---
title: "Nonadiabatic molecular dynamics"
description: "Follow molecular wave packets from potential surfaces to transitions, geometric phase and reproducible comparisons of quantum and trajectory dynamics."
canonical_url: "https://sandboxphysics.com/stories/nonadiabatic-dynamics/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/nonadiabatic-dynamics/"
---

FR14

# Nonadiabatic molecular dynamics

Sandbox Physics · 2026-10-28

A light pulse can send a molecule toward several possible products. The nuclei move across electronic energy surfaces, and near a small gap the electronic state can change. Start with a vibrating bond, learn how a wave packet branches, then compare quantum evolution, mean forces and surface hopping. Interference connects this simple picture to current research.

## Start with a bond that can stretch

A potential-energy surface tells the nuclei which way the electronic energy slopes. One surface often suffices near a stable bond. Excited molecules can approach a second surface so closely that the electrons and nuclei must be followed together. The difficulty is then concrete: how much probability leaves in each channel, and what information does a cheaper approximation lose?

One arrival can leave in two electronic channels. Conceptual diagram; positions and heights are schematic.

The first three chapters build surfaces, moving electronic bases and a single-passage transition law. Chapters four to seven compare dynamics, introduce a conical intersection and follow phase through recombination and loss of coherence. The final two chapters teach a reproducible comparison and a close reading of primary research. Each chapter includes a worked example, a prediction to test and exercises with explanations.

1. L1 · 1

   ## [How electrons create potential-energy surfaces](https://sandboxphysics.com/stories/nonadiabatic-dynamics/potential-energy-surfaces/)

   Use a vibrating bond to understand energy surfaces, nuclear wave packets and reaction exits before adding a second electronic state.

2. L2 · 2

   ## [What changes when the electronic basis moves](https://sandboxphysics.com/stories/nonadiabatic-dynamics/moving-electronic-basis/)

   Derive derivative coupling from nuclear kinetic energy and compare adiabatic and diabatic representations with a two-state rotation.

3. L2 · 3

   ## [How much probability changes channel in one passage](https://sandboxphysics.com/stories/nonadiabatic-dynamics/landau-zener-passage/)

   Define gap slopes and channel labels, calculate the Landau–Zener parameter, and test fast and slow limits with a worked example.

4. L3 · 4

   ## [Three dynamics methods for the same preparation](https://sandboxphysics.com/stories/nonadiabatic-dynamics/three-dynamics/)

   Compare quantum packets, Ehrenfest mean forces and fewest-switches surface hopping with common initial conditions and exit windows.

5. L3 · 5

   ## [How two surfaces form a conical intersection](https://sandboxphysics.com/stories/nonadiabatic-dynamics/conical-intersections/)

   Derive the two conditions for a real two-state degeneracy, construct a local cone, and examine how the incident path affects branching.

6. L3 · 6

   ## [Why paths around a conical intersection can cancel](https://sandboxphysics.com/stories/nonadiabatic-dynamics/geometric-phase-interference/)

   Derive a two-state loop phase and connect the electronic eigenvector sign to a controlled two-port interference distribution.

7. L3 · 7

   ## [When two nuclear packets can still interfere](https://sandboxphysics.com/stories/nonadiabatic-dynamics/coherence-and-decoherence/)

   Connect amplitude addition to reduced electronic coherence and distinguish spatial separation, phase averaging and trajectory decoherence corrections.

8. L4 · 8

   ## [What makes a dynamics comparison convincing](https://sandboxphysics.com/stories/nonadiabatic-dynamics/reproducible-benchmarks/)

   Define exits and flux, check conservation and convergence, and separate sampling error, numerical error and method bias.

9. L4 · 9

   ## [Reading interference and molecular-benchmark papers](https://sandboxphysics.com/stories/nonadiabatic-dynamics/reading-nonadiabatic-research/)

   Read fixed versions of the 2016 interference paper and the 2025 benchmark roadmap, distinguishing representation, limited reproduction and open problems.

## Experiments along the route

- [Set a molecular vibration in motion](https://sandboxphysics.com/labs/morse-molecular-bond-breaking/)
- [Send the same preparation through three dynamics methods](https://sandboxphysics.com/labs/nonadiabatic-avoided-crossing/)
- [Follow a two-component packet through a conical intersection](https://sandboxphysics.com/labs/molecular-conical-intersection/)
- [Change the loop and compare interference](https://sandboxphysics.com/labs/conical-geometric-phase/)
- [Measure branching probabilities and numerical error](https://sandboxphysics.com/labs/nonadiabatic-method-benchmark/)

The experiments use defined low-dimensional Hamiltonians and simulated records. The two-coordinate conical model and the controlled path-interference model answer different questions. Their parameters are not fitted to a named molecule. The research chapter identifies the separate Shin–Metiu calculation used in the 2016 paper.

## Sources and calculation scope

1. [C. A. Mead & D. G. Truhlar, On the determination of Born–Oppenheimer nuclear motion wave functions including complications due to conical intersections and identical nuclei, J. Chem. Phys. 70, 2284–2296 (1979)](https://doi.org/10.1063/1.437734)

   Published original connecting conical intersections with nuclear-motion phase. Bibliography and the 1983 erratum are recorded by the authors’ group. This is further reading; the guided Lab derives its phase from Berry’s fixed two-state example.

2. [John C. Tully, Molecular dynamics with electronic transitions, J. Chem. Phys. 93, 1061–1071 (1990)](https://doi.org/10.1063/1.459170)

   Published primary method paper. Sections II–III define fewest switches and its one-dimensional test models. Our three-method comparison uses the simple avoided-crossing Hamiltonian; the nuclear packet, finite windows and numerical settings are stated with each saved run.

3. [Tully 1990 original paper, author-text scan](https://xuv.scs.illinois.edu/chem540/GroupProjects/Benke_Hammer_SourcePaper1.pdf)

   Open copy of the original paper for checking the transition rule and model equations. The displayed Lab comparison is generated by the repository solver, not digitized experimental data.

4. [M. V. Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. Lond. A 392, 45–57 (1984)](https://michaelberryphysics.wordpress.com/wp-content/uploads/2013/07/berry120.pdf)

   Published primary derivation: equations (5)–(6) separate dynamical and geometrical phase; section 3 treats a degeneracy. The path experiment is a controlled two-state model, with the reduction and phase comparison specified on its page.

5. [C. Zener, Non-adiabatic crossing of energy levels, Proc. R. Soc. Lond. A 137, 696–702 (1932)](https://doi.org/10.1098/rspa.1932.0165)

   Published original result for a linear-in-time diabatic gap and constant coupling. The course defines the slope as the slope of the full diabatic energy difference, avoiding a factor-of-two ambiguity.

6. [Curchod, Agostini & Gross, An Exact Factorization Perspective on Quantum Interferences in Nonadiabatic Dynamics, arXiv:1604.02351v2](https://arxiv.org/html/1604.02351v2)

   Fixed 30 June 2016 author version; published in J. Chem. Phys. 145, 034103 (2016), DOI 10.1063/1.4958637. Reading scope: equations (5)–(6), (14)–(18), and Figures 3–7. Its Shin–Metiu electron–ion calculation differs from the Tully and conical teaching models.

7. [Cigrang et al., Roadmap for Molecular Benchmarks in Nonadiabatic Dynamics, arXiv:2502.14569v3](https://arxiv.org/pdf/2502.14569v3)

   Fixed 4 July 2025 author version associated with the published Perspective, DOI 10.1021/acs.jpca.5c02171. Sections II A–F discuss systems, dynamics methods, electronic structure, initial conditions, observables and experimental comparisons. This is a benchmark roadmap, not a completed universal ranking.