3. The number of fundamental modes of vibration is 27 ( 3 x 11 - 6 = 27). These modes of vibration (normal modes) give rise to • absorption bands (IR) A mode in which atoms move to rotate (change the orientation of) the molecule. 4. 3. Fundamental vibrational modes do not cause translation or rotation of the molecule as a whole. Octahedral Group, Oh – common e.g. allowed or forbidden, whether a molecule should have dipole moment, whether a given vibrational mode should be visible in the infrared or not, etc. Translational Modes Rotational Modes A mode in which all atoms are moving in the same direction, equivalent to moving the molecule. Theoretical derivation 2.1. Amplitudes, however, depend on masses. 2. Here we will assume a basic familiarity with point groups and discuss how group theory can be used to determine the symmetry properties of molecular vibrations. To better understand the relationship between the two phases we can consider the [PbI 6] 4-ion. Each normal mode of vibration has a fixed frequency. For each normal mode, there is a vibrational quantum number. 2. given in section 2. For a linear molecule, there are 3 translations and 2 rotations of the system, so the number of normal modes is 3 n – 5. 1. All atoms of the molecule move with the same frequency and usually in-phase i.e. Calculations and comparison with some available experi- mental results are given in section 3. Each fundamental mode can be excited independently. The complex vibrations of a molecule are the superposition of relatively simple vibrations called the normal modes of vibration. 2. 1. ν (s) O-H 3657 cm-1 IR active 3756 cm-1 1595 cm-1 δ (s) H-O-H IR active, degenerated All IR absorptions result not only in a vibrational excitation but also in transitions There are 3 rotational modes for nonlinear molecules, and 2 rotational modes for linear molecules. Every atom in a molecule can move in three possible directions relative to a Cartesian coordinate, so for a molecule of n atoms there are 3 n degrees of freedom. They are independent vibrations that can simultaneously occur in a molecule. 3 o define the breathing mode vectors on a diagram, Figure 6 o can be represented as an expansion and contraction of the angles involved C 3v E2C 3 3! Vibrational Spectroscopy (IR, Raman) Vibrational spectroscopy. The point group is also C 2v but the molecule has 11 atoms. Since the molecular geometry can distort along each of these degrees of freedoms, these constitute vibrational normal modes. 1 illustrates the six vibrational modes of an octahedral XY 6 molecule: the A 1g, E g, T 2g vibrations are Raman-active, the T 1u ones are infrared-active, the T 2u are silent [].The vibrational modes … every non-linear molecule has 3N-6 vibrations , where N is the number of atoms. 5 In the 3N representation, six of the irreducible representations correspond to translations and rotations of the molecule. Degrees of Freedom and Vibrational Modes 1. To a first approximation, [PbI 6] 4-has an octahedral structure and Fig. Octahedral thirteen-atomic molecule AB6C6. In this case we would have to draw up a C 2v character table showing the symmetries of all 27 vibrations. SYMMETRY SPECIES - INTERNAL COORDINATES We consider the modes of vibrations of a thirteen-atomic octahedral molecule AB6C6 as shown in fig. v"(aH#N#H N-H "in"-plane bends a 3 a 2 a 1 N H H H Figure 6 Setup for the breathing modes o it is clear the breathing modes have the same reducible representation as all pass zero crossings and turning points at the same time.