[gpaw-users] problem with LCAO coefficients - probably in spherical harmonics

[Ask Hjorth Larsen]

Dear Ondřej

2017-02-16 23:46 GMT+01:00 Ondřej Krejčí via gpaw-users
<gpaw-users at listserv.fysik.dtu.dk>:
> Dear GPAW developers!
>
> I'm trying to calculate a STM current by means of the Chen rules and
> wave-functions restored from LCAO coefficients (and some empirical
> exponential as an radial function).  This works pretty well when the Pi
> orbital of molecules (pz orbitals of C, N etc.) is dominating in the
> current, however when I try to implement d-orbitals (for some metal organic
> molecules), I get some really asymmetric signal, even though the
> wavefunction of the eigen-state looks absolutely symmetric in the cube file.
> I looked into the files with radial functions and all the valence radial
> functions seems to be positive (especially in the far distance), therefore
> it is in agreement with my STM code.
> Thus, I'm thinking that there is some different sign convention in the
> spherical harmonics for the GPAW basis set. For me: p_y = Np*y/r,
> p_z=Np*z/r,  p_x = Np*y/r, Nd*(x*y)/r^2 ... where N are just normalization
> constants > 0. Am I right, or the mistake is somewhere else? For other LCAO
> codes (Fireball, FHI-AIMS) I'm getting proper and symmetrical current maps.
>
> If somebody would like to see the way I'm obtaining the LCAO coefficients, I
> put it here:
>
> n_max_ ... last eigen-state in the calculations
> n_min_ ... first eigen-state in the calculations
> num_at_ ... number of atoms in the calcultions
> Ynum = 4 for 'sp' orbs, 9 for 'spd' orbs (only valence)
>

(mail software botches whitespace so script omitted)

>
> This procedure sometimes gives me a crazy wavefunction, if Hydorgens are not
> the last  atoms of the molecule, it seems that - h += calc.wfs.setups[j].nao
> - is sometimes shifted by one, but this can be easily overcome.

What does it mean that "h += calc.wfs.setups[j].nao" is sometimes
shifted by one?

Excerpt from gpaw/c/sharmonic.py (which generates C code for spherical
harmonics) below:

The first few harmonics are listed below::
 +----+---------------------+-__---------------------------------------+
 |  L | l |  m | r^l * Y    | \/ (r^l * Y)                             |
 +----+---s----+------------+------------------------------------------+
 |  0 | 0 |  0 | 1          | (0, 0, 0)                                |
 +----+---p----+------------+------------------------------------------+
 |  1 | 1 | -1 | y          | (0, 1, 0)                                |
 |  2 | 1 |  0 | z          | (0, 0, 1)                                |
 |  3 | 1 |  1 | x          | (1, 0, 0)                                |
 +----+---d----+------------+------------------------------------------+
 |  4 | 2 | -2 | xy         | ( y,  x,  0)                             |
 |  5 | 2 | -1 | yz         | ( 0,  z,  y)                             |
 |  6 | 2 |  0 | 3z^2-r^2   | (-x, -y, 2z)                             |
 |  7 | 2 |  1 | xz         | ( z,  0,  x)                             |
 |  8 | 2 |  2 | x^2-y^2    | ( x, -y,  0)                             |
 +----+---f----+------------+------------------------------------------+
 |  9 | 3 | -3 | 3x^2y-y^3  | (          2xy,       x^2-y^2,        0) |
 | 10 | 3 | -2 | xyz        | (           yz,            xz,       xy) |
 | 11 | 3 | -1 | 5yz^2-yr^2 | (         -2xy, 4z^2-x^2-3y^2,      8yz) |
 | 12 | 3 |  0 | 5z^3-3zr^2 | (         -2xz,          -2yz, 3z^2-r^2) |
 | 13 | 3 |  1 | 5xz^2-xr^2 | (4z^2-3x^2-y^2,          -2xy,      8xz) |
 | 14 | 3 |  2 | x^2z-y^2z  | (          2xz,          -2yz,  x^2-y^2) |
 | 15 | 3 |  3 | x^3-3xy^2  | (      x^2-y^2,          -2xy,        0) |
 +----+--------+----------+--------------------------------------------+


Best regards
Ask

>
> Thank you for any help and suggestions!
> All the best,
> Ondrej Krejci
>
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