Electron density and implication for bonding in Cu

We report highly accurate measurements for the low-order Fourier components of the crystal potential in copper. These were obtained by transmission electron diffraction using a small probe and multiple scattering analysis. They were used to refine the $\text{Cu}\phantom{\rule{0.3em}{0ex}}3d$ radial wave function. An accurate charge-deformation map and a $3d$ orbital radial wave function were obtained by using a multipole refinement of the structure factors obtained from combined quantitative electron diffraction and $\ensuremath{\gamma}$-ray diffraction measurements. The results show a large change in the $3d$ orbital radial function from $d$-band formation and $d\ensuremath{-}s$ band crossing ($d\ensuremath{-}s$ hybridization). Band theory calculations are in excellent agreement with the measurements and show that the charge deformation in Ag is very similar to that in Cu. Our findings are in general agreement with the monovalent description of these metals.