Improvements on the minimax algorithm for the Laplace transformation of orbital energy denominators

详细信息    查看全文

• 作者：Benjamin Helmich-Paris ; ^{b.helmichparis@vu.nl" class="auth_mail" title="E-mail the corresponding author} ; Lucas Visscher ^{l.visscher@vu.nl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Laplace transformation ; Mø ; ller&ndash ; Plesset perturbation theory ; Remez algorithm ; Newton&ndash ; Maehly algorithm ; Deflation
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：321
• 期：Complete
• 页码：927-931
• 全文大小：234 K

文摘

We present a robust and non-heuristic algorithm that finds all extremum points of the error distribution function of numerically Laplace-transformed orbital energy denominators. The extremum point search is one of the two key steps for finding the minimax approximation. If pre-tabulation of initial guesses is supposed to be avoided, strategies for a sufficiently robust algorithm have not been discussed so far. We compare our non-heuristic approach with a bracketing and bisection algorithm and demonstrate that 3 times less function evaluations are required altogether when applying it to typical non-relativistic and relativistic quantum chemical systems.