Dear Mihail Atanasov,

You wrote:

> We are studying spin-orbit coupling effects in TM complexes using ZORA
> calculations and we
>
> use TAPE15 to extract ZORA eigenvectors for the KS-orbitals of
> 3d-character. The procedure
>
> runs quite well and we were able to get interesting information for
> tetrahedral and D2d distorted
>
> tetrahedral complexes of Ni2+. However there is a problem with
> V(OH2)63+ complex which is
>
> of S6 symmetry but we use C(I) because of pecularities with the ADF in
> the present release.
>
> In this symmetry the program lists all 10 double group A1/2.g species
> without making use
>
> of the Kramers degeneracy, otherwise the program would use only xy+,
> x2-y2+, xz-, yz-, z2+
>
> or alternatively the same space orbitals but with opposite spin. That
> is why TAPE15 gives
>
> 210 eigenvectors and not 105 – the Kramers independent ones.
> Newetheless we can leave
>
> with this. However what is the assignment of the component of the
> eigenvectors?
>
> For example we have the 10 d-orbitals appearing from 25A1/2.g to
> 34A1/2.g; in the list
>
> of the A1.g symmetries the orbitals dz2, dx2-y2, dxy, dxz and dyz are
> Number 4, 7 10, 13, 16 from
>
> the total of 105 functions without spin. How do you order the spin
> orbitals in the eigenvectors:
>
> dz2+dz2- dx2-y2+dx2-y2-dxy+dxy-dxz+dxz-dyz+dyz- or first the alfa
> spins for the 105 orbitals
>
> and than the 105 orbitals for beta spins from 106 to 210. We checked
> both alternatives and neither of them
>
> gives the correct eigenvalues, which we judge from an non-relativistic
> calculation. In the higher symmetries
>
> you always give the possibility to get the Klebsh-Gordon coefficients
> using the command “print spinorbit”.
>
> The C(I) case you don’t use this and obviously diagonalize the totat
> 210x210 matrix, this is highly iniconomic.
>
> We will appreciate help in this matter,
>
Remark: In order to use time-reversal symmetry for the symmetries C(I)
or nosym,
one has to use quaternion algebra. This is not used in ADF.

On TAPE15 you will find A1/2.g%Eigen-Low_A the eigenvectors for A1/2.g
symmetry
on the basis of A.g orbitals with spin alpha and A.g orbitals with spin
beta.
Suppose one has 105 orbitals in A.g symmetry. Then the order is:
The first 44100 (210**2) coefficients are the real part:
eignvector 1: 105 numbers for spin alpha, next 105 numbers for spin beta
eigenvector 2: 105 numbers for spin alpha, next 105 numbers for spin beta,
....
eigenvector 105:..
the next 44100 are the imaginary part:
eignvector 1: 105 numbers for spin alpha, next 105 numbers for spin beta
eigenvector 2: 105 numbers for spin alpha, next 105 numbers for spin beta,
....
eigenvector 105:..

In the next adf-export version a SFO analysis is given in the output,
if one has one scalar relativistic fragment which is the whole molecule
in the 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
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Received on 2004-03-26 09:43:24