 LMTO: Linear MuffinTin Orbitals 
Definition:  A special basis
set for
ab
initio
electronic structure
calculations. 
Explanation:  The delocalized wave
function of a metal
or any other
crystalline material
always exhibits two
completely different
regions. While it
oscillates rapidly
in the region of the
atomic cores,
thereby reflecting
the high kinetic
energy of the
electrons, it is a
relatively smooth
function between the
atoms. Therefore,
most
ab
initio
methods partition
the space of a
crystal into spheres
around the cores and
the interstitial
space (Figure 1).
When viewed in two
dimensions, such a
partitioning scheme
strongly resembles
the muffintin pan;
hence, it is given
the name as
muffintin
approximation and
muffintin orbitals.
In fact, the a
number of
strategies to
partition the
aforementioned two
regions led to a
large variety of
ab
initio
methods available
today.
The extremely
efficient LMTO
method which is
applied in
several Steel ab
initio projects
simply discards the
interstitial space
by blowing up the
atomic spheres until
they overlap
(atomic sphere
approximation) and
fill up the entire
space. For the
region inside the
spheres, a minimal
basis is used
consisting of one
s, three
p and five
d orbitals at
each atomic site;
for that outside of
the spheres, rapidly
decaying Hankel
functions are used.
Employing an
atomlike basis
set results
an ab
initio
method, which is not
only quite fast but
also gets quite
close to the
chemist’s idea of
atoms and bonds.
Indeed, LMTO theory
allows more
solid state
quantum chemical
insight than the
planewave
codes, which is more
flexible in
computation. 
Picture / Figure / Diagram: 

Fig. 1: (a) Schematic drawing of a muffintin potential, (b) the atomic sphere approximation (ASA), and (c) a muffintin pan that gave the partitioning scheme its name.


SFBLink:  The TBLMTOASA program code from Stuttgart is used in the Steel ab initio project in order to analyze the bonding situation in selected structural motifs which appear in metals, steels, or carbides. The applied density functional theory (→DFT) code and the implemented Crystal Orbital Hamilton Population (→COHP) technique ideally complement each other. 
References:  [1] G. Krier, O. Jepsen, A. Burkhardt, O. K. Andersen, The TBLMTOASA program, version 4.7, MaxPlanckInstitut für Festkörperforschung, Stuttgart, Germany. [2] O. K. Andersen, Phys. Rev. B 1975, 12, 3060. [3] H. Skriver, The LMTO Method, Springer, Berlin 1984. [4] O. K. Andersen, in The Electronic Structure of Complex Systems (Eds: P. Phariseau, W. M. Temmerman), Plenum, New York 1984. [5] O. K. Andersen, O. Jepsen, Phys. Rev. Lett. 1984, 53, 2571. 

