Orbit-orbit relativistic correction calculated with all-electron molecular explicitly correlated Gaussians

An algorithm for calculating the first-order electronic orbit-orbit magnetic interaction correction for an electronic wave function expanded in terms of all-electron explicitly correlated molecular Gaussian (ECG) functions with shifted centers is derived and implemented. The algorithm is tested in calculations concerning the H₂ molecule. It is also applied in calculations for LiH and H₃⁺ molecular systems. The implementation completes our work on the leading relativistic correction for ECGs and paves the way for very accurate ECG calculations of ground and excited potential energy surfaces (PESs) of small molecules with two and more nuclei and two and more electrons, such as HeH^-, H₃⁺, HeH₂⁺, and LiH₂⁺. The PESs will be used to determine rovibrational spectra of the systems.