AUTOMATON: A Program That Combines a Probabilistic Cellular Automata and a Genetic Algorithm for Global Minimum Search of Clusters and Molecules

Abstract

A novel program for the search of global minimum structures of atomic clusters and molecules in the gas phase, AUTOMATON, is introduced in this work. This program involves the following: first, the generation of an initial population, using a simplified probabilistic cellular automaton method, which allows easy control of the adequate distribution of atoms in space; second, the fittest individuals are selected to evolve, through genetic operations (mating and mutations), until the best candidate for a global minimum surfaces.In addition, we propose a simple way to build the descendant structures by establishing a ranking of genes to be inherited. Thus, by means of a chemical formula checker procedure, genes are transferred to the offspring, ensuring that they always have the appropriate type and number of atoms. It is worth noting that a fraction of the fittest group is subject to mutation operations. This program also includes algorithms to identify duplicate structures: one based on geometric similarity and another on the similar distribution of atomic charges. The effectiveness of the program was evaluated in a group of 45 molecules, considering organic and organometallic compounds (benzene, cyclopentadienyl anion, and ferrocene), Zintl ion clusters [Sn 9−m−n Ge m Bi n ] (4−n)− (n = 1−4 and m = 0−(9−n)), star-shaped clusters (Li 7 E 5+ , E = BH, C, Si, Ge) and a variety of boron-based clusters. The global minimum and the lowest-energy isomers reported in the literature were found for all the cases considered in this article. These results successfully prove AUTOMATON's effectiveness on the identification of energetically preferred structures of a wide variety of chemical species.

(Li6Si5)2–5: The Smallest Cluster‐Assembled Materials Based on Aromatic Si56− Rings

“…GM structures of (Li 5 Si 5 ) 2 2− (Li 6 Si 5 ) 2 and (Li 7 Si 5 ) 2 2+ clusters, according to our global optimization algorithms, are depicted in Figure a. The most striking result is that these dimers preserve key structural patterns from the monomers .…”

“…GM structures of (Li 5 Si 5 ) 2 2À (Li 6 Si 5 ) 2 and (Li 7 Si 5 ) 2 2 + clusters, according to our global optimization algorithms, [24][25][26][27][28] are depicted in Figure 1a.T he most striking result is that these dimers preserve key structural patterns from the monomers. [15] They are formed by two LiSi 5 Li units, where the Si 5 rings are placed almostp arallel and slightly displaced with respectt oe ach other,a nd sandwiching aL i 8 or Li 7 fragment in (Li 5 Si 5 ) 2 2À , (Li 6 Si 5 ) 2 ,o r( Li 7 Si 5 ) 2 2 + ,r espectively.B esides, one lithium atom is bridging one Si 5 edge in (Li 6 Si 5 ) 2 ,w hereas two lithium atoms are bridging two consecutive Si 5 edges in (Li 7 Si 5 ) 2 2 + (see Figure 1a).…”

“…Firstly, the lowest energy structures of the smallest oligomer (Li 6 Si 5 ) 2 and its lithiated, (Li 7 Si 5 ) 2 2+ and delithiated (Li 5 Si 5 ) 2 2− counterparts, as well as the trimer (Li 6 Si 5 ) 3 , were identified by means of three independent searches. The first two searches used two genetic algorithm methods (GEGA and AUTOMATON) and the third one used a stochastic method, which is our implementation of the KICK method of Addicoat, hereinafter referred to as the KICK method. Secondly, the lowest energy structures of the larger oligomers, (Li 6 Si 5 ) 4 and (Li 6 Si 5 ) 5 , were identified using solely the KICK method.…”

Searching for double σ- and π-aromaticity in borazine derivatives

“…(a) The potential energy surface (PES) of systems, 4, 6 and 8, was explored via the AUTOMATON program. 33 This program uses a probabilistic automaton method to generate an initial population that evolves to the best individual (global minimum, GM) through genetic operations. The searches were performed via the PBE0 34 functional in conjunction with the SDDALL 35,36 basis.…”

NWPEsSe: an Adaptive-Learning Global Optimization Algorithm for Nanosized Cluster Systems

“…Examples of global optimization algorithms used on a variety of systems (aperiodic or periodic) have been reported in the literature and include Li , 37 Ir , 38 Pt , 39 graphene-supported Pt , 40 MgOsupported AuPd, 41 TiCl 4 -capped MgCl 2 plate (Ziegler-Natta catalyst), 42 to name a few. Other general-purpose codes include PDECO, 43 GEGA, 37 GMIN, 44 TGMIN, 45 AUTOMATON, 46 etc. However, some of these codes are either not readily available, lack the interface to common computational chemistry programs, or are simply designed for specific systems.…”