Global optimization of clusters using electronic structure methods

A very recently developed optimization algorithm for carbon clusters (C n s) (Yen and Lai J Chem Phys 142:084313, 2015) is combined separately with different empirical bond-order potentials which were proposed also for carbon materials, and they are applied to calculate the lowest energy structures of C n s studying their structural changes at different size n. Based on predicted structures, we evaluate the practicality of four analytic bond-order empirical potentials, namely the Tersoff, Tersoff–Erhart–Albe, first-generation Brenner and second-generation Brenner (SGB) potentials. Generally, we found that the cluster C n (n = 3–60) obtained by the SGB potential undergoes a series of dramatic structural transitions, i.e., from a linear → a single ring → a multi-ring/quasi-two-dimensional bowl-like → three-dimensional fullerene-like shape; such variability of structural forms was not seen in the other three potentials. On closer examination of the C n s calculated using this potential and further comparing them with those obtained by the semiempirical density functional tight-binding theory calculations, we found that these C n are more realistic than similar works reported in the literature. In this respect, due to its potential applications in the study of chemically complex systems of different atoms especially chemical reactions (Che et al. Theor Chem Acc 102:346, 1999), the SGB potential can, moreover, be used to investigate larger size C n , and calculated structural results by this potential are naturally input configurations for higher-level density functional theory calculations. Another most remarkable finding in the present work is the C n results calculated by Tersoff–Erhart–Albe empirical potential. It predicts a two-dimensional development of graphene structure, exhibiting always a zigzag edge in the optimized clusters. This empirical potential can thus be applied to study graphene-related materials such as that shown in a recent paper (Yoon et al. J Chem Phys 139:204702, 2013).

All-solid-state batteries present a promising alternative to traditional Li-ion batteries, offering higher energy density and enhanced safety. However, their widespread application is impeded by challenges such as high interfacial resistance. Both experimental and computational studies have identified cation interdiffusion as a significant phenomenon at these interfaces[1], exemplified by Co-diffusion from the cathode LiCoO2 to the solid electrolyte Li1+xAlxTi2-x(PO4)3 (LATP). However, the impact of cation interdiffusion on interfacial resistance, particularly Li-ion transport, remains unclear. Therefore, our study employs first-principles calculations to analyze Co insertion into LATP and its effect on Li-ion conductivity. Although ab initio molecular dynamics (AIMD) provides precise descriptions of electron interactions and atomic forces[2], it is computationally expensive. To balance accuracy and efficiency, a pre-trained machine learning interatomic potential, CHGNet, and fine-tuned with single-point calculations as the training data. In previous work[3], we attempted to use machine learning potentials to rapidly screen energetically favorable structures, laying the groundwork for the present study. With the fine-tuned model, we conducted machine learning molecular dynamics (MLMD) simulations, which can perform long-timescales simulations. The results indicate that Co insertion notably impedes Li-ion transport in LATP near the LATP/LCO interface. The AIMD results indicate increased activation energy during the charging and discharging processes, along with a decrease in ionic conductivity. The activation energy results also demonstrate that MLMD can achieve precision comparable to AIMD, effectively bridging the gap between electronic structure methods and empirical potentials. Therefore, we can further simulate long-time and large-scale interfacial structures to analyze interfacial composition and ion migration mechanisms, to address the interfacial issues in all-solid-state batteries. These suggests that at the LATP/LiCoO2 interface, Co migration trapped Li-ions in local lattices, raising interfacial impedance. Therefore, preventing Co migrating from the electrode material to the solid electrolyte is key to enhancing interfacial impedance. These findings offer valuable insights for enhancing interfaces in all-solid-state batteries performance. The AIMD results indicate increased activation energy during the charging and discharging processes, along with a decrease in ionic conductivity. The results also demonstrate that MLMD can achieve precision comparable to AIMD, effectively bridging the gap between electronic structure methods and empirical potentials. This enables further simulations of long-term and large-scale interfacial structures to analyze interfacial composition and ion migration mechanisms. The findings suggest that at the LATP/LiCoO₂ interface, Co migration traps Li-ions in local lattice sites, thereby increasing interfacial impedance. Consequently, preventing Co migration from the electrode material to the solid electrolyte is essential for improving interfacial performance. These insights provide valuable guidance for enhancing the interfaces and overall performance of all-solid-state batteries.

Modelling aluminium clusters with an empirical many-body potential

Adsorption structures and energetics of molecules on metal surfaces: Bridging experiment and theory

The design of novel cathode materials for Li-ion batteries would greatly benefit from accurate first-principles predictions of structural, electronic, and magnetic properties as well as intercalation voltages in compounds containing transition-metal elements. For such systems, density-functional theory (DFT) with standard (semi-)local exchange-correlation functionals is of limited use as it often fails due to strong self-interaction errors that are especially relevant in the partially filled $d$ shells. Here, we perform a detailed comparative study of the phospho-olivine cathode materials Li$_x$MnPO$_4$, Li$_x$FePO$_4$, and the mixed transition metal Li$_x$Mn$_{1/2}$Fe$_{1/2}$PO$_4$ ($x=0, 1/4, 1/2, 3/4, 1$) using four electronic-structure methods: DFT, DFT+$U$, DFT+$U$+$V$, and HSE06. We show that DFT+$U$+$V$, with onsite $U$ and intersite $V$ Hubbard parameters determined from first principles and self-consistently with respect to the structural parameters by means of density-functional perturbation theory (linear response), provides the most accurate description of the electronic structure of these challenging compounds. In particular, we demonstrate that DFT+$U$+$V$ displays very clearly "digital" changes in oxidation states of the transition-metal ions in all compounds, including the mixed-valence phases occurring at intermediate Li concentrations, leading to voltages in remarkable agreement with experiments. We show that the inclusion of intersite Hubbard interactions is essential for the accurate prediction of thermodynamic quantities, balancing the drive for localization induced by the onsite $U$ with intersite $V$ orbital hybridizations.

In this work, the ability of methods based on empirical potentials to simulate the effects of radiation damage in graphite is examined by comparing results for point defects, found using ab initio calculations based on density functional theory (DFT), with those given by two state of the art potentials: the Environment-Dependent Interatomic Potential (EDIP) and the Adaptive Intermolecular Reactive Empirical Bond Order potential (AIREBO). Formation energies for the interstitial, the vacancy and the Stone–Wales (5775) defect are all reasonably close to DFT values. Both EDIP and AIREBO can thus be suitable for the prompt defects in a cascade, for example. Both potentials suffer from arefacts. One is the pinch defect, where two α-atoms adopt a fourfold-coordinated sp3 configuration, that forms a cross-link between neighbouring graphene sheets. Another, for AIREBO only, is that its ground state vacancy structure is close to the transition state found by DFT for migration. The EDIP fails to reproduce the ground state self-interstitial structure given by DFT, but has nearly the same formation energy. Also, for both potentials, the energy barriers that control diffusion and the evolution of a damage cascade, are not well reproduced. In particular the EDIP gives a barrier to removal of the Stone–Wales defect as 0.9 eV against DFT's 4.5 eV. The suite of defect structures used is provided as supplementary information as a benchmark set for future potentials.

BackgroundProtein structure prediction (PSP) has important applications in different fields, such as drug design, disease prediction, and so on. In protein structure prediction, there are two important issues. The first one is the design of the structure model and the second one is the design of the optimization technology. Because of the complexity of the realistic protein structure, the structure model adopted in this paper is a simplified model, which is called off-lattice AB model. After the structure model is assumed, optimization technology is needed for searching the best conformation of a protein sequence based on the assumed structure model. However, PSP is an NP-hard problem even if the simplest model is assumed. Thus, many algorithms have been developed to solve the global optimization problem. In this paper, a hybrid algorithm, which combines genetic algorithm (GA) and tabu search (TS) algorithm, is developed to complete this task.ResultsIn order to develop an efficient optimization algorithm, several improved strategies are developed for the proposed genetic tabu search algorithm. The combined use of these strategies can improve the efficiency of the algorithm. In these strategies, tabu search introduced into the crossover and mutation operators can improve the local search capability, the adoption of variable population size strategy can maintain the diversity of the population, and the ranking selection strategy can improve the possibility of an individual with low energy value entering into next generation. Experiments are performed with Fibonacci sequences and real protein sequences. Experimental results show that the lowest energy obtained by the proposed GATS algorithm is lower than that obtained by previous methods.ConclusionsThe hybrid algorithm has the advantages from both genetic algorithm and tabu search algorithm. It makes use of the advantage of multiple search points in genetic algorithm, and can overcome poor hill-climbing capability in the conventional genetic algorithm by using the flexible memory functions of TS. Compared with some previous algorithms, GATS algorithm has better performance in global optimization and can predict 3D protein structure more effectively.

Computational chemistry has led to the greater understanding of the molecular world, from the interaction of molecules, to the composition of molecular species and materials. Of the families of computational chemistry approaches available, the main families of electronic structure methods that are capable of accurate and/or reliable predictions of energetic, structural, and spectroscopic properties are ab initio methods and density functional theory (DFT). The focus of this dissertation is to improve the accuracy of predictions and computational efficiency (with respect to memory, disk space, and computer processing time) of some computational chemistry methods, which, in turn, can extend the size of molecule that can be addressed, and, for other methods, DFT, in particular, gain greater insight into which DFT methods are more reliable than others. Much, though not all, of the focus of this dissertation is upon transition metal species – species for which much less method development has been targeted or insight about method performance has been well established. The ab initio approach that has been targeted in this work is the correlation consistent composite approach (ccCA), which has proven to be a robust, ab initio computational method for main group and first row transition metal-containing molecules yielding, on average, accurate thermodynamic properties, i.e., within 1 kcal/mol of experiment for main group species and within 3 kcal/mol of experiment for first row transition metal molecules. In order to make ccCA applicable to systems containing any element from the periodic table, development of the method for second row transition metals and heavier elements, including lower p-block (5p and 6p) elements was pursued. The resulting method, the relativistic pseudopotential variant of ccCA (rp-ccCA), and its application are detailed for second row transition metals and lower p-block elements. Because of the computational cost of ab initio methods, DFT is a popular choice for the study of transition metals. Despite this, the most reliable density functionals for the prediction of energetic properties (e.g. enthalpy of formation, ionization potential, electron affinity, dissociation energy) of transition metal species, have not been clearly identified. The examination of DFT performance for first and second row transition metal thermochemistry (i.e., enthalpies of formation) was conducted and density functionals for the study of these species were identified. And, finally, to address the accuracy of spectroscopic and energetic properties, improvements for a series of density functionals have been established. In both DFT and ab initio methods, the harmonic approximation is typically employed. This neglect of anharmonic effects, such as those related to vibrational properties (e.g. zero-point vibrational energies, thermal contributions to enthalpy and entropy) of molecules, generally results in computational predictions that are not in agreement with experiment. To correct for the neglect of anharmonicity, scale factors can be applied to these vibrational properties, resulting in better alignment with experimental observations. Scale factors for DFT in conjunction with both the correlation and polarization consistent basis sets have been developed in this work.

ABACUS (Atomic-orbital Based Ab initio Computation at USTC) is an open-source software for first-principles electronic structure calculations and molecular dynamics simulations. It mainly features density functional theory (DFT) and molecular dynamics functions and is compatible with both plane wave basis sets and numerical atomic orbital basis sets. ABACUS serves as a platform that facilitates the integration of various electronic structure methods, such as Kohn-Sham DFT, stochastic DFT, orbital-free DFT, real-time time-dependent DFT, etc. In addition, with the aid of high-performance computing, ABACUS is designed to perform efficiently and provide massive amounts of first-principles data for generating general-purpose machine learning potentials, such as deep potential with attention models. Furthermore, ABACUS serves as an electronic structure platform that interfaces with several artificial intelligence-assisted algorithms and packages, such as DeePKS-kit, DeePMD, DP-GEN, DeepH, DeePTB, HamGNN, etc.

In this article, we look at the option of using a stochastic optimisation technique, namely genetic algorithm (GA) in association with density functional theory (DFT) to find out the global minimum structures of (MgF2)n clusters with the range of n being between 2 and 10. To confirm whether the structures are indeed the acceptable ones, we go on to evaluate several properties like IR spectroscopic modes, vertical excitation energy, cluster formation energy, vertical ionisation potential and the HOMO–LUMO gap. We stress on the fact that an initial estimation of structure using GA, on two empirical potentials (with and without inclusion of polarisation), leads to a very quick convergence to structures which are quite close to the structures obtained from quantum chemical calculations done from the outset, such as using a DFT calculation. The general structural trend of these systems to form three-dimensional networks is also clear from our study. The lowest energy isomers of these clusters show preference for four-membered Mg2F2 and six-membered Mg3F3 rings. In the IR spectra of (MgF2)n clusters, a blueshift of the Mg–F symmetric stretch and a redshift of asymmetric Mg–F stretching as n increases are obtained.

Global geometry optimization of metal clusters is an important problem in nanophysics. The starting geometries of the clusters generated with empirical or other model potentials are generally optimized further by density functional theory (DFT)-based energy minimization. For this purpose, several algorithms such as simulated annealing, genetic algorithms, basin hopping, etc. are used. Our building-up procedure generates putative lower-energy structures of metal (M) clusters, Mn+1, Mn+2, etc., by anchoring one or more metal atoms in the vicinity of the minima of the molecular electrostatic potential (MESP) of Mn. Here, we report an application of this method to Agn clusters, for 5 ≤ n ≤ 20, followed up by DFT-based geometry optimization, generating several lower-energy structures than those reported in the literature. New low-energy isomers are obtained by applying the same procedure to the test case of mixed-metal clusters, NinAgm, for n + m = 4 and 5. In conclusion, our MESP-based building-up procedure offers a new general methodology for generating lower-energy geometries of metal clusters.

The need for sources of efficient and renewable energy has become an issue of great importance in recent years. Fossil fuels are diminishing in supply, and they not only pollute the environment, but have also proven to be inefficient in many cases, losing a large portion of the total energy generated to waste heat, instead of usable energy. The first work this thesis addresses is the development of a Genetic Algorithm (GA) optimization method for the search and discovery of semiconductor materials for use in thermoelectric devices. The specific material in question is the Silicon Germanium superlattice. This structure made of alternating layers of Si and Ge is known to be one of the better materials for thermoelectric energy generation at elevated temperature, along with Bismuth-Telluride that targets room temperature. Previously, it has been shown that random multilayer (RML) structures can lower thermal conductivity as compared to periodic superlattices due to phonon localization. However, it was unknown which specific RML would yield the lowest thermal conductivity, due to the large design space from which these RML’s can be generated. Considering this, a global and non-smooth optimization method was employed to search for the best possible structure. Results not only showed that the thermal conductivity could be lowered even further, but that there was an optimal average period for the RML’s that produced the best results.The second work discussed in this thesis concerns itself with the development of a Neural Network Potential (NNP) for use in Molecular Dynamics (MD) simulations. There are multiple methods for running MD including ab-initiomethods such as Density Functional Theory (DFT) calculations and classical MD with the use of empirical potentials. Unfortunately, DFT is too time consuming for systems larger than a few hundred atoms, and empirical potentials can be inaccurate. Therefore, a NNP for bulk Silicon trained on DFT was developed, and it was shown that the phonon dispersion for Si could be accurately reproduced.

Density functional theory (DFT) is the most widely used electronic structure method, due to its simplicity and cost effectiveness. The accuracy of a DFT calculation depends not only on the choice of the density functional approximation (DFA) adopted but also on the electron density produced by the DFA. SCAN is a modern functional that satisfies all known constraints for meta-GGA functionals. The density-driven errors, defined as energy errors arising from errors of the self-consistent DFA electron density, can hinder SCAN from achieving chemical accuracy in some systems, including water. Density-corrected DFT (DC-DFT) can alleviate this shortcoming by adopting a more accurate electron density which, in most applications, is the electron density obtained at the Hartree-Fock level of theory due to its relatively low computational cost. In this work, we present extensive calculations aimed at determining the accuracy of the DC-SCAN functional for various aqueous systems. DC-SCAN (SCAN@HF) shows remarkable consistency in reproducing reference data obtained at the coupled cluster level of theory, with minimal loss of accuracy. Density-driven errors in the description of ionic aqueous clusters are thoroughly investigated. By comparison with the orbital-optimized CCD density in the water dimer, we find that the self-consistent SCAN density transfers a spurious fraction of an electron across the hydrogen bond to the hydrogen atom (H*, covalently bound to the donor oxygen atom) from the acceptor (OA) and donor (OD) oxygen atoms, while HF makes a much smaller spurious transfer in the opposite direction, consistent with DC-SCAN (SCAN@HF) reduction of SCAN overbinding due to delocalization error. While LDA seems to be the conventional extreme of density delocalization error, and HF the conventional extreme of (usually much smaller) density localization error, these two densities do not quite yield the conventional range of density-driven error in energy differences. Finally, comparisons of the DC-SCAN results with those obtained with the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method show that DC-SCAN represents a more accurate approach to reducing density-driven errors in SCAN calculations of ionic aqueous clusters. While the HF density is superior to that of SCAN for noncompact water clusters, the opposite is true for the compact water molecule with exactly 10 electrons.

Obtaining the global minimum in the potential energy hypersurface of nanoclusters is a very difficult task, due to the large number of degrees of freedom and the vast number of local minima. However, the discovery of such minima provides the geometrical arrangement that is more likely to occur, which is a key step in computing the properties of such particles. Here we developed a genetic algorithm (GA) including a gradient adjustment in each local optimization, to obtain an efficient GA, which is particularly useful when the algorithm is coupled with electronic structure methods. The idea is first validated, and then used to predict the minima of large sodium nanoclusters up to one hundred atoms. To validate the algorithm, we analyzed its efficiency in obtaining the global minima of Lennard-Jones clusters, whose solutions are well known and can be used as benchmark. The new GA is compared to a random search and a standard GA. For exploring the potential energy surface of sodium clusters, we employ the Density-Functional Tight-Binding (DFTB) method, with parameters that have been tuned specifically to such clusters, thus enhancing its reliability for this specific application.

Using a combination of density functional theory (DFT), classical potentials, molecular dynamics, and nudged elastic band (NEB) calculations, we explore the diffusion of xenon in uranium dioxide (UO${}_{2}$). We compare migration barriers of empirical potentials with DFT by performing NEB calculations and subsequently we use the DFT-validated empirical potentials to calculate vacancy clusters, with and without xenon, to determine the migration path and barrier of xenon in bulk UO${}_{2}$. We find the following: (i) Two empirical potentials out of four tested agree qualitatively with DFT derived energetics for Schottky defect migration; (ii) through the use of molecular dynamics with empirical potentials, we have found a path for the diffusion of xenon-tetravacancy clusters (Xe$+2{V}_{\mathrm{U}}+2$${V}_{\mathrm{O}}$); (iii) this path has an energy barrier significantly lower than previously reported paths by nearly 1 eV; (iv) we examine the physical contributions to the migration pathway and find the barrier is largely electrostatic and that xenon contributes very little to the barrier height; (v) once a uranium vacancy attaches to a xenon-Schottky defect, the resulting xenon-tetravacancy cluster is strongly bound; and (vi) as xenon in a tetravacancy, a xenon-double Schottky defect can diffuse in a concerted manor with a comparable barrier to xenon in a tetravacancy, but two of the oxygen vacancies are only weakly bound to the defect.