Simulated annealing method for molecular constants calculation: the electronic transition A²Σ⁺–X²Π of N₂O⁺ radical 000–000 and 001–001 band cases

Abstract

The Simulated Annealing (SA) method is here first adopted to retrieve the molecular constants used to fit wavenumbers into a model, from a vibrational band of the electronic transition A${}^2{\mathrm{\Sigma }}^{+}-X^2\mathrm{\Pi }$ of the N${}_2$O${}^{+}$ radical, 000–000, starting from a set of molecular constants obtained in a previous work, and varying their values within a range in order to mimic an error in each one parameter used. The SA calculations have been carried out following the proposal of Vanderbilt and Louie for performing a minimisation of an objective function where the parameters are continuous variables whose values can vary. Through SA, the 280 experimentally wavenumbers from the previous work were reduced using a Hamiltonian model and new molecular constants obtained. A comparison among the results obtained through a nonlinear deterministic model and the retrieved values obtained using the SA shows that the simulated annealing can be considered as a very strong method for molecular constants determination. Second, intending to test the SA method in a direct fit to obtain the molecular constants, the 142 wavenumbers from the 001–001 band A${}^2{\mathrm{\Sigma }}^{+}-X^2\mathrm{\Pi }$ electronic transition of the N${}_2$O${}^{+}$ were studied in this work and the molecular constants analysed.

GRAPHICAL ABSTRACT

Keywords:

• Molecular constants
• simulated annealing
• N${}_2$O${}^{+}$ radical
• nonlinear models

Acknowledgements

The authors would like to thank the Pró-Reitoria de Pós-Graduação, Pesquisa e Inovação of Universidade Federal Fluminense (PROPPI-UFF), the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for support. A. S. Martins would like to thanks the financial support of the FAPERJ funding agency by the grant E-26/110.318/2014.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

${}^{†}$ Parameter fixed in the calculations.

Additional information

Funding

The work was supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (309365/2014-7); Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro (E-26/110.318/2014); Pró-Reitoria de Pós-Graduação, Pesquisa e Inovação of Universidade Federal Fluminense (PROPPI-UFF).