# What is the relation between surface tension and initial molecular harmonic?

Initial harmonic is measured as Hartree/Bohr^2 ( like IHarmonic=n in Gaussian Software ). As I am from physics background I am used to look at features from their dimension point of view: Actually surface tension is the only physical feature that I know is compatible with Force / Distance. I was wondering if there is any relation between the surface tension and initial harmonic.

Update: Another physical feature is spring constant which is not irrelevant also !

• Aren't these the same units as the spring constant $k$ from a classical spring obeying Hooke's law $F=-kx$? – Curt F. Apr 22 '15 at 4:07
• @CurtF. yes it is. I was thinking that in Molecular Mechanics, atoms are assumed as oscillating particles on springs. The stronger the spring, the smaller the volume. If we look at the whole system as a bag of oscillating particles ( if we can ! ) , the surface tension can be proportional to this constant ( instead of springs avoiding outward movement, it can be assumed as surface tension doing the same job inward ) . Is there such a concept ? – Aug Apr 22 '15 at 4:19

Surface tension arises from the fewer neighbors that molecules at the surface have, relative to the number of neighbors for molecules in the bulk.

For example, consider a simple model of rigid identical spheres in a hexagonal closest packing. In the bulk, there are 12 spheres in contact with a given sphere, which could be thought of as 6 spheres at vertices of a regular hexgon surrounding the given sphere, 3 spheres in a triangle below and 3 spheres in a tringle above.

At a surface, at least 3 of the neighboring spheres would be absent.

Considering an interaction energy between neighboring spheres, the loss of interaction energy (due to fewer than 12 neighbors per sphere) will be proportional to the surface area of the system of spheres. The minimum energy of the system will be when surface area of the arrangement of spheres is minimized.

For the above reason, the units of surface tension are Energy/surface area, which the OP correctly points out is the same as force/distance.

From the above explanation, particularly that even for rigid spheres always in direct contact the Energy/surface area (force/distance) relationship arises, it can be understood that surface tension has no particular relationship with a force constant between molecules (or between atoms of a molecule). Instead, surface tension is related to the energy difference between a molecule with maximum neighbors and a molecule with fewer neighbors.

Considering a simple harmonic oscillator, energy vs distance is a parabola. There is no horizonal asymptote. Regardless of what the force constant is, there is always infinite energy required to remove a neighbor. In reality, intermolecular force will approach zero at infinite distance between molecules. It is the difference between energy at equilibrium seperation and infinite separation that is relavent to surface tension, and force constant does not provide this information.

The terms "initial molecular harmonic" and "initial harmonic" are not standard chemistry terms and only have meaning in the context of a particular computer program. "Initialharmonic" or "Iharmonic" refers to a force constant that can be for linear stretching, bending about a vertex that is an atom, or dihedral bending, etc.
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