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.

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.

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).

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.

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.

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.

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.

1H NMR global diatropicity in copper hydride complexes.

Understanding the magnetic response of electrons in nanoclusters is essential to interpret their NMR spectra thereby providing guidelines for their synthesis towards various target applications. Here, we consider two copper hydride clusters that have applications in hydrogen storage and release under standard temperature and pressure. Through Born-Oppenheimer molecular dynamics simulations, we study dynamics effects and their contributions to the NMR peaks. Finally, we examine the electrons' magnetic response to an applied external magnetic field using the gauge-including magnetically induced currents theory. Local diatropic currents are generated in both clusters but an interesting global diatropic current also appears. This diatropic current has contributions from three µ3-H hydrides and six Cu atoms that form a chain together with three S atoms from the closest ligands resulting in a higher shielding of these hydrides' 1H NMR response. This explains the unusual upfield chemical shift compared to the common downfield shift in similarly coordinated hydrides both observed in previous experimental reports.

A new active learning approach for adsorbate-substrate structural elucidation in silico.

Adsorbate interactions with substrates (e.g. surfaces and nanoparticles) are fundamental for several technologies, such as functional materials, supramolecular chemistry, and solvent interactions. However, modeling these kinds of systems in silico, such as finding the optimum adsorption geometry and energy, is challenging, due to the huge number of possibilities of assembling the adsorbate on the surface. In the current work, we have developed an artificial intelligence (AI) approach based on an active learning (AL) method for adsorption optimization on the surface of materials. AL uses machine learning (ML) regression algorithms and their uncertainties to make a decision (based on a policy) for the next unexplored structures to be computed, increasing, though, the probability of finding the global minimum with a small number of calculations. The methodology allows an accurate and automated structural elucidation of the adsorbate on the surface, based on the minimization of the total electronic energy. The new AL method for adsorption optimization was developed and implemented in the quantum machine learning software/agent for material design and discovery (QMLMaterial) program and was applied for C60@TiO2 anatase (101). It marks another software extension with a new feature in addition to the automatic structural elucidation of defects in materials and of nanoparticles as well. SCC-DFTB calculations were used to build the complex search surfaces with a reasonably low computational cost. An artificial neural network (NN) was employed in the AL framework evaluated together with two uncertainty quantification methods: K-fold cross-validation and non-parametric bootstrap (BS) resampling. Also, two different acquisition functions for decision-making were used: expected improvement (EI) and the lower confidence bound (LCB).

Self-Consistent Auxiliary Density Perturbation Theory.

The working equations for the extension of auxiliary density perturbation theory (ADPT) to hybrid functionals, employing the variational fitting of the Fock potential, are derived. The response equations in the resulting self-consistent ADPT (SC-ADPT) are solved iteratively with an adapted Eirola-Nevanlinna algorithm. As a result, a memory and CPU time efficient implementation of perturbation theory free of four-center electron repulsion integrals (ERIs) is obtained. Our validation calculations of SC-ADPT static and dynamic polarizabilities show quantitative agreement with corresponding coupled perturbed Hartree-Fock and Kohn-Sham results employing four-center ERIs. The comparison of SC-ADPT hybrid functional polarizabilities with coupled cluster reference calculations yield semiquantitative agreement. The presented systematic study of the dynamic polarizabilities of oligothiophenes shows that hybrid functionals can overcome the pathological misplacement of excitation poles by the local density and generalized gradient approximations. Good agreement with experimental dynamic polarizabilities for all studied oligothiophenes is achieved with range-separated hybrid functionals in the framework of SC-ADPT.

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.

Variational Density Fitting with a Krylov Subspace Method.

In this work, we present the implementation of a variational density fitting methodology that uses iterative linear algebra for solving the associated system of linear equations. It is well known that most difficulties with this system arise from the fact that the coefficient matrix is in general ill-conditioned and, due to finite precision round-off errors, it may not be positive definite. The dimensionality, given by the number of auxiliary functions, also poses a challenge in terms of memory and time demand since the coefficient matrix is dense. The methodology presented is based on a preconditioned Krylov subspace method able to deal with indefinite ill-conditioned equation systems. To assess its potential, it has been combined with double asymptotic electron repulsion integral expansions as implemented in the deMon2k package. A numerical study on a set of problems with up to 130,000 auxiliary functions shows its effectiveness to alleviate the abovementioned problematic. A comparison with the default methodology used in deMon2k based on a truncated eigenvalue decomposition of the coefficient matrix indicates that the proposed method exhibits excellent robustness and scalability when implemented in a parallel setting.

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.

Range-Separated Hybrid Functionals with Variational Fitted Exact Exchange.

This work presents a variationally fitted long-range exact exchange algorithm that can be used for the computation of range-separated hybrid density functionals in the linear combination of Gaussian type orbital (LCGTO) approximation. The obtained LCGTO energy and gradient expressions are free of four-center integrals and employ modified three-center integral recurrence relations to obtain optimal computational performance. The accuracy and performance of selected range-separated hybrid functionals with variational fitted long-range exact exchange are analyzed and discussed. A parallel implementation is presented and benchmarked.

Accuracy of auxiliary density functional theory hybrid calculations for activation and reaction enthalpies of pericyclic reactions.

Auxiliary density functional theory (ADFT) hybrid calculations are based on the variational fitting of the Coulomb and Fock potential and, therefore, are free of four-center electron repulsion integrals. So far, ADFT hybrid calculations have been validated successfully for standard enthalpies of formation. In this work the accuracy of ADFT hybrid calculations for the description of pericyclic reactions was quantitatively validated at the B3LYP/6-31G*/GEN-A2* level of theory. Our comparison with conventional Kohn-Sham density functional theory (DFT) results shows that the DFT and ADFT activation and reaction enthalpies are practically indistinguishable. A systematic study of various functionals (PBE, B3LYP, PBE0, CAMB3LYP, CAMPBE0 and HSE06) and basis sets (6-31G*, DZVP-GGA and aug-cc-pVXZ; X = D, T and Q) revealed that the ADFT HSE06/aug-cc-pVTZ/GEN-A2* level of theory yields best balanced accuracy for the activation and reaction enthalpies of the studied pericyclic reactions. With the successfully validate ADFT composite approach consisting of PBE/DZVP-GGA/GEN-A2* structure and transition state optimizations and single-point HSE06/aug-cc-pVTZ/GEN-A2* energy calculations, an accurate, reliable and efficient computational approach for the study of pericyclic reactions in systems at the nanometer scale is proposed.

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.

Robust and Efficient Auxiliary Density Perturbation Theory Calculations.

A new iterative solver for the recently developed time-dependent auxiliary density perturbation theory is presented. It is based on the Eirola-Nevanlinna algorithm for large nonsymmetric linear equation systems. The new methodology is validated by static and dynamic polarizability calculations of small molecules. Comparison between the analytic and iterative solutions of the response equation system shows excellent agreement for the calculated static and dynamic polarizabilities. The new iterative solver reduces the formal scaling from [Symbol: see text](N(4)) to [Symbol: see text](N(3)). Furthermore, the observed computational scaling for linear alkane chains is N(1.6). This subquadratic behavior is possible in systems with a few hundred atoms because of the very small prefactors of the [Symbol: see text](N(3)) and [Symbol: see text](N(2)) steps remaining in the iterative solver. To demonstrate the potential of this new methodology, static polarizabilities of giant fullerenes up to C960, with more than 14,000 basis functions, are calculated.