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Iwamoto Y, Tanimura Y. Linear absorption spectrum of a quantum two-dimensional rotator calculated using a rotationally invariant system-bath Hamiltonian. J Chem Phys 2018; 149:084110. [DOI: 10.1063/1.5044585] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yuki Iwamoto
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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Szymański S. Spin-lattice relaxation of the methyl group protons in solids revisited: damped quantum rotation approach. J Chem Phys 2012; 137:034513. [PMID: 22830717 DOI: 10.1063/1.4734251] [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
Proton spin-lattice relaxation of the methyl group in solids had been one of the most thoroughly addressed theoretical problems in nuclear magnetic resonance (NMR) spectroscopy, considered at different levels of sophistication. For systems with substantial quantum tunneling effects, several quantum mechanical treatments were reported, although in practical applications the quantum models were always augmented with or replaced by the classical jump model. However, the latter has recently proved invalid in the description of NMR line shape effects in variable-temperature spectra of hindered methyl groups, while the competing theory of damped quantum rotation (DQR) was shown to be adequate. In this work, the spin-lattice relaxation issue for the methyl protons is readdressed using the latter theory. The main outcome is that, while the existing formulas for the relaxation rates remain unchanged, the crucial parameter entering them, the correlation time of the relevant random process, need to be reinterpreted. It proves to be the inverse of one of the two quantum-rate constants entering the DQR model, neither of which, when taken separately, can be related to the jump process. It can be identified with one describing the life-time broadening of the tunnel peaks in inelastic neutron scattering (INS) spectra of the methyl groups. Such a relationship between the relaxation and INS effects was reported from another laboratory long ago, but only for the low-temperature limit where thermal population of the excited torsional levels of the methyl group can be neglected. The whole spectrum of cases encountered in practical relaxation studies on protonated methyl groups is addressed for the first time. Preliminary experimental confirmation of this novel approach is reported, based on already published NMR data for a single crystal of methylmalonic acid. The once extensively debated issues of quenching of the coherent tunneling and of the classical limit in the dynamics of the methyl groups are readdressed and presented in a consistent manner.
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Affiliation(s)
- S Szymański
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warszawa, Poland.
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Szymański S. Theory of damped quantum rotation in nuclear magnetic resonance spectra. III. Nuclear permutation symmetry of the line shape equation. J Chem Phys 2009; 131:244504. [PMID: 20059076 DOI: 10.1063/1.3276452] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The damped quantum rotation (DQR) theory describes manifestations in nuclear magnetic resonance spectra of the coherent and stochastic dynamics of N-fold molecular rotors composed of indistinguishable particles. The standard jump model is only a limiting case of the DQR approach; outside this limit, the stochastic motions of such rotors have no kinematic description. In this paper, completing the previous two of this series, consequences of nuclear permutation symmetry for the properties of the DQR line shape equation are considered. The systems addressed are planar rotors, such as aromatic hydrocarbons' rings, occurring inside of molecular crystals oriented in the magnetic field. Under such conditions, oddfold rotors can have nontrivial permutation symmetries only for peculiar orientations while evenfold ones always retain their intrinsic symmetry element, which is rotation by 180 degrees about the N-fold axis; in specific orientations the latter can gain two additional symmetry elements. It is shown that the symmetry selection rules applicable to the classical rate processes in fluids, once recognized as having two diverse aspects, macroscopic and microscopic, are also rigorously valid for the DQR processes in the solid state. However, formal justification of these rules is different because the DQR equation is based on the Pauli principle, which is ignored in the jump model. For objects like the benzene ring, exploitation of these rules in simulations of spectra using the DQR equation can be of critical significance for the feasibility of the calculations. Examples of such calculations for the proton system of the benzene ring in a general orientation are provided. It is also shown that, because of the intrinsic symmetries of the evenfold rotors, many of the DQR processes, which such rotors can undergo, are unobservable in NMR spectra.
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Affiliation(s)
- S Szymański
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01-224 Warszawa, Poland.
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Prager M, Pawlukojc A, Wischnewski A, Wuttke J. Inelastic neutron scattering study of methyl groups rotation in some methylxanthines. J Chem Phys 2007; 127:214509. [DOI: 10.1063/1.2803187] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Ratajczyk T, Szymański S. Theory of damped quantum rotation in nuclear magnetic resonance spectra. II. Numerical simulations for the benzene rotor. J Chem Phys 2007; 127:184504. [DOI: 10.1063/1.2785180] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Gutsche P, Schmitt H, Haeberlen U, Ratajczyk T, Szymanski S. Fingerprints of Damped Quantum Rotation Observed in Solid-State Proton NMR Spectra. Chemphyschem 2006; 7:886-93. [PMID: 16596612 DOI: 10.1002/cphc.200500572] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
(1)H NMR spectra of the methyl group in an oriented crystal sample of methylmalonic acid with all three non-methyl protons replaced by deuterons are interpreted in terms of the damped quantum rotation (DQR) theory of NMR line shapes. The DQR approach offers a perfect theoretical reproduction of the observed spectra while the conventional Alexander-Binsch line-shape model shows evident defects in the present case. The temperature trends of the quantities characterizing the coherent and incoherent dynamics of the methyl group in the DQR approach (the effective tunnelling frequency and two coherence-damping rates) derived from the spectra are fairly reproduced using a model reported previously. The present findings provide further evidence of limitations to the validity of the common belief that molecular rate processes in condensed phases are necessarily classical.
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Affiliation(s)
- Peter Gutsche
- Max-Planck Institute for Medical Research, 69120 Heidelberg, Germany
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Ratajczyk T, Szymański S. Theory of damped quantum rotation in NMR spectra. I. Fundamental aspects. J Chem Phys 2005; 123:204509. [PMID: 16351283 DOI: 10.1063/1.2131868] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The damped quantum rotation (DQR) theory, formulated originally for methyl-like atomic groupings, is now extended to hindered (N>3)-fold molecular rotors, such as the cyclopentadienyl, benzene, and cycloheptatrienyl rings in solid phase environments. It heightens the significance of the Pauli principle in shaping up the stochastic dynamics of such objects, reflected in NMR line shapes. The corresponding NMR line-shape equation is derived; its stochastic part is shown for the first time to have the double commutator form for any values of the quantum-mechanical (coherence-damping) rate constants entering it. Constraints on the relative magnitudes of such constants are determined under which the DQR line-shape equation is converted into the phenomenological Alexander-Binsch equation describing classical jumps of the rotor. When all the quantum rate constants happen to be equal, the phenomenological model of equal jump rates between any two of the N (equivalent) orientations of the rotor is reproduced. On the other hand, the seemingly most plausible (for N>3) nearest-neighbor hopping model does not have any peculiar grounds in the DQR approach. For the special instances of stochastic molecular motions addressed in this work, the extended DQR formalism affords a quantification of the "degree of classicality" represented by a complete set of the relevant quantum rate constants. In view of our earlier experimental findings for the methyl rotors, the very occurrence of the nonclassical DQR effects seems unquestionable even for the objects of the size of benzene. The question of under what circumstances such effects can be big enough to be detected experimentally will be addressed in Part II of this work.
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Affiliation(s)
- T Ratajczyk
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01-224 Warszawa, Poland
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Würger A. Resonant coupling of free quantum rotors in inclusion compounds. PHYSICAL REVIEW LETTERS 2002; 88:063002. [PMID: 11863803 DOI: 10.1103/physrevlett.88.063002] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2001] [Indexed: 05/23/2023]
Abstract
NH3 groups in certain Hofmann clathrates form almost free one-dimensional quantum rotors with energy levels E(n) = n(2)B and angular momentum n (planck constant), where n = 0, +/-1, +/-2,.... Recent neutron scattering experiments revealed a surprising temperature dependence for the linewidths of the n = 0 <--> 1, 0 <--> 2, and 1 <--> 2 transitions. We propose a novel line broadening mechanism based on rotor-rotor coupling and obtain a simple analytic expression for the widths that depends on the rotor level occupation and on the 3-proton spin degeneracies of initial and final states. Our model provides, without adjustable parameters, a good fit both to the temperature dependence of the observed widths and to their relative magnitude.
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Affiliation(s)
- Alois Würger
- Université Bordeaux 1, CPMOH, 351 cours de la Libération, 33405 Talence, France
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Szymański S, Olejniczak Z, Detken A, Haeberlen U. Iterative lineshape analysis of quadrupolar echo spectra of a damped CD(3) quantum rotor: preliminary evidence of a novel mechanism of stochastic spin exchange. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2001; 148:277-288. [PMID: 11237633 DOI: 10.1006/jmre.2000.2252] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
It is demonstrated that the wealth of information about damped quantum rotation of CD(3) groups, contained in quadrupolar echo spectra, can be fully explored in a broad temperature range using a method of iterative analysis of the spectral lineshapes. The recently reported lineshape equation which, apart from the quantum tunneling and the dissipative Alexander--Binsch terms, contains an additional dissipative term having no classical analog is shown to be capable of describing even subtle details of the spectra of a crystal of acetylsalicylic acid--CD(3) oriented specifically in the magnetic field. Preliminary evidence of the occurrence of this novel dissipative mechanism in the system studied is reported. The results obtained seem to suggest that there is no "classical limit" in the dissipative behavior of this system.
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Affiliation(s)
- S Szymański
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
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Szymański S. Nuclear magnetic resonance line shapes of methyl-like quantum rotors in low-temperature solids. J Chem Phys 1999. [DOI: 10.1063/1.479289] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Prager M, Heidemann A. Rotational Tunneling and Neutron Spectroscopy: A Compilation. Chem Rev 1997; 97:2933-2966. [PMID: 11851482 DOI: 10.1021/cr9500848] [Citation(s) in RCA: 209] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. Prager
- Institut Laue-Langevin, B.P. 156, F-38042 Grenoble, France
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Cleemput MV, Buekenhoudt A, Gerven LV, Horsewill AJ. Quantum and classical dynamics of a methyl group with tunneling frequency 3.4 MHz studied by low field NMR. J Chem Phys 1995. [DOI: 10.1063/1.470515] [Citation(s) in RCA: 20] [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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2H NMR studies for the examination of methyl group rotations between their classical and quantum mechanical limits. ACTA ACUST UNITED AC 1993. [DOI: 10.1007/bf01316710] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Buekenhoudt A. Temperature dependence of methyl reorientation at intermediate hindering potentials. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 46:5377-5386. [PMID: 10004318 DOI: 10.1103/physrevb.46.5377] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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van der Putten D, Diezemann G, Fujara F, Hartmann K, Sillescu H. Methyl group dynamics in α‐crystallized toluene as studied by deuteron spin–lattice relaxation. J Chem Phys 1992. [DOI: 10.1063/1.462130] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Prager M, Asmussen B, Press W, Blank H, Carlile CJ. Rotational spectra and the phase diagram of CH4/Ar mixtures. J Chem Phys 1991. [DOI: 10.1063/1.461458] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Diezemann G, Sillescu H, van der Putten D. Spin lattice relaxation rates of tunnelling CD3 groups. ACTA ACUST UNITED AC 1991. [DOI: 10.1007/bf01309425] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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