  The ultimate goal of electronic structure calculations is to make the left
and right hand sides of the titled ``equation'' as close as possible. This
requires high-precision treatment of relativistic, correlation, and quantum
electrodynamics (QED) effects simultaneously. While both relativistic and QED
effects can readily be built into the many-electron Hamiltonian, electron
correlation is more difficult to describe due to the exponential growth of the
number of parameters in the wave function. Compared with the spin-free case,
spin-orbit interaction results in the loss of spin symmetry and concomitant
complex algebra, thereby rendering the treatment of electron correlation even
more difficult. Possible solutions to these issues are highlighted here.
