Exploration of Free Energy Surface of the Au10 Nanocluster at Finite Temperature.

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.

Correction: Structure effects of Pt15 clusters for the oxygen reduction reaction: first-principles calculations.

Correction for 'Structure effects of Pt15 clusters for the oxygen reduction reaction: first-principles calculations' by Peter L. Rodríguez-Kessler et al., Phys. Chem. Chem. Phys., 2023, https://doi.org/10.1039/d2cp05188e.

Structure effects of Pt15 clusters for the oxygen reduction reaction: first-principles calculations.

In the present work, the lowest energy structures and electronic properties of Pt15 clusters are investigated using molecular dynamics simulations. The results showed that the most stable configuration is a capped pyramidal structure, which is 0.8 kal mol-1 lower in energy than a layered structure previously reported [V. Kumar and Y. Kawazoe, Evolution of Atomic and Electronic Structure of Pt Clusters: Planar, Layered, Pyramidal, Cage, Cubic, and Octahedral Growth, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 77, 205418.]. The result is further confirmed by using both the PW91/cc-pVDZ-PP and PBE/PW approaches including the other representative isomers for Pt15. Due to the interesting structure arrangements found, we have investigated the catalytic activities for the oxygen reduction reaction. We found that the most stable Pt15 clusters are plausible catalyts for the ORR according to their interaction with oxygen species, which is consistent with experiments of Pt clusters with atomicity below 20. The results of the structure, electronic, adsorption and vibrational properties of the clusters are provided.

Relative Populations and IR Spectra of Cu38 Cluster at Finite Temperature Based on DFT and Statistical Thermodynamics Calculations.

The relative populations of Cu38 isomers 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 Cu38 clusters and the effect of temperature on their 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 populations and IR spectra are considered via Boltzmann factors. The computed 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 spectrum. Our results show that the disordered structure dominates at high temperatures and the overall Boltzmann-weighted spectrum is composed of a mixture of spectra from several individual isomers.

Effects of Temperature on Enantiomerization Energy and Distribution of Isomers in the Chiral Cu13 Cluster.

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.

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

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.

Cu-Doped KCl Unfolded Band Structure and Optical Properties Studied by DFT Calculations.

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.

Exploration of Free Energy Surface and Thermal Effects on Relative Population and Infrared Spectrum of the Be6B11- Flux-Ional Cluster.

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.

Structure and Bonding in CE5- (E=Al-Tl) Clusters: Planar Tetracoordinate Carbon versus Pentacoordinate Carbon.

The structure, bonding, and stability of clusters with the empirical formula CE5- (E=Al-Tl) have been analyzed by means of high-level computations. The results indicate that, whereas aluminum and gallium clusters have C2v structures with a planar tetracoordinate carbon (ptC), their heavier homologues prefer three-dimensional C4v forms with a pentacoordinate carbon center over the ptC one. The reason for such a preference is a delicate balance between the interaction energy of the fifth E atom with CE4 and the distortion energy. Moreover, bonding analysis shows that the ptC systems can be better described as CE4- , with 17-valence electrons interacting with E. The ptC core in these systems exhibits double aromatic (both σ and π) behavior, but the σ contribution is dominating.

Revisiting the racemization mechanism of helicenes.

Herein we propose a general mechanism for the racemization of [n]helicenes up to n = 24. It is a concerted process for n = 4-7, but a multi-step mechanism is followed for n≥ 8, involving 2n- 14 intermediates. The changes in the barriers are a delicate consequence of the steric hindrance and the π-interactions.

Does H4SO5 exist?

The possible existence of H4SO5 in aqueous sulfuric acid is analyzed in detail. For bare H4SO5, the computed free energy barrier for the exergonic transformation of H4SO5 into the H2SO4H2O complex is only 3.8 kcal mol-1. The presence of water or sulfuric acid catalyzes the dehydration to such an extent that it becomes almost a barrierless process. In the gas phase, dehydration of H4SO5 is an autocatalytic reaction as the water molecule produced by the decomposition of one H4SO5 molecule induces further dissociation. Thus, in solution, the surrounding water molecules make the para-sulfuric acid a very vulnerable species to exist. The simulated Raman spectra also corroborate the absence of H4SO5 in solution.

Dynamical behavior of boron clusters.

Several of the lowest energy structures of small and medium sized boron clusters are two-dimensional systems made up of a pair of concentric rings. In some cases, the barriers to the rotation of one of those rings relative to the other are remarkably low. We find that a combination of electronic and geometrical factors, including apparently the relative sizes and symmetries of the inner and outer rings, are decisive for the diminished barriers to in-plane rotation in these two dimensional clusters. A sufficiently large outer ring is important; for instance, expansion of the outer ring by a single atom may reduce the barrier significantly. A crucial factor for an apparent rotation is that the σ-skeleton of the individual rings remains essentially intact during the rotation. Finally, the transition state for the rotation of the inner ring comprises the transformation of a square into a diamond, which may be linked to a mechanism suggested decades ago for the isomerization of carboranes and boranes.

10-π-Electron arenes à la carte: structure and bonding of the [E-(CnHn)-E](n-6) (E = Ca, Sr, Ba; n = 6-8) complexes.

In this paper, we provide solid evidence to show that among an overwhelming structural diversity, alkaline earth metals (Ca, Sr, Ba) have the ability to form inverted sandwich compounds with C6H6, C7H7(+), and C8H8(2+) of Dnh symmetry and general formula [E-(CnHn)-E](n-6) (n = 6-8) with planar 10-π-electron aromatic cores by virtue of transferring two electrons per metal atom to the ring. However, the origin of the orbital interaction between the metals and the carbon ring is quite different; while [E-(C6H6)-E] complexes are dominated by δ-interactions, both π- and δ-interactions are important in [E-(C7H7)-E](+) and [E-(C8H8)-E](2+) complexes.

Nonclassical 21-Homododecahedryl Cation Rearrangement Revisited.

The degenerate rearrangement in the 21-homododecahedryl cation (1) has been studied via density functional theory computations and Born-Oppenheimer Molecular Dynamics simulations. Compound 1 can be described as a highly fluxional hyperconjugated carbocation. Complete scrambling of 1 can be achieved by the combination of two unveiled barrierless processes. The first one is a "rotation" of one of the six-membered rings via a 0.8 kcal·mol(-1) barrier, and the second one is a slower interconvertion between two hyperconjomers via an out-of-plane methine bending (ΔG(⧧) = 4.0 kcal·mol(-1)).

How strong are the metallocene-metallocene interactions? Cases of ferrocene, ruthenocene, and osmocene.

An exhaustive exploration of the potential energy surfaces of ferrocene, ruthenocene and osmocene dimers has been performed. Our computations involving dispersion show that only four different isomers are present in each metallocene dimer. The collective action of small interaction energies of dispersive nature leads to a dissociation energy of 7.5 kcal mol(-1) for the ferrocene dimer. Dispersion has strong effects on the geometrical parameters, reducing the M···M distances by almost 1 Å. Our results also reveal that inclusion of entropic factors modifies the relative stability of the complexes. The nature of bonding is examined using the energy decomposition analysis and the non-covalent interaction index. Both analyses indicate that dispersion is the major contributing factor in stabilizing a metallocene dimer.

Intramolecular structure and dynamics of mequinol and guaiacol in the gas phase: Rotationally resolved electronic spectra of their S1 states.

The molecular structures of guaiacol (2-methoxyphenol) and mequinol (4-methoxyphenol) have been studied using high resolution electronic spectroscopy in a molecular beam and contrasted with ab initio computations. Mequinol exhibits two low frequency bands that have been assigned to electronic origins of two possible conformers of the molecule, trans and cis. Guaiacol also shows low frequency bands, but in this case, the bands have been assigned to the electronic origin and vibrational modes of a single conformer of the isolated molecule. A detailed study of these bands indicates that guaiacol has a vibrationally averaged planar structure in the ground state, but it is distorted along both in-plane and out-of-plane coordinates in the first electronically excited state. An intramolecular hydrogen bond involving the adjacent -OH and -OCH3 groups plays a major role in these dynamics.

Potential energy surfaces of WC6 clusters in different spin states.

Stochastic explorations of the structural possibilities of neutral WC6 clusters in several spin states lead to very rich and complex potential energy surfaces, with geometries quite different from those of pure carbon clusters at the PBE0/def2-TZVP level. The global minimum is predicted to be a triplet-state semicyclic C6 conformation having every carbon in direct coordination to the W atom. Interaction energies are comparable to those of C7 clusters, revealing very strong W-C bonding. Our results suggest that C-C interactions in the clusters should be considered as intermediate between single and double bonds.