Atomic polar tensor definition

Such a matrix is not independent on the coordinate system, but the trace is. Cioslowski has proposed a definition of atomic charges as one-third of the trace over the APT, denoted Generalized Atomic Polar Tensor (GAPT) charges.The charge on atom A is defined as... 

Pq, is expressed in Cartesian coordinates. These polar tensors T), can be derived from experimental intensities by elementary coordinate transformation. If the axes x, y, and z are chosen such that the bonds are oriented along one of the axes, then the derivatives can be used to interpret the changes of the electron clouds during a vibration. Besides, considering the definitions of the axes, it is possible to transfer atomic polar tensors between similar molecules and to estimate their intensities (Person and Newton, 1974 Person and Overend, 1977). 

For planar molecules the perpendicular charge fluxes are zero by symmetry, and the atomic charge may be extracted from the perpendicular elements of the atomic polar tensor. The definition given above for the oxygen charge is thus quite general namely, for planar molecules ... 

Analysis of the derivatives of dipole moments with respect to nuclear displacements (the atomic polar tensors) gives rise to yet another definition of atomic charges. The GAPT (generalized atomic polar tensor) atomic charges ate... 

Expeiimental data, definitions of coordinates, molecular geomehy data, and L and P3 matrices for med l chloride are given in section 3.3. The calculated atomic polar tensor matrix is given below (in units of D A ) [124]. 

Coordinate definitions, Lg and P matrices for H2O used in evaluating the atomic polar tensor elements are as given in section 3.3. With the aid of relation (4.14) die Pg matrix is transformed into vibrational polar tensor, while the rotational polar tensor is calculated using a permanent dipole moment value of-1.85 D [34]. The two submatrices obtained are as follows (in units of D A l) ... 

Momany s idea has led to a new definition of atomic charges. It would be possible to write volumes about atomic charges (AC), a concept that has no a precise definition in QM formalism, but is of extreme utility in practical applications. Many definitions of AC are based on manipulations of the molecular wave function, as, for example, the famous Mulliken charges. Other definitions are based on different analyses of the QM definition of the charge density, as for example Bader s charges.There are also charges derived from other theoretical approaches, such as the electronegativity equalization, or from experimental values, such as from the vibrational polar tensors. 

In general, the polarizability is a tensor whose invariants, trace and anisotropy, give rise to polarized and fully depolarized light scattering, respectively. Collision-induced light scattering is caused by the excess polarizability of a collisional pair (or a larger complex of atoms or molecules) that arises from the intermolecular interactions. In Section I.l, we are concerned with the definition, measurement, and computation of interaction-induced polarizabilities and their invariants. 

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