The effective on-site Coulomb interaction (Hubbard U ) between localized d electrons in 3d, 4d, and 5d transition metals is calculated employing a parameter-free realization of the constrained random-phase approximation using Wannier functions within the full-potential linearized augmented-plane-wave method. The U values lie between 1.5 and 5.7 eV and depend on the crystal structure, spin polarization, d electron number, and d orbital filling. On the basis of the calculated U parameters, we discuss the strength of the electronic correlations and the instability of the paramagnetic state toward the ferromagnetic one for 3d metals. 3 However, in these models the Coulomb and also the one-particle hopping matrix elements are typically empirical parameters that are determined such that the employed model reproduces experimental results of interest.For a long time, DFT-LDA and many-body model Hamiltonian methods have been separate and complementary approaches. This has drastically changed with the advent of the dynamical mean-field theory (DMFT), 4 which merged with the LDA to become a novel computational method referred to as LDA + DMFT, 5 which developed into a modern many-body approach for treating correlated electron materials. In retrospect, the so-called LDA + U method, 6 an early attempt to correct the LDA functional by introducing a simple mean-field-like Hubbard U term for localized d or f states, and today routinely applied to a broad spectrum of systems, can be regarded as its static limit. Both LDA + U and LDA + DMFT as well as other approaches not mentioned here rely on the Hubbard U as an additional parameter. Frequently, the exact value of U is unknown, which impedes the predictive power of these approaches.The problem of calculating the parameter-free Hubbard U for transition metals (TMs), i.e., from first principles, has been addressed by several authors.7-11 A number of different approaches have been proposed. Among them, the constrained local-density approximation (cLDA) 9 is the most popular. However, the cLDA is known to give unreasonably large U values for late TMs due to difficulties in compensating for the self-screening error of the localized electrons.10 Furthermore, the frequency dependence of U is unattainable. On the other hand, the constrained random-phase approximation (cRPA), though numerically much more demanding, does not suffer from these difficulties. In contrast to the cLDA, it also allows access to individual Coulomb matrix elements, e.g., on-site, off-site, intra-orbital, interorbital, and exchange.The aim of this Rapid Communication is to present a systematic study of the effective on-site Coulomb interaction (Hubbard U) between localized d electrons in TMs determined by means of first-principles calculations. Previous cRPA studies of U in TMs have focused only on the nonmagnetic (NM) state of the 3d series, and the results appeared to be strongly dependent on the parameters used in the cRPA schemes. 10,11 In the present work, we propose an alternative simple parameter-free c...