Various vacancy and interstitial defect migration mechanisms were characterized for crystalline material by using a tight-binding approach, and super-cells which contained 64 or 216 atoms. Defect configurations were investigated which corresponded to minima and the pathways that connected them. A modified eigenvector approach was used to locate true transition states. The fact that only one Hessian eigenvector was needed to define the up-hill search direction was exploited. Conjugate gradient minimization in the tangent space was used to produce a hybrid algorithm. Two versions of the approach were considered; one in which second derivatives were available, but full diagonalization of the Hessian would be the most time-consuming step. In the other, only first derivatives of the energy were known.

Defect migration in crystalline silicon L.J.Munro, D.J.Wales: Physical Review B, 1999, 59[6], 3969-80