= Stipulated bond dissociation model
Take an invented <diatomic molecule> with a <Morse potential>, setting the separated-atom <energy> to zero:
$$
V(r)=D_e\left[\left(1-e^{-a(r-r_e)}\right)^2-1\right],\qquad
D_e=2.0000\,\mathrm{eV},\qquad A=\hbar\omega_e=0.2000\,\mathrm{eV}.
$$
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 are
$$
\epsilon_v=A\left(v+\tfrac12\right)-\frac{A^2}{4D_e}\left(v+\tfrac12\right)^2,
\qquad v=0,1,\ldots,\quad v+\tfrac12<\frac{2D_e}{A}.
$$
Consequently,
$$
E_{\rm ZP}=\frac A2-\frac{A^2}{16D_e}=0.09875\,\mathrm{eV},\qquad
D_0=2.0000-0.09875=1.90125\,\mathrm{eV}.
$$
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>.
\Image[/bond-dissociation-well-and-zero-point.png]
{title=<Bond potential-well depth> and <ground-state dissociation energy> reach the same separated-atom limit from different starting <energies>}
{id=image-bond-dissociation-well-and-zero-point}
{description=Original stipulated <Morse potential> with $D_e=2\,\mathrm{eV}$ and $A=0.2\,\mathrm{eV}$. The horizontal coordinate is $a(r-r_e)$; the horizontal $v=0$ line is an <energy eigenvalue>, not a classical trajectory or a measured spectrum.}
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 $T=300\,\mathrm K$,
$$
N_{\rm A}D_e\approx192.971\,\mathrm{kJ\,mol^{-1}},\qquad
N_{\rm A}D_0\approx183.443\,\mathrm{kJ\,mol^{-1}},\qquad
\Delta_{\rm diss}H^{\circ}\approx187.184\,\mathrm{kJ\,mol^{-1}}.
$$
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.
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