Distinguish bond depth, equilibrium and restoring slope

Energy is not force

A stable bond balances competing effects: electron-nuclear attraction and repulsive contributions produce an energy minimum at a finite separation. Force depends on the direction of energy change with distance, not on whether potential energy is positive or negative. Choosing zero at separated atoms makes a bound minimum negative; changing the reference would not change forces.

Read the supplied landscape

Use x=r/re and U=D[(1−exp(−2(x−1)))²−1]. This is an original parameterized Morse-shaped teaching potential. At x=1, the exponential is one, so U=−D. Far apart, the exponential tends to zero, and U approaches zero. The depth D is thus the minimum-to-asymptote energy, not the slope or equilibrium distance.

Interpret the two sides

On the stretched side, U rises with increasing separation. The force points toward smaller r, opposing the stretch. On the compressed side, increasing r lowers U, so the force points outward. The ledger supplies the local slope with respect to dimensionless x; it is not a force in newtons. To obtain a force one would need the actual distance scale and energy per molecule, not simply attach force units to a molar energy slope.

Work an original comparison

For D=400 kJ/mol, x=1 gives −400 kJ/mol. At x=1.5, exp(−1)≈.36788 and U≈−240.17 kJ/mol. Raising the separation from the minimum to that point increases potential energy by about159.83 kJ/mol. A deeper D=600 well scales these energies by1.5 without changing the model’s minimum at x=1.

State the limit of the evidence

The nuclei do not actually sit motionless at the minimum in the lowest quantum vibrational state. Zero-point energy and thermal corrections distinguish a well depth from experimentally defined dissociation quantities. This module does not calculate vibrational levels or trajectories. Compare two curves with the same depth but different widths conceptually: they could have the same minimum-to-asymptote energy and different stiffness. Depth alone cannot determine every bonding property.

Evidence and safety boundary

Conceptual sources checked 30 October 2026: NIST Morse potential, Bond energetics. All prose, numerical packets and diagrams are original; no textbook exercises or images are reproduced. The activity is supplied mathematical or synthetic evidence, not a performed materials experiment. No unknown substances, heating, high voltage or chemical synthesis are requested. Retain prior predictions and a changed-case explanation; numerical agreement alone does not certify independent understanding or practical competence.