Related Experiment Video
Updated: Jul 17, 2026

06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Pauling resonant structures in real space through electron number probability distributions
A Martín Pendas1, E Francisco, M A Blanco
1Departamento de Química Física y Analítica, Facultad de Química, Universidad de Oviedo, 33006 Oviedo, Spain.
The Journal of Physical Chemistry. A
|February 9, 2007
Summary
This study introduces a hierarchy of electron probability distributions for analyzing molecular structures. It enables partitioning molecular energy into atomic contributions, advancing the interacting quantum atoms approach.
Area of Science:
- Quantum chemistry
- Computational chemistry
- Theoretical chemistry
Background:
- Electron probability distributions are fundamental to understanding molecular structure and bonding.
- Existing methods for analyzing molecular energy contributions can be complex.
- The interacting quantum atoms approach offers a way to partition molecular properties.
Purpose of the Study:
- To present a general hierarchy of coarse-grained electron probability distributions.
- To explore the partitioning of molecular energy into structural contributions.
- To extend the interacting quantum atoms approach for analyzing resonant structures.
Main Methods:
- Developing a hierarchy of electron probability distributions based on space partitioning.
- Partitioning the physical space into atomic regions.
- Applying the concepts to the hydrogen molecule for detailed analysis.
Main Results:
- A general hierarchy of electron probability distributions is established.
- Orbital invariant treatment of resonant structures is facilitated.
- Molecular energy and its components are successfully partitioned into structure contributions.
- A complete statistical and energetic decomposition into covalent and ionic terms for the hydrogen molecule is presented.
Conclusions:
- The proposed hierarchy provides a framework for analyzing electron distributions and molecular energy.
- This approach offers a valuable extension to the interacting quantum atoms method.
- The study demonstrates the utility of partitioning for understanding chemical bonding in molecules like H2.
Related Concept Videos
Resonance and Hybrid Structures
According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
The Pauli Exclusion Principle
The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
The Quantum-Mechanical Model of an Atom
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. Schrödinger...
Electronic Structure of Atoms
An atom comprises protons and neutrons, which are contained inside the dense, central core called the nucleus, with electrons present around the nucleus. Taking into account the wave–particle duality of electrons and the uncertainty in position around the nucleus, quantum mechanics provides a more accurate model for the atomic structure. It describes atomic orbitals as the regions around the nucleus where electrons of discrete energy exist, characterized by four quantum numbers: n, l, ml, and...
The de Broglie Wavelength
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
Atomic Orbitals
An atomic orbital represents the three-dimensional regions in an atom where an electron has the highest probability to reside. The radial distribution function indicates the total probability of finding an electron within the thin shell at a distance r from the nucleus. The atomic orbitals have distinct shapes which are determined by l, the angular momentum quantum number. The orbitals are often drawn with a boundary surface, enclosing densest regions of the cloud.

