iMechanica - Comments for "Journal Club for July 2018: Mechanics using Quantum Mechanics"
https://www.imechanica.org/node/22476
Comments for "Journal Club for July 2018: Mechanics using Quantum Mechanics"en"Do you think this argument
https://www.imechanica.org/comment/29747#comment-29747
<a id="comment-29747"></a>
<p><em>In reply to <a href="https://www.imechanica.org/comment/29746#comment-29746">Dear Prof. Suryanarayana,</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>"<span>Do you think this argument is correct in theory?</span> "</p>
<p>No, even when a single k-point is employed, a plane-wave code is employing periodic boundary conditions, i.e., there is interaction between a system and its replicas. The typical strategy is to utilize a large enough vacuum such that this interaction is negligible relative to the accuracy of interest. However, depending on the type of system (e.g. those which have dipole moment), the convergence with vacuum can be extremely slow.</p>
<p>"<span>Also, I would like to know if the above mentioned codes are available on Github or Is there any plan, in future, to implement them in some open-source software packages?"</span></p>
<p><span>SPARC and SQDFT have already been released as open source codes. They can be found accompanying the paper. The others will be released as open source in the near future.</span></p>
<p> </p>
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</ul>Sun, 29 Jul 2018 21:25:59 +0000Phanish Suryanarayanacomment 29747 at https://www.imechanica.orgDear Prof. Suryanarayana,
https://www.imechanica.org/comment/29746#comment-29746
<a id="comment-29746"></a>
<p><em>In reply to <a href="https://www.imechanica.org/comment/29734#comment-29734">Re: DFT calculations for dislocations</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p dir="ltr"><span>Dear Prof. Suryanarayana,</span></p>
<p dir="ltr"> </p>
<p dir="ltr"><span>Thanks for picking this topic. </span></p>
<p dir="ltr"><span>I ,also, have a question regarding the boundary condition when DFT approaches has been employed in the plane-wave basis(aka Fourier basis). </span> </p>
<p dir="ltr"><span>As already mentioned by you this approach is restricted to periodic boundary conditions</span><span>. </span><span>I read few papers which are calculating surface energies (and interface energy) using plane wave basis approach by creating vacuum in one direction and using only one kpoint in that direction[1,2]. The argument is that the vacuum and single kpoint does not allow the interaction between the surfaces. Do you think this argument is correct in theory?</span> </p>
<p dir="ltr"><span>If yes, then using same argument can we create vacuum in all directions and restrict our kpoints in the vicinity of atoms rather than distributing them in supercell(which contains vacuum also). The only difference will be that we will be needing more than one kpoints in the directions of vacuum for kpoint convergence. The interaction between kpoints from nearby periodic cells can be restricted if kpoints are in vicinity of atoms. Kindly let me know your thoughts on this.</span></p>
<p dir="ltr"><span>Also, I would like to know if the above mentioned codes are available on Github or Is there any plan, in future, to implement them in some open-source software packages?</span></p>
<p><span>Thank you,</span><span> </span></p>
<p dir="ltr"><span>[1] Miguel Fuentes-Cabrera, M. I. Baskes, Anatoli V. Melechko, and Michael L. Simpson, 2008. Bridge structure for the graphene/Ni(111) system: A first principles study. </span><span>Physical review B 77, 035405.</span> </p>
<p dir="ltr"><span>[2] Zhiping Xu and Markus J Buehler. Interface structure and mechanics between graphene and metal substrates: a first-principles study. Journal of Physics Condensed Matter 22 485301.</span></p>
<p><span> </span></p>
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</ul>Sun, 29 Jul 2018 15:23:24 +0000Arpit Agrawalcomment 29746 at https://www.imechanica.orgRe: Cubic scaling in DFT...
https://www.imechanica.org/comment/29736#comment-29736
<a id="comment-29736"></a>
<p><em>In reply to <a href="https://www.imechanica.org/comment/29735#comment-29735">Re: Faster DFT calculations</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>1. ``However, the use of multigrid does not change the cubic-scaling with respect to the number of atoms, which is a consequence of the underlying eigenproblem.''</p>
<p>Oh, I see.</p>
<p>2. ``[CheFSI's] performance is very weakly dependent on the spectral width of the matrix being diagonalized...''</p>
<p>Thanks for clarifying this part too, and indeed, for taking care to address all other issue I raised.</p>
<p>Best,</p>
<p>--Ajit</p>
<p> </p>
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</ul>Tue, 24 Jul 2018 03:49:53 +0000Ajit R. Jadhavcomment 29736 at https://www.imechanica.orgRe: Faster DFT calculations
https://www.imechanica.org/comment/29735#comment-29735
<a id="comment-29735"></a>
<p><em>In reply to <a href="https://www.imechanica.org/comment/29733#comment-29733">Faster DFT calculations</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>"You mention the cubic scaling with # of atoms, which implies the limitation of only a few hundred atoms. The first thing to strike me when I read it was this: how about multi-gridding?"</p>
<p>There have been efforts like the ones you referenced for developing multigrid preconditioning for the DFT problem, which can be used to reduce the prefactor associated with real-space DFT calculations. However, the use of multigrid does not change the cubic-scaling with respect to the number of atoms, which is a consequence of the underlying eigenproblem. Indeed, the scaling can be made linear by employing the nearsightedness principle, as discussed in my post. As is to be expected, the prefactor associated with linear-scaling approaches is significantly larger than the cubic-scaling approaches.</p>
<p>"So I was wondering whether your approach already makes use of it or what."</p>
<p>We do not utilize the multigrid preconditioning for our diagonalization based formulations and implementations (e.g. SPARC). Instead, we employ partial diagonalization based on CheFSI [28] whose performance is very weakly dependent on the spectral width of the matrix being diagonalized, therefore alleviating the need for preconditioning.</p>
<p>"Could you please share your thoughts on MG for DFT? Is it suitable? Does it work for the kind of (mechanics-related) problems you mention above? What are the constraints for using MG in DFT?"</p>
<p>Multigrid preconditioning can significantly reduce the prefactor associated with real-space DFT calculations. However, as mentioned above, it does not improve the scaling. Furthermore, methods like CheFSI alleviate the need for preconditioning, making them highly competitive. Finally, the complexity of multigrid in terms of formulation and implementation for eigenvalue problems (rather than the usual linear systems of equations) makes them less desirable.</p>
<p>[28] Zhou, Y., Saad, Y., Tiago, M.L. and Chelikowsky, J.R., 2006. Self-consistent-field calculations using Chebyshev-filtered subspace iteration. <em>Journal of Computational Physics</em>, <em>219</em>(1), pp.172-184.</p>
<p> </p>
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</ul>Tue, 24 Jul 2018 01:59:52 +0000Phanish Suryanarayanacomment 29735 at https://www.imechanica.orgRe: DFT calculations for dislocations
https://www.imechanica.org/comment/29734#comment-29734
<a id="comment-29734"></a>
<p><em>In reply to <a href="https://www.imechanica.org/comment/29731#comment-29731">DFT calculations for dislocations</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>"What is the simplest crystal defect for DFT calculations?"</p>
<p>In general, the simplest defect will be point defects, e.g., vacancy.</p>
<p>"Does it have to be a periodic arrangement of defects or it is possible to analyze a single defect?"</p>
<p>Traditionally, DFT approaches have employed the plane-wave basis (i.e., Fourier basis). Therefore, they are restricted to periodic boundary conditions, which translates to a periodic arrangement of defects. Using real-space methods like the one I described in my post (e.g. SPARC), it is possible to impose Dirichlet or periodic boundary conditions or a combination thereof. However, a number of questions remain, the main one being: what are the appropriate boundary conditions on the electronic structure quantities? (Recall that we are dealing with an eigenvalue problem). Indeed, an alternative to finding and applying such boundary conditions is to coarse-grain DFT [21,22].</p>
<p> "Are you aware of any DFT calculations for dislocations?"</p>
<p>Given their importance, there have been a number of efforts to study dislocations using DFT. Three broad classes of strategies that are adopted are: (i) Quadrupole or dipole method, e.g., [23,24], (ii) Development of new boundary conditions, e.g., [25,26], and (iii) Multiscale methods, e.g., [27]. Each of these approaches have their own limitations and strengths in terms of accuracy, efficiency, and the quantities they can calculate.</p>
<p> </p>
<p>[23] Bigger, J.R.K., McInnes, D.A., Sutton, A.P., Payne, M.C., Stich, I., King-Smith, R.D., Bird, D.M. and Clarke, L.J., 1992. Atomic and electronic structures of the 90 partial dislocation in silicon. <em>Physical review letters</em>, <em>69</em>(15), p.2224.</p>
<p>[24] Dezerald, L., Proville, L., Ventelon, L., Willaime, F. and Rodney, D., 2015. First-principles prediction of kink-pair activation enthalpy on screw dislocations in bcc transition metals: V, Nb, Ta, Mo, W, and Fe. <em>Physical Review B</em>, <em>91</em>(9), p.094105.</p>
<p> [25] Woodward, C. and Rao, S.I., 2002. Flexible ab initio boundary conditions: Simulating isolated dislocations in bcc Mo and Ta. <em>Physical review letters</em>, <em>88</em>(21), p.216402.</p>
<p> [26] Yasi, J.A., Hector Jr, L.G. and Trinkle, D.R., 2010. First-principles data for solid-solution strengthening of magnesium: From geometry and chemistry to properties. <em>Acta Materialia</em>, <em>58</em>(17), pp.5704-5713.</p>
<p>[27] Lu, G., Tadmor, E.B. and Kaxiras, E., 2006. From electrons to finite elements: A concurrent multiscale approach for metals. <em>Physical Review B</em>, <em>73</em>(2), p.024108.</p>
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</ul>Mon, 23 Jul 2018 22:27:25 +0000Phanish Suryanarayanacomment 29734 at https://www.imechanica.orgFaster DFT calculations
https://www.imechanica.org/comment/29733#comment-29733
<a id="comment-29733"></a>
<p><em>In reply to <a href="https://www.imechanica.org/node/22476">Journal Club for July 2018: Mechanics using Quantum Mechanics</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p>Dear Phanish,</p>
<p>I had read with interest this great description which you have written. (Very good condensation.) A thought had struck me right on the first read. However, something else (including travel) came up in the meanwhile. ... Anyway, I am glad that there still is some time left to discuss it...</p>
<p>OK. Refer to your very first paragraph. You mention the cubic scaling with # of atoms, which implies the limitation of only a few hundred atoms. The first thing to strike me when I read it was this: how about multi-gridding?</p>
<p>So I was wondering whether your approach already makes use of it or what. (Sorry, no time to go through the papers you list... So, just asking...)</p>
<p>However, I also did a rapid Google search today and found, e.g., this: <a href="http://homepages.uni-paderborn.de/wgs/Dpubl/pss_217_685.pdf">http://homepages.uni-paderborn.de/wgs/Dpubl/pss_217_685.pdf</a> and this: <a href="https://repository.lib.ncsu.edu/bitstream/handle/1840.2/203/Bernholc_2000_Physical_Review_B_1713.pdf">https://repository.lib.ncsu.edu/bitstream/handle/1840.2/203/Bernholc_200...</a> . Both are c. 2000 papers. There must have been more studies and developments since then.</p>
<p>Could you please share your thoughts on MG for DFT? Is it suitable? Does it work for the kind of (mechanics-related) problems you mention above? What are the constraints for using MG in DFT? ... Would like to know your views... Thanks in advance.</p>
<p>Best,</p>
<p>--Ajit</p>
<p> </p>
<p> </p>
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</ul>Mon, 23 Jul 2018 13:58:36 +0000Ajit R. Jadhavcomment 29733 at https://www.imechanica.orgDFT calculations for dislocations
https://www.imechanica.org/comment/29731#comment-29731
<a id="comment-29731"></a>
<p><em>In reply to <a href="https://www.imechanica.org/node/22476">Journal Club for July 2018: Mechanics using Quantum Mechanics</a></em></p>
<div class="field field-name-comment-body field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><p><span>Dear Phanish:</span></p>
<p>Thanks for the excellent discussion. You mention defects. What is the simplest crystal defect for DFT calculations? Does it have to be a periodic arrangement of defects or it is possible to analyze a single defect? Are you aware of any DFT calculations for dislocations? Thanks. Regards,Arash</p>
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</ul>Mon, 23 Jul 2018 02:38:18 +0000Arash_Yavaricomment 29731 at https://www.imechanica.org