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We herein demonstrate that capacitance spectroscopy (CS) experimentally allows access to the energy associated with the quantum mechanical ground state of many-electron systems. Priorly, electrochemical capacitance, C[ρ], was previously understood from conceptual and computational density functional theory (DFT) calculations. Thus, we herein propose a quantum mechanical experiment-based variational method for electron charging processes based on an experimentally-designed functional of the ground state electron density. In this methodology, the electron state density, ρ, and an energy functional of the electron density, E[ρ], can be obtained from CS data. CS allows the derivative of the electrochemical potential with respect to the electron density, (δ[small mu, Greek, macron][ρ]/δρ), to be obtained as a unique functional of the energetically minimised system, i.e., β/C[ρ], where β is a constant (associated with the size of the system) and C[ρ] is an experimentally observable quantity. Thus the ground state energy (at a given fixed external potential) can be obtained simply as E[ρ], from the experimental measurement of C[ρ]. An experimental data-set was interpreted to demonstrate the potential of this quantum mechanical experiment-based variational principle.

Meningiomas are usually considered to be benign central nervous system tumors; however, they show heterogenous clinical, histolopathological and cytogenetic features associated with a variable outcome. In recent years important advances have been achieved in the identification of the genetic/molecular alterations of meningiomas and the signaling pathways involved. Thus, monosomy 22, which is often associated with mutations of the NF2 gene, has emerged as the most frequent alteration of meningiomas; in addition, several other genes (e.g. AKT1, KLF4, TRAF7, SMO) and chromosomes have been found to be recurrently altered often in association with more complex karyotypes and involvement of multiple signaling pathways. Here we review the current knowledge about the most relevant genes involved and the signaling pathways targeted by such alterations. In addition, we summarize those proposals that have been made so far for classification and prognostic stratification of meningiomas based on their genetic/genomic features.

The absolute chemical hardness η for a chemical system under a steady external potential υ containing N electrons and an energy E(N) was defined by Robert Parr and Ralph Pearson as η = (δ2 E/δN 2)υ. Chemical hardness is a widely accepted concept in chemistry that serves as a reactivity index for describing the stability of compounds and reaction mechanisms in the framework of hard and soft acid and base theory. In a previous study, we demonstrated that it is possible to formulate a total energy functional of electronic density that is directly correlated to the experimental data obtained from mesoscopic electrochemical systems. The present study extends the use of this experimentally designed functional to determine and analyze the chemical hardness of mesoscopic electrochemical systems directly from the experimental data. We demonstrate that it is possible to rapidly scan the physical properties and chemical reactivity indexes of mesoscopic electrochemical systems at different external potentials and a finite temperature using the grand canonical ensemble.

TiO2 electrochemical biosensors represent an option for biomolecules recognition associated with diseases, food or environmental contaminants, drug interactions and related topics. The relevance of TiO2 biosensors is due to the high selectivity and sensitivity that can be achieved. The development of electrochemical biosensors based on nanostructured TiO2 surfaces requires knowing the signal extracted from them and its relationship with the properties of the transducer, such as the crystalline phase, the roughness and the morphology of the TiO2 nanostructures. Using relevant literature published in the last decade, an overview of TiO2 based biosensors is here provided. First, the principal fabrication methods of nanostructured TiO2 surfaces are presented and their properties are briefly described. Secondly, the different detection techniques and representative examples of their applications are provided. Finally, the functionalization strategies with biomolecules are discussed. This work could contribute as a reference for the design of electrochemical biosensors based on nanostructured TiO2 surfaces, considering the detection technique and the experimental electrochemical conditions needed for a specific analyte.

The quantum rate theory predicts the electron transfer rate between quantum states governed by the ratio between the quantum conductance and capacitance (Phys. Chem. Chem. Phys. 2020, 22, 26109−26112). This rate is important not only for describing the quantumness of the electron transfer of electrochemical reactions but also for understanding electron transport in molecular electronics (Phys. Chem. Chem. Phys. 2020, 22 (19), 10828−10832). Additionally, this quantum rate principle is applicable for describing conductive and capacitive V-shapes of graphene (Carbon 2021, 184 821−827). In the present work, we demonstrate the relationship between the quantum rate theory for a single-layer graphene and the relativistic quantum mechanical theory of electrons according to the Dirac equation. As the merger of quantum mechanics and relativity theory, quantum rate theory is the key to analyzing quantum electrodynamics in two-dimensional structures (e.g., honeycomb-like carbon such as graphene) using an inexpensive benchtop electrochemical setup. In this study, the quantum rate model for graphene is introduced along with its applicability to the diffusionless electrochemical transport of electrons, as exemplified for molecular films comprising redox switches. This didactic approach demonstrates that the best means of conducting electron transport in graphene is the AC mode of electric current modulation, in which electric displacement current is imperative. A maximum quantum rate of electron transport occurs at the Dirac point, where net carrier concentrations are at their minimum, in contrast to the traditional DC mode of modulating conductance. This analysis opens an avenue of possibilities for fabricating quantum devices with electronic semiconducting accuracy, for example, biological sensors in complex environments.

Molecular and supramolecular systems are essentially mesoscopic in character. The electron self-exchange, in the case of energy fluctuations, or electron transfer/transport, in the case of the presence of an externally driven electrochemical potential, between mesoscopic sites is energetically driven in such a manner where the electrochemical capacitance (C) is fundamental. Thus, the electron transfer/transport through channels connecting two distinct energetic (ΔE) and spatially separated mesoscopic sites is capacitively modulated. Remarkably, the relationship between the quantum conductance (G) and the standard electrochemical rate constant (k), which is indispensable to understanding the physical and chemical characteristics governing electron exchange in molecular scale systems, was revealed to be related to C, that is, C = G/k. Accordingly, C is the proportional missing term that controls the electron transfer/transport in mesoscopic systems in a wide-range, and equally it can be understood from first principles density functional quantum mechanical approaches. Indeed the differences in energy between states is calculated (or experimentally accessed) throughout the electrochemical capacitance as ΔE = β/C, and thus constitutes the driving force for G and/or k, where β is only a proportional constant that includes the square of the unit electron charge times the square of the number of electron particles interchanged.

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