolation is smooth, then it cannot be formulated as any GC ensemble. This proves that interpolation of electronic properties between integer electron numbers is inconsistent with any form of ensemble averaging. This emphasizes the role of derivative discontinuities and the critical role of a subsystems surroundings in determining its properties.

Communication: Reduced density matrices in molecular systems: Grand-canonical electron states

Grand-canonical like descriptions of many electron atomic and molecular open systems which are characterized by a non-integer number of electrons are presented. Their associated reduced density matrices (RDMs) are obtained by introducing the contracting mapping for this type of distributions. It is shown that there is loss of information when connecting RDMs of different order by partial contractions. The energy convexity property of these systems simplifies the description. Consequently, this formulation opens the possibility to a new look for chemical descriptors such as chemical potential and reactivity among others. Examples are presented to discuss the theoretical aspects of this work.

Charge transfer and chemical potential in 1,3-dipolar cycloadditions

We revisit the role of the electronic chemical potential as the indicator for the tendency of chemical species to attract or donate electrons. Studying a set of 1,3-dipolar cycloadditions shows that the classical Mulliken expression is insufficient in some cases to accurately predict the direction of electron transfer. Agreement with experimental results can be achieved by including the effects of interactions between the reacting partners in the working equation used to calculate the chemical potential. We present a simple revision of the Mulliken expression, inspired by previous work from Gázquez, Cedillo, and Vela, that incorporates the interactions between the reagents in an approximate manner. The revised formula adequately describes the experimental data. We also explore how different methods for computing the ionization potential and electron affinity affect our results.

Finite temperature grand canonical ensemble study of the minimum electrophilicity principle

We analyze the minimum electrophilicity principle of conceptual density functional theory using the framework of the finite temperature grand canonical ensemble. We provide support for this principle, both for the cases of systems evolving from a non-equilibrium to an equilibrium state and for the change from one equilibrium state to another. In doing so, we clearly delineate the cases where this principle can, or cannot, be used.

The HSAB principle from a finite-temperature grand-canonical perspective

We provide a new proof for Pearson’s hard/soft acid/base (HSAB) principle. Unlike alternative proofs, we do not presuppose a simplified parabolic dependence on the energy of the system with respect to changes in its number of electrons. Instead, we use the more physically grounded finite-temperature formulation of the grand-canonical ensemble. We show that under the usual assumptions regarding the chemical potentials and hardnesses of the involved species, the HSAB rule holds for a wide range of temperatures.

Perturbed reactivity descriptors: the chemical hardness

A simple framework to study the effects of (small) external perturbations on conceptual density functional theory descriptors is discussed. Based on this, the general expressions recently presented for the perturbed chemical potential are revisited. Additionally, new formulas that take into account the effect of the molecular environment on the chemical hardness are derived. Some consequences of this framework are analyzed in the context of several magnitudes that characterize charge transfer reactions. It is expected that the resulting formulas provide more accurate results when the unperturbed chemical potentials and chemical hardnesses of the reagents are not significantly different between them.

Conceptual DFT analysis of the regioselectivity of 1,3-dipolar cycloadditions: nitrones as a case of study

The regioselectivity of the 1,3-dipolar cycloaddition of a model nitrone with a set of dipolarophiles, presenting diverse electronic effects, is analyzed using conceptual density functional theory (DFT) methods. We deviate from standard approaches based on frontier molecular orbitals and formulations of the local hard/soft acid/base principle and use instead the dual descriptor. A detailed analysis is carried out to determine the influence of the way to calculate the dual descriptor, the computational procedure, basis set and choice of method to condensate the values of this descriptor. We show that the qualitative regioselectivity predictions depend on the choice of “computational conditions”, something that indicates the danger of using black-box computational set-ups in conceptual DFT studies.

Comments on “On the non-integer number of particles in molecular system domains: treatment and description”

We analyze a recent proposal of Bochicchio for obtaining smooth (i.e., differentiable) models for the dependency of the ground-state energy with respect to the number of electrons in molecular systems. We go deeper into the foundations of this approach, highlighting the need to differentiate between the states and operators of the isolated and perturbed systems. We show that this model implies a relation between the energies of the isolated and the perturbed systems which is similar to the relation between the energies of interacting molecular orbitals in Klopman and Salem’s model of chemical reactivity.

Communication: Two types of flat-planes conditions in density functional theory

Using results from atomic spectroscopy, we show that there are two types of flat-planes conditions. The first type of flat-planes condition occurs when the energy as a function of the number of electrons of each spin, Nα and Nβ, has a derivative discontinuity on a line segment where the number of electrons, Nα + Nβ, is an integer. The second type of flat-planes condition occurs when the energy has a derivative discontinuity on a line segment where the spin polarization, Nα - Nβ, is an integer, but does not have a discontinuity associated with an integer number of electrons. Type 2 flat planes are rare-we observed just 15 type 2 flat-planes conditions out of the 4884 cases we tested-but their mere existence has implications for the design of exchange-correlation energy density functionals. To facilitate the development of functionals that have the correct behavior with respect to both fractional number of electrons and fractional spin polarization, we present a dataset for the chromium atom and its ions that can be used to test new functionals.

How Biochemical Environments Fine-Tune a Redox Process: From Theoretical Models to Practical Applications

In this study, we give a new physical insight into how enzymatic environments influence a redox process. This is particularly important in a biochemical context, in which oxidoreductase enzymes and low-molecular-weight cofactors create a microenvironment, fine-tuning their specific redox potential. We present a new theoretical model, quantitatively backed up by quantum chemically calculated data obtained for key biological sulfur-based model reactions involved in preserving the cellular redox homeostasis during oxidative stress. We show that environmental effects can be quantitatively predicted from the thermodynamic cycle linking ΔΔ G(OX/RED)ref-ligand values to the differential interaction energy ΔΔ Gint of the reduced and oxidized species with the environment. Our obtained data can be linked to hydrogen-bond patterns found in protein active sites. The thermodynamic model is further understood in the framework of molecular orbital theory. The key insight of this work is that the intrinsic properties of neither a redox couple nor the interacting environment (e.g., ligand) are enough by themselves to uniquely predict reduction potentials. Instead, system-environment interactions need to be considered. This study is of general interest as redox processes are pivotal to empower, protect, or damage organisms. Our presented thermodynamic model allows a pragmatically evaluation on the expected influence of a particular environment on a redox process, necessary to fully understand how redox processes take place in living organisms.