Group Dipole Derivatives as Infrared Intensity Parameters

Group Dipole Derivatives as Infrared Intensity Parameters 

Expression (1.50) defines die relation between observed absorption intensity of the molecular vibration and die Cartesian components of die d le moment derivatives with respect to die normal coordinate. A transformation firom dp/d( to dp/dSj derivatives is then performed using the relation 

The index G refers to a molecular-fixed Cartesian system in which die dipole moment derivatives with respect to normal coordinates are obtained. The summation is over the group symmetry coordinates. Eq. (3.70) can be solved if the Cartesian ctmqionents of dpo/dQ are known. Introducing Eq. (3.70) into Eq. (1.50) the following relation between the dipole derivatives dpQ/dSj and the intensity A)( is obtained 

Such initialization of the mathematical approach provides the opportunity to determine the quantities dpg/dSj in an iterative refinement process. 

A second Cartesian reference system, still molecule-fixed, oriented as dictated by the symmetry elements of the group of atoms associated with Sj is introduced. It is designated by gjf (i = 1, 2, 3). The dipole derivatives dpQ/dSj are expressed in the group local Cartesian system as 

---

D. Group Dipole Derivatives as Infrared Intensity Parameters.72... 

---