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Number of vibrational modes

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For a molecule with N atoms, the positions of all N nuclei depend on a total of 3 N coordinates, so that the molecule has 3 N degrees of freedom including translation, rotation and vibration. Translation corresponds to movement of the center of mass whose position can be described by 3 cartesian coordinates. A nonlinear molecule can rotate about any of three mutually perpendicular axes and therefore has 3 rotational degrees of freedom. For a linear molecule, rotation about the molecular axis does not involve movement of any atomic nucleus, so there are only 2 rotational degrees of freedom which can vary the atomic coordinates. An equivalent argument is that the rotation of a linear molecule changes the direction of the molecular axis in space, which can be described by 2 coordinates corresponding to latitude and longitude. For a nonlinear molecule, the direction of one axis is described by these two coordinates, and the orientation of the molecule about this axis provides a third r...
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48)Revealed: What to expect on Republic Day 2021and what not to

India Republic Day -- Republic Day 2021: In 2020it was the agitation against the Citizenship Amendment Act (CAA). Nowthousands of farmersmainly from Punjab and Haryanahave been camping at the sides of Delhi for more than a couple of monthsdemanding the Centre repeal the three farm laws. To the second year in a stripRepublic Day celebrations from the national capital will be placed under the shadow of raging protests against laws transferred by the Centre. In 2020it was the agitation against the Citizenship Amendment Act (CAA). This timethousands of farmersmainly from Punjab and Haryanahave been camping at the sides of Delhi for more than a couple of monthsdemanding the Centre repeal the three farm laws. This specific years Republic Day ornement will also be the first major general public event in pandemic moments. What is new this year The presentation will be pared down the number of spectatorsthe size of walking in line contingents and other side sights. The spectator size has bee...
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Vibrational coordinates

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The coordinate of a normal vibration is a combination of changes in the positions of atoms in the molecule. When the vibration is excited the coordinate changes sinusoidally with a frequency ν , the frequency of the vibration. Internal coordinates edit Internal coordinates are of the following types, illustrated with reference to the planar molecule ethylene, Stretching: a change in the length of a bond, such as C–H or C–C Bending: a change in the angle between two bonds, such as the HCH angle in a methylene group Rocking: a change in angle between a group of atoms, such as a methylene group and the rest of the molecule. Wagging: a change in angle between the plane of a group of atoms, such as a methylene group and a plane through the rest of the molecule, Twisting: a change in the angle between the planes of two groups of atoms, such as a change in the angle between the two methylene groups. Out–of–plane: a change in the angle between any one of the C–H bonds and the plane defi...
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