Rotational Spectroscopy of Non-Linear Polyatomic Molecules

Since a molecule rotates about its center of mass, it is convenient to define the coordinates for the axes of rotation of a molecule about its center of mass. The first step is to determine the center of mass of the molecule. The point that the center of mass of a molecule is located is defined as X, Y, Z. The center of mass of a molecule is determined as follows  

Problem Determine the center of mass (X, Y, Z) of water. The bond angle is 104.5° and the bond distance ofO-H is 0.0958 nm. 

Solution The stmcture of a water molecule is shown in the figure below. 

The values for X,Y, and Z are solved for by using each relationship in Equation 7-3. 

Based on the coordinate system used in the diagram, the oxygen atom is at the origin hence Xo = 0. The position of each hydrogen atom is given below. 

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