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Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

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Spherical Density Functional Theory and Atoms in Molecules.

¹Department of Theoretical Physics , University of Debrecen , H-4002 Debrecen , Hungary.

The Journal of Physical Chemistry. A

|December 31, 2019

Summary

This summary is machine-generated.

Spherically symmetric densities uniquely determine molecular and solid potentials. These densities follow a Schrödinger-like equation, revealing an effective potential related to wave function expectation values.

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Area of Science:

Quantum Chemistry
Computational Materials Science

Background:

Recent findings show that a unique set of spherically symmetric densities can determine the external potential in molecules and solids.
Understanding the behavior and properties of these densities is crucial for advancing quantum mechanical theories.

Purpose of the Study:

To demonstrate that spherically symmetric densities obey a Schrödinger-like differential equation.
To present the exact effective potential in terms of wave function expectation values.
To explore the relationship between these densities and atomic properties.

Main Methods:

Derivation of a Schrödinger-like differential equation for spherically symmetric densities.
Formulation of the effective potential using expectation values of wave functions.

Main Results:

Spherically symmetric densities satisfy a differential equation equivalent to the Euler equation.
The exact effective potential is explicitly determined by wave function expectation values.
These densities exhibit properties analogous to those of atoms.

Conclusions:

The study establishes a novel differential equation governing spherically symmetric densities.
A new method for calculating the effective potential is introduced.
The concept of spherically symmetric densities offers a distinct perspective compared to "Atoms in Molecules".