Direct minimization technique for metals in density functional theory

We present a scheme to solve the Kohn-Sham equations of density functional theory using orthonormal wave functions and an independent pseudo-Hamiltonian matrix. Our ansatz is based on a direct minimization of the electronic free energy with conjugate-gradient techniques. In contrast to previous approaches, continuous changes in the occupation numbers and subspace rotations are naturally included and allow therefore for exponential convergence. The algorithm is demonstrated for Mo bulk and surfaces.

Figure 1

Convergence of the free energy for a two-atom bcc Mo cell for different values of $\kappa$ (see text). Initial guess: linear combination of atomic orbitals (lcao) (full symbols) or random numbers (empty symbols).

Figure 2

Convergence of the free energy for a 20-layer bcc Mo (111) slab. The inset shows the exponential convergence of forces for the direct minimization.