Visualization of electronic and vibrational polarizabilities and hyperpolarizabilities

At the molecular level of any observed nonlinear optical behavior, one find s the polarizability and hyperpolarizability tensors. These quantities are nowadays easily calculated for small- to intermediate-sized molecules. Howe ver, to gain further insight into these properties, pictorial approaches ar e valuable. Here we extend the work of Chopra et al. [J. Phys. Chem., 93, 7 120 (1989)] to obtain a method that may be used in order to understand how average (hyper)polarizabilities are distributed over the molecular frame. T he pictures obtained represent (hyper)polarizability moments and give a des cription 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 electro nic and vibrational pictorializations of either the polarizability or the f irst hyperpolarizability. (C) 2000 John Wiley & Sons, Inc.