Properties and applications of the average interparticle distance

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Molecular Modeling

Background:

• Molecular size and shape are crucial for predicting chemical properties and reactivity.
• Existing methods for quantifying molecular size, such as isodensity contours, have limitations.
• Understanding electron-electron and electron-nuclear interactions is fundamental to molecular energy calculations.

Purpose of the Study:

• To introduce a novel method for defining origin-invariant molecular size and shape using moment operators.
• To establish relationships between these new size measures and experimentally observed steric effects.
• To correlate average inter-particle distances with fundamental components of the Hartree-Fock energy.

Main Methods:

• Utilizing first and second moment operators to derive origin-invariant descriptors for molecular size and shape.
• Calculating average electron-electron and electron-nuclear distances within molecules.
• Comparing the derived molecular size measure with existing theoretical volume calculations (isodensity contours).
• Correlating predicted steric effects with experimental data for various substituents.

Main Results:

• The defined molecular size measure shows good correlation with molecular volume from isodensity contours.
• The molecular size measure effectively predicts experimentally observed steric effects.
• Average electron-electron distances correlate well with Coulomb energy, particularly for localized molecular orbitals.
• Average electron-nuclear distances are closely related to electron-nuclear attraction energy.

Conclusions:

• First and second moment operators provide robust, origin-invariant measures of molecular size and shape.
• These measures have predictive power for steric effects and offer insights into molecular energy components.
• The approach offers a new perspective on quantifying molecular properties relevant to chemical reactivity and interactions.