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

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

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

Interacting Electrons, Spin Statistics, and Information Theory

We consider a nearly (or quasi) uniform gas of interacting electrons for which spin statistics play a crucial role. A previously developed procedure, based on the extension of the Levy–Lieb constrained search principle and Monte Carlo sampling of electron configurations in space, allows us to approximate the form of the kinetic-energy functional. For a spinless electron gas, this procedure led to a correlation term, which had the form of the Shannon entropy, but the resulting kinetic-energy functional does not satisfy the Lieb–Thirring inequality, which is rigorous and one of the most general relations regarding the kinetic energy. In this paper, we show that when the fermionic character of the electrons is included via a statistical spin approach, our procedure leads to correlation terms, which also have the form of the Shannon entropy and the resulting kinetic-energy functional does satisfy the Lieb–Thirring inequality. In this way we further strengthen the connection between Shannon entropy and electron correlation and, more generally, between information theory and quantum mechanics

Liouville-type equations for the n-particle distribution functions of an open system

In this work we derive a mathematical model for an open system that exchanges particles and momentum with a reservoir from their joint Hamiltonian dynamics. The complexity of this many-particle problem is addressed by introducing a countable set of n-particle phase space distribution functions just for the open subsystem, while accounting for the reservoir only in terms of statistical expectations. From the Liouville equation for the full system we derive a set of coupled Liouville-type equations for the n-particle distributions by marginalization with respect to reservoir states. The resulting equation hierarchy describes the external momentum forcing of the open system by the reservoir across its boundaries, and it covers the effects of particle exchanges, which induce probability transfers between the n- and (n+1)-particle distributions. Similarities and differences with the Bergmann-Lebowitz model of open systems (P.G.Bergmann, J.L. Lebowitz, Phys.Rev., 99:578--587 (1955)) are discussed in the context of the implementation of these guiding principles in a computational scheme for molecular simulations

Classical-path integral adaptive resolution in molecular simulation: towards a smooth quantum-classical coupling

Simulations that couple different classical molecular models in an adaptive way by changing the number of degrees of freedom on the fly, are available within reasonably consistent theoretical frameworks. The same does not occur when it comes to classical-quantum adaptivity. The main reason for this is the difficulty in describing a continuous transition between the two different kind of physical principles: probabilistic for the quantum and deterministic for the classical. Here we report the basic principles of an algorithm that allows for a continuous and smooth transition by employing the path integral description of atoms.Comment: 8 pages 4 figure

An analytic expression for the electronic correlation term of the kinetic functional

We propose an analytic formula for the non-local Fisher information functional, or electronic kinetic correlation term, appearing in the expression of the kinetic density functional. Such an explicit formula is constructed on the basis of well-founded physical arguments and a rigorous mathematical prescription

Adaptive Molecular Resolution Approach in Hamiltonian Form: An Asymptotic Analysis

Adaptive Molecular Resolution approaches in Molecular Dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in the way the change of molecular resolution is made in a buffer/transition region. In particular a central question concerns the possibility of the existence of a global Hamiltonian which, by describing the change of resolution, is at the same time physically consistent, mathematically well defined and numerically accurate. In this paper we present an asymptotic analysis of the adaptive process complemented by numerical results and show that under certain mathematical conditions a Hamiltonian, which is physically consistent and numerically accurate, may exist. Such conditions show that molecular simulations in the current computational implementation require systems of large size and thus a Hamiltonian approach as the one proposed, at this stage, would not be practical from the numerical point of view. However, the Hamiltonian proposed provides the basis for a simplification and generalization of the numerical implementation of adaptive resolution algorithms to other molecular dynamics codes

Adaptive Resolution Simulation (AdResS): A Smooth Thermodynamic and Structural Transition from Atomistic to Coarse Grained Resolution and Vice Versa in a Grand Canonical Fashion

The AdResS method in molecular dynamics (MD) allows, in a grand canonical (GC) fashion, to change on-the-fly the number of degrees of freedom of a system, allowing to pass from atomistic (AT) to coarse-grained (CG) resolution and vice versa as a function of the position of the molecule in the simulation box. The coupling of resolutions is made in a thermodynamically consistent way, though in the current formulation, in the region where the molecule changes resolution, neither thermodynamic nor structural properties can be preserved. Here we propose an extension of the method where basic thermodynamic and structural properties can be systematically controlled also in the transition region; this assures a very smooth change from one molecular representation to the other. Moreover, we provide a rigorous argument which shows that if in the region where the molecules change resolution the radial distribution function (RDF) is the same as in the AT and CG region, then the AT region is, from the statistical point of view, equivalent to a subsystem embedded in a larger full AT system, at least up to a second order approximation