In search of the ‘impenetrable’ volume of a molecule in a noncovalent complex

ABSTRACT

We propose to characterise the “impenetrable” volumes of molecules A and B in a complex A---B by finding that contour of its electronic density that separates the molecular surfaces of A and B but leaves them almost touching. The volume of the complex within that contour is always less than within the 0.001 au contour. The percent difference measures the interpenetration of the two molecules at equilibrium, and is found to directly correlate with the binding energy of the complex. We interpret the volume of each molecule that is enclosed by the almost-touching contour as that molecule's impenetrable volume relative to its particular partner. The percents by which the molecules' relative impenetrable volumes differ from their 0.001 au volumes in the free states also correlate with the strengths of the interactions. This allows the “absolute” impenetrable volume of any molecule to be estimated as ∼25% of its 0.001 au volume in the free state. However this absolute impenetrable volume is only approached by the molecule in a relatively strong interaction.

KEYWORDS:

• Molecular volumes
• van der Waals radii
• impenetrable molecular volumes
• noncovalent intermolecular complexes
• electronic density contours

Disclosure statement

No potential conflict of interest was reported by the authors.