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Márquez-Mijares M, Roncero O, Villarreal P, González-Lezana T. Theoretical methods for the rotation–vibration spectra of triatomic molecules: distributed Gaussian functions compared with hyperspherical coordinates. INT REV PHYS CHEM 2018. [DOI: 10.1080/0144235x.2018.1514187] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Maykel Márquez-Mijares
- Instituto Superior de Tecnologías y Ciencias Aplicadas InsTec, Havana University, Quinta de los Molinos, Havana, Cuba
| | - Octavio Roncero
- Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas IFF-CSIC, Madrid, Spain
| | - Pablo Villarreal
- Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas IFF-CSIC, Madrid, Spain
| | - Tomás González-Lezana
- Instituto de Física Fundamental, Consejo Superior de Investigaciones Científicas IFF-CSIC, Madrid, Spain
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Kalus R, Karlický F, Lepetit B, Paidarová I, Gadea FX. Photoabsorption spectrum of helium trimer cation--theoretical modeling. J Chem Phys 2013; 139:204310. [PMID: 24289357 DOI: 10.1063/1.4832736] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The photoabsorption spectrum of He3(+) is calculated for two semiempirical models of intracluster interactions and compared with available experimental data reported in the middle UV range [H. Haberland and B. von Issendorff, J. Chem. Phys. 102, 8773 (1995)]. Nuclear delocalization effects are investigated via several approaches comprising quantum samplings using either exact or approximate (harmonic) nuclear wavefunctions, as well as classical samplings based on the Monte Carlo methodology. Good agreement with the experiment is achieved for the model by Knowles et al., [Mol. Phys. 85, 243 (1995); Mol. Phys. 87, 827 (1996)] whereas the model by Calvo et al., [J. Chem. Phys. 135, 124308 (2011)] exhibits non-negligible deviations from the experiment. Predictions of far UV absorption spectrum of He3(+), for which no experimental data are presently available, are reported for both models and compared to each other as well as to the photoabsorption spectrum of He2(+). A simple semiempirical point-charge approximation for calculating transition probabilities is shown to perform well for He3(+).
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Affiliation(s)
- René Kalus
- Centre of Excellence IT4Innovations and Department of Applied Mathematics, VSB-Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava, Czech Republic
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Barreto PR, Albernaz AF, Capobianco A, Palazzetti F, Lombardi A, Grossi G, Aquilanti V. Potential energy surfaces for interactions of H2O with H2, N2 and O2: A hyperspherical harmonics representation, and a minimal model for the H2O–rare-gas-atom systems. COMPUT THEOR CHEM 2012. [DOI: 10.1016/j.comptc.2011.12.024] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2022]
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Karlický F, Lepetit B, Kalus R, Gadéa FX. Vibrational spectrum of Ar3(+) and relative importance of linear and perpendicular isomers in its photodissociation. J Chem Phys 2011; 134:084305. [PMID: 21361537 DOI: 10.1063/1.3555275] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The photodissociation dynamics of the argon ionized trimer Ar(3)(+) is revisited in the light of recent experimental results of Lepère et al. [J. Chem. Phys. 134, 194301 (2009)], which show that the fragment with little kinetic energy is always a neutral one, thus the available energy is shared by a neutral and ionic fragments as in Ar(2)(+). We show that these results can be interpreted as the photodissociation of the linear isomer of the system. We perform a 3D quantum computation of the vibrational spectrum of the system and study the relative populations of the linear (trimer-core) and perpendicular (dimer-core) isomers. We then show that the charge initially located on the central atom in the ground electronic state of the linear isomer migrates toward the extreme ones in the photoexcitation process such that photodissociation of the linear isomer produces a neutral central atom at rest in agreement with measured product state distributions.
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Affiliation(s)
- Frantisek Karlický
- Regional Centre of Advanced Technologies and Materials, Department of Physical Chemistry, Faculty of Science, Palacký University, Olomouc, Czech Republic.
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Wang D, Kuppermann A. Analytical Derivation of Row-Orthonormal Hyperspherical Harmonics for Triatomic Systems. J Phys Chem A 2009; 113:15384-410. [DOI: 10.1021/jp906473n] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Desheng Wang
- Arthur Amos Noyes Laboratory of Chemical Physics, Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125
| | - Aron Kuppermann
- Arthur Amos Noyes Laboratory of Chemical Physics, Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125
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Velilla L, Lepetit B, Aguado A, Beswick JA, Paniagua M. The H(3) (+) rovibrational spectrum revisited with a global electronic potential energy surface. J Chem Phys 2009; 129:084307. [PMID: 19044823 DOI: 10.1063/1.2973629] [Citation(s) in RCA: 79] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this paper, we have computed the rovibrational spectrum of the H(3) (+) molecule using a new global potential energy surface, invariant under all permutations of the nuclei, that includes the long range electrostatic interactions analytically. The energy levels are obtained by a variational calculation using hyperspherical coordinates. From the comparison with available experimental results for low lying levels, we conclude that our accuracy is of the order of 0.1 cm(-1) for states localized in the vicinity of equilateral triangular configurations of the nuclei, and changes to the order of 1 cm(-1) when the system is distorted away from equilateral configurations. Full rovibrational spectra up to the H(+)+H(2) dissociation energy limit have been computed. The statistical properties of this spectrum (nearest neighbor distribution and spectral rigidity) show the quantum signature of classical chaos and are consistent with random matrix theory. On the other hand, the correlation function, even when convoluted with a smoothing function, exhibits oscillations which are not described by random matrix theory. We discuss a possible similarity between these oscillations and the ones observed experimentally.
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Affiliation(s)
- Luis Velilla
- Departamento de Química Física, Facultad de Ciencias C-XIV, Universidad Autónoma de Madrid, 28049, Madrid, Spain
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Karlický F, Lepetit B, Kalus R, Paidarová I, Gadéa FX. Modeling of HeN+ clusters. II. Calculation of He3+ vibrational spectrum. J Chem Phys 2008; 128:124303. [PMID: 18376915 DOI: 10.1063/1.2841019] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We have computed the vibrational spectrum of the helium ionized trimer He(3)(+) using three different potential energy surfaces [D. T. Chang and G. L. Gellene, J. Chem. Phys. 119, 4694 (2003); E. Scifoni et al., ibid. 125, 164304 (2006); I. Paidarova et al., Chem. Phys. 342, 64 (2007)]. Differences in the details of these potential energy surfaces induce discrepancies between bound state energies of the order of 0.01 eV. The effects of the geometric phase induced by the conical intersection between the ground electronic potential energy surface and the first excited one are studied by computing vibrational spectra with and without this phase. The six lowest vibrational bound states are negligibly affected by the geometric phase. Indeed, they correspond to wavefunctions localized in the vicinity of the linear symmetric configurations and can be assigned well defined vibrational quantum numbers. On the other hand, higher excited states are delocalized, cannot be assigned definite vibrational quantum numbers, and the geometric phase shifts their energies by approximately 0.005 eV.
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Affiliation(s)
- Frantisek Karlický
- Department of Physics, Faculty of Science, University of Ostrava, 30 dubna 22, 701 03 Ostrava, Czech Republic
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Karlický F, Lepetit B, Kalus R, Gadéa FX. Calculation of argon trimer rovibrational spectrum. J Chem Phys 2007; 126:174305. [PMID: 17492861 DOI: 10.1063/1.2721564] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Rovibrational spectra of Ar3 are computed for total angular momenta up to J=6 using row-orthonormal hyperspherical coordinates and an expansion of the wave function on hyperspherical harmonics. The sensitivity of the spectra to the two-body potential and to the three-body corrections is analyzed. First, the best available semiempirical pair potential (HFDID1) is compared with our recent ab initio two-body potential. The ab initio vibrational energies are typically 1-2 cm-1 higher than the semiempirical ones, which is related to the slightly larger dissociation energy of the semiempirical potential. Then, the Axilrod-Teller asymptotic expansion of the three-body correction is compared with our newly developed ab initio three-body potential. The difference is found smaller than 0.3 cm-1. In addition, we define approximate quantum numbers to describe the vibration and rotation of the system. The vibration is represented by a hyper-radial mode and a two-degree-of-freedom hyperangular mode, including a vibrational angular momentum defined in an Eckart frame. The rotation is described by the total angular momentum quantum number, its projection on the axis perpendicular to the molecular plane, and a hyperangular internal momentum quantum number, related to the vibrational angular momentum by a transformation between Eckart and principal-axes-of-inertia frames. These quantum numbers provide a qualitative understanding of the spectra and, in particular, of the impact of the nuclear permutational symmetry of the system (bosonic with zero nuclear spin). Rotational constants are extracted from the spectra and are shown to be accurate only for the ground hyperangular mode.
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Affiliation(s)
- Frantisek Karlický
- Department of Physics, University of Ostrava, 30 dubna 22, 701 03 Ostrava, Czech Republic
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Lombardi A, Palazzetti F, Peroncelli L, Grossi G, Aquilanti V, Sevryuk MB. Few-body quantum and many-body classical hyperspherical approaches to reactions and to cluster dynamics. Theor Chem Acc 2006. [DOI: 10.1007/s00214-006-0195-0] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Kuppermann A. Incorporating the Geometric Phase Effect in Triatomic and Tetraatomic Hyperspherical Harmonics. J Phys Chem A 2006; 110:809-16. [PMID: 16405357 DOI: 10.1021/jp054597m] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Hyperspherical harmonics in the democratic row-orthonormal hyperspherical coordinates are very appropriate basis sets for performing reactive scattering calculations for triatomic and tetraatomic systems. The mathematical conditions for incorporating the geometric phase effect in these harmonics are given. These conditions are implemented for triatomic systems, and their explicit analytical expressions in terms of Jacobi polynomials, in both the absence and presence of the geometric phase effect, are given.
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Affiliation(s)
- Aron Kuppermann
- Arthur Amos Noyes Laboratory of Chemical Physics, Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
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Aquilanti V, Lombardi A, Sevryuk MB. Phase-space invariants for aggregates of particles: Hyperangular momenta and partitions of the classical kinetic energy. J Chem Phys 2004; 121:5579-89. [PMID: 15366980 DOI: 10.1063/1.1785785] [Citation(s) in RCA: 38] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Rigorous definitions are presented for the kinematic angular momentum K of a system of classical particles (a concept dual to the conventional angular momentum J), the angular momentum L(xi) associated with the moments of inertia, and the contributions to the total kinetic energy of the system from various modes of the motion of the particles. Some key properties of these quantities are described-in particular, their invariance under any orthogonal coordinate transformation and the inequalities they are subject to. The main mathematical tool exploited is the singular value decomposition of rectangular matrices and its differentiation with respect to a parameter. The quantities introduced employ as ingredients particle coordinates and momenta, commonly available in classical trajectory studies of chemical reactions and in molecular dynamics simulations, and thus are of prospective use as sensitive and immediately calculated indicators of phase transitions, isomerizations, onsets of chaotic behavior, and other dynamical critical phenomena in classical microaggregates, such as nanoscale clusters.
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Affiliation(s)
- Vincenzo Aquilanti
- Dipartimento di Chimica, Università di Perugia, Via Elce di Sotto 8, I-06123 Perugia, Italy
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Kuppermann A. Hyperspherical Harmonics for Tetraatomic Systems. 2. The Weak Interaction Region. J Phys Chem A 2004. [DOI: 10.1021/jp048874l] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Aron Kuppermann
- Arthur Amos Noyes Laboratory of Chemical Physics, Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125
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Aquilanti V, Tonzani S. Three-body problem in quantum mechanics: Hyperspherical elliptic coordinates and harmonic basis sets. J Chem Phys 2004; 120:4066-73. [PMID: 15268573 DOI: 10.1063/1.1644098] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Elliptic coordinates within the hyperspherical formalism for three-body problems were proposed some time ago [V. Aquilanti, S. Cavalli, and G. Grossi, J. Chem. Phys. 85, 1362 (1986)] and recently have also found application, for example, in chemical reaction theory [see O. I. Tolstikhin and H. Nakamura, J. Chem. Phys. 108, 8899 (1998)]. Here we consider their role in providing a smooth transition between the known "symmetric" and "asymmetric" parametrizations, and focus on the corresponding hyperspherical harmonics. These harmonics, which will be called hyperspherical elliptic, involve products of two associated Lame polynomials. We will provide an expansion of these new sets in a finite series of standard hyperspherical harmonics, producing a powerful tool for future applications in the field of scattering and bound-state quantum-mechanical three-body problems.
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