<html><head></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; ">Dear Wang,<div><br></div><div> I remember that I put down a formula for that in my PhD thesis (<a href="http://www.sissa.it/cm/thesis/2010/SclauzeroG_PhDthesis.pdf">http://www.sissa.it/cm/thesis/2010/SclauzeroG_PhDthesis.pdf</a>), if this may help you (see eq. 2.74 at page 58). I'm sure you could find it in many other places, though.</div><div><br></div><div> I believe there's no such thing as the Rcut you write in your formula below. As you say, the atomic wavefunctions are built from the radial part R_nl(r), which is taken from the pseudopotential file, and the spherical harmonics. However you should not forget that there is also structure factor which comes from the translation of the nucleus from the origin.</div><div>The integral is done in reciprocal space for each k-point, hence a k-dependence is added to the atomic wavefunction when transforming it to the G-basis (have a look in PW/atomic_wfc.f90).</div><div><br></div><div>The following paper might also be useful to you:</div><div><br></div><div><div style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 7.9px/normal Times; "><span class="Apple-style-span" style="font-size: 18px; ">Solid State Communications, Vol. 95, No. 10, pp. 685-690, 1995</span></div></div><div><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div><span class="Apple-style-span" style="font-size: 18px; ">HTH</span></div><div><span class="Apple-style-span" style="font-size: 18px; "><br></span></div><div><span class="Apple-style-span" style="font-size: 18px; ">GS</span></div><div><br><div><div>Il giorno 31/mar/2011, alle ore 12.27, xirainbow ha scritto:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div><font class="Apple-style-span" size="4">Dear all:</font></div><div><font class="Apple-style-span" size="4"> I want to know the calculational equation of partial density of state(PDOS) in QE.</font></div><div>
<font class="Apple-style-span" size="4"> I could not find the equation on any paper. I think it may be:</font></div><div><font class="Apple-style-span" size="4">\int_0^{Rcut} \Psi(\vec r)*R_n(r)*Y_{lm}(\theta,\phi)*r^2 dr d\theta d\phi.</font></div>
<div><font class="Apple-style-span" size="4">where the Psi(\vec r) is the KS wave function of solid. Y_{lm}(\theta,\phi) is the spherical harmonics. R_n(r) is the the radial wave function of a isolated atom.</font></div>
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<font class="Apple-style-span" size="4"> If I was right, what is the formation of R_n(r)?</font></div><div><font class="Apple-style-span" size="4"><br></font></div><div><font class="Apple-style-span" size="4">Thanks in advance:)</font></div>
<font class="Apple-style-span" size="4"><br>-- <br>____________________________________<br>Hui Wang<br>School of physics, Fudan University, Shanghai, China</font><br>
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<span class="Apple-style-span" style="border-collapse: separate; color: rgb(0, 0, 0); font-family: Helvetica; font-size: medium; 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: 0px; "><div><span class="Apple-style-span" style="color: rgb(126, 126, 126); font-size: 16px; font-style: italic; "><br class="Apple-interchange-newline">§ Gabriele Sclauzero, EPFL SB ITP CSEA</span></div><div><font class="Apple-style-span" color="#7E7E7E"><i> PH H2 462, Station 3, CH-1015 Lausanne</i></font></div></span>
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