Simulation of crystal and liquid potassium via restricted path-integral molecular dynamics

Abstract

The path-integral molecular-dynamics method is employed to study the effect of temperature on a simple metal ͑potassium͒ model system. The simple metal undergoes a phase transformation upon heating. Calculated dynamic properties indicate that the atomic motion changes from a vibrational to a diffusive character identifying the transformation as melting. Calculated structural properties further confirm the transformation. Ionic vibrations in the crystal state and the loss of long-range order during melting modify the electronic structure and in particular localize the electrons inside and at the border of the ion core.

Formation of bound states in expanded metal studied via path integral molecular dynamics

“…We use a recent quantum molecular dynamics method applicable to the simulation of many fermion systems at finite temperature. The RPIMD method was introduced elsewhere [15][16][17]. This method makes use of (a) the discretized path integral representation of quantum particles as closed necklaces of P classical particles (beads) with quantum exchange treated through crosslinking of the chains [18]; (b) the non-locality of crosslinking along the chains [19]; (c) the restricted path integral [20] to resolve the problem of negative weights to the partition function due to exchange of indistinguishable particles.…”

“…We solve the equations of motion with a leap-frog scheme and an integration time step of 2.8 × 10 −16 s. We use P = 400 beads for the electron necklaces in order to ensure convergence of the path integral at the temperatures and densities studied [16,17]. We eliminate all phonons by holding the ions at fixed positions.…”

“…We eliminate all phonons by holding the ions at fixed positions. The temperature is maintained at a value for which the electrons are in a nearly degenerate regime at high density [16,17]. It is known that the simulation of stiff harmonic chains suffers from non-ergodicity.…”

“…This term is essential for the observation of bound states on an expanded lattice since electron localization is driven by the on-site electron-electron Coulomb repulsion. The ion-electron potential is denoted as V ps , and we use for simplicity an empty core local pseudopotential [16,17] with a core radius R c = 1.5 Å. The fourth term is the effective harmonic potential for distinguishable quantum particles [21].…”

“…In this paper, we revisit Mott's original argument by investigating the correlated electronic structure of an expanded three-dimensional hydrogenoid body-centred cubic (bcc) crystal at finite temperature. This system will serve as a non-trivial model for testing the usefulness of the restricted path integral molecular dynamics (RPIMD) method for the study of strongly correlated electronic systems [15][16][17]. The RPIMD is a recent quantum molecular dynamics method applicable to the simulation of many-fermion systems at finite temperature.…”