### Abstract

Approaches related to graph theory are investigated which allow a better understanding and yield routes for systematic enlargement and improvement of experimental spectroscopic line lists of molecules. The proposed protocols are based on the fact that quantum mechanics builds, in a simple and natural way, large-scale, weighted, undirected graphs, whereby the vertices are discrete energy levels, the edges are transitions, and the weights are transition intensities. A small part of molecular quantum mechanical graphs can be probed experimentally via high-resolution spectroscopic techniques, while the complete graph encompassing the full line list information for a given molecule can be obtained through sophisticated variational nuclear motion computations. Both approaches yield what one may call spectroscopic networks (SNs). It is shown on the example of the HD^{16}O isotopologue of the water molecule that both the measured and the computed one-photon absorption SNs have a scale-free behavior with all of the usual consequences, including appearance of hubs, robustness, error tolerance, and the "small-world" property. For the complete computed "deterministic" network the scale-free property holds if a realistic intensity cut-off is employed during its build-up, thus introducing "stochasticity". The graph-theoretical view of molecular spectra offers several new ideas for improving the accuracy and robustness of the information systems containing high-resolution spectroscopic data.

Original language | English |
---|---|

Pages (from-to) | 99-103 |

Number of pages | 5 |

Journal | Journal of Molecular Spectroscopy |

Volume | 266 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 2011 |

### Fingerprint

### Keywords

- Graph theory
- HD O
- Quantum chemistry
- Spectroscopic network
- Spectroscopy

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Spectroscopy
- Atomic and Molecular Physics, and Optics

### Cite this

**Spectroscopic networks.** / Császár, A.; Furtenbacher, T.

Research output: Contribution to journal › Article

*Journal of Molecular Spectroscopy*, vol. 266, no. 2, pp. 99-103. https://doi.org/10.1016/j.jms.2011.03.031

}

TY - JOUR

T1 - Spectroscopic networks

AU - Császár, A.

AU - Furtenbacher, T.

PY - 2011/4

Y1 - 2011/4

N2 - Approaches related to graph theory are investigated which allow a better understanding and yield routes for systematic enlargement and improvement of experimental spectroscopic line lists of molecules. The proposed protocols are based on the fact that quantum mechanics builds, in a simple and natural way, large-scale, weighted, undirected graphs, whereby the vertices are discrete energy levels, the edges are transitions, and the weights are transition intensities. A small part of molecular quantum mechanical graphs can be probed experimentally via high-resolution spectroscopic techniques, while the complete graph encompassing the full line list information for a given molecule can be obtained through sophisticated variational nuclear motion computations. Both approaches yield what one may call spectroscopic networks (SNs). It is shown on the example of the HD16O isotopologue of the water molecule that both the measured and the computed one-photon absorption SNs have a scale-free behavior with all of the usual consequences, including appearance of hubs, robustness, error tolerance, and the "small-world" property. For the complete computed "deterministic" network the scale-free property holds if a realistic intensity cut-off is employed during its build-up, thus introducing "stochasticity". The graph-theoretical view of molecular spectra offers several new ideas for improving the accuracy and robustness of the information systems containing high-resolution spectroscopic data.

AB - Approaches related to graph theory are investigated which allow a better understanding and yield routes for systematic enlargement and improvement of experimental spectroscopic line lists of molecules. The proposed protocols are based on the fact that quantum mechanics builds, in a simple and natural way, large-scale, weighted, undirected graphs, whereby the vertices are discrete energy levels, the edges are transitions, and the weights are transition intensities. A small part of molecular quantum mechanical graphs can be probed experimentally via high-resolution spectroscopic techniques, while the complete graph encompassing the full line list information for a given molecule can be obtained through sophisticated variational nuclear motion computations. Both approaches yield what one may call spectroscopic networks (SNs). It is shown on the example of the HD16O isotopologue of the water molecule that both the measured and the computed one-photon absorption SNs have a scale-free behavior with all of the usual consequences, including appearance of hubs, robustness, error tolerance, and the "small-world" property. For the complete computed "deterministic" network the scale-free property holds if a realistic intensity cut-off is employed during its build-up, thus introducing "stochasticity". The graph-theoretical view of molecular spectra offers several new ideas for improving the accuracy and robustness of the information systems containing high-resolution spectroscopic data.

KW - Graph theory

KW - HD O

KW - Quantum chemistry

KW - Spectroscopic network

KW - Spectroscopy

UR - http://www.scopus.com/inward/record.url?scp=79955925130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955925130&partnerID=8YFLogxK

U2 - 10.1016/j.jms.2011.03.031

DO - 10.1016/j.jms.2011.03.031

M3 - Article

VL - 266

SP - 99

EP - 103

JO - Journal of Molecular Spectroscopy

JF - Journal of Molecular Spectroscopy

SN - 0022-2852

IS - 2

ER -