# [Wien] Some questions about wavefunctions

Peter Blaha pblaha at theochem.tuwien.ac.at
Thu Sep 6 10:41:19 CEST 2012

```The wf is written als psi(r)_k = Sum(K) c_K exp(iKr)

So obviously the 3 numbers are the K-vectors (full reciprocal space
lattice vectors) and the number is the corresponding c_K coefficient.
This c_K is here just a real number, sumetimes it could be a complex number.
and of course the c_K is different for each eigenvalue (1. 2.... energy)

>                      1.ENERGY   2.ENERGY   3.ENERGY   4.ENERGY
> 5.ENERGY   6.ENERGY   7.ENERGY   8.ENERGY   9.ENERGY
>     0   0   0
>                     0.397668   0.000000   0.000000   0.000000
> 0.874538   0.000000   0.000000   0.000000   0.000000       REALPART
>    -1  -1  -1
>                     0.160571  -0.213744   0.063162   0.076688
> Q1) The meaning of "K-vectors" (for example, 0 0 0 or -1 -1 -1 or -1 1
> -1 ...)
> Do they mean the direction(or axis) of the plane waves?
>
> Q2) The meaning of "REALPART"
> What is the reason to write ENERGY1~9(marked REALPART) and ENERGY10~15
> separately?
>
> Q3) The meaning of "#.ENERGY"s
> I think they are the corresponding (linear-combination) 'coefficients'.
> Then, what is the shape of the basis?
> (Is there any recommendable book or paper to find the informations about
> this basis set?)
>
> (2) In case of switching ALM in case.in2
>
> It prints the expansion coefficient Alm, Blm, ...
>
> Q4) The authenticity of Alm, Blm, ...
> For example, according to the equation (2.4) in UG,
> [wavefunction inside atomic sphere] = SUMlm [ ( Alm * ul + Blm * ul_dot
> ) * Ylm ]
> Then, how can I get the informations about ul and ul_dot?
> (Or, the calculated Alm, Blm, ... values are containing ul and ul_dot?)
>
> Thank you for reading this mail.
> Any response will be very helpful for me.
> (If I have some misunderstanding, please point out my mistakes!)
>
> With best regards
>
> Kyohn
>
>
>
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>

--
Peter Blaha
Inst.Materials Chemistry
TU Vienna
Getreidemarkt 9
A-1060 Vienna
Austria
+43-1-5880115671
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