Wilson's Matrix Method for Calculating Molecular Vibration Frequencies and Normal Modes for Smart Materials

Abstract

This book chapter provides an in-depth exploration of Wilson's matrix method, a computational technique used to calculate molecular vibration frequencies and normal modes in smart materials. The chapter begins with an introduction to molecular vibrations and normal modes, emphasizing their importance in understanding material behavior at the molecular level. It then delves into the theoretical foundation and practical steps involved in Wilson's matrix method, highlighting its use of force constants and eigenvalue calculations to determine vibrational frequencies and associated modes. The chapter further examines the application of Wilson's matrix method to smart materials, emphasizing their unique vibrational characteristics and the role of molecular vibrations in shaping their functionality. The advancements in the method, including the inclusion of anharmonicity and improved force constant determination, are discussed, along with the integration of enhanced computational techniques and increased computational power.