This post comes out of my great appreciation for just how well Yoshio Nishimoto’s DFTB (density functional-based tight binding method) implementation in GAMESS-US runs, both as an additional functionality in an already considerable program and in comparison to a few other programs I’ve worked with to do the same.

Also, the use of unmodified Slater-Koster files in the GAMESS-US implementation is a nice touch.

This all begins at the dftb.org website with the downloading of available Slater-Koster parameter files for available sets of elements. Note that your favorite elements might not yet have parameters – or parameters within any given parameter set – for immediate use. Until others publish new parameter sets and post them somewhere – and if you’re an academic – you might consider giving Stefan Grimme’s XTB serious consideration.

Additionally! A recent find while looking for new parameter sets was the KIST Integrated Force Field Platform (kiff.vfab.org), providing the complete set of DFTB parameters and up-to-date ReaxFF parameters as well.

Basic Input Format

A few key points (highlighted in the generic pointer input file) below:

! $scf soscf=.t. fdiff=.f. shift=.f. extrap=.f. damp=.t. diis=.f. $end
 $system modio=31 $end
 $basis gbasis=dftb $end
! $dftb ndftb=2 dampxh=.t. dampex=4.0 itypmx=0 etemp=300 $end
 $dftb ndftb=3 dampxh=.t. dampex=4.0 disp=skhp etemp=300 
disppr(1)=0.31,0.386,0.386,0.000,0.000,0.000,0.000,3.5,3.5,3.5,
3.5,3.5,3.5,0.80,0.69,1.382,1.382,1.382,1.064,1.064,1.064,3.8,3.8,
3.8,3.8,3.8,3.8,2.50 $end
 $dftb hubder(1)=-0.1857,-0.1492 $end
 $dftbsk
C C "/path/to/skfiles/3ob-3-1/C-C.skf"
C Si "/path/to/skfiles/3ob-3-1/C-Si.skf"
C H "/path/to/skfiles/3ob-3-1/C-H.skf"
Si C "/path/to/skfiles/3ob-3-1/Si-C.skf"
Si Si "/path/to/skfiles/3ob-3-1/Si-Si.skf"
Si H "/path/to/skfiles/3ob-3-1/Si-H.skf"
H C "/path/to/skfiles/3ob-3-1/H-C.skf"
H Si "/path/to/skfiles/3ob-3-1/H-Si.skf"
H H "/path/to/skfiles/3ob-3-1/H-H.skf"
 $end $data

C1
C   6.0        -2.775607   0.000000    0.000000
...
H   1.0        -2.809590   0.000420    50.594100
 $end

1. There have been many improvements to the DFTB code. The myweb.liu.edu/~nmatsuna/gamess manual (among others hosted *not* on the official GAMESS-US website) is among the first that *always* come up when searching out GAMESS-US keywords – and it’s several years out of date (esp. for DFTB keywords). The 2019.1 manual has a significantly expanded $DFTB section, including calls for including dispersion corrections from the original $DFT block.

2. No $SCF – as the manual states, converger specifications are pre-defined in the ITYPMX keyword, with additional keywords in the $DFTB block (esp. ETEMP) available to aid in problematic convergence.

3. One big $DFTBSK – as addressed on Jan Jensen’s initial post about running DFTB in GAMESS-US, GAMESS-US will only read atom pairs needed for the atoms listed in the $DATA section. You are fine to simply make an all-encompassing $DFTBSK block for all pairs in a parameter folder and write that to the input file.

4. DISPPR for SKHP – a mild manual issue. For the “Slater–Kirkwood + bond number polarizability dependence” dispersion correction, the current manual states that “For DISP=SKHP, a set for a species has 14 parameters. The first six are the polarizabilities depending on the number of bonds, and the next six are cutoff length, and the last is atomic charge.” You’ll note that 6 + 6 + 1 adds up to 13. The 14 numbers needed for each element in this keyword begins with the covalent atomic radius for the element. In the absence of a list for those values, Table S1.1 (freely available) from “DFTB Parameters for the Periodic Table: Part 1, Electronic Structure” is an excellent resource. I did not bother to address the “different covalent radii values for different hybridizations” issue and have seen little on the topic related to DFTB calculations. For the other 13 numbers, the DFTB+ manual contains a set in Appendix E and reproduced below, with notes to consider other publications for more and different versions of the same elements (and note the NOTES column in the Appendix E table for P and S). Local copy of the manual – 2019Aug24_DFTBplus_manual.pdf

Element Polarisability (6 #'s) ---- [Å3]Cutoff (6 #'s) -- [Å]Chrg

O 0.560 0.560 0.000 0.000 0.000 0.0003.8 3.8 3.8 3.8 3.8 3.8 3.15
N 1.030 1.030 1.090 1.090 1.090 1.0903.8 3.8 3.8 3.8 3.8 3.8 2.82
C 1.382 1.382 1.382 1.064 1.064 1.0643.8 3.8 3.8 3.8 3.8 3.8 2.50
H 0.386 0.386 0.000 0.000 0.000 0.0003.5 3.5 3.5 3.5 3.5 3.5 0.80
P 1.600 1.600 1.600 1.600 1.600 1.6004.7 4.7 4.7 4.7 4.7 4.7 4.50
S 3.000 3.000 3.000 3.000 3.000 3.0004.7 4.7 4.7 4.7 4.7 4.7 4.80

5. HUBDER – If you don’t specify Hubbard Derivatives in your input file, GAMESS-US will include them from internal values. Values appear to be the set from the 3ob-3-1 parameter set and are available in the set’s README file (reproduced from that file below for available elements).

List of all atomic Hubbard derivatives (atomic units):

Br = -0.0573
 C = -0.1492
Ca = -0.0340
Cl = -0.0697
 F = -0.1623
 H = -0.1857
 I = -0.0433
 K = -0.0339
Mg = -0.02
 N = -0.1535
Na = -0.0454
 O = -0.1575
 P = -0.14
 S = -0.11
Zn = -0.03

6. HUBDER order – the order for these numbers is as per the FIRST appearance of the element in the $DATA block. This is ieasy to see if you don’t specity the HUBDER values in the input file and simply let GAMESS-US write out the “HUBBARD DERIVATIVES” block in your DFTB3 run.

7. $DFT Dispersion – according to the manual, you can now use more the traditional dispersion corrections in $DFTB calculations. In the $DFTB block, use DISP=DFT, then modify your $DFT section as you otherwise would – and include DC=.T. in your $DFT block.

8. DFTB Block Summary in the output file – below for a DFTB3 run of a CH-containing molecule using the 3ob-3-1 SK parameters:

 **********************************************************
 **  DENSITY-FUNCTIONAL TIGHT-BINDING (DFTB) CALCULATION **
 **********************************************************
       WRITTEN BY YOSHIO NISHIMOTO (NAGOYA UNIVERSITY)

  NUMBER OF SPECIES:  2
         SPECIES 1 :  H       WITH S     ORBITAL
         SPECIES 2 :  C       WITH S+P   ORBITALS
 
      $DFTB OPTIONS
      -------------
  NDFTB  =       3     SCC    =       T     DFTB3  =       T
  SRSCC  =       F     DAMPXH =       T     DAMPEX =    4.00
  DISP   =NONE         ITYPMX =       0     ETEMP  =    0.00
  MODESD =       0     MODGAM =       8     PRTORB =       F

 --- SCC CALCULATION ---
      INCLUDE 3RD ORDER CORRECTION

 SETTING HUBBARD DERIVATIVES FOR DFTB3
  H       :     -0.14920 (USER DEFINED)
  C       :     -0.18570 (USER DEFINED)
      USE X-H DAMPING:  4.00000

 BROYDEN'S CHARGE MIXING

 4 SLATER-KOSTER FILES WILL BE READ

 START READING SLATER-KOSTER FILES

 1  1 (H        - H       ) = /home/ec2-user/3ob-3-1/H-H.skf
 1  2 (H        - C       ) = /home/ec2-user/3ob-3-1/H-C.skf
 2  1 (C        - H       ) = /home/ec2-user/3ob-3-1/C-H.skf
 2  2 (C        - C       ) = /home/ec2-user/3ob-3-1/C-C.skf

DFTB2

Starting with the less keyword-involved run, below is a completely generic DFTB2 input file with no funny business in the $DFTB block to aid in convergence (my first test would be to change ETEMP to something higher, which has often done the trick when a run won’t complete its first SCF cycle in 200 steps).

 $contrl runtyp=optimize icharg=0 maxit=200 $end
 $system mwords=100 $end
 $system modio=31 $end
 $basis gbasis=dftb $end
 $dftb ndftb=2 dampxh=.t. dampex=4.0 itypmx=0 etemp=0 $end
 $data
C1
C   6.0        -2.775607   0.000000    0.000000
…
H   1.0        -2.809590   0.000420    50.594100
 $end
  $dftbsk
 C C "/path/to/dftb/params/pbc-0-3/C-C.skf"
 C H "/path/to/dftb/params/pbc-0-3/C-H.skf"
 H C "/path/to/dftb/params/pbc-0-3/H-C.skf"
 H H "/path/to/dftb/params/pbc-0-3/H-H.skf"
  $end

DFTB3

A more involved DFTB3 input file, including (1) the SKHP dispersion-correction and carriage returns to show that all 14 numbers are there – in order of appearance – for the atoms in $DATA, (2) the $SCF block as a comment that is ignored by DFTB calculations, (3) a reordering of all keywords above the $DATA block (because why not?), (4) the HUBDER values in order of appearance in the $DATA block, and (5) the Si-containing pairs in the $DFTBSK block just to show that their presence isn’t an issue for the run.

! $scf soscf=.t. fdiff=.f. shift=.f. extrap=.f. damp=.t. diis=.f. $end
 $system modio=31 $end
 $basis gbasis=dftb $end
 $dftb ndftb=3 dampxh=.t. dampex=4.0 disp=skhp etemp=300 
disppr(1)=
0.31,0.386,0.386,0.000,0.000,0.000,0.000,3.5,3.5,3.5,3.5,3.5,3.5,0.80,
0.69,1.382,1.382,1.382,1.064,1.064,1.064,3.8,3.8,3.8,3.8,3.8,3.8,2.50
$end
 $dftb hubder(1)=-0.1857,-0.1492 $end
 $dftbsk
C C "/path/to/skfiles/3ob-3-1/C-C.skf"
C Si "/path/to/skfiles/3ob-3-1/C-Si.skf"
C H "/path/to/skfiles/3ob-3-1/C-H.skf"
Si C "/path/to/skfiles/3ob-3-1/Si-C.skf"
Si Si "/path/to/skfiles/3ob-3-1/Si-Si.skf"
Si H "/path/to/skfiles/3ob-3-1/Si-H.skf"
H C "/path/to/skfiles/3ob-3-1/H-C.skf"
H Si "/path/to/skfiles/3ob-3-1/H-Si.skf"
H H "/path/to/skfiles/3ob-3-1/H-H.skf"
 $end 
 $data

C1
H   1.0        -2.775607   0.000000    0.000000
C   6.0        -3.775607   0.000000    0.000000
....
H   1.0        -2.809590   0.000420    50.594100
 $end

And, just to keep you from bouncing between tabs, the $DFTB section from the 2019.1 version of the manual (obviously check there at some point for changes and improvements).

$DFTB group                  (relevant for GBASIS=DFTB)

Density-functional tight-binding (DFTB) is turned on by
selecting GBASIS=DFTB in $BASIS.  $DFTB controls optional
parameters for a DFTB calculation.  DFTB is formulated in a
two-center approximation utilizing implicitly a minimal
pseudoatomic orbital basis set with corresponding,
pretabulated one- and two-center integrals.   Because of
this, many properties (for instances, multipoles higher
than dipoles) and many options are ignored or not available
in the current implementations of DFTB.  DFTB also uses an
independent SCF driver (SCF in DFTB is also called SCC, see
below), so most SCF options are not available for DFTB.

Only SCFTYP=RHF and UHF are implemented. SCFTYP=ROHF is
available, only when all SPNCST values are zero. DFTB does
not explicitly use symmetry (C1 throughout) since integrals
are never computed during the calculations.  Slater-Koster
tables are only defined for spherical functions (5d) so
DFTB sets ISPHER=1.  Most $GUESS options do not work for
DFTB (DFTB does not use initial orbitals in the usual
sense).  Other than the default (METHOD=HUCKEL, which is
ignored), only METHOD=MOREAD works (note that SCC-DFTB can
use initial charges on atoms, derived from the orbitals).

RUNTYP=OPTIMIZE, HESSIAN and RAMAN are available for full
(non-FMO) DFTB and FMO-DFTB. Excited state calculations for
full DFTB may be performed through the standard (linear-
response) time-dependent formalism (only closed shell). PCM
can be used for both ground and excited state calculations,
and energy and gradient can be evaluated.

In DFTB calculation, the atom type is determined by its
name, not its nuclear charge as elsewhere in GAMESS. The
nuclear charge (the second column in $DATA) is used only in
population analysis, but not in SCF.  DFTB uses a notion of
"species", which means an atomic type.  The species are
numbered according to the order in which atoms appear in
$DATA. For instances, in water there are two species, O and
H.  An atomic type of each species needs MAXANG, which for
most but not all atoms is set automatically.


NDFTB  order of the Taylor expansion of the total energy
       around a reference density in the DFTB model.
       = 1 NCC-DFTB, also called DFTB1.
           NCC stands for non-charge-consistent, i.e., no
           explicity charge-charge interaction term is
           included in the energy calculation.
       = 2 SCC-DFTB, also called DFTB2.
           SCC means a self-charge-consistent approach,
           and SCC implies that SCF iterations are carried
           out that converge monopolar charges towards
           self-consistency.
       = 3 DFTB3, including 3rd order correction using
           Hubbard derivatives (HUBDER).
           In order to reproduce the published DFTB3
           approach, it is necessary to also specify
           DAMPXH=.TRUE. to add other terms.
           Gaus, M. et al. J. Chem. Theory Comput. 2011,
           7, 931-948 is referred to as Gaus2011 below.
           Default: 2.

DAMPXH =  a flag to include the damping function for X-H
          atomic pair in DFTB3. See also DAMPEX, and eq 21
          in Gaus2011.
          The damping function is used when at least one
          atom in a pair is "H". "HYDROGEN" and any other
          name will turn off the damping.
          Default: .FALSE.

DAMPEX =  an exponent used in the damping function for X-H
          atomic pairs.  The default value is 4.0 (taken
          from the 3OB parameter set).

SRSCC  =  a flag to perform shell-resolved SCC calculation.
          If set to .FALSE., the code uses the Hubbard
          value for an s orbital for p and d orbitals,
          ignoring their Hubbard values defined in Slater-
          Koster tables.
          Using .TRUE. enables the use of proper Hubbard
          values for p and d orbitals, implemented only
          for DFTB1 and DFTB2.
          Default: .FALSE.

ITYPMX    Convergence method of SCC calculations.
       = -1 Use standard GAMESS convergence methods.
            SOSCF and DIIS are supported, but DEM is not.
       = 0  Broyden's method.
            Interpolation is applied for atomic
            (or shell-resolved when SRSCC=.TRUE.)
            charges, but not Hamiltonian matrix.
       = 1  (reserved)
       = 2  DIIS for charges.
            Default: 0.

ETEMP  = electronic temperature in Kelvin. Non-zero values
         of ETEMP help SCF convergence of nearly-degenerate
         systems by smearing occupation numbers around the
         Fermi-level. Only the Fermi-Dirac distribution
         function is available as a smearing function.  The
         default value is 0 Kelvin, meaning the smearing
         function is not used.
         ETEMP is implemented only for SCFTYP=RHF and when
         FMO is not used.

DISP     dispersion model for DFTB.
       = NONE no Dispersion correction.
       = UFF  UFF-type dispersion correction.
              Parameters for atomic numbers up to 54 are
              available internally or can be supplied in
              DISPPR for any atom.
              Built-in parameters are taken from Rappe
              et al. J. Am. Chem. Soc. 1992, 114, 10024.
       = SK   The Slater-Kirkwood type dispersion
              correction omitting the change polarizability
              depending on the number of bonds.
              No default values of DISPPR are available.
              Some are listed in the manual of the DFTB+
              program.
       = SKHP The Slater--Kirkwood type dispersion with
              the dependence of polarizabilities on the
              number of bonds.
       = DFT  Use so-called DFT-D. See $DFT for further
              details. DISP=GRIMME is a synonym.

DISPPR   an array of parameters used for dispersion
         correction, listed in sets for each species.
         For DISP=UFF, DISPPR(1) and DISPPR(2) define the
         non-bonded distance (Angs.) and energy (kcal/mol)
         for the first species, respectively, and so on.
         For DISP=SK, a set for a species has 3 parameters,
         the polarizability (Angstrom^3), cutoff length
         (Angstrom), and atomic charge.
         For DISP=SKHP, a set for a species has 14
         parameters. The first six are the polarizabilities
         depending on the number of bonds, and the next six
         are cutoff length, and the last is atomic charge.
         Default: see DISP.

HUBDER   an array of Hubbard derivatives for each species
         (1 per species) used only for DFTB3 calculations.
         Default values are set for the elements included
         in the 3OB parameters (Br, C, Ca, Cl, F, H, I,
         K, Mg, N, Na, O, P, S, Zn).

MAXANG   array of maximum angular momentum of each species,
         which determines the number of basis functions.
         DFTB uses only valence orbitals and electrons!
         Most elements have proper default values, but for
         some atomic types (i.e., species) you need to
         manually define the values.

QREF     array of the number of reference electrons of each
         species.  QREF is usually automatically taken from
         Slater-Koster parameters, so this option is seldom
         used.

SPNCST   an array of spin constants used in unrestricted
         (UHF) DFTB calculation. Provide 6 spin constants,
         W_{ss}, W_{sp}, W_{pp}, W_{sd}, W_{pd}, & W_{dd},
         for each species in a continuous array. Constants
         for some elements can be found in the manual of
         the DFTB+ program.

PARAM    specifies the directory from which DFTB parameters
         are taken. If you wish to mix parameters from
         different directories, this option cannot be used.
         Specifying PARAM means no $DFTBSK; otherwise,
         $DFTBSK is read.
         Nota bene-bene: the actual path for parameters includes
         $DFTBPAR, defined in rungms. All directory names
         used in PARAM should be ** UPPER CASE **, as 3OB-3-1 in
         ~/gamess/dftb/param/3OB-3-1 where
         $DFTBPAR=~/gamess/auxdata/DFTB
         PARAM=3OB-3-1
         The length of PARAM is maximum 8 characters!
         Each parameter file name has a limit of 150 characters.
         GAMESS includes 3OB-3-1 and MATSCI03 (properly called
         matsci-0-3), which you may specify in PARAM.
         3ob-3-1 should be used with DFTB3 (biochemistry+water).
         matsci-0-3 should be used with DFTB2 (iorganics).
         You can find more parameter sets at dftb.org.
         Before using DFTB parameters, ~/gamess/dftb/README.dftb
         should be consulted regarding lisense and citations.
         Default: "", meaning that $DFTBSK is read.

ISPDMP   An array of integer specifying species X to which
         the X--H damping function (DAMPXH) is applied. By
         default, with DAMPXH=.TRUE., ISPDMP for all
         elements is 1 (apply). Setting 1 for H does not
         do anything.

                        * * *


The following options are FMO-DFTB specific (Nishimoto, Y.
et al. J. Chem. Theory Comput. 2014, 10, 4801-4812.).

FMO-DFTB has many limitations and some FMO options are not
supported (for instance, multilayer FMO etc).  Only single
layer, restricted closed-shell FMO2/3-DFTB1/2/3
are implemented at present. SRSCC, ETEMP etc are not
available. The analytic gradient is available for FMO-DFTB,
requiring solving SCZV as in other FMO methods.

MODESD = controls the behavior of ES-DIM (electrostatic
         dimer) approximation (bit additive).
         1 Calculate interfragment repulsive energy for ES
           dimers (almost never used).
         2 Add up all ES-DIM energies. This means that
           individual ES dimer energies are not calculated,
           but only their total lump sum, computed with the
           dynamic load balancing.
         4 Lump ES-DIM routine with static load balancing.
           The bits of 2 or 4 are mutually exclusive.
           Default: 0 (i.e., individual ES dimer energies).

MODGAM = controls the calculation of gamma values
         (interatomic 1/R-like function) in FMO-DFTB2 and
         FMO-DFTB3 (bit additive).
         0 Calculate gamma values on the fly.
         1 Calculate once and prestore gamma values in
           triangular matrix.
         2 Calculate once and prestore gamma values in
           square matrix.
         4 With the bits of 1 or 2, the calculation of
           gamma values is parallelized with GDDI.
           The bits of 1 or 2 are mutually exclusive. These
           options are faster but takes more memory.
         8 Using this option omits computing ESP in dimer
           and trimer calculations by accumulating
           contributions of each fragment and subtracting
           double-counting contributions.
           Default: 8

                        * * *


The following options are relevant to second- and
third-order derivative calculations (RUNTYP=HESSIAN and
RAMAN).

CPCONV = Convergence criterion during coupled-pertrubed DFTB
         iterations, similar to CONV in $SCF. In DFTB,
         the program uses Mulliken charges for testing the
         convergence, but not density matrix itself.
         By default, CPCONV=1.0D-06.

MXCPIT = Maximum number of coupled-perturbed DFTB iterations.
         By default, MXCPIT=50.

DEGTHR = An array of two degeneracy thresholds. If the
         difference of two eigenvalues are less than the
         threshold, two orbitals are seen as degenerated.
         The first threshold is employed in solving
         coupled-perturbed equations, while the second
         threshold is in computing third-order derivatives
         analytically. By default, these are set to 1.0D-12
         and 1.0D-08, whieh are usually reasonable.

ARAMAN = A flag to compute third-order derivatives (static
         hyperpolarizability and polarizability derivative)
         analytically, in addition to Hessian. If this
         option is activated, users do not have to give
         $HESSIAN and $DIPDR in the input, and
         non-resonance Raman spectra can be simulated by
         a single run. This option requires that RUNTYP must
         be RAMAN. By default, ARAMAN=.FALSE.

                        * * *


The following optinos are relevant to long-ranged corrected
DFTB. The formulation is based on Lutsker, V. et al. 2015,
143, 184107. With LC-DFTB, using ITYPMX=-1 options is highly
recommended.

LCDFTB = A flag to activate long-range correctios

EMU    = A parameter for long-range corrections. The meaning
         is very similar to MU in $DFT. By default, EMU=0.0,
         and this corresponds to regular DFTB.

ICUT   = A parameter applied in the screening using the
         Schwarz inequiality. The meaning is similar to ICUT
         in $CONTRL. By default, the screening is not
         employed, but this is usually as fast as ICUT=9,
         depending on the performance of the math library.