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

Abstract

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.

Theoretical Prediction of Structures, Vibrational Circular Dichroism, and Infrared Spectra of Chiral Be4B8 Cluster at Different Temperatures

“…These effects make beryllium-doped boron clusters interesting research objects. Particularly attractive are Be 6 B 11 − chiral helices, as reported by Gou et al [ 21 ], Yanez et al [ 18 ], and Garcia-Buelna et al [ 33 ], as a low-lying and fluxional isomer. Later, chemical bonding and the mechanism of formation studies of the beryllium-doped boron chiral cluster Be 6 B 10 2− and coaxial triple-layered Be 6 B 10 2− sandwich structure were reported [ 16 , 55 ].…”

“…Since molecular properties depend greatly on their geometry [ 32 , 33 ], boron clusters exhibit a large number of molecular properties that have potential applications in medicine [ 34 , 35 , 36 , 37 ], molecular motors [ 21 , 23 , 38 ], superhard materials [ 39 ], hydrogen storage [ 40 ], batteries [ 41 , 42 , 43 , 44 ], catalysis [ 45 ], and energy materials [ 46 ], among many others.…”

“…In these structures, chirality arises due to the formation of a boron helix. However, only a few theoretical studies have been carried out on vibrational circular dichroism (VCD) and infrared spectroscopy (IR) as a function of temperature in beryllium–boron clusters [ 33 , 60 ]. We emphasize that there are neither theoretical nor experimental studies of VCD/IR spectra in chiral Be 4 B 8 clusters, although VCD/IR spectra give insight into the geometrical structure [ 61 , 62 , 63 , 64 ].…”

“…IR frequencies are related to the second derivative of the potential energy and are useful in identifying transition states and computing thermodynamics through the vibrational partition function [ 33 , 76 , 77 ]. The structure of neutral boron clusters B 11 , B 16 , and B 17 was probed by IR [ 78 ].…”

“…The DFT VCD/IR spectra depend on the functional and basis set employed [ 63 ] and significantly on the lowest-energy achiral and chiral structures, so we need to efficiently sample the free energy surface to find the distribution of isomers at different temperatures [ 32 , 33 , 79 , 80 , 81 ]. A considerable change in the isomer distribution and the energetic separation among them are the first notable effects of temperature [ 33 ]. Useful materials work at finite temperatures; in those conditions, Gibbs free energy is minimized [ 82 ] and determines the putative global minimum at a given temperature [ 33 ], whereas the entropy of the atomic cluster is maximized [ 82 ].…”