Normal Modes
Application of Normal mode calculations in optical spectroscopy | Phym 221 – Assignment 4
1. Introduction
Normal modes are used to describe the different vibration motion in molecules. There are different types of modes for molecules in different motions and each has a certain symmetry associated with it.
2. Overview of Normal Modes
Generally, normal modes are independent atoms in a molecule that are in motion such that they do not disturb the motion of the other molecules. Normal modes as implied by the name are orthogonal to each other. In order to discuss the quantum-mechanical equations that govern the molecular vibration it is important to convert Cartesian coordinates into normal coordinates. The atom vibration in polyatomic molecules is represented by normal coordinates. The normal coordinates and the vibrational wave function can be characterized into a point group they belong to.
3. Degrees of freedom
3N is a number such that N represents the number of nuclei present in the molecule. 3N is also the total number of coordinates needed to describe the location of a molecule in a three dimensional space. 3N is most commonly referred to as the degree of freedom
3N, the total number of degrees of freedom, can be divided into: * Transitional degrees of freedom are three coordinates to describe the transitional motion around the centre of mass. * Rotational degrees of freedom are 3 coordinates to describe the rotational motion of a non linear molecule. * The remaining coordinates are used to describe vibrational motion, a non linear molecule has 3N – 6 vibrational degrees of freedom whereas a linear molecule has 3N – 5 degrees of freedom
Example:
In CO2 N = 3 which implies 3N = 9 therefore carbon dioxide has 9 degrees of freedom,3 transitional, 2 rotational, the remaining 4 degrees are vibrational degrees of freedom, also consistent with 3N – 5 = 4
4. Mathematical introduction of Normal Modes
If the external field is not an
1. Introduction
Normal modes are used to describe the different vibration motion in molecules. There are different types of modes for molecules in different motions and each has a certain symmetry associated with it.
2. Overview of Normal Modes
Generally, normal modes are independent atoms in a molecule that are in motion such that they do not disturb the motion of the other molecules. Normal modes as implied by the name are orthogonal to each other. In order to discuss the quantum-mechanical equations that govern the molecular vibration it is important to convert Cartesian coordinates into normal coordinates. The atom vibration in polyatomic molecules is represented by normal coordinates. The normal coordinates and the vibrational wave function can be characterized into a point group they belong to.
3. Degrees of freedom
3N is a number such that N represents the number of nuclei present in the molecule. 3N is also the total number of coordinates needed to describe the location of a molecule in a three dimensional space. 3N is most commonly referred to as the degree of freedom
3N, the total number of degrees of freedom, can be divided into: * Transitional degrees of freedom are three coordinates to describe the transitional motion around the centre of mass. * Rotational degrees of freedom are 3 coordinates to describe the rotational motion of a non linear molecule. * The remaining coordinates are used to describe vibrational motion, a non linear molecule has 3N – 6 vibrational degrees of freedom whereas a linear molecule has 3N – 5 degrees of freedom
Example:
In CO2 N = 3 which implies 3N = 9 therefore carbon dioxide has 9 degrees of freedom,3 transitional, 2 rotational, the remaining 4 degrees are vibrational degrees of freedom, also consistent with 3N – 5 = 4
4. Mathematical introduction of Normal Modes
If the external field is not an