Dear all,

Valentina Vetere wrote:

>I have really problems in understanding the 2-component wavefunction you use in
>the code. Sorry if I'm writing you several question about the same subject, but
>for me thinks are not enougth clear for the moment.
>For the scalar calculations..no problem, everythinks is very clear, also in the
>documentation. For the 2 component..(I have also read all the V. lenthe thesis ,
>and many books chapters on the subject) I understand nothing for the moment.
>The documentation gives almost no description of such wavefunction. I mean we go
>from real wavefunction to SO ones that have imaginary part. But there is no
>explication how to deal with.
>The atomic case is easy.Several books of phisic derive with spherical harmonics
>and CG coefficency the solution of atomic states.
>But here we use slater function and molecular orbitals and I found no examples
>for this. What I thougth is that you compute CG coefficency for the atomic case
>After you use such starting linear combination of elementary basis fuction mixed
>by SO true the CG coefficency to write the MO. Is it the way?In the famous T21
>file and also the T14 we should have all the
>information to restart a calculation..so the wavefunction should be there.
>But when I make it ascii, it is more complex than reading directly the binary!
>(sorry for the joke, but is really complex). I mean take the Pmat, the density
>matrix. Is a matrix..no? Imagine I obtained one of 171 numbers divited in 3
>column. is it a 57*3 matrix? It seems strange to me(is it a projection on the x,
>y, z axis?)..or is only a problem of space and so we have to to read line after
>line? Also in the user documentation there is no
>explication about the SO in the t21.
>
>It will be possible to have an example, where starting from a file, t21, t14, or
>the output..you write the wavefunction with all coefficency for slater function,
>cg coefiicency, fit etc..
>I do not know like HD molecule, the
>smallest basis set and to see total wavefunction..with or without SFO, I do not
>mind. ?
>

With adf2004.01 it is possible to see in the output the spinors in terms
of the
scalar relativistic orbitals.

In the examples directory there is an example
$ADFBIN/examples/e_TlH_SO_ananlysis.
See also the Examples document in our Documentation
http://www.scm.com/Doc/Doc2004.01
at the moment the TlH_SO_annalysis example is at
http://www.scm.com/Doc/Doc2004.01/Examples/page23.html
Written there is:

In order to get the spin-orbit coupled
population analysis, one should have one scalar relativistic fragment,
which is the whole molecule.
The SFOs in this case are the scalar relativistic orbitals,
which are already orthonormal, because one has only one fragment which
is the whole molecule.

The output gives something like:

 =======================
 Double group symmetry : *** J1/2 ***
 =======================

                                       === J1/2:1 ===

 Spinors expanded in SFOs
....
Spinor: 21 22 23 24
 occup: 1.00 1.00 1.00 0.00
 ------ ---- ---- ---- ----
 SFO SIGMA
   13.alpha: 0.7614+0.0000i 0.0096+0.0000i 0.0052+0.0000i
-0.0006+0.0000i
   14.alpha: 0.0154+0.0000i -0.9996+0.0000i 0.0208+0.0000i
-0.0077+0.0000i
   15.alpha: -0.0146+0.0000i 0.0185+0.0000i 0.9849+0.0000i
0.1625+0.0000i
 SFO PI:x
    8.beta : 0.4578+0.0000i 0.0091+0.0000i 0.0112+0.0000i
0.0030+0.0000i
    9.beta : 0.0005+0.0000i -0.0074+0.0000i -0.1119+0.0000i
0.6910+0.0000i
 SFO PI:y
    8.beta : 0.0000+0.4578i 0.0000+0.0091i 0.0000+0.0112i
0.0000+0.0030i
    9.beta : 0.0000+0.0005i 0.0000-0.0074i 0.0000-0.1119i
0.0000+0.6910i
....

Left out are a lot of small numbers. The meaning is that a spinor
of J_z=1/2 symmetry can have SIGMA and PI character, for example,
the 21st spinor with occupation number 1.0, is approximately
(21 J_z=1/2) = 0.76 (13 SIGMA alpha) + 0.46 (8 PI:x beta) + i 0.46 (8
PI:y beta)

For the atomic case you could look in the
$ADFHOME/examples/adf/e_SO_Bi2/outpt.

The spin-orbit coupling in ADF is based on work by Prof. J.G. Snijders.
Documentation can be found in his thesis (1979),
which is unfortuantely not generally available.

Clebsch-Gordan coefficients are used to couple scalar relativistic single
group symmetry adapted molecular orbitals
with spin to make double group symmetry adapted spinors, which are
used in the spin-orbit coupled calculation.
Note that one can not restart a spin-orbit coupled calculation.

Best regards,
Erik van Lenthe
----------------------------------------------------------------------
Dr. Erik van Lenthe, Scientific Computing & Modelling NV
Vrije Universiteit, Theoretische Chemie, De Boelelaan 1083
1081 HV Amsterdam, The Netherlands
Phone: +31 20 44 47625 FAX: +31 20 44 47629
e-mail: vanlenthe@scm.com WWW: http://www.scm.com
----------------------------------------------------------------------
Received on 2004-06-23 10:34:52