Publisher DOI: 10.1021/acs.jctc.0c00497
Title: Rigorous lower bounds for the ground state energy of molecules by employing necessary N-representability conditions
Language: English
Authors: Chaykin, Denis 
Jansson, Christian 
Keil, Frerich 
Lange, Marko 
Ohlhus, Kai Torben  
Rump, Siegfried M.  
Issue Date: 13-Nov-2020
Source: Journal of Chemical Theory and Computation 12 (16): 7342-7356 (2020)
Journal: Journal of chemical theory and computation 
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 or numerically more exact for a given basis set by full CI. However, Nakata et al. ( J. Chem. Phys.200111482828292) observed that due to numerical errors the semidefinite solver produced erroneous results with a lower bound significantly larger than the full CI energy. For the LiH, CH–, NH–, OH, OH–, and HF molecules violations within one mhartree were observed. We applied the software VSDP which takes all numerical errors due to floating-point arithmetic operations into consideration. For two test libraries VSDP provides tight rigorous error bounds lower than full CI energies reported with an accuracy of 0.1 to 0.01 mhartree. Only little computation work must be spent in order to compute close rigorous error bounds for the ground state energy.
ISSN: 1549-9618
Institute: Chemische Reaktionstechnik V-2 
Zuverlässiges Rechnen E-19 
Document Type: Article
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