We present a method for improving the speed of geometry relaxation by using a
harmonic approximation for the interaction potential between nearest neighbor
atoms to construct an initial Hessian estimate. The model is quite robust, and
yields approximately a 30% or better reduction in the number of calculations
compared to an optimized diagonal initialization. Convergence with this
initializer approaches the speed of a converged BFGS Hessian, therefore it is
close to the best that can be achieved. Hessian preconditioning is discussed,
and it is found that a compromise between an average condition number and a
narrow distribution in eigenvalues produces the best optimization.Comment: 9 pages, 3 figures, added references, expanded optimization sectio