Path Integral Molecular Dynamics Methods

We present the aspects of the path integral molecular dynamics (PIMD) method relative to (a) its theoretical fundamental principles, (b) its applicability to model quantum systems and (c) its implementation as a simulation tool. The PIMD method is based on the discretized path integral representation of quantum mechanics. In this representation, a quantum particle is isomorphic to a closed polymer chain. The problem of the indistinguishability of quantum particles is tackled with a non-local exchange potential. When the exact density matrix of the quantum particles is used, the exchange potential is exact. We use a high temperature approximation to the density matrix leading to an approximate form of the exchange potential. This quantum molecular dynamics method allows the simulation of collections of quantum particles at finite temperature. Our algorithm can be made to scale linearly with the number of quantum states on which the density matrix is projected. Therefore, it can be optimized to run efficiently on parallel computers. We apply the PIMD method to the electron plasma in 3-dimension. The kinetic and potential energies are calculated and compared with results for similar systems simulated with a variational Monte Carlo method. Both results show good agreements with each other at all the densities studied. The method is then use to model the thermodynamic behavior of a simple alkali metal. In these simulations, ions and valence electrons are treated as classical and quantum particles, respectively. The simple metal undergoes a phase transformation upon heating. Furthermore, to demonstrate the richness of behaviors that can be studied with the PIMD method, we also report on the metal to insulator transition in a hydrogenoid lattice. Finally, in previous studies of alkali metals, electrons interacted with ions via local pseudo-potentials, an extension of the method to modeling electrons in non-local pseudo-potentials is also presented with applications.