Ab initio molecular dynamics: Analytically continued energy functionals and insights into iterative solutions

We present a new method for performing finite-temperature ab initio total-energy calculations at long length scales, which we demonstrate with a dynamics calculation of 50 Å-long phonon modes in silicon. The method involves both a prescription for the analytic continuation of tradional fermionic energy functionals into the space of nonorthonormal single-particle orbitals (speeding convergence to the minimum) and insights into the common computational physics problem of solving by iterative refinement for the state of a complex system as a function of a continuous external parameter.