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.

Lowest-energy structures, the distribution of isomers, and their molecular properties depend significantly on geometry and temperature. Total energy computations using DFT methodology are typically carried out at a temperature of zero K; thereby, entropic contributions to the total energy are neglected, even though functional materials work at finite temperatures. In the present study, the probability of the occurrence of one particular Be₄B₈ isomer at temperature T is estimated by employing Gibbs free energy computed within the framework of quantum statistical mechanics and nanothermodynamics. To identify a list of all possible low-energy chiral and achiral structures, an exhaustive and efficient exploration of the potential/free energy surfaces is carried out using a multi-level multistep global genetic algorithm search coupled with DFT. In addition, we discuss the energetic ordering of structures computed at the DFT level against single-point energy calculations at the CCSD(T) level of theory. The total VCD/IR spectra as a function of temperature are computed using each isomer’s probability of occurrence in a Boltzmann-weighted superposition of each isomer’s spectrum. Additionally, we present chemical bonding analysis using the adaptive natural density partitioning method in the chiral putative global minimum. The transition state structures and the enantiomer–enantiomer and enantiomer–achiral activation energies as a function of temperature evidence that a change from an endergonic to an exergonic type of reaction occurs at a temperature of 739 K.

In this study, we report the lowest energy structure of bare Cu₁₃ nanoclusters as a pair of enantiomers at room temperature. Moreover, we compute the enantiomerization energy for the interconversion from minus to plus structures in the chiral putative global minimum for temperatures ranging from 20 to 1300 K. Additionally, employing nanothermodynamics, we compute the probabilities of occurrence for each particular isomer as a function of temperature. To achieve that, we explore the free energy surface of the Cu₁₃ cluster, employing a genetic algorithm coupled with density functional theory. Moreover, we discuss the energetic ordering of isomers computed with various density functionals. Based on the computed thermal population, our results show that the chiral putative global minimum strongly dominates at room temperature.

The unfolded band structure and optical properties of Cu-doped KCl crystals were computed by first principles within the framework of density functional theory, implemented in the ABINIT software program, utilizing pseudopotential approximation and a plane-wave basis set. From a theoretical point of view, Cu substitution into pristine KCl crystals requires calculation by the supercell (SC) method. This procedure shrinks the Brillouin zone, resulting in a folded band structure that is difficult to interpret. To solve this problem and gain insight into the effect of copper ions (Cu⁺) on electronic properties, the band structure of SC KCl:Cu was unfolded to make a direct comparison with the band structure of the primitive cell (PC) of pristine KCl. To understand the effect of Cu substitution on optical absorption, we calculated the imaginary part of the dielectric function of KCl:Cu through a sum-over-states formalism and broke it down into different band contributions by partially making an iterated cumulative sum (ICS) of selected valence and conduction bands. Consequently, we identified those interband transitions that give rise to the absorption peaks due to the Cu⁺ ion. These transitions involve valence and conduction bands formed by the Cu-3d and Cu-4s electronic states.

The first step in comprehending the properties of Au₁₀ clusters is understanding the lowest energy structure at low and high temperatures. Functional materials operate at finite temperatures; however, energy computations employing density functional theory (DFT) methodology are typically carried out at zero temperature, leaving many properties unexplored. This study explored the potential and free energy surface of the neutral Au₁₀ nanocluster at a finite temperature, employing a genetic algorithm coupled with DFT and nanothermodynamics. Furthermore, we computed the thermal population and infrared Boltzmann spectrum at a finite temperature and compared it with the validated experimental data. Moreover, we performed the chemical bonding analysis using the quantum theory of atoms in molecules (QTAIM) approach and the adaptive natural density partitioning method (AdNDP) to shed light on the bonding of Au atoms in the low-energy structures. In the calculations, we take into consideration the relativistic effects through the zero-order regular approximation (ZORA), the dispersion through Grimme’s dispersion with Becke–Johnson damping (D3BJ), and we employed nanothermodynamics to consider temperature contributions. Small Au clusters prefer the planar shape, and the transition from 2D to 3D could take place at atomic clusters consisting of ten atoms, which could be affected by temperature, relativistic effects, and dispersion. We analyzed the energetic ordering of structures calculated using DFT with ZORA and single-point energy calculation employing the DLPNO-CCSD(T) methodology. Our findings indicate that the planar lowest energy structure computed with DFT is not the lowest energy structure computed at the DLPN0-CCSD(T) level of theory. The computed thermal population indicates that the 2D elongated hexagon configuration strongly dominates at a temperature range of 50–800 K. Based on the thermal population, at a temperature of 100 K, the computed IR Boltzmann spectrum agrees with the experimental IR spectrum. The chemical bonding analysis on the lowest energy structure indicates that the cluster bond is due only to the electrons of the 6 s orbital, and the Au d orbitals do not participate in the bonding of this system.