Some of the most popular ways to treat quantum critical materials, that is, materials close to a magnetic instability, are based on the Landau functional. The central quantity of such approaches is the average magnitude of spin fluctuations, which is very difficult to measure experimentally or compute directly from the first principles. We calculate the parameters of the Landau functional for Pd and use these to connect the critical fluctuations beyond the local-density approximation and the band structure.The physics and materials science of weak itinerant ferromagnetic metals and highly renormalized paramagnets near magnetic instabilities has attracted renewed theoretical interest. This is a result of recent discoveries of materials with highly non-conventional metallic properties, especially, non-Fermi liquid scalings, metamagnetic behavior, and unconventional superconductivity, in several cases co-existing with ferromagnetism. Discoveries in the last three years alone include the co-existing ferromagnetism and superconductivity of Unfortunately, although model theories have been put forth, there is still not an established material specific (first principles) theoretical understanding of these phenomena. One difficulty is the usual starting point for first principles theories, density functional theory (DFT) as implemented in the local density approximation (LDA). This already includes most spin degrees of freedom, including dynamical fluctuations, as evidenced by its formally exact description of the uniform electron gas as well as its well documented success in accurately describing a wide variety of itinerant magnetic materials. However, the electron gas, upon which most density functionals are built, is not near any critical point for densities relevant to the solid state, and furthermore the proximity to itinerant magnetism of a metal is an extremely non-local quantity, in particular depending on the electronic density of states at the Fermi level N (E F ). Therefore, the exact DFT, which by definition includes all fluctuations and describes the ground state magnetization exactly, is likely to be extremely nonlocal and probably nonanalytical for the materilas near a quantum critical point.On the other hand, the LDA, while providing a good description of most itinerant ferromagnets that are not near critical points, fails to include the soft critical fluctuations in the materials of interest here. Since fluctuations are generically antagonistic to ordering, the result is that magnetic moments and magnetic energies of weak itinerant ferromagnets near critical points are overestimated in the LDA, as opposed to LDA's failure to describe (as mentioned, this latter material shows a metamagnetic quantum critical point). The basic theoretical difficulty in correcting the LDA for these materials is that there is some unknown and possibly strongly material dependent cross-over in energy (and possibly non-trivially in momentum) separating quantum critical fluctuations, not included in the LDA, from the dynamical f...