  In this work we introduce a Linearized version of the Koringa Khon and
Rostoker method (LKKR) and show it to be equivalent to the Linearized Muffin
Tin Orbitals method (LMTO). We then present higher derivative versions of both
methods, e.g. HDKKR and HDMTO and show them to be partially distinct (not
equivalent). In particular HDKKR basis set does not have an equivalent ground
state for the Khon Sham (KS) Hamiltonian as the HDKKR basis set and has greater
variational power than the HDMTO one. Because the KS method, for Density
Functional Theory (DFT), is variational HDKKR will give better ground state
energies than HDMTO. However HDKKR is much harder to work with then HDMTO
requiring much greater computer resources so HDMTO can often be preferred.
