0000008914 00000 n 0000001393 00000 n Since the polarizability ellipsoid returns to its initial value after rotating only 180o, the selection rule for rotational Raman spectroscopy of a linear molecule is:)J' 0, ±2 The)J= 0 transitions correspond to Rayleigh scattering and are very intense - however, this scattering is unimportant in … For a hydrogen molecule, H2, the induced dipole is greater if the molecular axis is parallel to the field direction than if it is perpendicular to it. However, spherical rotors are inactive in both Raman and microwave spectroscopy (they are isotropically polarisable and have no permanent electric dipole), so may not be studied by either technique. @�ފ�Q�ƪ���=j�fG��Z�5xֆ oD::�sD�h�h�� 0000009600 00000 n 0000002117 00000 n 0000004940 00000 n 0000007445 00000 n The gross selection rule for rotational Raman spectroscopy is that the molecule must be anisotropically polarisable, which means that the distortion induced in the electron distribution in the molecule by an electric field must be dependent upon the orientation of the molecule in the field. 0000013442 00000 n i.e. The scattered radiation must thus have lost energy, i.e. 0000016667 00000 n It is said to be isotropically polarisable. 0000012815 00000 n Analysis becomes much more difficult for polyatomic molecules, need to apply group theory to decide if a particular vibrational mode is Raman active. endstream endobj 1810 0 obj <> endobj 1811 0 obj <> endobj 1812 0 obj <>stream Thus, for linear molecules the energy levels are described by a single moment of inertia and a single quantum number, $${\displaystyle J}$$, which defines the magnitude of the rotational angular momentum. be at a higher wavenumber than the incident radiation. 0000098988 00000 n 0000001288 00000 n Rotation about each unique axis is associated with a set of quantized energy levels dependent on the moment of inertia about that axis and a quantum number. We can apply the rotational selection rules to predict the form of the spectrum. 0000003757 00000 n v�� 2) Anharmonic Approximation Δn = ±1, ±2, ±3,… The Raman effect was first reported by C. V. Raman and K. S. Krishnan, and independently by GrigoryLandsberg and Leonid Mandelstam, in 1928. 0000010307 00000 n Many linear molecules are inactive in microwave rotational spectroscopy, so one great use of Raman spectroscopy is in the study of such molecules. Only molecules, whose polarisability changes during the vibration or the rotation, are Raman active. This is a complex idea, but basically the polarizability tensor transforms in the same way as second order functions of x, y, and z such as x 2, yz, x 2-y 2, and so on. %PDF-1.5 %���� h��Wmo�6�+��b���b� M�^�뵸d�A>��.��ā���)9o����a7�H�")�|�p'�w�! 0000010056 00000 n 0000002353 00000 n These transitions give rise to the anti-Stokes lines: Note that in both portions of the spectrum, the spacing between adjacent lines is 4B, allowing measurement of B and hence calculation of the moment of inertia and bond lengths of the molecule, just as was possible with microwave spectroscopy. 0000006200 00000 n 0000035850 00000 n 0000004917 00000 n 0000010284 00000 n %PDF-1.3 %���� Note that all linear molecules have anisotropic polarisabilities, so they may all be studied by rotational Raman spectroscopy. 0000013920 00000 n When the molecule makes a transition with ΔJ = +2, then the interaction has imparted energy to the molecule. 1809 0 obj <> endobj � W� Due to the dipole requirement, molecules such as HF and HCl have pure rotational spectra and molecules such as H 2 and N 2 are rotationally inactive. 0000013280 00000 n �r9�e�Z� ���~9�_�"����7/�9=�׹_b��h��˛tM7���=��>t-��c��P��Epb�z?�!�t����S�8�T�P��2�j5+氕�W��[�h��q��*!��sv��Q޼�'R��DI�e��a�rdz��l�[UٖdeU�ӒH�rޱ�?��Wnw�oN�9�l^?V�? When the molecule makes a transition of ΔJ = -2, the incoming photon receives energy from the molecule, and thus the scattered  radiation must have a higher energy, i.e. 0000002619 00000 n �A$�$�$H(b�@B�0�E��a�r�c�lBs�B�v�$R�^�z�@?3)I���|�@�E^��u:��T&z�ȗn�^=�ף:�q�zģ�qjP�j�ytF������PdT�$2&�5ݕ�l�� ��б��p�.|J��>��ghf�D3",��0hF�A3�4��t�:��/���a��)���#�Ҽ�@�NG����3t����@�b�]X۫f~U��/a�9��t��g�ǚ�饏���^\ϓ�J$����D�i���,9�y�Pf�q,�=n��`�>�KO�7���_~jd;E>������~.�e�����e�k���V��FG�_�>��i�E��l]%���G6��D�V��� 0000012034 00000 n We saw this already during the classical derivation of the Rayleigh and the Raman mechanism in Section 2.4.2.1. 0000015410 00000 n 0000015387 00000 n M������b�*��v�����f���0���!������@C^|��8�D�b��e�|�x ��y�P�&����@�A�v_�Q � oc�g Free rotation is not possible for molecules in liquid or solid phases due to the presence of intermolecular forces. This diagram is a simplified representation of a typical rotational Raman spectrum. 0000013597 00000 n 0000012374 00000 n The origin of the ±2 selection rule is somewhat complex, but it should be easy to see, via a conservation of angular momentum argument, that since two photons are involved (an incoming photon that is absorbed and a scattered photon that is emitted), and each has photon has an angular momentum of one unit, the maximum change in the angular momentum of the molecule is two units. In a gas, Raman scattering (an inelastic scattering) can occur simultaneously with a change in vibrational, rotational or electronic energy of a molecule. 0000056880 00000 n Specific Selection Rule: 1) Harmonic Approximation Δn = ±1. v. Thus a hydrogen molecule is anisotropically polarisable. 0000096424 00000 n ��!d�-�8\)���4'l���� 4hT��k z�9���B�*�X�0��l��I��L"U�ѦU:��Zv�܁e�y�?����Em�*< 0 1828 0 obj <>/Filter/FlateDecode/ID[<153F315D24E26A033C29F89C84357AE7><90E672F3F20EE14A9A00FFD6805A0FAC>]/Index[1809 36]/Info 1808 0 R/Length 104/Prev 1113966/Root 1810 0 R/Size 1845/Type/XRef/W[1 3 1]>>stream 0000013943 00000 n 0000102012 00000 n Molecules with no improper axis of rotation are optically active. 0000006177 00000 n endstream endobj startxref A molecule in the gas phase is free to rotate relative to a set of mutually orthogonal axes of fixed orientation in space, centered on the center of mass of the molecule. If your molecule has no symmetry element, all modes will be Raman active. 92 0 obj << /Linearized 1 /O 94 /H [ 1393 746 ] /L 460229 /E 122398 /N 18 /T 458271 >> endobj xref 92 47 0000000016 00000 n 0000101806 00000 n %%EOF An atom has a spherical electron distribution, and the dipole induced by an electric field of given strength is the same regardless of the orientation of the atom in that field. 0000003779 00000 n 0000119894 00000 n Note that S ... Raman spectroscopy Molecular vibrations are Raman active if the polarizability tensor for the molecule changes. The Rayleigh line arises from the unscattered radiation that passes through the sample. Selection rules only permit transitions between consecutive rotational levels: ΔJ = J ± 1, and require the molecule to contain a permanent dipole moment. It is often considerably broader than the other lines in the spectrum, and lies at the wavenumber of the incident radiation. 0000011471 00000 n 0000121948 00000 n 0000013058 00000 n Many linear molecules are inactive in microwave rotational spectroscopy, so one great use of Raman spectroscopy is in the study of such molecules.