Related Experiment Video
Updated: Mar 29, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
9.1K
A Density Functional Theory View of Quantum Phase Transitions.
Á Nagy1,2, M Calixto3, E Romera2,4
1Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, Hungary.
Journal of Chemical Theory and Computation
|November 21, 2015
Summary
A one-to-one map exists between ground state wave functions and control parameters in Density Functional Theory (DFT). Monotonous functions and Rényi entropy can also serve as control parameters, offering new avenues for DFT research.
Area of Science:
- Quantum Chemistry
- Computational Physics
- Density Functional Theory
Background:
- Density Functional Theory (DFT) utilizes electron density to determine system properties.
- Wu et al. established a link between DFT "density" and the "control parameter" (external potential).
Purpose of the Study:
- To demonstrate a one-to-one mapping between ground state wave functions and control parameters.
- To explore alternative methods for manipulating control parameters in DFT.
Main Methods:
- Proving the existence of a one-to-one correspondence between wave functions and control parameters.
- Investigating the impact of strictly monotonous functions on density and control parameters.
- Analyzing the relationship between Rényi entropy and control parameters.
Main Results:
- A unique ground state wave function corresponds to each control parameter.
- Strictly monotonous functions can generate new densities and corresponding control parameters.
- A one-to-one map exists between Rényi entropy and the control parameter.
Conclusions:
- The control parameter is uniquely determined by the ground state wave function.
- Rényi entropy can be effectively utilized as a control parameter in DFT.
- This work provides new insights into the fundamental relationships within Density Functional Theory.
Related Concept Videos
02:31Phase Transitions
23.7K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
23.7K
01:21Phase Transitions
64
A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
64
01:20The Phase Rule
107
The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
107
02:45The Quantum-Mechanical Model of an Atom
61.6K
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
61.6K
02:33Phase Transitions: Sublimation and Deposition
20.9K
Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
20.9K
01:19Phase Diagram
7.3K
The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
7.3K