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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.

The iterative Krylov solver MINRES for linear equation systems has been implemented into auxiliary density perturbation theory. To this end, the MINRES solver was incorporated into the Eirola-Nevanlinna algorithm for large nonsymmetric matrices. As a result, the formal scaling of ADPT is reduced from O ( Naux4 ) to O ( Naux3 ), being Naux the number of auxiliary functions. Moreover, with MINRES this scaling can be further reduced by the use of the double asymptotic expansion of the two-center electron repulsion integrals. This state-of-the-art solver allows first-principles quantum-mechanical calculations of response properties for large systems with thousands of atoms at the nanometric scale. Comparison between the analytic and iterative solutions show excellent agreement for static and dynamical polarizabilities. To demonstrate the robustness of this newly implemented methodology, static polarizabilities of microbiologically relevant systems with more than 100,000 auxiliary functions and 28,000 basis functions are presented in this work.

The parallel-tempering molecular dynamics (PTMD) method is a key computational tool to explore complex potential energy surfaces. As a result of its computational cost, it has mainly been coupled to force-field approaches despite the interest it could also represent for ab initio studies. In this article, we present the native implementation of the PTMD algorithm in the deMon2k code which is the first implementation of this approach in a DFT code based on localized basis set. To take advantage of the intrinsic parallel nature of the PTMD algorithm without modifying the Message Passing Interface (MPI) scheme dedicated to the calculation of the electronic structure, a two-layer MPI architecture was implemented. Both synchronous and asynchronous communications between processes for configuration exchanges were implemented in order to test the parallel efficiency of the code. This article presents the implementation details and their application to describe phase changes in the water hexamer (H 2 O) 6 at the DFT level.

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).

Active learning (AL) has been successfully applied in materials science for the global optimization of clusters and defects in materials. Many important chemistry problems require the structural elucidation of molecules as a first step to the mechanistic elucidation of complex heterogeneous catalysis phenomena. Theoretical methods coupled with global optimization algorithms are successfully used for this purpose. However, it is challenging to find the global minimum structure together with the proper electronic spin multiplicity. In this work, we present an AL implementation for global optimization of atomic clusters where the spin multiplicity is considered in the search loop (SM@AL). The method was implemented in the QMLMaterial software, interfaced with the deMon2k program to perform local structure optimizations. In this work, we present applications of SM@AL for the global optimization, in terms of molecular structure and electronic spin of 3Al@Si11, where Si11 is doped by 3 Al, and Mo4C2 with spin multiplicities 2, 4 and 6 and 1, 3, 5, 7, 9 and 11, respectively.

The working equations for the variational fitting of the Coulomb potential in finite systems with symmetry-adapted auxiliary functions are derived and presented. The computationally efficient construction of the symmetry transformation matrix from symmetry equivalent atoms and function transformation matrices is discussed in details. We show that for totally symmetric electron densities only the totally symmetric parts of the fitting equation systems in auxiliary density functional theory have to be solved. This approach is validated on test molecules with point group symmetries C∞v,C2v,C3v,Cs,Oh,Td,D5d,D5h,D6h and Ih for Hartree-Fock, the local density approximation, the generalized gradient approximation and hybrid functionals. In all cases, the self-consistent field energy differences between the converged unconstrained and symmetry-adapted density fitting is well below 1 kcal/mol. The large reduction in the dimensionality of the corresponding linear equation systems is explored in the calculation of giant fullerenes in Ih symmetry. For these systems, the symmetry-adapted density fitting using truncated eigenvalue decomposition is computationally more efficient than the recently introduced iterative density fitting with the Krylov subspace method MINRES. This illustrates the computational advantage of symmetry-adapted density fitting.

The study of materials in the nanoscale regime has important applications for catalytic reactions, the energy industry and medicine. We performed exploratory density functional theory calculations for molybdenum disulphide (MoS2) and calcium carbonate (CaCO3) nanoparticles (NPs), the former being developed as a hydrogenation and coke-prevention catalyst and the latter representing the catalytic support in some reservoirs. Utilizing Born–Oppenheimer Molecular Dynamics with reduced masses as a global optimization method, we found Mo8S16 and Mo16S32 NPs with lower-lying energies than those of locally optimized crystal geometries. Our results suggest that MoS2 NPs prefer a tetragonal lattice arrangement which is in agreement with previous studies of smaller MoS2 NPs. It remains to be seen how prenucleation MoS2 clusters of the hexagonal phase are formed. The CaCO3 NPs showed small energy differences between vastly different conformations. Therefore, in order to capture only their supporting effects in reservoirs, one should consider keeping a substantial part of the models fixed.

Context Analytic exchange-correlation kernel formulations are of the outermost importance for density functional theory (DFT) perturbation calculations. In this paper, the working equation for the exchange-correlation kernel of the generalized gradient approximation (GGA) for perturbation dependent auxiliary functions is derived and discussed in the framework of auxiliary density functional theory (ADFT). The presented new formulation is extended to the unrestricted approach, too. A comprehensive discussion of the implementation of the GGA ADFT kernel, using either the native exchange-correlation functional implementations in deMon2k or the ones from the LibXC library, is given. Calculations with analytic exchange-correlation kernels are compared to their finite difference counterparts. The obtained results are in quantitative agreement. Nevertheless, analytic GGA ADFT kernel implementations show substantial improvement in the computational performance. Similar results are reported for analytic second derivatives of effective core potential (ECP) and model core potential (MCP) matrix elements when compared to their finite difference counterparts in molecular frequency analyses. Method All calculations are performed in the framework of ADFT as implemented in deMon2k. In the ADFT analytic frequency calculations, auxiliary density perturbation theory was used. The underlying two-center exchange-correlation kernel matrix elements are calculated by numerical integration either with analytic or finite difference kernel expressions. Validation calculations are performed with the VWN and PBE functionals employing DFT-optimized DZVP basis sets in conjunction with automatically generated GEN-A2 auxiliary density function sets. In the (Pt 3 Cu) n cluster benchmark calculations, the RPBE functional was used. For Pt atoms, the quasi-relativistic LANL2DZ effective core potential with the corresponding valence basis set was employed, whereas for Cu atoms, the all-electron DFT-optimized TZVP basis was applied. The auxiliary density was expanded by the automatically generated GEN-A2* auxiliary function set. We run all benchmark calculations in parallel on 24 cores.

Thermodynamic properties of the small sodium clusters Na6,Na8 and Na10 have been studied by Born–Oppenheimer molecular dynamics (BOMD) simulations. The simulations were performed with auxiliary density functional theory as implemented in the deMon2k code. This approach has already proved accurate for the calculations of thermodynamic properties of larger sodium clusters. The Nosé–Hoover chain thermostat was applied to control the temperature. BOMD simulations were performed in the temperature range from 250 to 1000 K. The obtained trajectories were analyzed using the multiple-histogram method in order to obtain continuous functions for the energies and heat capacities. For the Na6 and Na8 clusters, besides the fragmentation of the clusters at higher temperature, no other characteristic features in the heat capacity curves are found. On the other hand, a small peak at low temperature was found in the Na10 heat capacity curve which is characteristic for molecular melting. Our analysis of the Na10 melting shows that electronic structure parameters are better suited than geometrical ones to describe the melting process due to the fluctional nature of the clusters. We find that energetical resorting of the occupied cluster orbitals is characteristic for the Na10 cluster melting.

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.