# Manual¶

EMTO is divided into 5 subprograms called BMDL, KSTR, SHAPE, KGRN, and KFCD. In a typical calculation the programs are also executed in this order.

## BMDL¶

BMDL calculates the Madelung potentials, which only depend on the crystal structure of the system. Below are the input parameters of BMDL.

Parameter Explanation Default value
JOBNAM Name for the output files
DIR001 Directory, where the Madelung matrix JOBNAM.mdl will be stored.
NL Number of orbitals in the Madelung matrix. 5, 6 or 7
Rest of the input parameters are exactly same as in KSTR.

## KSTR¶

KSTR computes the energy dependent slope matrix in real space.

Parameter Explanation Default value
JOBNAM Name for the output files
DIR001 Directory, where the slope matrix JOBNAM.tfh will be stored.
DIR006 Directory, where the output file JOBNAM.prn will be stored.
MSGL Determines what/how much will be printed on screen. 1
MODE Bulk (B) or a surface (S) calculation. B
STORE Store the slope matrix (Y). Do not store the slope matrix (N). Y (always)
HIGH Compute (Y) or do not compute (N) terms, for which $$l'>l_{max}$$. Y (always)
NL Number of orbitals (possible choices: 1, 2, 3, 4 or 5). 4
NLH The number of terms, for which $$l'>l_{max}$$. 9 or 11
NLW The number of positive energy Watson spheres. 9
NDER The number of slope matrix energy derivatives. 6 (at least 4)
ITRANS Screening matrix. 3 (always)
NPRN Determines the level of output printing in JOBNAM.prn
(K*W^2) The reference point of the slope matrix Taylor expansion. 0
DMAX The radius of the effective cluster in units of lattice constant A. Its value depends on the crystal structure and should be carefully chosen, because it determines the amount of lattice vectors and atomic sites.
RWATS Determines the radius of the Watson sphere, which radius becomes DMAX + RWATS. 0.1
NQ The number of atomic sites in the unit cell.
LAT Determines the underlying Bravais lattice:
1: Simple cubic
2: Face centered cubic
3: Body centered cubic
4: Hexagonal close packed
5: Simple tetragonal
6: Body centered tetragonal
7: Rhombohedral
8: Simple orthogonal
9: Base centered orthorhombic
10: Body centered orthorhombic
11: Face centered orthorhombic
12: Simple monoclinic
13: Base centered monoclinic
14: Triclinic
IPRIM 1 if default primitive lattice vectors are used. 0 if user defined vectors are used.
NGHBP Number of unit cells in the effective cluster 13
A,B,C Lattice constants
BSX,BSY,BSZ Lattice vectors in units of A
QX,QY,QZ Basis vectors in units of A
a/w Hard sphere radius in units the Wigner-Seitz radius 0.7
LAMDA Constants in the Madelung matrix Ewald sum

## SHAPE¶

SHAPE reads the slope matrix JOBNAM.tfh created by KSTR and computes the so called shape function, which transforms any integral over the unit cell into an integral over a sphere surrounding the unit cell.

Parameter Explanation Default value
JOBNAM Name of the input and output files
FOR001 Directory of the slope matrix JOBNAM.tfh
DIR002 Directory, where the shape function JOBNAM.shp will be stored
DIR006 Directory, where the output file JOBNAM.prn will be stored
MSGL Determines what/how much will be printed on screen. 1
Lmax The number of orbitals in the shape function 30
NSR Number of points in the radial grid the shape functions are calculated over 129
NFI Number of points on the numerical integral grid 30
NPRN If 1, the radial grid will be printed in the output file JOBNAM.prn. If 0, it will not be printed
IVEF Determines the break points of the shape function Voronoi polyhedron for the radial grid 3
0: No break points
1: Only faces
2: Faces and edges
3: Faces, edges, and vertices

## KGRN¶

KGRN solves the actual self-consistent Kohn-Sham equations by using the so called Korringa-Kohn-Rostoker Green’s function technique.

Parameter Explanation Default value
JOBNAM Name of the input and output files
STRT A = Start the calculation from scratch. B = Resume using former results. N = Start a new calculation, but using former kmesh etc. A
FOR001 Directory of the slope matrix *.tfh
DIR002 Directory, where the potential JOBNAM.pot will be stored
DIR003 Directory, where the atomic information JOBNAM.atm will be stored
FOR004 Directory of the Madelung matrix *.mdl
DIR006 Directory, where the output file JOBNAM.prn will be stored
DIR009 Directory, where the energy mesh JOBNAM.zms will be stored
DIR010 Directory, where the charge density JOBNAM.chd will be stored
MSGL Determines what/how much will be printed on screen. 1
EXPAN Single (S), double (D) or modified double (M) Taylor expansion for the slope matrix in the kink-elimination equation. When the semicore states lie far from the Fermi level, the single expansion (S) might not be accurate enough to describe all of the occupied electronic states of the valence band in which case D or M becomes necessary. S
FCD Y, if the full charge density should be calculated. N, if not. Y
FUNC Determines whether to use the atomic sphere approximation (ASA) or the spherical cell approximation (SCA) to solve the Poisson equation of the electrostatic potential. SCA
NITER Maximum number of iterations in the main self-consistent DFT loop. 50
NLIN Maximum number of iterations in the Dyson equation. 30
NPRN Determines what/how much will be printed in the output file JOBNAM.prn
NCPA Maximum number of iterations in coherent potential approximation (CPA) loop. 7
NT The total number of so called sublattices. Atomic sites, which are occupied by identical elements and have identical spatial symmetry (except for a simple rotation) and magnetic moments, belong in the same sublattice. Using sublattices makes the calculations faster, because only one atomic site needs to calculated; the information is then just copied to the rest of the atomic sites in the same sublattice.
MNTA The number of different atomic species in a given atomic site. For a “normal” calculation this value is always 1 and for a CPA calculation it would be > 1
MODE 2D or 3D space. 3D (always)
FRC Determines whether (Y) or not (N) forces should be calculated. N
DOS With D the density of states (DOS) will be calculated. With F the Fermi surface. With N neither. N
OPS Not used. N (always)
AFM Calculation is: ferromagnetic (F), non magnetic (P), fixed total spin (M, check also MMOM), or fixed individual spins (m, check also Fix).
CRT M or m for a metallic system. I for an insulator. M
Lmaxh The number of orbitals in the full charge density calculation. 8 or 10
Lmaxt The number of tails. 2 - 4
NFI Determines the number of mesh points in the numerical Gaussian integration method. 31
FIXG Determines the way the so called muffin-tin zero $$V_0$$ is calculated. The muffin-tin zero is defined as an average of the true potential in the interstitial region: $$V_0 = \frac{1}{\Omega - \sum_R \frac{4\pi s_R^3}{3}}\int_{int} V(r)\,dr$$. 2 (always)
SHF Determines the point where the electrostatic, kinetic, and the exchange-correlation stress tensors are calculated. 0
SOFC Y = soft-core approximation. N = frozen core approximation. Z = all-electron frozen core contribution. In soft-core approximation the core states are updated after every self-consistent iteration. Frozen core approximation uses fixed atomistic core states throughout the calculation. Y
KMSH Determines the k-mesh generation algorithm. G
IBZ Determines the Brillouin zone. Should be the same number as LAT in BMDL and KSTR.
NKX,NKY,NKZ The number of k points.
FBZ Y, if the full Brillouin zone should be used. N, if not. N
KMESH2 Not used.
ZMSH Determines the shape of the z-mesh, along which the Green’s function is calculated. C
NZ1 Ceiling for the number of points in the z-mesh. After each iteration the number of points becomes $$NZ=\min(NZ+2,NZ1)$$. 16
NZ2,NZ3,NRES Parameters for the Fermi function integral. 16,8,4
NZD The number of energy points in the DOS calculation. 200
DEPTH Determines the width of the z-mesh. This value should be chosen in such a way that all valence states lie inside the area defined by the z-mesh contour integral.
IMAGZ DOS and the Fermi surface calculations use their own z-mesh and this parameter controls the imaginary part of the complex points in that z-mesh. 0.005 - 0.05
EPS Parameter related to the energy integral. 0.1 - 0.2
ELIM Defines the crossing point of the z-mesh and the real axis as $$E_F - ELIM$$, where $$E_F$$ is the Fermi energy (ZMSH = M or m). Used especially with semicore states.
AMIX Density mixing parameter of the simple linear mixing scheme. 0.01 - 0.1
EFMIX Mixing parameter for the Fermi energy mixing. 1.0 or 0.4, if CRT = I
VMTZ This parameter can be used to shift the muffin-tin zero (FIXG = 3).
MMOM Total magnetic moment in a fixed spin calculation (AFM = M).
TOLE Convergence criterion of the total energy. 1.d-7
TOLEF Convergence criterion of the Fermi energy. 1.d-7
TOLCPA Convergence criterion of the CPA loop. 1.d-6
TFERMI The Fermi temperature in Kelvins. Used when ZMSH = F. 500
SWS The average Wigner-Seitz radius, i.e. the volume of the unit cell, in bohr.
NSWS Not used.
DSWS Not used.
ALPCPA The screened impurity model parameter of CPA. Technically its value should be determined by doing a supercell calculation without CPA. Normally 0.6 is used for systems like Fe-Cr and 0.9 for systems like Pd-Ag. 0.6 - 1.0
EFGS Initial guess for the Fermi level. 0.0
HX The distance between points on the linear path. The linear path is a part of the Fermi energy z-mesh lying slightly above the presumed Fermi level on the real axis. It is used to easily find the Fermi level by closing the z-mesh contour at different points on the linear path without changing the rest of the z-mesh. 0.1 (< 0.3)
NX The number of trial points on the z-mesh linear path. 5
NZ0 Initial number of z-mesh points. <= NZ1
STMP Y = Temporary disk storage at DIR011 will be used. A = RAM will be used. N = No temporaty storage is used. The option A is the fastest, but one needs to make sure that there is enough RAM available. Y or A
Symb List of elements present in a calculation.
IQ Atomic site.
IT Sublattice.
ITA The types of atoms occupying a given atomic site (in a CPA calculation).
NZ Atomic number.
CONC The concentration of a type of atom in a given atomic site. In a CPA calculation the concentrations have to add up to unity at each atomic site.
Sm(ws) The size of the local muffin-tin zero in units of S. 1.0
S(ws) The size of the potential spheres in units of WS 1.0
WS(wst) The size of the atomic spheres in ASA in units of the atomic Wigner-Seitz spheres. 1.0
QTR Initial charge transfer.
SPLT Initial magnetic moment.
Fix When AFM=m this spin is fixed to the value of SPLT (Y) or it is not fixed (N). N
IEX Determines which exchange-correlation functional to use. 4 (LDA)
NP The number of radial grid points in the Poisson equation solver. 251
NES The number of times the atomic orbital energies are adjusted in the Dirac equation solver. 15
NITER The maximum number of iterations in the Dirac solver. 100
IWAT If IWAT = 1, the potential DV(I) is corrected either with a term ION/RWAT or ION/DR(I), where ION is the number of electrons of a given atomic species. DR(I) is the point I of the radial mesh. If IWAT = 0, this correction is not performed. 0
NPRNA Determines how much information will be printed in the output file JOBNAM.prn. If NPRNA = 1, the radial mesh, potentials, electron density, and the orbitals will be printed in addition to the normal printouts. 0
VMIX Mixing parameter of the potential. 0.3
RWAT The radius of the Watson sphere. 3.5
RMAX Controls the distribution of points in the atomic radial mesh. 20.0
DX A step size controlling the number of points in the atomic radial mesh. Small values of DX lead to high number of points and vice versa. 0.03
TEST Convergence criterion in the Poisson equation and the orbital Dirac equations. 1.0E-12
TESTE Convergence criterion in the Poisson equation and the orbital Dirac equations. 1.0E-12
TESTY Convergence criterion in the Poisson equation and the orbital Dirac equations. 1.0E-12
TESTV Convergence criterion in the Poisson equation and the orbital Dirac equations. 1.0E-12

## KFCD¶

KFCD takes the converged total electron density created by KGRN and evaluates the DFT total energy functional in order to produce the ground state total energy of the system. The exchange-correlation energy is calculated as a perturbative correction over the exchange-correlation treatment of KGRN.

Parameter Explanation Default value
JOBNAM Name of the input and output files.
STRNAM Name of the structure output files of BMDL, KSTR, and SHAPE.
DIR001 Directory of the slope matrix STRNAM.tfh.
DIR002 Directory of the electron density JOBNAM.chd.
DIR003 Directory of the shape function STRNAM.shp.
DIR004 Directory of Madelung matrix STRNAM.mdl.
DIR006 Directory where the output file JOBNAM.prn will be stored.
MSGL Determines what/how much will be printed on screen. 1
Lmaxs When the shape function is expanded as a sum of spherical harmonics $$Y_L(r)$$, Lmaxs determines the number of terms in this sum. 30
NTH The number of points in the spherical numerical grid for the polar angle $$\theta$$. 41
NFI The number of points in the spherical numerical grid for the azimuthal angle $$\phi$$. 81
FPOT Determines whether the full potential is calculated (Y) or not (N). EXPERIMENTAL FEATURE! N
OVCOR If OVCOR = Y, a correction is added to the electrostatic potential, which is meant to mitigate the overlap error between adjacent unit cells. This overlap error is caused by the divergence of the potential at large $$l$$ values. If OVCOR = N, the correction is not added to the potential. Y
UBG If UBG = Y, a test for the accuracy of the Coulomb term is performed. In this test the Madelung constant is calculated for point charges embedded in a uniform field and then compared to the Madelung constant calculated in KSTR. If UBG = N, this test is not performed. N
NPRN Determines how much information will be printed in the output file JOBNAM.prn. N