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Ireland R, Jeszenszki P, Mátyus E, Martinazzo R, Ronto M, Pollak E. Lower Bounds for Nonrelativistic Atomic Energies. ACS PHYSICAL CHEMISTRY AU 2021; 2:23-37. [PMID: 35098243 PMCID: PMC8796283 DOI: 10.1021/acsphyschemau.1c00018] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/27/2021] [Indexed: 11/29/2022]
Abstract
A recently developed lower bound theory for Coulombic problems (E. Pollak, R. Martinazzo, J. Chem. Theory Comput. 2021, 17, 1535) is further developed and applied to the highly accurate calculation of the ground-state energy of two- (He, Li+, and H-) and three- (Li) electron atoms. The method has been implemented with explicitly correlated many-particle basis sets of Gaussian type, on the basis of the highly accurate (Ritz) upper bounds they can provide with relatively small numbers of functions. The use of explicitly correlated Gaussians is developed further for computing the variances, and the necessary modifications are here discussed. The computed lower bounds are of submilli-Hartree (parts per million relative) precision and for Li represent the best lower bounds ever obtained. Although not yet as accurate as the corresponding (Ritz) upper bounds, the computed bounds are orders of magnitude tighter than those obtained with other lower bound methods, thereby demonstrating that the proposed method is viable for lower bound calculations in quantum chemistry applications. Among several aspects, the optimization of the wave function is shown to play a key role for both the optimal solution of the lower bound problem and the internal check of the theory.
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Affiliation(s)
- Robbie
T. Ireland
- Institute
of Chemistry, ELTE, Eötvös
Loránd University, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary,School of
Chemistry, University of Glasgow, University Avenue, G12 8QQ, Glasgow, United Kingdom
| | - Peter Jeszenszki
- Institute
of Chemistry, ELTE, Eötvös
Loránd University, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary
| | - Edit Mátyus
- Institute
of Chemistry, ELTE, Eötvös
Loránd University, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary,E-mail:
| | - Rocco Martinazzo
- Department
of Chemistry, University of Milan, Milan, 20122, Italy,Institute of Molecular Science and Technologies
(ISTM), Consiglio
Nazionale delle Ricerche (CNR), Milan, 20133, Italy,
| | - Miklos Ronto
- Chemical
and Biological Physics Department, Weizmann
Institute of Science, 76100, Rehovot, Israel
| | - Eli Pollak
- Chemical
and Biological Physics Department, Weizmann
Institute of Science, 76100, Rehovot, Israel,
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Muolo A, Mátyus E, Reiher M. H 3 + as a five-body problem described with explicitly correlated Gaussian basis sets. J Chem Phys 2019; 151:154110. [PMID: 31640358 DOI: 10.1063/1.5121318] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Various explicitly correlated Gaussian (ECG) basis sets are considered for the solution of the molecular Schrödinger equation with particular attention to the simplest polyatomic system, H3 +. Shortcomings and advantages are discussed for plain ECGs, ECGs with the global vector representation, floating ECGs and their numerical projection, and ECGs with complex parameters. The discussion is accompanied with particle density plots to visualize the observations. In order to be able to use large complex ECG basis sets in molecular calculations, a numerically stable algorithm is developed, the efficiency of which is demonstrated for the lowest rotationally and vibrationally excited states of H2 and H3 +.
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Affiliation(s)
- Andrea Muolo
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Edit Mátyus
- Institute of Chemistry, ELTE, Eötvös Loránd University, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Markus Reiher
- ETH Zürich, Laboratory of Physical Chemistry, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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