<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Dear Fangyong, <div class=""><br class=""></div><div class="">within the GPW scheme, the orbitals are described by contracted Gaussian functions, </div><div class="">whereas electron density is expanded in plane-waves. You are right that the extent of </div><div class="">the Gaussian functions is finite, which is controlled by eps values that are eventually </div><div class="">related to EPS_DEFAULT. You are also right wrt to the plane-waves, whose truncation </div><div class="">is controlled by CUTOFF. However, contrary to the cutoff of conventional PW codes, </div><div class="">the latter differs by a factor of 4, which due to the fact that the density is the sum of the </div><div class="">orbitals squared combined with the application of the Shannon-Nyquist sampling theorem. </div><div class="">Lastly, within the GAPW approach, the Gaussian functions are indeed also periodic </div><div class="">Gaussians. </div><div class=""><br class=""></div><div class="">Best, </div><div class="">Thomas</div><div class=""><div><br class=""><blockquote type="cite" class=""><div class="">Am 08.12.2020 um 06:22 schrieb Fangyong Yan <<a href="mailto:fyya...@gmail.com" class="">fyya...@gmail.com</a>>:</div><br class="Apple-interchange-newline"><div class=""><div dir="ltr" style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class="">Hi, Professor Hutter,<div class=""><br class=""></div><div class="">I read your paper, and I think when you calculate the electron density based on periodic Gaussian, you need to truncate the periodic Gaussian because it is an infinite series, but it decays fast since the periodic Gaussian is a localized basis set. Am I understanding correctly? </div><div class=""><br class=""></div><div class="">For electron density represented by planewaves, it also has the same problem, it is an infinite series, and has to be truncated, which is the planewave cutoff. </div><div class=""><br class=""></div><div class="">Another question, in the Gaussian augmented planewave method, the atomic hard and soft electron density, they are atom-based electron density, and are represented by Gaussian functions, they are also periodic Gaussian, in order to fulfill the periodicity, am I correct? Thanks!</div><div class=""><br class=""></div><div class="">Fangyong</div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><br class=""></div></div><br style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;" class=""><div class="gmail_quote" style="caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none;"><div dir="ltr" class="gmail_attr">On Fri, Dec 4, 2020 at 9:49 AM Fangyong Yan <<a href="mailto:fyya...@gmail.com" class="">fyya...@gmail.com</a>> wrote:<br class=""></div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;"><div dir="ltr" class=""><div class="">Dear Professor Hutter, </div><div class=""><br class=""></div>I will read the paper. Thanks!<div class=""><br class=""></div><div class="">Fangyong</div></div><br class=""><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Fri, Dec 4, 2020 at 4:37 AM <<a href="mailto:hut...@chem.uzh.ch" target="_blank" class="">hut...@chem.uzh.ch</a>> wrote:<br class=""></div><blockquote class="gmail_quote" style="margin: 0px 0px 0px 0.8ex; border-left-width: 1px; border-left-style: solid; border-left-color: rgb(204, 204, 204); padding-left: 1ex;">Hi<br class=""><br class="">yes, it is periodic Gaussians. For details of the calculation<br class="">read the publications:<br class=""><br class=""> Lippert, G; Hutter, J; Parrinello, M.<br class=""> MOLECULAR PHYSICS, 92 (3), 477-487 (1997).<br class=""> A hybrid Gaussian and plane wave density functional scheme.<br class=""> <a href="https://doi.org/10.1080/002689797170220" rel="noreferrer" target="_blank" class="">https://doi.org/10.1080/002689797170220</a><br class=""><br class=""> VandeVondele, J; Krack, M; Mohamed, F; Parrinello, M; Chassaing, T;<br class=""> Hutter, J. COMPUTER PHYSICS COMMUNICATIONS, 167 (2), 103-128 (2005).<br class=""> QUICKSTEP: Fast and accurate density functional calculations using a<br class=""> mixed Gaussian and plane waves approach.<br class=""> <a href="https://doi.org/10.1016/j.cpc.2004.12.014" rel="noreferrer" target="_blank" class="">https://doi.org/10.1016/j.cpc.2004.12.014</a><br class=""><br class="">--------------------------------------------------------------<br class="">Juerg Hutter Phone : ++41 44 635 4491<br class="">Institut für Chemie C FAX : ++41 44 635 6838<br class="">Universität Zürich E-mail:<span class="Apple-converted-space"> </span><a href="mailto:hut...@chem.uzh.ch" target="_blank" class="">hut...@chem.uzh.ch</a><br class="">Winterthurerstrasse 190<br class="">CH-8057 Zürich, Switzerland<br class="">---------------------------------------------------------------<br class=""><br class="">-----<a href="mailto:cp...@googlegroups.com" target="_blank" class="">cp...@googlegroups.com</a><span class="Apple-converted-space"> </span>wrote: -----<br class="">To: "cp2k" <<a href="mailto:cp...@googlegroups.com" target="_blank" class="">cp...@googlegroups.com</a>><br class="">From: "<a href="mailto:fy...@gmail.com" target="_blank" class="">fy...@gmail.com</a>"<span class="Apple-converted-space"> </span><br class="">Sent by:<span class="Apple-converted-space"> </span><a href="mailto:cp...@googlegroups.com" target="_blank" class="">cp...@googlegroups.com</a><br class="">Date: 12/04/2020 08:42AM<br class="">Subject: [CP2K:14345] how does CP2K construct electron density in real-space FFT mesh point? Is the Gaussian product a periodic Gaussian product?<br class=""><br class="">Hi,<span class="Apple-converted-space"> </span><br class=""><br class="">The electron density in real-space FFT mesh point is defined as:<br class=""><br class="">n(Ri) = summation of m, n {P_mn * Gaussian_mn(Ri),<span class="Apple-converted-space"> </span><br class=""><br class="">Ri is the grid point, m and n are the index for the Gaussian basis set, P_mn is the density matrix, Gaussian_mn(Ri) is the product of Gaussian basis set m and Gaussian basis set n,<br class=""><br class="">my question is:<br class="">1)<span class="Apple-converted-space"> </span><br class="">is Gaussian_mn(Ri) a periodic Gaussian? (Product Gaussian is also a Gaussian).<span class="Apple-converted-space"> </span><br class="">That is,<br class=""><br class="">Gaussian_mn(Ri) = Gaussian_mn(Ri+L_unitcell), where L_unitcell is the length for the unit cell in either 1,2 or 3 dimension.<span class="Apple-converted-space"> </span><br class="">2) if it is the periodic Gaussian, and it should be in order to fulfill the periodicity of electron density, how do you do the calculation?<span class="Apple-converted-space"> </span><br class="">Because the periodic Gaussian is actually an infinite series, that is,<br class="">Gaussian(Ri) = summation of L (Gaussian(Ri+L), where L = n*L_unitcell, and n is an integer and span from minus infinite to positive infinite.<br class=""><br class="">Thanks!<br class=""><br class="">Fangyong<br class=""><br class=""><br class=""><br class=""><br class=""><br class=""><br class=""> <span class="Apple-converted-space"> </span>--<span class="Apple-converted-space"> </span><br class=""> You received this message because you are subscribed to the Google Groups "cp2k" group.<br class=""> To unsubscribe from this group and stop receiving emails from it, send an email to<span class="Apple-converted-space"> </span><a href="mailto:cp2k%2Bun...@googlegroups.com" target="_blank" class="">cp...@googlegroups.com</a>.<br class=""> To view this discussion on the web visit<span class="Apple-converted-space"> </span><a href="https://groups.google.com/d/msgid/cp2k/e023de64-1040-49bd-a228-2aa4cf0732a5n%40googlegroups.com" rel="noreferrer" target="_blank" class="">https://groups.google.com/d/msgid/cp2k/e023de64-1040-49bd-a228-2aa4cf0732a5n%40googlegroups.com</a>.<br class=""><br class=""><br class="">--<span class="Apple-converted-space"> </span><br class="">You received this message because you are subscribed to the Google Groups "cp2k" group.<br class="">To unsubscribe from this group and stop receiving emails from it, send an email to<span class="Apple-converted-space"> </span><a href="mailto:cp2k%2Bun...@googlegroups.com" target="_blank" class="">cp...@googlegroups.com</a>.<br class="">To view this discussion on the web visit<span class="Apple-converted-space"> </span><a href="https://groups.google.com/d/msgid/cp2k/OFE157B452.F6F180E1-ONC1258634.0034CF74-C1258634.0034DAA2%40lotus.uzh.ch" rel="noreferrer" target="_blank" class="">https://groups.google.com/d/msgid/cp2k/OFE157B452.F6F180E1-ONC1258634.0034CF74-C1258634.0034DAA2%40lotus.uzh.ch</a>.<br class=""></blockquote></div></blockquote></div><div style="caret-color: rgb(0, 0, 0); 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