{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"8fd56577fde2fa50114035c31dbbeb2c92b861c4996dc49c689e55d2d75ef9a2","created":"2026-10-03T07:17:58Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"a0e65b596621715542a5456707c33a385b8d002b2043da0a55b756681e840e16","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"chem.nonadiabatic-dynamics.trajectory-method","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Fully quantum simulation of molecules is too expensive, so chemists move atoms along classical paths and let them hop between electronic states. Existing recipes are ad hoc and fail in known test cases.","posed_since":"","precise":"Derive a mixed quantum-classical method in which nuclei follow independent trajectories and that (i) reproduces exact population dynamics within 0.05 absolute at all times for the three Tully one-dimensional models and the spin-boson model over the coupling and temperature ranges of standard benchmarks, (ii) yields Boltzmann-weighted state populations at long times (detailed balance), (iii) gives correct decoherence without adjustable parameters, and (iv) costs no more per trajectory than surface hopping (one electronic-structure call per nuclear time step). An answer is the method with its derivation from the exact equations, or a proof that independent trajectories cannot satisfy (i) to (iii) together.","problem_ref":null,"references":"","settled_by":"Derivation plus benchmarks against numerically exact multiconfigurational time-dependent Hartree results on standard models.","status_note":"","title":"A consistent trajectory method for coupled electron-nuclear dynamics","topic_ref":"aa1669ae0dd7fb5df9048991b7b6472f6d13dde0228a4ba5521d38de86ed2a38"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"f93e2b5c1ca0cffff7e6f74d07e01d9574771c1102b2710e03955b40dfd4ad16","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"569e9395cdb9511afb215dcad55bc71f645330dcf2e20ea510a10bc7822617b8","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"L-NXB8aHGPo18HKEFwme8GpAJE6Y9gR_9D-lwOekAb3ZiQxOGXF7W3hnX6s5wZUSqUVprvtBlJz7owHXoy36AA"},"schema":"pubphys.envelope/1"},"record_hash":"f93e2b5c1ca0cffff7e6f74d07e01d9574771c1102b2710e03955b40dfd4ad16","leaf_index":882}