Augmented Lagrangian Method for Optimizing Non-Orthogonal Orbitals

<p>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. </p><p>In contrast to the orthogonal-orbital-based electronic structure theory, SCWF includes spin eigenfunctions to satisfy the eigen states as the operator </p><p>of the square of the spin. </p><p>To obtain the ground-state energy of SCWF, therefore, it is necessary to optimize the orbital and the spin-coupling coefficients simultaneously. </p><p>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.</p><p>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.</p>

Augmented Lagrangian Method for Optimizing Non-Orthogonal Orbitals

<p>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. </p><p>In contrast to the orthogonal-orbital-based electronic structure theory, SCWF includes spin eigenfunctions to satisfy the eigen states as the operator </p><p>of the square of the spin. </p><p>To obtain the ground-state energy of SCWF, therefore, it is necessary to optimize the orbital and the spin-coupling coefficients simultaneously. </p><p>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.</p><p>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.</p>

Single charge exchange in collision of fast protons with hydrogen molecules

Single charge transfer process in collision of energetic protons with molecular hydrogens is theoretically studied using a first-order two-effective-center Born approximation. The correct boundary conditions are incorporated in the formalism and the Hartree–Fock molecular wave function for molecular targets and the residual ions are used to calculate the transition amplitude. The interference patterns in the capture differential cross-sections (DCSs) for a given fixed orientation of the molecule, due to the scattering from the two-atomic centers in the molecular targets, are examined. The dependence of the DCSs upon the angle between the molecular axis and the direction of the incident velocity is theoretically investigated. Both average differential and integral cross-sections are calculated. The obtained results are compared with the available experimental data.