17,500 Years In The Making – A Small Contribution To The 3rd Edition Of “Star Maps: History, Artistry, and Cartography”

Above: One of my all-time favorite images – a mural within the Lascaux Caves, possibly depicting three (now) prominent asterisms in the nighttime skies of winter.

I had been forwarded along a link from the now-defunct spacetoday.org site back in ’08 or ’09 about a possibly astronomical origin to one particular wall painting within the Lascaux Caves in southwestern France. Someone, either in an expedition or with photos from the documentation, must have had some amateur astronomy background (because most professional astronomers only enter caves when they’re obtaining data) and noticed that the groupings of stars on either side of one connect-the-dots now-extinct auroch (note the timing here – the bull is, astronomically-speaking, a later invention) had the right placement – and nearly the right counts – to maybe, kinda, sorta, possibly be as if someone had drawn the Orion Belt stars (and their collective +1) and a 25x zoom of our second-closest open cluster – the Pleiades (M45) – on either side of a cluster of black dots on an auroch’s head that could represent our closest open cluster – the Hyades.

This type of ancient astronomy history sticks *hard* in my brain, leading to the usual scouring of information online for other reports, images, refutations, etc. This then lead to my including the story way back in a November, 2009 constellation-of-the-month article for the SAS’s Astronomical Chronicle and, with clarifying image, in the December 2016 article of the short-lived Upstate New York Stargazing series.

For someone wanting the unmodified image from the mural, there remains a high-res download available from baerchen3.wp.com.

It should come as no surprise that our ancestors would want to take the most mystical part of their day – the night – inside with them. There is no shortage of civilizations combining small clusters of stars in the sky with fantastical stories (see: the Northern Constellations), and seeing patterns in otherwise random visuals has probably been a solid feature in our brains far longer than any crafted image we’re likely to find buried in any ancient community (see: Pareidolia).

Above: A screencap of the relevant image and associated star chart from “Star Maps: History, Artistry, and Cartography.” Click for a larger view.

If, in fact, this mural was intended to represent the arrangement of what we know as Orion’s Belt, what we know as Taurus the Bull, and what we now call the Pleiades, it raises a host of questions. Is there somehow a direct, herd-migratory line from this cave painting to the walls of Babylon and into early western mythology? Was there a single painter? Was the head or were the stars painted first? If more than one person did it, same question – did someone add the stars to a head, or add the head to the stars? If we looked hard enough on either side of the current belt in the nighttime sky, would we see remnants of a far distant supernova in the background that might have appeared to the cave dwellers as a new, bright fourth star? Alternatively, how much trouble did Ukleois (remember, he’s French) get into by adding the fourth star to the Belt? Did the painter, intending to remove the fourth star after admonishing Ukle-çois for his vandalism, die in a violent way during the morning hunt for breakfast, leaving the fourth star there for all time? Is the right-most or the left-most fourth star the wrong one? Did anyone take fingerprints of these two stars to see which was different from the middle two to know which was the unwanted addition? Was the painting a deep thought of artistic expression by Jean-Ukle that should be deeply read into as a marker of Paleolithic human endeavor, or was it a particularly miserable rainy Tuesday night and Jean-Ukle was simply lamenting not being able to enjoy a bucolic moonlight stroll by spending the evening instead scribbling on a flat piece of cave while getting mildly blotto from the carbon monoxide?

We may never have the answers to these questions.

In the meantime, I have ended up contributing to the astronomical literature in the tiniest of ways to this earliest of anti-memes (because it did not come to you – you had to go to it) in the newly printed 3rd Edition of Nick Kanas’ excellent (e)book “Star Maps: History, Artistry, and Cartography,“ available at amazon and wherever fine Springer Praxis books are sold.

He’s a fellow amateur astronomer, so I liked him already. Additionally (from the amazon bio)…

Dr. Nick Kanas is an Emeritus Professor of Psychiatry at the University of California, San Francisco, where he directed the group therapy training program and wrote a book entitled Group Therapy for Schizophrenic Patients. For over 20 years, he conducted research in group therapy, and for over 15 years after that he was the Principal Investigator of NASA-funded psychological research on astronauts and cosmonauts. In 1999, Dr. Kanas received the Aerospace Medical Association Raymond F. Longacre Award for Outstanding Accomplishment in the Psychological and Psychiatric Aspects of Aerospace Medicine. In 2008, he received the International Academy of Astronautics Life Science Award. He has over 230 scientific publications.

Dr. Kanas is the coauthor of Space Psychology and Psychiatry (now in its 2nd edition), which won the 2004 International Academy of Astronautics Life Science Book Award. In 2015, he authored Humans in Space: The Psychological Hurdles, which won the 2016 International Academy of Astronautics Life Science Book Award. 

Dr. Kanas has been an amateur astronomer for over 50 years. He has collected antiquarian celestial maps for over 30 years and has given talks on the history of celestial cartography to amateur and professional groups.  He is the author of Star Maps: History, Artistry, and Cartography (now in its 2nd edition), and Solar System Maps: From Antiquity to the Space Age. An avid science fiction reader, Dr. Kanas has given talks and participated on panels at numerous World Science Fiction Conventions. He has published articles for Analog Science Fiction and Fact magazine and won the Analog AnLab 2015 readers’ poll award for Best Fact Article of the year. He has published three science fiction novels for the Springer Science and Fiction series: The New Martians, The Protos Mandate, and The Caloris Network. Except for his group therapy book, all of his books are published by Springer.

Check his website (nickkanas.com), follow him on twitter (@nick_kanas), give a listen to an interview on The Space Show (and subscribe and support it, as it is excellent), and go buy a copy of the book.

Free Astronomy Magazine – September-October 2019 Issue Available For Reading And Download

Above: Yup, Leo might be on to something. A Leonid Kulik photo of a small snippet of the Tunguska aftermath.

The most recent issue of Free Astronomy Magazine (September-October 2019) is available for your reading and downloading pleasure at www.astropublishing.com (click the link to go directly to the issue).

With an excellent two-part feature (1 and 2) celebrating the 50th anniversary of the Apollo 11 Moon Landing now in publication history, FAM returns to its regularly-scheduled programming of excellent original content and selected reports from the planet’s leading astronomy and space science institutions.

The science highlight for me this month is the article “The early days of the Milky Way revealed by Gaia,” for which those with access can read the journal article at “Uncovering the birth of the Milky Way through accurate stellar ages with Gaia.”

For those wanting a quick look at what the issue has to offer, the Table of Contents is reproduced below.

September-October 2019

The web browser-readable version of the issue can be found here:

September-October 2019 – www.astropublishing.com/5FAM2019/

Jump right to the PDF download (20 MB): September-October 2019

A Quick Guide To Running DFTB (With Available Parameters) In GAMESS-US

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
3.8,3.8,3.8,3.8,2.50 $end
$dftb hubder(1)=-0.1857,-0.1492 $end
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

C 6.0 -2.775607 0.000000 0.000000
H 1.0 -2.809590 0.000420 50.594100

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:


         SPECIES 1 :  H       WITH S     ORBITAL
         SPECIES 2 :  C       WITH S+P   ORBITALS
  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


  H       :     -0.14920 (USER DEFINED)
  C       :     -0.18570 (USER DEFINED)
      USE X-H DAMPING:  4.00000




 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


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
C   6.0        -2.775607   0.000000    0.000000
H   1.0        -2.809590   0.000420    50.594100
 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"


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 
 $dftb hubder(1)=-0.1857,-0.1492 $end
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"

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

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
       = 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+
       = 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

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
         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

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

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.