51
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Charry J, Pedraza-González L, Reyes A. On the physical interpretation of the nuclear molecular orbital energy. J Chem Phys 2017; 146:214103. [PMID: 28576090 PMCID: PMC5453789 DOI: 10.1063/1.4984098] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2017] [Accepted: 05/11/2017] [Indexed: 11/14/2022] Open
Abstract
Recently, several groups have extended and implemented molecular orbital (MO) schemes to simultaneously obtain wave functions for electrons and selected nuclei. Many of these schemes employ an extended Hartree-Fock approach as a first step to find approximate electron-nuclear wave functions and energies. Numerous studies conducted with these extended MO methodologies have explored various effects of quantum nuclei on physical and chemical properties. However, to the best of our knowledge no physical interpretation has been assigned to the nuclear molecular orbital energy (NMOE) resulting after solving extended Hartree-Fock equations. This study confirms that the NMOE is directly related to the molecular electrostatic potential at the position of the nucleus.
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Affiliation(s)
- Jorge Charry
- Department of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30 #45-03, Bogotá, Colombia
| | - Laura Pedraza-González
- Department of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30 #45-03, Bogotá, Colombia
| | - Andrés Reyes
- Department of Chemistry, Universidad Nacional de Colombia, Ave. Cra. 30 #45-03, Bogotá, Colombia
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52
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Gharabaghi M, Shahbazian S. Incorporating nuclear vibrational energies into the "atom in molecules" analysis: An analytical study. J Chem Phys 2017; 146:154106. [PMID: 28433028 DOI: 10.1063/1.4979994] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Abstract
The quantum theory of atoms in molecules (QTAIM) is based on the clamped nucleus paradigm and solely working with the electronic wavefunctions, so does not include nuclear vibrations in the AIM analysis. On the other hand, the recently extended version of the QTAIM, called the multi-component QTAIM (MC-QTAIM), incorporates both electrons and quantum nuclei, i.e., those nuclei treated as quantum waves instead of clamped point charges, into the AIM analysis using non-adiabatic wavefunctions. Thus, the MC-QTAIM is the natural framework to incorporate the role of nuclear vibrations into the AIM analysis. In this study, within the context of the MC-QTAIM, the formalism of including nuclear vibrational energy in the atomic basin energy is developed in detail and its contribution is derived analytically using the recently proposed non-adiabatic Hartree product nuclear wavefunction. It is demonstrated that within the context of this wavefunction, the quantum nuclei may be conceived pseudo-adiabatically as quantum oscillators and both isotropic harmonic and anisotropic anharmonic oscillator models are used to compute the zero-point nuclear vibrational energy contribution to the basin energies explicitly. Inspired by the results gained within the context of the MC-QTAIM analysis, a heuristic approach is proposed within the context of the QTAIM to include nuclear vibrational energy in the basin energy from the vibrational wavefunction derived adiabatically. The explicit calculation of the basin contribution of the zero-point vibrational energy using the uncoupled harmonic oscillator model leads to results consistent with those derived from the MC-QTAIM.
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Affiliation(s)
- Masumeh Gharabaghi
- Faculty of Chemical and Petroleum Sciences, Shahid Beheshti University, G. C., Evin, P.O. Box 19395-4716, 19839 Tehran, Iran
| | - Shant Shahbazian
- Department of Physics, Shahid Beheshti University, G. C., Evin, P.O. Box 19395-4716, 19839 Tehran, Iran
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53
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Bubin S, Adamowicz L. Lowest ^{2}S Electronic Excitations of the Boron Atom. PHYSICAL REVIEW LETTERS 2017; 118:043001. [PMID: 28186809 DOI: 10.1103/physrevlett.118.043001] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2016] [Indexed: 06/06/2023]
Abstract
A theoretical ab initio approach for calculating bound states of small atoms is developed and implemented. The approach is based on finite-nuclear-mass [non-Born-Oppenheimer (non-BO)] nonrelativistic variational calculations performed with all-particle explicitly correlated Gaussian functions and includes the leading relativistic and quantum electrodynamics energy corrections determined using the non-BO wave functions. The approach is applied to determine the total and transition energies for the lowest four ^{2}S electronic excitations of the boron atom. The transition energies agree with the available experimental values within 0.2-0.3 cm^{-1}. Previously, such accuracy was achieved for three- and four-electron systems.
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Affiliation(s)
- Sergiy Bubin
- Department of Physics, School of Science and Technology, Nazarbayev University, Astana 010000, Kazakhstan
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
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54
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Joyce T, Varga K. Matrix elements of explicitly correlated Gaussian basis functions with arbitrary angular momentum. J Chem Phys 2016; 144:184106. [PMID: 27179470 DOI: 10.1063/1.4948708] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new algorithm for calculating the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for quantum-mechanical calculations of atoms with arbitrary angular momentum is presented. The calculations are checked on several excited states of three and four electron systems. The presented formalism can be used as unified framework for high accuracy calculations of properties of small atoms and molecules.
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Affiliation(s)
- Tennesse Joyce
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
| | - Kálmán Varga
- Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee 37235, USA
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55
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Stanke M, Palikot E, Adamowicz L. Algorithms for calculating mass-velocity and Darwin relativistic corrections with n-electron explicitly correlated Gaussians with shifted centers. J Chem Phys 2016; 144:174101. [PMID: 27155619 DOI: 10.1063/1.4947553] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Algorithms for calculating the leading mass-velocity (MV) and Darwin (D) relativistic corrections are derived for electronic wave functions expanded in terms of n-electron explicitly correlated Gaussian functions with shifted centers and without pre-exponential angular factors. The algorithms are implemented and tested in calculations of MV and D corrections for several points on the ground-state potential energy curves of the H2 and LiH molecules. The algorithms are general and can be applied in calculations of systems with an arbitrary number of electrons.
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Affiliation(s)
- Monika Stanke
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, ul. Grudzia̧dzka 5, Toruń, PL 87-100, Poland
| | - Ewa Palikot
- Institute of Physics, Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, ul. Grudzia̧dzka 5, Toruń, PL 87-100, Poland
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry and Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
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56
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Jones K, Kirnosov N, Sharkey KL, Adamowicz L. Charge asymmetry and rovibrational excitations of HD+. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1177666] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Keith Jones
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
| | - Nikita Kirnosov
- Department of Physics, University of Arizona, Tucson, AZ, USA
| | - Keeper L. Sharkey
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ, USA
- Department of Physics, University of Arizona, Tucson, AZ, USA
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57
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Ludeña EV, Iza P, Cornejo M, Zambrano D. Non-Born–Oppenheimer electron, nuclear and nuclear–electron second-order density matrices for exactly solvable four-particle model system. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1840-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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58
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Bubin S, Formanek M, Adamowicz L. Universal all-particle explicitly-correlated Gaussians for non-Born–Oppenheimer calculations of molecular rotationless states. Chem Phys Lett 2016. [DOI: 10.1016/j.cplett.2016.01.056] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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59
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Goli M, Shahbazian S. Muon-Substituted Malonaldehyde: Transforming a Transition State into a Stable Structure by Isotope Substitution. Chemistry 2016; 22:2525-31. [PMID: 26749489 DOI: 10.1002/chem.201504318] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2015] [Indexed: 12/25/2022]
Abstract
Isotope substitutions are usually conceived to play a marginal role on the structure and bonding pattern of molecules. However, a recent study [Angew. Chem. Int. Ed. 2014, 53, 13706-13709; Angew. Chem. 2014, 126, 13925-13929] further demonstrates that upon replacing a proton with a positively charged muon, as the lightest radioisotope of hydrogen, radical changes in the nature of the structure and bonding of certain species may take place. The present report is a primary attempt to introduce another example of structural transformation on the basis of the malonaldehyde system. Accordingly, upon replacing the proton between the two oxygen atoms of malonaldehyde with the positively charged muon a serious structural transformation is observed. By using the ab initio nuclear-electronic orbital non-Born-Oppenheimer procedure, the nuclear configuration of the muon-substituted species is derived. The resulting nuclear configuration is much more similar to the transition state of the proton transfer in malonaldehyde rather than to the stable configuration of malonaldehyde. The comparison of the "atoms in molecules" (AIM) structure of the muon-substituted malonaldehyde and the AIM structure of the stable and the transition-state configurations of malonaldehyde also unequivocally demonstrates substantial similarities of the muon-substituted malonaldehyde to the transition state.
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Affiliation(s)
- Mohammad Goli
- Faculty of Chemistry, Shahid Beheshti University, G. C., Evin, P.O. Box 19395-4716, Tehran, 19839, Iran), Fax
| | - Shant Shahbazian
- Faculty of Chemistry, Shahid Beheshti University, G. C., Evin, P.O. Box 19395-4716, Tehran, 19839, Iran), Fax.
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60
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Kirnosov N, Sharkey KL, Adamowicz L. Ortho–para nuclear-spin isomerization energies for all bound vibrational states of ditritium (T2) from non-Born–Oppenheimer variational calculations performed with explicitly correlated all-particle Gaussian functions. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.10.017] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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61
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62
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Yang Y, Kylänpää I, Tubman NM, Krogel JT, Hammes-Schiffer S, Ceperley DM. How large are nonadiabatic effects in atomic and diatomic systems? J Chem Phys 2015; 143:124308. [DOI: 10.1063/1.4931667] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yubo Yang
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
| | - Ilkka Kylänpää
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
- Department of Physics, Tampere University of Technology, P.O. Box 692, FI-33101 Tampere, Finland
| | - Norm M. Tubman
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
| | - Jaron T. Krogel
- Oak Ridge National Laboratory, Materials Sciences & Technology Division, Oak Ridge, Tennessee 37831, USA
| | | | - David M. Ceperley
- Department of Physics, University of Illinois, Urbana, Illinois 61801, USA
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63
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Sirjoosingh A, Pak MV, Brorsen KR, Hammes-Schiffer S. Quantum treatment of protons with the reduced explicitly correlated Hartree-Fock approach. J Chem Phys 2015; 142:214107. [DOI: 10.1063/1.4921303] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Andrew Sirjoosingh
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
| | - Michael V. Pak
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
| | - Kurt R. Brorsen
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
| | - Sharon Hammes-Schiffer
- Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Ave., Urbana, Illinois 61801, USA
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64
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Nakatsuji H, Nakashima H. Solving the Schrödinger equation of molecules by relaxing the antisymmetry rule: Inter-exchange theory. J Chem Phys 2015; 142:194101. [DOI: 10.1063/1.4919843] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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65
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Mátyus E, Szidarovszky T, Császár AG. Modelling non-adiabatic effects in H₃⁺: solution of the rovibrational Schrödinger equation with motion-dependent masses and mass surfaces. J Chem Phys 2015; 141:154111. [PMID: 25338885 DOI: 10.1063/1.4897566] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Introducing different rotational and vibrational masses in the nuclear-motion Hamiltonian is a simple phenomenological way to model rovibrational non-adiabaticity. It is shown on the example of the molecular ion H3(+), for which a global adiabatic potential energy surface accurate to better than 0.1 cm(-1) exists [M. Pavanello, L. Adamowicz, A. Alijah, N. F. Zobov, I. I. Mizus, O. L. Polyansky, J. Tennyson, T. Szidarovszky, A. G. Császár, M. Berg et al., Phys. Rev. Lett. 108, 023002 (2012)], that the motion-dependent mass concept yields much more accurate rovibrational energy levels but, unusually, the results are dependent upon the choice of the embedding of the molecule-fixed frame. Correct degeneracies and an improved agreement with experimental data are obtained if an Eckart embedding corresponding to a reference structure of D(3h) point-group symmetry is employed. The vibrational mass of the proton in H3(+) is optimized by minimizing the root-mean-square (rms) deviation between the computed and recent high-accuracy experimental transitions. The best vibrational mass obtained is larger than the nuclear mass of the proton by approximately one third of an electron mass, m(opt,p)((v))=m(nuc,p)+0.31224m(e). This optimized vibrational mass, along with a nuclear rotational mass, reduces the rms deviation of the experimental and computed rovibrational transitions by an order of magnitude. Finally, it is shown that an extension of the algorithm allowing the use of motion-dependent masses can deal with coordinate-dependent mass surfaces in the rovibrational Hamiltonian, as well.
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Affiliation(s)
- Edit Mátyus
- Institute of Chemistry, Eötvös University, P.O. Box 32, H-1518 Budapest 112, Hungary
| | - Tamás Szidarovszky
- MTA-ELTE Research Group on Complex Chemical Systems, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
| | - Attila G Császár
- Institute of Chemistry, Eötvös University, P.O. Box 32, H-1518, Budapest 112, Hungary and MTA-ELTE Research Group on Complex Chemical Systems, Pázmány Péter sétány 1/A, H-1117 Budapest, Hungary
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66
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Sharkey KL, Kirnosov N, Adamowicz L. Direct non-Born-Oppenheimer variational calculations of all bound vibrational states corresponding to the first rotational excitation of D 2 performed with explicitly correlated all-particle Gaussian functions. J Chem Phys 2015; 142:174307. [DOI: 10.1063/1.4919417] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Affiliation(s)
- Keeper L. Sharkey
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA
| | - Nikita Kirnosov
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
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67
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Para–ortho isomerization of H2+. Non-Born–Oppenheimer direct variational calculations with explicitly correlated all-particle Gaussian functions. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2014.12.060] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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68
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Goli M, Shahbazian S. Hidden aspects of the Structural theory of chemistry: MC-QTAIM analysis reveals "alchemical" transformation from a triatomic to a diatomic structure. Phys Chem Chem Phys 2015; 17:245-55. [PMID: 25388361 DOI: 10.1039/c4cp03722g] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
The Structural theory of chemistry introduces chemical/molecular structure as a combination of relative arrangement and bonding patterns of atoms in a molecule. Nowadays, the structure of atoms in molecules is derived from the topological analysis of the quantum theory of atoms in molecules (QTAIM). In this context, a molecular structure is varied by large geometrical variations and concomitant reorganization of electronic structure that usually take place in chemical reactions or under extreme hydrostatic pressure. In this report, a new mode of structural variation is introduced within the context of the newly proposed multi-component QTAIM (MC-QTAIM) that originates from the mass variation of nuclei. Accordingly, XCN and CNX series of species are introduced where X stands for a quantum particle with a unit of positive charge and a variable mass that is varied in discrete steps between the mass of a proton and a positron. Ab initio non-Born-Oppenheimer (non-BO) calculations are done on both series of species and the resulting non-BO wavefunctions are used for the MC-QTAIM analysis, revealing a triatomic structure for the proton mass and a diatomic structure for the positron mass. In both series of species, a critical mass between that of proton and positron mass is discovered where the transition from triatomic to diatomic structure takes place. This abrupt structural transformation has a topological nature resembling the usual phase transitions in thermodynamics. The discovered mass-induced structural transformation is a hidden aspect of the Structural theory which is revealed only beyond the BO paradigm, when nuclei are treated as quantum waves instead of clamped point charges.
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Affiliation(s)
- Mohammad Goli
- Faculty of Chemistry, Shahid Beheshti University, G. C., Evin, P.O. Box 19395-4716, Tehran, Iran19839.
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69
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Petrignani A, Berg MH, Grussie F, Wolf A, Mizus II, Polyansky OL, Tennyson J, Zobov NF, Pavanello M, Adamowicz L. Communication: Visible line intensities of the triatomic hydrogen ion from experiment and theory. J Chem Phys 2014; 141:241104. [DOI: 10.1063/1.4904440] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Affiliation(s)
- Annemieke Petrignani
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
| | - Max H. Berg
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
| | - Florian Grussie
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
| | - Andreas Wolf
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany
| | - Irina I. Mizus
- Institute of Applied Physics, Russian Academy of Science, Ulyanov Street 46, Nizhnii Novgorod 603950, Russia
| | - Oleg L. Polyansky
- Institute of Applied Physics, Russian Academy of Science, Ulyanov Street 46, Nizhnii Novgorod 603950, Russia
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Jonathan Tennyson
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Nikolai F. Zobov
- Institute of Applied Physics, Russian Academy of Science, Ulyanov Street 46, Nizhnii Novgorod 603950, Russia
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, The University of Arizona, Tucson, Arizona 85721, USA
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70
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Formanek M, Sharkey KL, Kirnosov N, Adamowicz L. A comparison of two types of explicitly correlated Gaussian functions for non-Born-Oppenheimer molecular calculations using a model potential. J Chem Phys 2014; 141:154103. [PMID: 25338877 DOI: 10.1063/1.4897634] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new functional form of the explicitly correlated Gaussian-type functions (later called Gaussians or ECGs) for performing non-Born-Oppenheimer (BO) calculations of molecular systems with an arbitrary number of nuclei is presented. In these functions, the exponential part explicitly depends on all interparticle distances and the preexponential part depends only on the distances between the nuclei. The new Gaussians are called sin/cos-Gaussians and their preexponential part is a product of sin and/or cos factors. The effectiveness of the new Gaussians in describing non-BO pure vibrational states is investigated by comparing them with r(m)-Gaussians containing preexponential multipliers in the form of non-negative powers of internuclear distances (the internuclear distance in the diatomic case). The testing is performed for a diatomic system with the nuclei interacting through a Morse potential. It shows that the new sin/cos-Gaussian basis set is capable of providing equally accurate results as obtained with the r(m)-Gaussians. However, especially for lower vibrational states, more sin/cos-Gaussians are needed to reach a similar accuracy level as obtained with the r(m)-Gaussians. Implementation of the sin/cos-Gaussians in non-BO calculations of diatomic and, in particular, of triatomic systems, which will follow, will provide further assessment of the efficiency of the new functions.
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Affiliation(s)
- Martin Formanek
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
| | - Keeper L Sharkey
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA
| | - Nikita Kirnosov
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
| | - Ludwik Adamowicz
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
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71
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Simmen B, Mátyus E, Reiher M. Electric transition dipole moment in pre-Born-Oppenheimer molecular structure theory. J Chem Phys 2014; 141:154105. [PMID: 25338879 DOI: 10.1063/1.4897632] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This paper presents the calculation of the electric transition dipole moment in a pre-Born-Oppenheimer framework. Electrons and nuclei are treated equally in terms of the parametrization of the non-relativistic total wave function, which is written as a linear combination of basis functions constructed from explicitly correlated Gaussian functions and the global vector representation. The integrals of the electric transition dipole moment are derived corresponding to these basis functions in both the length and the velocity representation. The calculations are performed in laboratory-fixed Cartesian coordinates without relying on coordinates which separate the center of mass from the translationally invariant degrees of freedom. The effect of the overall motion is eliminated through translationally invariant integral expressions. The electric transition dipole moment is calculated between two rovibronic levels of the H2 molecule assignable to the lowest rovibrational states of the X (1)Σ(g)(+) and B (1)Σ(u)(+) electronic states in the clamped-nuclei framework. This is the first evaluation of this quantity in a full quantum mechanical treatment without relying on the Born-Oppenheimer approximation.
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Affiliation(s)
- Benjamin Simmen
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Edit Mátyus
- Eövtös University, Institute of Chemistry, P.O. Box 32, H-1518, Budapest 112, Hungary
| | - Markus Reiher
- ETH Zürich, Laboratorium für Physikalische Chemie, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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72
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Stanke M, Adamowicz L. Non-Born-Oppenheimer calculations of the pure vibrational spectrum of T₂ including relativistic corrections. J Chem Phys 2014; 141:154302. [PMID: 25338891 DOI: 10.1063/1.4897631] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
Abstract
We report very accurate calculations of the complete pure vibrational spectrum of the T2 molecule with an approach where the Born-Oppenheimer (BO) approximation is not assumed. As the considered states correspond to the zero total angular momentum, their non-BO wave functions are spherically symmetric and are expanded in terms of all-particle, one-center, spherically symmetric explicitly correlated Gaussian functions multiplied by even nonnegative powers of the internuclear distance. The nonrelativistic energies of the states obtained in the non-BO calculations are corrected for the relativistic effects of the order of α(2) (where α is the fine structure constant) calculated as expectation values of the operators representing these effects.
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Affiliation(s)
- Monika Stanke
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudzia̧dzka 5, 87-100 Toruń, Poland
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA
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73
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Sims JS, Hagstrom SA. Hylleraas-configuration-interaction nonrelativistic energies for the 1S ground states of the beryllium isoelectronic sequence. J Chem Phys 2014; 140:224312. [DOI: 10.1063/1.4881639] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023] Open
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74
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Sharkey KL, Adamowicz L. An algorithm for nonrelativistic quantum-mechanical finite-nuclear-mass variational calculations of nitrogen atom inL= 0,M= 0 states using all-electrons explicitly correlated Gaussian basis functions. J Chem Phys 2014; 140:174112. [DOI: 10.1063/1.4873916] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
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75
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Tung WC, Adamowicz L. Accurate potential energy curve of the LiH+ molecule calculated with explicitly correlated Gaussian functions. J Chem Phys 2014; 140:124315. [DOI: 10.1063/1.4869517] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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76
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Kirnosov N, Sharkey K, Adamowicz L. Charge asymmetry in the rovibrationally excited HD molecule. J Chem Phys 2014; 140:104115. [PMID: 24628160 DOI: 10.1063/1.4867912] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
Abstract
The recently developed method for performing all-particle non-Born-Oppenheimer variational calculations on diatomic molecular systems excited to the first excited rotational state and simultaneously vibrationally excited is employed to study the charge asymmetry and the level lifetimes of the HD molecule. The method uses all-particle explicitly correlated Gaussian functions. The nonlinear parameters of the Gaussians are optimized with the aid of the analytical energy gradient determined with respect to these parameters.
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Affiliation(s)
- Nikita Kirnosov
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
| | - Keeper Sharkey
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA
| | - Ludwik Adamowicz
- Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
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77
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Bubin S, Adamowicz L. Prediction of (1)P Rydberg energy levels of beryllium based on calculations with explicitly correlated Gaussians. J Chem Phys 2014; 140:024301. [PMID: 24437871 DOI: 10.1063/1.4858275] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Benchmark variational calculations are performed for the seven lowest 1s(2)2s np ((1)P), n = 2...8, states of the beryllium atom. The calculations explicitly include the effect of finite mass of (9)Be nucleus and account perturbatively for the mass-velocity, Darwin, and spin-spin relativistic corrections. The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. Basis sets of up to 12,500 optimized Gaussians are used. The maximum discrepancy between the calculated nonrelativistic and experimental energies of 1s(2)2s np ((1)P) →1s(2)2s(2) ((1)S) transition is about 12 cm(-1). The inclusion of the relativistic corrections reduces the discrepancy to bellow 0.8 cm(-1).
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Affiliation(s)
- Sergiy Bubin
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Ludwik Adamowicz
- Department of Chemistry and Biochemistry and Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
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78
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Bubin S, Prezhdo OV. Excited states of positronic lithium and beryllium. PHYSICAL REVIEW LETTERS 2013; 111:193401. [PMID: 24266470 DOI: 10.1103/physrevlett.111.193401] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2013] [Revised: 09/19/2013] [Indexed: 06/02/2023]
Abstract
Using a variational method with an explicitly correlated Gaussian basis, we study the e(+)-Li and e(+)-Be complexes in the ground and lowest excited states with higher spin multiplicity. Our calculations provide rigorous theoretical confirmation that a positron can be attached to the excited states: 1s2s2p 4P(o) and 1s²2s2p 3P(o) for e(+)-Li and e(+)-Be, respectively. The result is particularly notable for the e(+)-Be complex, as the excited 3P(o) state lies below the autoionization threshold. We report accurate binding energies, annihilation rates and structural properties of these positron-atom systems. The existence of the ground and metastable excited states with bound positron opens up a new route to the presently lacking experimental verification of stability of a positron binding to any neutral atom.
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Affiliation(s)
- Sergiy Bubin
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
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79
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Sharkey KL, Kirnosov N, Adamowicz L. An algorithm for non-Born-Oppenheimer quantum mechanical variational calculations of N = 1 rotationally excited states of diatomic molecules using all-particle explicitly correlated Gaussian functions. J Chem Phys 2013; 139:164119. [PMID: 24182016 DOI: 10.1063/1.4826450] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
An algorithm for quantum mechanical variational calculations of bound states of diatomic molecules corresponding to the total angular momentum quantum number equal to one (N = 1) is derived and implemented. The approach employs all-particle explicitly correlated Gaussian function for the wave-function expansion. The algorithm is tested in the calculations of the N = 1, v = 0, ..., 22 states of the HD(+) ion.
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Affiliation(s)
- Keeper L Sharkey
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA
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80
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Lesiuk M, Jeziorski B, Moszynski R. On the large interelectronic distance behavior of the correlation factor for explicitly correlated wave functions. J Chem Phys 2013; 139:134102. [DOI: 10.1063/1.4822045] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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81
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Sirjoosingh A, Pak MV, Swalina C, Hammes-Schiffer S. Reduced explicitly correlated Hartree-Fock approach within the nuclear-electronic orbital framework: Applications to positronic molecular systems. J Chem Phys 2013; 139:034103. [DOI: 10.1063/1.4812259] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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82
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Sirjoosingh A, Pak MV, Swalina C, Hammes-Schiffer S. Reduced explicitly correlated Hartree-Fock approach within the nuclear-electronic orbital framework: Theoretical formulation. J Chem Phys 2013; 139:034102. [DOI: 10.1063/1.4812257] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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83
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Aguirre NF, Villarreal P, Delgado-Barrio G, Posada E, Reyes A, Biczysko M, Mitrushchenkov AO, de Lara-Castells MP. Including nuclear quantum effects into highly correlated electronic structure calculations of weakly bound systems. J Chem Phys 2013; 138:184113. [DOI: 10.1063/1.4803546] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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84
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Goli M, Shahbazian S. Toward the multi-component quantum theory of atoms in molecules: a variational derivation. Theor Chem Acc 2013. [DOI: 10.1007/s00214-013-1365-5] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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85
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Simmen B, Mátyus E, Reiher M. Elimination of the translational kinetic energy contamination in pre-Born–Oppenheimer calculations. Mol Phys 2013. [DOI: 10.1080/00268976.2013.783938] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Benjamin Simmen
- ETH Zurich, Laboratorium für Physikalische Chemie, , Zurich, Switzerland
| | - Edit Mátyus
- Laboratory of Molecular Structure and Dynamics, Institute of Chemistry, Eötvös University, Pázmány Péter sétány , Budapest, Hungary
| | - Markus Reiher
- ETH Zurich, Laboratorium für Physikalische Chemie, , Zurich, Switzerland
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86
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Tung WC, Pavanello M, Sharkey KL, Kirnosov N, Adamowicz L. Analytical energy gradient used in variational Born-Oppenheimer calculations with all-electron explicitly correlated Gaussian functions for molecules containing one π electron. J Chem Phys 2013; 138:124101. [PMID: 23556703 DOI: 10.1063/1.4795094] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An algorithm for variational calculations of molecules with one π electron performed with all-electron explicitly correlated gaussian (ECG) functions with floating centers is derived and implemented. The algorithm includes the analytic gradient of the Born-Oppenheimer electronic energy determined with respect to the ECG exponential parameters and the coordinates of the gaussian centers. The availability of the gradient greatly accelerates the variational energy minimization. The algorithm is tested in calculations of four electronic excited states, c(3)Π(u), C(1)Π(u), i(3)Π(g), and I(1)Π(g), of the hydrogen molecule at a single internuclear distance specific to each state. With the use of the analytical energy gradient, the present calculations yield new, lowest-to-date, variational energy upper bounds for all four states.
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Affiliation(s)
- Wei-Cheng Tung
- Department of Chemistry and Biochemistry, University of Arizona, Tucson, Arizona 85721, USA
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87
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Stanke M, Adamowicz L, Kedziera D. Selection of a Gaussian basis set for calculating the Bethe logarithm for the ground state of the hydrogen atom. Mol Phys 2013. [DOI: 10.1080/00268976.2012.762464] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Monika Stanke
- a Department of Physics , Nicholas Copernicus University , Toruń , Poland
| | - Ludwik Adamowicz
- b Department of Chemistry and Biochemistry , University of Arizona , Tucson , USA
| | - Dariusz Kedziera
- c Department of Chemistry , Nicholas Copernicus University , Toruń , Poland
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