Smoothed Particle Method for Real-Space Electronic Structure Calculations

We present a meshfree particle method for real-space electronic structure calculations based on symmetric smoothed particle hydrodynamics (SSPH). As a simple example, we applied SSPH to the Schrödinger equation for a one-dimensional harmonic oscillator. The results calculated using SSPH are in good agreement with analytical solutions. We compared results for different cases of kernel function, smoothing length, number of particles, and the order of the Taylor series expansion. The results using SSPH and the higher-order finite-difference method are also compared. Our results indicate that SSPH can be applied to real-space electronic structure calculations that require high accuracy.