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Understanding the properties of Au$_{10}$ clusters entails identifying the lowest energy structure at cold and warm temperatures. While functional materials operate at finite temperatures, energy computations using density functional theory are typically performed at zero temperature, resulting in unexplored properties. Our study undertook an exploration of the potential and free energy surface of the neutral Au$_{10}$ nanocluster at finite temperatures by employing a genetic algorithm combined with density functional theory and nanothermodynamics. We computed the thermal population and infrared Boltzmann spectrum at a finite temperature, aligning the results with validated experimental data. The Zero-Order Regular Approximation (ZORA) gave consideration to relativistic effects, and dispersion was incorporated using Grimme's dispersion D3BJ with Becke-Johnson damping. Moreover, nanothermodynamics was utilized to account for temperature contributions. The computed thermal population strongly supports the dominance of the 2D elongated hexagon configuration within a temperature range of 50 to 800 K. Importantly, at a temperature of 100 K, the calculated IR Boltzmann spectrum aligns with the experimental IR spectrum. Lastly, the chemical bonding analysis on the lowest energy structure indicates a closed-shell Au-Au interaction with a weak or partially covalent character., Comment: 5 figures

The UV-visible and IR properties of the Cu$_{38}$ nanocluster depend to a great extent on the temperature. Density functional theory and nanothermodynamics can be combined to compute the geometrical optimization of isomers and their spectroscopic properties in an approximate manner. In this article, we investigate entropy-driven isomer distributions of Cu$_{38}$ clusters and the effect of temperature on their UV-visible and IR spectra. An extensive, systematic global search is performed on the potential and free energy surfaces of Cu38 using a two-stage strategy to identify the lowest-energy structure and its low-energy neighbors. The effects of temperature on the UV and IR spectra are considered via Boltzmann probability. The computed UV-visible and IR spectrum of each isomer is multiplied by its corresponding Boltzmann weight at finite temperature. Then, they are summed together to produce a final temperature-dependent, Boltzmann-weighted UV-visible and IR spectrum. Additionally, Molecular Dynamics simulation of the Cu$_{38}$ nanocluster was performed to gain insight into the system dynamics and make a three-dimensional movie of the system with atomistic resolution. Our results show the thermal populations at the absolute temperature of Cu38 cluster, and the disordered structure that dominates at high temperatures., Comment: 41 pages, 6 figures

This study reports the lowest energy structure of bare Cu$_{13}$ nanoclusters as a pair of enantiomers for temperatures ranging from 20 to 1200 K. Moreover, we compute the enantiomerization energy for the interconversion from $\mathcal{M}$ to $\mathcal{P}$ structures in the chiral putative global minimum for temperatures ranging from 20 to 1300 K. Additionally, employing statistical thermodynamics and nanothermodynamics, we compute the Boltzmann Probability for each particular isomer as a function of temperature. To achieve that, we explore the free energy surface of the Cu$_{13}$ cluster, employing a genetic algorithm coupled with density functional theory and statistical thermodynamics. Moreover, we discuss the energetic ordering of structures computed at the DFT level and compared to high level DLPNO-CCSD(T1) reference energies, and we present chemical bonding analysis using the AdNDP method in the chiral putative global minimum. Based on the computed relative abundances, our results show that the chiral putative global minimum strongly dominates for temperatures ranging from 20 to 1100 K., Comment: 10 pages, 6 figures

The lowest-energy structure, distribution of isomers, and their molecular properties depend significantly on the geometry and temperature. The total energy computations under DFT methodology are typically carried out at zero temperature; thereby, entropic contributions to total energy are neglected, even though functional materials work at finite temperature. In the present study, the probability of occurrence of one particular Be$_4$B$_8$ isomer at temperature T is estimated within the framework of quantum statistical mechanics and nanothermodynamics. To locate a list of all possible low-energy chiral and achiral structures, an exhaustive and efficient exploration of the potential/free energy surface is done by employing a multilevel multistep global genetic algorithm search coupled to DFT. Moreover, 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 computed VCD/IR spectrum of each isomer is multiplied by their corresponding Boltzmann weight at temperature T; then, they are summed together to produce a final Boltzmann weighted 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., Comment: 49 pages, 12 figures

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 challenging due to a combinatorial explosion problem. The relative populations and spectroscopic properties of a molecule that are a function of temperature can be approximately computed by employing statistical thermodynamics. Here, we investigate temperature-entropy-driven isomers distribution on Be$_6$B$_{11}^{-}$ fluxional cluster 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 Be$_6$B$_{11}^{-}$ cluster 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 spectrum 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.

We computed the optical properties and the folded and unfolded band structure of Cu-doped KCl crystals. The calculations use the plane-wave pseudo-potential approach implemented in the ABINIT electronic structure package within the first-principles density-functional theory framework. Cu substitution into pristine KCl crystals requires calculation by the supercell (SC) method from a theoretical perspective. 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 cuprous ion (Cu+) on electronic properties; We unfolded the band structure of SC KCl:Cu to directly compare 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. As a result, we identified those interband transitions that give rise to the absorption peaks due to the Cu ion. These transitions include valence and conduction bands formed by the Cu-3d and Cu-4s electronic states. To investigate the effects of doping position, we consider different doping positions, where the Cu dopant occupies all the substitutional sites replacing host K cations. Our results indicate that the doping position's effects give rise to two octahedral shapes in the geometric structure. The distorted-twisted octahedral square bipyramidal geometric-shape induces a difference in the crystal field splitting energy compared to that of the perfect octahedral square bipyramidal geometric-shape., Comment: 39 total pages, 30 article, and 9 references. There are 19 figures done with gnuplot high-quality

A full band-structure ab initio calculation of the degree of spin polarization (DSP) in stressed bulk Si and bulk GaAs is reported. For Si, we found that compressive stress causes the DSP signal peak to decrease slightly in magnitude and to shift to higher energies.