Local unitary transformation method toward practical electron correlation calculations with scalar relativistic effect in large-scale molecules

In order to perform practical electron correlation calculations, 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); and ibid. 137, 144101 (2012)], which is based on the locality of relativistic effects, has been combined with the linear-scaling divide-and-conquer (DC)-based Hartree-Fock (HF) and electron correlation methods, such as the second-order Moller-Plesset (MP2) and the coupled cluster theories with single and double excitations (CCSD). Numerical applications in hydrogen halide molecules, (HX)_n (X = F, Cl, Br, and I), coinage metal chain systems, M_n (M = Cu and Ag), and platinum-terminated polyynediyl chain, trans,trans-{(p-CH₃C₆H ₄)₃P}₂(C₆H₅)Pt(C≡C) ₄Pt(C₆H₅){(p-CH₃C₆H ₄)₃P}₂, clarified that the present methods, namely DC-HF, MP2, and CCSD with the LUT-IODKH Hamiltonian, reproduce the results obtained using conventional methods with small computational costs. The combination of both LUT and DC techniques could be the first approach that achieves overall quasi-linear-scaling with a small prefactor for relativistic electron correlation calculations.