The NRL Tight-Binding Fitting Code

The fitting code is not easy to be used by non-specialists. It is designed for the creation of our parameter library to be used by the Static code and the MD code.

The only posible use of this code for a non-expert is when there is a need for generating a set of tight-binding parameters which have a shorter range. In that case we can provide the input file and the only thing the user has to do is to vary the cutoff function parameter.

Description of Fitting Code Input

The example below is a sample input file taken from our fit to germanium. The actual input data is in the leftmost column. There should be no blank lines in the final input.

Save your final input file under the name "SKIN".

Input Name of variable Explanation

Mode=0 MODE Version 1

16 100 2 0.0001 NSTRUC, MAXIT, IOPT, EPS Numb of structures or lattice constants,Maximum number of iterations,Strict descent method,Convergence criterion

0.00000 0.2 1.0 1.0 AVGE, SYMWGHT, SYMDIV, SYMMUL Reference total energy, Weight of symmetrized bands,Reduces weight,Increases weight (Only needed for the symmetrized version)

QLMT=F LQLMT F=energy bands formatted as shown below T=energy bands input from separate files.

ge102sk TITLE Label for the first set of energy band data that follow (ge for germanium,102 for lattice constant 10.2 Bohr)

1.50 0 8 EMAX, NBLOW, NBANDMAX When QLMT=F EMAX is not used.When QLMT=T then bands with values larger than EMAX+Fermi level will not be included in the fit,NBLOW is not yet activated but it must be set to zero, NBANDMAX is the maximum number of bands.

JSPINS=1, 0.005 F JSPINS, TKB, LSTRUC JSPINS is intended for a spin polarized code, TKB=temperature broadening, F=the data for the lattice parameter that follows are included in the fit, T= not included in the fit.

0d0 0.75367 8.0 SHIFT, EFERMI, ZFILL SHIFT=0. , EFERMI=Fermi level used only when LQLMT=T, ZFILL=Number of valence electrons.

-0.409103 2 300.0 TRUEE, DIVIDE, WTE TRUEE=Total energy in Rydberg truncated before the decimal,DIVIDE=Number of atoms in unit cell,WTE=weight for fitting the total energy.

89 NPTS Number of k-points for the set of energy bands that follows.

0 0 0 1.00000000000000000 8 X, Y, Z, WEIGHT, NBAND X,Y,Z are the cartesian coordinates of the k-points for QLMT=F and lattice coordinates for QLMT=T, WEIGHT=Weight of k-point, NBAND=Number of energy bands for the particular k-point.

-.62975 .37364 .37364 .37364 .49980 .58281 .58281 .58281 Eigenvalues These are the eigenvalues for the first k-point. This process repeats until the k-point list is exhausted (in this case, a total of 89 k-points).

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.0 WT Band weights

0 NSYMKP 0 Indicates that no symmetrized bands will be used

ge104sk
1.50 0 8
JSPINS=1, 0.005 F
0d0 0.75367 8.0
-0.417298 2 300.0
89
0 0 0 1.00000000000000000 8
-.63405 .33282 .33282 .33282 .41898 .54112 .54112 .54112
etc.
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.0
0 Repeat this process for each structure to be fit.

.121129895271E+01 0 1 exp -.197031010828E+00 0 2 s -.147246836815E+01 0 3 s -.404947755887E+02 0 4 s -.221390177434E+03 0 5 s .366830032879E+00 0 6 p -.275983210546E+01 0 7 p -.100953340876E+03 0 8 p .239392944849E+04 0 9 p .122714678806E+01 1 10 t2g .639716703820E+01 1 11 t2g -.266521805137E+02 1 12 t2g .363778209932E+02 1 13 t2g .964883787949E+00 1 14 eg .419370464185E+01 1 15 eg -.353425964684E+02 1 16 eg .404532361580E+03 1 17 eg .105259876640E+04 0 18 sss -.190561649271E+03 0 19 -.251980650278E+02 0 20 .100359282774E+02 0 21 sps -.430821179023E+01 0 22 .326945384960E+00 0 23 -.217820428726E+02 0 24 pps .196274770650E+00 0 25 .113595290864E+01 0 26 -.315567254011E+02 0 27 ppp .858753164946E+01 0 28 -.177547961817E+01 0 29 -.582635424778E+02 1 30 sds .117267249375E+02 1 31 -.123949178334E+01 1 32 .152194272235E+02 1 33 pds -.203199371941E+00 1 34 .438599662935E+00 1 35 -.571676942648E+00 1 36 pdp -.779705456424E+01 1 37 .107617582636E+00 1 38 -.239141569816E+03 1 39 dds .402553355228E+03 1 40 -.141290233843E+03 1 41 -.121269276657E+03 1 42 ddp .340373295876E+02 1 43 .107669411640E+02 1 44 -.417122837381E+05 1 45 ddd .613072520780E+05 1 46 -.207809859115E+05 1 47 .351968575390E+01 0 48 sss ov .327563082867E+00 0 49 -.117626578245E+00 0 50 -.696890859054E+02 0 51 sps ov .139118545649E+02 0 52 .381865888245E+01 0 53 -.136143834902E+02 0 54 pps ov .842365524259E+01 0 55 -.196821172426E+01 0 56 -.608653304529E+00 0 57 ppp ov .248710150793E+00 0 58 -.205151104387E-01 0 59 .175091655281E+00 1 60 sds ov .386388917472E-01 1 61 .715520547503E-02 1 62 -.274192135009E-01 1 63 pds ov -.123165750929E-01 1 64 -.182615562440E-02 1 65 .564350567469E+00 1 66 pdp ov .141050727933E+00 1 67 .304460349316E-01 1 68 .116451760475E+00 1 69 dds ov .744861280305E-01 1 70 .691445130370E-01 1 71 -.164475988822E+01 1 72 ddp ov -.137692214205E+00 1 73 .172522552266E-01 1 74 -.619359277322E+00 1 75 ddd ov .224107487894E+00 1 76 .125402873053E+00 1 77 .131134825347E+01 0 78 sss exp .819672007519E+00 0 79 sps .973962618879E+00 0 80 pps .116187136874E+01 0 81 ppp .107556938178E+01 1 82 sds .982546255171E+00 1 83 pds .112373328862E+01 1 84 pdp .150000000000E+01 1 85 dds .150000000000E+01 1 86 ddp .168811062467E+01 1 87 ddd .997986666439E+00 0 88 sss exp ov .124638907353E+01 0 89 sps .108538212809E+01 0 90 pps .780591344396E+00 0 91 ppp .921452935914E+00 1 92 sds .869558939484E+00 1 93 pds .112272507954E+01 1 94 pdp .102127303819E+01 1 95 dds .103455530122E+01 1 96 ddp .103939497896E+01 1 97 ddd
PARAM Then an initial guess of the tight-parameters follow. In general there will be 97 for a single element and 330 for binary material.

1 4 KINDS, KBAS KINDS=number of kinds of atoms, KBAS=Number of orbitals (s,x,y,z in this case of Ge)

1.6 13.0 0.00 1.6 13. 0.0 0.5 1.5 0.1 RMIN, RMAX, RWGHT RMIN=min distance, RMAX=max distance,RWGHT. This activates penalty functions for controlling the distance dependence of the TB parameters. The first triplet corresponds to the energy matrix H,the second triplet to the overlap matrix S and the third triplet keeps the exponent parameter between RMIN and RMAX. When RWGHT=0 the penalty function is not operating.

0 0 0 0 0 JPRDSQ, JPRNDX, JPRHRI, JPRLMN, JPRNBR Printing parameters for debugging purposes.

0 1 0 0 0 JSREAL, JSOVER, JSHALF, JSWATE, JSW5 The only important parameter is JSOVER. JSOVER=0 orthogonal TB procedure JSOVER=1 non-orthogonal

Structural information for each lattice in the fit follows:
8 NV NV=matrix size (8 for Ge)

2 NATOMS Number of atoms in the unit cell.

0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5
PLV Unscaled Primitive lattice vectors.

10.2 10.2 10.2 SCALE Scale factors (in this case, the lattice parameter.

4 4 4 ND1, ND2, ND3 Param. determining the search for neighbors.

1 0 0 0 0 0 0 KKIND, POSN, POSQ KKIND= index for the atom kind, POSN=Atom coordinates(Cartesian), POSQ=0,0,0

1 0.25 0.25 0.25 0 0 0 Same for second atom.

12.5 DNN Parameter cutoff distance. Making this shorter decreases the number of neighbors used in TB calculations, making the programs faster at the possible expense of accuracy.

8 2 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 10.4 10.4 10.4 4 4 4 1 0 0 0 0 0 0 1 0.25 0.25 0.25 0 0 0 12.5
Repeated for each structure in the fit.

Input	Name of variable	Explanation
Mode=0	MODE	Version 1
16 100 2 0.0001	NSTRUC, MAXIT, IOPT, EPS	Numb of structures or lattice constants,Maximum number of iterations,Strict descent method,Convergence criterion
0.00000 0.2 1.0 1.0	AVGE, SYMWGHT, SYMDIV, SYMMUL	Reference total energy, Weight of symmetrized bands,Reduces weight,Increases weight (Only needed for the symmetrized version)
QLMT=F	LQLMT	F=energy bands formatted as shown below T=energy bands input from separate files.
ge102sk	TITLE	Label for the first set of energy band data that follow (ge for germanium,102 for lattice constant 10.2 Bohr)
1.50 0 8	EMAX, NBLOW, NBANDMAX	When QLMT=F EMAX is not used.When QLMT=T then bands with values larger than EMAX+Fermi level will not be included in the fit,NBLOW is not yet activated but it must be set to zero, NBANDMAX is the maximum number of bands.
JSPINS=1, 0.005 F	JSPINS, TKB, LSTRUC	JSPINS is intended for a spin polarized code, TKB=temperature broadening, F=the data for the lattice parameter that follows are included in the fit, T= not included in the fit.
0d0 0.75367 8.0	SHIFT, EFERMI, ZFILL	SHIFT=0. , EFERMI=Fermi level used only when LQLMT=T, ZFILL=Number of valence electrons.
-0.409103 2 300.0	TRUEE, DIVIDE, WTE	TRUEE=Total energy in Rydberg truncated before the decimal,DIVIDE=Number of atoms in unit cell,WTE=weight for fitting the total energy.
89	NPTS	Number of k-points for the set of energy bands that follows.
0 0 0 1.00000000000000000 8	X, Y, Z, WEIGHT, NBAND	X,Y,Z are the cartesian coordinates of the k-points for QLMT=F and lattice coordinates for QLMT=T, WEIGHT=Weight of k-point, NBAND=Number of energy bands for the particular k-point.
-.62975 .37364 .37364 .37364 .49980 .58281 .58281 .58281	Eigenvalues	These are the eigenvalues for the first k-point. This process repeats until the k-point list is exhausted (in this case, a total of 89 k-points).
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.0	WT	Band weights
0	NSYMKP	0 Indicates that no symmetrized bands will be used
ge104sk 1.50 0 8 JSPINS=1, 0.005 F 0d0 0.75367 8.0 -0.417298 2 300.0 89 0 0 0 1.00000000000000000 8 -.63405 .33282 .33282 .33282 .41898 .54112 .54112 .54112 etc. 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.0 0		Repeat this process for each structure to be fit.
.121129895271E+01 0 1 exp -.197031010828E+00 0 2 s -.147246836815E+01 0 3 s -.404947755887E+02 0 4 s -.221390177434E+03 0 5 s .366830032879E+00 0 6 p -.275983210546E+01 0 7 p -.100953340876E+03 0 8 p .239392944849E+04 0 9 p .122714678806E+01 1 10 t2g .639716703820E+01 1 11 t2g -.266521805137E+02 1 12 t2g .363778209932E+02 1 13 t2g .964883787949E+00 1 14 eg .419370464185E+01 1 15 eg -.353425964684E+02 1 16 eg .404532361580E+03 1 17 eg .105259876640E+04 0 18 sss -.190561649271E+03 0 19 -.251980650278E+02 0 20 .100359282774E+02 0 21 sps -.430821179023E+01 0 22 .326945384960E+00 0 23 -.217820428726E+02 0 24 pps .196274770650E+00 0 25 .113595290864E+01 0 26 -.315567254011E+02 0 27 ppp .858753164946E+01 0 28 -.177547961817E+01 0 29 -.582635424778E+02 1 30 sds .117267249375E+02 1 31 -.123949178334E+01 1 32 .152194272235E+02 1 33 pds -.203199371941E+00 1 34 .438599662935E+00 1 35 -.571676942648E+00 1 36 pdp -.779705456424E+01 1 37 .107617582636E+00 1 38 -.239141569816E+03 1 39 dds .402553355228E+03 1 40 -.141290233843E+03 1 41 -.121269276657E+03 1 42 ddp .340373295876E+02 1 43 .107669411640E+02 1 44 -.417122837381E+05 1 45 ddd .613072520780E+05 1 46 -.207809859115E+05 1 47 .351968575390E+01 0 48 sss ov .327563082867E+00 0 49 -.117626578245E+00 0 50 -.696890859054E+02 0 51 sps ov .139118545649E+02 0 52 .381865888245E+01 0 53 -.136143834902E+02 0 54 pps ov .842365524259E+01 0 55 -.196821172426E+01 0 56 -.608653304529E+00 0 57 ppp ov .248710150793E+00 0 58 -.205151104387E-01 0 59 .175091655281E+00 1 60 sds ov .386388917472E-01 1 61 .715520547503E-02 1 62 -.274192135009E-01 1 63 pds ov -.123165750929E-01 1 64 -.182615562440E-02 1 65 .564350567469E+00 1 66 pdp ov .141050727933E+00 1 67 .304460349316E-01 1 68 .116451760475E+00 1 69 dds ov .744861280305E-01 1 70 .691445130370E-01 1 71 -.164475988822E+01 1 72 ddp ov -.137692214205E+00 1 73 .172522552266E-01 1 74 -.619359277322E+00 1 75 ddd ov .224107487894E+00 1 76 .125402873053E+00 1 77 .131134825347E+01 0 78 sss exp .819672007519E+00 0 79 sps .973962618879E+00 0 80 pps .116187136874E+01 0 81 ppp .107556938178E+01 1 82 sds .982546255171E+00 1 83 pds .112373328862E+01 1 84 pdp .150000000000E+01 1 85 dds .150000000000E+01 1 86 ddp .168811062467E+01 1 87 ddd .997986666439E+00 0 88 sss exp ov .124638907353E+01 0 89 sps .108538212809E+01 0 90 pps .780591344396E+00 0 91 ppp .921452935914E+00 1 92 sds .869558939484E+00 1 93 pds .112272507954E+01 1 94 pdp .102127303819E+01 1 95 dds .103455530122E+01 1 96 ddp .103939497896E+01 1 97 ddd	PARAM	Then an initial guess of the tight-parameters follow. In general there will be 97 for a single element and 330 for binary material.
1 4	KINDS, KBAS	KINDS=number of kinds of atoms, KBAS=Number of orbitals (s,x,y,z in this case of Ge)
1.6 13.0 0.00 1.6 13. 0.0 0.5 1.5 0.1	RMIN, RMAX, RWGHT	RMIN=min distance, RMAX=max distance,RWGHT. This activates penalty functions for controlling the distance dependence of the TB parameters. The first triplet corresponds to the energy matrix H,the second triplet to the overlap matrix S and the third triplet keeps the exponent parameter between RMIN and RMAX. When RWGHT=0 the penalty function is not operating.
0 0 0 0 0	JPRDSQ, JPRNDX, JPRHRI, JPRLMN, JPRNBR	Printing parameters for debugging purposes.
0 1 0 0 0	JSREAL, JSOVER, JSHALF, JSWATE, JSW5	The only important parameter is JSOVER. JSOVER=0 orthogonal TB procedure JSOVER=1 non-orthogonal
		Structural information for each lattice in the fit follows:
8	NV	NV=matrix size (8 for Ge)
2	NATOMS	Number of atoms in the unit cell.
0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5	PLV	Unscaled Primitive lattice vectors.
10.2 10.2 10.2	SCALE	Scale factors (in this case, the lattice parameter.
4 4 4	ND1, ND2, ND3	Param. determining the search for neighbors.
1 0 0 0 0 0 0	KKIND, POSN, POSQ	KKIND= index for the atom kind, POSN=Atom coordinates(Cartesian), POSQ=0,0,0
1 0.25 0.25 0.25 0 0 0		Same for second atom.
12.5	DNN	Parameter cutoff distance. Making this shorter decreases the number of neighbors used in TB calculations, making the programs faster at the possible expense of accuracy.
8 2 0.5 0.5 0.0 0.5 0.0 0.5 0.0 0.5 0.5 10.4 10.4 10.4 4 4 4 1 0 0 0 0 0 0 1 0.25 0.25 0.25 0 0 0 12.5		Repeated for each structure in the fit.