<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Dear Yang: please always address your correspondence to the pw_forum list, rather than to its individual members<br><div><br><html>Begin forwarded message:</html><br class="Apple-interchange-newline"><blockquote type="cite"><div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="4" color="#000000" style="font: 14.0px Helvetica; color: #000000"><b>From: </b></font><font face="Helvetica" size="4" style="font: 14.0px Helvetica">Fan Yang <<a href="mailto:shrek_826@yahoo.com.cn">shrek_826@yahoo.com.cn</a>></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="4" color="#000000" style="font: 14.0px Helvetica; color: #000000"><b>Date: </b></font><font face="Helvetica" size="4" style="font: 14.0px Helvetica">April 7, 2008 5:29:40 AM GMT+02:00</font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="4" color="#000000" style="font: 14.0px Helvetica; color: #000000"><b>To: </b></font><font face="Helvetica" size="4" style="font: 14.0px Helvetica">Stefano Baroni <<a href="mailto:baroni@sissa.it">baroni@sissa.it</a>></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="4" color="#000000" style="font: 14.0px Helvetica; color: #000000"><b>Subject: </b></font><font face="Helvetica" size="4" style="font: 14.0px Helvetica"><b>Re: [Pw_forum] How to calculate the d-band center?</b></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font face="Helvetica" size="4" color="#000000" style="font: 14.0px Helvetica; color: #000000"><b>Reply-To: </b></font><font face="Helvetica" size="4" style="font: 14.0px Helvetica">Fan Yang <<a href="mailto:shrek_826@yahoo.com.cn">shrek_826@yahoo.com.cn</a>></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><br></div> </div><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div><div style="font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><p>Dear sir,</p><p> Thanks for your reply, but I'm not sure whether I've got your words. </p><p> First, an arbitrary cutoff should be choosed, then each interval (<font color="#0080ff">abscissa</font><span class="Apple-converted-space"> </span>of PDOS, X-coordinate) located in this slected region would have a height (<font color="#0000ff">ordinate</font><span class="Apple-converted-space"> </span>of PDOS, Y-coordinate). The d-band center should be defined as the sum of<span class="Apple-converted-space"> </span><em>the product of internal multiplied by height</em> divided by the total number of heights, namely, (X1*Y1+X2*Y2+...+Xn*Yn)/(Y1+Y2+...+Yn). Am I right?</p></div></div></span></blockquote><div><br></div>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.<br><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div><div style="font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><p> Another question, whether the using of arbitrary cutoff would affect the value of d-band center?</p></div></div></span></blockquote><div><br></div>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" ...</div><div><br></div><div>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 ...</div><div><br></div><div>cheers - SB</div><div><br><blockquote type="cite"><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div><div style="font-family: 'times new roman', 'new york', times, serif; font-size: 12pt; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><p> Best Regards,</p><p> Fan</p><div> <br class="webkit-block-placeholder"></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><br> </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">======================================</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Fan Yang</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">PH.D Candidate in Electrochemistry </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">College of Chemistry and Molecular Science </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Wuhan University,<em>430072</em>,Hubei Province,China </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><em>E-mail:<a href="mailto:shrek_826@yahoo.com.cn">shrek_826@yahoo.com.cn</a></em></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">======================================</div><div style="font-size: 12pt; font-family: 'times new roman', 'new york', times, serif; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><br><br><div style="font-size: 12pt; font-family: 'times new roman', 'new york', times, serif; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">----- Original Message ----<br>From: Stefano Baroni <<a href="mailto:baroni@sissa.it">baroni@sissa.it</a>><br>To: Fan Yang <<a href="mailto:shrek_826@yahoo.com.cn">shrek_826@yahoo.com.cn</a>>; PWSCF Forum <<a href="mailto:pw_forum@pwscf.org">pw_forum@pwscf.org</a>><br>Sent: Friday, April 4, 2008 6:17:24 PM<br>Subject: Re: [Pw_forum] How to calculate the d-band center?<br><br>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<div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><br><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">On Apr 4, 2008, at 5:20 AM, Fan Yang wrote:<br class="Apple-interchange-newline"><blockquote type="cite"><span class="Apple-style-span" style="word-spacing: 0px; font: normal normal normal 14px/normal Helvetica; text-transform: none; color: rgb(0, 0, 0); text-indent: 0px; white-space: normal; letter-spacing: normal; border-collapse: separate; orphans: 2; widows: 2; "><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><div style="font-size: 12pt; font-family: 'times new roman', 'new york', times, serif; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><br> Dear everyone,</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "> 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<span class="Apple-converted-space"> </span><span style="font-style: italic; font-family: Symbol; ">a<span class="Apple-converted-space"> </span></span><em>with width<span class="Apple-converted-space"> </span><span style="font-style: italic; ">W</span></em><span class="Apple-converted-space"> </span>. 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 <em>range</em> of d-band energy by applying rectangular model ? how to get the d-band center from PDOS?</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "> Thanks inadvance.</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">======================================</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Fan Yang</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">PH.D Candidate in Electrochemistry </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">College of Chemistry and Molecular Science </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Wuhan University,<em>430072</em>,Hubei Province,China </div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><em>E-mail:<a href="mailto:shrek_826@yahoo.com.cn" target="_blank" rel="nofollow" ymailto="mailto:shrek_826@yahoo.com.cn">shrek_826@yahoo.com.cn</a></em></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">======================================</div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "></div></div><br><hr size="1">You rock. That's why Blockbuster's offering you<span class="Apple-converted-space"> </span><a href="http://us.rd.yahoo.com/evt=47523/*http://tc.deals.yahoo.com/tc/blockbuster/text5.com" target="_blank" rel="nofollow">one month of Blockbuster Total Access</a>, No Cost._______________________________________________<br>Pw_forum mailing list<br><a href="mailto:Pw_forum@pwscf.org" target="_blank" rel="nofollow" ymailto="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</a><br><a href="http://www.democritos.it/mailman/listinfo/pw_forum" target="_blank" rel="nofollow">http://www.democritos.it/mailman/listinfo/pw_forum</a><br></div></span></blockquote></div><br><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><span class="Apple-style-span" style="word-spacing: 0px; font: normal normal normal 14px/normal Helvetica; text-transform: none; color: rgb(0, 0, 0); text-indent: 0px; white-space: normal; letter-spacing: normal; border-collapse: separate; orphans: 2; widows: 2; "><div style="word-wrap: break-word; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">---</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">Stefano Baroni - SISSA</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">&</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">DEMOCRITOS National Simulation Center - Trieste</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)</span></font></div><div style="min-height: 14px; font: normal normal normal 12px/normal Helvetica; margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><br style="font-size: 12px; "></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">Please, if possible, don't</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">send me MS Word or PowerPoint attachments</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">Why? See:</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" color="#0023e9" size="3"><span class="Apple-style-span" style="font-size: 12px; "><a href="http://www.gnu.org/philosophy/no-word-attachments.html" target="_blank" rel="nofollow">http://www.gnu.org/philosophy/no-word-attachments.html</a></span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" color="#0023e9" size="3"><span class="Apple-style-span" style="font-size: 12px; "><br class="webkit-block-placeholder"></span></font></div></div></div></span><br class="Apple-interchange-newline"></div><br></div></div><br></div></div><br><hr size="1">You rock. That's why Blockbuster's offering you<span class="Apple-converted-space"> </span><a href="http://us.rd.yahoo.com/evt=47523/*http://tc.deals.yahoo.com/tc/blockbuster/text5.com">one month of Blockbuster Total Access</a>, No Cost.</div></span></blockquote></div><br><div> <span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-align: auto; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: 2; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-border-horizontal-spacing: 0px; -webkit-border-vertical-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; "><div style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">---</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">Stefano Baroni - SISSA</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">&</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">DEMOCRITOS National Simulation Center - Trieste</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; font-size: 12px; "><br style="font-size: 12px; "></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; font-size: 12px; "><span class="Apple-style-span" style="font-size: 14px; "><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">La morale est une logique de l'action comme la logique est une morale de la pensée - Jean Piaget</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "><br></span></font></div></span></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">Please, if possible, don't</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">send me MS Word or PowerPoint attachments</span></font></div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; ">Why? See:</span></font><font class="Apple-style-span" size="3"><span class="Apple-style-span" style="font-size: 12px; "> </span></font><font class="Apple-style-span" color="#0023E9" size="3"><span class="Apple-style-span" style="font-size: 12px; "><a href="http://www.gnu.org/philosophy/no-word-attachments.html">http://www.gnu.org/philosophy/no-word-attachments.html</a></span></font></div><div><font class="Apple-style-span" color="#0023E9" size="3"><span class="Apple-style-span" style="font-size: 12px; "><br class="webkit-block-placeholder"></span></font></div></div></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"></div></span><br class="Apple-interchange-newline"> </div><br></body></html>