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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 (Pt3Cu)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. [ABSTRACT FROM AUTHOR]

The stability and reactivity of Pd4Ni4 and Pd4Cu4 clusters embedded on graphene modified by monovacancy and nitrogen doping were investigated using auxiliary density functional theory (ADFT) calculations. The most stable structure of the Pd4Ni4 cluster is found in high spin multiplicity, whereas the lowest stable energy structure of the Pd4Cu4 cluster is a close shell system. The interaction energies between the bimetallic clusters and the defective graphene systems are significantly higher than those reported in the literature for the Pd‐based clusters deposited on pristine graphene. It is observed that the composites studied present a HOMO‐LUMO gap less than 1 eV, which suggests that they may present a good chemical reactivity. Therefore, from the results obtained in this work it can be inferred that the single vacancy graphene and pyridinic N‐doped graphene are potentially good support materials for Pd‐based clusters. [ABSTRACT FROM AUTHOR]

In this work, the reactions of quadricyclane with dimethyl azodicarboxylate (DMAD) and of quadricyclane with diethyl azodicarboxylate (DEAD) in gas phase and in water environments were studied by a first-principles investigation within the framework of auxiliary density functional theory (ADFT). For these type of organic reactions is known that water is required to accelerate them. Since the reason of why this occur is still unknown, this work aims to gain insight into this reaction mechanism. For this investigation, the generalized gradient approximation as well as a hybrid functional were employed. The obtained optimized structures for the reactants, of the products and of the transition states are reported, together with the corresponding frequency analysis results and the reaction profiles. Along the proposed concerted reaction mechanism, a critical points search of the electron density and a charge analysis were performed. The calculated potential energy barriers of these reactions in gas phase and in water environments are compared. In agreement with experiment, the obtained results indicate that both reactions occur faster in water than in gas phase. This study shows that there is a change in the polarity of the two most important carbon atoms of the formed compounds along the reactions and that the decrease of the activation energy barrier which occurs in liquid phase in these reactions is because the structures of the main transition states are stabilized by the water environment. Therefore, the here obtained results demonstrate the important role played by the water-molecule framework into the activation energy barrier and structures of the molecules that participate in the DMAD and DEAD cycloaddition reactions. [ABSTRACT FROM AUTHOR]

With the rise of quantum mechanical/molecular mechanical (QM/MM) methods, the interest in the calculation of molecular assemblies has increased considerably. The structures and dynamics of such assemblies are usually governed to a large extend by intermolecular interactions. As a result, the corresponding potential energy surfaces are topological rich and possess many shallow minima. Therefore, local structure optimizations of QM/MM molecular assemblies can be challenging, in particular if optimization constraints are imposed. To overcome this problem, structure optimization in normal coordinate space is advocated. To do so, the external degrees of freedom of a molecule are separated from the internal ones by a projector matrix in the space of the Cartesian coordinates. Here we extend this approach to Cartesian constraints. To this end, we devise an algorithm that adds the Cartesian constraints directly to the projector matrix and in this way eliminates them from the reduced coordinate space in which the molecule is optimized. To analyze the performance and stability of the constrained optimization algorithm in normal coordinate space, we present constrained minimizations of small molecular systems and amino acids in gas phase as well as water employing QM/MM constrained optimizations. All calculations are performed in the framework of auxiliary density functional theory as implemented in the program deMon2k. [ABSTRACT FROM AUTHOR]

Path-Integral Molecular Dynamics (PIMD) method is key to include nuclear quantum effects (NQEs) in molecular dynamics simulations which can influence a variety of properties. As a first application of the interface between the i-PI code and the deMon2k electronic structure code, we apply it to evaluate NQEs on the 13 C isotropic nuclear shielding/chemical shift of a set of linear carboxylate ions solvated by a water cluster. A quantum mechanics / molecular mechanics treatment of the electronic structure in conjunction with relevant combination of thermostat and number of replicas in the PIMD algorithm allows for a good convergence of the 13 C isotropic nuclear shielding values regardless of the considered carboxylate. The simulations demonstrate that regardless of the considered carboxylate ion and carbon atom, inclusion of NQEs always improves agreement with the experimental data when looking at relative 13 C isotropic chemical shifts in a given compound. The present study thus paves the ways to new applications of the deMon2k code, whether it be for pure quantum mechanics or quantum mechanics / molecular mechanics simulations, for simulations taking into account NQEs. [ABSTRACT FROM AUTHOR]

Singlet oxygen ( 1 O 2 ) comes in two flavors—namely the dominant lower-energy a 1 Δ g state and the higher-energy shorter-lived b 1 Σ g + state—and plays a key role in many photochemical and photobiological reactions. For this reason, and because of the large size of the systems treated, many papers have appeared with density-functional theory (DFT) treatments of the reactions of 1 O 2 with different chemical species. The present work serves as a reminder that the common assumption that it is enough to fix the spin multiplicity as unity is not enough to insure a correct treatment of singlet oxygen. We review the correct group theoretical treatment of the three lowest energy electronic states of O 2 which, in the case of 1 O 2 is often so badly explained in the relevant photochemical literature that the explanation borders on being incorrect and prevents, rather than encourages, a correct treatment of this interesting and important photochemical species. We then show how many electronic structure programs, such as a freely downloadable and personal-computer compatible Linux version of deMon2k, may be used, together with the multiplet sum method (MSM), to obtain a more accurate estimation of the potential energy curves (PECs) of the two 1 O 2 states. Applications of the MSM DFT method to 1 O 2 appear to be extremely rare as we were only able to find one correct application of the DFT MSM (or rather a very similar approach) to 1 O 2 in our literature search. Here we treat both the a 1 Δ g and b 1 Σ g + state with a wide variety of density-functional approximations (DFAs). Various strengths and weaknesses of different DFAs emerge through our application of the MSM method. In particular, the quality of the a 1 Δ g excitation energy reflects how well functionals are able to describe the spin-flip energy in DFT while the quality of the b 1 Σ g + excitation energy reflects how well functionals are able to describe the spin-pairing energy in DFT. Finally, we note that improvements in DFT-based excited-state methods will be needed to describe the full PECs of 1 O 2 including both the equilibrium bond lengths and dissociation behavior. [ABSTRACT FROM AUTHOR]

A pseudo-diagonalization (PD) algorithm based on the annihilation of the occupied-virtual Kohn-Sham matrix elements is developed in the framework of auxiliary density functional theory (ADFT). The working equations are presented, and their parallel implementation in deMon2k is discussed. To avoid any matrix diagonalization in the PD ADFT self-consistent field (SCF) calculations, the pseudo-diagonalization of the Kohn-Sham matrix is accompanied by the iterative density fitting with the MINRES approach. In order to explore the sparsity of the ADFT Kohn-Sham matrix, localized molecular orbitals (LMOs) are used. Our analysis of the PD ADFT SCF shows that the LMOs remain localized throughout the SCF. Surprisingly, we found this behavior not only for naturally localizable systems such as alkane chains and water clusters but also for less localizable systems such as fullerenes and hydrogen saturated graphene sheets. Despite the very different extensions of the converged molecular orbitals in PD and Roothaan-Hall ADFT SCF calculations, both methods yield, within the given SCF tolerance, nearly identical converged SCF energies. [ABSTRACT FROM AUTHOR]

Parallelization of the source code of a program is nowadays an essential tool in order to improve the calculation speed, whereby different problems need different strategies. This article will describe how the different main parts of the program deMon2k have been parallelized over the last 2 decades. Additional, the efficiency of the parallelization will be presented. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The evolution of variational Coulomb fitting from a purely practical scheme to reduce computational burden to a formal variant of Hohenberg–Kohn–Sham density functional theory (auxiliary density functional theory, ADFT) is discussed. After a summary of the historical evolution, an analysis of its connection with the Hohenberg–Kohn theorem is given, some implications for the Euler equation and for time-dependent DFT are given and some implications for the deMon2k code delineated. [ABSTRACT FROM AUTHOR]

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 , C 2 v , C 3 v , C s , O h , T d , D 5 d , D 5 h , D 6 h and I h 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 I h 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. [ABSTRACT FROM AUTHOR]

Population analyses are part of the theoretical chemist’s toolbox. They provide means to extract information about the repartition of the electronic density among molecules or solids. The values of atomic multipoles in a molecule can shed light on its electrostatic properties and may help to predict how different molecules could interact or to rationalize chemical reactivity for instance. Not being physical observables to which a quantum mechanical operator can be associated, atomic charges and higher order atomic multipoles cannot be defined unambiguously in a molecule, and therefore, several population schemes (PS) have been devised in the last decades. In the context of density functional theory (DFT), PS based on the electron density seem to be best grounded. In particular, some groups have proposed various iterative schemes the outcomes of which are very encouraging. Modern implementations of DFT that are for example based on density fitting techniques permit the investigation of molecular systems comprising of hundreds of atoms. However, population analyses following iterative schemes may become very CPU time consuming for such large systems. In this article, we investigate if the computationally less expensive analyses of the variationally fitted electronic densities can be safely carried out instead of the Kohn-Sham density. It is shown that as long as flexible auxiliary function sets including f and g functions are used, the multipoles extracted from the fitted densities are extremely close to those obtained from the KS density. We further assess if the multipoles obtained through the Hirshfeld’s approach, in its standard or iterative form, can be a useful approach to calculate interaction energies in non-covalent complexes. Relative energies computed with the AMOEBA polarizable forced field combined to iterative Hirshfeld multipoles are encouraging. [ABSTRACT FROM AUTHOR]