Periodic Supercell Research Articles

Accurate Neural Network Fine-Tuning Approach for Transferable Ab Initio Energy Prediction across Varying Molecular and Crystalline Scales.

Existing machine learning models attempt to predict the energies of large molecules by training small molecules, but eventually fail to retain high accuracy as the errors increase with system size. Through an orbital pairwise decomposition of the correlation energy, a pretrained neural network model on hundred-scale data containing small molecules is demonstrated to be sufficiently transferable for accurately predicting large systems, including molecules and crystals. Our model introduces a residual connection to explicitly learn the pairwise energy corrections, and employs various low-rank retraining techniques to modestly adjust the learned network parameters. We demonstrate that with as few as only one larger molecule retraining the base model originally trained on only small molecules of (H2O)6, the MP2 correlation energy of the large liquid water (H2O)64 in a periodic supercell can be predicted at chemical accuracy. Similar performance is observed for large protonated clusters and periodic poly glycine chains. A demonstrative application is presented to predict the energy ordering of symmetrically inequivalent sublattices for distinct hydrogen orientations in the ice XV phase. Our work represents an important step forward in the quest for cost-effective, highly accurate and transferable neural network models in quantum chemistry, bridging the electronic structure patterns between small and large systems.

Simultaneous low-frequency vibration isolation and energy harvesting via attachable metamaterials

In this study, we achieved energy localization and amplification of flexural vibrations by utilizing the defect mode of plate-attachable locally resonant metamaterials, thereby realizing compact and low-frequency vibration energy suppression and energy harvesting with enhanced output performance. We designed a cantilever-based metamaterial unit cell to induce local resonance inside a periodic supercell structure and form a bandgap within the targeted low-frequency range of 300–450 Hz. Subsequently, a defect area was created by removing some unit cells to break the periodicity inside the metamaterial, which led to the isolation and localization of the vibration energy. This localized vibration energy was simultaneously converted into electrical energy by a piezoelectric energy harvester coupled with a metamaterial inside the defect area. Consequently, a substantially enhanced energy harvesting output power was achieved at 360 Hz, which was 43-times higher than that of a bare plate without metamaterials. The proposed local resonant metamaterial offers a useful and multifunctional platform with the capability of vibration energy isolation and harvesting, while exhibiting easy handling via attachable designs that can be tailored in the low-frequency regime.

Automatic order detection and restoration through systematically improvable variational wave functions

Variational wave function are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte Carlo and modern variational optimization techniques including automatic differentiation. The resulting , consisting of several slices of optimized projectors, is highly expressive and systematically improvable. We benchmark this form on the two-dimensional Hubbard model, using both cylindrical and large, fully periodic supercells. The computed ground-state energies are competitive with the best variational results. Moreover, the optimized wave functions predict the correct ground-state order with near full symmetry restoration (i.e., translation invariance) despite initial states with incorrect orders. The can become a tool for local order prediction, leading to a new paradigm for variational studies of bulk systems. It can also be viewed as an approach to produce accurate and systematically improvable wave functions in a convenient form of nonorthogonal Slater determinants (e.g., for quantum chemistry) at polynomial computational cost. Published by the American Physical Society 2024

Ab Initio Study on the Vibrational and Electronic Properties of Radiation-Induced Defects in Potassium Bromide

The vibrational and electronic properties of several basic radiation defects in potassium bromide are computed at the quantum mechanical level using a periodic supercell approach based on hybrid functionals, an all-electron Gaussian-type basis set, and the Crystalcomputer code. The exciton energy in alkali halides is sufficient to create lattice defects, such as F–H Frenkel defect pairs, resulting in a relatively high concentration of single defects and their complexes. Here, we consider eight defects: the electronic F+- and F-centers (bromine vacancy without and with trapped electrons) and their dimers; hole H-center (neutral bromine atom forming the dumbbell ion with a regular Br− ion.); VK-center (Br2− molecular ion consisting of a hole and two regular ions); and two complex Br3− defects, combinations of several simple defects. The local geometry and the charge- and spin-density distributions of all defects are analyzed. Every defect shows its characteristic features in Raman spectra, and their comparison with available experimental data is discussed.

Solution of the Schrödinger equation for quasi-one-dimensional materials using helical waves

We formulate and implement a spectral method for solving the Schrödinger equation, as it applies to quasi-one-dimensional materials and structures. This allows for computation of the electronic structure of important technological materials such as nanotubes (of arbitrary chirality), nanowires, nanoribbons, chiral nanoassemblies, nanosprings and nanocoils, in an accurate, efficient and systematic manner. Our work is motivated by the observation that one of the most successful methods for carrying out electronic structure calculations of bulk/crystalline systems — the plane-wave method — is a spectral method based on eigenfunction expansion. Our scheme avoids computationally onerous approximations involving periodic supercells often employed in conventional plane-wave calculations of quasi-one-dimensional materials, and also overcomes several limitations of other discretization strategies, e.g., those based on finite differences and atomic orbitals. The basis functions in our method — called helical waves (or twisted waves) — are eigenfunctions of the Laplacian with symmetry adapted boundary conditions, and are expressible in terms of plane waves and Bessel functions in helical coordinates.We describe the setup of fast transforms to carry out discretization of the governing equations using our basis set, and the use of matrix-free iterative diagonalization to obtain the electronic eigenstates. Miscellaneous computational details, including the choice of eigensolvers, use of a preconditioning scheme, evaluation of oscillatory radial integrals and the imposition of a kinetic energy cutoff are discussed. We have implemented these strategies into a computational package called HelicES (Helical Electronic Structure). We demonstrate the utility of our method in carrying out systematic electronic structure calculations of various quasi-one-dimensional materials through numerous examples involving nanotubes, nanoribbons and nanowires. We also explore the convergence properties of our method, and assess its accuracy and computational efficiency by comparison against reference finite difference, transfer matrix method and plane-wave results. We anticipate that our method will find applications in computational nanomechanics and multiscale modeling, for carrying out transport calculations of interest to the field of semiconductor devices, and for the discovery of novel chiral phases of matter that are of relevance to the burgeoning quantum hardware industry.

Multiple k-Point Nonadiabatic Molecular Dynamics for Ultrafast Excitations in Periodic Systems: The Example of Photoexcited Silicon.

With the rapid development of ultrafast experimental techniques for the research of carrier dynamics in solid-state systems, a microscopic understanding of the related phenomena, particularly a first-principle calculation, is highly desirable. Nonadiabatic molecular dynamics (NAMD) offers a real-time direct simulation of the carrier transfer or carrier thermalization. However, when applied to a periodic supercell, there is no cross-k-point transitions during the NAMD simulation. This often leads to a significant underestimation of the transition rate with the single-k-point band structure in a supercell. In this work, based on the surface hopping scheme used for NAMD, we propose a practical method to enable the cross-k transitions for a periodic system. We demonstrate our formalism by showing that the hot electron thermalization process by the multi-k-point NAMD in a small silicon supercell is equivalent to such simulation in a large supercell with a single Γ point. The simulated hot carrier thermalization process of the bulk silicon is compared with the recent ultrafast experiments, which shows excellent agreements. We have also demonstrated our method for the hot carrier coolings in the amorphous silicons and the GaAlAs_{2} solid solutions with the various cation distributions.

The trigonal structure as a reference to access the spontaneous polarization of wurtzite crystals

The trigonal structure as a reference to access the spontaneous polarization of wurtzite crystals

Reflections of High-Frequency Pulsed Ultrasound by Underwater Acoustic Metasurfaces Composed of Subwavelength Phase-Gradient Slits

We numerically and experimentally investigated the behavior of high-frequency underwater ultrasounds reflected by gradient acoustic metasurfaces. Metasurfaces were fabricated with a periodic array of gradient slits along the surface of a steel specimen. The finite element method was adopted for the acoustics–structure interaction problem to design the metasurfaces and simulate the reflected fields of the incident ultrasound. Our metasurfaces yielded anomalous reflection, specular reflection, apparent negative reflection, and radiation of surface-bounded modes for ultrasonic waves impinging on the metasurfaces at different incident angles. The occurrence of these reflection behaviors could be explained by the generalized Snell’s law for a gradient metasurface with periodic supercells. We showed that at some incident angles, strong anomalous reflection could be generated, which could lead to strong retroreflection at specific incident angles. Furthermore, we characterized the time evolution of the reflections using pulsed ultrasound. The simulated transient process revealed the formation of propagating reflected ultrasound fields. The experimentally measured reflected ultrasound signals verified the distinct reflection behaviors of the metasurfaces; strong anomalous reflection steering the ultrasound pulse and causing retroreflection was observed. This study paves the way for designing underwater acoustic metasurfaces for ultrasound imaging and caustic engineering applications using pulsed ultrasound in the high-frequency regime.

Local Excitations of a Charged Nitrogen Vacancy in Diamond with Multireference Density Matrix Embedding Theory

We investigate the negatively charged nitrogen-vacancy center in diamond using periodic density matrix embedding theory (pDMET). To describe the strongly correlated excited states of this system, the complete active space self-consistent field (CASSCF) followed by n-electron valence state second-order perturbation theory (NEVPT2) was used as the impurity solver. Since the NEVPT2-DMET energies show a linear dependence on the inverse of the size of the embedding subspace, we performed an extrapolation of the excitation energies to the nonembedding limit using a linear regression. The extrapolated NEVPT2-DMET first triplet-triplet excitation energy is 2.31 eV and that for the optically inactive singlet-singlet transition is 1.02 eV, both in agreement with the experimentally observed vertical excitation energies of ∼2.18 eV and ∼1.26 eV, respectively. This is the first application of pDMET to a charged periodic system and the first investigation of the NV- defect using NEVPT2 for periodic supercell models.

Achieving strength and ductility synergy via a nanoscale superlattice precipitate in a cast Mg-Y-Zn-Er alloy

Achieving strength and ductility synergy via a nanoscale superlattice precipitate in a cast Mg-Y-Zn-Er alloy

Calculation of dislocation binding to helium-vacancy defects in tungsten using hybrid ab initio-machine learning methods

Calculation of dislocation binding to helium-vacancy defects in tungsten using hybrid ab initio-machine learning methods

Metagrating absorber: design and implementation.

The extent to which the introduction of subwavelength spatial modulation of electromagnetic properties improves absorption performances is studied. The proposed absorber represents an evolution from the Salisbury screen, whereby the uniform resistive layer is replaced by a metagrating. A periodic supercell that supports only the specular reflection is first designed, and load impedances are then engineered to suppress this diffraction mode. To experimentally demonstrate the concept, four prototypes are fabricated and tested in the microwave domain around 10 GHz. Furthermore, the performances assessed by a merit factor derived from Rozanov's bound show that the use of metagratings opens up good perspectives for improving the state of the art. Our findings can pave the way toward the development of high performance absorbers for applications across a broad frequency spectrum.

Density functional thermodynamic description of spin, phonon and displacement degrees of freedom in antiferromagnetic-to-paramagnetic phase transition in YNiO3

Density functional thermodynamic description of spin, phonon and displacement degrees of freedom in antiferromagnetic-to-paramagnetic phase transition in YNiO3

Tailoring the resonances on Fibonacci spiral fractal metasurface for miniaturized multi-band microwave applications

Tailoring the resonances on Fibonacci spiral fractal metasurface for miniaturized multi-band microwave applications

Unified ab initio description of Fröhlich electron-phonon interactions in two-dimensional and three-dimensional materials

\textit{Ab initio} calculations of electron-phonon interactions including the polar Fr\"ohlich coupling have advanced considerably in recent years. The Fr\"ohlich electron-phonon matrix element is by now well understood in the case of bulk three-dimensional (3D) materials. In the case of two-dimensional (2D) materials, the standard procedure to include Fr\"ohlich coupling is to employ Coulomb truncation, so as to eliminate artificial interactions between periodic images of the 2D layer. While these techniques are well established, the transition of the Fr\"ohlich coupling from three to two dimensions has not been investigated. Furthermore, it remains unclear what error one makes when describing 2D systems using the standard bulk formalism in a periodic supercell geometry. Here, we generalize previous work on the \textit{ab initio} Fr\"ohlich electron-phonon matrix element in bulk materials by investigating the electrostatic potential of atomic dipoles in a periodic supercell consisting of a 2D material and a continuum dielectric slab. We obtain a unified expression for the matrix element, which reduces to the existing formulas for 3D and 2D systems when the interlayer separation tends to zero or infinity, respectively. This new expression enables an accurate description of the Fr\"ohlich matrix element in 2D systems without resorting to Coulomb truncation. We validate our approach by direct \textit{ab initio} density-functional perturbation theory calculations for monolayer BN and MoS$_2$, and we provide a simple expression for the 2D Fr\"ohlich matrix element that can be used in model Hamiltonian approaches. The formalism outlined in this work may find applications in calculations of polarons, quasiparticle renormalization, transport coefficients, and superconductivity, in 2D and quasi-2D materials.

A Novel Method for Analyzing Inhomogeneous Metasurfaces

A new method for analyzing multispectral inhomogeneous metasurfaces is presented, which includes several types of particles. Our proposed method (PM) suggests a new semianalytical technique to solve the total effective polarizabilities of inhomogeneous arrays. Here, we propose the inhomogeneity in which metasurface can be regarded as constituting arrays of periodic supercells. Closed-form relations are suggested to calculate the interaction constants inside the supercells, and the local effective polarizabilities are obtained with the aid of these relations. Then, the conventional interaction constants are used to calculate the total effective polarizabilities of an array. To evaluate the generality and accuracy of our PM, the reflection and transmission coefficients of different arrays consisting of isotropic and bianisotropic particles are analyzed with this method, and the results are compared to those of an HFSS simulator. Our method is a step forward in analyzing and synthesizing inhomogeneous and multispectral metasurfaces.

Heat-current filtering for Green–Kubo and Helfand-moment molecular dynamics predictions of thermal conductivity: Application to the organic crystal [formula omitted]-HMX

Heat-current filtering for Green–Kubo and Helfand-moment molecular dynamics predictions of thermal conductivity: Application to the organic crystal [formula omitted]-HMX

A first principles study of the adsorption and hydrogenation of formic acid on a Cu3Zn material: Implication for bulk alloying effect on CO2 hydrogenation reactivity of Cu/ZnO-based catalysts

A first principles study of the adsorption and hydrogenation of formic acid on a Cu3Zn material: Implication for bulk alloying effect on CO2 hydrogenation reactivity of Cu/ZnO-based catalysts

Implicit Solvation Methods for Catalysis at Electrified Interfaces.

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization.

Multifunctional reflected lenses based on aperiodic acoustic metagratings

Acoustic metagratings (AMs) have provided diverse routes for sound modulations based on high-efficiency diffractions created by periodic supercell structures. The emergence of the extension of the generalized Snell's law (GSL), covering both acoustic diffractions and phase modulations, has promoted the design of the AMs with aperiodic phase profiles, which have a great potential in designing high-performance multifunctional devices. However, the realization of reflected aperiodic AMs and its associated multifunctional devices remain a challenge. To overcome this, we here theoretically design and experimentally demonstrate a class of reflected aperiodic AMs and multifunctional acoustic lenses. By using the extension of the GSL, we can overcome the limitations of the GSL (such as the phase gradient and the incident critical angle) and experimentally demonstrate theoretical predictions of sound reflections created by the aperiodic AMs with arbitrary phase gradients under a full-angle incidence. Additionally, we experimentally design a multifunctional reflected lens composed of two selected aperiodic AMs. Interestingly, by simply adjusting the incident angle of sound, we can realize the transformation between the beam splitting and the Bessel-like beam without changing the structure of the lens. Our work paves a way for modulating sound reflections and designing reflected multifunctional devices with promising applications.