{
  "annotation_id": "77146091-5d47-40a0-b7d5-f7c4eaf9eca1",
  "date_created": "2026-03-02T18:00:53.578000Z",
  "date_modified": "2026-03-02T18:00:53.578000Z",
  "file_hash": "a8783d5cfe4ff656a6a304885d5ab2a3e0b01204093be400d44c45f9a945fecd",
  "private": false,
  "record": {
    "abstract": "We present explicit form of non-adiabatic coupling (NAC) elements of nuclear\nSchroedinger equation (SE) for a coupled tri-state electronic manifold in terms\nof mixing angles of real electronic basis functions. If the adiabatic-diabatic\ntransformation (ADT) angles are the mixing angles of electronic basis, ADT\nmatrix transforms NAC terms to exactly zeros and brings diabatic form of SE.\nADT and NAC matrices satisfy a curl condition and find a novel relation among\nthe mixing angles for irrotational case. We also find that extended\nBorn-Oppenheimer (EBO) equations have meaningful solution and can reproduce\nnumerically exact results only when the equations are gauge invariant.",
    "arxiv_id": "physics/0410015",
    "authors": [
      "Biplab Sarkar",
      "Satrajit Adhikari"
    ],
    "categories": [
      "physics.chem-ph"
    ],
    "title": "Extended Born-Oppenheimer equation for tri-state system",
    "url": "https://arxiv.org/abs/physics/0410015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c1eca276-8ade-4a88-8dd5-4e25b215208e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}