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Ab Initio Calculations of P NMR Chemical Shielding Anisotropy Tensors in Phosphates: The Effect of Geometry on Shielding Todd M. Alam Department of Aging and Reliability in Bulk Materials, Sandia National Laboratories, Albuquerque, N M 87185-1407
Molecular geometry variations have a pronounced influence on the magnitude and orientation of the phosphorous ( P) nuclear magnetic resonance (NMR) chemical shielding anisotropy (CSA) tensor (σ) in phosphates. Ab initio calculations of the P σ tensor as a function of internal bond angles and bond lengths for simple phosphate systems are described. The CSA tensors were calculated using GAUSSIAN 94 implementation of the gauge-including atomic orbital (GIAO) method, at the Hartree-Fock (HF) level. Both the isotropic value of the chemical shielding and the principal components of the anisotropic tensor were determined. It is demonstrated that differences in the behavior of the isotropic values and the principal components of the CSA tensor can provide a powerful tool to investigate structural variations. 31
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The ability to calculate and correlate material properties directly with molecular structure remains an important objective in material science. The correlation of the chemical shift or magnetic shielding in nuclear magnetic resonance (NMR) spectroscopy with bond angles, bond length, coordination number and interactions with neighboring atoms has seen a long and rich history in a wide variety of applications. Recently there has been renewed interest in the development of more accurate correlations between N M R observables and the local structure in amorphous materials, including polymers (i), composites, mineral oxides (2,5) and glasses.(0 Because the use of standard scattering techniques can prove difficult in amorphous systems, N M R spectroscopy has become a powerful tool to probe the local and medium range order in these amorphous materials. The determination of the N M R chemical shift or chemical shielding anisotropy (CSA) tensor from quantum mechanical methods remains a crucial
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© 1999 American Chemical Society
In Modeling NMR Chemical Shifts; Facelli, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
321 component in the future development of structural correlations. The prediction of N M R parameters using ab initio techniques has under gone major advancements in the last decade (5), including solutions to the gauge dependence of the chemical shift (6), improvements in the basis sets, and the extension to higher levels of theory including density functional theory (DFT) techniques.(7,5) Advances in computational speed have also relaxed many of the restrictions involved in previous investigations of large sized molecular clusters. With these advances there have been an increasing number of ab initio investigations for a wide variety of nuclei, including B (6), C (1,9,10% N (9,10), 0 (9-11), S i (3,12-16), P (10,17-21), Seand Cd. (10,22) A complication encountered in amorphous inorganic materials is the formation of three-dimensional networks, compared to the one-dimensional chains common in synthetic organic polymers. This network formation can lead to a very large number of structural variables that may influence the observed N M R C S A tensor. Due to this increased complexity it therefore becomes crucial to separate and distinguish the effects of different structural variations on the observed NMR spectra. In our laboratory we are particularly interested in obtaining a measure of structure and distribution for ultraphosphate glasses. There have been a limited number of calculations for phosphorous ( P) systems, including semi-empirical correlations between structure and the isotropic chemical shift in phosphate glasses.(18-21) To aid in the development of future NMR-structure correlations in phosphate glasses, ab initio N M R calculations of the P C S A tensor in simple phosphate systems were initiated and are presented here. The influence of bond lengths, bond angles and torsional angles on the C S A tensor are discussed. In addition, analysis of both the isotropic values and the principal components of the anisotropic shielding tensor are presented, providing a method of distinguishing different structural changes.
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H
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Theoretical Method and Model Structures The chemical shift anisotropy (CSA) tensors were calculated using the parallel version of the GAUSSIAN 94 software package (23) on a multi-node SGI O N Y X processor. The gauge-including atomic orbital (GIAO) method (24) at both the Hartree-Fock (HF) and density functional theory (DFT) level of theory were employed for the calculation of the shielding tensors. Four uniform basis sets were previously investigated with various combinations of polarization and diffuse functions: STO-3G, 3-21G, 6-31G and 6-311G.(25) The majority of the shielding results presented here were obtained using HF methods at the 6-311++G(2d,2p) level. A l l geometry re-optimizations employed the DFT B3LYP hybrid functional, utilizing Becke's exchange functional and the L Y P correlation functional.(7,26,27) A detailed study of basis set dependence of P CSA tensor in phosphates, including a comparison between HF and DFT methods, has previously been reported (25), and will not be detailed here. 31
In Modeling NMR Chemical Shifts; Facelli, J., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
322 Not all 9 components of σ are typically reported when describing the chemical shielding tensor. Instead, the 3 principal components (or eigen values) in a principal axis system (PAS) are reported. The CSA tensor can also be described by three additional parameters; 1) the isotropic value (or trace), a , of the shielding tensor and is defined as iso
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0*=-jK+
