Tin tetrachloride,

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Atomic, Molecular & Optical Physics · Molecular structure and spectra

Invariance, Ch Character tables at work: vibrations, selection rules and splitting

Problem

Tin tetrachloride, SnCl4\mathrm{SnCl_4}, is tetrahedral with point group TdT_d. Use the TdT_d character table (classes EE, 8C38C_3, 3C23C_2, 6S46S_4, 6σd6\sigma_d; basis functions (x,y,z)→T2(x,y,z)\to T_2, (Rx,Ry,Rz)→T1(R_x,R_y,R_z)\to T_1). ((a)) Find χ3N\chi_{3N} and decompose it. ((b)) Find Γvib\Gamma_{\rm vib}. ((c)) Decompose the direct product T1⊗T2T_1\otimes T_2. ((d)) Using the vanishing integral theorem, decide whether an A1→A2A_1\to A_2 transition is allowed by electric-dipole absorption.

Browse the problem library