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Article

Exploration of Free Energy Surface and Thermal Effects on Relative Population and Infrared Spectrum of the Be6B11 Fluxional Cluster

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Departamento de Investigación en Polímeros y Materiales, Edificio 3G, Universidad de Sonora, Blvd. Luis Encinas y Rosales S/N, Centro, Hermosillo 83000, Mexico
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Departamento de Investigación en Fisica, Edifcio 3M, Universidad de Sonora, Blvd. Luis Encinas y Rosales S/N, Centro, Hermosillo 83000, Mexico
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Unidad Académica de Ciencias Químicas, Área de Ciencias de la Salud, Universidad Autónoma de Zacatecas, Km. 6 Carretera Zacatecas-Guadalajara s/n, Ejido La Escondida, Zacatecas 98160, Mexico
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Departamento de Fundamentos del Conocimiento, Centro Universitario del Norte, Universidad de Guadalajara, Carretera Federal No. 23, Km. 191, Colotlán 46200, Mexico
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Departamento de Ciencias Quimico Biologicas, Edifico 5A, Universidad de Sonora, Blvd. Luis Encinas y Rosales S/N, Centro, Hermosillo 83000, Mexico
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Centro de Investigaciones en Óptica, A.C., León 37150, Mexico
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Author to whom correspondence should be addressed.
Materials 2021, 14(1), 112; https://doi.org/10.3390/ma14010112
Received: 27 November 2020 / Revised: 23 December 2020 / Accepted: 24 December 2020 / Published: 29 December 2020
(This article belongs to the Section Materials Chemistry)
The starting point to understanding cluster properties is the putative global minimum and all the nearby local energy minima; however, locating them is computationally expensive and difficult. The relative populations and spectroscopic properties that are a function of temperature can be approximately computed by employing statistical thermodynamics. Here, we investigate entropy-driven isomers distribution on Be6B11 clusters and the effect of temperature on their infrared spectroscopy and relative populations. We identify the vibration modes possessed by the cluster that significantly contribute to the zero-point energy. A couple of steps are considered for computing the temperature-dependent relative population: First, using a genetic algorithm coupled to density functional theory, we performed an extensive and systematic exploration of the potential/free energy surface of Be6B11 clusters to locate the putative global minimum and elucidate the low-energy structures. Second, the relative populations’ temperature effects are determined by considering the thermodynamic properties and Boltzmann factors. The temperature-dependent relative populations show that the entropies and temperature are essential for determining the global minimum. We compute the temperature-dependent total infrared spectra employing the Boltzmann factor weighted sums of each isomer’s infrared spectrum and find that at finite temperature, the total infrared spectrum is composed of an admixture of infrared spectra that corresponds to the spectra of the lowest-energy structure and its isomers located at higher energies. The methodology and results describe the thermal effects in the relative population and the infrared spectra. View Full-Text
Keywords: global minimum; infrared spectrum; boron cluster; fluxional; density functional theory; temperature; Boltzmann factors; Gibbs free energy; entropy; Grimme’s approach (DFT-D3); IR spectra global minimum; infrared spectrum; boron cluster; fluxional; density functional theory; temperature; Boltzmann factors; Gibbs free energy; entropy; Grimme’s approach (DFT-D3); IR spectra
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MDPI and ACS Style

Buelna-Garcia, C.E.; Cabellos, J.L.; Quiroz-Castillo, J.M.; Martinez-Guajardo, G.; Castillo-Quevedo, C.; de-Leon-Flores, A.; Anzueto-Sanchez, G.; Martin-del-Campo-Solis, M.F. Exploration of Free Energy Surface and Thermal Effects on Relative Population and Infrared Spectrum of the Be6B11 Fluxional Cluster. Materials 2021, 14, 112. https://doi.org/10.3390/ma14010112

AMA Style

Buelna-Garcia CE, Cabellos JL, Quiroz-Castillo JM, Martinez-Guajardo G, Castillo-Quevedo C, de-Leon-Flores A, Anzueto-Sanchez G, Martin-del-Campo-Solis MF. Exploration of Free Energy Surface and Thermal Effects on Relative Population and Infrared Spectrum of the Be6B11 Fluxional Cluster. Materials. 2021; 14(1):112. https://doi.org/10.3390/ma14010112

Chicago/Turabian Style

Buelna-Garcia, Carlos E.; Cabellos, José L.; Quiroz-Castillo, Jesus M.; Martinez-Guajardo, Gerardo; Castillo-Quevedo, Cesar; de-Leon-Flores, Aned; Anzueto-Sanchez, Gilberto; Martin-del-Campo-Solis, Martha F. 2021. "Exploration of Free Energy Surface and Thermal Effects on Relative Population and Infrared Spectrum of the Be6B11 Fluxional Cluster" Materials 14, no. 1: 112. https://doi.org/10.3390/ma14010112

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