scholarly journals Computational Quantum Chemistry for Multiple-Site Heisenberg Spin Couplings Made Simple: Still Only One Spin–Flip Required

2015 ◽  
Vol 6 (10) ◽  
pp. 1982-1988 ◽  
Author(s):  
Nicholas J. Mayhall ◽  
Martin Head-Gordon
Keyword(s):  
Quantum Chemistry ◽  
Multiple Site ◽  
Heisenberg Spin ◽  
Computational Quantum Chemistry ◽  
Spin Flip ◽  
Computational Quantum

Computational predictions of metal-macrocycle stability constants require accurate treatments of local solvent and pH effects

2021 ◽  
Author(s):  
Brian Gentry ◽  
Tae Hoon Choi ◽  
William S. Belfield ◽  
John A. Keith
Keyword(s):  
Quantum Chemistry ◽  
Rational Design ◽  
Chelating Agents ◽  
Ph Effects ◽  
Detailed Understanding ◽  
Metal Interactions ◽  
Solvent Phase ◽  
Computational Quantum Chemistry ◽  
Computational Predictions ◽  
Computational Quantum

Rational design of molecular chelating agents requires a detailed understanding of physicochemical ligand-metal interactions in solvent phase. Computational quantum chemistry methods should be able to provide this, but computational reports...

scholarly journals Rayleigh-Ritz Majorization Error Bounds for the Linear Response Eigenvalue Problem

2019 ◽  
Vol 17 (1) ◽  
pp. 653-667
Author(s):  
Zhongming Teng ◽  
Hong-Xiu Zhong
Keyword(s):  
Eigenvalue Problem ◽  
Quantum Chemistry ◽  
Error Bounds ◽  
Linear Response ◽  
Computational Quantum Chemistry ◽  
Matrix Anal ◽  
Deflating Subspaces ◽  
Important Notion ◽  
Theoretical Foundations ◽  
Computational Quantum

Abstract In the linear response eigenvalue problem arising from computational quantum chemistry and physics, one needs to compute a few of smallest positive eigenvalues together with the corresponding eigenvectors. For such a task, most of efficient algorithms are based on an important notion that is the so-called pair of deflating subspaces. If a pair of deflating subspaces is at hand, the computed approximated eigenvalues are partial eigenvalues of the linear response eigenvalue problem. In the case the pair of deflating subspaces is not available, only approximate one, in a recent paper [SIAM J. Matrix Anal. Appl., 35(2), pp.765-782, 2014], Zhang, Xue and Li obtained the relationships between the accuracy in eigenvalue approximations and the distances from the exact deflating subspaces to their approximate ones. In this paper, we establish majorization type results for these relationships. From our majorization results, various bounds are readily available to estimate how accurate the approximate eigenvalues based on information on the approximate accuracy of a pair of approximate deflating subspaces. These results will provide theoretical foundations for assessing the relative performance of certain iterative methods in the linear response eigenvalue problem.

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