# [Wien] Some questions about wavefunctions

Kyohn Ahn kyohn1004 at gmail.com
Thu Sep 6 01:54:56 CEST 2012

```Dear WIEN2k users,

I hope to calculate some properties using the informations of wavefunctions.
If I could understand the format of wavefunctions,
I will be able to make a simple program to calculate some properties I want.

http://zeus.theochem.tuwien.ac.at/pipermail/wien/2010-July/013407.html
http://zeus.theochem.tuwien.ac.at/pipermail/wien/2009-October/012079.html
http://zeus.theochem.tuwien.ac.at/pipermail/wien/2009-February/012197.html
http://zeus.theochem.tuwien.ac.at/pipermail/wien/2006-August/007606.html
http://zeus.theochem.tuwien.ac.at/pipermail/wien/2005-August/005665.html
and I read userguide, introduction(by S. Cottenier), and Singh's book.

However I don't understanding some ideas still.
So... could you help me?

(1) In case of using WFPRI in case.in1

Here are the informations about the wavefunctions of TiC in case.output1.

====================================================================================================

RECIPROCAL LATTICE VECTORS

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  -0.173605
0.164494   0.365820   0.065700  -0.251862       REALPART
1  -1  -1
0.160571   0.010807   0.216013   0.093693  -0.173605
0.207857  -0.281200   0.207174  -0.066659       REALPART
-1   1  -1
0.160571  -0.073154  -0.153052   0.163648  -0.173605
0.014673  -0.085825  -0.397011   0.157074       REALPART
-1  -1   1
0.160571  -0.151398   0.000200  -0.180654  -0.173605
-0.387024   0.001205   0.124138  -0.342276       REALPART
1   1  -1
0.160571   0.151398  -0.000200   0.180654  -0.173605
-0.387024   0.001205   0.124138   0.342276       REALPART
1  -1   1
0.160571   0.073154   0.153052  -0.163648  -0.173605
0.014673  -0.085825  -0.397011  -0.157074       REALPART
-1   1   1
0.160571  -0.010807  -0.216013  -0.093693  -0.173605
0.207857  -0.281200   0.207174   0.066659       REALPART
1   1   1
0.160571   0.213744  -0.063162  -0.076688  -0.173605
0.164494   0.365820   0.065700   0.251862       REALPART
0   0  -2
0.121667  -0.042756   0.043178   0.176478   0.023874
0.000000   0.000000   0.000000  -0.065440       REALPART
...

RECIPROCAL LATTICE VECTORS

10.ENERGY  11.ENERGY  12.ENERGY  13.ENERGY  14.ENERGY
15.ENERGY
0   0   0
0.000000   0.000000   0.000000   0.000000  -0.302844
0.000000
-1  -1  -1
0.094600   0.291365   0.000000   0.000000  -0.220060
-0.351710
1  -1  -1
-0.319063   0.225903   0.000000   0.000000  -0.220060
0.351710
...

====================================================================================================

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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