Search

We present a protocol for automated fitting of magnetic Moment Tensor Potential explicitly including magnetic moments in its functional form. For the fitting of this potential we use energies, forces, stresses, and magnetic forces (negative derivatives of energies with respect to magnetic moments) of configurations selected with an active learning algorithm. These selected configurations are computed using constrained density functional theory, which enables calculating energies and their derivatives for both equilibrium and non-equilibrium (excited) magnetic states. We test our protocol on the system of B1-CrN and demonstrate that the automatically trained magnetic Moment Tensor Potential reproduces mechanical, dynamical, and thermal properties, of B1-CrN in the paramagnetic state with respect to density functional theory and experiments.

We developed a method for fitting machine-learning interatomic potentials with magnetic degrees of freedom, namely, magnetic Moment Tensor Potentials (mMTP). The main feature of our method consists in fitting mMTP to magnetic forces (negative derivatives of energies with respect to magnetic moments) as obtained spin-polarized density functional theory calculations. We test our method on the bcc Fe-Al system with different compositions. Specifically, we calculate formation energies, equilibrium lattice parameter, and total cell magnetization. Our findings demonstrate an accurate correspondence between the values calculated with mMTP and those obtained by DFT at zero temperature. Additionally, using molecular dynamics, we estimate the finite-temperature lattice parameter and capture the cell expansion as was previously revealed in experiment. Furthermore, we demonstrate that fitting to magnetic forces increases the reliability of structure relaxation (or, equilibration), in the sense of ensuring that every relaxation run ends up with a successfully relaxed structure (the failure may otherwise be caused by falsely driving a configuration away from the region covered in the training set).

Transition-metal compounds represent a fascinating playground for exploring the intricate relationship between structural distortions, electronic properties, and magnetic behaviour, holding significant promise for technological advancements. Among these compounds, YBaCo$_4$O$_{7}$ (Y114) is attractive due to its manifestation of a ferrimagnetic component at low temperature intertwined with distortion effect due to the charge disproportionation on Co ions, exerting profound impact on its magnetic properties. In this perspective paper, we study the structural and magnetic intricacies of the Y114 crystal using a novel first-principles methodology. Traditionally, the investigation of such materials has relied heavily on computational modelling using density-functional theory (DFT) with the on-site Coulomb interaction correction $U$ (DFT+$U$) based on the Hubbard model (sometimes including Hund's exchange coupling parameter $J$, DFT+$U$+$J$) to unravel their complexities. Herein, we analysed the spurious effects of magnetic-moment delocalisation and spillover to non-magnetic ions in the lattice on electronic structure and magnetic properties of Y114. To overcome this problem we have applied constrained DFT (cDFT) based on the potential self-consistency approach, and comprehensively explore the Y114 crystal's characteristics in its ferrimagnetic order. We find that cDFT yields magnetic moments of Co ions much closer to the experimental values than Hubbard model with the parameters $U$ and $J$ fitted to reproduce experimental lattice constants. cDFT allows for an accurate prediction of magnetic properties using oxidation states of magnetic ions as well-defined parameters. Through this perspective, we not only enhance our understanding of the magnetic interactions in Y114 crystal, but also pave the way for future investigations into magnetic materials.

Density functional perturbation theory is a well-established method to study responses of molecules and solids, especially responses to atomic displacements or to different perturbing fields (electric, magnetic). Like for density functional theory, the treatment of metals is delicate, due to the Fermi-Dirac statistics and electronic bands crossing the Fermi energy. At zero temperature, there is an abrupt transition from occupied states to unoccupied ones, usually addressed with smearing schemes. Also, at finite temperature, fractional occupations are present, and the occupation numbers may vary in response to the perturbation. The present work establishes the characteristics of density functional perturbation theory stemming from the underlying variational principle, in the case of metals. After briefly reviewing variational density functional theory for metals, the convexity of the entropy function of the occupation number is analyzed, and, at finite temperature, the benefit of resmearing the Fermi-Dirac broadening with the Methfessel-Paxton one is highlighted. Then the variational expressions for the second-order derivative of the free energy are detailed, exposing the different possible gauge choices. The influence of the inaccuracies in the unperturbed wavefunctions from the prior density functional theory calculation is studied. The whole formalism is implemented in the ABINIT software package.

Wavelets and Multiwavelets have lately been adopted in Quantum Chemistry to overcome challenges presented by the two main families of basis sets: Gaussian atomic orbitals and plane waves. In addition to their numerical advantages (high precision, locality, fast algorithms for operator application, linear scaling with respect to system size, to mention a few) they provide a framework which narrows the gap between the theoretical formalism of the fundamental equations and the practical implementation in a working code. This realization led us to the development of the Python library called VAMPyR, (Very Accurate Multiresolution Python Routines). VAMPyR encodes the binding to a C++ library for Multiwavelet calculations (algebra, integral and differential operator application) and exposes the required functionality to write simple Python code to solve among others, the Hartree--Fock equations, the generalized Poisson Equation, the Dirac equation and the time-dependent Schr\"odinger equation up to any predefined precision. In this contribution we will outline the main features of Multiresolution Analysis using multiwavelets and we will describe the design of the code. A few illustrative examples will show the code capabilities and its interoperability with other software platforms.

The many-body wave function of an $N$-electron system within a relativistic framework can be described by the Dirac equation. Unfortunately, the Dirac operator $\hat{\mathfrak{D}}$ is unbounded and in case we would describe anions we will observe the variational collapse of wavefunction of $N+1$ electron. Thus, it is necessary to avoid it and an alternative approach is based on applying the square of the Dirac operator $\hat{\mathfrak{D}}^{2}$. This approach is especially suitable for a multiwavelet framework: its implementation in an integral equation form is readily available and the completeness of the multiwavelet basis guarantees that the matrix representation of $\hat{\mathfrak{D}}^{2}$ in the occupied space is identical to the square of the matrix representation of $\hat{\mathfrak{D}}$. This equivalence is not valid in a finite basis set. The use of the $\hat{\mathfrak{D}}^{2}$ operator within a multiwavelet framework is able to achieve higher precision compared to the $\hat{\mathfrak{D}}$, consistent with the quadratic nature of the error estimates in a variational framework., Comment: Submitted to Theoretical Chemistry Accounts

The importance of relativistic effects in quantum chemistry is widely recognized, not only for heavier elements but throughout the periodic table. At the same time, relativistic effect are strongest in the nuclear region, where the description of electrons through linear combination of atomic orbitals becomes more challenging. Furthermore, the choice of basis sets for heavier elements is limited compared to lighter elements where precise basis sets are available. Thanks to the framework of multiresolution analysis, multiwavelets provide an appealing alternative to overcome this challenge: they lead to robust error control and adaptive algorithms that automatically refine the basis set description until the desired precision is reached. This allows to achieve a proper description of the nuclear region. In this work we extended the Multiwavelet-based code MRChem to the scalar zero-order regular approximation (ZORA) framework. We validated our implementation comparing the total energies for a small set of elements and molecules. To confirm the validity of our implementation, we compared both against a radial numerical code for atoms and the plane-wave based code exciting.

The challenge of achieving ultrafast switching of electric polarization in ferroelectric materials remains unsolved, as there is no experimental evidence of such switching to date. In this study, we have developed an enhanced model that describes switching within a two-dimensional space of generalized coordinates at THz pulses. Our findings indicate that stable switching in barium titanate cannot be achieved through a single linearly polarized pulse. When the intensity of the linearly polarized pulse reaches a certain threshold, the sample experiences depolarization, but not stable switching. Our study also reveals that phonon friction plays a minor role in the switching dynamics and provides an estimate of the optimal parameters of the perturbing pulse with the lowest intensity that results in depolarization of an initially polarized sample.

New techniques in core-electron spectroscopy are necessary to resolve the structures of oxides of $f$-elements and other strongly correlated materials that are present only as powders and not as single crystals. Thus, accurate quantum chemical methods need to be developed to calculate core spectroscopic properties in such materials. In this contribution, we present an important development in this direction, extending our fully adaptive real-space multiwavelet basis framework to tackle the 4-component Dirac-Coulomb-Breit Hamiltonian. We show that Multiwavelets are able to reproduce one-dimensional grid-based approaches. They are however a fully three-dimensional approach which can later on be extended to molecules and materials. Our Multiwavelet implementation attained precise results irrespective of the chosen nuclear model, provided that the error threshold is tight enough and the chosen polynomial basis is sufficiently large. Furthermore, our results confirmed that in two-electron species, the magnetic and Gauge contributions from $s$-orbitals are identical in magnitude and can account for the experimental evidence from $K$ and $L$ edges.

In the last decades, material discovery has been a very active research field driven by the need to find new materials for many different applications. This has also included materials with heavy elements, beyond the stable isotopes of lead, as most actinides exhibit unique properties that make them useful in various applications. Furthermore, new heavy elements beyond actinides, collectively referred to as super-heavy elements (SHEs), have been synthesized, filling previously empty space of Mendeleev periodic table. Their chemical bonding behavior, of academic interest at present, would also benefit of state-of-the-art modeling approaches. In particular, in order to perform first-principles calculations with planewave basis sets, one needs corresponding pseudopotentials. In this work, we present a series of scalar- and fully-relativistic optimized norm-conserving Vanderbilt pseudopotentials (ONCVPs) for thirty-four actinides and super-heavy elements, for three different exchange-correlation functionals (PBE, PBEsol and LDA). The scalar-relativistic version of these ONCVPs is tested by comparing equations of states for crystals, obtained with \textsc{abinit} 9.6, with those obtained by all-electron zeroth-order regular approximation (ZORA) calculations, without spin-orbit coupling, performed with the Amsterdam Modeling Suite \textsc{band} code. $\Delta$-Gauge and $\Delta_1$-Gauge indicators are used to validate these pseudopotentials. This work is a contribution to the PseudoDojo project, in which pseudopotentials for the whole periodic table are developed and systematically tested. The pseudopotential files are available on the PseudoDojo web-interface pseudo-dojo.org in psp8 and UPF2 formats, both suitable for \textsc{abinit}, the latter being also suitable for Quantum ESPRESSO.

Hardness is a materials' property with implications in several industrial fields, including oil and gas, manufacturing, and others. However, the relationship between this macroscale property and atomic (i.e., microscale) properties is unknown and in the last decade several models have unsuccessfully tried to correlate them in a wide range of chemical space. The understanding of such relationship is of fundamental importance for discovery of harder materials with specific characteristics to be employed in a wide range of fields. In this work, we have found a physical descriptor for Vickers hardness using a symbolic-regression artificial-intelligence approach based on compressed sensing. SISSO (Sure Independence Screening plus Sparsifying Operator) is an artificial-intelligence algorithm used for discovering simple and interpretable predictive models. It performs feature selection from up to billions of candidates obtained from several primary features by applying a set of mathematical operators. The resulting sparse SISSO model accurately describes the target property (i.e., Vickers hardness) with minimal complexity. We have considered the experimental values of hardness for binary, ternary, and quaternary transition-metal borides, carbides, nitrides, carbonitrides, carboborides, and boronitrides of 61 materials, on which the fitting was performed. The found descriptor is a non-linear function of the microscopic properties, with the most significant contribution being from a combination of Voigt-averaged bulk modulus, Poisson's ratio, and Reuss-averaged shear modulus. Results of high-throughput screening of 635 candidate materials using the found descriptor suggest the enhancement of material's hardness through mixing with harder yet metastable structures (e.g., metastable VN, TaN, ReN$_2$, Cr$_3$N$_4$, and ZrB$_6$ all exhibit high hardness).

Recently, several research groups announced reaching the point of metallization of hydrogen above 400 GPa. Following the mainstream of extensive investigations of compressed polyhydrides, in this work we demonstrate that small (4 atom %) doping of molecular hydrogen by strontium leads to a dramatic reduction in the metallization pressure to about 200 GPa. Studying the high-pressure chemistry of the Sr-H system at 56-180 GPa, we observed the formation of several previously unknown compounds: C2/m-Sr$_3$H$_{13}$, pseudocubic SrH$_6$, SrH$_9$ with cubic F-43m Sr sublattice, and pseudotetragonal P1-SrH$_{22}$, the metal hydride with the highest hydrogen content discovered so far. Unlike Ca and Y, strontium forms molecular semiconducting polyhydrides, whereas calcium and yttrium polyhydrides are high-Tc superconductors with an atomic H sublattice. The latter phase, SrH$_{22}$ or Sr$_{0.04}$H$_{0.96}$, may be considered as a convenient model of the consistent bandgap closure and metallization of hydrogen. Using the impedance measurements in diamond anvil cells at 300-440 K, we estimated the direct bandgap of the Pm-3n-like compound P1-SrH$_6$ to be 0.44-0.51 eV at 150 GPa, and its metallization pressure to be 220 GPa. Together with the machine learning interatomic potentials, the impedance spectroscopy allowed us to estimate the diffusion coefficients of hydrogen D$_H$ = 1.0-2.8 E-10 m$^2$/s in SrH$_6$ and 1.2-2.1 E-9 m$^2$/s in P1-SrH$_{22}$ at 500-600 K., Comment: Supporting information was compressed and reduced by 2 times to 36 figures