[Pw_forum] Fwd: How to calculate the d-band center?

[Stefano Baroni]

Dear Yang: please always address your correspondence to the pw_forum  
list, rather than to its individual members

Begin forwarded message:

> From: Fan Yang <shrek_826 at yahoo.com.cn>
> Date: April 7, 2008 5:29:40 AM GMT+02:00
> To: Stefano Baroni <baroni at sissa.it>
> Subject: Re: [Pw_forum] How to calculate the d-band center?
> Reply-To: Fan Yang <shrek_826 at yahoo.com.cn>
>
> Dear sir,
>
>         Thanks for your reply, but I'm not sure whether I've got  
> your words.
>
>         First, an arbitrary cutoff should be choosed, then each  
> interval (abscissa of PDOS, X-coordinate) located in this slected  
> region would have a height (ordinate of PDOS, Y-coordinate). The d- 
> band center should be defined as the sum of the product of internal  
> multiplied by height divided by the total number of heights, namely,  
> (X1*Y1+X2*Y2+...+Xn*Yn)/(Y1+Y2+...+Yn). Am I right?
>

I am confused, in turn. It should simply be integral: $ 
\int_{E_1}^{E_2} E n(E) dE$, where $E_1$ and $E_2$ are the lowe and  
upper cutoffs.
>         Another question, whether the using of  arbitrary cutoff  
> would affect the value of d-band center?
>

of course, it will. this simply reflects the fact that the very  
concept of "d-band center" is (slightly) ill defined. The more  
isolated the band is, the less sensitive the value of the integral  
will be on the choice of the cutoffs, the more well defined the  
concept of "d-band center" ...

If I may dare to give you a suggestion, never try to implement any  
formula, before you think you understand to some degree of confidence  
the concepts on which the formula is based. simple drwaing by hands,  
drafts notes, trila-and-error will help ... I know it may be hard, but  
it is the only path to learning ...

cheers - SB

>         Best Regards,
>
>                               Fan
>
>
>
>
> ======================================
> Fan Yang
> PH.D Candidate in Electrochemistry
> College of Chemistry and Molecular Science
> Wuhan University,430072,Hubei Province,China
> E-mail:shrek_826 at yahoo.com.cn
> ======================================
>
>
> ----- Original Message ----
> From: Stefano Baroni <baroni at sissa.it>
> To: Fan Yang <shrek_826 at yahoo.com.cn>; PWSCF Forum  
> <pw_forum at pwscf.org>
> Sent: Friday, April 4, 2008 6:17:24 PM
> Subject: Re: [Pw_forum] How to calculate the d-band center?
>
> calculate the first moment of the DOS, using some arbitrary cutoff  
> at the low- and high-energy sides of the d bands, as assigned by  
> visual inspection. The second moment would give the width (kind of).  
> SB
>
> On Apr 4, 2008, at 5:20 AM, Fan Yang wrote:
>>
>>  Dear everyone,
>>          Does anyone know how to calculate the d-band center of  
>> transition metals? According to the Friedel Model, the d-band is  
>> treated as a rectangular density of states centred on energy a with  
>> width W . However, the PDOS we obtained from calculation is usually  
>> irregular with sharp peaks, not a rectangular. Then comes to the  
>> question:  how to decide the range of d-band energy by applying  
>> rectangular model ?  how to get the d-band center from PDOS?
>>          Thanks inadvance.
>> ======================================
>> Fan Yang
>> PH.D Candidate in Electrochemistry
>> College of Chemistry and Molecular Science
>> Wuhan University,430072,Hubei Province,China
>> E-mail:shrek_826 at yahoo.com.cn
>> ======================================
>>
>> You rock. That's why Blockbuster's offering you one month of  
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>
> ---
> Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
> Trieste
> [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)
>
> Please, if possible, don't  send me MS Word or PowerPoint attachments
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>
>
>
>
>
> You rock. That's why Blockbuster's offering you one month of  
> Blockbuster Total Access, No Cost.

---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

La morale est une logique de l'action comme la logique est une morale  
de la pensée - Jean Piaget

Please, if possible, don't  send me MS Word or PowerPoint attachments
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