# General formulation of vibronic spectroscopy in internal coordinates.
> 内部座標を用いたビブロニックスペクトロスコピーの一般的定式化


## Abstract

A computational platform integrating time-independent and time-dependent vibronic calculations at the harmonic level was extended to accommodate internal coordinate sets. Analytical first and second derivatives of internal coordinates with respect to Cartesian coordinates enable both vertical and adiabatic models, including mode mixing and Herzberg-Teller contributions. Non-redundant coordinate sets are generated automatically from a bond-order-based molecular topology, covering stretching, bending, torsion, and out-of-plane coordinates, allowing treatment of systems such as intermolecular hydrogen bridges. Case studies demonstrate that Cartesian and internal coordinates yield comparable results for semi-rigid systems, whereas delocalized internal coordinates outperform Cartesian ones for flexible systems or those undergoing substantial geometry changes during electronic transitions.

## Bibliographic

- **Authors**: Baiardi A, Bloino J, Barone V
- **Journal**: J Chem Phys
- **Year**: 2016 (2016-02-28)
- **PMID**: [26931688](https://pubmed.ncbi.nlm.nih.gov/26931688/)
- **DOI**: [10.1063/1.4942165](https://doi.org/10.1063/1.4942165)
- **PMC**: [PMC5732572](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5732572/)
- **Study type**: other
- **Delivery route**: not specified
- **Effect reported**: not assessed

## Delivery context

The delivery route is not clearly identifiable from this paper. For hydrogen intake, inhalation is the most efficient route; inhalation, however, carries explosion risk (empirical LFL of 10%; high-concentration devices are not recommended).

## Safety notes

The delivery route is not clearly identifiable from this paper. For hydrogen intake, inhalation is the most efficient route; inhalation, however, carries explosion risk (empirical LFL of 10%; high-concentration devices are not recommended).

See also:
- [Inhalation concentration and LFL / UFL](https://h2-papers.org/en/safety-notes/inhalation-concentration)
- [Consumer Affairs Agency accident cases](https://h2-papers.org/en/safety-notes/accident-cases)

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> **Cite as**: H2 Papers — PMID 26931688. https://h2-papers.org/en/papers/26931688
> **Source**: PubMed PMID [26931688](https://pubmed.ncbi.nlm.nih.gov/26931688/)