GPAW: An open Python package for electronic structure calculations.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Ab initio metadynamics determination of temperature-dependent free-energy landscape in ultrasmall silver clusters.

Ab initio metadynamics enables the extraction of free-energy landscapes having the accuracy of first-principles electronic structure methods. We introduce an interface between the PLUMED code that computes free-energy landscapes and enhanced-sampling algorithms and the Atomic Simulation Environment (ASE) module, which includes several ab initio electronic structure codes. The interface is validated with a Lennard-Jones cluster free-energy landscape calculation by averaging multiple short metadynamics trajectories. We use this interface and analysis to estimate the free-energy landscape of Ag5 and Ag6 clusters at 10, 100, and 300 K with the radius of gyration and coordination number as collective variables, finding at most tens of meV in error. Relative free-energy differences between the planar and non-planar isomers of both clusters decrease with temperature in agreement with previously proposed stabilization of non-planar isomers. Interestingly, we find that Ag6 is the smallest silver cluster where entropic effects at room temperature boost the non-planar isomer probability to a competing state. The new ASE-PLUMED interface enables simulating nanosystem electronic properties under more realistic temperature-dependent conditions.

Real-time time-dependent density functional theory implementation of electronic circular dichroism applied to nanoscale metal-organic clusters.

Electronic circular dichroism (ECD) is a powerful spectroscopy method for investigating chiral properties at the molecular level. ECD calculations with the commonly used linear-response time-dependent density functional theory (LR-TDDFT) framework can be prohibitively costly for large systems. To alleviate this problem, we present here an ECD implementation within the projector augmented-wave method in a real-time-propagation TDDFT framework in the open-source GPAW code. Our implementation supports both local atomic basis sets and real-space finite-difference representations of wave functions. We benchmark our implementation against an existing LR-TDDFT implementation in GPAW for small chiral molecules. We then demonstrate the efficiency of our local atomic basis set implementation for a large hybrid nanocluster and discuss the chiroptical properties of the cluster.

Large-Z limit in atoms and solids from first principles.

We present density functional theory (DFT) calculations of atomic ionization potentials and lattice constants of simple solids from low atomic numbers Z to the large-Z limit. We compare different kinetic energy functional approximations [Kohn-Sham (KS) vs simple orbital-free functionals] and, in the case of orbital free, also different methods for including the nuclear potential (all-electron with the projector augmented wave method vs local pseudopotentials). For both ionization potentials and lattice constants, all-electron orbital-free DFT does yield the general trend of KS DFT for moderate values of the atomic number Z. For large values of Z, all-electron orbital-free DFT deviates from the KS DFT results. Local pseudopotentials give a better qualitative description by adding shell oscillations to the orbital-free DFT model. We show that both all-electron orbital-free DFT and KS DFT have a finite value for nonrelativistic lattice constants in the large-Z limit.

Silver-Stabilized Guanine Duplex: Structural and Optical Properties.

Recent experimental duplexes of DNA stabilized by Ag cations, pairing homostrands of guanine-guanine, cytosine-cytosine, adenine-thymine, and thymine-thymine, display much higher stability than the Watson-Crick paired DNA duplexes; these broaden the range of applications for DNA nanotechnology. Here we focus on silver-stabilized guanine duplexes in water. Using hybrid quantum mechanics/molecular mechanics simulations, we propose an atomic structure for the Ag+-mediated guanine duplex with two nucleobases per strand, G2-Ag2+-G2. We then compare experimental and time-dependent density functional theory-simulated electronic circular dichroism (ECD) spectra to validate our results. Both experimental and simulated ECD share two negative peaks around 220 and 280 nm, with no positive signal in the measured wavelength range. We found that the left- or right-handed disposition of bases in the structure has a decisive effect on the signs of the ECD. We conclude that G2-Ag2+-G2 is left-hand-oriented, and extrapolation of this orientation to longer strands gives rise to a left-hand-oriented parallel helix stabilized by interplanar H bonds.

Optical Properties of Silver-Mediated DNA from Molecular Dynamics and Time Dependent Density Functional Theory.

We report a combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics and time-dependent density functional (TDDFT) study of metal-mediated deoxyribonucleic acid (M-DNA) nanostructures. For the Ag + -mediated guanine tetramer, we found the maug-cc-pvdz basis set to be sufficient for calculating electronic circular dichroism (ECD) spectra. Our calculations further show that the B3LYP, CAM-B3LYP, B3LYP*, and PBE exchange-correlation functionals are all able to predict negative peaks in the measured ECD spectra within a 20 nm range. However, a spurious positive peak is present in the CAM-B3LYP ECD spectra. We trace the origins of this spurious peak and find that is likely due to the sensitivity of silver atoms to the amount of Hartree⁻Fock exchange in the exchange-correlation functional. Our presented approach provides guidance for future computational investigations of other Ag + -mediated DNA species.

Self-consistent assessment of Englert-Schwinger model on atomic properties.

Our manuscript investigates a self-consistent solution of the statistical atom model proposed by Berthold-Georg Englert and Julian Schwinger (the ES model) and benchmarks it against atomic Kohn-Sham and two orbital-free models of the Thomas-Fermi-Dirac (TFD)-λvW family. Results show that the ES model generally offers the same accuracy as the well-known TFD-15vW model; however, the ES model corrects the failure in the Pauli potential near-nucleus region. We also point to the inability of describing low-Z atoms as the foremost concern in improving the present model.

Excitation-dependent fluorescence from atomic/molecular layer deposited sodium-uracil thin films.

Atomic/molecular layer deposition (ALD/MLD) offers unique possibilities in the fabrication of inorganic-organic thin films with novel functionalities. Especially, incorporating nucleobases in the thin-film structures could open new avenues in the development of bio-electronic and photonic devices. Here we report an intense blue and widely excitation-dependent fluorescence in the visible region for ALD/MLD fabricated sodium-uracil thin films, where the crystalline network is formed from hydrogen-bonded uracil molecules linked via Na atoms. The excitation-dependent fluorescence is caused by the red-edge excitation shift (REES) effect taking place in the red-edge of the absorption spectrum, where the spectral relaxation occurs in continuous manner as demonstrated by the time-resolved measurements.

Redox Potentials from Ab Initio Molecular Dynamics and Explicit Entropy Calculations: Application to Transition Metals in Aqueous Solution.

We present a complete methodology to consistently estimate redox potentials strictly from first-principles, without any experimental input. The methodology is based on (i) ab initio molecular dynamics (MD) simulations, (ii) all-atom explicit solvation, (iii) the two-phase thermodynamic (2PT) model, and (iv) the use of electrostatic potentials as references for the absolute electrochemical scale. We apply the approach presented to compute reduction potentials of the following redox couples: Cr2+/3+, V2+/3+, Ru(NH3)62+/3+, Sn2+/4+, Cu1+/2+, FcMeOH0/1+, and Fe2+/3+ (in aqueous solution) and Fc0/1+ (in acetonitrile). We argue that fully quantum-mechanical simulations are required to correctly model the intricate dynamical effects of the charged complexes on the surrounding solvent molecules within the solvation shell. Using the proposed methodology allows for a computationally efficient and statistically stable approach to compute free energy differences, yielding excellent agreement between our computed redox potentials and the experimental references. The root-mean-square deviation with respect to experiment for the aqueous test set and the two exchange-correlation density functionals used, PBE and PBE with van der Waals corrections, are 0.659 and 0.457 V, respectively. At this level of theory, depending on the functional employed, its ability to correctly describe each particular molecular complex seems to be the factor limiting the accuracy of the calculations.

Silver-Mediated Double Helix: Structural Parameters for a Robust DNA Building Block.

The DNA double helix is a versatile building block used in DNA nanotechnology. To potentiate the discovery of new DNA nanoscale assemblies, recently, silver cations have been introduced to pair DNA strands by base-Ag+-base bonding rather than by Watson-Crick pairing. In this work, we study the classical dynamics of a parallel silver-mediated homobase double helix and compare it to the dynamics of the antiparallel double helix. Our classical simulations show that only the parallel double helix is highly stable through the 100 ns simulation time. A new type of H-bond previously proposed by our collaboration and recently observed in crystal-determined helices drives the physicochemical stabilization. Compared to the natural B-DNA form, the metal-mediated helix has a contracted axial base pair rise and smaller numbers of base pairs per turn. These results open the path for the inclusion of this robust metal-mediated building block into new nanoscale DNA assemblies.

Accurate schemes for calculation of thermodynamic properties of liquid mixtures from molecular dynamics simulations.

We explore different schemes for improved accuracy of entropy calculations in aqueous liquid mixtures from molecular dynamics (MD) simulations. We build upon the two-phase thermodynamic (2PT) model of Lin et al. [J. Chem. Phys. 119, 11792 (2003)] and explore new ways to obtain the partition between the gas-like and solid-like parts of the density of states, as well as the effect of the chosen ideal "combinatorial" entropy of mixing, both of which have a large impact on the results. We also propose a first-order correction to the issue of kinetic energy transfer between degrees of freedom (DoF). This problem arises when the effective temperatures of translational, rotational, and vibrational DoF are not equal, either due to poor equilibration or reduced system size/time sampling, which are typical problems for ab initio MD. The new scheme enables improved convergence of the results with respect to configurational sampling, by up to one order of magnitude, for short MD runs. To ensure a meaningful assessment, we perform MD simulations of liquid mixtures of water with several other molecules of varying sizes: methanol, acetonitrile, N, N-dimethylformamide, and n-butanol. Our analysis shows that results in excellent agreement with experiment can be obtained with little computational effort for some systems. However, the ability of the 2PT method to succeed in these calculations is strongly influenced by the choice of force field, the fluidicity (hard-sphere) formalism employed to obtain the solid/gas partition, and the assumed combinatorial entropy of mixing. We tested two popular force fields, GAFF and OPLS with SPC/E water. For the mixtures studied, the GAFF force field seems to perform as a slightly better "all-around" force field when compared to OPLS+SPC/E.

Piezoelectric coefficients and spontaneous polarization of ScAlN.

We present a computational study of spontaneous polarization and piezoelectricity in Sc(x)Al(1-x)N alloys in the compositional range from x = 0 to x = 0.5, obtained in the context of density functional theory and the Berry-phase theory of electric polarization using large periodic supercells. We report composition-dependent values of piezoelectric coefficients e(ij), piezoelectric moduli d(ij) and elastic constants C(ij). The theoretical findings are complemented with experimental measurement of e33 for a series of sputtered ScAlN films carried out with a piezoelectric resonator. The rapid increase with Sc content of the piezoelectric response reported in previous studies is confirmed for the available data. A detailed description of the full methodology required to calculate the piezoelectric properties of ScAlN, with application to other complex alloys, is presented. In particular, we find that the large amount of internal strain present in ScAlN and its intricate relation with electric polarization make configurational sampling and the use of large supercells at different compositions necessary in order to accurately derive the piezoelectric response of the material.

Silver (I) as DNA glue: Ag(+)-mediated guanine pairing revealed by removing Watson-Crick constraints.

Metal ion interactions with DNA have far-reaching implications in biochemistry and DNA nanotechnology. Ag(+) is uniquely interesting because it binds exclusively to the bases rather than the backbone of DNA, without the toxicity of Hg(2+). In contrast to prior studies of Ag(+) incorporation into double-stranded DNA, we remove the constraints of Watson-Crick pairing by focusing on homo-base DNA oligomers of the canonical bases. High resolution electro-spray ionization mass spectrometry reveals an unanticipated Ag(+)-mediated pairing of guanine homo-base strands, with higher stability than canonical guanine-cytosine pairing. By exploring unrestricted binding geometries, quantum chemical calculations find that Ag(+) bridges between non-canonical sites on guanine bases. Circular dichroism spectroscopy shows that the Ag(+)-mediated structuring of guanine homobase strands persists to at least 90 °C under conditions for which canonical guanine-cytosine duplexes melt below 20 °C. These findings are promising for DNA nanotechnology and metal-ion based biomedical science.

The Role of Hydrogen Bonds in the Stabilization of Silver-Mediated Cytosine Tetramers.

DNA oligomers can form silver-mediated duplexes, stable in gas phase and solution, with potential for novel biomedical and technological applications. The nucleobase-metal bond primarily drives duplex formation, but hydrogen (H-) bonds may also be important for structure selection and stability. To elucidate the role of H-bonding, we conducted theoretical and experimental studies of a duplex formed by silver-mediated cytosine homopobase DNA strands, two bases long. This silver-mediated cytosine tetramer is small enough to permit accurate, realistic modeling by DFT-based quantum mechanics/molecular mechanics methods. In gas phase, our calculations found two energetically favorable configurations distinguished by H-bonding, one with a novel interplane H-bond, and the other with planar H-bonding of silver-bridged bases. Adding solvent favored silver-mediated tetramers with interplane H-bonding. Overall agreement of electronic circular dichroism spectra for the final calculated structure and experiment validates these findings. Our results can guide use of these stabilization mechanisms for devising novel metal-mediated DNA structures.

Orbital-free density functional theory implementation with the projector augmented-wave method.

We present a computational scheme for orbital-free density functional theory (OFDFT) that simultaneously provides access to all-electron values and preserves the OFDFT linear scaling as a function of the system size. Using the projector augmented-wave method (PAW) in combination with real-space methods, we overcome some obstacles faced by other available implementation schemes. Specifically, the advantages of using the PAW method are twofold. First, PAW reproduces all-electron values offering freedom in adjusting the convergence parameters and the atomic setups allow tuning the numerical accuracy per element. Second, PAW can provide a solution to some of the convergence problems exhibited in other OFDFT implementations based on Kohn-Sham (KS) codes. Using PAW and real-space methods, our orbital-free results agree with the reference all-electron values with a mean absolute error of 10 meV and the number of iterations required by the self-consistent cycle is comparable to the KS method. The comparison of all-electron and pseudopotential bulk modulus and lattice constant reveal an enormous difference, demonstrating that in order to assess the performance of OFDFT functionals it is necessary to use implementations that obtain all-electron values. The proposed combination of methods is the most promising route currently available. We finally show that a parametrized kinetic energy functional can give lattice constants and bulk moduli comparable in accuracy to those obtained by the KS PBE method, exemplified with the case of diamond.

Evidence of superatom electronic shells in ligand-stabilized aluminum clusters.

Ligand-stabilized aluminum clusters are investigated by density functional theory calculations. Analysis of Kohn-Sham molecular orbitals and projected density of states uncovers an electronic shell structure that adheres to the superatom complex model for ligand-stabilized aluminum clusters. In this current study, we explain how the superatom complex electron-counting rule is influenced by the electron-withdrawing ligand and a dopant atom in the metallic core. The results may guide the prediction of new stable ligand-stabilized (superatom) complexes, regardless of core and electron-withdrawing ligand composition.

Electronic and vibrational signatures of the Au102(p-MBA)44 cluster.

Optical absorption of a gold nanocluster of 102 Au atoms protected by 44 para-mercaptobenzoic acid (p-MBA) ligands is measured in the range of 0.05-6.2 eV (mid-IR to UV) by a combination of several techniques for purified samples in solid and solution phases. The results are compared to calculations for a model cluster Au(102)(SMe)(44) based on the time-dependent density functional theory in the linear-response regime and using the known structure of Au(102)(p-MBA)(44). The measured and calculated molar absorption coefficients in the NIR-vis region are comparable, within a factor of 2, in the absolute scale. Several characteristic features are observed in the absorption in the range of 1.5-3.5 eV. The onset of the electronic transitions in the mid-IR region is experimentally observed at 0.45 ± 0.05 eV which compares well with the lowest calculated transition at 0.55 eV. Vibrations in the ligand layer give rise to fingerprint IR features below the onset of low-energy metal-to-metal electronic transitions. Partial exchange of the p-MBA ligand to glutathione does not affect the onset of the electronic transitions, which indicates that the metal core of the cluster is not affected by the ligand exchange. The full spectroscopic characterization of the Au(102)(p-MBA)(44) reported here for the first time gives benchmarks for further studies of manipulation and functionalization of this nanocluster to various applications.

Quantum size effects in ambient CO oxidation catalysed by ligand-protected gold clusters.

Finely dispersed nanometre-scale gold particles are known to catalyse several oxidation reactions in aerobic, ambient conditions. The catalytic activity has been explained by various complementary mechanisms, including support effects, particle-size-dependent metal-insulator transition, charging effects, frontier orbital interactions and geometric fluxionality. We show, by considering a series of robust and structurally well-characterized ligand-protected gold clusters with diameters between 1.2 and 2.4 nm, that electronic quantum size effects, particularly the magnitude of the so-called HOMO-LUMO energy gap, has a decisive role in binding oxygen to the nano-catalyst in an activated form. This can lead to the oxidation reaction 2CO + O(2) â†’ 2CO(2) with low activation barriers. Binding of dioxygen is significant only for the smallest particles with a metal core diameter clearly below 2 nm. Our results suggest a potentially viable route to practical applications using ligand-protected gold clusters for green chemistry.

Chirality and electronic structure of the thiolate-protected Au38 nanocluster.

Structural, electronic, and optical properties of the thiolate-protected Au(38)(SR)(24) cluster are studied by density-functional theory computations (R = CH(3) and R = C(6)H(13)) and by powder X-ray crystallography (R = C(12)H(25)). A low-energy structure which can be written as Au(23)@(Au(SR)(2))(3)(Au(2)(SR)(3))(6) having a bi-icosahedral core and a chiral arrangement of the protecting gold-thiolate Au(x)(SR)(y) units yields an excellent match between the computed (for R = C(6)H(13)) and measured (for R = C(12)H(25)) powder X-ray diffraction function. We interpret in detail the electronic structure of the Au(23) core by using a particle-in-a-cylinder model. Although the alkane thiolate ligands are achiral, the chiral structure of the ligand layer yields strong circular dichroism (CD) in the excitations below 2.2 eV for Au(38)(SCH(3))(24). Our calculated CD spectrum is in quantitative agreement with the previously measured low-energy CD signal of glutathione-protected Au(38)(SG)(24). Our study demonstrates a new mechanism for the strong chiral response of thiolate-protected gold clusters with achiral metal cores and ligands.

Microbiological quality of saffron from the main producer countries.

A microbiological study of saffron spice was undertaken in the context of a European research project (Methodologies for Implementing International Standards for Saffron Purity and Quality, the acronym for which is SAFFIC), analyzing 79 samples obtained from the main producer countries, namely Greece, Iran, Italy, Morocco, and Spain. Current microbiological quality criteria are the same as for other spices, but saffron is added in minute quantities during the cooking process, so the health risk associated with microbial contamination might be lower. We did not detect Salmonella either by culture or by PCR methods in any sample, and Escherichia coli was only found in five samples. Enterobacteriaceae were frequently found (70.9% of the samples), but most of them belonged to species of probable environmental origin. Aerobic sporulated bacteria were also common, but only three samples contained Bacillus cereus at low levels (<200 CFU g(-1)). Clostridium perfringens counts were also very low, with only one sample reaching >100 CFU g(-1), an acceptable value. Overall, microbial contamination in saffron was markedly lower than it was in other spices.