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Xu M, Felker PM, Bačić Z. H 2O inside the fullerene C 60: Inelastic neutron scattering spectrum from rigorous quantum calculations. J Chem Phys 2022; 156:124101. [PMID: 35364860 DOI: 10.1063/5.0086842] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a methodology that, for the first time, allows rigorous quantum calculation of the inelastic neutron scattering (INS) spectra of a triatomic molecule in a nanoscale cavity, in this case, H2O inside the fullerene C60. Both moieties are taken to be rigid. Our treatment incorporates the quantum six-dimensional translation-rotation (TR) wave functions of the encapsulated H2O, which serve as the spatial parts of the initial and final states of the INS transitions. As a result, the simulated INS spectra reflect the coupled TR dynamics of the nanoconfined guest molecule. They also exhibit the features arising from symmetry breaking observed for solid H2O@C60 at low temperatures. Utilizing this methodology, we compute the INS spectra of H2O@C60 for two incident neutron wavelengths and compare them with the corresponding experimental spectra. Good overall agreement is found, and the calculated spectra provide valuable additional insights.
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Affiliation(s)
- Minzhong Xu
- Department of Chemistry, New York University, New York, New York 10003, USA
| | - Peter M Felker
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, USA
| | - Zlatko Bačić
- Department of Chemistry, New York University, New York, New York 10003, USA
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Xu M, Felker PM, Bačić Z. Light molecules inside the nanocavities of fullerenes and clathrate hydrates: inelastic neutron scattering spectra and the unexpected selection rule from rigorous quantum simulations. INT REV PHYS CHEM 2020. [DOI: 10.1080/0144235x.2020.1794097] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Minzhong Xu
- Department of Chemistry, New York University, New York, NY, USA
| | - Peter M. Felker
- Department of Chemistry and Biochemistry, University of California, Los Angeles, CA, USA
| | - Zlatko Bačić
- Department of Chemistry, New York University, New York, NY, USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai, People's Republic of China
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Felker PM, Bačić Z. Flexible water molecule in C60: Intramolecular vibrational frequencies and translation-rotation eigenstates from fully coupled nine-dimensional quantum calculations with small basis sets. J Chem Phys 2020; 152:014108. [DOI: 10.1063/1.5138992] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Affiliation(s)
- Peter M. Felker
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, USA
| | - Zlatko Bačić
- Department of Chemistry, New York University, New York, New York 10003, USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
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Xu M, Felker PM, Mamone S, Horsewill AJ, Rols S, Whitby RJ, Bačić Z. The Endofullerene HF@C 60: Inelastic Neutron Scattering Spectra from Quantum Simulations and Experiment, Validity of the Selection Rule, and Symmetry Breaking. J Phys Chem Lett 2019; 10:5365-5371. [PMID: 31454486 DOI: 10.1021/acs.jpclett.9b02005] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Accurate quantum simulations of the low-temperature inelastic neutron scattering (INS) spectra of HF@C60 are reported for two incident neutron wavelengths. They are distinguished by the rigorous inclusion of symmetry-breaking effects in the treatment and having the spectra computed with HF as the guest, rather than H2 or HD, as in the past work. The results demonstrate that the precedent-setting INS selection rule, originally derived for H2 and HD in near-spherical nanocavities, applies also to HF@C60, despite the large mass asymmetry of HF and the strongly mixed character of its translation-rotation eigenstates. This lends crucial support to the theoretical prediction made earlier that the INS selection rule is valid for any diatomic molecule in near-spherical nanoconfinement. The selection rule remains valid in the presence of symmetry breaking but is modified slightly in an interesting way. Comparison is made with the recently published experimental INS spectrum of HF@C60. The agreement is very good, apart from one peak for which our calculations suggest a reassignment. This reassignment is consistent with the measured INS spectrum presented in this work, which covers an extended energy range.
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Affiliation(s)
- Minzhong Xu
- Department of Chemistry , New York University , New York , New York 10003 , United States
| | - Peter M Felker
- Department of Chemistry and Biochemistry , University of California , Los Angeles , California 90095-1569 , United States
| | - Salvatore Mamone
- School of Physics & Astronomy , University of Nottingham , Nottingham NG7 2RD , United Kingdom
| | - Anthony J Horsewill
- School of Physics & Astronomy , University of Nottingham , Nottingham NG7 2RD , United Kingdom
| | - Stéphane Rols
- Institut Laue-Langevin , CS 20156, 38042 Grenoble , France
| | - Richard J Whitby
- Chemistry, Faculty of Engineering and Physical Sciences , University of Southampton , Southampton SO17 1BJ , United Kingdom
| | - Zlatko Bačić
- Department of Chemistry , New York University , New York , New York 10003 , United States
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai , 3663 Zhongshan Road North , Shanghai 200062 , China
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Rashed E, Dunn JL. Interactions between a water molecule and C 60 in the endohedral fullerene H 2O@C 60. Phys Chem Chem Phys 2019; 21:3347-3359. [PMID: 30688323 DOI: 10.1039/c8cp04390f] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A water molecule encapsulated inside a C60 fullerene cage behaves almost like an asymmetric top rotor, as would be expected of an isolated water molecule. However, inelastic neutron scattering (INS) experiments show evidence of interactions between the water molecule and its environment [Goh et al., Phys. Chem. Chem. Phys., 2014, 16, 21330]. In particular, a resolved splitting of the 101 rotational level into a singlet and a doublet indicates that the water molecule experiences an environment of lower symmetry than the icosahedral symmetry of a C60 cage. Recent calculations have shown that the splitting can be explained in terms of electrostatic quadrupolar interactions between the water molecule and the electron clouds of nearest-neighbour C60 molecules, which results in an effective environment of S6 symmetry [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274 and Bačić et al., Faraday Discussions, 2018, 212, 547-567]. We use symmetry arguments to obtain a simple algebraic expression, expressed in terms of a linear combination of products of translational and rotational basis functions, that describes the effect on a water molecule of any potential of S6 symmetry. We show that we can reproduce the results of the electrostatic interaction model up to ≈12 meV in terms of two unknown parameters only. The resulting potential is in a form that can readily be used in future calculations, without needing to use density functional theory (DFT) for example. Adjusting parameters in our potential would help identify whether other symmetry-lowering interactions are also present if experimental results that resolve splittings in higher-energy rotational levels are obtained in the future. As another application of our model, we show that the results of DFT calculations of the variation in energy as a water molecule moves inside the cage of an isolated C60 molecule, where the water molecule experiences an environment of icosahedral symmetry, can also be reproduced using our model.
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Affiliation(s)
- Effat Rashed
- School of Physics & Astronomy, University Park, Nottingham, UK.
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Bačić Z, Vlček V, Neuhauser D, Felker PM. Effects of symmetry breaking on the translation-rotation eigenstates of H 2, HF, and H 2O inside the fullerene C 60. Faraday Discuss 2018; 212:547-567. [PMID: 30226507 DOI: 10.1039/c8fd00082d] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Splittings of the translation-rotation (TR) eigenstates of the solid light-molecule endofullerenes M@C60 (M = H2, H2O, HF) attributed to the symmetry breaking have been observed in the infrared (IR) and inelastic neutron scattering spectra of these species in the past couple of years. In a recent paper [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274], we established that the electrostatic, quadrupolar interaction between the guest molecule M and the twelve nearest-neighbor C60 cages of the solid is the main source of the symmetry breaking. The splittings of the three-fold degenerate ground states of the endohedral ortho-H2, ortho-H2O and the j = 1 level of HF calculated using this model were found to be in excellent agreement with the experimental results. Utilizing the same electrostatic model, this theoretical study investigates the effects of the symmetry breaking on the excited TR eigenstates of the three species, and how they manifest in their simulated low-temperature (5-6 K) near-IR (NIR) and far-IR (FIR) spectra. The TR eigenstates are calculated variationally for both the major P and minor H crystal orientations. For the H orientation, the calculated splittings of all of the TR levels of these species are less than 0.1 cm-1. For the dominant P orientation, the splittings vary strongly depending on the character of the excitations involved. In all of the species, the splittings of the higher rotationally excited levels are comparable in magnitude to those for the j = 1 levels. For the levels corresponding to purely translational excitations, the calculated splittings are about an order of magnitude smaller than those of the purely rotational eigenstates. Based on the computed TR eigenstates, the low-temperature NIR (for M = H2) and FIR (for M = HF and H2O) spectra are simulated for both the P and H orientations, and also combined as their weighted sum (0.15H + 0.85P). The weighted sum spectra computed for M = H2 and HF match quantitatively the corresponding measured spectra, while for M = H2O, the weighted sum FIR spectrum predicts features that can potentially be observed experimentally.
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Affiliation(s)
- Zlatko Bačić
- Department of Chemistry, New York University, New York, NY 10003, USA. and NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai, 200062, China
| | - Vojtěch Vlček
- Department of Chemistry and Biochemistry, University of California, Los Angeles, CA 90095-1569, USA.
| | - Daniel Neuhauser
- Department of Chemistry and Biochemistry, University of California, Los Angeles, CA 90095-1569, USA.
| | - Peter M Felker
- Department of Chemistry and Biochemistry, University of California, Los Angeles, CA 90095-1569, USA.
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Bačić Z. Perspective: Accurate treatment of the quantum dynamics of light molecules inside fullerene cages: Translation-rotation states, spectroscopy, and symmetry breaking. J Chem Phys 2018; 149:100901. [PMID: 30219006 DOI: 10.1063/1.5049358] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
In this perspective, I review the current status of the theoretical investigations of the quantum translation-rotation (TR) dynamics and spectroscopy of light molecules encapsulated inside fullerenes, mostly C60 and C70. The methodologies developed in the past decade allow accurate quantum calculations of the TR eigenstates of one and two nanoconfined molecules and have led to deep insights into the nature of the underlying dynamics. Combining these bound-state methodologies with the formalism of inelastic neutron scattering (INS) has resulted in the novel and powerful approach for the quantum calculation of the INS spectra of a diatomic molecule in a nanocavity with an arbitrary geometry. These simulations have not only become indispensable for the interpretation and assignment of the experimental spectra but are also behind the surprising discovery of the INS selection rule for diatomics in near-spherical nanocavities. Promising directions for future research are discussed.
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Affiliation(s)
- Zlatko Bačić
- Department of Chemistry, New York University, New York, New York 10003, USA
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Kalugina YN, Roy PN. Potential energy and dipole moment surfaces for HF@C60: Prediction of spectral and electric response properties. J Chem Phys 2017; 147:244303. [DOI: 10.1063/1.5006589] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yulia N. Kalugina
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
| | - Pierre-Nicholas Roy
- Department of Chemistry, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
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Felker PM, Bačić Z. Accurate quantum calculations of translation-rotation eigenstates in electric-dipole-coupled H2O@C60 assemblies. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.02.027] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Felker PM, Bačić Z. Electric-dipole-coupled H2O@C60 dimer: Translation-rotation eigenstates from twelve-dimensional quantum calculations. J Chem Phys 2017; 146:084303. [DOI: 10.1063/1.4976526] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Peter M. Felker
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, USA
| | - Zlatko Bačić
- Department of Chemistry, New York University, New York, New York 10003, USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
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Felker PM, Vlček V, Hietanen I, FitzGerald S, Neuhauser D, Bačić Z. Explaining the symmetry breaking observed in the endofullerenes H2@C60, HF@C60, and H2O@C60. Phys Chem Chem Phys 2017; 19:31274-31283. [DOI: 10.1039/c7cp06062a] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Symmetry breaking has been recently observed in the endofullerenes M@C60 (M = H2, HF, H2O), manifesting in the splittings of the three-fold degenerate ground states of the endohedral ortho-H2, ortho-H2O and the j = 1 level of HF.
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Affiliation(s)
- Peter M. Felker
- Department of Chemistry and Biochemistry
- University of California
- Los Angeles
- USA
| | - Vojtěch Vlček
- Department of Chemistry and Biochemistry
- University of California
- Los Angeles
- USA
| | - Isaac Hietanen
- Department of Physics and Astronomy
- Oberlin College
- Oberlin
- USA
| | | | - Daniel Neuhauser
- Department of Chemistry and Biochemistry
- University of California
- Los Angeles
- USA
| | - Zlatko Bačić
- Department of Chemistry
- New York University
- New York
- USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai
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Felker PM, Bačić Z. Translation-rotation states of H2 in C60: New insights from a perturbation-theory treatment. J Chem Phys 2016; 145:084310. [DOI: 10.1063/1.4961650] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Affiliation(s)
- Peter M. Felker
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, USA
| | - Zlatko Bačić
- Department of Chemistry, New York University, New York, New York 10003, USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
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Felker PM, Bačić Z. Communication: Quantum six-dimensional calculations of the coupled translation-rotation eigenstates of H2O@C60. J Chem Phys 2016; 144:201101. [DOI: 10.1063/1.4953180] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Peter M. Felker
- Department of Chemistry and Biochemistry, University of California, Los Angeles, California 90095-1569, USA
| | - Zlatko Bačić
- Department of Chemistry, New York University, New York, New York 10003, USA
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
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Mamone S, Jiménez-Ruiz M, Johnson MR, Rols S, Horsewill AJ. Experimental, theoretical and computational investigation of the inelastic neutron scattering spectrum of a homonuclear diatomic molecule in a nearly spherical trap: H2@C60. Phys Chem Chem Phys 2016; 18:29369-29380. [DOI: 10.1039/c6cp06059e] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
In this paper we report a methodology for calculating the inelastic neutron scattering spectrum of homonuclear diatomic molecules confined within nano-cavities of spherical symmetry.
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Affiliation(s)
- Salvatore Mamone
- School of Physics and Astronomy
- University of Nottingham
- NG7 2RD Nottingham
- UK
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Mamone S, Johnson MR, Ollivier J, Rols S, Levitt MH, Horsewill AJ. Symmetry-breaking in the H2@C60 endofullerene revealed by inelastic neutron scattering at low temperature. Phys Chem Chem Phys 2016; 18:1998-2005. [DOI: 10.1039/c5cp07146a] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The fine structure of the rotational ground state of molecular ortho-hydrogen confined inside the fullerene cage C60 is investigated by inelastic neutron scattering (INS).
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Affiliation(s)
- Salvatore Mamone
- School of Physics and Astronomy
- University of Nottingham
- NG7 2RD Nottingham
- UK
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