The local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys. 136, 244102 (2012)], which is based on the locality of relativistic effects, has been extended to a four-component Dirac-Coulomb Hamiltonian. In the previous study, the LUT scheme was applied only to a one-particle IODKH Hamiltonian with non-relativistic two-electron Coulomb interaction, termed IODKHC. The current study extends the LUT scheme to a two-particle IODKH Hamiltonian as well as one-particle one, termed IODKHIODKH, which has been a real bottleneck in numerical calculation. The LUT scheme with the IODKHIODKH Hamiltonian was numerically assessed in the diatomic molecules HX and X 2 and hydrogen halide molecules, (HX) n (X F, Cl, Br, and I). The total Hartree-Fock energies calculated by the LUT method agree well with conventional IODKHIODKH results. The computational cost of the LUT method is reduced drastically compared with that of the conventional method. In addition, the LUT method achieves linear-scaling with respect to the system size and a small prefactor.
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