Visualization of electronic and vibrational polarizabilities and hyperpolarizabilities

At the molecular level of any observed nonlinear optical behavior, one finds the polarizability and hyperpolarizability tensors. These quantities are nowadays easily calculated for small- to intermediate-sized molecules. However, to gain further insight into these properties, pictorial approaches are valuable. Here we extend the work of Chopra et al. [J. Phys. Chem., 93, 7120 (1989)] to obtain a method that may be used in order to understand how average (hyper)polarizabilities are distributed over the molecular frame. The pictures obtained represent (hyper)polarizability moments and give a description of local contributions to the total electric property. Furthermore, the formal foundations of the proposed method are developed to be used to represent both the electronic and the vibrational components of the (hyper)polarizabilities. The theory is applied to a series of push–pull polyenes. One important conclusion is the lack of any similarity between the electronic and vibrational pictorializations of either the polarizability or the first hyperpolarizability. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 78: 348–377, 2000