Global optimization

Current and future machine learning approaches for modeling atmospheric cluster formation

The formation of strongly bound atmospheric molecular clusters is the first step towards forming new aerosol particles. Recent advances in the application of machine learning models open an enormous opportunity for complementing expensive quantum chemical calculations with efficient machine learning predictions. In this Perspective, we present how data-driven approaches can be applied to accelerate cluster configurational sampling, thereby greatly increasing the number of chemically relevant systems that can be covered.

Finding Excited-State Minimum Energy Crossing Points on a Budget: Non-Self-Consistent Tight-Binding Methods

The automated exploration and identification of minimum energy conical intersections (MECIs) is a valuable computational strategy for the study of photochemical processes. Due to the immense computational effort involved in calculating non-adiabatic derivative coupling vectors, simplifications have been introduced focusing instead on minimum energy crossing points (MECPs), where promising attempts were made with semiempirical quantum mechanical methods. A simplified treatment for describing crossing points between almost arbitrary diabatic states based on a non-self-consistent extended tight-binding method, GFN0-xTB, is presented. Involving only a single diagonalization of the Hamiltonian, the method can provide energies and gradients for multiple electronic states, which can be used in a derivative coupling-vector-free scheme to calculate MECPs. By comparison with high-lying MECIs of benchmark systems, it is demonstrated that the identified geometries are good starting points for further MECI refinement with ab initio methods.

Enhancing the Performance of Global Optimization of Platinum Cluster Structures by Transfer Learning in a Deep Neural Network

The global optimization of metal cluster structures is an important research field. The traditional deep neural network (T-DNN) global optimization method is a good way to find out the global minimum (GM) of metal cluster structures, but a large number of samples are required. We developed a new global optimization method which is the combination of the DNN and transfer learning (DNN-TL). The DNN-TL method transfers the DNN parameters of the small-sized cluster to the DNN of the large-sized cluster to greatly reduce the number of samples. For the global optimization of Pt₉ and Pt₁₃ clusters in this research, the T-DNN method requires about 3-10 times more samples than the DNN-TL method, and the DNN-TL method saves about 70-80% of time. We also found that the average amplitude of parameter changes in the T-DNN training is about 2 times larger than that in the DNN-TL training, which rationalizes the effectiveness of transfer learning. The average fitting errors of the DNN trained by the DNN-TL method can be even smaller than those by the T-DNN method because of the reliability of transfer learning. Finally, we successfully obtained the GM structures of Pt_n (n = 8-14) clusters by the DNN-TL method.

Insight into Substrate Recognition by Urea-Based Helical Foldamer Catalysts Using a DFT Global Optimization Approach

Peptides and foldamers have recently gained increasing attention as chiral catalysts to achieve challenging (asymmetric) transformations. We previously reported that short helically folded aliphatic oligoureas in combination with achiral Brønsted bases are effective H-bonding catalysts for C-C bond-forming reactions─i.e., the conjugate addition of 1,3-dicarbonyl pronucleophiles to nitroalkenes─with high reactivity and selectivity and at remarkably low chiral catalyst/substrate molar ratios. This theoretical investigation at the density functional theory level of theory, aims to both analyze how the substrates of the reaction interact with the foldamer catalyst and rationalize a chain-length dependence effect on the catalytic properties. We confirm that the first two ureas are the only H-bond donors available to interact with external molecules. Moreover, each urea site interacts with one of the two reactants allowing a short distance between the two reacting carbons, thus facilitating the conjugated addition. Additionally, it was observed that the molecular recognition and catalyst-substrate interactions are mainly governed by electrostatic interactions but not orbital interactions (see from NBO if this is finally true). On these grounds, an electrostatic potential (ESP) analysis showed an important internal charge separation in the catalyst, the positive ESP region being concentrated around the first two ureas, with its area extending as the number of residues increases.

An Improved Self-Adaptive Differential Evolution with the Neighborhood Search Algorithm for Global Optimization of Bimetallic Clusters

Global optimization of multicomponent cluster structures is considerably time-consuming due to the existence of a vast number of isomers. In this work, we proposed an improved self-adaptive differential evolution with the neighborhood search (SaNSDE) algorithm and applied it to the global optimization of bimetallic cluster structures. The cross operation was optimized, and an improved basin hopping module was introduced to enhance the searching efficiency of SaNSDE optimization. Taking (PtNi)_N (N = 38 or 55) bimetallic clusters as examples, their structures were predicted by using this algorithm. The traditional SaNSDE algorithm was carried out for comparison with the improved SaNSDE algorithm. For all the optimized clusters, the excess energy and the second difference of the energy were calculated to examine their relative stabilities. Meanwhile, the bond order parameters were adopted to quantitatively characterize the cluster structures. The results reveal that the improved SaNSDE algorithm possessed significantly higher searching capability and faster convergence speed than the traditional SaNSDE algorithm. Furthermore, the lowest-energy configurations of (PtNi)₃₈ clusters could be classified as the truncated octahedral and disordered structures. In contrast, all the optimal (PtNi)₅₅ clusters were approximately icosahedral. Our work fully demonstrates the high efficiency of the improved algorithm and advances the development of global optimization algorithms and the structural prediction of multicomponent clusters.

Hydrogen-Bond Topology Is More Important Than Acid/Base Strength in Atmospheric Prenucleation Clusters

We explored the hypothesis that on the nanoscale level, acids and bases might exhibit different behavior than in bulk solution. Our study system consisted of sulfuric acid, formic acid, ammonia, and water. We calculated highly accurate Domain-based Local pair-Natural Orbital- Coupled-Cluster/Complete Basis Set (DLPNO-CCSD(T)/CBS) energies on DFT geometries and used the resulting Gibbs free energies for cluster formation to compute the overall equilibrium constants for every possible cluster. The equilibrium constants combined with the initial monomer concentrations were used to predict the formation of clusters at the top and the bottom of the troposphere. Our results show that formic acid is as effective as ammonia at forming clusters with sulfuric acid and water. The structure of formic acid is uniquely suited to form hydrogen bonds with sulfuric acid. Additionally, it can partner with water to form bridges from one side of sulfuric acid to the other, hence demonstrating that hydrogen bonding topology is more important than acid/base strength in these atmospheric prenucleation clusters.

Notes on Fitting and Analysis Frameworks for QENS Spectra of (Soft) Colloid Suspensions

With continuously improving signal-to-noise ratios, a statistically sound analysis of quasi-elastic neutron scattering (QENS) spectra requires to fit increasingly complex models which poses several challenges. Simultaneous fits of the spectra for all recorded values of the momentum transfer become a standard approach. Spectrometers at spallation sources can have a complicated non-Gaussian resolution function which has to be described most accurately. At the same time, to speed up the fitting, an analytical convolution with this resolution function is of interest. Here, we discuss basic concepts to efficient approaches for fits of QENS spectra based on standard MATLAB and Python fit algorithms. We illustrate the fits with example data from IN16B, BASIS, and BATS.

Basin Hopping Genetic Algorithm for Global Optimization of PtCo Clusters

In general, searching the lowest-energy structures is considerably more time-consuming for bimetallic clusters than for monometallic ones because of the presence of an increasing number of homotops and geometrical isomers. In this article, a basin hopping genetic algorithm (BHGA), in which the genetic algorithm is implanted into the basin hopping (BH) method, is proposed to search the lowest-energy structures of 13-, 38-, and 55-atom PtCo bimetallic clusters. The results reveal that the proposed BHGA, as compared with the standard BH method, can markedly improve the convergent speed for global optimization and the possibility for finding the global minima on the potential energy surface. Meanwhile, referencing the monometallic structures in initializations may further raise the searching efficiency. For all the optimized clusters, both the excess energy and the second difference of the energy are calculated to examine their relative stabilities at different atomic ratios. The bond order parameter, the similarity function, and the shape factor are also adopted to quantitatively characterize the cluster structures. The results indicate that the 13- and the 55-atom systems tend to be icosahedral despite different degrees of lattice distortions. In contrast, for the 38-atom system, Pt₁₀Co₂₈, Pt₁₁Co₂₇, Pt₁₇Co₂₁, Pt₁₉Co₁₉, Pt₂₀Co₁₈, and Pt₃₀Co₈ tend to be disordered, while Pt₂₁Co₁₇ presents a defected face-centered cubic (fcc) structure, and the remaining clusters are perfect fcc. The methodology and results of this work have referential significance to the exploration of other alloy clusters.

Automatic Generation of Flexible-Monomer Intermolecular Potential Energy Surfaces

A method is developed for automatic generation of nonreactive intermolecular two-body potential energy surfaces (PESs) including intramonomer degrees of freedom. This method, called flex-autoPES, is an extension of the autoPES method developed earlier, which assumes rigid monomers. In both cases, the whole PES development proceeds without any human intervention. The functional form used is a sum of products of site-site functions (both atomic and off-atomic sites can be used). The leading terms with sites involving different monomers are of physically motivated form. The long-range part of a PES is computed from monomer properties without using any dimer information. The close-range part is fitted to dimer interaction energies computed using electronic structure methods. Virtually any method can be used in such calculations, but the use of symmetry-adapted perturbation theory provides a seamless connection to the long-range part of the PES. The performance of the flex-autoPES code was tested by developing a full-dimensional PES for the water dimer and PESs including only some soft intramonomer degrees of freedom for the ethylene glycol dimer and for the ethylene glycol-water dimer. In the case of the water dimer, the root-mean-square error (RMSE) of the PES from the data points with negative total energies is 0.03 kcal/mol, and we expect this PES to be more accurate than any previously published PES of this type. For the ethylene glycol dimer and the ethylene glycol-water dimers, the analogous RMSEs are 0.25 and 0.1 kcal/mol, respectively.

Globally optimal catalytic fields for a Diels-Alder reaction

In a previous paper [M. Dittner and B. Hartke, J. Chem. Theory Comput. 14, 3547 (2018)], we introduced a preliminary version of our GOCAT (globally optimal catalyst) concept in which electrostatic catalysts are designed for arbitrary reactions by global optimization of distributed point charges that surround the reaction. In this first version, a pre-defined reaction path was kept fixed. This unrealistic assumption allowed for only small catalytic effects. In the present work, we extend our GOCAT framework by a sophisticated and robust on-the-fly reaction path optimization, plus further concomitant algorithm adaptions. This allows smaller and larger excursions from a pre-defined reaction path under the influence of the GOCAT point-charge surrounding, all the way to drastic mechanistic changes. In contrast to the restricted first GOCAT version, this new version is able to address real-life catalysis. We demonstrate this by applying it to the electrostatic catalysis of a prototypical Diels-Alder reaction. Without using any prior information, this procedure re-discovers theoretically and experimentally established features of electrostatic catalysis of this very reaction, including a field-dependent transition from the synchronous, concerted textbook mechanism to a zwitterionic two-step mechanism, and diastereomeric discrimination by suitable electric field components.

Exploring self-organization of molecular tether molecules on a gold surface by global structure optimization

We employ nondeterministic global cluster structure optimization, based on the evolutionary algorithms paradigm, to model the self-assembly of complex molecules on a surface. As a real-life application example directly related to many recent experiments, we use this approach for the assembly of triazatriangulene "platform" molecules on the Au(111) surface. Without additional restrictions like spatial discretizations, coarse-graining or precalculated adsorption poses, and despite the proof-of-principle character of this study, we achieve satisfactory qualitative agreement with several experimental observations and can provide answers to questions that experiments on these species had left open so far. © 2019 Wiley Periodicals, Inc.

Size-guided multi-seed heuristic method for geometry optimization of clusters: Application to benzene clusters

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size-guided multi-seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest-energy configurations of the cluster with n - 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc.

Two Perturbations for Geometry Optimization of Off-lattice Bead Protein Models

Referring to the optimization algorithm previously developed for atomic clusters, the present author develops an efficient method for geometry optimization of a coarse-grained protein model expressed with two kinds of beads (hydrophilic and hydrophobic ones). In the method, two types of geometrical perturbations, center-directed bead move and one bead rotation, are used to explore new configurations and local optimizations are performed after the perturbations. The center-directed bead move is used for hydrophobic beads and the one bead rotation is performed for both hydrophobic and hydrophilic beads. The optimization method was applied to protein models consisting of 13, 20, 21, and 34 beads. The present method produced the global minima of the 13-, 21-, and 34-bead models reported in the literature and updated the lowest energies of the protein models with 20 beads. These results indicate that the present method is efficient for searching for optimal structures of proteins.

Structure evolution of nanoparticulate Fe2O3

The atomic structure and properties of nanoparticulate Fe2O3 are characterized starting from its smallest Fe2O3 building unit through (Fe2O3)n clusters to nanometer-sized Fe2O3 particles. This is achieved by combining global structure optimizations at the density functional theory level, molecular dynamics simulations by employing tailored, ab initio parameterized interatomic potential functions and experiments. With the exception of nearly tetrahedral, adamantane-like (Fe2O3)2 small (Fe2O3)n clusters assume compact, virtually amorphous structures with little or no symmetry. For n = 2-5 (Fe2O3)n clusters consist mainly of two- and three-membered Fe-O rings. Starting from n = 5 they increasingly assume tetrahedral shape with the adamantane-like (Fe2O3)2 unit as the main building block. However, the small energy differences between different isomers of the same cluster-size make precise structural assignment for larger (Fe2O3)n clusters difficult. The tetrahedral morphology persists for Fe2O3 nanoparticles with up to 3 nm in diameter. Simulated crystallization of larger nanoparticles with diameters of about 5 nm demonstrates pronounced melting point depression and leads to formation of ε-Fe2O3 single crystals with hexagonal morphology. This finding is in excellent agreement with the results obtained for Fe2O3 nanopowders generated by laser vaporization and provides the first direct indication that ε-Fe2O3 may be thermodynamically the most stable phase in this size regime.

Heavy periodane

The potential energy surface of the hypothetical NaMgAlSiPSCl system (heavy periodane) is exhaustively analyzed via the gradient embedded genetic algorithm (GEGA) in combination with density functional theory (DFT) computations. The electronegativity differences among the elements in both the second and third rows of the periodic table indicate that low-energy heavy periodane structures are obtained when highly electronegative and electropositive elements are bound together, but the global minimum of the heavy periodane system is completely different to its second-row analog (LiBeBCNOF).