The role of local optimizations in evolutionary process of atomic clusters modeling

The application of genetic algorithms in a physical problem of modeling of isolated atomic clusters is the topic of our research. Evolutionary algorithms are a mechanism of the global optimization learning about the solution of the search space. This mechanism plays the role of giving the candidates to global optima. We can use the local optimization in the evolutionary process to improve the efficiency of our algorithm. The goal of our work is evaluation of the influence of the local optimization methods (type of simple gradient) on the growing of the efficiency and accuracy of the evolutionary process in optimization of atomic clusters modeling

First-principles molecular structure search with a genetic algorithm

The identification of low-energy conformers for a given molecule is a fundamental problem in computational chemistry and cheminformatics. We assess here a conformer search that employs a genetic algorithm for sampling the low-energy segment of the conformation space of molecules. The algorithm is designed to work with first-principles methods, facilitated by the incorporation of local optimization and blacklisting conformers to prevent repeated evaluations of very similar solutions. The aim of the search is not only to find the global minimum, but to predict all conformers within an energy window above the global minimum. The performance of the search strategy is: (i) evaluated for a reference data set extracted from a database with amino acid dipeptide conformers obtained by an extensive combined force field and first-principles search and (ii) compared to the performance of a systematic search and a random conformer generator for the example of a drug-like ligand with 43 atoms, 8 rotatable bonds and 1 cis/trans bond

Group Leaders Optimization Algorithm

We present a new global optimization algorithm in which the influence of the leaders in social groups is used as an inspiration for the evolutionary technique which is designed into a group architecture. To demonstrate the efficiency of the method, a standard suite of single and multidimensional optimization functions along with the energies and the geometric structures of Lennard-Jones clusters are given as well as the application of the algorithm on quantum circuit design problems. We show that as an improvement over previous methods, the algorithm scales as N^2.5 for the Lennard-Jones clusters of N-particles. In addition, an efficient circuit design is shown for two qubit Grover search algorithm which is a quantum algorithm providing quadratic speed-up over the classical counterpart

Unconstrained Global Optimization of Molecules on Surfaces: From globally optimized structures to scanning-probe data

The adsorption of molecules on a surface plays a vital role in heterogeneous catalysis. For a proper unterstanding of the reaction mechanisms involved, the adsorption ge ometry of the molecules on the surface needs to be known. So far, experimental data from tunneling microscopes and spectroscopy, such as STM and IRAS are the main ways to obtain such knowledge. Due to the vast search space of adsorption geometries, especially for oligomers, optimizations using ab initio methods can be used to confirm the experimental data only if good initial guesses are available. Global optimization can serve two purposes in these situations. On the one hand it allows for a thorough investigation of the given search space, which can provide good initial guesses for subsequent high-level structural refinements. On the other hand, given a known reaction mechanism, it could also be used to find catalysts that influence e.g. the relevant bonds. With respect to this idea the topic of this thesis is to find a local optimization method cheap enough such that the total computational cost of global optimization does not exceed availability and yet good enough that the results are meaningful to the problem at hand. With this in mind multiple force field and semiempirical methods have been tested and evaluated mainly on benzene, acetophenone and ethyl pyruvate on Pt(111) surfaces. Some other adsorbates have also been tested shortly. In addition to these global optimization results, DFT geometry optimizations of ethyl pyruvate on Pt(111) have been performed and the structures of the best adsorption geometry from global optimization and from DFT are compared. Furthermore, from the DFT data STM images have been calculated that are compared to experimental results. The theoretical and experimental STM images agree well

Toward Fast and Reliable Potential Energy Surfaces for Metallic Pt Clusters by Hierarchical Delta Neural Networks.

Data-driven machine learning force fields (MLFs) are more and more popular in atomistic simulations and exploit machine learning methods to predict energies and forces for unknown structures based on the knowledge learned from an existing reference database. The latter usually comes from density functional theory calculations. One main drawback of MLFs is that physical laws are not incorporated in the machine learning models, and instead, MLFs are designed to be very flexible to simulate complex quantum chemistry potential energy surface (PES). In general, MLFs have poor transferability, and hence, a very large trainset is required to span all the target feature space to get a reliable MLF. This procedure becomes more troublesome when the PES is complicated, with a large number of degrees of freedom, in which building a large database is inevitable and very expensive, especially when accurate but costly exchange-correlation functionals have to be used. In this manuscript, we exploit a high-dimensional neural network potential (HDNNP) on Pt clusters of sizes from 6 to 20 as one example. Our standard level of energy calculation is DFT GGA (PBE) using a plane wave basis set. We introduce an approximate but fast level with the PBE functional and a minimal atomic orbital basis set, and then, a more accurate but expensive level, using a hybrid functional or nonlocal vdW functional and a plane wave basis set, is reliably predicted by learning the difference with HDNNP. The results show that such a differential approach (named ΔHDNNP) can deliver very accurate predictions (error <10 meV/atom) in reference to converged basis set energies as well as more accurate but expensive xc functionals. The overall speedup can be as large as 900 for a 20 atom Pt cluster. More importantly, ΔHDNNP shows much better transferability due to the intrinsic smoothness of the delta potential energy surface, and accordingly, one can use much smaller trainset data to obtain better accuracy than the conventional HDNNP. A multilayer ΔHDNNP is thus proposed to obtain very accurate predictions versus expensive nonlocal vdW functional calculations in which the required trainset is further reduced. The approach can be easily generalized to any other machine learning methods and opens a path to study the structure and dynamics of Pt clusters and nanoparticles