Hyperpolarisability tensors

Thus at low fields the ratio of the two components of the hyperpolarisability tensor is 3 1. At high fields Xzzz saturates and Xzxxtends to zero>as shown in... 

D.A. Long The polarisability and hyperpolarisability tensors . In Nonlinear Raman Spectroscopy and its Chemical Applications, ed. by W. Kiefer, D.A. Long (Reidel, Dordrecht 1982)... 

Both tensors are described in a different frame of reference the tensor is given in the laboratory frame of reference based on the plane of incidence, whereas the hyperpolarisability tensor in the molecular frame of reference defined by the symmetry of the molecule. An Euler transform relates both, leading to rather lengthy expressions between the corresponding tensor components, which are best handled and manipulated with the aid of a symbolic programming language such as Maple or Mathematica. 

A variable temperature study of the cross-relaxation dynamics of methoxy groups on silica in hyperpolarised Xe has been reported. Mesopore size and diffusion have been studied for silica glasses using Xe NMR spectroscopy. " The Xe chemical shift tensor has been determined in a silicalite single crystal using hyperpolarised Xe NMR spectroscopy. ... 

SFG spectroscopy is the only spectroscopy capable of producing vibrational water spectra of the air-water interface. The analysis is simplified by the symmetry of the interface and the symmetry of the molecule which reduces the number of independent tensor elements of the hyperpolar-isability. The water molecule belongs to the point group C2v and the number of independent tensor elements is reduced to five caa, Paca, Pbbc, and Of these, only i,bc, aac, and Pccc are non-zero for the symmetric stretch and Pccm and Paca are non-zero for the anti-symmetric stretch. We denote the tilt angle between the molecular C2 axis and the surface normal and as the twist angle of the molecular plane with respect to the surface plane. Then, the relationship between the molecular hyperpolarisability, and the macroscopic hyperpolarisability, for the symmetric stretch after Euler angle transformations yields ... 

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