|Publisher URL:||http://www.optimization-online.org/DB_HTML/2016/11/5730.html||Title:||Rigorous results in electronic structure calculations||Language:||English||Authors:||Chaykin, Denis
Ohlhus, Kai Torben
Rump, Siegfried M.
|Issue Date:||Nov-2016||Source:||Optimization online: 1-37 (2016)||Journal:||Optimization online||Abstract (english):||
Electronic structure calculations, in particular the computation of the ground state energy, lead to challenging problems in optimization. These problems are of enormous importance in quantum chemistry for calculations of properties of solids and molecules. Minimization methods for computing the ground state energy can be developed by employing a variational approach, where the second-order reduced density matrix defines the variable. This concept leads to large-scale semidefinite programming problems that provide a lower bound for the ground state energy. Upper bounds of the ground state energy can be calculated for example with the Hartree-Fock method. However, Nakata, Nakatsuji, Ehara, Fukuda, Nakata, and Fujisawa observed, that due to numerical errors the semidefinite solver produced erroneous results with a lower bound significantly larger than the Hartree-Fock upper bound. Violations within one mhartree were observed. We present here a method for solving electronic structure problems where all numerical errors are taken into consideration. In particular this method provides rigorous error bounds without violations as mentioned above.
|URI:||http://hdl.handle.net/11420/7814||Institute:||Chemische Reaktionstechnik V-2
Zuverlässiges Rechnen E-19
|Appears in Collections:||Publications without fulltext|
Show full item record
checked on Dec 5, 2021
Add Files to Item
Note about this record
Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.