Augmented Lagrangian Method for Optimizing Non-Orthogonal Orbitals

We applied augmented Lagrangian method to optimize molecular wave function based on non-orthogonal orbitals (Spin coupled wave function; SCWF) for its grand-state energy.

In contrast to the orthogonal-orbital-based electronic structure theory, SCWF includes spin eigenfunctions to satisfy the eigen states as the operator

of the square of the spin.

To obtain the ground-state energy of SCWF, therefore, it is necessary to optimize the orbital and the spin-coupling coefficients simultaneously.

In this study, the spin-coupling and the orbital coefficients are optimized with the augmented Lagrangian method under the constrain of normality of the wave function.

We employed this SCWF method to compute dissociative potential energy surfaces (PESs) of H₂, H₂^-, He₂⁺, and HLi. The obtained PESs by the SCWF method are close to these by full configuration interaction theory. These results indicate that the augmented Lagrangian method is effective to optimize SCWF.