[DFTB-Plus-User] basis set

[Jacek Jakowski]

Hello,

I need to calculate dipole moment integrals in dftb: <a|x|b>, <a|y|b>
and <a|z|b>.
I have a  question about the  underlying basis set used for
parametrization of  DFTB.


We all know that the basis set in DFTB is minimal (and of course not
used explicitly but through parametrization of  2-center integrals)
and only valence electrons are covered. I checked literature, and most
of the DFTB papers just state that there is some  basis set.
Some papers state  that   DFTB uses  Slater basis functions.  There is
some infromation about basis set  in the documentation of the
waveplot.
So I looked into documentation of waveplot and this link gives info
about basis  set
http://www.dftb-plus.info/fileadmin/DFTB-Plus/public/tools/waveplot/wfcs/wfc.mio-0-1.hsd.
This is where I really got confused. I hope you can help me to clarify this.

We can see  in the above  that for wave function file that for example
for  s function of carbon (and also for  p function) we have  we have
4  exponents and
4x3=12 corresponding coefficients. Similarly for hydrogen we have   3
exponents and 3x3 coefficients. For oxygen we have    five exponents
and 5x3=15 corresponding coefficients.
That is for each exponent we have we have   three coefficients  (one
row per exponent).


Here are my detailed questions:

1)   Why do we have  more than one exponent for hydrogen?   This looks
like contracted gaussian  fitted to Slater orbitals.
  The above numbers in the basis set description  do not seem  to be
a Slater type basis set, but rather STO-nG type basis set.
 Am I correct?  Is it really Slater basis set  or STO-nG basis set
used to parametrize  DFTB integrals?

2) If the  DFTB  basis set is  indeed STO-nG then:
      (a) what is the value of n? Is it n=3 (in that case we would
have STO-3G). But if n=3 then why do we have  4 exponents  for carbon
s and p functions.
          Is it STO-3G for hydrogen and STO-4G for carbon ????
      (b) why there are always three coefficients per each  exponent?
One could combination coefficient but what are the remaining two
coefficients.

3) Can anyone explain this the basis set format to  me?
I would like to use this basis set  (or any other info) to write a
small program that can  calculate matrix of   dipole moment integrals.
Is there any small program already existing that calculate such  matrix?

I would be very grateful for any suggestion from you that would help
to figure out how to calculate dipole  moment integrals.
This is very important for my research.


With best regards,

Jacek