To explore the formation of noncollinear magnetic configurations in materials with strongly correlated electrons, we derive a noncollinear LSDA+U model involving only one parameter U, as opposed to the difference between the Hubbard and Stoner parameters U − J. Computing U in the constrained random phase approximation, we investigate noncollinear magnetism of uranium dioxide UO 2 and find that the spin-orbit coupling (SOC) stabilizes the 3k ordered magnetic ground state. The estimated SOC strength in UO 2 is as large as 0.73 eV per uranium atom, making spin and orbital degrees of freedom virtually inseparable. Using a multipolar pseudospin Hamiltonian, we show how octupolar and dipole-dipole exchange coupling help establish the 3k magnetic ground state with canted ordering of uranium f -orbitals. The cooperative Jahn-Teller effect does not appear to play a significant part in stabilizing the noncollinear 3k state, which has the lowest energy even in an undistorted lattice. The choice of parameter U in the LSDA+U model has a notable quantitative effect on the predicted properties of UO 2 , in particular on the magnetic exchange interaction and, perhaps trivially, on the band gap: The value of U = 3.46 eV computed fully ab initio delivers the band gap of 2.11 eV in good agreement with experiment, and a balanced account of other pertinent energy scales. * sergei.dudarev@ukaea.uk † cesare.franchini@univie.ac.at. (6) Here,N = m,σĉ † m,σĉm,σ is the operator of the total number of electrons on a site,n kl = σĉ † k,σĉ l,σ , and M = m,ξ,ξ ′ĉ † m,ξ σ ξξ ′ĉ m,ξ ′