Sherwood, MH
1993
Comparing, Modeling, and Assigning Chemical-Shift Tensors in the Cartestian, Irreducible Spherical, and Icosahedral Representations
Alderman, D.W.; Sherwood, M.H. and Grant, D.M.
Journal of Magnetic Resonance, 101:188-197, 1993. Funded by US Department of Energy, Division of Chemical Sciences and Office of Basic Energy Sciences.
A measure of the difference between two chemical-shift tensors is developed by defining the scalar distance between them. Chemical-shift tensors are treated as functions whose domain is the surface of a sphere and the mathematical definition of the quadratic distance between two functions is invoked. Expressions for the distance between two chemical-shift tensors are developed in the Cartesian and irreducible spherical representations and in a new icosahedral representation. A representation wherein the chemical-shift tensor is specified by the shifts when the magnetic field is along six directions defined by the vertices of an icosahedron is developed and its properties are discussed. The expression for the distance between two tensors is found to be particularly attractive and useful in this icosahedral representation. The distance between tensors computed in the icosahedral representation is useful in fitting linear models to tensor data. It is shown how such fitting can contribute to the assignment of tensors obtained from single-crystal studies. A quantitative figure of merit useful for comparing multiple assignment possibilities is developed. The results derived are applicable to any physical phenomenon described by real zero-rank and second-rank tensors.
Chemical-Shift-Chemical-Shift Correlation Spectroscopy in Powdered Solids
Hughes, C.D.; Sherwood, M.H.; Alderman, D.W. and Grant, D.M.
Journal of Magnetic Resonance, 102:58-72, 1993. Funded by US Department of Energy.
Sample reorientation during the mixing time of a two-dimensional NMR exchange experiment allows the measurement of chemical-shift tensors in powdered samples whose one-dimensional powder patterns are too complex to reliably analyze. This technique has the advantages that the chemical-shift anisotropy has an unscaled representation, the artifacts caused by cross polarization, spin relaxation, and partial sample orientation can be accounted for, the experiment is relatively easy to perform, and no spinning sidebands interfere. The method is useful for sorting out the principal values of overlapping chemical-shift tensors.
1992
Chemical Shift-Chemical Shift Correlation Spectroscopy in Powdered Solids
Hughes, C.D.; Sherwood, M.H.; Alderman, D.W. and Grant, D.M.
Fifth Coal Chemistry Conference and Workshop, Rockford, IL, June 1992. Funded by US Department of Energy.
Sample reorientation during the mixing time of a two-dimensional NMR exchange experiment allows the measurements of chemical shift tensors in powdered samples whose one-dimensional powder patterns are too complex to reliably analyze. This technique has the advantages that the chemical shift anisotropy has an unscaled representation, the artifacts caused by cross polarization, spin relaxation and partial sample orientation can be accounted for, the experiment is relatively easy to perform, and no spinning sidebands interfere. The method is useful for sorting out the principal values of overlapping chemical shift tensors.
1991
Carbon-13 Chemical Shift Tensors in Polycyclic Aromatic Compounds. 2. Single-Crystal Study of Naphthalene
Sherwood, M.H.; Facelli, J.C.; Alderman, D.W. and Grant, D.M.
Journal of the American Chemistry Society, 113:750-753, 1991. Funded by US Department of Energy.
Carbon-13 chemical shift tensors have been determined in single crystal nephthalene. The high field component of every tensor is oriented perpendicular to the molecular plane, as in other aromatic compounds. The bridgehead carbon tensor is nearly axially symmetric, with its low field component approximately perpendicular to the central bridging bond, in agreement with theoretical predictions. Protonated carbon tensors in naphalene are more asymmetric, with their low-field components directed approximately along the C-H bonds. The Pople model of chemical shielding with MNDO wave functions reproduces the experimental in-plane shielding components. These calculations show that the in-plane components of the carbon shift tensors are governed by the bond orders of the adjacent bonds, and shift tensors thus provide valuable information relating to aromaticity. The measured tensors deviate significantly from the symmetry of an isolated naphthalene molecule because of the lower symmetry of the molecular site in the crystal.
1990
Two-Dimensional Chemical-Shift Tensor Correlation Spectroscopy. Analysis of Sensitivity and Optimal Measurement Directions
Alderman, D.W.; Sherwood, M.H. and Grant, D.M.
Journal of Magnetic Resonance, 86, 60-69, 1990. Funded by US Department of Energy.
Chemical-shift tensors can be determined from a single crystal placed in six or more orientations in a magnetic field. The sensitivity of this determination as a function of the selected crystal orientations is considered with a statistical figure of merit. A variety of configurations are examined, and it is found that the set of six orientations based on the vertices of an icosahedron optimizes the figure of merit and results in the most sensitive determination of the tensor. The relationship of these optimal orientations to those used previously in two-dimensional chemical-shift tensor correlation spectroscopy is discussed. It is shown that the high symmetry of the icosahedron simplifies the design on which the construction of a new sample orienting mechanism may be based.
Carbon-13 Chemical Shift Tensors in Polycyclic Aromatic Compounds. 2. Single-Crystal Study of Naphthalene
Sherwood, M.H.; Facelli, J.C.; Alderman, D.W. and Grant, D.M.
Am. Chem. Soc., 1990 (In press). Funded by US Department of Energy.
Carbon-13 chemical shift tensors have been determined in single crystal nephthalene. The high field component of every tensor is oriented perpendicular to the molecular plane, as in other aromatic compounds. The bridgehead carbon tensor is nearly axially symmetric, with its low field component approximately perpendicular to the central bridging bond, in agreement with theoretical predictions. Protonated carbon tensors in naphalene are more asymmetric, with their low-field components directed approximately along the C-H bonds. The Pople model of chemical shielding with MNDO wave functions reproduces the experimental in-plane shielding components. These calculations show that the in-plane components of the carbon shift tensors are governed by the bond orders of the adjacent bonds, and shift tensors thus provide valuable information relating to aromaticity. The measured tensors deviate significantly from the symmetry of an isolated naphthalene molecule because of the lower symmetry of the molecular site in the crystal.
1989
Two-Dimensional Chemical Shift Tensor Correlation Spectroscopy. Analysis of Sensitivity and Optimal Measurement Directions
Alderman, D.W.; Sherwood, M.H. and Grant, D.M.
Accepted for publication in J. Mag. Res., 1989. Funded by US Department of Energy.
Chemical shift tensors can be determined from a single crystal placed in six or more orientations in a magnetic field. The sensitivity of this determination as a function of the selected crystal orientations is considered with a statistical figure of merit. A variety of configurations are examined, and it is found that the set of six orientations based on the vertices of an icosahedron optimizes the figure of merit and results in the most sensitive determination of the tensor. The relationship of these optimal orientations to those used previously in two-dimensional chemical shift tensor correlation spectroscopy is discussed. It is shown that the high symmetry of the icosahedron simplifies the design on which the construction of a new sample orienting mechanism may be based.
Sherwood, MH
1993
Comparing, Modeling, and Assigning Chemical-Shift Tensors in the Cartestian, Irreducible Spherical, and Icosahedral Representations
Alderman, D.W.; Sherwood, M.H. and Grant, D.M.
Journal of Magnetic Resonance, 101:188-197, 1993. Funded by US Department of Energy, Division of Chemical Sciences and Office of Basic Energy Sciences.
A measure of the difference between two chemical-shift tensors is developed by defining the scalar distance between them. Chemical-shift tensors are treated as functions whose domain is the surface of a sphere and the mathematical definition of the quadratic distance between two functions is invoked. Expressions for the distance between two chemical-shift tensors are developed in the Cartesian and irreducible spherical representations and in a new icosahedral representation. A representation wherein the chemical-shift tensor is specified by the shifts when the magnetic field is along six directions defined by the vertices of an icosahedron is developed and its properties are discussed. The expression for the distance between two tensors is found to be particularly attractive and useful in this icosahedral representation. The distance between tensors computed in the icosahedral representation is useful in fitting linear models to tensor data. It is shown how such fitting can contribute to the assignment of tensors obtained from single-crystal studies. A quantitative figure of merit useful for comparing multiple assignment possibilities is developed. The results derived are applicable to any physical phenomenon described by real zero-rank and second-rank tensors.
Chemical-Shift-Chemical-Shift Correlation Spectroscopy in Powdered Solids
Hughes, C.D.; Sherwood, M.H.; Alderman, D.W. and Grant, D.M.
Journal of Magnetic Resonance, 102:58-72, 1993. Funded by US Department of Energy.
Sample reorientation during the mixing time of a two-dimensional NMR exchange experiment allows the measurement of chemical-shift tensors in powdered samples whose one-dimensional powder patterns are too complex to reliably analyze. This technique has the advantages that the chemical-shift anisotropy has an unscaled representation, the artifacts caused by cross polarization, spin relaxation, and partial sample orientation can be accounted for, the experiment is relatively easy to perform, and no spinning sidebands interfere. The method is useful for sorting out the principal values of overlapping chemical-shift tensors.
1992
Chemical Shift-Chemical Shift Correlation Spectroscopy in Powdered Solids
Hughes, C.D.; Sherwood, M.H.; Alderman, D.W. and Grant, D.M.
Fifth Coal Chemistry Conference and Workshop, Rockford, IL, June 1992. Funded by US Department of Energy.
Sample reorientation during the mixing time of a two-dimensional NMR exchange experiment allows the measurements of chemical shift tensors in powdered samples whose one-dimensional powder patterns are too complex to reliably analyze. This technique has the advantages that the chemical shift anisotropy has an unscaled representation, the artifacts caused by cross polarization, spin relaxation and partial sample orientation can be accounted for, the experiment is relatively easy to perform, and no spinning sidebands interfere. The method is useful for sorting out the principal values of overlapping chemical shift tensors.
1991
Carbon-13 Chemical Shift Tensors in Polycyclic Aromatic Compounds. 2. Single-Crystal Study of Naphthalene
Sherwood, M.H.; Facelli, J.C.; Alderman, D.W. and Grant, D.M.
Journal of the American Chemistry Society, 113:750-753, 1991. Funded by US Department of Energy.
Carbon-13 chemical shift tensors have been determined in single crystal nephthalene. The high field component of every tensor is oriented perpendicular to the molecular plane, as in other aromatic compounds. The bridgehead carbon tensor is nearly axially symmetric, with its low field component approximately perpendicular to the central bridging bond, in agreement with theoretical predictions. Protonated carbon tensors in naphalene are more asymmetric, with their low-field components directed approximately along the C-H bonds. The Pople model of chemical shielding with MNDO wave functions reproduces the experimental in-plane shielding components. These calculations show that the in-plane components of the carbon shift tensors are governed by the bond orders of the adjacent bonds, and shift tensors thus provide valuable information relating to aromaticity. The measured tensors deviate significantly from the symmetry of an isolated naphthalene molecule because of the lower symmetry of the molecular site in the crystal.
1990
Two-Dimensional Chemical-Shift Tensor Correlation Spectroscopy. Analysis of Sensitivity and Optimal Measurement Directions
Alderman, D.W.; Sherwood, M.H. and Grant, D.M.
Journal of Magnetic Resonance, 86, 60-69, 1990. Funded by US Department of Energy.
Chemical-shift tensors can be determined from a single crystal placed in six or more orientations in a magnetic field. The sensitivity of this determination as a function of the selected crystal orientations is considered with a statistical figure of merit. A variety of configurations are examined, and it is found that the set of six orientations based on the vertices of an icosahedron optimizes the figure of merit and results in the most sensitive determination of the tensor. The relationship of these optimal orientations to those used previously in two-dimensional chemical-shift tensor correlation spectroscopy is discussed. It is shown that the high symmetry of the icosahedron simplifies the design on which the construction of a new sample orienting mechanism may be based.
Carbon-13 Chemical Shift Tensors in Polycyclic Aromatic Compounds. 2. Single-Crystal Study of Naphthalene
Sherwood, M.H.; Facelli, J.C.; Alderman, D.W. and Grant, D.M.
Am. Chem. Soc., 1990 (In press). Funded by US Department of Energy.
Carbon-13 chemical shift tensors have been determined in single crystal nephthalene. The high field component of every tensor is oriented perpendicular to the molecular plane, as in other aromatic compounds. The bridgehead carbon tensor is nearly axially symmetric, with its low field component approximately perpendicular to the central bridging bond, in agreement with theoretical predictions. Protonated carbon tensors in naphalene are more asymmetric, with their low-field components directed approximately along the C-H bonds. The Pople model of chemical shielding with MNDO wave functions reproduces the experimental in-plane shielding components. These calculations show that the in-plane components of the carbon shift tensors are governed by the bond orders of the adjacent bonds, and shift tensors thus provide valuable information relating to aromaticity. The measured tensors deviate significantly from the symmetry of an isolated naphthalene molecule because of the lower symmetry of the molecular site in the crystal.
1989
Two-Dimensional Chemical Shift Tensor Correlation Spectroscopy. Analysis of Sensitivity and Optimal Measurement Directions
Alderman, D.W.; Sherwood, M.H. and Grant, D.M.
Accepted for publication in J. Mag. Res., 1989. Funded by US Department of Energy.
Chemical shift tensors can be determined from a single crystal placed in six or more orientations in a magnetic field. The sensitivity of this determination as a function of the selected crystal orientations is considered with a statistical figure of merit. A variety of configurations are examined, and it is found that the set of six orientations based on the vertices of an icosahedron optimizes the figure of merit and results in the most sensitive determination of the tensor. The relationship of these optimal orientations to those used previously in two-dimensional chemical shift tensor correlation spectroscopy is discussed. It is shown that the high symmetry of the icosahedron simplifies the design on which the construction of a new sample orienting mechanism may be based.