--- title: "When a Molecular Bond Breaks Interactive Lab | Sandbox Physics" description: "An ideal spring always returns. A molecular bond can let go. Kick a bound vibrational wavepacket into motion. Watch part of it return while another part escapes along a Morse potential, then compare the same preparation with an ideal spring." canonical_url: "https://sandboxphysics.com/labs/morse-molecular-bond-breaking/" language: "en" page_type: "lab" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/labs/morse-molecular-bond-breaking/" last_modified: "2026-10-21" --- VIBRATE / SPLIT / ESCAPE # When a Molecular Bond Breaks Kick a bound vibrational wavepacket into motion. Watch part of it return while another part escapes along a Morse potential, then compare the same preparation with an ideal spring. > Interactive simulation: open this page in a web browser to change the parameters and run the model. One dimensionless nuclear coordinate on a fixed electronic potential. The initial state is a momentum-kicked Morse ground state. This is not a laser-pulse calculation or a calibrated molecular species. Probability beyond a finite stretch is not an asymptotic dissociation yield. THE BOND / THE WAVE / THE ESCAPE PROBABILITY BEYOND STRETCH SIX $0\%$ EVOLUTION TIME $\tau=0$ READ THE PROBABILITY ## What stays. What leaves. ### Every instant on one map Time runs downward. Drag the white cursor. Gold marks stretch six; it is an observation boundary, not a detector or a wall. 0 1.5 ### A probability profile Cyan: now. Gray: initial preparation. Gold: pinned prediction. The plot has an adaptive vertical scale. ENERGY DRIFT $0$ NORM DRIFT $0$ EDGE WEIGHT $0$ HIGH-FREQUENCY WEIGHT $0$ INDEPENDENT SIMULATED MEASUREMENTS ### Stop time. Prepare again. Measure. Sample one stretch coordinate from each of 768 independently prepared molecules. The histogram comes only from those records; its axis includes every sample. Ideal joint position readout, without blur or loss. Moving the time cursor preserves old records; changing preparation clears them. Samples are not a wavefunction reconstruction or a continuous movie of one molecule. Equations, coordinates and boundaries $$ x=q/\ell,\quad\tau=\frac{\hbar t}{m\ell^2},\quad E_* =\frac{\hbar^2}{m\ell^2} $$ Length, time and energy are dimensionless. No specific molecular mass or experimental time scale is assigned. Positive stretch points outward; in the two-coordinate model the second coordinate is positive upward in the flat map. $$ \begin{gathered}i\partial_\tau\psi=H\psi,\quad H=-\tfrac12\partial_x^2+V(x)\\V(x)=D(1-e^{-ax})^2\\V_{\mathrm{spring}}(x)=Da^2x^2\end{gathered} $$ The exact Morse ground state is prepared and multiplied by a momentum-kick phase. The stretch coordinate extends over the real line as an effective vibration model. Rotation, electronic transitions, pulse preparation and environmental loss are omitted. The far-region fraction is a finite-time position probability, not a continuum spectral projection. $$ \begin{gathered}\psi(x,0)\propto z^{\lambda-1/2}e^{-z/2}e^{ip_0x}\\z=2\lambda e^{-ax},\quad\lambda=\sqrt{2D}/a\end{gathered} $$ A periodic Fourier grid and symmetric split-step propagation solve the declared Hamiltonian. No absorption or propagation renormalization is used. Edge occupation, high-wave-number weight and relative energy drift are checked; the view warns if the chosen run loses numerical resolution. - [NIST DLMF — Morse oscillator](https://dlmf.nist.gov/18.39) - [NIST CCCBDB — Anharmonic vibrational levels](https://cccbdb.nist.gov/vibnotesx.asp) Sources establish the model context; this illustrative parameter set is not a fit or a reproduction of those experimental data. Physics tutorial ## When a Molecular Bond Breaks **Background** Kick a bound vibrational wavepacket into motion. Watch part of it return while another part escapes along a Morse potential, then compare the same preparation with an ideal spring. **Why it matters** Connect the energy landscape to the changing probability, then ask what a measurement actually records. Start with the essentials - **Focus question**: An ideal spring always returns. A molecular bond can let go. - **One-sentence intuition**: Anharmonicity makes the outer wall flatten. A kicked bound state contains many energies, so part of the wavepacket can escape while another part returns. ### Core mathematical model #### Hamiltonian $$ H=-\frac12\partial_x^2+D(1-e^{-ax})^2 $$ Dimensionless units set the effective mass and reduced Planck constant to one. All propagation is unitary; no time-step renormalization is used. #### Bound energy levels $$ E_n=a\sqrt{2D}(n+\tfrac12)-\frac{a^2}{2}(n+\tfrac12)^2 $$ The number of bound levels is finite. These are analytic reference energies, not peaks inferred from the position samples. ### Common difficulties #### A landscape is not a trajectory **Typical misconception** The bright spot is one atom moving on a literal surface. **Better mental model** It is a nuclear configuration probability. Energy is plotted vertically only as a visualization. #### Scope **Typical misconception** The simulation predicts a particular molecule. **Better mental model** One dimensionless nuclear coordinate on a fixed electronic potential. The initial state is a momentum-kicked Morse ground state. This is not a laser-pulse calculation or a calibrated molecular species. Probability beyond a finite stretch is not an asymptotic dissociation yield. ### Run the experiment 1. 01 #### Compare Start with the first two presets and select the same time in both. Pin a frame before changing the preparation. **What to observe:** The outgoing probability grows as the kick increases; an ideal spring returns it. 2. 02 #### Read the axes Switch between landscape and density views, then inspect the data row. **What to observe:** Potential height, density brightness and probability relief are distinct quantities with explicit display scales. 3. 03 #### Acquire Sample independent preparations at one chosen instant. Move time and confirm the old records stay fixed. Export the raw CSV. **What to observe:** A finite sample fluctuates. It does not reconstruct the complex wavefunction or reveal a continuous path. Physical conclusion One dimensionless nuclear coordinate on a fixed electronic potential. The initial state is a momentum-kicked Morse ground state. This is not a laser-pulse calculation or a calibrated molecular species. Probability beyond a finite stretch is not an asymptotic dissociation yield. Quantum & fields · Starter path ## Start from a single measurement Predict outcomes and collect counts, building from one qubit to wave packets, bound states and two-photon interference. [Start here → **Quantum State & Born Measurement** Predict a probability, turn the analyzer, then compare it with the frequency of acquired shots. Observe · 15 min](https://sandboxphysics.com/labs/qubit-state/) 1. [1 Quantum State & Born Measurement](https://sandboxphysics.com/labs/qubit-state/) 2. [2 Stern–Gerlach Sequence](https://sandboxphysics.com/labs/stern-gerlach-sequence/) 3. [3 Wave Packet & Uncertainty](https://sandboxphysics.com/labs/wave-packet-uncertainty/) 4. [4 Quantum Harmonic Oscillator](https://sandboxphysics.com/labs/quantum-harmonic-oscillator/) 5. [5 Which Path & Quantum Eraser](https://sandboxphysics.com/labs/quantum-eraser/) 6. [6 Hong–Ou–Mandel Two-Photon Interference](https://sandboxphysics.com/labs/hong-ou-mandel/) [View the full path →](https://sandboxphysics.com/topics/quantum/#starter-path)