Polarizabilities of susceptibility in different coordinate systems

The numerical value of some molecular properties, e.g., the energy and 

The expressions for other moleeular quantities depend upon the ehoiee of origin for the coordinate system to which they are referred, for example, in a translation of the origin 

The Hermitian operator Vap appearing in the transformation law, equation (39), for Uaj3, see equation (28), is defined 

Some response tensors cannot he uniquely defined. They intrinsically depend upon the origin of the coordinate system, e.g., electric quadrupole polarizability [56,66], However, there exist translationally invariant molecular properties (that are, in principle, experimentally measurable), although they are expressed in terms of origin-dependent tensors. 

As an example, let us discuss the case of the electric moment (15) induced by a static external electric field having a uniform gradient. The equation that describes the change of the mixed third-rank electric polarizability tensor (19) with respect to a change to the origin of the coordinate system is 

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Polarizabilities of susceptibility in different coordinate systems Acknowledgements... 

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