University:
Purdue University
Course:
CHM 42400 | Analytical Chemistry II
Academic year:

2022
Views:

354

Pages:

8
Author:

Medonosh0

Objectives: 1. Coordinate-independent visualization of molecular tensors. 2. Describe sagittary representations for the resonant molecular tensor. Note: Citations to the contents of these slides should reference the following textbook: Simpson, Garth J. (2017) Nonlinear Optical Polarization Analysis in Chemistry and Biology (Cambridge University Press, ISBN 978-0-521-51908-3). 1 Visual representations Computational chemistry typically produces outputs as tables of 18 or 27 numbers. 1. It can be difficult to connect these numbers to particular molecular structural motifs. 2. For a particular vibrational transition, the coordinate system of the molecule will generally be different that the local mode of the transition of interest. 3. Very different sets of tensor elements are recovered depending on the particular choice of the internal molecular coordinates selected. Numerical representation 2 Visual representations Computational chemistry typically produces outputs as tables of 18 or 27 numbers. 1. It can be difficult to connect these numbers to particular molecular structural motifs. 2. For a particular vibrational transition, the coordinate system of the molecule will generally be different that the local mode of the transition of interest. 3. Very different sets of tensor elements are recovered depending on the particular choice of the internal molecular coordinates selected. Numerical representation 3 Transition moment. n 0 Each one-photon resonance that collectively contributes to the linear polarizability is described by a transition moment, which is a vector property in the molecule. The linear polarizability matrix is constructed by the Kronecker product of the transition moment with its transposed conjugate. 4 Raman polarizability.  0n The Raman tensor is a 3×3 matrix. As long as the virtual states in the Raman process are far from resonance (i.e., adiabatic limit), the tensor is symmetric Just like the moment of inertia matrix, the symmetric Raman tensor can be described by three principal eigenvectors and their corresponding eigenvalues. In this reference frame, only the three diagonal elements within the Raman matrix are nonzero. 5 Raman polarizability. Red, dashed lines indicate principal Raman elements with negative sign. Solid, blue lines indicate positive sign.  0n 6 Vibrationally Resonant SFG. The combined representations for the transition moment and Raman tensor together with the assumed complexvalued lineshape function recover the resonant contributions to the molecular tensor in any arbitrary coordinate system. n 0  0n  ijk res  Sn ir     ij 0n k n0 7 Electronically Resonant SHG. The combined representations for the transition moment and TPA tensor together with the assumed complexvalued lineshape function recover the resonant contributions to the molecular tensor in any arbitrary coordinate system. n 0  0n  ijk res  Sn  2     i 0n jk n0 Lineshape resonance about Order flips relative to vib. SFG 2 instead of ir. 8