Spectral Quadrature method for accurate electronic structure calculations of metals and insulators

详细信息    查看全文

• 作者：Phanisri P. Pratapa^a ; Phanish Suryanarayana^a ; ^{phanish.suryanarayana@ce.gatech.edu" class="auth_mail" title="E-mail the corresponding author} ; John E. Pask^b
• 关键词：Density Functional Theory ; Spectral quadrature ; Clenshaw&ndash ; Curtis ; Linear-scaling ; Metallic systems ; Atomic forces
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：200
• 期：Complete
• 页码：96-107
• 全文大小：728 K

文摘

We present the Clenshaw–Curtis Spectral Quadrature (SQ) method for real-space b=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515004166&_mathId=si29.gif&_user=111111111&_pii=S0010465515004166&_rdoc=1&_issn=00104655&md5=7a234c808a1a87d7269277cd8c193aae" title="Click to view the MathML source">O(N)$\mathcal{O}\left(N\right)$ Density Functional Theory (DFT) calculations. In this approach, all quantities of interest are expressed as bilinear forms or sums over bilinear forms, which are then approximated by spatially localized Clenshaw–Curtis quadrature rules. This technique is identically applicable to both insulating and metallic systems, and in conjunction with local reformulation of the electrostatics, enables the b=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515004166&_mathId=si29.gif&_user=111111111&_pii=S0010465515004166&_rdoc=1&_issn=00104655&md5=7a234c808a1a87d7269277cd8c193aae" title="Click to view the MathML source">O(N)$\mathcal{O}\left(N\right)$ evaluation of the electronic density, energy, and atomic forces. The SQ approach also permits infinite-cell calculations without recourse to Brillouin zone integration or large supercells. We employ a finite difference representation in order to exploit the locality of electronic interactions in real space, enable systematic convergence, and facilitate large-scale parallel implementation. In particular, we derive expressions for the electronic density, total energy, and atomic forces that can be evaluated in b=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515004166&_mathId=si29.gif&_user=111111111&_pii=S0010465515004166&_rdoc=1&_issn=00104655&md5=7a234c808a1a87d7269277cd8c193aae" title="Click to view the MathML source">O(N)$\mathcal{O}\left(N\right)$ operations. We demonstrate the systematic convergence of energies and forces with respect to quadrature order as well as truncation radius to the exact diagonalization result. In addition, we show convergence with respect to mesh size to established b=MathURL&_method=retrieve&_eid=1-s2.0-S0010465515004166&_mathId=si33.gif&_user=111111111&_pii=S0010465515004166&_rdoc=1&_issn=00104655&md5=aa9de04966f7f9b14ed820d2fad4365a" title="Click to view the MathML source">O(N³)$\mathcal{O}\left(N^3\right)$ planewave results. Finally, we establish the efficiency of the proposed approach for high temperature calculations and discuss its particular suitability for large-scale parallel computation.