Quantum Mechanical Modeling of the Vibrational Spectra of Minerals with a Focus on Clays

We present an overview of how to use quantum mechanical calculations to predict vibrational frequencies of molecules and materials such as clays and silicates. Other methods of estimating vibrational frequencies are mentioned, such as classical molecular dynamics simulations; references are given for additional information on these approaches. Herein, we discuss basic vibrational theory, calculating Raman and infrared intensities, steps for creating realistic models, and applications to spectroscopy, thermodynamics, and isotopic fractionation. There are a wide variety of programs and methods that can be employed to model vibrational spectra, but this work focuses on hybrid density functional theory (DFT) approaches. Many of the principles are the same when used in other programs and DFT methods, so a novice can benefit from simple examples that illustrate key points to consider when modeling vibrational spectra. Other methods and programs are listed to give the beginner a starting point for exploring and choosing which approach will be best for a given problem. The modeler should also be aware of the numerous analytical methods available for obtaining information on vibrations of atoms in molecules and materials. In addition to traditional infrared and Raman spectroscopy, sum-frequency generation (SFG) and inelastic neutron scattering (INS) are also excellent techniques for obtaining vibrational frequency information in certain circumstances.