An accurate analytical parametrization for the exchange-correlation free energy of the homogeneous electron gas, including interpolation for partial spin polarization, is derived via thermodynamic analysis of recent restricted path integral Monte Carlo (RPIMC) data. This parametrization constitutes the local spin density approximation (LSDA) for the exchange-correlation functional in density fu...

Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which is often employed to seek a projection to best represent the data in a least-squares sense, but if the original data is nonlinear structure, the performance...

We use time-dependent spin-density-functional theory to study dynamical magnetic phenomena. First, we recall that the local-spindensity approximation (LSDA) fails to account correctly for magnetic fluctuations in the paramagnetic state of iron and other itinerant ferromagnets. Next, we construct a gradient-dependent density functional that does not suffer from this problem of the LSDA. This fun...

The zero temperature Mott transition region in antiferromagnetic, spin S = 52 MnO is probed using the correlated band theory LSDA + U method. The first transition encountered is an insulator–insulator volume collapse within the rocksalt structure that is characterized by an unexpected Hund’s rule violating ‘spin-flip’ moment collapse. This spin-flip to S = 12 takes fullest advantage of the anis...

The curse of dimensionality is a problem of machine learning algorithm which is often encountered on study of high-dimensional data, while LSDA (Locality Sensitive Discriminant Analysis) can solve the problem of curse of dimensionality. However, LSDA can not fully reflect the requirements that the manifold learning for neighborhood, by using the adaptive neighborhood selection method to measure...

The application of the density-functional theory in the local approximation to magnetic materials is discussed and illustrated by examples. The magnetic properties of the 3d elemental metals as well a s their cohesive properties are described by means of self-consistent local-spin-density (LSD) calculations and by using the LSD-Stoner method. The application of the LSD approximation to narrow-b...

We present a self-interaction-free density-functional theory ~DFT! for the treatment of both the static properties of the ground states and the photoionization processes of many-electron systems. The method is based on the Krieger-Li-Iafrate ~KLI! treatment of the optimized effective potential ~OEP! theory and the incorporation of an explicit self-interaction correction ~SIC! term. Such an exte...