Active-learning for global optimization of Ni-Ceria nanoparticles: The case of Ce4-xNixO8- x (x = 1, 2, 3).

Ni-CeO2 nanoparticles (NPs) are promising nanocatalysts for water splitting and water gas shift reactions due to the ability of ceria to temporarily donate oxygen to the catalytic reaction and accept oxygen after the reaction is completed. Therefore, elucidating how different properties of the Ni-Ceria NPs relate to the activity and selectivity of the catalytic reaction, is of crucial importance for the development of novel catalysts. In this work the active learning (AL) method based on machine learning regression and its uncertainty is used for the global optimization of Ce(4-x)NixO(8-x) (x = 1, 2, 3) nanoparticles, employing density functional theory calculations. Additionally, further investigation of the NPs by mass-scaled parallel-tempering Born-Oppenheimer molecular dynamics resulted in the same putative global minimum structures found by AL, demonstrating the robustness of our AL search to learn from small datasets and assist in the global optimization of complex electronic structure systems.

Pd8 Cluster: Too Small to Melt? A BOMD Study.

The question of whether a solid-liquid phase transition occurs in small clusters poses a fundamental challenge. In this study, we attempt to elucidate this phenomenon through a thorough examination of the thermal behavior and structural stability of Pd8 clusters employing ab initio simulations. Initially, a systematic global search is carried out to identify the various isomers of the Pd8 cluster. This is accomplished by employing an ab initio basin-hopping algorithm and using the PBE/SDD scheme integrated in the Gaussian code. The resulting isomers are further refined through reoptimization using the deMon2k package. To ensure the structural firmness of the lowest-energy isomer, we calculated normal modes. The structural stability as a function of temperature is analyzed through the Born-Oppenheimer molecular dynamics (BOMD) approach. Multiple BOMD trajectories at distinct simulated temperatures are examined with data clustering analysis to determine cluster isomers. This analysis establishes a connection between the potential energy landscape and the simulated temperature. To address the question of cluster melting, canonical parallel-tempering BOMD runs are performed and analyzed with the multiple-histogram method. A broad maximum in the heat capacity curve indicates a melting transition between 500 and 600 K. To further examine this transition, the mean-squared displacement and the pair-distance distribution function are calculated. The results of these calculations confirm the existence of a solid-liquid phase transition, as indicated by the heat capacity curve.

GAMaterial-A genetic-algorithm software for material design and discovery.

Genetic algorithms (GAs) are stochastic global search methods inspired by biological evolution. They have been used extensively in chemistry and materials science coupled with theoretical methods, ranging from force-fields to high-throughput first-principles methods. The methodology allows an accurate and automated structural determination for molecules, atomic clusters, nanoparticles, and solid surfaces, fundamental to understanding chemical processes in catalysis and environmental sciences, for instance. In this work, we propose a new genetic algorithm software, GAMaterial, implemented in Python3.x, that performs global searches to elucidate the structures of atomic clusters, doped clusters or materials and atomic clusters on surfaces. For all these applications, it is possible to accelerate the GA search by using machine learning (ML), the ML@GA method, to build subsequent populations. Results for ML@GA applied for the dopant distributions in atomic clusters are presented. The GAMaterial software was applied for the automatic structural search for the Ti6 O12 cluster, doping Al in Si11 (4Al@Si11 ) and Na10 supported on graphene (Na10 @graphene), where DFTB calculations were used to sample the complex search surfaces with reasonably low computational cost. Finally, the global search by GA of the Mo8 C4 cluster was considered, where DFT calculations were made with the deMon2k code, which is interfaced with GAMaterial.

Efficient implementation of time-dependent auxiliary density functional theory.

The random phase approximation of time-dependent auxiliary density functional theory (TDADFT) is rederived from auxiliary density perturbation theory. Our exhaustive validation of TDADFT reveals an upshift of the excitation energies by ∼0.1 eV with respect to standard time-dependent density functional theory. For the computationally efficient implementation of TDADFT, floating point operation optimized three-center electron repulsion integral recurrence relations and their double asymptotic expansions are implemented into the Davidson solver. The computational efficiency of TDADFT is benchmarked with four sets of molecules comprising alkanes, fullerenes, DNA fragments, and zeolites. The results show that TDADFT has a computational scaling between 1.3 and 1.9 with respect to the number of basis functions, which is lower than the scaling of standard time-dependent density functional theory. Due to its computational simplifications, TDADFT is particularly well suited for Born-Oppenheimer molecular dynamics simulations. As illustrative examples, we present the temperature effects on the gas-phase absorption spectra of benzene, naphthalene, and anthracene.

How important is the amount of exact exchange for spin-state energy ordering in DFT? Case study of molybdenum carbide cluster, Mo4C2.

Since the form of the exact functional in density functional theory is unknown, we must rely on density functional approximations (DFAs). In the past, very promising results have been reported by combining semi-local DFAs with exact, i.e. Hartree-Fock, exchange. However, the spin-state energy ordering and the predictions of global minima structures are particularly sensitive to the choice of the hybrid functional and to the amount of exact exchange. This has been already qualitatively described for single conformations, reactions, and a limited number of conformations. Here, we have analyzed the mixing of exact exchange in exchange functionals for a set of several hundred isomers of the transition metal carbide, Mo4C2. The analysis of the calculated energies and charges using PBE0-type functional with varying amounts of exact exchange yields the following insights: (1) The sensitivity of spin-energy splitting is strongly correlated with the amount of exact exchange mixing. (2) Spin contamination is exacerbated when correlation is omitted from the exchange-correlation functional. (3) There is not one ideal value for the exact exchange mixing which can be used to parametrize or choose among the functionals. Calculated energies and electronic structures are influenced by exact exchange at a different magnitude within a given distribution; therefore, to extend the application range of hybrid functionals to the full periodic table the spin-energy splitting energies should be investigated.

Automatic structural elucidation of vacancies in materials by active learning.

Finding the optimum structures of non-stoichiometric or berthollide materials, such as (1D, 2D, 3D) materials or nanoparticles (0D), is challenging due to the huge chemical/structural search space. Computational methods coupled with global optimization algorithms have been used successfully for this purpose. In this work, we have developed an artificial intelligence method based on active learning (AL) or Bayesian optimization for the automatic structural elucidation of vacancies in solids and nanoparticles. AL uses machine learning regression algorithms and their uncertainties to take decisions (from a policy) on the next unexplored structures to be computed, increasing the probability of finding the global minimum with few calculations. The methodology allows an accurate and automated structural elucidation for vacancies, which are common in non-stoichiometric (berthollide) materials, helping to understand chemical processes in catalysis and environmental sciences, for instance. The AL vacancies method was implemented in the quantum machine learning software/agent for material design and discovery (QMLMaterial). Also, two additional acquisition functions for decision making were implemented, besides the expected improvement (EI): the lower confidence bound (LCB) and the probability of improvement (PI). The new software was applied for the automatic structural search for graphite (C36) with 3 (C36-3) and 4 (C36-4) carbon vacancies and C60 (C60-4) fullerene with 4 carbon vacancies. DFTB calculations were used to build the complex search surfaces with reasonably low computational cost. Furthermore, with the AL method for vacancies, it was possible to elucidate the optimum oxygen vacancy distribution in CaTiO3 perovskite by DFT, where a semiconductor behavior results from oxygen vacancies. Throughout the work, a Gaussian process with its uncertainty was employed in the AL framework using different acquisition functions (EI, LCB and PI), and taking into account different descriptors: Ewald sum matrix and sine matrix. Finally, the performance of the proposed AL method was compared to random search and genetic algorithm.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Variational fitting of the Fock exchange potential with modified Cholesky decomposition.

The variational fitting of the Fock potential employing localized molecular orbitals requires either the inversion of the local two-center Coulomb matrices or alternatively the solution of corresponding linear equation systems with these matrices. In both cases, the method of choice is the Cholesky decomposition of the formally positive definite local two-center Coulomb matrices. However, due to finite-precision round-off errors, the local Coulomb matrices may be indefinite, and thus, the Cholesky decomposition is not applicable. To overcome this problem, we propose to make use of a modified Cholesky decomposition based on the indefinite factorization of local two-center Coulomb matrices. To this end, the working equations for the use of the modified Cholesky decomposition within the variational fitting of the Fock potential are presented. Benchmark calculations with global and range-separated hybrid functionals show that the proposed method can improve considerably the workload balance in parallel calculations.

Molecular Simulations with in-deMon2k QM/MM, a Tutorial-Review.

deMon2k is a readily available program specialized in Density Functional Theory (DFT) simulations within the framework of Auxiliary DFT. This article is intended as a tutorial-review of the capabilities of the program for molecular simulations involving ground and excited electronic states. The program implements an additive QM/MM (quantum mechanics/molecular mechanics) module relying either on non-polarizable or polarizable force fields. QM/MM methodologies available in deMon2k include ground-state geometry optimizations, ground-state Born-Oppenheimer molecular dynamics simulations, Ehrenfest non-adiabatic molecular dynamics simulations, and attosecond electron dynamics. In addition several electric and magnetic properties can be computed with QM/MM. We review the framework implemented in the program, including the most recently implemented options (link atoms, implicit continuum for remote environments, metadynamics, etc.), together with six applicative examples. The applications involve (i) a reactivity study of a cyclic organic molecule in water; (ii) the establishment of free-energy profiles for nucleophilic-substitution reactions by the umbrella sampling method; (iii) the construction of two-dimensional free energy maps by metadynamics simulations; (iv) the simulation of UV-visible absorption spectra of a solvated chromophore molecule; (v) the simulation of a free energy profile for an electron transfer reaction within Marcus theory; and (vi) the simulation of fragmentation of a peptide after collision with a high-energy proton.

A Chemical View on X-ray Photoelectron Spectroscopy: the ESCA Molecule and Surface-to-Bulk XPS Shifts.

In this paper we remind the reader of a simple, intuitive picture of chemical shifts in X-ray photoelectron spectroscopy (XPS) as the difference in chemical bonding between the probed atom and its neighbor to the right in the periodic table, the so called Z+1 approximation. We use the classical ESCA molecule, ethyl trifluoroacetate, and 4d-transition metals to explicitly demonstrate agreement between core-level shifts computed as differences between final core-hole states and the approach where each core-ionized atom is replaced by a Z+1 atom. In this final state, or total energy picture, the XPS shift arises due to the more or less unfavorable chemical bonding of the effective nitrogen in the carbon geometry for the ESCA molecule. Surface core level shifts in metals are determined by whether the Z+1 atom as an alloy segregates to the surface or is more soluble in the bulk. As further illustration of this more chemical picture, we compare the geometry of C 1s and O 1s core-ionized CO with that of, respectively, NO+ and CF+ . The scope is not to propose a new method to compute XPS shifts but rather to stress the validity of this simple interpretation.

Evolution of the Spin Magnetic Moments and Atomic Valence of Vanadium in VCux+, VAgx+, and VAux+ Clusters (x = 3-14).

The atomic structures, bonding characteristics, spin magnetic moments, and stability of VCux+, VAgx+, and VAux+ (x = 3-14) clusters were examined using density functional theory. Our studies indicate that the effective valence of vanadium is size-dependent and that at small sizes some of the valence electrons of vanadium are localized on vanadium, while at larger sizes the 3d orbitals of the vanadium participate in metallic bonding eventually quenching the spin magnetic moment. The electronic stability of the clusters may be understood through a split-shell model that partitions the valence electrons in either a delocalized shell or localized on the vanadium atom. A molecular orbital analysis reveals that in planar clusters the delocalization of the 3d orbital of vanadium is enhanced when surrounded by gold due to enhanced 6s-5d hybridization. Once the clusters become three-dimensional, this hybridization is reduced, and copper most readily delocalizes the vanadium's valence electrons. By understanding these unique features, greater insight is offered into the role of a host material's electronic structure in determining the bonding characteristics and stability of localized spin magnetic moments in quantum confined systems.

Analytic second derivatives from auxiliary density perturbation theory.

The working equations for the calculation of analytic second energy derivatives in the framework of auxiliary density functional theory (ADFT) are presented. The needed perturbations are calculated with auxiliary density perturbation theory (ADPT) which is extended to perturbation dependent basis and auxiliary functions sets. The obtained ADPT equation systems are solved with the Eirola-Nevanlinna algorithm. The newly developed analytic second ADFT energy derivative approach was implemented in deMon2k and validated with respect to the corresponding finite difference approach by calculating the harmonic frequencies of small molecules. Good agreement between these two methodologies is found. To analyze the scaling of the new analytic second ADFT energy derivatives with respect to the number of processors in parallel runs, the harmonic frequencies of the carbon fullerene C240 are calculated with varying numbers of processors. Fair scaling up to 720 processors was found. As showcase applications, symmetry unrestricted optimization and frequency analyses of icosahedral carbon fullerenes with up to 960 atoms are presented.

Efficient calculation of the rotational g tensor from auxiliary density functional theory.

The computation of the rotational g tensor with the recently developed auxiliary density functional theory (ADFT) gauge including atomic orbital (GIAO) methodology is presented. For the rotational g tensor, the calculation of the magnetizability tensor represents the most demanding computational task. With the ADFT-GIAO methodology, the CPU time for the magnetizability tensor calculation can be dramatically reduced. Therefore, it seems most desirable to employ the ADFT-GIAO methodology also for the computation of the rotational g tensor. In this work, the quality of rotational g tensors obtained with the ADFT-GIAO methodology is compared with available experimental data as well as with other theoretical results at the Hartree-Fock and coupled-cluster level of theory. It is found that the agreement between the ADFT-GIAO results and the experiment is good. Furthermore, we also show that the ADFT-GIAO g tensor calculation is applicable to large systems like carbon nanotube models containing hundreds of atom and thousands of basis functions.

Transition-state searches in metal clusters by first-principle methods.

Elucidation of the chemical reactivity of metal clusters is often cumbersome due to the nonintuitive structures of the corresponding transition states. In this work, a hierarchical transition-state algorithm as implemented in the deMon2k code has been applied to locate transition states of small sodium clusters with 6-10 atoms. This algorithm combines the so-called double-ended interpolation method with the uphill trust region method. The minimum structures needed as input were obtained from Born-Oppenheimer molecular dynamics simulations. To connect the found transition states with the corresponding minimum structures, the intrinsic reaction coordinates were calculated. This work demonstrates how nonintuitive rearrangement mechanisms can be studied in metal clusters.

Efficient calculation of nuclear spin-rotation constants from auxiliary density functional theory.

The computation of the spin-rotation tensor within the framework of auxiliary density functional theory (ADFT) in combination with the gauge including atomic orbital (GIAO) scheme, to treat the gauge origin problem, is presented. For the spin-rotation tensor, the calculation of the magnetic shielding tensor represents the most demanding computational task. Employing the ADFT-GIAO methodology, the central processing unit time for the magnetic shielding tensor calculation can be dramatically reduced. In this work, the quality of spin-rotation constants obtained with the ADFT-GIAO methodology is compared with available experimental data as well as with other theoretical results at the Hartree-Fock and coupled-cluster level of theory. It is found that the agreement between the ADFT-GIAO results and the experiment is good and very similar to the ones obtained by the coupled-cluster single-doubles-perturbative triples-GIAO methodology. With the improved computational performance achieved, the computation of the spin-rotation tensors of large systems or along Born-Oppenheimer molecular dynamics trajectories becomes feasible in reasonable times. Three models of carbon fullerenes containing hundreds of atoms and thousands of basis functions are used for benchmarking the performance. Furthermore, a theoretical study of temperature effects on the structure and spin-rotation tensor of the H(12)C-(12)CH-DF complex is presented. Here, the temperature dependency of the spin-rotation tensor of the fluorine nucleus can be used to identify experimentally the so far unknown bent isomer of this complex. To the best of our knowledge this is the first time that temperature effects on the spin-rotation tensor are investigated.

QM/MM calculations with deMon2k.

The density functional code deMon2k employs a fitted density throughout (Auxiliary Density Functional Theory), which offers a great speed advantage without sacrificing necessary accuracy. Powerful Quantum Mechanical/Molecular Mechanical (QM/MM) approaches are reviewed. Following an overview of the basic features of deMon2k that make it efficient while retaining accuracy, three QM/MM implementations are compared and contrasted. In the first, deMon2k is interfaced with the CHARMM MM code (CHARMM-deMon2k); in the second MM is coded directly within the deMon2k software; and in the third the Chemistry in Ruby (Cuby) wrapper is used to drive the calculations. Cuby is also used in the context of constrained-DFT/MM calculations. Each of these implementations is described briefly; pros and cons are discussed and a few recent applications are described briefly. Applications include solvated ions and biomolecules, polyglutamine peptides important in polyQ neurodegenerative diseases, copper monooxygenases and ultra-rapid electron transfer in cryptochromes.

Nature of valence transition and spin moment in Ag(n)V(+) clusters.

Evolution in the atomic structure, bonding characteristics, stability, and the spin magnetic moment of neutral and cationic AgnV clusters has been investigated using first-principles density functional approach with gradient corrected functional. It is shown that at small sizes, the V 4s states hybridize with Ag states to form 1S and 1P like superatomic orbitals, whereas the 3d states are localized on V giving the V atom an effective valence of 1 or 2. Starting from Ag8V(+), the V 3d states begin to participate in the bonding by hybridizing with the nearly free electron gas to form 1D superatomic orbitals increasing the V atom effective valence toward 5. For the cationic clusters, this changing valence results in three shell closures that lead to stable species. These occur for cationic clusters containing 5, 7, and 14 Ag atoms. The first two stable species correspond to filled 1S and 1P shells in two and three dimensions with a valence of 2 for V, whereas the closure at 14 Ag atoms correspond to filled 1S, 1P, and 1D shells with V site exhibiting a valence of 5. The transition from filled 1S and 1P shells to filled 1S, 1P, and 1D shells is confirmed by a quenching of the spin magnetic moment. The theoretical findings are consistent with the observed drops in intensity in the mass spectrum of AgnV(+) clusters after 5, 7, and 14 Ag atoms.

Robust and efficient variational fitting of Fock exchange.

We propose a new variational fitting approach for Fock exchange that requires only the calculation of analytical three-center electron repulsion integrals. It relies on localized molecular orbitals and Hermite Gaussian auxiliary functions. The working equations along with a detailed description of the implementation are presented. The computational performance of the new algorithm is analyzed by benchmark calculations on systems with different dimensionality. Comparison with standard four-center and three-center electron repulsion integral Hartree-Fock calculations shows an excellent accuracy-performance relation.

QMLMaterial─A Quantum Machine Learning Software for Material Design and Discovery.

Structural elucidation of chemical compounds is challenging experimentally, and theoretical chemistry methods have added important insight into molecules, nanoparticles, alloys, and materials geometries and properties. However, finding the optimum structures is a bottleneck due to the huge search space, and global search algorithms have been used successfully for this purpose. In this work, we present the quantum machine learning software/agent for materials design and discovery (QMLMaterial), intended for automatic structural determination in silico for several chemical systems: atomic clusters, atomic clusters and the spin multiplicity together, doping in clusters or solids, vacancies in clusters or solids, adsorption of molecules or adsorbents on surfaces, and finally atomic clusters on solid surfaces/materials or encapsulated in porous materials. QMLMaterial is an artificial intelligence (AI) software based on the active learning method, which uses machine learning regression algorithms and their uncertainties for decision making on the next unexplored structures to be computed, increasing the probability of finding the global minimum with few calculations as more data is obtained. The software has different acquisition functions for decision making (e.g., expected improvement and lower confidence bound). Also, the Gaussian process is available in the AI framework for regression, where the uncertainty is obtained analytically from Bayesian statistics. For the artificial neural network and support vector regressor algorithms, the uncertainty can be obtained by K-fold cross-validation or nonparametric bootstrap resampling methods. The software is interfaced with several quantum chemistry codes and atomic descriptors, such as the many-body tensor representation. QMLMaterial's capabilities are highlighted in the current work by its applications in the following systems: Na20, Mo6C3 (where the spin multiplicity was considered), H2O@CeNi3O5, Mg8@graphene, Na3Mg3@CNT (carbon nanotube).

Magnetizability tensors from auxiliary density functional theory.

The working equations for the calculation of the magnetizability tensor in the framework of auxiliary density functional theory with gauge including atomic orbitals (ADFT-GIAO) are derived. Unlike in the corresponding conventional density functional theory implementations the numerical integration of the GIAOs is avoided in ADFT-GIAO. Our validation shows that this simplification has no effect on the accuracy of the methodology. As a result, a reliable and efficient implementation for the calculation of magnetizabilities of systems with more than 1000 atoms and 14,000 basis functions is presented.