Shannon Entropy and Many-Electron Correlations: Theoretical Concepts, Numerical Results and Collins Conjecture

In this paper I will discuss the overlap between the concept of Shannon Entropy and the concept of electronic correlation. Quantum Monte Carlo numerical results for the uniform electron gas are also presented; these latter on the one hand enhance the hypothesis of a direct link between the two concepts but on the other hand leave a series of open questions which may be employed to trace a roadmap for the future research in the field.Comment: 27 pages with 3 figure

Some fundamental problems for an energy conserving adaptive resolution molecular dynamics scheme

Adaptive resolution molecular dynamics (MD) schemes allow for changing the number of degrees of freedom on the fly and preserve the free exchange of particles between regions of different resolution. There are two main alternatives on how to design the algorithm to switch resolution using auxiliary ''switching'' functions; force based and potential energy based approach. In this work we show that, in the framework of classical MD, the latter presents fundamental conceptual problems which make unlikely, if not impossible, the derivation of a robust algorithm based on the potential energy.Comment: 4 pages, 1 figure (color); Phys.Rev.E (2007) in pres

Levy-Lieb principle: The bridge between the electron density of Density Functional Theory and the wavefunction of Quantum Monte Carlo

The constrained-search principle introduced by Levy and Lieb, is proposed as a practical, though conceptually rigorous, link between Density Functional Theory (DFT) and Quantum Monte Carlo (QMC). The resulting numerical protocol realizes in practice the implicit key statement of DFT: "Given the three dimensional electron density of the ground state of a system of N electrons with external potential v(r) it is possible to find the corresponding 3N-dimensional wavefunction of ground state." From a numerical point of view, the proposed protocol can be employed to speed up the QMC procedure by employing DFT densities as a pre-selection criterion for the sampling of wavefunctions.Comment: 9 pages, 1 figure, paper in press in Chemical Physics Letters, 201

Bader's interatomic surface and Bohmian mechanics

A Thomas-Fermi statistical analysis of Bader's interatomic surface developed in a previous work (L.Delle Site, Phys.Lett.A 286 61-64 (2001)) is here extended by considering exchange effects and electron density's inhomogeneity at basic level via Thomas-Fermi-Dirac-Weizsacker model. The results obtained show interesting connections with bohmian mechanics and lead to a statistical interpretation of the chemical properties of condensed systems at atomistic level.Comment: 8 pages, no figure

On the geometry of the consumer's surplus line integral

Consumer's surplus can be seen as a correct measure of the change in welfare under special conditions on the preferences of the consumer. The note addresses the question whether the intuitive appeal of the consumer''s surplus concept in the one-price change case extends into cases where several prices of inter-related goods change. An intuitively justified attribution of the change in welfare is conjectured. Sufficient conditions for this attribution to be exactly consistent with the geometry of the consumer''s surplus line integral are discussed.

Grand-Canonical Adaptive Resolution Centroid Molecular Dynamics: Implementation and Application

We have implemented the Centroid Molecular Dynamics scheme (CMD) into the Grand Canonical-like version of the Adaptive Resolution Simulation Molecular Dynamics (GC-AdResS) method. We have tested the implementation on two different systems, liquid parahydrogen at extreme thermodynamic conditions and liquid water at ambient conditions; the reproduction of structural as well as dynamical results of reference systems are highly satisfactory. The capability of performing GC-AdResS CMD simulations allows for the treatment of a system characterized by some quantum features and open boundaries. This latter characteristic not only is of computational convenience, allowing for equivalent results of much larger and computationally more expensive systems, but also suggests a tool of analysis so far not explored, that is the unambiguous identification of the essential (quantum) degrees of freedom required for a given property

Solvation of positive ions in water: The dominant role of water-water interaction

Local polarization effects, induced by mono and divalent positive ions in water, influence (and in turn are influenced by) the large scale structural properties of the solvent. Experiments can only distinguish this process of interplay in a generic qualitative way. Instead, first principles quantum calculations can address the question at both electronic and atomistic scale, accounting for electronic polarization as well as geometrical conformations. For this reason we study the extension of the scales' interconnection by means of first principle Car-Parrinello molecular dynamics applied to systems of different size. In this way we identify the general aspects dominating the physics of the first solvation shell and their connection to the effects related to the formation of the outer shells and eventually the bulk. We show that while the influence of the ions is extended to the first shell only, the water-water interaction is instead playing a dominant role even within the first shell independently from the size or the charge of the ion.Comment: 4 pages 3 figures (color

Nanoscale domains in ionic liquids: A statistical mechanics definition for molecular dynamics studies

One of the many open questions concerning Ionic Liquids (ILs) is the existence of nanoscale supramolecular domains which characterize the bulk. The hypothesis of their existence does not meet a general consensus since their definition seems to be based on ad hoc arbitrary criteria rather than on general and solid first principles of physics. In this work, we propose a suitable definition of supramolecular domains based on first principles of statistical mechanics. Such principles can be realized through the application of a recently developed computational tool which employs adaptive molecular resolution. The method can identify the smallest region of a liquid for which the atomistic details are strictly required, while the exterior plays the role of a generic structureless thermodynamic reservoir. We consider four different imidazolium-based ILs and show that indeed one can quantitatively represent the liquid as a collection of atomistically self-contained nanodroplets embedded in a generic thermodynamic bath. Such nanodroplets express a characteristic length scale for heterogeneity in ILs.Comment: 9 page