Journal Article

# Systematic cluster growth: a structure search method for transition metal clusters

04 Mar 2021-Physical Chemistry Chemical Physics (The Royal Society of Chemistry)-Vol. 23, Iss: 8, pp 4935-4943
Abstract: The systematic cluster growth (SCG) method is a biased structure search strategy based on a seeding process for investigating the structural evolution and growth pattern of transition metal clusters. In SCG, a set of initial structures with size n are constructed based on the equilibrium structures of the preceding n − 1 cluster isomers by adding a single atom at all inequivalent binding sites. This strategy requires a relatively low number of evaluations for global minima localization on the potential energy surface, allowing its application in first-principles calculations. The performance of SCG is tested by using the Lennard Jones (LJ) potential energy surface. The 93.7% of the best-known solutions for Lennard Jones clusters were found for n ≤ 80 by using a relatively low number of local optimizations. Most importantly, by using SCG combined with DFT calculations (SCG-DFT), we revisit and provide the ground state structures and growth pattern for transition metal clusters TMn (where TM = Ti, Ni, Cu, Ag, Pt; and n = 6–14). The application of the code for doped clusters is also discussed. A detailed description of the present method for generating the structures of the clusters is provided.

Topics: Cluster (physics) (55%),
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Journal Article
Abstract: Here, we report density functional theory calculations combined with the k-means clustering algorithm and the Spearman rank correlation analysis to investigate the stability mechanisms of eight-atom binary metal AB clusters, where A and B are Fe, Co, Ni, Cu, Ga, Al, and Zn (7 unary and 21 binary clusters). Based on the excess energy analysis, the six most stable binary clusters are NiAl, NiGa, CoAl, FeNi, NiZn, and FeAl, and except for FeNi, their highest energetic stabilities can be explained by the hybridization of the d- and sp-states, which is maximized at the 50% composition, i.e., A4B4. Based on the Spearman correlation analysis, the energetic stability of the binary clusters increases with an increase in the highest occupied molecule orbital-lowest unoccupied molecular orbital (HOMO-LUMO) energy separation, which can be considered as a global descriptor. Furthermore, reducing the total magnetic moment values increases the stability for binary clusters without the Fe, Co, and Ni species, while the binary FeB, CoB, and NiB clusters increase their energetic stability with a decrease in the cluster radius, respectively, i.e., an energetic preference for compact structures.

Topics: Cluster (physics) (52%)

1 Citations

Open accessJournal Article
01 Sep 2021-Molecules
Abstract: 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.

Topics: , Population (52%)

1 Citations

Journal Article
Abstract: Structure is the key to understanding the properties of metal nanoclusters. Finding a globally optimal structure on an extremely complex potential energy surface is a great challenge for theoretica...

Topics: Nanoclusters (58%)

Journal Article
Abstract: Recently, P V Nhat et al, have discussed and commented on our article (DOI: 101039/D0CP04018E) for the case of the most stable structure of Ag15 They have found a new most stable structure (labeled as 15-1) in comparison to the putative global minimum reported by us, which is a four layered 1-4-6-4 stacking structure with a C2v point group (15-2) In this reply, we have performed a larger structure search which allowed us to confirm the results of Nhat et al The results show the existence of multiple isoenergetic isomers with similar structure motifs for the Ag15 system, increasing the problem complexity to locate the global minimum The results in regard to the structure and electronic properties of the new lowest energy structure are discussed

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Journal Article
Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif

Topics: , ,  ... read more

117,932 Citations

Journal Article
Georg Kresse1, Jürgen Furthmüller2Institutions (2)
15 Oct 1996-Physical Review B
Abstract: We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order ${\mathit{N}}_{\mathrm{atoms}}^{3}$ operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special metric'' and a special preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order ${\mathit{N}}_{\mathrm{atoms}}^{2}$ scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach ${\mathit{N}}_{\mathrm{atoms}}$. We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. \textcopyright{} 1996 The American Physical Society.

Topics: DIIS (51%)

64,484 Citations

Open accessJournal Article
Peter E. Blöchl1Institutions (1)
15 Dec 1994-Physical Review B
Abstract: An approach for electronic structure calculations is described that generalizes both the pseudopotential method and the linear augmented-plane-wave (LAPW) method in a natural way. The method allows high-quality first-principles molecular-dynamics calculations to be performed using the original fictitious Lagrangian approach of Car and Parrinello. Like the LAPW method it can be used to treat first-row and transition-metal elements with affordable effort and provides access to the full wave function. The augmentation procedure is generalized in that partial-wave expansions are not determined by the value and the derivative of the envelope function at some muffin-tin radius, but rather by the overlap with localized projector functions. The pseudopotential approach based on generalized separable pseudopotentials can be regained by a simple approximation.

Topics: , Pseudopotential (58%)

48,474 Citations

Open accessJournal Article
Walter Kohn1, L. J. Sham1Institutions (1)
15 Nov 1965-Physical Review
Abstract: From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of $\frac{2}{3}$.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.

Topics: Jellium (56%), Hartree–Fock method (55%), Thomas–Fermi model (55%) ... read more

42,177 Citations

Open accessJournal Article
P. C. Hohenberg1, Walter Kohn2Institutions (2)
09 Nov 1964-Physical Review
Abstract: This paper deals with the ground state of an interacting electron gas in an external potential $v(\mathrm{r})$. It is proved that there exists a universal functional of the density, $F[n(\mathrm{r})]$, independent of $v(\mathrm{r})$, such that the expression $E\ensuremath{\equiv}\ensuremath{\int}v(\mathrm{r})n(\mathrm{r})d\mathrm{r}+F[n(\mathrm{r})]$ has as its minimum value the correct ground-state energy associated with $v(\mathrm{r})$. The functional $F[n(\mathrm{r})]$ is then discussed for two situations: (1) $n(\mathrm{r})={n}_{0}+\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}(\mathrm{r})$, $\frac{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{n}}{{n}_{0}}\ensuremath{\ll}1$, and (2) $n(\mathrm{r})=\ensuremath{\phi}(\frac{\mathrm{r}}{{r}_{0}})$ with $\ensuremath{\phi}$ arbitrary and ${r}_{0}\ensuremath{\rightarrow}\ensuremath{\infty}$. In both cases $F$ can be expressed entirely in terms of the correlation energy and linear and higher order electronic polarizabilities of a uniform electron gas. This approach also sheds some light on generalized Thomas-Fermi methods and their limitations. Some new extensions of these methods are presented.