Quantum Nuclear Dynamics¶
Quantum nuclear dynamics studies how the nuclei move once the electronic structure problem has already been solved — how a wavepacket evolves in time across one or more coupled potential energy surfaces, how population transfers between electronic states, and what spectroscopic signatures (like an absorption spectrum) that motion produces. Where the Electronic Structure Theory workflow answers "what are the states of this molecule, at this geometry?", this workflow answers "what happens next?" — it builds directly on top of that earlier workflow rather than replacing it.
This is a beginner-level map of the pipeline, not a full tutorial — each stage below points to the dedicated section that covers it in depth, and some of those dedicated sections (distortion generation, diabatization) don't exist on the site yet.
What this workflow produces¶
Starting from a set of electronic states already characterized (e.g. via CASSCF/XMCQDPT), this workflow builds a vibronic coupling model for a handful of relevant vibrational modes, propagates a nuclear wavepacket on it using MCTDH, and extracts state populations over time and a simulated absorption spectrum.
Recommended workflow¶
Electronic Structure of the Molecule
(see the Electronic Structure Theory workflow)
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Generate Distorted Geometries
along the normal coordinates
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Diabatization
diabatic energies + couplings at each distorted geometry
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Select a Few Relevant Modes
for the nuclear dynamics
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Generate the Operator File (MCTDH)
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Wave Packet Propagation (MCTDH)
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Population Analysis + Absorption Spectrum
Step 1 — Generate distorted geometries along the normal coordinates¶
Starting from the optimized equilibrium geometry, the molecule is displaced along each of its normal coordinates (the same normal modes that come out of a Gaussian frequency calculation) to generate a set of distorted geometries around that minimum. These distorted structures are what let the next step probe how the electronic states — and the coupling between them — actually change as the nuclei move, rather than only knowing their values at the single equilibrium point.
Dedicated section coming later
A full, dedicated walkthrough of how these distorted geometries are generated in practice will be added separately. For now, this page only describes where the step sits in the overall pipeline.
Step 2 — Diabatization¶
Running the electronic structure method (the same CASSCF/XMCQDPT machinery used at the equilibrium geometry) at each distorted geometry gives a set of adiabatic state energies at each point. Diabatization transforms these into diabatic energies and couplings — a representation that varies smoothly with geometry and stays well-defined even where adiabatic states come close together or cross, which is exactly the regime nuclear dynamics calculations need to describe correctly.
Dedicated section coming later
Like Step 1, the full diabatization procedure will get its own dedicated section. For now, this page only describes where it sits in the pipeline: it consumes the distorted-geometry electronic structure results from Step 1 and produces the diabatic energies/couplings that feed directly into the operator file in Step 4.
Step 3 — Select a few relevant modes¶
Not every normal mode contributes meaningfully to the dynamics of interest. From the full set of normal coordinates, a small subset is selected — typically the modes that show the strongest diabatic coupling or the largest gradient along the relevant electronic transition — to keep the nuclear dynamics calculation computationally tractable. This is a judgment call specific to the molecule and the states involved, similar in spirit to choosing an active space in the electronic structure workflow: too few modes and the model misses real physics, too many and the calculation becomes intractable.
Step 4 — Generate the operator file (MCTDH)¶
Basic tutorial
Operator File Generation — prerequisites, operator-make.sh, and the resulting vibronic Hamiltonian.
The diabatic energies and couplings (Step 2), expressed in terms of the selected modes (Step 3), are assembled into an MCTDH operator file — the explicit vibronic Hamiltonian that the wavepacket will actually propagate on. This is where everything from the earlier steps gets turned into a single, concrete input that MCTDH can read.
Step 5 — Wave packet propagation (MCTDH)¶
Basic tutorial
Wave Packet Propagation — input/output structure and how the propagation actually works.
With the operator file in hand, MCTDH propagates a nuclear wavepacket in time across the coupled surfaces it describes. This is the computationally heavy step of the whole workflow, and it's what turns a static vibronic coupling model into an actual time-dependent picture of the molecule's dynamics.
Step 6 — Population analysis¶
Basic tutorial
Tracking how much of the wavepacket resides on each electronic state as a function of time shows how population transfers between states — the direct dynamical signature of, for example, internal conversion between the states built into the operator file in Step 4.
Step 7 — Absorption spectrum¶
Basic tutorial
The same propagation also gives access to the autocorrelation function of the wavepacket, whose Fourier transform is a simulated absorption spectrum — a directly comparable-to-experiment output that reflects the full vibronic structure built up over Steps 1–5, not just the vertical excitation energies from the electronic structure workflow alone.
Worked example¶
A complete worked example — one molecule taken through distortion generation, diabatization, mode selection, operator file generation, and wave packet propagation with real MCTDH input/output files, in the same style as the Diels-Alder reaction worked example — is planned but not yet available.