  Orbital optimization procedure is widely called in electronic structure
simulation. To efficiently find the orbital optimization solution, we developed
a new second order orbital optimization algorithm, co-iteration augmented
Hessian (CIAH) method. In this method, the orbital optimization is embedded in
the diagonalization procedure for augmented Hessian (AH) eigenvalue equation.
Approximations for Hessian matrix can be easily employed in this method to
improve the computational costs. We numerically performed the CIAH algorithm
with SCF convergence of 20 challenging systems and Boys localization of C60
molecule. We found that CIAH algorithm has better SCF convergence and less
computational costs than direct inversion iterative subspace (DIIS) algorithm.
The numerical tests suggest that CIAH is a stable, reliable and efficient
algorithm for orbital optimization problem.

Chemical Physics