Density functional theory in the canonical ensemble I General formalism
TLDR
In this paper, the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble (GCE) was extended to the CE and the correlation functions were stripped off of their asymptotic behaviour.Abstract:
Density functional theory stems from the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble (GCE). However, as recent work shows, although its extension to the canonical ensemble (CE) is not straightforward, work in nanopore systems could certainly benefit from a mesoscopic DFT in the CE. The stumbling block is the fixed $N$ constraint which is responsible for the failure in proving the interchangeability of density profiles and external potentials as independent variables. Here we prove that, if in the CE the correlation functions are stripped off of their asymptotic behaviour (which is not in the form of a properly irreducible $n$-body function), the HKSM theorem can be extended to the CE. In proving that, we generate a new {\it hierarchy} of $N$-modified distribution and correlation functions which have the same formal structure that the more conventional ones have (but with the proper irreducible $n$-body behaviour) and show that, if they are employed, either a modified external field or the density profiles can indistinctly be used as independent variables. We also write down the $N$-modified free energy functional and prove that the thermodynamic potential is minimized by the equilibrium values of the new hierarchy.read more
Citations
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Colloidal gels: equilibrium and non-equilibrium routes
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Confocal microscopy of colloids
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Ab initio molecular dynamics: basic concepts, current trends and novel applications
TL;DR: Ab initio molecular dynamics (AIMD) is a rapidly evolving and growing technology that allows chemical processes in condensed phases to be studied in an accurate and unbiased way as discussed by the authors.
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Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media - topical review
TL;DR: In this paper, a review of spatially confined, non-equilibrium physics in nanoporous media is presented. And a particular emphasis is put on texture formation upon crystallisation in nanopore-confined condensed matter, a topic both of high fundamental interest and of increasing nanotechnological importance.
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Bridging scales from molecular simulations to classical thermodynamics: density functional theory of capillary condensation in nanopores
TL;DR: In this paper, the non-local density functional theory (NLDFT) with properly chosen parameters of intermolecular interactions bridges the scale gap from molecular simulations to macroscopic thermodynamics.
References
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Self-Consistent Equations Including Exchange and Correlation Effects
Walter Kohn,L. J. Sham +1 more
TL;DR: In this paper, the Hartree and Hartree-Fock equations are applied to a uniform electron gas, where the exchange and correlation portions of the chemical potential of the gas are used as additional effective potentials.
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P. C. Hohenberg,Walter Kohn +1 more
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TL;DR: In this article, the authors present a mathematical model for time-dependent correlation functions and response functions in liquid solvers, based on statistical mechanics and molecular distribution functions, and show that these functions are related to time correlation functions in Ionic and Ionic liquids.
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