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Lacerda EG, Sauer SPA, Mikkelsen KV, Coutinho K, Canuto S. Theoretical study of the NMR chemical shift of Xe in supercritical condition. J Mol Model 2018; 24:62. [PMID: 29464335 DOI: 10.1007/s00894-018-3600-4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2017] [Accepted: 01/29/2018] [Indexed: 12/23/2022]
Abstract
In this work we investigate the level of theory necessary for reproducing the non-linear variation of the 129Xe nuclear magnetic resonance (NMR) chemical shift with the density of Xe in supercritical conditions. In detail we study how the 129Xe chemical shift depends under supercritical conditions on electron correlation, relativistic and many-body effects. The latter are included using a sequential-QM/MM methodology, in which a classical MD simulation is performed first and the chemical shift is then obtained as an average of quantum calculations of 250 MD snapshots conformations carried out for Xe n clusters (n = 2 - 8 depending on the density). The analysis of the relativistic effects is made at the level of 4-component Hartree-Fock calculations (4c-HF) and electron correlation effects are considered using second order Møller-Plesset perturbation theory (MP2). To simplify the calculations of the relativistic and electron correlation effects we adopted an additive scheme, where the calculations on the Xe n clusters are carried out at the non-relativistic Hartree-Fock (HF) level, while electron correlation and relativistic corrections are added for all the pairs of Xe atoms in the clusters. Using this approach we obtain very good agreement with the experimental data, showing that the chemical shift of 129Xe in supercritical conditions is very well described by cluster calculations at the HF level, with small contributions from relativistic and electron correlation effects.
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Affiliation(s)
- Evanildo G Lacerda
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark.
- Instituto de Física da Universidade de São Paulo, Rua do Matão 1371, 05508-090, São Paulo, SP, Brazil.
| | - Stephan P A Sauer
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark
| | - Kurt V Mikkelsen
- Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark
| | - Kaline Coutinho
- Instituto de Física da Universidade de São Paulo, Rua do Matão 1371, 05508-090, São Paulo, SP, Brazil
| | - Sylvio Canuto
- Instituto de Física da Universidade de São Paulo, Rua do Matão 1371, 05508-090, São Paulo, SP, Brazil
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2
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Mandal A, Hunt KLC. Gauge-invariant expectation values of the energy of a molecule in an electromagnetic field. J Chem Phys 2016; 144:044109. [PMID: 26827204 DOI: 10.1063/1.4938564] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, we show that the full Hamiltonian for a molecule in an electromagnetic field can be separated into a molecular Hamiltonian and a field Hamiltonian, both with gauge-invariant expectation values. The expectation value of the molecular Hamiltonian gives physically meaningful results for the energy of a molecule in a time-dependent applied field. In contrast, the usual partitioning of the full Hamiltonian into molecular and field terms introduces an arbitrary gauge-dependent potential into the molecular Hamiltonian and leaves a gauge-dependent form of the Hamiltonian for the field. With the usual partitioning of the Hamiltonian, this same problem of gauge dependence arises even in the absence of an applied field, as we show explicitly by considering a gauge transformation from zero applied field and zero external potentials to zero applied field, but non-zero external vector and scalar potentials. We resolve this problem and also remove the gauge dependence from the Hamiltonian for a molecule in a non-zero applied field and from the field Hamiltonian, by repartitioning the full Hamiltonian. It is possible to remove the gauge dependence because the interaction of the molecular charges with the gauge potential cancels identically with a gauge-dependent term in the usual form of the field Hamiltonian. We treat the electromagnetic field classically and treat the molecule quantum mechanically, but nonrelativistically. Our derivation starts from the Lagrangian for a set of charged particles and an electromagnetic field, with the particle coordinates, the vector potential, the scalar potential, and their time derivatives treated as the variables in the Lagrangian. We construct the full Hamiltonian using a Lagrange multiplier method originally suggested by Dirac, partition this Hamiltonian into a molecular term Hm and a field term Hf, and show that both Hm and Hf have gauge-independent expectation values. Any gauge may be chosen for the calculations; but following our partitioning, the expectation values of the molecular Hamiltonian are identical to those obtained directly in the Coulomb gauge. As a corollary of this result, the power absorbed by a molecule from a time-dependent, applied electromagnetic field is equal to the time derivative of the non-adiabatic term in the molecular energy, in any gauge.
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Affiliation(s)
- Anirban Mandal
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
| | - Katharine L C Hunt
- Department of Chemistry, Michigan State University, East Lansing, Michigan 48824, USA
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3
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Jankowska M, Kupka T, Stobiński L, Faber R, Lacerda EG, Sauer SPA. Spin-orbit ZORA and four-component Dirac-Coulomb estimation of relativistic corrections to isotropic nuclear shieldings and chemical shifts of noble gas dimers. J Comput Chem 2015; 37:395-403. [DOI: 10.1002/jcc.24228] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2015] [Revised: 09/28/2015] [Accepted: 10/01/2015] [Indexed: 11/11/2022]
Affiliation(s)
- Marzena Jankowska
- Faculty of Chemistry; University of Opole; 48, Oleska Str. 45-052 Opole Poland
| | - Teobald Kupka
- Faculty of Chemistry; University of Opole; 48, Oleska Str. 45-052 Opole Poland
| | - Leszek Stobiński
- Polish Academy of Sciences; Institute of Physical Chemistry; 44/52, Kasprzaka, Str. 01-224 Warsaw Poland
- Faculty of Chemical and Process Engineering; Warsaw University of Technology; Warynskiego 1 00-645 Warsaw Poland
| | - Rasmus Faber
- Department of Chemistry; University of Copenhagen; Universitetsparken 5 DK-2100 Copenhagen Denmark
| | - Evanildo G. Lacerda
- Department of Chemistry; University of Copenhagen; Universitetsparken 5 DK-2100 Copenhagen Denmark
| | - Stephan P. A. Sauer
- Department of Chemistry; University of Copenhagen; Universitetsparken 5 DK-2100 Copenhagen Denmark
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Makulski W. (129) Xe and (131) Xe nuclear magnetic dipole moments from gas phase NMR spectra. MAGNETIC RESONANCE IN CHEMISTRY : MRC 2015; 53:273-279. [PMID: 25594841 DOI: 10.1002/mrc.4191] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2014] [Revised: 10/04/2014] [Accepted: 10/22/2014] [Indexed: 06/04/2023]
Abstract
(3) He, (129) Xe and (131) Xe NMR measurements of resonance frequencies in the magnetic field B0=11.7586 T in different gas phase mixtures have been reported. Precise radiofrequency values were extrapolated to the zero gas pressure limit. These results combined with new quantum chemical values of helium and xenon nuclear magnetic shielding constants were used to determine new accurate nuclear magnetic moments of (129) Xe and (131) Xe in terms of that of the (3) He nucleus. They are as follows: μ((129) Xe) = -0.7779607(158)μN and μ((131) Xe) = +0.6918451(70)μN . By this means, the new 'helium method' for estimations of nuclear dipole moments was successfully tested. Gas phase NMR spectra demonstrate the weak intermolecular interactions observed on the (3) He and (129) Xe and (131) Xe shielding in the gaseous mixtures with Xe, CO2 and SF6 .
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Affiliation(s)
- Włodzimierz Makulski
- Laboratory of NMR Spectroscopy, Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093, Warsaw, Poland
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5
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Standara S, Kulhánek P, Marek R, Straka M. 129Xe NMR chemical shift in Xe@C60calculated at experimental conditions: Essential role of the relativity, dynamics, and explicit solvent. J Comput Chem 2013; 34:1890-8. [DOI: 10.1002/jcc.23334] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2013] [Revised: 04/17/2013] [Accepted: 04/19/2013] [Indexed: 11/11/2022]
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Olejniczak M, Bast R, Saue T, Pecul M. A simple scheme for magnetic balance in four-component relativistic Kohn–Sham calculations of nuclear magnetic resonance shielding constants in a Gaussian basis. J Chem Phys 2012; 136:014108. [DOI: 10.1063/1.3671390] [Citation(s) in RCA: 67] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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7
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Garbacz P, Piszczatowski K, Jackowski K, Moszynski R, Jaszuński M. Weak intermolecular interactions in gas-phase nuclear magnetic resonance. J Chem Phys 2011; 135:084310. [DOI: 10.1063/1.3624658] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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8
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Standara S, Kulhánek P, Marek R, Horníček J, Bouř P, Straka M. Simulations of 129Xe NMR chemical shift of atomic xenon dissolved in liquid benzene. Theor Chem Acc 2011. [DOI: 10.1007/s00214-011-0930-z] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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9
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Wang L, Yang M. Theoretical studies of potential energy surface and rotational spectra of Xe-H(2)O van der Waals complex. J Chem Phys 2009; 129:174305. [PMID: 19045345 DOI: 10.1063/1.3005645] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work we report an ab initio intermolecular potential energy surface and theoretical spectroscopic studies for Xe-H(2)O complex. The ab initio energies are calculated with CCSD(T) method and large basis sets (aug-cc-pVQZ for H and O and aug-cc-pVQZ-PP for Xe) augmented by a {3s3p2d2f1g} set of bond functions. This potential energy surface has a global minimum corresponding to a planar and nearly linear hydrogen bonded configuration with a well depth of 192.5 cm(-1) at intermolecular distance of 4.0 A, which is consistent with the previous determined potential by Wen and Jager [J. Phys. Chem. A 110, 7560 (2006)]. The bound state calculations have been performed for the complex by approximating the water molecule as a rigid rotor. The theoretical rotational transition frequencies, isotopic shifts, nuclear quadrupole coupling constants, and structure parameters are in good agreement with the experimental observed values. The wavefunctions are analyzed to understand the dynamics of the ground and the first excited states.
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Affiliation(s)
- Lin Wang
- State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China
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10
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Straka M, Lantto P, Vaara J. Toward Calculations of the 129Xe Chemical Shift in Xe@C60 at Experimental Conditions: Relativity, Correlation, and Dynamics. J Phys Chem A 2008; 112:2658-68. [DOI: 10.1021/jp711674y] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Affiliation(s)
- Michal Straka
- Laboratory of Physical Chemistry, Department of Chemistry, University of Helsinki, P.O. Box 55 (A. I. Virtasen aukio 1), FIN-00014 Helsinki, Finland, Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo n. 2., CZE-16610 Praha 6, Czech Republic, and NMR Research Group, Department of Physical Sciences, University of Oulu, P. O. Box 3000, FIN-90014 Oulu, Finland
| | - Perttu Lantto
- Laboratory of Physical Chemistry, Department of Chemistry, University of Helsinki, P.O. Box 55 (A. I. Virtasen aukio 1), FIN-00014 Helsinki, Finland, Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo n. 2., CZE-16610 Praha 6, Czech Republic, and NMR Research Group, Department of Physical Sciences, University of Oulu, P. O. Box 3000, FIN-90014 Oulu, Finland
| | - Juha Vaara
- Laboratory of Physical Chemistry, Department of Chemistry, University of Helsinki, P.O. Box 55 (A. I. Virtasen aukio 1), FIN-00014 Helsinki, Finland, Institute of Organic Chemistry and Biochemistry, Academy of Sciences of the Czech Republic, Flemingovo n. 2., CZE-16610 Praha 6, Czech Republic, and NMR Research Group, Department of Physical Sciences, University of Oulu, P. O. Box 3000, FIN-90014 Oulu, Finland
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Hanni M, Lantto P, Iliaš M, Jensen HJA, Vaara J. Relativistic effects in the intermolecular interaction-induced nuclear magnetic resonance parameters of xenon dimer. J Chem Phys 2007; 127:164313. [DOI: 10.1063/1.2777143] [Citation(s) in RCA: 35] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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12
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Antusek A, Jaszuński M, Rizzo A. Ab initiostudy of interaction-induced NMR shielding constants in mixed rare gas dimers. J Chem Phys 2007; 126:074303. [PMID: 17328601 DOI: 10.1063/1.2446955] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
The interaction-induced contribution to the NMR shielding constants in homonuclear A2 and heteronuclear AB (A,B=He,Ne,Ar) dimers is obtained ab initio by employing a coupled cluster singles and doubles with perturbative treatment of triples wave function model and extended correlation-consistent basis sets. The second virial coefficients entering the expansion of the property with the density are then computed in a fully quantum mechanical approach, for temperatures ranging from the limit of dissociation of the dimer to well above standard conditions. The results can be used to describe the density and temperature dependence of the shielding constants in binary mixtures of helium, neon, and argon. The predicted effects should be observable for the interaction of 21Ne with other rare gases.
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Affiliation(s)
- Andrej Antusek
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44, 01224 Warsaw, Poland
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Ruiz EJ, Sears DN, Pines A, Jameson CJ. Diastereomeric Xe chemical shifts in tethered cryptophane cages. J Am Chem Soc 2007; 128:16980-8. [PMID: 17177449 DOI: 10.1021/ja066661z] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Cryptophane cages serve as host molecules to a Xe atom. Functionalization of cryptophane-A has permitted the development of Xe as a biosensor. Synthetic routes used to prepare cryptophanes result in racemic mixtures of the chiral cages. In the preparation of a tethered cryptophane-A cage for biosensor applications, some achiral and chiral substituents such as left-handed amino acids have been used. When the substituent is achiral, the NMR signal of the Xe atom in the functionalized cage in solution is a single isotropic peak, since the Xe shielding tensor components in the R and L cages differ by no more than the signs of the off-diagonal elements. Chiral substituents can split the cage-encapsulated Xe NMR signal into one or more sets of doublets, depending on the number of asymmetric centers in the substituent. We carry out quantum mechanical calculations of Xe nuclear magnetic shielding for the Xe atom at the same strategic position within an L cryptophane-A cage, under the influence of chiral potentials that represent r or l substituents outside the cage. Calculations of the Xe shielding response in the Lr and Ll diastereomeric pairs permit the prediction of the relative order of the Xe chemical shifts in solutions containing the Rl and Ll diastereomers. Where the substituent itself possesses two chiral centers, comparison of the calculated isotropic shielding responses in the Llr, Lrl, Rll, and Lrr systems, respectively, permits the prediction of the Xe spectrum of diastereomeric systems in solutions containing Llr, Rlr, Lll, and Rll systems. Assignment of the peaks observed in the experimental Xe NMR spectra is therefore possible, without having to undertake the difficult synthetic route that produces a single optically pure enantiomer.
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Affiliation(s)
- E Janette Ruiz
- Department of Chemistry, University of California at Berkeley, Berkeley, CA 94720, USA
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14
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Sears DN, Vukovic L, Jameson CJ. Xe nuclear magnetic resonance line shapes in channels decorated with paramagnetic centers. J Chem Phys 2006; 125:114708. [PMID: 16999502 DOI: 10.1063/1.2338809] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
To make predictions of the Xe NMR line shapes for Xe in channels decorated with paramagnetic centers, we consider a model system using the O(2) molecule as the paramagnetic center. The previously calculated quantum mechanical Xe@O(2) hyperfine tensor for various configurations of Xe in the presence of O(2) provides a model for the hyperfine response of Xe atom to the presence of a paramagnetic center. The averaging is carried out using the same grand canonical Monte Carlo methodology as for calculating NMR line shapes for Xe in diamagnetic channels, modified to include the effects of the hyperfine tensor response. We explore the temperature dependence of the Xe line shapes, the dependence on the concentration, and the symmetry of distribution of embedded paramagnetic centers, on the orientation of the paramagnetic center axis with respect to the channel axis, and on the radial distance of the paramagnetic center from the axis of the channel. We predict Xe line shape signatures of the presence and orientation of paramagnetic centers and deduce which tensor elements provide measures of concentration and radial distance of paramagnetic centers from the channel axis.
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Affiliation(s)
- Devin N Sears
- Department of Chemistry, University of Alberta, Edmonton Alberta, T6G 2G2, Canada
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15
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Vukovic L, Jameson CJ, Sears DN. Intermolecular hyperfine tensor for Xe@O2. Density and temperature dependence of Xe chemical shifts in oxygen gas. Mol Phys 2006. [DOI: 10.1080/00268970500525614] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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16
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Ueda T, Omi H, Yukioka T, Eguchi T. High-Pressure129Xe NMR Study of the Intermolecular Interaction of Xenon Confined in Activated Carbon Fiber (ACF). BULLETIN OF THE CHEMICAL SOCIETY OF JAPAN 2006. [DOI: 10.1246/bcsj.79.237] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
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17
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Omi H, Ueda T, Kato N, Miyakubo K, Eguchi T. Local structure of xenon adsorbed in the nanospaces of zeolites as studied by high-pressure 129Xe NMR. Phys Chem Chem Phys 2006; 8:3857-66. [DOI: 10.1039/b604633a] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
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18
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Jameson CJ, Sears DN, Murad S. Molecular dynamics averaging of Xe chemical shifts in liquids. J Chem Phys 2004; 121:9581-92. [PMID: 15538880 DOI: 10.1063/1.1807817] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
The Xe nuclear magnetic resonance chemical shift differences that afford the discrimination between various biological environments are of current interest for biosensor applications and medical diagnostic purposes. In many such environments the Xe signal appears close to that in water. We calculate average Xe chemical shifts (relative to the free Xe atom) in solution in eleven liquids: water, isobutane, perfluoro-isobutane, n-butane, n-pentane, neopentane, perfluoroneopentane, n-hexane, n-octane, n-perfluorooctane, and perfluorooctyl bromide. The latter is a liquid used for intravenous Xe delivery. We calculate quantum mechanically the Xe shielding response in Xe-molecule van der Waals complexes, from which calculations we develop Xe (atomic site) interpolating functions that reproduce the ab initio Xe shielding response in the complex. By assuming additivity, these Xe-site shielding functions can be used to calculate the shielding for any configuration of such molecules around Xe. The averaging over configurations is done via molecular dynamics (MD). The simulations were carried out using a MD technique that one of us had developed previously for the simulation of Henry's constants of gases dissolved in liquids. It is based on separating a gaseous compartment in the MD system from the solvent using a semipermeable membrane that is permeable only to the gas molecules. We reproduce the experimental trends in the Xe chemical shifts in n-alkanes with increasing number of carbons and the large chemical shift difference between Xe in water and in perfluorooctyl bromide. We also reproduce the trend for a given solvent of decreasing Xe chemical shift with increasing temperature. We predict chemical shift differences between Xe in alkanes vs their perfluoro counterparts.
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Affiliation(s)
- Cynthia J Jameson
- Department of Chemistry, MC-111, University of Illinois at Chicago, Chicago, Illinois 60607-7061, USA
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Hanni M, Lantto P, Runeberg N, Jokisaari J, Vaara J. Calculation of binary magnetic properties and potential energy curve in xenon dimer: Second virial coefficient of 129Xe nuclear shielding. J Chem Phys 2004; 121:5908-19. [PMID: 15367019 DOI: 10.1063/1.1785146] [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
Quantum chemical calculations of the nuclear shielding tensor, the nuclear quadrupole coupling tensor, and the spin-rotation tensor are reported for the Xe dimer using ab initio quantum chemical methods. The binary chemical shift delta, the anisotropy of the shielding tensor Delta sigma, the nuclear quadrupole coupling tensor component along the internuclear axis chi( parallel ), and the spin-rotation constant C( perpendicular ) are presented as a function of internuclear distance. The basis set superposition error is approximately corrected for by using the counterpoise correction (CP) method. Electron correlation effects are systematically studied via the Hartree-Fock, complete active space self-consistent field, second-order Møller-Plesset many-body perturbation, and coupled-cluster singles and doubles (CCSD) theories, the last one without and with noniterative triples, at the nonrelativistic all-electron level. We also report a high-quality theoretical interatomic potential for the Xe dimer, gained using the relativistic effective potential/core polarization potential scheme. These calculations used valence basis set of cc-pVQZ quality supplemented with a set of midbond functions. The second virial coefficient of Xe nuclear shielding, which is probably the experimentally best-characterized intermolecular interaction effect in nuclear magnetic resonance spectroscopy, is computed as a function of temperature, and compared to experiment and earlier theoretical results. The best results for the second virial coefficient, obtained using the CCSD(CP) binary chemical shift curve and either our best theoretical potential or the empirical potentials from the literature, are in good agreement with experiment. Zero-point vibrational corrections of delta, Delta sigma, chi (parallel), and C (perpendicular) in the nu=0, J=0 rovibrational ground state of the xenon dimer are also reported.
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Affiliation(s)
- Matti Hanni
- NMR Research Group, Department of Physical Sciences, P.O. Box 3000, FIN-90014 University of Oulu, Finland
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Jameson CJ, Stueber D. The nuclear magnetic resonance line shapes of Xe in the cages of clathrate hydrates. J Chem Phys 2004; 120:10200-14. [PMID: 15268044 DOI: 10.1063/1.1718349] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
We report, for the first time, a prediction of the line shapes that would be observed in the (129)Xe nuclear magnetic resonance (NMR) spectrum of xenon in the cages of clathrate hydrates. We use the dimer tensor model to represent pairwise contributions to the intermolecular magnetic shielding tensor for Xe at a specific location in a clathrate cage. The individual tensor components from quantum mechanical calculations in clathrate hydrate structure I are represented by contributions from parallel and perpendicular tensor components of Xe-O and Xe-H dimers. Subsequently these dimer tensor components are used to reconstruct the full magnetic shielding tensor for Xe at an arbitrary location in a clathrate cage. The reconstructed tensors are employed in canonical Monte Carlo simulations to find the Xe shielding tensor component along a particular magnetic field direction. The shielding tensor component weighted according to the probability of finding a crystal fragment oriented along this direction in a polycrystalline sample leads to a predicted line shape. Using the same set of Xe-O and Xe-H shielding functions and the same Xe-O and Xe-H potential functions we calculate the Xe NMR spectra of Xe atom in 12 distinct cage types in clathrate hydrates structures I, II, H, and bromine hydrate. Agreement with experimental spectra in terms of the number of unique tensor components and their relative magnitudes is excellent. Agreement with absolute magnitudes of chemical shifts relative to free Xe atom is very good. We predict the Xe line shapes in two cages in which Xe has not yet been observed.
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Affiliation(s)
- Cynthia J Jameson
- Department of Chemistry, M/C-111, University of Illinois at Chicago, Chicago, IL 60607-7061, USA
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Abstract
It is now generally recognized that overlap-exchange interactions are the primary cause of the medium-dependent magnetic shielding (chemical shift) in all noble gases except helium, although the attractive electrostatic-dispersion (van der Waals) interactions play an indirect role in determining the penetration of the interacting species into the repulsive overlap-exchange region. The short-range nature of these overlap-exchange interactions, combined with the fact that they often can be approximated by simple functions of the overlap of the wave functions of the interacting species, suggests a useful semiempirical model of these chemical shifts. In it the total shielding is the sum of shieldings due to pairwise interactions of the noble gas atom with the individual atoms of the medium, with the "atomic" shielding terms either estimated by simple functions of the atomic overlap integrals averaged over their Boltzmann-weighted separations, or determined by fits to experimental data in systems whose complexity makes the former procedure impractical. Results for (129)Xe chemical shifts in the noble gases and in a variety of molecular and condensed systems, including families of n-alkanes, straight-chain alcohols, and the endohedral compounds Xe@C(60) and Xe@C(70) are encouraging for the applicability of the model to systems of technical and biomedical interest.
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Forgeron MAM, Wasylishen RE, Penner GH. Investigation of Magnetic Shielding in Xenon Difluoride Using Solid-State NMR Spectroscopy and Relativistic Density Functional Theory. J Phys Chem A 2004. [DOI: 10.1021/jp031279j] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Michelle A. M. Forgeron
- Department of Chemistry, Gunning/Lemieux Chemistry Centre, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
| | - Roderick E. Wasylishen
- Department of Chemistry, Gunning/Lemieux Chemistry Centre, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
| | - Glenn H. Penner
- Department of Chemistry, Gunning/Lemieux Chemistry Centre, University of Alberta, Edmonton, Alberta, Canada T6G 2G2
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Stueber D, Jameson CJ. The chemical shifts of Xe in the cages of clathrate hydrate Structures I and II. J Chem Phys 2004; 120:1560-71. [PMID: 15268283 DOI: 10.1063/1.1632895] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
We report, for the first time, a calculation of the isotropic NMR chemical shift of 129Xe in the cages of clathrate hydrates Structures I and II. We generate a shielding surface for Xe in the clathrate cages by quantum mechanical calculations. Subsequently this shielding surface is employed in canonical Monte Carlo simulations to find the average isotropic Xe shielding values in the various cages. For the two types of cages in clathrate hydrate Structure I, we find the intermolecular shielding values [sigma(Xe@5(12) cage)-sigma(Xe atom)]=-214.0 ppm, and [sigma(Xe@5(12)6(2) cage)-sigma(Xe atom)]=-146.9 ppm, in reasonable agreement with the values -242 and -152 ppm, respectively, observed experimentally by Ripmeester and co-workers between 263 and 293 K. For the 5(12) and 5(12)6(4) cages of Structure II we find [sigma(Xe@5(12) cage)-sigma(Xe atom)]=-206.7 ppm, and [sigma(Xe@5(12)6(4) cage)-sigma(Xe atom)]=-104.7 ppm, also in reasonable agreement with the values -225 and -80 ppm, respectively, measured in a Xe-propane type II mixed clathrate hydrate at 77 and 220-240 K by Ripmeester et al.
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Affiliation(s)
- Dirk Stueber
- Department of Chemistry, M/C-111, University of Illinois at Chicago, Chicago, Illinois 60607-7061, USA
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Sears DN, Jameson CJ. Theoretical calculations of the Xe chemical shifts in cryptophane cages. J Chem Phys 2003. [DOI: 10.1063/1.1625364] [Citation(s) in RCA: 33] [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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Jameson C, Murad S. On using the NMR chemical shift to assess polar–nonpolar cross-intermolecular interactions. Chem Phys Lett 2003. [DOI: 10.1016/j.cplett.2003.09.070] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Sears DN, Jameson CJ, Harris RA. Nuclear magnetic shielding and chirality. I. The shielding tensor of Xe interacting with Ne helices. J Chem Phys 2003. [DOI: 10.1063/1.1586698] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
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Sears DN, Jameson CJ, Harris RA. Nuclear magnetic shielding and chirality. II. The shielding tensor of a naked spin in Ne helices. J Chem Phys 2003. [DOI: 10.1063/1.1586699] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
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