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Nakatsuji H, Nakashima H. Potential curves of the lower nine states of Li2 molecule: Accurate calculations with the free complement theory and the comparisons with the SAC/SAC-CI results. J Chem Phys 2022; 157:094109. [DOI: 10.1063/5.0101315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The free-complement (FC) theory proposed for solving the Schrödinger equation of atoms and molecules highly accurately was applied to the calculations of the potential curves of the lower nine states of the Li2 molecule. The results were compared with the accurate experimental Rydberg-Klein-Rees (RKR) potential curves available. They overlap completely with each other without any shift everywhere for all the states of Li2. At all the calculated points on the seven potential curves ranging between -14.83 ~ -15.00 hartree, the average difference was only 0.0583 kcal/mol and the maximum difference was only +0.165 kcal/mol. For the vertical excitation energies from the ground state curve to the seven excited states, the differences between theory and experiment were 0.000645 eV in average and their maximum difference was -0.00720 eV. The potential properties calculated with the FC theory also agreed well with the experimental values. These results show a high potentiality of the FC theory as a highly predictive quantum chemistry theory. For comparison, as an example of the Hartree-Fock based theory popular in modern quantum chemistry, we adopted the SAC-CI theory using a highly flexible basis set. While the FC theory gave the absolute agreements with experiments, the SAC-CI potential curves compare reasonably well with experiments only after shifting-down of the SAC-CI curves by 5.727 kcal/mol. The differences of the excitation energies between SAC-CI and experiments were 0.00428 eV in average and the maximum difference was +0.10967 eV. The SAC-CI results reported in 1985 were less accurate but still reasonable.
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Affiliation(s)
- Hiroshi Nakatsuji
- Quantum Chemistry Research Institute, Quantum Chemistry Research Institute, Japan
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Haritan I, Gilary I, Amitay Z, Moiseyev N. Characteristic footprints of an exceptional point in the dynamics of Li dimer under a laser field. J Chem Phys 2015; 143:154308. [PMID: 26493908 DOI: 10.1063/1.4931774] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
Non-hermitian quantum mechanics is a formalism that excels in describing time-dependent states such as resonances. As one, it opens up a window to explore new and undiscovered phenomena. Under this formalism coalescence of two eigenstates and a deficient spectrum are a possible situation. These situations are unique and can occur solely in specific conditions known as Exceptional Points (EPs). An EP holds unique characteristics. One of which is a switch-like behavior: upon adiabatically changing the conditions in a closed loop around the EP, the population of one resonance can be transferred completely to another resonance. The phenomenon was not experimentally observed in an atomic or molecular system so far, although experiments involving nonlinear PT symmetry optics and microwave cavities have already indicated its existence. In this work, we demonstrate and confirm that the switch-like behavior exists in the spectrum of a lithium dimer taking into account both the rotations and the vibrations of the system. Moreover, a footprint of the EP is also shown to exist in the photo-association process of the lithium dimer. In this process, the EP's resonances serve as the mean to associate two free lithium atoms into a dimer. Based on this, we suggest a corresponding experiment to demonstrate for the first time the EP phenomenon in a molecular system.
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Affiliation(s)
- Idan Haritan
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Ido Gilary
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Zohar Amitay
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
| | - Nimrod Moiseyev
- Schulich Faculty of Chemistry, Technion-Israel Institute of Technology, Haifa 32000, Israel
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3
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Sanli A, Beser B, Edwardson JR, Magnier S, Ahmed EH, Marjatta Lyyra A. Electronic transition dipole moment and radiative lifetime calculations of sodium dimer ion-pair states. J Chem Phys 2015; 143:104304. [DOI: 10.1063/1.4929925] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- Aydin Sanli
- Physics Department, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Bediha Beser
- Physics Department, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - John R. Edwardson
- Physics Department, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Sylvie Magnier
- Laboratoire de Physique des Lasers, Atomes et Molecules, UMR-CNRS 8523, Universite Lille 1-Sciences et Technologies, F-559655 Villeneuve d’Ascq, France
| | - Ergin H. Ahmed
- Physics Department, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - A. Marjatta Lyyra
- Physics Department, Temple University, Philadelphia, Pennsylvania 19122, USA
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Musiał M, Kucharski SA. First Principle Calculations of the Potential Energy Curves for Electronic States of the Lithium Dimer. J Chem Theory Comput 2014; 10:1200-11. [DOI: 10.1021/ct401076e] [Citation(s) in RCA: 38] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Monika Musiał
- Institute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice, Poland
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Le Roy RJ, Dattani NS, Coxon JA, Ross AJ, Crozet P, Linton C. Accurate analytic potentials for Li2(X Σ1g+) and Li2(A Σ1u+) from 2 to 90 Å, and the radiative lifetime of Li(2p). J Chem Phys 2009; 131:204309. [DOI: 10.1063/1.3264688] [Citation(s) in RCA: 89] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
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Je¸drzejewski-Szmek Z, Grochola A, Jastrzebski W, Kowalczyk P. The 51Πu electronic state of the lithium dimer. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.07.042] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Qi P, Bai J, Ahmed E, Lyyra AM, Kotochigova S, Ross AJ, Effantin C, Zalicki P, Vigué J, Chawla G, Field RW, Whang TJ, Stwalley WC, Knöckel H, Tiemann E, Shang J, Li L, Bergeman T. New spectroscopic data, spin-orbit functions, and global analysis of data on the AΣu+1 and bΠu3 states of Na2. J Chem Phys 2007; 127:044301. [PMID: 17672684 DOI: 10.1063/1.2747595] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
The lowest electronically excited states of Na2 are of interest as intermediaries in the excitation of higher states and in the development of methods for producing cold molecules. We have compiled previously obtained spectroscopic data on the A 1Sigmau+ and b 3Piu states of Na2 from about 20 sources, both published and unpublished, together with new sub-Doppler linewidth measurements of about 15,000 A<--X transitions using polarization spectroscopy. We also present new ab initio results for the diagonal and off-diagonal spin-orbit functions. The discrete variable representation is used in conjunction with Hund's case a potentials plus spin-orbit effects to model data extending from v=0 to very close to the 3 2S+3 2P12 limit. Empirical estimates of the spin-orbit functions agree well with the ab initio functions for the accessible values of R. The potential function for the A state includes an exchange potential for S+P atoms, with a fitted coefficient somewhat larger than the predicted value. Observed and calculated term values are presented in an auxiliary (EPAPS) file as a database for future studies on Na2.
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Affiliation(s)
- P Qi
- Physics Department, Temple University, Philadelphia, Pennsylvania 19122-6082, USA
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9
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Kubkowska M, Grochola A, Jastrzebski W, Kowalczyk P. The C1Πu and states in Li2: Experiment and comparison with theory. Chem Phys 2007. [DOI: 10.1016/j.chemphys.2007.02.001] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Minaev B. Ab initio study of low-lying triplet states of the lithium dimer. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2005; 62:790-9. [PMID: 16099708 DOI: 10.1016/j.saa.2005.03.006] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2005] [Revised: 03/02/2005] [Accepted: 03/02/2005] [Indexed: 05/04/2023]
Abstract
Observation of Bose-Einstein condensation in Li27 initiated the interest in the scattering length of two ground state lithium atoms when they approach each other as a radical pair triplet aSigmau+3 state. But some properties of this state are still unknown. In present work, a number of low-lying triplet states of lithium molecule are calculated by multi-configuration self-consistent field (MCSCF) and response techniques with account of spin-orbit coupling, spin-spin coupling and some other magnetic perturbations. The singlet-triplet transition probabilities to the ground state are also presented. Most results are connected with the weakly bound lowest triplet a3Sigmau+ state, whose radiative lifetime and spin-splitting are unknown so far in spite of its great importance in Bose-Einstein condensation. Calculations indicate that this state has a very small spin-splitting, lambdass=-0.01 cm-1, which is negligible in comparison with the line-width in experimental Fourier transform spectra published so far. Similar splitting is obtained for the upper state of the 1(3)Sigmag+--a3Sigmau+ transition. This is in agreement with experimental rovibronic analysis of the 1(3)Sigmag+--a3Sigmau+ band system in which the triplet structure was not resolved. The radiative lifetime of the a3Sigmau+ state is predicted to exceed 10 h.
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Affiliation(s)
- Boris Minaev
- State University of Technology, Cherkassy 18006, Ukraine.
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Adohi-Krou A, Martin F, Ross AJ, Linton C, Le Roy RJ. Isotope effects and Born-Oppenheimer breakdown in excited singlet states of the lithium dimer. J Chem Phys 2004; 121:6309-16. [PMID: 15446926 DOI: 10.1063/1.1786920] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Observation of infrared electronic transitions involving the 1 (1)Deltag state of 7Li2 has instigated an investigation of Born-Oppenheimer breakdown in four singlet electronic states correlating with (2s+2s), (2s+2p), and (2p+2p) lithium atoms. The 1 (1)Deltag state, which correlates at long range with (2p+2p) atoms, has been observed in emission from the (5p) (1)Piu Rydberg state and in 1 (1)Deltag-B (1)Piu bands, in both instances following optical-optical double-resonance excitation. The latter transition was observed previously for the lighter isotopomer, 6Li2 [C. Linton, F. Martin, P. Crozet, A. J. Ross, and R. Bacis, J. Mol. Spectrosc. 158, 445 (1993)]. By analyzing multiple-isotopomer data for several electronic systems simultaneously, we have determined the electronic isotope shifts and the leading vibrational and/or rotational Born-Oppenheimer breakdown terms for the X (1)Sigmag+, A (1)Sigmau+, B (1)Piu, and 1 (1)Deltag states of the lithium dimer. This paper also reports Fourier transform measurements of the B-X absorption spectra of 6Li2 and 7Li2, which were required to better define the bottom portion of the B (1)Piu state potential.
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Affiliation(s)
- A Adohi-Krou
- Laboratoire de Spectrometrie Ionique et Moleculaire, CNRS et Universite Lyon I (UMR 5579) Domaine Scientifique de la Doua, 69626 Villeurbanne, France
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