This letter presents an efficient algorithm for local unitary transformation based on the spin-free infinite-order two-component relativistic method for the two-electron interaction, which is assisted by one-center relativistic two-electron integral (TEI) database. The database stores a set of TEIs, one for each element–basis set combination. The algorithm is numerically assessed for hydrogen halide chains, (HX)n (X = Cl and At), Aun, Ir(ppy)3, Pt3(C7H7)2(HCN)3, and PtCl2(NH3)2. The computational cost (time and memory size) at the Hartree–Fock level is lower than that of the conventional method, especially for small and medium-sized molecules.
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