Capacitance, the Next of Kin to Chemical Softness and Density of States, an Unexpected Perk of Being the “Middle Child”

Abstract

The capacitance characterizes abilities of various systems to store energy in the form of energy density of electric field. The spatial distribution of electrons exhibits a nonuniform relationship with external potential of atomic nuclei as a consequence of shielding or bonding, and other localized or delocalized charges. Respectively, the stored system energy is affected through thermodynamic displacement. Considering the general resemblance of capacitance definition with two other physical quantities used in the field of chemical physics, the chemical softness or the density of states, it is important to uniquely express this function in nanoscale materials to characterize phenomena resulting from confinement of few electrons generally characterized by density distribution. The exact fundamental linkages and differences between these functions have to be recognized to deal with unintuitive quantum mechanical effects related to the design, development, and comprehending the working principle of nanoscale materials and devices. The locally defined self-capacitance in atomic resolution systems is addressed here to draw the essential links between reactivity and physically observed properties resulting from the energy dispersion or entropy effects in molecular materials.

Spatially resolved characterization of electron localization and delocalization in molecules: Extending the Kohn‐Resta approach

“…PS‐FID describes in a quasi‐classical manner available information about electron momentum at each point of the position space and serves as an effective electron localization descriptor . It is interesting that almost the same quantity (termed as the “local capacitance”) was proposed recently from other considerations and was found to be correlated with electronic polarizability of atoms.…”

“…an effective electron localization descriptor. [46] It is interesting that almost the same quantity (termed as the "local capacitance") was proposed recently from other considerations [109] and was found to be correlated with electronic polarizability of atoms.…”

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

“…This connection can be extended to a local sense and permits us to define what is identified as local capacitance, whose integration in the whole space is equal to capacitance; consequently, it is possible to identify the contributions of the different regions in the electrode to the total capacitance. As recently pointed out, 17 softness can be linked to experimental measured quantities, in this case, to the one obtained by electrochemistry measurements, and JDFT provides an alternative evaluation scheme. Within the JDFT theory, as applied to an electrode−electrolyte system, global and local softness are properties of the complete interface.…”

“…The approximate relation comes from the fact that capacitance is measured without imposing the condition of the constant external potential. This approximation allows for introducing a definition of local total capacitance for the interface, an alternative to that introduced by Szarek: …”

“…The relation of quantum capacitance with the chemical reactivity density functional theory has been well established within the Hohenberg and Kohn formalism. − Recently, the connection of softness, a DFT reactivity index, with quantum capacitance was pointed out for molecular systems, but no assembly has been established between quantum capacitance and softness using JDFT, which can comprehensively reveal the electronic contributions of each component of an electrified interface subjected to different chemical potentials. In this work, we discuss the relation of the capacitance with softness for an electrochemical capacitor.…”