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For a diatomic molecule, let $V(r)$ be the electronic potential energy at bond length $r$, with the atomic nuclei treated as fixed while finding the electronic energy. Choose zero at infinitely separated chemical atoms in the specified electronic quantum states. If the minimum occurs at $r_e$, the bond potential-well depth isThe bottom of this curve describes an equilibrium bond length, not an attainable motionless vibrational quantum state. Changing the zero of potential energy shifts both endpoints equally and leaves $D_e$ unchanged. A quantum harmonic oscillator approximates the curve near its minimum but rises without limit, so that local approximation alone cannot supply a dissociation asymptote. A Morse potential supplies both a minimum and a finite separated-fragment limit.^[ref]

A molecular nitrogen experiment used a $0.5\mathrm{mm}$ pulsed nozzle and two skimmers. A $5\mathrm{cm}$ tube raised the rotational temperature. Opposed vacuum-ultraviolet laser pulses excited selected molecular levels and, about $10\mathrm{ns}$ later, selectively ionized excited nitrogen fragments. A microchannel plate detector, phosphor screen and camera recorded radii.^[ref]

The measured squared radii were fitted against molecular excitation energies, referenced to the parent ground state:The intercept at zero radius gave the excited-product threshold; the fitted slope absorbed the detector scale. A wavemeter monitored the excitation source; scanning the probe covered the recoil Doppler shift. Subtracting the atomic excitation energies converted the intercept to ground-product $D_0$.^[ref]

An apertured grounded plate and detector timing rejected faster competing channels. Selecting fragment electronic states distinguished nearby thresholds. Agreement of $D_e$ across isotopes after zero-point energy correction tested consistency. The method still requires correctly assigned levels, adequate near-threshold signal and stable imaging; a signal drop alone can reflect another channel or a barrier.^[ref]

This measurement determines a state-resolved ground-state dissociation energy. Obtaining a finite-temperature bond-dissociation enthalpy requires the thermal increments above; obtaining a bond potential-well depth requires the zero-point energy correction. The three quantities describe different starting conditions for the same specified separation.

Write $s=v+1/2$ and complete the square in the Morse oscillator energy:The finite bound-level sequence approaches the dissociation limit at the vertex of this extrapolated parabola. Thus the bond potential-well depth isThe continuous vertex is a convenient way to identify the limit; it is not an additional normalizable bound level at the threshold.

The ground-state dissociation energy starts at the lowest vibrational level, rather than the minimum of the potential. The zero-point energy of the Morse oscillator isSubtracting it from the bond potential-well depth givesThis distinction matters whenever a dissociation energy is inferred from a vibrational spectrum.

Take an invented diatomic molecule with a Morse potential, setting the separated-atom energy to zero:Here $a$ is an inverse length, $r_e$ the equilibrium bond length, and ${\omega }_e=a\sqrt{2D_e/\mu }$, with reduced mass $\mu$. These stipulated parameters describe a simple model, not a measured chemical substance. For the one-dimensional Morse oscillator, energy eigenvalues above the minimum areConsequently,The harmonic estimate $A/2=0.1000\mathrm{eV}$ is slightly larger than this model's exact zero-point energy. The physical bound-level restriction matters: the quadratic expression is not an infinite ladder of vibrational quantum states.

For a separate thermal illustration using this same stipulated $D_0$, assume an ideal gas, fully active molecular rotation of the parent, negligible thermal molecular vibration, and negligible electronic excitation for all species. Each monatomic product contributes $\delta h=5RT/2$; the diatomic molecule contributes $7RT/2$. Thus the net increment is $3RT/2$, with molar gas constant $R$. At $T=300\mathrm{K}$,This last result follows from the stated thermal model, not a universal correction for every chemical bond. Frozen rotations, accessible excited states, different fragment composition, or a condensed phase change the thermal increments.