1
|
Oliveira AP, Alencar A, Jalbert G, Rocha AB. Electron-molecule collisions with explicit rovibrational resolution at MRCI level and using even tempered basis sets. J Chem Phys 2021; 155:194110. [PMID: 34800958 DOI: 10.1063/5.0066256] [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
A method for calculating the generalized oscillator strengths (GOSs) and differential cross section (DCS) with vibration and rotation resolution is presented. The importance of accounting for the rotational contribution is to be emphasized since it has not previously been considered in GOS calculations. Although largely neglected due to its small effect on various properties, the rotational resolution proved to be fundamental in the study of certain phenomena, such as the interference between rotational states in a molecule. As the general goal of this work is to obtain theoretical values comparable to high resolution experiments, special care was taken on the calculation of the electronic part of the scattering amplitude, particularly in what concerns the choice of the atomic basis set. Accordingly, even-tempered basis sets have proved to lead to good results. The helium atom was taken as a model system for this aspect of the problem. Then, GOS and DCS, for explicit vibrational and rotational transitions, were calculated for hydrogen and nitrogen molecules. For higher accuracy, a non-Franck-Condon approach was used to obtain transitions involving vibrational states. The resultant values have shown good agreement with the available experimental data.
Collapse
Affiliation(s)
- A P Oliveira
- Universidade Federal do Rio de Janeiro, UFRJ, Instituto de Química, Av. Athos da Silveira Ramos, 149, Rio de Janeiro, RJ 21941-909, Brazil
| | - Amanda Alencar
- Universidade Federal do Rio de Janeiro, UFRJ, Instituto de Física, Av. Athos da Silveira Ramos, 149, Rio de Janeiro, RJ 21941-909, Brazil
| | - Ginette Jalbert
- Universidade Federal do Rio de Janeiro, UFRJ, Instituto de Física, Av. Athos da Silveira Ramos, 149, Rio de Janeiro, RJ 21941-909, Brazil
| | - A B Rocha
- Universidade Federal do Rio de Janeiro, UFRJ, Instituto de Química, Av. Athos da Silveira Ramos, 149, Rio de Janeiro, RJ 21941-909, Brazil
| |
Collapse
|
2
|
Siłkowski M, Zientkiewicz M, Pachucki K. Accurate Born-Oppenheimer potentials for excited Σ+ states of the hydrogen molecule. ADVANCES IN QUANTUM CHEMISTRY 2021. [DOI: 10.1016/bs.aiq.2021.05.012] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
3
|
Austad J, Borgoo A, Tellgren EI, Helgaker T. Bonding in the helium dimer in strong magnetic fields: the role of spin and angular momentum. Phys Chem Chem Phys 2020; 22:23502-23521. [DOI: 10.1039/d0cp03259j] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Investigation of the electronic spectra and novel bonding mechanisms in helium dimers in strong magnetic fields.
Collapse
Affiliation(s)
- Jon Austad
- Hylleraas Centre for Quantum Molecular Sciences
- Department of Chemistry
- University of Oslo
- N-0315 Oslo
- Norway
| | - Alex Borgoo
- Hylleraas Centre for Quantum Molecular Sciences
- Department of Chemistry
- University of Oslo
- N-0315 Oslo
- Norway
| | - Erik I. Tellgren
- Hylleraas Centre for Quantum Molecular Sciences
- Department of Chemistry
- University of Oslo
- N-0315 Oslo
- Norway
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences
- Department of Chemistry
- University of Oslo
- N-0315 Oslo
- Norway
| |
Collapse
|
4
|
Lehtola S, Dimitrova M, Sundholm D. Fully numerical electronic structure calculations on diatomic molecules in weak to strong magnetic fields. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1597989] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Susi Lehtola
- Department of Chemistry, University of Helsinki, Helsinki, Finland
| | - Maria Dimitrova
- Department of Chemistry, University of Helsinki, Helsinki, Finland
| | - Dage Sundholm
- Department of Chemistry, University of Helsinki, Helsinki, Finland
| |
Collapse
|
5
|
Kirrander A, Jungen C, Donovan RJ, Lawley KP. Heavy Rydberg states: large amplitude vibrations. Faraday Discuss 2018; 212:175-190. [PMID: 30318538 DOI: 10.1039/c8fd00096d] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
Extremely large vibrational amplitude (≈8700 a.u.) heavy Rydberg levels in the HH[combining macron]1Σ+g state, located only 25 cm-1 below the ion-pair dissociation limit, are reported. The calculations are done using a hybrid log derivative/multichannel quantum defect approach that accounts for predissociation and is capable of dealing with any number of long-range closed channels, and of providing positions and widths for the heavy Rydberg resonances. In this case, resonance positions can be reproduced qualitatively using a simple diabatic model (however, the resonance widths cannot). Absolute quantum defects are derived for the vibrational series ranging from ν = 0 to ν = 2010. The influence of the Coulomb potential and continuity of heavy Rydberg behavior throughout the 1Σ+g manifold of states is demonstrated.
Collapse
Affiliation(s)
- Adam Kirrander
- EaStCHEM, School of Chemistry, University of Edinburgh, David Brewster Road, EH9 3FJ Edinburgh, UK.
| | - Christian Jungen
- Department of Physics and Astronomy, University College London, London WC1E 6BT, UK
| | - Robert J Donovan
- EaStCHEM, School of Chemistry, University of Edinburgh, David Brewster Road, EH9 3FJ Edinburgh, UK.
| | - Kenneth P Lawley
- EaStCHEM, School of Chemistry, University of Edinburgh, David Brewster Road, EH9 3FJ Edinburgh, UK.
| |
Collapse
|
6
|
Beyer M, Merkt F. Communication: Heavy-Rydberg states of HD and the electron affinity of the deuterium atom. J Chem Phys 2018; 149:031102. [PMID: 30037250 DOI: 10.1063/1.5043186] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The electron affinity of the deuterium atom has been determined to be 6086.81(27) cm-1 from a measurement of the difference between the D+ + H- and H+ + D- ion-pair dissociation energies and a thermochemical cycle involving the electron affinity of H and the ionization energies of H and D. Heavy-Rydberg states and the ion-pair dissociation thresholds of HD were accessed with good efficiency using a three-photon excitation sequence through the B Σu+1 (v = 22, N = 1) and H¯ Σg+1 (v = 9, N = 0) intermediate levels and the threshold positions were determined using the method of threshold-ion-pair-production spectroscopy.
Collapse
Affiliation(s)
- Maximilian Beyer
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| | - Frédéric Merkt
- Laboratorium für Physikalische Chemie, ETH Zürich, 8093 Zürich, Switzerland
| |
Collapse
|
7
|
|
8
|
Glushkov V, Wilson S. The Coulson–Fischer wave functions for the ground and excited states of H 2and HeH +: parametrisation using distributed Gaussian basis sets. Mol Phys 2014. [DOI: 10.1080/00268976.2014.931604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
9
|
Wang J, Kim KS, Baerends EJ. Electron pair density in the lowest 1Σ(u)(+) and 1Σ(g)(+) states of H2. J Chem Phys 2011; 135:074111. [PMID: 21861560 DOI: 10.1063/1.3624571] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
We demonstrate and advocate the use of observable quantities derived from the two-electron reduced density matrix - pair densities, conditional densities, and exchange-correlation holes--as signatures of the type of electron correlation in a chemical bond. The prototype cases of the lowest (1)Σ(u)(+) and (1)Σ(g)(+) states of H(2), which exhibit large variation in types of bonding, ranging from strongly ionic to covalent, are discussed. Both the excited (1)Σ(g)(+) and (1)Σ(u)(+) states have been interpreted as essentially consisting of (natural) orbital configurations with an inner electron in a contracted 1sσ(g) orbital and an outer electron in a diffuse (united atom type, Rydberg) orbital. We show that nevertheless totally different correlation behavior is encountered in various states when comparing them at a common internuclear distance. Also when following one state along the internuclear distance coordinate, strong variation in correlation behavior is observed, as expected. Switches between ionic to covalent character of a state occur till very large distances (40 bohrs for states approaching the 1s3[script-l] asymptotic limit, and 282 bohrs for states approaching the 1s4[script-l] limit).
Collapse
Affiliation(s)
- Jian Wang
- School of Science, Huzhou University, Zhejiang 10083, China.
| | | | | |
Collapse
|
10
|
Ivanov TI, de Lange CA, Ubachs W. Spectral identification of diffuse resonances in H2 above the n = 2 dissociation limit. J Chem Phys 2011; 134:054309. [PMID: 21303122 DOI: 10.1063/1.3544300] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The resonance structure in molecular hydrogen above the n = 2 dissociation limit is experimentally investigated in a 1 XUV + 1 VIS coherent two-step laser excitation process, with subsequent ionization of H(n = 2) products. Diffuse spectral features exhibiting widths of several cm(-1) in the excitation range of 118,500-120,500 cm(-1) are probed. Information on angular momentum selection rules for parallel and crossed polarizations, combination differences, the para-ortho distinction, extrapolation from rovibrational structure in the bound region below the n = 2 threshold, and mass-selective detection of H(2)(+) parent and H(+) daughter fragments is used as input. This allows for an assignment of the diffuse resonances observed in terms of (1)Σ(g)(+), (1)Π(g), and (1)Δ(g) states, specified with vibrational and rotational quantum numbers.
Collapse
Affiliation(s)
- T I Ivanov
- Institute for Lasers, Life and BioPhotonics, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
| | | | | |
Collapse
|
11
|
|
12
|
Vieitez MO, Ivanov TI, Reinhold E, de Lange CA, Ubachs W. Spectroscopic observation and characterization of H(+)H(-) heavy Rydberg states. J Phys Chem A 2009; 113:13237-45. [PMID: 19921940 DOI: 10.1021/jp9039918] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
A series of discrete resonances was observed in the spectrum of H2, which can be unambiguously assigned to bound quantum states in the 1/R Coulombic potential of the H+H- ion-pair system. Two-step laser excitation was performed, using tunable extreme ultraviolet radiation at lambda = 94-96 nm in the first step, and tunable ultraviolet radiation in the range lambda = 310-350 nm in the second step. The resonances, detected via H+ and H2+ ions produced in the decay process, follow a sequence of principal quantum numbers (n = 140-230) associated with a Rydberg formula in which the Rydberg constant is mass scaled. The series converges upon the ionic H+H- dissociation threshold. This limit can be calculated without further assumptions from known ionization and dissociation energies in the hydrogen system and the electronegativity of the hydrogen atom. A possible excitation mechanism is discussed in terms of a complex resonance. Detailed measurements are performed to unravel and quantify the decay of the heavy Rydberg states into molecular H2+ ions, as well as into atomic fragments, both H(n = 2) and H(n = 3). Lifetimes are found to scale as n3.
Collapse
Affiliation(s)
- M O Vieitez
- Laser Centre, Vrije Universiteit, Amsterdam, Netherlands
| | | | | | | | | |
Collapse
|
13
|
Corongiu G, Clementi E. Energy and density analysis of the H2 molecule from the united atom to dissociation: the 3Sigma(g)+ and 3Sigma(u)+ states. J Chem Phys 2009; 131:184306. [PMID: 19916603 DOI: 10.1063/1.3259551] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The first 14 (3)Sigma(g)(+) and the first 15 (3)Sigma(u)(+) states of the H(2) molecule are computed with full configuration interaction both from Hartree-Fock molecular orbitals and Heitler-London atomic orbitals within the Born-Oppenheimer approximation, following recent studies for the (1)Sigma(g)(+) and (1)Sigma(u)(+) manifolds [Corongiu and Clementi, J. Chem. Phys. 131, 034301 (2009) and J. Phys. Chem. (in press)]. The basis sets utilized are extended and optimized Slater-type functions and spherical Gaussian functions. The states considered correspond to the configurations (1s(1)nl(1)) with n from 1 to 5; the internuclear separations sample the distances from 0.01 to 10,000 bohrs. For the first three (3)Sigma(g)(+) and (3)Sigma(u)(+) states and for the fourth and fifth (3)Sigma(g)(+) states, our computed energies at the equilibrium internuclear separation, when compared to the accurate values by Staszewska and Wolniewicz and by Kołos and Rychlewski, show deviations of about 0.006 kcal/mol, a test on the quality of our computations. Motivation for this work comes not only from obtaining potential energy curves for the high excited states of H(2) but also from characterizing the electronic density evolution from the united atom to dissociation to provide a detailed analysis of the energy contributions from selected basis subsets and to quantitatively decompose the state energies into covalent and ionic components. Furthermore, we discuss the origin of the seemingly irregular patterns in potential energy curves in the two manifolds, between 4 and 6-9 bohrs--there are two systems of states: the first, from the united atom to about 4 bohrs, is represented by functions with principal quantum number higher than the one needed at dissociation; this system interacts at around 4 bohrs with the second system, which is represented by functions with principal quantum number corresponding to one of the dissociation products.
Collapse
Affiliation(s)
- Giorgina Corongiu
- Dipartimento di Scienze Chimiche e Ambientali, Universita dell'Insubria, Via Valleggio 11, I-22100 Como, Italy.
| | | |
Collapse
|
14
|
Corongiu G, Clementi E. Energy and Density Analyses of the 1Σu+ States in the H2 Molecule from the United Atom to Dissociation. J Phys Chem A 2009; 113:14791-9. [DOI: 10.1021/jp9049395] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Giorgina Corongiu
- Dipartimento di Scienze Chimiche e Ambientali, Università dell’Insubria, Via Valleggio 11, I-22100 Como, Italy
| | | |
Collapse
|
15
|
Corongiu G, Clementi E. Energy and density analyses of the H2 molecule from the united atom to dissociation: The ∑1g+ states. J Chem Phys 2009; 131:034301. [DOI: 10.1063/1.3168506] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
|
16
|
Vieitez MO, Ivanov TI, Reinhold E, de Lange CA, Ubachs W. Observation of a Rydberg series in H+H-: a heavy Bohr atom. PHYSICAL REVIEW LETTERS 2008; 101:163001. [PMID: 18999662 DOI: 10.1103/physrevlett.101.163001] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2008] [Indexed: 05/27/2023]
Abstract
We report on the realization of a heavy "Bohr atom," through the spectroscopic observation of a Rydberg series of bound quantum states at principal quantum numbers n=140 to 230. The system is made heavy by replacing an electron inside a hydrogen atom by a composite H- particle, thus forming a H+H- Coulombically bound system obeying the physical laws of a generalized atom with appropriate mass scaling.
Collapse
Affiliation(s)
- M O Vieitez
- Laser Centre, Vrije Universiteit, De Boelelaan 1081, Amsterdam, The Netherlands
| | | | | | | | | |
Collapse
|
17
|
|
18
|
Osterwalder A, Wüest A, Merkt F, Jungen C. High-resolution millimeter wave spectroscopy and multichannel quantum defect theory of the hyperfine structure in high Rydberg states of molecular hydrogen H2. J Chem Phys 2004; 121:11810-38. [PMID: 15634145 DOI: 10.1063/1.1792596] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
Experimental and theoretical methodologies have been developed to determine the hyperfine structure of molecular ions from detailed studies of the Rydberg spectrum and have been tested on molecular hydrogen. The hyperfine structure in l=0-3 Rydberg states of H2 located below the X 2Sigmag+(v+=0,N+=1) ground state of ortho H2+ has been measured in the range of principal quantum number n=50-65 at sub-MHz resolution by millimeter wave spectroscopy following laser excitation to np and nd Rydberg states using a variety of single-photon and multiphoton excitation sequences. The np1(1), nd1(1), and the nf1(0-3) Rydberg states were found to be metastable and to have lifetimes of more than 5 micros beyond n=50. Members of other series, such as the nd1(2), nd1(3), and the np1(0) series, were found to have lifetimes of more than 1 mus. Local perturbations induced by low-n Rydberg states belonging to series converging on rovibrationally excited levels of H2+ reduce the lifetimes in narrow ranges of n values. The hyperfine structure is strongly dependent on the value of the orbital angular momentum l. In the penetrating s and p states at n approximately 50 the exchange interaction dominates over the hyperfine interaction and the levels can be labeled by the total electron spin angular momentum quantum number S (S=0 or 1). In the less penetrating d and f Rydberg states, the hyperfine interaction between the core nuclear and electron spins is larger than the exchange interaction and the Rydberg states are of mixed singlet and triplet character. A procedure based on the Stark effect and on the systematic analysis of selection rules and combination differences was developed to determine the orbital and the total angular momentum quantum numbers l and F and to construct an energy map of p and f Rydberg levels between n=54 and 64 with relative positions of an accuracy of better than 1 MHz. Multichannel quantum defect theory (MQDT) was extended to treat the hyperfine structure in molecular Rydberg states and was used to analyze the observed hyperfine structure of the p and f Rydberg states of H2. The frame transformation between the Born-Oppenheimer channels described by the angular momentum coupling scheme (abetaJ) and the asymptotic channels described by the (e[bbetaS+]) coupling scheme was derived and enables an elegant treatment of all intermediate coupling cases. Purely ab initio quantum defect theory reproduced the experimentally determined positions to within 40 MHz for the p levels and 13 MHz for the f levels. By slight adjustments of the quantum defect functions and their energy dependences and by consideration of the p-f interaction, of the singlet-triplet splittings of the f levels, and of the departure of the ionic levels from pure coupling case (bbetaS+), the agreement between theory and experiment could be improved to 600 kHz. By comparing the results of MQDT calculations of the hyperfine structure of f Rydberg levels with those of coupled equations calculations, the frame transformation approximation of MQDT was shown to be accurate to within 300 kHz. The extrapolated ionic hyperfine structure of the X 2Sigmag+(v+=0,N+=1) ionic level corresponds to the ab initio prediciton of Babb and Dalgarno [Phys. Rev. A 46, R5317 (1992)] within the experimental error.
Collapse
Affiliation(s)
- A Osterwalder
- Physical Chemistry, ETH Zurich, CH-8093 Zurich, Switzerland
| | | | | | | |
Collapse
|
19
|
Spielfiedel * A, Palmieri † P, Mitrushenkov † AO. Ab initiocalculation of molecular hydrogen electronic states’ properties: transition matrix elements among triplet electronic states. Mol Phys 2004. [DOI: 10.1080/00268970412331286981] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
20
|
|
21
|
|
22
|
Staszewska G. Transition Moments between w3Πg State and the First Three 3Σu and 3Πu States of the Hydrogen Molecule. J Phys Chem A 2001. [DOI: 10.1021/jp003781z] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Grażyna Staszewska
- Institute of Physics, Nicholas Copernicus University, ul. Grudziadzka 5, 87-100 Toruń, Poland
| |
Collapse
|
23
|
Drira I. Ab Initio Calculation of the Electronic Transition Moments for Excited States of the H(2) Molecule. JOURNAL OF MOLECULAR SPECTROSCOPY 1999; 198:52-56. [PMID: 10527780 DOI: 10.1006/jmsp.1999.7934] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Ab initio MRCI electronic dipole transition moments were calculated for the singlet and triplet molecular states contributing to free-free and free-bound absorption in the far wings of the Lyman alpha and Lyman beta lines of hydrogen atom perturbed by another hydrogen atom in its ground state. Results are presented for internuclear distances ranging from 1.0a(0) to 50a(0) and for transitions between the X(1)Sigma(+)(g) ground state to all (1)Pi(u) and (1)Sigma(+)(u) states and between the b(3)Sigma(+)(u) state to all (3)Pi(g) and (3)Sigma(+)(g) states that dissociate at large internuclear distances into H (n = 2, 3) + H (n = 1). These results compare well with the previous theoretical calculations available for a few transitions. Copyright 1999 Academic Press.
Collapse
Affiliation(s)
- I Drira
- Section de Meudon, Observatoire de Paris, Meudon Principal Cedex, 92195, France
| |
Collapse
|