The discovery of unexpected isomers in sodium heptamers by Born–Oppenheimer molecular dynamics

Active-learning for global optimization of Ni-Ceria nanoparticles: The case of Ce4-xNixO8- x (x = 1, 2, 3)

Ni-CeO2 nanoparticles (NPs) are promising nanocatalysts for water splitting and water gas shift reactions due to the ability of ceria to temporarily donate oxygen to the catalytic reaction and accept oxygen after the reaction is completed. Therefore, elucidating how different properties of the Ni-Ceria NPs relate to the activity and selectivity of the catalytic reaction, is of crucial importance for the development of novel catalysts. In this work the active learning (AL) method based on machine learning regression and its uncertainty is used for the global optimization of Ce(4-x)NixO(8-x) (x = 1, 2, 3) nanoparticles, employing density functional theory calculations. Additionally, further investigation of the NPs by mass-scaled parallel-tempering Born-Oppenheimer molecular dynamics resulted in the same putative global minimum structures found by AL, demonstrating the robustness of our AL search to learn from small datasets and assist in the global optimization of complex electronic structure systems.

Underlying mechanisms of gold nanoalloys stabilization

Gold nanoclusters have attracted significant attention due to their unique physical-chemical properties, which can be tuned by alloying with elements such as Cu, Pd, Ag, and Pt to design materials for various applications. Although Au-nanoalloys have promising applications, our atomistic understanding of the descriptors that drive their stability is far from satisfactory. To address this problem, we considered 55-atom model nanoalloys that have been synthesized by experimental techniques. Here, we combined data mining techniques for creating a large sample of representative configurations, density functional theory for performing total energy optimizations, and Spearman correlation analyses to identify the most important descriptors. Among our results, we have identified trends in core-shell formation in the AuCu and AuPd systems and an onion-like design in the AuAg system, characterized by the aggregation of gold atoms on nanocluster surfaces. These features are explained by Au's surface energy, packing efficiency, and charge transfer mechanisms, which are enhanced by the alloys' preference for adopting the structure of the alloying metal rather than the low-symmetry one presented by Au55. These generalizations provide insights into the interplay between electronic and structural properties in gold nanoalloys, contributing to the understanding of their stabilization mechanisms and potential applications in various fields.

On the energetic and magnetic stability of neutral and charged lithium clusters doped with one and two yttrium atoms

DFT calculations were performed to study the effect on energetic and magnetic stability when clusters with up to 24 lithium atoms were doped with one and two atoms of yttrium. In this, the effect of the charge was considered. As a result, some stable structures were identified as possible magnetic superatoms, among them, the YLi₁₂⁺ cluster with an icosahedron geometry with a spin magnetic moment of 4 bohr magnetons. The participation of yttrium in the electron density of the unpaired electrons providing magnetism in clusters was corroborated at the level of a density of states (DOS) calculation and a spin density calculation. In particular, in the Y₂Li₁₂⁺ superatom, it was found that the encapsulated yttrium atom participates with 35.02% and the second yttrium atom with 15.04%. These percentages, with a contribution from p orbitals, but to a greater extent by d orbitals. The complementation to these percentages is due to the participation of the s and p orbitals of the lithium atoms. In general, doping with a second yttrium atom allowed to obtain a greater amount of high magnetic moments, and considering charged clusters allowed to obtain also high magnetic moments.

A Practical Algorithm to Solve the Near-Congruence Problem for Rigid Molecules and Clusters

We present an improved algorithm to solve the near-congruence problem for rigid molecules and clusters based on the iterative application of assignment and alignment steps with biased Euclidean costs. The algorithm is formulated as a quasi-local optimization procedure with each optimization step involving a linear assignment (LAP) and a singular value decomposition (SVD). The efficiency of the algorithm is increased by up to 5 orders of magnitude with respect to the original unbiased noniterative method and can be applied to systems with hundreds or thousands of atoms, outperforming all state-of-the-art methods published so far in the literature. The Fortran implementation of the algorithm is available as an open source library (https://github.com/qcuaeh/molalignlib) and is suitable to be used in global optimization methods for the identification of local minima or basins.

Assessment of Simultaneous Global Optimization of Geometry and Total Spin of Small Iron Clusters

In this work, simultaneous global optimization of geometry and total spin of small iron clusters Fe_n (3 ≤ n ≤ 40) is assessed using Simulated Annealing (SA) simulations with forces calculated at the DFT-based Tight-Binding (DFTB) level of theory. In order to optimize the total spin, the occupancies of α and β densities were allowed to relax at each SA step, resulting in a continuous variation of the total spin along the trajectory. The behavior and performance of the procedure were investigated running two series of 10 independent "long" molecular dynamics simulations and one series of 100 independent "short" simulations. Cluster structures optimized with the assessed methodology reproduced geometries and magnetic moments reported in a previous work very well where multiple fixed total spin and geometries of iron clusters were individually probed, and for some clusters, more stable global minima were found. Other properties such as binding energies and second energy differences were also calculated in order to compare with previously reported theoretical and experimental values. The few mismatches were found to be driven by quasi degenerated ground states with different magnetic moments or by states with crossing free energies at high temperatures.

First-principle study of the structures, growth pattern, and properties of (Pt3Cu)n, n = 1-9, clusters

In this work, a first-principles systematic study of (Pt₃Cu)_n, n = 1-9, clusters was performed employing the linear combination of Gaussian-type orbital auxiliary density functional theory approach. The growth of the clusters has been achieved by increasing the previous cluster by one Pt₃Cu unit at a time. To explore in detail the potential energy surface of these clusters, initial structures were obtained from Born-Oppenheimer molecular dynamics trajectories generated at different temperatures and spin multiplicities. For each cluster size, several dozens of structures were optimized without any constraints. The most stable structures were characterized by frequency analysis calculations. This study demonstrates that the obtained most stable structures prefer low spin multiplicities. To gain insight into the growing pattern of these systems, average bond lengths were calculated for the lowest stable structures. This work reveals that the Cu atoms prefer to be together and to localize inside the cluster structures. Moreover, these systems tend to form octahedra moieties in the size range of n going from 4 to 9 Pt₃Cu units. Magnetic moment per atom and spin density plots were obtained for the neutral, cationic, and anionic ground state structures. Dissociation energies, ionization potential, and electron affinity were calculated, too. The dissociation energy and the electron affinity increase as the number of Pt₃Cu units grows, whereas the ionization potential decreases.

Reliability of semiempirical and DFTB methods for the global optimization of the structures of nanoclusters

In this work, we explore the possibility of using computationally inexpensive electronic structure methods, such as semiempirical and DFTB calculations, for the search of the global minimum (GM) structure of chemical systems. The basic prerequisite that these inexpensive methods will need to fulfill is that their lowest energy structures can be used as starting point for a subsequent local optimization at a benchmark level that will yield its GM. If this is possible, one could bypass the global optimization at the expensive method, which is currently impossible except for very small molecules. Specifically, we test our methods with clusters of second row elements including systems of several bonding types, such as alkali, metal, and covalent clusters. The results reveal that the DFTB3 method yields reasonable results and is a potential candidate for this type of applications. Even though the DFTB2 approach using standard parameters is proven to yield poor results, we show that a re-parametrization of only its repulsive part is enough to achieve excellent results, even when applied to larger systems outside the training set.

A method for predicting basins in the global optimization of nanoclusters with applications to AlxCuy alloys

The problem of obtaining the geometrical configuration of a molecule that minimizes its potential energy is a very complicated one for a series of applications, ranging from determining the structure of biological macromolecules to nanoclusters of atoms. Global optimization tools are available for this task, and many of them are based in performing successive local optimizations, where the starting geometries for these steps are determined by an intelligent algorithm. Here we develop a method to save computing time in the optimization of nanoclusters by predicting if a given minimum has been previously visited during local optimization steps. Our application to Cu-Al nanoalloys indicates that it is possible to save a substantial amount of computational cost. The application also reveals new promising Al_xCu_y clusters and explain their stabilities in terms of the jellium model.

Hybrid ADFT Study of the C104 and C106 IPR Isomers

This work presents a hybrid auxiliary density functional theory (ADFT) study of the neutral and hexaanionic C₁₀₄ and C₁₀₆ fullerenes with the aim to determine their ground state structures. To this end, all C₁₀₄ and C₁₀₆ fullerene structures that obey the isolated pentagon rule (IPR) were optimized with the Perdew-Burke-Ernzerhof generalized gradient approximation followed by a single-point energy calculation with the PBE0 hybrid functional. Our studies show that this composite approach yields relative energies of giant fullerenes that are accurate to around 1 kcal/mol. As a result, the ground states of C₁₀₄, C₁₀₄^6-, and C₁₀₆^6- can be assigned to the isomers 234:C_s, 821:D₂, and 891:C_s, respectively. On the other hand, the energetically lowest lying IPR isomers of C₁₀₆, 331:C_s, 1194:C₂, 534:C₁ are separated by less than 1 kcal/mol which makes an unequivocal ground state assignment by hybrid DFT methods impossible. To guide future experiments, we also report the simulated IR and Raman spectra of the most stable neutral and hexaanionic C₁₀₄ and C₁₀₆ fullerenes.

Molecular Simulations with in-deMon2k QM/MM, a Tutorial-Review

deMon2k is a readily available program specialized in Density Functional Theory (DFT) simulations within the framework of Auxiliary DFT. This article is intended as a tutorial-review of the capabilities of the program for molecular simulations involving ground and excited electronic states. The program implements an additive QM/MM (quantum mechanics/molecular mechanics) module relying either on non-polarizable or polarizable force fields. QM/MM methodologies available in deMon2k include ground-state geometry optimizations, ground-state Born-Oppenheimer molecular dynamics simulations, Ehrenfest non-adiabatic molecular dynamics simulations, and attosecond electron dynamics. In addition several electric and magnetic properties can be computed with QM/MM. We review the framework implemented in the program, including the most recently implemented options (link atoms, implicit continuum for remote environments, metadynamics, etc.), together with six applicative examples. The applications involve (i) a reactivity study of a cyclic organic molecule in water; (ii) the establishment of free-energy profiles for nucleophilic-substitution reactions by the umbrella sampling method; (iii) the construction of two-dimensional free energy maps by metadynamics simulations; (iv) the simulation of UV-visible absorption spectra of a solvated chromophore molecule; (v) the simulation of a free energy profile for an electron transfer reaction within Marcus theory; and (vi) the simulation of fragmentation of a peptide after collision with a high-energy proton.

Magnesium oxide clusters as promising candidates for hydrogen storage

A magnesium oxide candidate for hydrogen storage is identified through Born–Oppenheimer molecular dynamics.

Exploring the Structure, Energetic, and Magnetic Properties of Neutral Small Lithium Clusters Doped with Yttrium: Supermagnetic Atom Research

Density functional theory calculations based on magnetic and energetic stability criteria were performed to study a series of yttrium-doped lithium neutral clusters. A relativistic approximation was employed to properly describe the energy and multiplicity of the given clusters' fundamental states. The interaction of the 4d-Y atomic orbitals with the sp-Li states had an important role in the magnetic and energetic behavior of the selected systems. The spin density was concentrated over the yttrium atom regardless of the size of the cluster. Li7Y is a new stable superatom due to its enhanced magnetic properties.

Accuracy of auxiliary density functional theory hybrid calculations for activation and reaction enthalpies of pericyclic reactions

Auxiliary density functional theory (ADFT) hybrid calculations are based on the variational fitting of the Coulomb and Fock potential and, therefore, are free of four-center electron repulsion integrals. So far, ADFT hybrid calculations have been validated successfully for standard enthalpies of formation. In this work the accuracy of ADFT hybrid calculations for the description of pericyclic reactions was quantitatively validated at the B3LYP/6-31G*/GEN-A2* level of theory. Our comparison with conventional Kohn-Sham density functional theory (DFT) results shows that the DFT and ADFT activation and reaction enthalpies are practically indistinguishable. A systematic study of various functionals (PBE, B3LYP, PBE0, CAMB3LYP, CAMPBE0 and HSE06) and basis sets (6-31G*, DZVP-GGA and aug-cc-pVXZ; X = D, T and Q) revealed that the ADFT HSE06/aug-cc-pVTZ/GEN-A2* level of theory yields best balanced accuracy for the activation and reaction enthalpies of the studied pericyclic reactions. With the successfully validate ADFT composite approach consisting of PBE/DZVP-GGA/GEN-A2* structure and transition state optimizations and single-point HSE06/aug-cc-pVTZ/GEN-A2* energy calculations, an accurate, reliable and efficient computational approach for the study of pericyclic reactions in systems at the nanometer scale is proposed.

ArbAlign: A Tool for Optimal Alignment of Arbitrarily Ordered Isomers Using the Kuhn-Munkres Algorithm

When assessing the similarity between two isomers whose atoms are ordered identically, one typically translates and rotates their Cartesian coordinates for best alignment and computes the pairwise root-mean-square distance (RMSD). However, if the atoms are ordered differently or the molecular axes are switched, it is necessary to find the best ordering of the atoms and check for optimal axes before calculating a meaningful pairwise RMSD. The factorial scaling of finding the best ordering by looking at all permutations is too expensive for any system with more than ten atoms. We report use of the Kuhn-Munkres matching algorithm to reduce the cost of finding the best ordering from factorial to polynomial scaling. That allows the application of this scheme to any arbitrary system efficiently. Its performance is demonstrated for a range of molecular clusters as well as rigid systems. The largely standalone tool is freely available for download and distribution under the GNU General Public License v3.0 (GNU_GPL_v3) agreement. An online implementation is also provided via a web server ( http://www.arbalign.org ) for convenient use.

A first-principles study of Ni n Pd n (n = 1 - 5) clusters

A first-principle investigation of structures and properties of Ni _n Pd _n (n=1-5) clusters is presented. For this study, the linear combination of Gaussian-type orbitals auxiliary density functional theory (LCGTO-ADFT) method has been employed. In order to determine the lowest energy structures, several isomers in different spin multiplicities were studied, for each cluster size. Initial structures, for which successive geometry optimization was computed without any constrain, were taken along Born-Oppenheimer molecular dynamics (BOMD) trajectories. To discriminate between minima and transition state structures, harmonic frequency analyses were performed at the optimized structures. Ground state structures, bond lengths, harmonic frequencies, dissociation energy, ionization potential, electron affinity and spin density plots are presented. This work demonstrates, that the Pd atoms prefer to allocate on the surface of the cluster structures whose core is formed by the 3d TM atoms type. Moreover, it has been observed that the ground-state structure spin multiplicity increases as the system size grows. The results of this study contribute to gain insight into how structures and energy properties change with cluster size in bimetallic Pd-based alloys.

A density functional study of Rh13

A density functional study was performed for the Rh13 cluster using the linear combination of Gaussian-type orbitals density functional theory (LCGTO-DFT) approach. The calculations employed both the local density approximation (LDA) as well as the generalized gradient approximation (GGA) in combination with a quasi-relativistic effective core potential (QECP). Initial structures for the geometry optimization were taken along Born–Oppenheimer molecular dynamics (BOMD) trajectories. The BOMD trajectories were performed at different temperatures and considered different potential energy surfaces (PES). As a result, several hundred isomers of the Rh13 cluster in different spin multiplicities were optimized with the aim to determine the lowest energy structures. All geometry optimizations were performed without any symmetry restriction. A vibrational analysis was performed to characterize these isomers. Structural parameters, relative stability energy, harmonic frequencies, binding energy, and most relevant Kohn–Sham (KS) molecular orbitals are reported. The obtained results are compared with available data from the literature. This study predicts a low symmetry biplanarlike structure as the ground-state structure of Rh13 with 11 unpaired electrons. This isomer was first noticed by inspection of first-principle Born–Oppenheimer molecular dynamics (BOMD) simulations between 300 and 600 K. This represents the most extensive theoretical study on the ground-state structure of the Rh13 cluster and underlines the importance of BOMD simulations to fully explore the PES landscapes of complicated systems.

Contribution of high-energy conformations to NMR chemical shifts, a DFT-BOMD study

This paper highlights the relevance of including the high-energy conformational states sampled by Born-Oppenheimer molecular dynamics (BOMD) in the calculation of time-averaged NMR chemical shifts. Our case study is the very flexible glycerol molecule that undergoes interconversion between conformers in a nonrandom way. Along the sequence of structures from one backbone conformer to another, transition states have been identified. The three (13)C NMR chemical shifts of the molecule were estimated by averaging their calculated values over a large set of BOMD snapshots. The simulation time needed to obtain a good agreement with the two signals present in the experimental spectrum is shown to be dependent on the atomic orbital basis set used for the dynamics, with a necessary longer trajectory for the most extended basis sets. The large structural deformations with respect to the optimized conformer geometries that occur along the dynamics are related to a kinetically driven conformer distribution. Calculated conformer type populations are in good agreement with experimental gas phase microwave results.

Graph theory meets ab initio molecular dynamics: atomic structures and transformations at the nanoscale

Social permutation invariant coordinates are introduced describing the bond network around a given atom. They originate from the largest eigenvalue and the corresponding eigenvector of the contact matrix, are invariant under permutation of identical atoms, and bear a clear signature of an order-disorder transition. Once combined with ab initio metadynamics, these coordinates are shown to be a powerful tool for the discovery of low-energy isomers of molecules and nanoclusters as well as for a blind exploration of isomerization, association, and dissociation reactions.