About MuffinTin Potential Crystal Input File XT.DAT
We shall go over what goes into defining the lattice and program controls.
This file needs to be made in two versions. One for the calculation
of the scattering phase shifts and the other for the calculation of the
EXAFS matrix elements.
I. Look at the input as defined by READ lines.
READ(5,100)TITLE
READ(5,101)SPA,ANG
READ(5,101)((RC(I,J),I=1,3),J=1,3)
READ(5,218)IPX,IREL
READ(5,102)NR
JJ=0
DO 4 IR=1,NR
READ(5,100)(NAME(I,IR),I=1,2)
READ(5,103)NRR(IR),Z(IR),ZC(IR),RMT(IR)
DO 4 J=1,N
JJ=JJ+1
READ(5,101)RK(1,JJ),RK(2,JJ),RK(3,JJ)
4 CONTINUE
READ(5,103)NHM,ALPHA,ATDIAM,FLOMT,EXPRES,RMTZ
14 DO 18 IR=1,NR
READ(5,218)L,NE,E,DE
IF(IPX.NE.1.AND.L.LT.0)GOTO 18
C IF IPX=1 RONUC IS CALLED TO CALCULATE MATRIX ELEMENTS FOR XRAY ABSORPTION
902 CALL RONUC(Z(IR),NGRID,ATL,XM,WM,RMT(IR),E,DE,NE,L,IR)
18 CONTINUE
100 FORMAT(9A8)
101 FORMAT(3F8.4)
102 FORMAT(I4)
103 FORMAT(I4,5F8.4)
218 FORMAT(2I4,2F8.4)
SUBROUTINE RONUC(Z,NM,VM,XM,WM,RM,E1,DE,NJE,LI,IR)
READ(5,10) NCORE,ECORE
10 FORMAT(I4,F11.5)
line01 [TITLE]
line02 [SPA] [ANG]
line03 { [RC(1,1)] [RC(2,1)] [RC(3,1)] for unit cell axis 1 }
line03.1 { [RC(1,2)] [RC(2,2)] [RC(3,2)] for unit cell axis 2 }
line03.2 { [RC(1,3)] [RC(2,3)] [RC(3,3)] for unit cell axis 3 }
line04 [IPX] [IREL]
line05 [NR]
line06 { [NAME(1)] for atom 1, emitter atom type }
line07 { [NRR(1)] [Z(1)] [ZC(1)] [RMT(1)] }
line08 { { [RK(1,1)] [RK(2,1)] [RK(3,1)] for position 1 } }
line08.1 { { [RK(1,2)] [RK(2,2)] [RK(3,2)] for position 2 } }
line08.2 { { ... } }
line09 { [NAME(2)] for atom 2 }
line10 { [NRR(2)] [Z(2)] [ZC(2)] [RMT(2)] }
line11 { { [RK(1,3)] [RK(2,3)] [RK(3,3)] for position NRR(1)+1 } }
line11.1 { { ... } }
line12 [NHM] [ALPHA] [ATDIAM] [FLOMT] [EXPRES] [RMTZ]
line13A { [L] [NE] [E] [DE] for atom 1 phase shift }
line13A.1 { [L] [NE] [E] [DE] for atom 2 phase shift }
line13A.2 { ... }
line13B { [L] [NE] [E] [DE] for atom 1 EXAFS matrix }
line14B { [NCORE] [ECORE] for atom 1 EXAFS matrix }
line13B.1 { [L] [NE] [E] [DE] for atom 2 EXAFS matrix }
line14B.1 { 1 0.0 for atom 2 EXAFS matrix }
line13B.2 { ... }
line14B.2 { ... }
II. Discussion of the details of each input line
Using Zinc Centered ZincOxide for Example
Input
Wyckoff, R. W. G., Crystal Structures, Interscience Publishers,
NY, 1965, defines the wurtzite structure for ZnO as a twomolecule hexagonal
unit with atoms arranged in the positions:
R: 0 0 0; 1/3 2/3 1/2
X: 0 0 u; 1/3 2/3 u+1/2
with sides a_{o} = 3.24950 Ang.
c_{o} = 5.2069 Ang.
and u = 0.345

line 01, Title :
TITLE  A descriptive name for the input file
Example: ZnO:ZnO Wurtzite STRUCTURE

line 02, Unit Cell Parameters :

SPA  lattice constant in A.U.

ANG  0 = atom positions are given in cartesian coordinates. 1 =
atom positions are given in units of the unit cell vectors; this option
is the form given by Wyckoff, R. W. G. in Crystal Structures.
Example: 6.1407 1.

lines 03, Axes of the Unit Cell :
RC(1,J),RC(2,J),RC(3,J)  X,Y,Z coordinates of the J'th axis of the
unit cell, in units of SPA. These describe the vectors of the
unit cell axes in cartesian coordinates.
Example: 0.8660 0.5000 0.0000
0.0000 1.0000 0.0000
0.0000 0.0000 1.6024
for ZnO in a hexagonal close packed lattice with c/a = 1.6024.

line 04, Results Control Parameters :

IPX  0 = scattering phase shifts are calculated. 1 = EXAFS matrix
elements.
Note: This determines how lines 13 and 14 are
read.

IREL  switch for requiring L.S term in phase shift calculation.
0 = no. 1 = yes.
Note: IREL = 1 has no meaning for the EXAFS matrix elements and the
muffintin potential program will automatically force IREL = 0 when IPX
= 1.
Example: 0 0
for a nonL.S calculation of phase shift

line 05, Inequivalent Atoms :
NR  how many unique atoms exist in the lattice and have data to be
read in.
Example: 2

line 06, Title of Atom 1, the Emitter Atom Type :
NAME(1)  title of atom 1. This atom type must contain the "excited"
atom, which is assumed to be the origin of the lattice and scattering events.
Example: ZINC

line 07, Atom 1 Information :

NRR(1)  number of atoms of type 1 in the unit cell

Z(1)  the atomic number of atoms of type 1

ZC(1)  the valence or ionicity of atoms of type 1

RMT(1)  the muffintin radius of atoms of type 1, in AU. This value
can come from various sources. There are two prime initial choices
for RMT; the atomic radius and the ionic radius, both as given by a periodic
table or similar source. A simple constraint for the muffintin radius
is to fit the RMT of two nearest neighbor atoms to the experimentally derived
bond distance between them.
Example: 2 30.0000 0.0000 2.2916

lines 08, Positions of Atoms of Type 1 :
RK(1,n),RK(2,n),RK(3,n)  coordinates of the n'th atom in the unit
cell for atoms of type 1, in units of SPA. If, from
line02, ANG = 0, the coordinates are cartesian X,Y,Z; if ANG = 1, the
coordinates are given in units of the vectors described.
Example: 0.0000 0.0000 0.0000
0.3333 0.6667 0.5000
for the emitter at the origin and another
atom at 1/3a,2/3a,1/2c of the hcp unit cell.

line 09, Title of Atom 2 :
The title of atom type 2.
Example: OXYGEN

line 10, Atom 2 Information :
The same as line07, but for atom type 2.
Example: 2 8.0000 0.0000 2.2916

line 11, Positions of Atoms of Type 2 :
The same as line08, but for atom type 2.
Example: 0.0000 0.0000 0.3450
0.3333 0.6667 0.8450

line 12, MuffinTin Control Parameters :

NHM  muffintin zero parameter. The muffintin zero value is estimated
from a sampling grid whose most accurate mesh is given by (NHM)^{3}
points spanning the unit cell. If NHM < 0, the muffintin zero
value is given by RMTZ. Typically, NHM = 8 is a good minimum and
NHM = 16 is pretty good.

ALPHA  exchange parameter for the
Xa multiple scattering method. In general, ALPHA
is about 0.7 for all but the lightest atoms where it rises to about 0.78.
For the lattice, it is usually sufficient to take ALPHA as an average of
the individual atom values. A compilation of ALPHA values for up
to Z=41 can be found from Karlheinz Schwarz, Phys. Rev. B 5 Num. 7, 2466
(1972). A simple algebraic formula for alpha that fits
Schwarz' data fairly well is alpha = (1/(Z+1.5) + 2/(Z+1.5)^{2})/3 + 0.697.

ATDIAM  "atomic diameter" of the monolayer, in AU. Used to calculate
SIGMA, the selfenergy for energy E (Im(E)), which is used in calculating
the phase shifts for the paired real/imaginary output of muf9.out.

FLOMT  fermi level offset from the muffintin zero, in Hartrees.
Also used to calculate SIGMA for muf9.out. SIGMA is evaluated using
the value of the energy measured from the fermi level of the lattice, so
this parameter is included to enable redefining the zero value of the energy;
E_{SIGMA }= E  FLOMT, where E = Energy  (muffintin zero
value).

EXPRES  "experimental" resolution of the data being theoretically modelled,
in eV. Also used to calculate SIGMA for muf9out. This is a
generic broadening term quadratically added to SIGMA to account for line
broadening due to experimental errors; machine resolution, detector resolution,
data processing, etc. SIGMA=SQRT(SIGMA^{2}+EXPRES^{2})

RMTZ  optional value for the muffintin zero; rather than letting the
program determine it, in Rydbergs.
Example: 16 0.7256 3.3947 0.2341 1.0000 0.0000

lines 13, Description of the State of Each Atomic
Type :
There are two cases described here: case A for scattering phase shifts,
case B for EXAFS matrix elements. These can not be included in the
same input file although both are described here. Two separate input
files must be made, one for each. Which input is appropriate is determined
by line04, IPX.
Note: It is certainly convenient (I don't know if it is necessary)
for the energy range and grid used for the two results to be the same.

Scattering Phase Shifts
There should be one line for each unique atom type, with the lines
listed in the same order as the atom types were given in.

L  maximum angular momentum state calculated for that atom type.
Note: L = 3 means that the 3+1 states, l = 0,1,2,3 (s,p,d,f), will
be calculated. Note: To skip calculating phase shifts for a particular atom type,
set L < 0 for that atom.

NE  number of energy grid points. I believe the limit to be 200.

E  initial energy (grid point 1) at which to calculate phase shifts, in
Hartrees. This energy must be ≥ FLOMT from line 12.

DE  energy increment between grid points, in Hartrees.
Example: 3 200 0.2500 0.0085
3 200 0.2500 0.0085
Note: Usually l=3 is the max. angular momentum state
necessary. If in doubt, run for l=4 and check that
the phase shifts are negligible (< 1E02 rad, say).

EXAFS Matrix Elements
This line need only have correct values for the first atom type, the
emitter. Being the "excited" atom, it is the atom that creates the
matrix elements.

L  initial angular momentum state(subshell) of the emitter atom before
being "excited". Both the L+1 and L1 transitions will be calculated (in that order)
as per dipole selection rules. Note: L=0 (s state) will output only
p matrix elements. L=1 (p state) will output both s and d matrix
elements.

NE  number of energy grid points. I believe the limit to be 200.

E  energy of the final state (emitted electron) relative to the muffintin
zero value, in Hartrees. Note: Energies below the fermi level do
not give meaningful results and can bog down the program. Energies
just at or just above the fermi level are the bare minimum energy that
needs to be run. Keep in mind that if you use the FLOMT, this energy
must be a bit bigger than the FLOMT to start with an effective energy slightly
greater than zero. (zero is a bad energy regardless of which calculation
method is used.)

DE  energy increment between grid points, in Hartrees.
Example: 1 200 0.2500 0.0085
3 36.39756
1 200 0.0000 0.0000
1 0.00000
Note: These are lines13B AND 14B. The emitter atom
type is the ZINC atom 2p state.

lines 14B, Additional Description of the State of Each Atomic Type for
EXAFS Matrix Elements :
These lines are only necessary for IPX = 1, output EXAFS Matrix Elements
for the emitter atom.

not used

EXAFS Matrix Elements
As for line 13B, this line need only have correct values for the first
atom type, the emitter.

NCORE  Index of the of the initial state wave function
of the emitter atom; i.e. position of wave function in the input file. If NCORE < 0, no calculation is performed
for that atom type; thus for all atom types other than the emitter atom
type just set NCORE = 1.

ECORE  energy eigenvalue of the subshell relative to the vacuum value,
in Hartrees. This number can be obtained from the HermanSkillman
results.
Example: See lines 13,B above.
Go to top of page
Created: April 8, 1999  Last Updated: April 12, 1999
By Mark D. Pauli