Just as the LMTO method breaks naturally into an atomic part and a
`solid' part, so do the programs. In general the `solid' part requires
potential parameters and structure constants as its input, from which it
generates bands, energy moments, densities-of-states, etc. The `atomic'
part takes moments as its input and calculates potential parameters from
it. The atomic part requires very little information beyond the moments
and E 
's or boundary conditions to completely specify the
electronic structure within an atomic sphere.
An LMTO calculation is self-consistent when the atomic part produces, from moments generated by the solid part, once again the same potential parameters that the solid part used to generate the moments in the first place. The self-consistency works by alternating between the solid part and atomic part, generating moments, then potential parameters, then moments again until the process converges. The program can be started either with the solid part, specifying potential parameters, or with the atomic part, specifying the moments.
Because the method is a linear one, only three functions can carry
charge inside a sphere ( 
) and
therefore the properties of a sphere, within the approximations of the
linear method are completely determined by the first three moments, the
atomic number and the E 's or boundary conditions at the surface
of the sphere. In some sense these numbers are `fundamental' to a
sphere; the atomic program will generate a self-consistent potential for
a specified set of moments and E 's and generate potential
parameters from it.
From the point of view of the bands, the Hamiltonian is completely specified by the potential parameters (and the structure constants). These are fundamental to the band program; it will generate moments from the eigenvectors of the Hamiltonian. Full self-consistency is achieved when the `input moments' coincide with the `output moments', or equivalently when the input pp's coincide with the output pp's.
The ASA program can start equally as well from either potential parameters or moments, though it is generally easier to start from the moments, if no prior information is available. This is because one can usually begin with a very simple starting guess (choosing the zeroth moment to be the charge of the free atom, the first and second to be zero) that is usually good enough to iterate towards self-consistency.
If potential parameters are available, you may choose to
begin directly with a band calculation and need not worry about the
moments. If you wish to make a self-consistent
calculation, you must also supply the principal quantum numbers for each
channel in the so-called P number described in the following
paragraphs.
To make a sphere self-consistent one needs the moments and also to
specify the boundary condition on the wave function at the sphere
radius, or the E of the wave function 
. For a given
potential, there is a unique correspondence between the logarithmic
derivative D at the sphere radius and E , so in
principle, it is possible to specify either one.
There is a set of numbers called P (one for each channel) that
supplies the information about both the principal quantum number and the
logarithmic derivative, D. P is defined as:
P = .5 - atan(D )/ 
+ n where n (its integer part) is the
principal quantum number; its fractional part varies smoothly from 0
(for the bottom extreme of the band for that principal quantum number)
to 1 (the top extreme of the band), and can be thought of as a
`continuously variable' principal quantum number. Here is a table of
P 
as function of D : D 10 5 1 0 -1 -2 -3 -4 -10 P
.03 .06 .25 .5 .75 .85 .90 .92 .97
P must be supplied to the atom program. The fractional part of P is
automatically supplied by the output of a band calculation (provided
the token IDMOD in category CLASS is not 1),
but you must supply P (in addition to the moments Q) if
you choose to begin with moments. P, together with the moments Q can be
input directly through the control file. A word on choices for the
fractional part of P: .3 is quite free- electron-like and suitable for
free-electron-like channels such as Si d electrons, while .8 is
quite tight-binding-like and suitable for deep states like Cu d orbitals.
If there is no information from the very beginning, .5 is a suitable
choice.
In self-consistency cycles, you have a choice, through the parameter
IDMOD described below, regarding the related pair of parameters P and
E . You may let P and E float to the center of gravity
of the occupied part of the band (most accurate for self-consistent
calculations); this is the default. You may also freeze alternatively P
or E in the self-consistency cycle.
The problem of `ghost' bands can be overcome by using the downfolding
procedure. Orbitals are separated in lower, intermediate and higher
sets. By switching on the automatic downfolding procedure,
this choice is done
automatically by the program. Lower waves contribute to the dimension
of the Hamiltonian matrix, H, and the overlap matrix, O, and carry
charge. Intermediate waves do not contribute to the dimension of H and
O, but carry charge. Higher waves are thrown away altogether. If it
is not known how to separate the orbitals the automatic downfolding can
be switched on before the self-consistency cycle. After a few
iterations, the downfolding indices don't change and if it is desired
the cycle can be stopped and started again with the proper division into
lower, intermediate, and higher set.
Calculations using the automatic downfolding should be
checked carefully. The token which makes the decomposition is
IDXDN.
IDXDN = 0 : automatic downfolding
IDXDN = 1 : low orbitals
IDXDN = 2 : intermediate orbitals
IDXDN = 3 : higher orbitals
More about this below under category CLASS and token IDXDN.