# Can the strength of a covalent bond be compared to the stiffness of a spring?

I am modelling a solid with the density functional theory. The solid contains different types of atoms. The atoms are covalently bonded. I want to estimate the strength of each bond. How can I do it?

My idea is to shift the atom for which I want to estimate bond strengths a little bit along the direction of each bond, and measure the energy of the solid for each shift.

This is similar to a calculation of the stiffness of a spring. Stretch the spring a little bit, and measure the force. When the force is stronger, the spring is stronger (assuming the same stretch for different springs).

Is my thinking correct for a covalent bond? Can it be likened to a spring? Does it mean that the bond is stronger if the force on the atom is larger if I stretch the bond to a certain distance?

• Yes you can use Hooke's law. This models diatomic molecules quite accurately for small displacements from equilibrium and so at low energy. Jul 23, 2023 at 9:54
• If you move one atom away from a neighbour you are presumably moving it toward atoms on the opposite side. In that case it is a collective motion involving multiple bonds. I believe normal mode analysis is the more general approach to this kind of problem. Jul 24, 2023 at 18:02

The simplest model for a bond is a quadratic potential like a spring. Bonds are assigned force constants to explain the vibrational frequencies observed in infrared spectroscopy. In the quantum-mechanical theoretical treatment, one talks of a harmonic oscillator.

To model how bonds break, you have to add some complexity and consider the anharmonic oscillator, perhaps with a Morse potential.

Stronger bonds have higher force constants (and higher frequencies).

My idea is to shift the atom for which I want to estimate bond strengths a little bit along the direction of each bond, and measure the energy of the solid for each shift.

Yes, you can do that. You just ("just") have to make sure the shifts are large enough to see the effect while small enough to not break the bond.

This Hooke's law is accurate only for strong covalent bonds and not far from the equilibrium distance. Anharmonicity occurs at larger distances from equilibrium.

I am modelling a solid with the density functional theory. The solid contains different types of atoms.

When performing a DFT calculation, you should not stretch the bond too much, the resulting energy (anharmonic part) will not be important for your calculation and will certainly be inaccurate.