Background: The majority of complex and advanced materials contain nanoparticles. The properties of these materials depend crucially on the size and shape of these nanoparticles. Wulff construction offers a simple method of predicting the equilibrium shape of nanoparticles given the surface energies of the material.Results: We review the mathematical formulation and the main applications of Wulff construction during the last two decades. We then focus to three recent extensions: active sites of metal nanoparticles for heterogeneous catalysis, ligand-protected nanoparticles generated as colloidal suspensions and nanoparticles of complex metal hydrides for hydrogen storage.Conclusion: Wulff construction, in particular when linked to first-principles calculations, is a powerful tool for the analysis and prediction of the shapes of nanoparticles and tailor the properties of shape-inducing species.

We present a computational study for the environment-dependent equilibrium shape of gold nanoparticles. By linking extensive quantum-mechanical calculations, based on density functional theory (DFT), to Wulff constructions, we predict the equilibrium shapes of clean and CO-covered gold nanoparticles. We construct atomistic models of nanoparticles with diameters up to several tenths of a nanometer, inaccessible by direct atomistic simulations. Au nanoparticles smaller than 16.3 nm in diameter have truncated octahedral shape, exposing only (111) and (100) faces. Larger nanoparticles also expose higher-index faces, mostly (332). We study the adsorption of CO on several different Au surfaces, and we use the results to obtain the interface energy between Au and CO at low pressure and temperature. These results are then used to obtain the equilibrium shape of Au nanoparticles in CO gas. In agreement with experimental data, Au nanoparticles in CO are found to be more spherical and more reactive compared to Au nanoparticles in noninteracting environments.

We present a computational screening study of ternary metal borohydrides for reversible hydrogen storage based on density functional theory. We investigate the stability and decomposition of alloys containing 1 alkali metal atom, Li, Na, or K $\left(M_1\right)$ ; and 1 alkali, alkaline earth or $3d/4d$ transition metal atom $\left(M_2\right)$ plus two to five ${\left({\text{BH}}_4\right)}^{-}$ groups, i.e., $M_1{M}_2{\left({\text{BH}}_4\right)}_{2–5}$ , using a number of model structures with trigonal, tetrahedral, octahedral, and free coordination of the metal borohydride complexes. Of the over 700 investigated structures, about $20$ were predicted to form potentially stable alloys with promising decomposition energies. The $M_1\left(\text{Al}/\text{Mn}/\text{Fe}\right){\left({\text{BH}}_4\right)}_4$ , $\left(\text{Li}/\text{Na}\right)\text{Zn}{\left({\text{BH}}_4\right)}_3$ , and $\left(\text{Na}/\text{K}\right)\left(\text{Ni}/\text{Co}\right){\left({\text{BH}}_4\right)}_3$ alloys are found to be the most promising, followed by selected $M_1\left(\text{Nb}/\text{Rh}\right){\left({\text{BH}}_4\right)}_4$ alloys.

Inelastic scattering and carrier capture by defects in semiconductors are the primary causes of hot-electron-mediated degradation of power devices, which holds up their commercial development. At the same time, carrier capture is a major issue in the performance of solar cells and light-emitting diodes. A theory of nonradiative (multiphonon) inelastic scattering by defects, however, is nonexistent, while the theory for carrier capture by defects has had a long and arduous history. Here we report the construction of a comprehensive theory of inelastic scattering by defects, with carrier capture being a special case. We distinguish between capture under thermal equilibrium conditions and capture under nonequilibrium conditions, e.g., in the presence of an electrical current or hot carriers where carriers undergo scattering by defects and are described by a mean free path. In the thermal-equilibrium case, capture is mediated by a nonadiabatic perturbation Hamiltonian, originally identified by Huang and Rhys and by Kubo, which is equal to linear electron-phonon coupling to first order. In the nonequilibrium case, we demonstrate that the primary capture mechanism is within the Born-Oppenheimer approximation (adiabatic transitions), with coupling to the defect potential inducing Franck-Condon electronic transitions, followed by multiphonon dissipation of the transition energy, while the nonadiabatic terms are of secondary importance (they scale with the inverse of the mass of typical atoms in the defect complex). We report first-principles density-functional-theory calculations of the capture cross section for a prototype defect using the projector-augmented wave, which allows us to employ all-electron wave functions. We adopt a Monte Carlo scheme to sample multiphonon configurations and obtain converged results. The theory and the results represent a foundation upon which to build engineering-level models for hot-electron degradation of power devices and the performance of solar cells and light-emitting diodes.

Cardiac remodeling is recognized as an important aspect of cardiovascular disease (CVD) progression. Machine learning (ML) techniques were applied to basic clinical parameters and electrocardiographic features, in order to detect abnormal left ventricular geometry (LVG) even before the onset of left ventricular hypertrophy (LVH), in a population without established CVD. The authors enrolled 528 patients with and without essential hypertension, but no other indications of CVD. All patients underwent a full echocardiographic evaluation and were classified into 3 groups; normal geometry (NG), concentric remodeling without LVH (CR), and LVH. Abnormal LVG was identified as increased relative wall thickness (RWT) and/or left ventricular mass index (LVMi). The authors trained supervised ML models to classify patients with abnormal LVG and calculated SHAP values to perform feature importance and interaction analysis. Hypertension, age, body mass index over the Sokolow‐Lyon voltage, QRS‐T angle, and QTc duration were some of the most important features. Our model was able to distinguish NG from CR+LVH combined, with 87% accuracy on an unseen test set, 75% specificity, 97% sensitivity, and area under the receiver operating curve (AUC/ROC) equal to 0.91. The authors also trained our model to classify NG and CR (NG + CR) against those with LVH, with 89% test set accuracy, 93% specificity, 67% sensitivity, and an AUC/ROC value of 0.89, for a 0.4 decision threshold. Our ML algorithm effectively detects abnormal LVG even at early stages. Innovative solutions are needed to improve risk stratification of patients without established CVD, and ML may enable progress in this direction.