Dear all,

Serguei.Patchkovskii wrote:
> For relativistic spin-orbit calculations, ADF will accept input
> with both "restricted" and "unrestricted" keywords. For "restricted"
> calculation, I end up with a set of singly occupied orbitals, which
> have (at least in principle) contributions from both spin-alpha
> and spin-beta basis functions. Naively, this is that I would expect
> spin-orbit coupling operator to do - so all seems to be fine.
>
> However, I am not able to understand what ADF is doing for the "spin-
> unrestricted" spin-orbit case (and ADF documentation on spin-orbit
> calculations is sketchy at best). The outcome of the calculation is
> a set of half-occupied orbitals. At least for the point group I am
> working with (Cs), these orbitals are always paired, so that each
> half-occupied orbital has a matching orbital, from a conjugated
> spinor irrep. The energies of these pairs closely match energies of
> the orbitals from scalar relativistic calculation.
>
> The only intepretation I was able to come up with, is that in a
> "spin-unrestricted" calculations, orbitals from conjugated irreps
> are constrained to form a linear combination with a value of sz
> of +/-0.5; these linear combination then form a non-interacting
> determinant with the value of Sz prescribed by the "CHARGE" keyword.
> If this is true, a "spin-unrestricted" calculation does NOT lead
> (except by accident) to proper eigenfuctions of spin-orbit Hamiltonian,
> but rather to some mixed state.
>
> So, now come the questions:
>
> 1. Is this interpretation of a "spin-unrestricted spin-orbit"
> calculation in ADF close to the truth?
>
> 2. If it is, what is the physical meaning of such calculation?
> What information can be extracted from it?
>
> 3. Can somebody point me to a publication, documenting this
> technique?

Answer:
1. Yes, close.
   Not, that this is not the noncollinear or collinear approach for
   doing spin-unrestricted spin-orbit coupled calculations.
   In a spin-restricted calculation with only an electric field present
   you will have Kramers symmetry, which means that always at
   least two spinors will have the same spinor energy.
   In the undocumented spin-unrestricted spin-orbit coupled calculations
   in ADF, it is assumed that one can still divide half of the spinors
   in spin-up (alpha) and the other half in spin-down (beta) spinors.
   This is not true,
   since spinors resulting from a spin-orbit coupled equation,
   will in general not be eigenfunctions of S_z,
   the z-component of the spin operator.
   The calculations are also called momentum spin-polarized calculations.

2. I do not know the physical meaning, only that
   a spin-restricted spin-orbit coupled calculation
   will not give highly accurate bond energies
   if open shells are involved, and this method somehow
   takes some spin-polarization effects into account.
   The bond energies that come out of such a calculation
   are close to the non-relativistic one for light molecules,
   and could be useful for heavier molecules.
   Again this is not the noncollinear or collinear approach for
   doing spin-unrestricted spin-orbit coupled calculations.
   This is being implemented and tested in ADF, and will be available
   in some future version.

3. The momentum-spin polarized calculations are also
   used for example in the BDF program:
   W. Liu and M. Dolg,
   Phys Rev A 57, 1721

Best regards,
Erik van Lenthe

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Dr. Erik van Lenthe SCIENTIFIC COMPUTING & MODELLING NV
Tel: +31 20 44 47615 Vrije Universiteit, Theoretische Chemie
secretary: 44 47519 De Boelelaan 1083
 fax: 44 47629 1081 HV Amsterdam, The Netherlands
 e-mail: vanlenthe@scm.com http://www.scm.com
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Received on 2002-07-31 13:05:49