[Wien] why we need to divide plasma frequency by root(2)?

Fri Oct 27 20:55:55 CEST 2017

Sorry, in line 859 I saw plasm2 and totally overlooked the SQRT:

858:           if(SPIN.and.(ASO.eq.'SO')) then
859:             WRITE(6,618) (SQRT(plasm2(npcol(i))),i=1,LCOL)

So what I previously posted was nonsense.  In looks like w_pl(up-spin) 
is what is outputted in case.outputjointup for a spin-polarized spin 
orbit calculation.

So, w_pl^2(dn-spin) = w_pl^2(up-spin).  Plugging that into the SP 
(without spin orbit) plasma frequency equation:

w_pl = sqrt( w_pl^2(up-spin) + w_pl^2(up-spin) )
w_pl = sqrt(2*w_pl^2(up-spin) )
w_pl = sqrt(2)*sqrt(w_pl^2(up-spin))
w_pl = sqrt(2)*w_pl(up-spin)

sqrt(2)*2.074 sqrt(2)*2.074 sqrt(2)*1.264

or case.inkram I think would need to be:

2.933 2.933 1.788

Note: Since sqrt(2) = 2/sqrt(2) [ 
http://mathforum.org/library/drmath/view/58248.html ], the above 
equation could also be written as:

w_pl = 2*w_pl(up-spin)/sqrt(2)

On 10/27/2017 10:53 AM, Gavin Abo wrote:
>
> Thanks.
>
> So if understand correctly, the w_pl^2(up-spin) is what is outputted 
> in case.outputjointup for a spin-polarized spin orbit calculation by 
> line 859 of joint.f in the post:
>
> https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg16552.html
>
> So, w_pl^2(dn-spin) = w_pl^2(up-spin).  Plugging that into the SP 
> (without spin orbit) plasma frequency equation from your post below:
>
> w_pl = sqrt( w_pl^2(up-spin) + w_pl^2(up-spin) )
> w_pl = sqrt(2*w_pl^2(up-spin) )
> w_pl = sqrt(2)*w_pl(up-spin)  <= This showing why we need to get rid 
> of the sqrt(2) by dividing the sqrt(2)*w_pl(up-spin) by the sqrt(2) to 
> get the plasma frequency w_pl equal to w_pl(up-spin).
>
> So one needs to calculate (w_pl^2(up-spin) + w_pl^2(up-spin))/sqrt(2) 
> [or (2*w_pl^2(up-spin))/sqrt(2)] to get the plasma frequency like in 
> the post at:
>
> https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg16017.html
>
> So the mistake I made was the missing multiplication by 2 in my 
> previous post:
>
> https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg16615.html
>
> 2*2.074/sqrt(2) 2*2.074/sqrt(2) 2*1.264/sqrt(2)
>
> or
>
> 2.933 2.933 1.788
>
> Or do I still have something not quite right?
>
> On 10/27/2017 12:44 AM, Fecher, Gerhard wrote:
>> The optics programm tells about the SP Plasma frequencies:
>> w_pl = sqrt( w_pl^2(up-spin) + w_pl^2(dn-spin) )
>>
>> where does this come from
>> remember the classical approach where the plasma frequency is proportional to root(n) with n being the density of free electrons (number of electrons per Volume)
>> now what do you have in the SP case ? Shouldn't that be root/n_up+n_dn) ?
>> The programm however delivers  w_up proportional to root(n_up) and w_dn prop to root(n_dn) and you see where the above equation is comming from
>>
>> Finally show what happens when the two densities are equal  n_up=n_dn and you see where the root(2) is coming from and when to use it
>>
>> (Note that the root(2) is here not because of surface plasmons)
>>
>> Ciao
>> Gerhard
>>
>> DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
>> "I think the problem, to be quite honest with you,
>> is that you have never actually known what the question is."
>>
>> ====================================
>> Dr. Gerhard H. Fecher
>> Institut of Inorganic and Analytical Chemistry
>> Johannes Gutenberg - University
>> 55099 Mainz
>> and
>> Max Planck Institute for Chemical Physics of Solids
>> 01187 Dresden
>> ________________________________________
>> Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Gavin Abo [gsabo at crimson.ua.edu]
>> Gesendet: Sonntag, 22. Oktober 2017 00:42
>> An:wien at zeus.theochem.tuwien.ac.at
>> Betreff: Re: [Wien] why we need to divide plasma frequency by root(2)?
>>
>> I could be wrong, but I think you just need to take the sqrt(2) of each plasma frequency:
>>
>> 2.074/sqrt(2) 2.074/sqrt(2) 1.264/sqrt(2)
>>
>> then put them in case.inkram (not case.injoint).
>>
>> You should be able to use multiple plasma frequencies in case.inkram but don't forget to add a Gamma for drude value for each of the plasma frequencies [https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg14495.html  ].
>>
>> On 10/21/2017 4:29 PM, Dr. K. C. Bhamu wrote:
>>
>> ---------------------case.injoint
>> xx
>> xx
>> 1                                              >> correction
>> 2.0740      2.0740      1.2640
>> xx
>> -----------------------------------
>>
>> were xx means no change in lines of case.inkram.
>>
>>
>>
>> At page numer  164 under section "8.11 KRAM (Kramers-Kronig transformation) in UG"
>>
>>
>> "For a metal, the Plasma-frequencies (intraband transitions) for up and dn should be added, but then divided by√2, before using x kram."
>>
>> Does it mean that we need to add all three components and then divide by root(2) and put a single number [(2.074+2.074+1.264)/root(2)=3.88] instead of all three in case.injoint?
>>
>>
>> kind regards
>>
>> Bhamu
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>

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